Dynamic modeling for startup and shutdown

Dynamic modeling for startup and shutdown

of a coupled reactor and distillation column

Jim Law

Delft, 8 May 2001 Supervision: Ir. J.P. Schmal Dr. ir. P.J.T. Verheijen Delft University of Technology Faculty of Applied Science Department of Chemical Technology Process systems engineering section

i

Summary Competing in a global market place forces chemical industry to be flexible and cost-effective in production. To optimize production the processes are modeled before they are built. Normally these models show the steady-state behavior. This, however, will be insufficient to show the flexibility of the process and guarantee safety and environmental constraints are met under all circumstances. Dynamic models are useful to give extra insight in the operability, flexibility and profitability of a process. The goals of this project are to build a model that will describe startup and shutdown behavior of a process and perform a simplified optimization of a specific startup procedure. For these goals a model has been constructed in gPROMS, which gives a representation of the dynamic behavior of a glycolether process. This process consists of a reactor, distillation column and recycle. The model consists of over 15 000 equations, which include the physical properties of the system. Further features of the model are the use of an equilibrium tray model, inclusion of liquid flows over the weir and dumping through the holes, inclusion of vapor flows through the holes and through the downcomer, addition and purge of inert, and a dynamic, single phase, plug-flow reactor of the shell-and-tube-type operating under turbulent flow conditions. All trends in the profiles of the model and ASPEN follow each other nicely and the steady-state is estimated to be 5-10% accurate compared to ASPEN. The model is capable of describing a shutdown, as long as vapor escapes through the downcomer from the reboiler. It is also capable of describing a startup in which the column is heated, inerts are purged, the reactor is heated and the steady-state is reached. All this is done without an external heat source, using only the heat generated by the reboiler. The results have not been verified experimentally. Several errors were made in modeling the process, such as an incorrect excess of MeOH in the reactor, incorrect surface areas for heat loss on the tray and in the reboiler, small reset rates for controllers in the condenser, large setpoint changes and high rates of temperature rise in the system. Their influences, however, are small, or can be corrected with longer calculation times. Drawbacks of the model are the long calculation times (2.5 hours) and numerical instabilities. Also, the model developed is not completely generic, but could be adapted for other systems. During a simplified optimization by factorial design of the startup-schedule used, only four optimization steps were needed to reduce the loss at the end-point by 28%, while only considering three variables. Though the absolute gain is only Hfl. 781, this demonstrates that optimization can lead to significant increases in profitability. Overall the model provides valuable insight in the processes that take place during dynamic operation of an interconnected reactor and distillation system.

ii

Preface The project presented here is a graduation assignment of the Delft University of Technology. It has been performed in the Process Systems Engineering group of the faculty of Chemical Engineering, under the supervision of ir. Pieter Schmal and dr. ir. Peter Verheijen. I would like to thank Pieter for always coming up with new ideas when the project was stuck and for the many fruitful discussions, as well as for always being available for questions. Peter I would like to thank for investigations into all little quirks of the variables till deep into the night. Further I would like to thank my parents for their constant support.

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Table of contents

Summary.................................................................................................................................... i

Preface ..................................................................................................................................... ii

Table of contents .................................................................................................................... iii

List of symbols......................................................................................................................... v

List of figures ........................................................................................................................ viii

List of tables............................................................................................................................. x

1 Introduction ...................................................................................................................... 1 1.1 Process modeling ....................................................................................................... 1

1.2 Scope.......................................................................................................................... 2

1.3 Outline of report .......................................................................................................... 2

2 Theory ............................................................................................................................... 3 2.1 Distillation columns..................................................................................................... 3

2.1.1 Mass balance ................................................................................................... 3 2.1.2 Energy balance ................................................................................................ 4 2.1.3 Liquid-Vapor equilibrium .................................................................................. 4 2.1.4 Tray hydrodynamics......................................................................................... 5

2.2 Reactors ..................................................................................................................... 7 2.2.1 Mass balance ................................................................................................... 7 2.2.2 Energy balance ................................................................................................ 8 2.2.3 Momentum balance.......................................................................................... 8 2.2.4 Heat transfer..................................................................................................... 8 2.2.5 Friction terms.................................................................................................... 9

2.3 Physical properties ................................................................................................... 10 2.3.1 Physical property models ............................................................................... 10

2.4 Startup ...................................................................................................................... 12

2.5 Optimization.............................................................................................................. 13

3 Modeling the process .................................................................................................... 17 3.1 Process basis ........................................................................................................... 17

3.1 Model structure......................................................................................................... 17

3.2 Physical properties ................................................................................................... 18

3.3 Distillation column..................................................................................................... 20 3.3.1 Tray model ..................................................................................................... 21 3.3.2 Condenser model ........................................................................................... 26 3.3.3 Reboiler model ............................................................................................... 28 3.3.4 Column model ................................................................................................ 31

iv

3.4 Reactor ..................................................................................................................... 31 3.4.1 Shell model..................................................................................................... 32 3.4.2 Wall model...................................................................................................... 34 3.4.3 Tube model .................................................................................................... 34 3.4.4 Reactor model ................................................................................................ 35

3.5 Reaction kinetics ...................................................................................................... 35

3.6 Other models ............................................................................................................ 37 3.6.1 PIC.................................................................................................................. 37 3.6.2 XC/CX-converters .......................................................................................... 38 3.6.3 Mixer............................................................................................................... 38 3.6.4 Connection breakers ...................................................................................... 39

3.7 The entire process.................................................................................................... 39

3.8 Equipment sizing and parameter determination....................................................... 41

3.9 gPROMS settings ..................................................................................................... 43

4 Modeling results............................................................................................................. 45 4.1 Steady-state ............................................................................................................. 45

4.2 Shutdown.................................................................................................................. 47

4.3 Startup ...................................................................................................................... 48 4.3.1 Startup schedule ............................................................................................ 48 4.3.2 The discontinuous phase of the distillation column........................................ 48 4.3.3 The total startup ............................................................................................. 49 4.3.4 Economics...................................................................................................... 50 4.3.5 Calculation times and computer dependencies ............................................. 51 4.3.6 Validation........................................................................................................ 52

4.4 Optimization.............................................................................................................. 52

4.5 Adaptability ............................................................................................................... 57

5 Conclusion and recommendations .............................................................................. 58 5.1 Conclusion ................................................................................................................ 58

5.2 Recommendations.................................................................................................... 59

References.............................................................................................................................. 60

Appendices

Appendix A: The conceptual process design

Appendix B: Derivation of equations

Appendix C: Physical property comparison

Appendix D: Equipment specification

Appendix E: Steady-state values

Appendix F: Shutdown data

Appendix G: Startup data

Appendix H: Optimizations

Appendix I: gPROMS model

v

List of symbols a interfacial area m2

A (cross-sectional) area m2 A constant in DIPPR equations - Awr energy dissipation per unit mass m2/s2 b model fitting parameters - B constant in DIPPR equations - bias controller bias - C concentration kmol/m3

C constant in DIPPR equations - Costsi,cumulative cumulative costs of component i Hfl. Cp heat capacity kJ/kmol.K d diameter m dP pressure difference Pa D constant in DIPPR equations - De hydraulic diameter m e heat transfer rate factor - E energy kJ/kmol E constant in DIPPR equations - Ea activation energy kJ/kmol Error deviation from setpoint of controllers - F molar flowrate of feed kmol/s ƒ friction factor - fi distribution of fractional changes in optimization for

variable i -

ƒ(x) objective function - g gravitational acceleration m/s2

g(x) inequality constraints - h heat transfer coefficient kW/m2.K h height m h(x) equality constraints - H enthalpy (reactor) kJ/m3

H enthalpy kJ/kmol hap height of apron m hid inner dirt coefficient kW/m2.K hod outer dirt coefficient kW/m2.K how height of liquid over the weir m ∆Hvap heat of vaporization kJ/kmol hw height of weir m k0 pre-exponential factor 1/gcat.min,

l/mol.gcat.min k mass transfer coefficient kmol/s K equilibrium constant - K constant for purge - Kgain gain for PI-controllers - KL constant for controlling level - KN2 constant for controlling N2 addition during shutdown - KP constant for controlling pressure - Ksd constant for increasing heat-loss during shutdown - KT constant for controlling temperature - KT23 constant for controlling the temperature on tray 23 - Kw friction loss factor - Kx constant for controlling fraction MP-1 - L liquid molar flowrate kmol/s level (clear) liquid level m leveleffective effective level m Lw length of weir m M moles kmol

vi

Mcat mass of catalyst g Mtot moles in liquid or vapor phase kmol Mwt molar weight kg/kmol n number of components - NC number of end contractions - Nu Nusselt number - Ntubes number of tubes - O(xi) error of magnitude xi - P pressure Pa Pi

sat saturated vapor pressure Pa Pset set pressure Pa Pr Prandtl number - Price price of component or heat flow Hfl. Q heat flow kW r reaction rate kmol/m3.s R ideal gas constant kJ/mol.K Re Reynolds number - Revenuei,cumulative cumulative revenue of component i Hfl. Rset inverse of reflux ratio kmol/kmol S surface area m2 Setpoint setpoint for controllers - Signal signal for controller - t time s T temperature K Ui heat transfer coefficient based on inner diameter of tube kW/m2.K Uair heat transfer coefficient for heat transfer to surroundings kW/m2.K V vapor molar flowrate kmol/s V volume m3

v velocity m/s <v> average velocity m/s Vmol molar volume m3/kmol w weight fraction - x molar fraction in liquid phase - x variables in objective function - X matrix of variables in objective function - y molar fraction in vapor phase - Y response of objective function - z molar fraction in feed - z axial direction m

Greek symbols: α lumped flow and friction coefficients - β liquid holdup in liquid phase m3/m3 ∆ difference - ε gas holdup in liquid phase m3/m3

η viscosity Pa.s λ conductivity W/m.K ν reaction coefficient - ξPO conversion of PO - ρ mass density kg/m3 ρmol molar density kmol/m3

τ reset rate for PI-controllers s τw shear force kg/m.s2

vii

Superscripts: * preliminary variable ** preliminary variable ‘ inverse 0 reference DC downcomer Holes holes I interface k step in optimization L liquid phase p phase product product purge purge r constant in Vredeveld equation reflux reflux T transposed V vapor phase Weir weir Subscripts: 0 base 1 location indicator 2 location indicator batch reaction batch in Tao et al. (1997) c cooling medium cond condenser dummy dummy variable F feed holes holes on tray i inner i component number in in liq liquid loss loss m number of reactions mix mixture N tray number n number of components new new not removed liquid remaining o outer out out outside outside pipe pipe between tray 1 and condenser reb reboiler recycle recycle ref reference remove removed liquid s shell su-line startup line t tube tr transferred between liquid and vapor phase test test variable (preliminary variable) tray tray used used vap vapor w wall z axial direction

viii

List of figures Figure 1.1. A simple heat-integrated process.......................................................................... 1 Figure 2.1. Steady-state tray of a distillation column............................................................... 3

Figure 2.2. Definition of subscripts for derivation of vapor flow equation. ............................... 5

Figure 2.3. Definition of subscripts for derivation of liquid dumping equation. ........................ 6

Figure 2.4. Definition of directions in the reactor. .................................................................... 7

Figure 2.5. Newton-Raphson and bisection methods for solving non-linear optimization problems.............................................................................................................. 14

Figure 3.1. Schematic of the process modeled. .................................................................... 17

Figure 3.2. The process as modeled. .................................................................................... 18

Figure 3.3. Determination of parameter for effective level. ................................................... 23

Figure 3.4. Determination of parameter for vapor flow. ......................................................... 24

Figure 3.5. Temperature difference between trays................................................................ 30

Figure 3.6. Influence of the number of discretization points (9/10). ...................................... 44

Figure 3.7. Influence of the number of discretization points (7/10). ...................................... 44

Figure 4.1. Cumulative cashflow............................................................................................ 51

Figure 4.2. Cumulative costs, lower contributions. ................................................................ 51

Figure 4.3. Cumulative costs, larger contributions. ............................................................... 51

Figure 4.4. Definitions of normalized points chosen in optimization...................................... 55 Figure A.1. Process flow scheme of the entire process....................................................... A-1

Figure A.2. Process flow diagram. ....................................................................................... A-2 Figure E.1. Steady-state temperature profiles. .................................................................... E-2

Figure E.2. Steady-state pressure profiles........................................................................... E-2

Figure E.3. Steady-state liquid flowrates over the weir........................................................ E-2

Figure E.4. Steady-state vapor flowrates through the holes................................................ E-2

Figure E.5. Steady-state liquid fractions of MeOH............................................................... E-3

Figure E.6. Steady-state liquid fractions of MP-2................................................................. E-3

Figure E.7. Steady-state vapor fractions of MeOH. ............................................................. E-3

Figure E.8. Steady-state vapor fractions of MP-2. ............................................................... E-3

ix

Figure F.1. Level profile during shutdown.............................................................................F-1

Figure F.2. Dumping profile during shutdown. .....................................................................F-1

Figure F.3. Vapor in downcomer-profile during shutdown. ..................................................F-1

Figure F.4. Vapor – liquid flows during shutdown. ...............................................................F-1

Figure F.5. Temperature profile during shutdown. ...............................................................F-2

Figure F.6. Pressure profile during shutdown. .....................................................................F-2

Figure F.7. Nitrogen fraction in vapor phase during shutdown. ...........................................F-2

Figure F.8. MP-2 in liquid and MeOH in vapor before and after shutdown. ........................F-2 Figure G.1. Liquid flow during startup (short). ...................................................................... G-2

Figure G.2. Vapor flow during startup (short). ..................................................................... G-2

Figure G.3. Dumping during startup (short). ........................................................................ G-2

Figure G.4. Vapor escaping through downcomer during startup (short). ............................ G-2

Figure G.5. Level profile during startup (short). ................................................................... G-3

Figure G.6. Temperature profile during startup (short). ...................................................... G-3

Figure G.7. Pressure profile during startup (short). ............................................................. G-3

Figure G.8. Pressure-drop profile during startup (short). .................................................... G-3

Figure G.9. Nitrogen fraction in vapor phase during startup (short). ................................... G-4

Figure G.10. Liquid flow during startup (total). ...................................................................... G-4

Figure G.11. Vapor flow during startup (total). ...................................................................... G-4

Figure G.12. Dumping during startup (total). ........................................................................ G-5

Figure G.13. Vapor escaping through downcomer during startup (total). ............................ G-5

Figure G.14. Level profile during startup (total). ................................................................... G-5

Figure G.15. Temperature profile during startup (total). ........................................................ G-5

Figure G.16. Pressure profile during startup (total). ............................................................. G-6

Figure G.17. Pressure-drop profile during startup (total). ..................................................... G-6

Figure G.18. Fraction of MeOH in the vapor phase (total). .................................................. G-6

Figure G.19. Fraction of MP-2 in the vapor phase (total). .................................................... G-6

Figure G.20. Fraction of MeOH in the liquid phase (total). ................................................... G-7

Figure G.21. Fraction of MP-2 in the liquid phase (total). ..................................................... G-7

Figure G.22. Feed and product flows (total). ........................................................................ G-7

Figure G.23. Temperatures in condenser and reboiler (total). ............................................. G-8

Figure G.24. Duties in condenser and reboiler (total). .......................................................... G-8

Figure G.25. Temperature profile in the tubes (total). .......................................................... G-9

Figure G.26. Temperature profile in the first shell (total). ..................................................... G-9

Figure G.27. Fraction of MP-2 in first tube (total). ................................................................ G-9

Figure G.28. Fraction of PO in first tube (total). .................................................................... G-9

Figure G.29. Fraction of MP-1 in first tube (total). .............................................................. G-10

Figure G.30. Fraction of MeOH in first tube (total). ............................................................. G-10

Figure G.31. Influence of catalyst flow on reaction rate (total). .......................................... G-10

x

List of tables Table 3.1. Controller parameters.......................................................................................... 37

Table 3.2. Prices of feed and product. ................................................................................. 40

Table 3.3. Calculation of MP-steam price. ........................................................................... 40

Table 3.4. Settings in gPROMS............................................................................................ 43 Table 4.1. Comparison of fractions MeOH and MP-2 in gPROMS and ASPEN.................. 45

Table 4.2. Comparison heat input and removal in gPROMS and ASPEN........................... 45

Table 4.3. Comparison of reboiler flows............................................................................... 46

Table 4.4. Influence of different variables on the process economics – base. .................... 53

Table 4.5. Optimization steps. .............................................................................................. 55

Table 4.6. Influence of different variables on the process economics – optimized.............. 56 Table C.1. Saturated vapor pressures, MeOH.................................................................... C-1

Table C.2. Heat of vaporization, MeOH. ............................................................................. C-1

Table C.3. Liquid heat capacity, MeOH. ............................................................................. C-1

Table C.4. Liquid density, MeOH. ....................................................................................... C-2

Table C.5. Liquid conductivity, MeOH................................................................................. C-2

Table C.6. Viscosity, MeOH. ............................................................................................... C-2 Table D.1. Distillation column.............................................................................................. D-1

Table D.2. Condenser. ........................................................................................................ D-1

Table D.3. Reboiler. ............................................................................................................ D-2

Table D.4. Reactor. ............................................................................................................ D-2

Table D.4. Other parameters used. .................................................................................... D-2

Table D.5. Controller parameters (also table 3.1)............................................................... D-2 Table E.1. Aspen input data................................................................................................ E-1

Table E.2. Steady-state streams. ....................................................................................... E-1 Table G.1. Startup schedule................................................................................................ G-1 Table H.1. Optimization data............................................................................................... H-1

Introduction

1

1 Introduction Chemical plants produce and compete in a global market. The size of such a marketplace, the amount of competitors and a constantly fluctuating demand, force the chemical industry to remain flexible and cost-effective. Costs must be cut in as many places as possible and means to obtain an advantage must be kept confidential. Of course the plants must also be operated safely and environmental constraints need to be met. 1.1 Process modeling To evaluate the performance of a certain plant it is normally modeled before it is built. This is usually a steady-state model, which needs less data to run than a dynamic model and can describe the state in which the process should spend the majority of its time. With a model performance can be optimized, costs minimized and safety and environmental constraints checked. Steady-state simulations, however important, will not show all aspects of the process. A simple heat integrated process, as shown in the figure below, runs nicely in steady-state, but can not reach steady-state without extra equipment. This means extra investments. Flexibility of production is also not taken into account, though changing markets demand fast product changes.

ReactorHeatexchanger

Figure 1.1. A simple heat-integrated process. Safety is also a concern. Accident statistics show that 46% of the accidents which occurred in petrochemical plants took place during operations such as startup and shutdown (Batres et al., 1997, Amundson et al., 1988). During accidents problems can also occur due to leakage of toxic material to the environment. Finally, one of the most important goals of chemical industry is to generate a profit. Steady-state process optimization contributes 3-5% to the profit margin of continuously operated chemical plants (Verwijs, 1994). For a pilot plant, startup costs are 10-20% of the construction costs and, on average, a startup requires 1-3 months (Kirk et al., 1996). It can be seen that a faster startup will lead to savings. To analyze operability, flexibility and profitability the best approach is to use dynamic models (Fraga et al., 2000). There are several reasons this is not done: • difficulty in handling dynamic behavior in a mixed integer non-linear programming

problem, • extensive demands on computational resources (Fraga et al., 2000), and • the fact that complex models are not very general and are normally used for a single and

usually unique installation (Gosiewski, 1993). Therefore, literature on dynamic modeling, including startup, is not abundant. If it exists, it describes unit operations separately, though interactions, such as recycles, can have a large effect on, for example, controllability (Morud and Skogestad, 1996, Denn and Lavie, 1982). Further, to call a model dynamic normally means it is a model capable of describing the time-response to a change in input variables from or near the steady-state (e.g. Löwe et al., 2000), such as a product switchover. Here dynamic modeling will mean a model capable of describing the time-response of a process from “non-operation” to operation. An example of this is the startup of a distillation column from the point at which it has no liquid holdup on the trays to steady-state operation.

Introduction

2

1.2 Scope Startup and shutdown are hardly unknown events in the process industry. Plants have been started up and shut down for decades, though these are not frequently occurring operations and not many people actually experience them (Rao et al., 1994). Most of the experience gained is empirical and confidential. The idea on which the project is based, is to gain a better understanding of startup and shutdown operation and to give general rules for generation of safe and economically desirable startup and shutdown procedures. This can be done if there is a model capable of describing the behavior during startup and shutdown, which could be optimized. Such a model, however, is not yet available. This leads to the goals of the project: • to build a first-principles model that will describe the startup and shutdown behavior of a

process, • to optimize the startup and shutdown procedures, taking into account factors such as

operability and safety, and • to formulate general rules for better startup and shutdown procedures. Unfortunately it has become evident, that calculation times are very large. The model developed consists of over 15 000 equations and requires between 2 and 3 hours of calculation time. This means that optimization times will be excessive within the time available for the project. Therefore the goals of the project have been revised. The revised goals of the project are: • to build a model that will describe the startup and shutdown behavior of a process, and • to perform a simplified optimization of a specific startup procedure. The model will be tested on a glycolether process, the conceptual process design of which was performed by van den Eijnden, IJsebaert, Regenbogen and Wieland (1998). 1.3 Outline of the report This report consists of 5 chapters describing modeling, implementation and results as outlined below. In chapter 2 the theory of modeling of a distillation column and a reactor is given, as well as rules for determining the physical properties of mixtures. Various procedures for startup and approaches to optimization are also presented. The emphasis in this chapter is on what is done in the literature. The gPROMS model constructed is given in chapter 3, where a description of the kinetics used and the choices made during the modeling process are presented. The emphasis of chapter 3 is on the specific implementation of the model. Chapter 4 contains the results obtained with the model for steady-state, shutdown and startup behavior. It shows that the process can be optimized and what the influence of various variables is. It also gives an impression of the ease with which the model can be used for other processes. Returning to the goals of the project the conclusions and recommendations will be given in chapter 5.

Theory

3

2 Theory In this chapter the theory used for establishing dynamic models for distillation columns and plug-flow reactors, as presented in the literature, will be given. This will include the physical property models required for modeling. These literature-models are not suitable for startup and shutdown, only for relatively small changes to the steady-state. The adjustments required for startup and shutdown will be presented in chapter 3. Startup procedures from the literature will also be presented, as well as methods for optimization of non-linear objective functions. 2.1 Distillation columns A rigorous dynamic model for process simulation, depicted in steady-state in figure 2.1, would include (e.g. Löwe et al. 2000): • mass balances, • energy balances, • equations for phase equilibrium, and • equations for the hydrodynamics of the tray.

Figure 2.1. Steady-state tray of a distillation column. For the interaction of liquid and vapor two types of models can be used, equilibrium and non-equilibrium models. The equilibrium model assumes liquid and vapor on a tray are in equilibrium, while the non-equilibrium model includes an inter-phase transfer relationship, and only assumes equilibrium at the interface of liquid and vapor. In this chapter both will be considered. 2.1.1 Mass balance For equilibrium models the generic component mass balance for component i on tray N can be given by:

,, 1 , 1 1 , 1 , ,

( )i NN i N N i N N i N N i N N i N

d MF z L x V y L x V y

dt − − + += ⋅ + ⋅ + ⋅ − ⋅ − ⋅ (2.1)

in which: , , ,

L Vi N i N tot i N totM x M y M= ⋅ + ⋅ (2.2)

and the top tray is tray number 1.

Theory

4

For non-equilibrium models component balances for both liquid and vapor phase must be given (Baur et al., 2001, Krishnamurthy and Taylor, 1985):

,, 1 , 1 , ,

( )Li N L L L

N i N N i N N i N i tr

d MF z L x L x M

dt − −= ⋅ + ⋅ − ⋅ + (2.3)

,, 1 , 1 , ,

( )Vi N V V V

N i N N i N N i N i tr

d MF z V y V y M

dt + += ⋅ + ⋅ − ⋅ − (2.4)

In non-equilibrium models the inter-phase transfer for each component (Mi,t) needs to be evaluated. Generally this is a function of the mass transfer coefficients, for example: , ( )V V V I

i t i i iM k y y= ⋅ − (2.5) Mass transfer coefficients are not readily available for multi-component mixtures. 2.1.2 Energy balance For equilibrium models the generic component energy balance for tray N can be given by:

, , 1 1 1 1( ) L L V V L V L VN N

N F N N F N N N N N N N N Nd E M

F H F H L H V H L H V H Qdt − − + +⋅

= ⋅ + ⋅ + ⋅ + ⋅ − ⋅ − ⋅ + (2.6)

For non-equilibrium models energy balances for both liquid and vapor phase must be given:

, 1 1( )L L

L L L L LN NN F N N N N N tr

d E M F H L H L H Q Edt − −⋅

= ⋅ + ⋅ − ⋅ + + (2.7)

, 1 1( )V V

V V V V VN NN F N N N N N tr

d E M F H V H V H Q Edt + +⋅

= ⋅ + ⋅ − ⋅ + − (2.8)

The inter-phase energy transfer will be given by a relationship like (Krishnamurthy and Taylor, 1985):

,1

( )exp( 1)

V nV V I V V

tr i t iVi

eE h a T T M He =

= ⋅ ⋅ − + ⋅− ∑ (2.9)

Here the heat transfer coefficients and rate factors for multi-component mixtures will be needed. 2.1.3 Liquid-vapor equilibrium In equilibrium models various methods can be applied to calculate the liquid-vapor equilibrium. Basically the K-value for the following equation needs to be determined:

ii

i

yKx

= (2.10)

The K-value can be calculated using equation of state models, such as models of the Redlich-Kwong type (Reid et al., 1988), or using models based on Raoult’s law with (UNIQUAC, UNIFAC) or without activity coefficients. For non-equilibrium models liquid and vapor are assumed to be in equilibrium at the liquid-vapor interface.

Theory

5

2.1.4 Tray hydrodynamics Tray hydrodynamics normally include liquid flow over the weir and vapor flow through the holes. The liquid flow is based on the Francis weir formula (Coulson and Richardson, 1997): 1.51.84 ( 0.1 )N mol w C ow owL L N h hρ= ⋅ ⋅ − ⋅ ⋅ ⋅ (2.11) with: ow wh level h= − (2.12) Nc is the number of end contractions, which equals zero for a liquid flowing over the weir in a distillation column. To take into account that the liquid level is larger than the level of clear liquid, the level in equation (2.12) can be replace by the effective level, where:

(1 )effectivelevellevel

ε=

− (2.13)

ε is in the order of 0.5 (Lockett, 1986), though it is not usually known for small flows. An equation for the vapor flow is derived using the general Bernoulli equation (Jansen and Warmoeskerken, 1991):

2

2 22 1 2 1

1

1( ) ( ) 02 wr

dP g h h v v Aρ

+ − + < > − < > + =∫ (2.14)

with:

22

12wr wA K v= ⋅ < >∑ (2.15)

The subscripts can be seen in the figure below, where the dashed line is the tray with holes.

Figure 2.2. Definition of subscripts for derivation of vapor flow equation. Assuming: • liquid density is not a function of the pressure, • vapor density in the hole does not vary due to pressure, • friction loss is mainly due to contraction of the flow-path (Jansen and Warmoeskerken,

1991), 2

1

0.45 (1 )wAKA

= ⋅ − (2.16)

• no holdup between phases, and • pressure on the liquid-vapor interface is given by: 2 NP P g levelρ= + ⋅ ⋅ (2.17)

equation (2.14) becomes:

2

1

Theory

6

2 21 2 22

1 1

1 1 1( ( ) 0.45 (1 )) 02 2 2

LN

V

P g level P A AvA A

ρρ

+ ⋅ ⋅ −+ < > ⋅ − ⋅ + ⋅ ⋅ − = (2.18)

and:

1

222 2

1 1

1 1 1( ) 0.45 (1 )2 2 2

LN

V

P P g level

vA AA A

ρρ

− − ⋅ ⋅

< > =− ⋅ + ⋅ ⋅ −

(2.19)

The molar flowrate then equals:

2,

holesN

mol vap

AV v

V= ⋅ < > (2.20)

The assumption of a constant vapor density is made for ease of calculation. What is not encountered in the literature, but can be derived in the same way as the molar flowrate for vapor flow, is liquid dumping through the holes of a tray. Operation with dumping causes low tray efficiencies, which are difficult to estimate (Lockett, 1986) and therefore it is normally avoided in steady state operation by proper design. For the purpose of use in the model developed it will be derived here. The basis is, once again, equation (2.14). Equation (2.15) and the same assumptions will also be used. The system will be defined slightly differently, as can be seen below:

Figure 2.3. Definition of subscripts for derivation of liquid dumping equation. Now, with subscript 1 denoting the liquid-vapor interface, equation (2.14) becomes:

2 21 1 12

2 2

1 1 1( ( ) 0.45 (1 )) 02 2 2

LN N

L

P P g level A AvA A

ρρ

+ − − ⋅ ⋅+ < > ⋅ − ⋅ + ⋅ ⋅ − = (2.21)

equation (2.19) becomes:

1

221 1

2 2

1 1 1( ) 0.45 (1 )2 2 2

LN N

L

P g level P

vA AA A

ρρ

++ ⋅ ⋅ −

< > =− ⋅ + ⋅ ⋅ −

(2.22)

and equation (2.20) becomes:

1

2

Theory

7

2,

Holes holes

mol liq

AL v

V= ⋅ < > (2.23)

Equations (2.11), (2.20) and (2.23) describe the main flows to and from a tray. 2.2 Reactors The reactor, which will be modeled, is a plug-flow reactor (tubular reactor). For dynamic modeling several main equations are important: • the mass balance, • the energy balance, • the momentum balance, • heat transfer relations, and • friction terms. All equations will be derived from first-principles, though for the energy balance a simpler form will be used (appendix B). Assumptions that will be made are: • magnetic, electrical, kinetic, potential and “other” energy is negligible, • no shaft work will be exerted on the system, • tubes are cylindrical, • the system is symmetrical, • the flow is turbulent, • there is no conductive heat transport in the axial direction in fluids, • no evaporation takes place, • there is no heat flux to the surroundings (infinitely thick insulation), • there is no temperature profile in the tube wall, • the density and heat capacity of all solids is constant, • thermal expansion is neglected, • the physical properties of the tube wall are independent of the temperature, and • all walls are considered to be smooth. Many of these assumptions are explained in appendix B. The following figure shows the directions within the reactor.

Figure 2.4. Definition of directions in the reactor. 2.2.1 Mass balance A dynamic component mass balance for liquid flowing through a pipe and reacting can be derived as shown in appendix B. Noting that mass and moles are interchangeable, the result is:

,1

( ) mi z i

i j jj

C v C rt z

ν=

∂ ∂ ⋅= − +∂ ∂ ∑ (2.24)

If no reaction takes place, the component mass balance reads:

r

θ

z

Theory

8

( )i z iC v C

t z∂ ∂ ⋅= −∂ ∂

(2.25)

2.2.2 Energy balance With the assumptions above the energy balance becomes an enthalpy balance. Including the other assumptions the enthalpy balance for a liquid flowing through a tube with diameter di becomes:

( ) 4 ( )z

i wi

H v H U T Tt z d

∂ ∂ ⋅= − + ⋅ ⋅ −∂ ∂

(2.26)

The derivation of this formula can be seen in appendix B. For heat-flow through a tube-wall the following enthalpy balance can be given:

2

,, , 2 2 2 2 2

o i o i

4 d4 d( ) ( )

(d d ) (d d )i s iw w i i

mol w p w w w c w

UT T UC T T T Tt z

ρ λ⋅ ⋅∂ ∂ ⋅ ⋅

⋅ ⋅ = ⋅ + ⋅ − + ⋅ −∂ ∂ − −

(2.27)

2.2.3 Momentum balance A dynamic momentum balance for flow of liquid through a tube can be given by:

2( ) ( )v v Pz z gw zt z z

ρ ρτ ρ

∂ ⋅ ∂ ⋅ ∂= − − − + ⋅∂ ∂ ∂

(2.28)

The derivation of this formula can be seen in appendix B. It is important to note the directions of vz, z, τw and gz (figure 2.4). 2.2.4 Heat transfer Heat transfer coefficients can be based on the inner or outer tube-diameters. The overall heat transfer coefficient, based on inner tube-diameters can be calculated (appendix B) from Sinnott (1996):

,

ln1 1 1 1 1

2

oi

ii i

o i o o o od w id i

dddd d

U d h d h h hλ

⋅

= ⋅ + ⋅ + + +⋅

(2.29)

The overall heat transfer coefficient needs to be split in the heat transfer coefficients on the tube side and on the shell side. Assuming there is no temperature profile over the wall in radial (r-)direction, and the temperature used is the temperature in the middle of the wall, the separate heat transfer coefficients can be given by:

ln1 1 1

4

oi

i

i w id i

ddd

U h hλ

⋅

= + +⋅

(2.30)

and:

Theory

9

,

ln1 1 1

4

oi

ii i

s i o o o od w

dddd d

U d h d h λ

⋅

= ⋅ + ⋅ +⋅

(2.31)

Within these equations the liquid film heat transfer coefficients need to be evaluated. For turbulent flow these can by found by (Sinnott, 1996, Jansen and Warmoeskerken, 1991):

0.14

0.8 0.330.023 Re Pre

w

h DNu η

λ η ⋅

= = ⋅ ⋅ ⋅

(2.32)

In which the Reynolds number is defined as:

Re z ev Dρη

⋅ ⋅= (2.33)

and the Prandtl number is defined as:

Pr pC ηλ⋅

= (2.34)

The hydraulic diameter is defined as 4 times the cross-sectional area over the wetted perimeter. For the hydraulic diameter in a tube this becomes: ,e i iD d= (2.35) and for the hydraulic diameter in a shell encompassing N tubes:

2 2

,shell tubes o

e oshell tubes o

D N dDD N d

− ⋅=

+ ⋅ (2.36)

2.2.5 Friction terms The shear force for turbulent flow can be given by (Beek and Muttzall):

212w zf vτ ρ= ⋅ ⋅ ⋅ (2.37)

It is important to realize that the shear force has a direction contrary to the flow. The friction factor for turbulent flow and smooth walls can be given by the Blasius equation (Jansen and Warmoeskerken, 1991): 0.254 0.316 Ref −= ⋅ 4000 < Re < 105 (2.38)

Theory

10

2.3 Physical properties To model a process it is necessary to know the physical properties of the materials involved. In systems with multiple components precise knowledge of all physical properties is not available. Often physical properties of mixtures are estimated using the physical properties of pure substances. As seen above, for modeling of distillation columns and reactors the following physical properties will be required: • conductivity, • density, • enthalpy, • heat capacity, • molecular weight, • partial vapor pressure, and • viscosity. Though many of these physical properties can be calculated or estimated for both liquid and vapor phase, the theory for determining them will be restricted to the phase for which the property will be needed in the model developed. The assumption that the liquid and gas-phases are ideal will be made to simplify mixing rules. 2.3.1 Physical property models Conductivity For multi-component mixtures the methods of Li and Rowley can be used (Reid et al., 1988) to calculate the liquid conductivity. These are complex methods, requiring superficial volume fractions or local molar fractions. Due to the fact that the conductivity of most organic liquids is between 0.10 and 0.17 W/m.K (Reid et al., 1988) the Vredeveld equation (Reid et al., 1977) can be used:

1

i

nr rmix i

iwλ λ

=

= ⋅∑ (2.39)

or with molar fractions:

,1 1,

j

rn nrmix i w i

j ij w j

x Mx M

λλ

= =

= ⋅ ⋅⋅∑ ∑ (2.40)

This is one method used, for example, by ASPEN. Most methods also require the pure component liquid conductivities. These have been collected in the DIPPR (Daubert and Danner, 1989) program and fit to a power law: 2 3 4

i A B T C T D T E Tλ = + ⋅ + ⋅ + ⋅ + ⋅ (2.41) Density In ideal mixtures the molar densities of the liquid and vapor-phases can be calculated by:

1,

1 ,

( )n

imol mix

i mol i

xρρ

−

=

= ∑ (2.42)

For non-ideal mixtures various other methods can be given (Reid et al., 1988). Pure component liquid densities have been collected in the DIPPR program and fit to:

Theory

11

,(1 (1 ) )D

Lmol i T

C

A

Bρ

+ −= (2.43)

Vapor densities follow directly from the ideal-gas law:

,Vmol i

PR T

ρ =⋅

(2.44)

Enthalpy Enthalpies of liquids and vapors, operating at constant pressure or assumed to be independent of the pressure, can be given by:

0

P

TL Li

T

H C dT= ⋅∫ (2.45)

and:

0

P

TV Vi

T

H C dT= ⋅∫ (2.46)

Alternatively the vapor-phase enthalpy can be given by: ,

V Li i vap iH H H= + ∆ (2.47)

The enthalpy of a mixture can be given by:

1

nL Lmix i i

iH x H

=

= ⋅∑ (2.48)

For the vapor-phase an identical relationship with yi can be used. The heats of vaporization for pure substances have been collected in the DIPPR program and fit to:

, exp( ln( ) )Evap i

BH A C T D TT

∆ = + + ⋅ + ⋅ (2.49)

Heat capacity Molar heat capacities of ideal fluids can be given by (Smith et al., 1987):

, ,1

nL Lp mix i p i

iC x C

=

= ⋅∑ (2.50)

yi would be used for vapor heat capacities. The liquid heat capacities of pure substances have been collected in the DIPPR program and fit to a power law, such as equation (2.41). Only for N2 the data have been fit to a different equation:

Theory

12

2 2

sinh sinh

Vp

C EC A B DC ET TT T

= + ⋅ + ⋅ ⋅ ⋅

(2.51)

Molecular weight The molecular weight of a mixture can be given by:

, ,1

nL Lwt mix i wt i

iM x M

=

= ⋅∑ (2.52)

For the vapor-phase an identical relationship with yi can be used. Partial vapor pressure Partial vapor pressures have been collected in the DIPPR program and fit to the same equation as (2.49). Viscosity The viscosity of an ideal liquid can be given by (Reid et al., 1988):

1

ln lnn

mix i ii

xη η=

= ⋅∑ (2.53)

Viscosity data have been collected in the DIPPR program and fit to the same equation as (2.49). 2.4 Startup Once a process has been modeled and built, the process will need to be started up to meet its design objective. Various procedures for startup of a distillation column have been given in the literature. In the most simple form the procedure for startup of a distillation column can be described as (Barolo et al., 1994, Ruiz et al., 1988 and Ganguly and Saraf, 1993): • fill the reboiler with liquid, • heat the liquid, • introduce total reflux and feed when sufficient reflux has accumulated, • end total reflux when all plates have been filled with liquid, • draw product and wait till steady-state is reached. Improvements suggested are: • introducing the feed after the sealing of the trays, • filling the reflux drum with feed mixture, • filling the reflux drum with light product initially, and • using partial backmixing equipment as condenser drum.

For startup of adiabatic reactors Verwijs (1994) gives the following procedure: • fill reactor system with a mixture of one reactant and product, while preheater is in

service, • feed this reactant into the reactor, while preheater is in service, • feed second reactant, when the flow of first reactant has reached the required initial

setpoint, and • increase total feed to reactor when flows of the reactants have reached required initial

setpoints and outlet temperature is above a certain minimum.

Theory

13

This procedure is used when the second reactant may never leave the reactor due to, for example, safety considerations. Verwijs (1994) and Verwijs et al. (1996) point out that the most important variable governing the conversion of the second reactant is the initial reactor temperature. Further they state, that: • finding the appropriate initial temperature at which the second reactant can be introduced

into the reactor, • finding the total flowrate at which the reactor can be started up safely, • finding the initial speed at which the second reactant can be introduced into the reactor,

and • finding the trajectory at which to decrease the initial temperature to normal value will be of importance for a successful and economical startup of the reactor in question. Therefore these variables could be used in optimizing reactor performance during startup. A difficulty during startup is control of the process. Automatic controllers are designed for controlling linear behavior. During startup the process undergoes large changes and behaves much more non-linear than it does in steady-state. This means the controllers will not function properly. For this reason control gains are normally not set at constant values during startup (Ratto and Paladino, 2001). Operators will make gradual shifts towards the target, thereby operating the controllers manually. Integral control is usually set at about zero. 2.5 Optimization One goal of formulating a model is to run simulations and make decisions based on the outcome. Often these decisions will be driven by the desire for greater profit and be based on economic criteria. A given model consists of a set of equations and for optimization purposes will contain an objective function. Optimization implies (where minimization or maximization can be used):

Minimize: f(x) x = [x1 x2 … xn]T

Subject to: hj(x) = 0 j = 1,2, …, m gj(x) ≥ 0 j = m+1, …, p

Here f(x) is the objective function, which is a function of n variables. There are a total of p constraints, which can be divided into equality constraints (hj) and inequality constraints (gj). The equality constraints are the model equations, such as heat and mass balances, and the inequality constraints are safety and operational constraints, such as maximum temperatures or flows. Objective functions can be linear or non-linear. Linear objective functions are either concave or convex, implying the existence of one optimum. To test if a function is concave or convex the Hessian matrix can be determined. This is the matrix of second derivatives (∇ 2f(x)) of the objective function. If all eigenvalues of the Hessian matrix are either ≥ 0 or ≤ 0 then the objective function is either convex or concave. Various methods have been developed for solving linear optimization problems, such as the Simplex algorithm (Edgar and Himmelblau, 1989). The Simplex algorithm searches the bounds of an objective function for an optimum, as the optimum of a linear optimization problem will always lie on a bound. Non-linear objective functions have both positive and negative eigenvalues of the Hessian matrix. This means that the objective function can have (many) local optima, which may not be equal to the absolute optimum. Unfortunately non-linear objective functions are very common. Examples of methods for solving non-linear objective functions are the Newton-Raphson method (Edgar and Himmelblau, 1989, Rice and Do, 1995) and the bisection method (Rice and Do, 1995).

Theory

14

For both the Newton-Raphson and bisection methods the objective function needs to be equated to zero. The goal then is to find the values of the variables that make the function zero. If the function itself is not available, this may pose a problem. The Newton-Raphson method linearizes the function locally to determine the slope. The next step in the iteration, with one optimization variable, is given by:

1 ( )( ( ))

kk k

kf xx x

d f xdx

+ = − (2.54)

Though convergence can be very fast, the derivative of the objective function is needed. For coupled non-linear equations this can be difficult to obtain and therefore this is a great disadvantage of the Newton-Raphson method. To find the values that make the function zero the bisection method requires finding an interval [a,b] in which the sign of the function changes. This interval is halved (c) and the function value is determined at this new point (f(c)). The new f(c) replaces f(a) or f(b), whichever has the same sign, and the process is repeated until a predefined tolerance is reached. For the bisection method no derivative is needed, the method is very simple and it always converges. The drawbacks are the need to find an interval in which the sign of the function changes and the slow convergence rate relative to other methods such as the Newton-Raphson method. Both methods can be seen graphically for one optimization variable in figure 2.5.

Figure 2.5. Newton-Raphson and bisection methods for solving non-linear optimization problems. All methods require data to estimate the next point. This could be either the objective function, which is not normally known in simulations, or simulation data itself. To get an estimate of the sensitivity of the objective function to pre-determined variables orthogonal (factorial) experimental design can be used (Edgar and Himmelblau, 1989). The factorial design can be given by the following relation: Y b X= ⋅ (2.55) or, for three variables, a combination of several: 0 1 1 2 2 3 3Y b b x b x b x= + ⋅ + ⋅ + ⋅ (2.56) In these equations the response variable Y could be e.g. the cash flow and X (x1,x2 and x3) are independently adjustable variables. In stead of using the values of the variables for x one could use normalized variables, such as for the temperature:

Newton-Raphson method

x(1) x(0)f(x)

x

Bisection method

ab c

d

f(x)

x

Theory

15

refT Tx

T−

=∆

(2.57)

By doing this all x are within [-1,1]. The base case could be defined as x=0, for all x. Therefore it can be seen that the first column of the X-matrix is a column of ones. For k variables, 2k experiments can be performed. These can be used to fit a sensitivity-function through the base case, using the least square method (Edgar and Himmelblau, 1989). The model fitting parameters can be obtained by: 1( )T Tb X X X Y−= ⋅ ⋅ ⋅ (2.58) Because the variables are chosen independently of each other, for the various elements of X can be said that: 0i j j ix x x x⋅ = ⋅ = (2.59) This means XT.X is a diagonal matrix and (XT.X)-1 simply consists of a diagonal matrix with the reciprocals of the diagonal elements of XT.X. By this method the sensitivity of Y with respect to the variables X has been found in the form of equation (2.56). This information can be used for estimating the next point to acquire data. Equation (2.56) is basically a Taylor-expansion in which the second and higher order terms are neglected. In one variable this is given by:

0

20 0

( ( ))( ) ( ) ( ) ( )x

d f xf x f x x x O xdx

= + ⋅ − + (2.60)

If we do not neglect the second order terms we get:

0 0

22 3

0 0 02

( ( )) 1 ( ( ))( ) ( ) ( ) ( ) ( )2!x x

d f x d f xf x f x x x x x O xdx dx

= + ⋅ − + ⋅ − + (2.61)

Assuming for the stepsize a deviation of 5% of the base value (f(x0)) will provide a sufficiently large step and neglecting higher order terms, it can be stated, that:

0 0

2 22 2 2

0 02 2

1 ( ( )) 1 ( ( ))0.05 ( ) ( ) ( )2! 2!x x

d f x d f xf x O x x x xdx dx

⋅ = = ⋅ − = ⋅ (2.62)

in which x0 = 0. Using the data collected the second derivative can be evaluated. With this information the new x can be determined as described below. This will be the new base case. The factorial design can be repeated until further optimization reveals a step in the opposite direction or a bound is hit. If a step in the opposite direction can be found, the final two points can be used as starting point for the an optimization analogous to the bisection method, with which the true optimum between the points can be determined. For three variables, using the factorial design method, three second derivatives need to be evaluated. Unfortunately, due to the points chosen for evaluation, four second derivatives can be calculated, which only differ in the signs of the coefficients of the variables. This will lead to one averaged second derivative, which is equal for all three variables. Applying the principle that, if the sensitivity to one variable is large, the stepsize should be small and vice versa, the 5% deviation in f(x0) will be distributed among the three variables

Theory

16

according to the size of the respective model fitting parameters (b). The distribution of fractional changes for variable xi will be given by:

3

1

1

5%1i

ix

i i

bf

b=

= ⋅∑

(2.63)

This means the new x can be given by:

0

0

2

2

( )

1 ( ( ))2!

ixi

x

f Y xx

d f xdx

⋅=

⋅ < > (2.64)

This can be converted back into the real variable which xi represents.

Modeling the process

17

3 Modeling the process One goal of the project is to construct a dynamic model capable of describing startup and shutdown behavior. In chapter 2 the theory as presented in the literature has been shown. Here the process-specific implementation of the model for simulation of startup and shutdown will be discussed, as well as deviations from the literature. After defining the basis of the process, an overview of the model structure will be given. Then the physical properties, all (sub-)models and reaction kinetics will be discussed. Finally an overview of settings used in gPROMS will be given. 3.1 Process basis The model constructed has been based on a conceptual process design performed by van den Eijnden, IJsebaert, Regenbogen and Wieland (1998). Their process flow diagram can be seen in appendix A, figure A.2. This process was chosen, because the glycolether process consists of units common to and important in industry, a reaction and separation section. It also incorporates a recycle, making the process a good candidate to look at the system as an interconnected whole, not just a collection of different unit operations. A third reason for choosing this case was availability of the design. The goal was not to design a process and risk focussing too much on design for startup, but rather to look at an existing process and attempt to formulate and optimize a startup strategy. Due to time constraints it was not possible to simulate the entire process. Still desiring to look at an interconnected startup the model was restricted to the reactor, first distillation column and the recycle, as can be seen in the figure below.

Figure 3.1. Schematic of the process modeled. 3.1 Model structure The process has been modeled in gPROMS (general PROcess Modelling System, Process Systems Enterprise Ltd., version 1.8.4 for Linux). gPROMS has been chosen due to the equation based approach, the relative ease of handling large problems and the optimization tool included in gPROMS. The following models have been constructed in gPROMS: • Distillation column

• Tray • Condenser • Reboiler

PO, MeOH

MeOH recycle

MP-2, MP-1, MDP, catalyst

catalyst


18

• Reactor • Tube • Wall • Shell • Conversion blocks

• Physical properties • PI-controller • Mixer • Connection breakers An overview of the process modeled, with all its sub-models, is given in the figure below.

Figure 3.2. The process as modeled. All names within the blocks are those used in the model, except for LP-steam, which will be explained below. The total reactor is named R5 and the column C. The model in annotated gPROMS-code is given in appendix I. 3.2 Physical properties Seven components can be present in the process. These are (in the order used in the model): 1. propylene-oxide (PO), 2. methanol (MeOH), 3. 2-methoxy-1-propanol (MP-1), 4. 1-methoxy-2-propanol (MP-2), 5. 4 isomers of methoxy-propoxy-propanol, lumped together (MDP), and 6. catalyst N(OCH3)3 (cat) or nitrogen (N2). Catalyst will only be present in the reactor and nitrogen only in the column. Therefore they both have been given number 6. It is assumed that nitrogen does not enter the liquid phase, as the temperature is far above its critical temperature and at a temperature of 100°C and a

Mix

XCins BreakTfeed

Mix_MeOH_feed

Break_recycle

Condenser

Shel TubeWall Tray 1

Catalyst

MeOH

PO

Mix_PO_feed

XCintCXouts

Tube2

Wall2

BFWLP-Steam

Product

Purge

LP-steam

CXoutt

Tray 19

Tray 25

Reboiler

MeOH

Catalyst

C

R5


19

pressure at 1 bar the molar fraction of N2 in water is 7.8*10-6 (Jansen and Warmoeskerken, 1991), which is negligible. Due to the absence of a database, various assumptions have been made to simplify the calculations of the physical properties for the mixtures. The main assumption, as stated earlier, is ideality of the liquid and vapor-phases, implying most physical properties can be estimated by the mole-average of the pure physical properties. This assumption has been made due to the low temperatures and pressures used, even though there are polar components present. For all properties it means that the relationships as presented in the theory can be used. It must be noted that only the vapor-phase molar density is a function of the pressure. All other physical properties are independent of the pressure. The only difference with the relationships presented in the theory is for the liquid conductivity. A different relation has been used from the Vredeveld-equation presented. The Vredeveld equation needs to be adapted if one of the components is not present at a certain time. This would mean it has a fraction 0. A fraction of 0 can not be used in equation (2.40) and it would have to be omitted, causing a discontinuity in the equation. If possible this should be avoided. Also it can be seen that the liquid conductivity is required only for the heat transfer coefficient. An error in the liquid conductivity will cause a change in the heat transfer coefficient of error2/3. Combined with the fact that the conductivity of most organic liquids is between the range 0.10 and 0.17 W/m.K, a simple summation has been used for the conductivity of the mixture:

1

n

mix i ii

xλ λ=

= ⋅∑ (3.1)

Another choice made was to use the liquid enthalpy and enthalpy of vaporization to determine the vapor enthalpy. It was estimated that the liquid heat capacity could be determined more accurate than the vapor heat capacity, due to the fact that the liquid phase is more dense than the vapor phase. This means equation 2.46 was not used. The only source that could be found, which contained almost all pure component physical properties, was ASPEN (Aspen Technology, Inc.). It was thought to be important to have one reference for all physical properties. This is done to ensure an identical basis for all components and to be able to make a comparison. Therefore the pure physical properties have been taken from ASPEN, as coefficients to the DIPPR-equations given in the theory. Only the physical properties of the catalyst could not be found. Therefore it was decided to assume the catalyst has the same physical properties as MP-1, the heavier of the two MP’s. Due to low pressures in the vapor-phase and the large excess of methanol in most liquid-phases the assumptions of ideality have been made. To check the quality of the physical properties the different physical properties of MeOH were compared to various references. This can be seen in appendix C for the temperature range of 293 – 450 K. PO, the lowest boiling main component, has a critical temperature of 482 K. This means no equations for liquid properties should be used above this temperature, otherwise the model will crash, because a negative number will be raised to a non-integer power in equation 2.32. All references for calculating the saturated vapor pressure (table C.1) and liquid density (table C.4) agree within 1%. The heat of vaporization (table C.2) has been given by Daubert and Danner (1989) to be about 3% accurate and deviations from measured values are no greater than 2 % in the range used and therefore assumed acceptable. The liquid heat capacity (table C.3) differs significantly for temperatures above the given range. The liquid conductivity (table C.5) shows large differences from two of the references for the higher temperature range. In both cases this is above the range for which the equation is valid. ASPEN uses linear extrapolation above the given temperature range and it will be assumed this is also valid for the model as no other comprehensive models are available. The liquid viscosity (table C.6) shows even larger differences in the higher temperature range. It


20

can be seen that this is far outside of the temperature range for which the formula is valid. Fortunately an error in viscosity is only important for the Reynolds and Prandtl number, causing the overall effect on the heat transfer coefficient to be the square root of the viscosity. Daubert and Danner (1989) give an accuracy of 10%. As the other variables were sufficiently accurate and it is important to use data from the same source, the liquid heat capacity, liquid conductivity and liquid viscosity will be used as found in ASPEN. If properties are required outside the temperature range for which they are valid, they will be extrapolated. This leads us to constructing three physical property databases: two for the column and one for the reactor. The difference is made for two reasons: • the reactor is a distributed model, and the physical properties model will also be

distributed, and • not all physical properties needed in the column are also needed in the reactor and vice

versa. The non-shared physical properties are the vapor phase properties in the column and the liquid conductivity and liquid viscosity in the reactor. Calculation of unnecessary variables can lead to longer calculation times. The third physical properties database is used for the N2, which will enter the column during shutdown. It could have been added as constants in the reboiler model, as it only includes calculation of the enthalpy of N2. 3.3 Distillation column The distillation column (C) consists of: • 25 tray models, 1 being the top tray, 25 the bottom, • a condenser model, and • a reboiler model. All these models include the model for determining physical properties and have been sub-divided into seven sections: • balances, • definitions, • hydrodynamics, • heat transfer, • geometry, • equilibrium, and • database physical properties. The models will be discussed along these lines, except for the physical properties, which have been discussed previously. The assumptions that have been made are: • both liquid and vapor are well-stirred, • liquid and vapor are in equilibrium with each other, • energy dissipation is zero or negligibly small with respect to the amount of mechanical

energy that changes from one form into another, • change in energy due to varying temperatures and evaporation/condensation is

significantly larger than change in energy due to changes in energy potential and impulse, • influence of surface tension is negligible, • there is no entrainment of liquid in the vapor and no holdup of vapor in the liquid, • the bottom of the column is cylindrical,


21

• the temperature is the same in both liquid and vapor phase, • there is no vapor flow from the top of the column to bottom, • there is no liquid flow from the reboiler to the tray above it, • the downcomers will not be modeled, • with respect to heat transfer, the condenser and reboiler are over-designed by 25%, • the trays are sieve trays, and • the holes in the sieve trays of the column were punched. 3.3.1 Tray model The tray was designed as a sieve tray, with a given diameter and area. The downcomer has not been included in the model. This was done with the idea that the downcomer does not influence the dynamics of the system very much and the downcomer could be added later, though it never was. Not modeling the downcomer means the downcomer is assumed to have no accumulation of mass or heat. In the total tray volume the downcomer volume has been incorporated, meaning a liquid volume of the downcomer area times approximately twice the liquid level is neglected. As the downcomer area is about 16 % of the tray, the inventory on the trays of the column is underestimated by about 24%. As most of the holdup in the column is in the condenser and reboiler, the total volume is underestimated by about 10%. The dynamic contribution besides the holdup is downcomer sealing. This is determined by the liquid level on the tray and has been incorporated in the model. For modeling purposes the areas of the holes can be summed, as the liquid and vapor are assumed to be well-mixed. The holes are larger than 3/16 inch (4.7 mm), so the influence of surface tension is negligible (Prince and Chan, 1965). As will be seen in the equations below weeping has not been included. The driving force for weeping is the static liquid head (Kister, 1992 and Prince and Chan, 1965), where waves in the liquid may cause weeping, or the surge of excess pressure in the wake of a rising bubble (Lockett, 1986), where vapor flowing through the holes causes weeping in its wake. Both driving forces can not be incorporated with the assumption of equilibrium as used in the model. Weeping is undesirable as it can be detrimental to separation efficiency, because liquid with concentrations nearing those of a higher tray would weep to a lower tray without sufficiently coming into contact with the liquid and vapor on the tray. In an equilibrium model the liquid weeping would have the same composition as that flowing over the weir, as the liquid and vapor are assumed to be well-mixed. This is another reason that weeping is neglected. Balances As mass transfer coefficients for multi-component mixtures are not readily available and due to the fact that the goal of the project was not to derive a “perfect” model for distillation, it has been decided to use an equilibrium model. This implies the liquid and vapor are well-stirred and the temperature in the liquid and vapor is the same. For the tray model, the component molar balance (equation 2.1) becomes:

,, 1 , 1 1 , 1

, ,

( ) V Holes Holesi N p p p p p p

N i N N i N N i Np L p Weir p DC

Holes Holesp p p pN i N N i N

p Weir p DC

d MF z L x V y

dt

L x V y

− − + += = =

= =

= ⋅ + ⋅ + ⋅

− ⋅ − ⋅

∑ ∑ ∑

∑ ∑ (3.2)

This immediately shows the extra features added to the standard model: • dumping, and • vapor escape through the downcomer.


22

Further, vapor is not assumed to flow from a higher tray to a lower tray and liquid is not assumed to flow from a lower tray to a higher tray, also meaning no liquid is entrained in the vapor and no vapor is entrained in the liquid phase. This could be added to the model, but it introduces extra equations and complexity and has not been done as yet. The indices 1 and 2 in the model denote the two phases liquid and vapor (L and V). Index 3 is reserved for the liquid dumping. For the fractions and enthalpies index 3 equals index 1. The difference is made to be able to use summations in the balances. Vapor flow through the downcomer has not been given a separate index. For the fractions and enthalpies index 2 is used for this flow. The flow-variable, VN

DC, has not been taken up in the vector of flows. The energy balance (equation 2.6) becomes:

, 1 1 1 1

( ) V Holes Holesp p p p p pN N

N F N N N N Np L p Weir p DC

Holes Holesp p p pN N N N N

p Weir p DC

d E MF H L H V H

dt

L H V H Q

− − + += = =

= =

⋅= ⋅ + ⋅ + ⋅

− ⋅ − ⋅ +

∑ ∑ ∑

∑ ∑ (3.3)

Though energy is used as variable in the accumulation term, energy and enthalpy will be used interchangeably (see derivation of the energy balance in appendix B). Definitions The definitions-section contains equations that define certain variables. These include the fact that the sum of all the molar fractions by definition must equal one:

1

1n

ii

x=

=∑ (3.4)

and:

1

1n

ii

y=

=∑ (3.5)

As stated above x(3) equals x(1). Both the molar and enthalpy balances contain an accumulation term, which contains both a liquid and vapor part. For an equilibrium model these can be lumped together for accumulation. Of course both liquid and vapor states need to be calculated separately. For this purpose equation 2.2 is used. Such an equation is also necessary for the En*MN term. This becomes: L L V V

N N N NE M M H M H⋅ = ⋅ + ⋅ (3.6) Hydrodynamics The liquid flow over the weir is given by a combination of equations (2.11), (2.12) and (2.13):

1.5

,

1 1.84 max(0, ( ))WeirN w effective w

mol liq

L L level hV

= ⋅ ⋅ ⋅ − (3.7)

The max-statement has been added to allow the equation to still be valid if the effective level drops below the weir-height. The effective level has been estimated as function of the vapor flow. β is defined as 1-ε. In stead of using the value 0.5 as steady state value as estimated in the literature, 0.6 was used, as estimated in the gPROMS standard distillation model. This leads to the following relation for the effective level:


23

0.01

0.01

VN

effective VN

F

level levelFβ

+= ⋅

+ (3.8)

The factor 0.01 was used to cause the effective level and level to become equal at low flowrates. To determine the upper bound the steady state flowrate was estimated from the conceptual process design to be around 0.17 kmol/s. It was chosen to let the deviation be less than 5 % at a flowrate of 0.10 kmol/s. The resulting factor 0.0135 was rounded down to 0.01. The deviations can be seen in the figure below.

Figure 3.3. Determination of parameter for effective level. It can be seen that for large flows the ratio of level over effective level becomes β and for small flows it goes to unity. The vapor flow through the holes to the tray above can be given by a combination of equations (2.19) and (2.20):

1

** 11

2, , 1 1 1 1( ) 0.45 (1 )2 2 2

LN N N

VHoles holes N

Nholes holesmol vap N

tray tray

P P g levelA

VA AVA A

ρρ

+

++

+

− − ⋅ ⋅

= ⋅− ⋅ + ⋅ ⋅ −

(3.9)

Three problems were encountered using this function. • The pressure difference can become negative, which is not allowed within a square root. • The derivative near a zero pressure difference becomes infinite. • Letting gPROMS calculate the denominator with the areas caused the program to crash. The third problem was solved by manually calculating the denominator, as it only consists of parameters. This meant a factor of 1.191 was added to the function. To tackle the first two problems the square root was split and a constant was added, changing (3.9) to:

* 1

1

, , 1 1 1

1.191( ) 0.02

LHoles holes N N N

N V Lmol vap N N N N N

A P P g levelVV abs P P g level

ρρ ρ

++

+ + +

− − ⋅ ⋅= ⋅ ⋅

⋅ − − ⋅ ⋅ + (3.10)

Parameter determination for effective level

0

0.2

0.4

0.6

0.8

1

1.2

1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00

Flow (kmol/s)

Bet

a (-)

0

10

20

30

40

50

60

70

Dev

iatio

n fr

om 0

.6 (%

)


24

The factor 0.02 was determined by calculating the ratio of total pressure difference over the square root of the total pressure difference plus a factor, compared to simply the square root of the total pressure difference. At a total pressure difference of around 0.1 Pa a 5% deviation was allowed and the factor of 0.016 was rounded up to 0.02. It would have been more correct to round it down, but these pressure differences are not significant in practical application and come in the range where weeping would become important. With the total pressure difference is meant the inclusion of the pressure contribution due to the liquid level. The deviations can be seen in the following figure:

Figure 3.4. Determination of parameter for vapor flow. In steady-state the total pressure difference is in the order of 102 and the factor 0.02 is negligible. For liquid dumping equations (2.22) and (2.23) can be combined to:

1

**

2, 1 1 1( ) 0.45 (1 )2 2 2

LN N N

LHoles holes NN

holes holesmol liq

tray tray

P g level PA

LA AVA A

ρρ

++ ⋅ ⋅ −

= ⋅− ⋅ + ⋅ ⋅ −

(3.11)

Due to the same reasons as for the vapor flow, and for reasons of similarity with equation (3.9), equation (3.11) was written to:

* 1

, 1

1.191( ) 0.02

LHoles holes N N NN L L

mol liq N N N N

A P P g levelLV abs P P g level

ρρ ρ

+

+

− − ⋅ ⋅= ⋅ ⋅

⋅ − − ⋅ ⋅ + (3.12)

It may be noted that in both the vapor flow and liquid dumping equations the total pressure difference can become negative, which would cause negative flows. This is the switching point between the two equations. In the case of dumping the negative flow is actually the dumping flow. But dumping equations may not give a positive value. To stop this from happening the following two equations have been added:

*

1 max(0, )Holes HolesN NV V+ = (3.13)

and:

Parameter determination for vapor flow

0

10

20

30

40

0.001 0.01 0.1 1 10

Pressure difference (Pa)

Diff

eren

ce (%

)


25

3

* 10min(0, )Holes HolesN N

w

levelL Lh

−−= − ⋅ (3.14)

Equation (3.12) has the capability to generate an outflow even when there is no liquid on the tray. This is caused by the fact, that when using an equilibrium model the pressure is only determined by the temperature and the molar fractions on the tray, not by the absolute amounts of material. Therefore the second part has been added, to make the outflow more

dependent on the liquid level. The idea was to add a factor (310level

level

−− ), but this still

caused an outflow larger than the amount of liquid on the tray. To artificially bring the weeping outflow down the level was divided by the weir-height. Of course it is better to make the factor max(0, 31 0

w

le ve lh

−− ), but in practice the level never came below 10-3. This is due to the fact

that this factor was chosen under the assumption that the holes in the sieve trays of the column were punched. In that case it is conceivable that the holes have small edges. These were assumed to be 1 mm high and cause the liquid on the tray to never become less than this due to dumping. This explains the factor 10-3. Another possibility in dynamic operation is loss of liquid sealing of the downcomer. In steady-state this is undesirable and can be avoided by proper design (Kister, 1990). To model this an equation like (3.10) is used. The pressure difference now is not a function of liquid level, so this is omitted. First a variable for the pressure difference is used. Due to the fact that the first part could become excessively large, it was scaled, arbitrarily using one steady-state estimate for pressures to bring the variable to within its bounds:

11,

1

(109906 109478) 0.02(109906 109478)( ) 0.02

DC N NN test

N N

P PV

abs P P+

++

− +−= ⋅

−− + (3.15)

The factor 0.02 was used as above. The vapor flow into the downcomer is given by:

1

, , 1 1

1,

( ) (109906 109478)(109906 109478) 0.02

max(0, ( )) max(0, )

w effective apDCN V

mol vap N N

DCeffective ap N test

L level hV

V

sign level h V

α ρ+

+ +

+

⋅ − −= ⋅− +⋅ ⋅

⋅ − ⋅

(3.16)

The area for flow is the weir length times the difference between the effective level of liquid on the tray and the height of the apron, but only when this is greater than zero. Also the pressure difference needs to be greater than zero. Therefore the two max-statements have been added. All friction coefficients were lumped into α and the equation is scaled back. A flow-equation using α was the original one used. gPROMS gives α as 0.03 for flow through the holes, meaning 1

α equals 5.774. This is significantly different from the factor 1.191 used in

the equations above. The model is very sensitive to this factor with respect to stability, though the size of the flow is not influenced much by it. The inventory on the tray is influenced by it. Therefore the factor 1.191 is used as often as possible and use of α, such as here, could be considered ‘a first try’. As pressure drop is an important variable it has been added in the form: 1

LN N NdP P P g levelρ+= − − ⋅ ⋅ (3.17)

Heat transfer To take into account heat loss to the surroundings the following equation has been added:


26

( )N air tray outside NQ U S T T= ⋅ ⋅ − (3.18) With figure 12.1 from Sinnott (1996), using organics with a heat transfer coefficient around 1 kW/(m2.K) and air with a heat transfer coefficient around 0.1 kW/(m2.K), a heat transfer coefficient to outside air can be estimated at 0.1 kW/(m2.K). The outside temperature was assumed constant (18°C). Geometry If the physical properties and equilibrium concentrations are known a relation is needed between the amount of moles in the liquid and vapor phase. This has been given by the geometric constraint: , ,

L Vmol liq mol vap trayM V M V V⋅ + ⋅ = (3.19)

In other words, the volumes of liquid and vapor are restricted to the total tray volume. Such a constraint can also be given to determine the (clear) liquid level:

,L

mol liq

tray

M Vlevel

A⋅

= (3.20)

Equilibrium The equilibrium of an ideal gas and an ideal liquid can be calculated by using Raoult’s law (Smith and van Ness, 1987): sat

i i iy P x P⋅ = ⋅ (3.21) Nitrogen is not assumed to be present in the liquid phase, wherefore this equation is only valid for the other components and 6 0x = has been added. 3.3.2 Condenser model The condenser was designed to be a cooling tower, which is cooled by air. This imposes restrictions on the maximum and minimum cooling capacities, and the temperature range in which it can operate. The dynamics have not been modeled further than these restrictions. For the condenser model the sections of definitions, geometry and equilibrium are identical to those of the tray model, except that they use variables of the condenser, in stead of variables of the tray. These will not be discussed. Index 1 still denotes the liquid phase and index 2 the vapor phase. Balances One addition to the condenser is a startup-line, with which the condenser could be filled, for example with liquid from the reboiler. It will not be used in the startup or shutdown procedures. Liquid can leave the condenser as reflux or as product. Vapor can leave the condenser as product or purge. This gives the following component molar balance:

,1 ,1 , ,

,

( ) producti cond p p

i su line i reb cond i condp reflux

productp p

cond i condp purge

d MV y L x L x

dt

V y

−=

=

= ⋅ + ⋅ − ⋅

− ⋅

∑

∑ (3.22)

The energy balance reads:


27

1 1

( ) productV L p pcond cond

su line reb cond condp reflux

productp p

cond cond cond lossp purge

d E M V H L H L Hdt

V H Q Q

−=

=

⋅= ⋅ + ⋅ − ⋅

− ⋅ + +

∑

∑ (3.23)

Hydrodynamics Two controllers are added for controlling the level (P1) and the condenser duty (P2) in the condenser. The in-signals are defined by: ,in L controlSignal level− = (3.24) and:

, 610P cond

in Q control T condK PSignal K T−

⋅= + ⋅ (3.25)

The level control will be coupled with the reflux to the column. This is done to be able to still use the controller when there is no product being removed. The in-signal for the condenser duty can be used to control either the pressure or the temperature (the K-constants). It will only be used to control the pressure. This means the reflux-rate can be given by: max(0, )reflux

cond outL Signal= (3.26) The reflux-flowrate may never become negative. The rate of heat removal can be give by:

313.15

min(1, max(0, )) max(1.25 , min(0, ))5

condcond out

TQ bias Signal−= ⋅ ⋅ (3.27)

Air-cooled cooling towers are normally used for process temperatures above 65°C (Sinnott, 1996). It was assumed that the cooling tower would work normally when the condenser temperature is above 45°C and not function at all when the condenser temperature drops below 40°C. This explains the first min/max-section. The condenser was further assumed to give a maximum cooling 25% larger than that for which it was designed (the controller bias). Also, it was assumed not to be able to give any heating. To be able to run the column at infinite reflux the reflux ratio in the model was defined as:

'productcond

set refluxcond

LRL

= (3.28)

This is exactly the inverse of the conventional definition for the reflux rate (hence the ‘). This has been done to give a better definition of infinite reflux. ‘Infinite’ is not useable in gPROMS, but zero is. For the results and appendix D the conventional definition will be used. The vapor flowing from tray 1 to the condenser does not have to flow through a volume of liquid, it can be given by the following equation:

* 11

1, , 1 ( ) 0.02tube cond

Vcondmol vap N N

A P PV

abs P PV α ρ +

−= ⋅

− +⋅ ⋅ (3.29)


28

where α is given by:

21 1 1( ) 0.45 (1 )2 2 2

pipe pipe

tray tray

A AA A

α = − ⋅ + ⋅ ⋅ − (3.30)

Once again equation (3.30) was not used in the model due to instabilities, but was evaluated manually. To stop the flow from being negative it was given by: *

1 1max(0, )V V= (3.31) The purge can be given by the following equation:

* 5max(0,3.56 10 ( ))purge

cond cond setV P P−= ⋅ ⋅ − (3.32) The factor 3.56*10-5 was determined by allowing the purge to be no greater than 0.1 kmol/s, with a set pressure of 1 bar. Furthermore, it needs to be possible to close the purge manually. For this reason equation (3.33) was added:

*purge purge

cond condV K V= ⋅ (3.33) The process modeled did not have a vapor product, so: 0purge

condV = (3.34) To examine the pressure difference between the top of the column and the condenser and for numerical stability, the following variable was added: 1cond conddP P P= − (3.35) If this pressure difference ever becomes zero, especially if the derivative at that point also becomes zero, the simulation will crash. Heat transfer The heat transfer equation is identical to equation (3.18), except that it was multiplied by Ksd. This was added for shutdown. During shutdown the holdup of the trays decreases. The heat-loss to the surroundings causes the trays to cool down. This cooling is done a lot faster than in the condenser, which is not emptied and retains a large mass holdup. As it was desirable to generate shutdown values to use during startup, the condenser also needed to be at the temperature of the surroundings. Because there is no reflux to the column and no vapor flowing to the condenser in shutdown, there is no interaction between the condenser and the rest of the column. To cause the temperature to reach the temperature of the surroundings faster this factor was added. In shutdown it is given an arbitrary value of 10, while in startup and in steady-state it is given a value of 1. 3.3.3 Reboiler model The reboiler was designed to be a horizontal thermosyphon reboiler. For modeling purposes it was assumed to be a kettle reboiler, integrated in the bottom of the column. The bottom of the column was assumed to be cylindrical to use the same geometry as on the trays. In the reboiler model the sections of definitions, heat transfer, geometry and equilibrium are identical to those of the tray model, except that they use variables of the reboiler, in stead of variables of the tray. These will not be discussed. Index 1 still denotes the liquid phase and index 2 the vapor phase, but for the entering streams 1 denotes the liquid from the downcomer and 2 denotes the liquid dumping through the holes.


29

Balances A startup-line has been added to allow liquid from the reboiler to be pumped into the condenser. As mentioned above, it will not be used. The component molar balance, for all components except N2, is:

,

25 ,25 , ,

, ,

( ) Holes Holesi reb p p p p

i reb i reb su line i rebp Weir p DC

product productreb i reb reb i reb

d ML x V y L x

dt

L x V y

−= =

= ⋅ − ⋅ − ⋅

− ⋅ − ⋅

∑ ∑ (3.36)

The component balance for N2 is:

2

2 2 2

,, , ,

( ) HolesN reb p p product

N in reb N reb reb N rebp DC

d MV V y V y

dt =

= − ⋅ − ⋅∑ (3.37)

The energy balance is:

2 225 25 , ,( ) Holes Holes

p p p p Lreb rebN in N in reb reb su line reb

p Weir p DC

product L product Vreb reb reb reb reb loss

d E M L H V H V H L Hdt

L H V H Q Q

−= =

⋅= ⋅ + ⋅ − ⋅ − ⋅

− ⋅ − ⋅ + +

∑ ∑ (3.38)

Hydrodynamics Two controllers are added for controlling the level (P1) and the reboiler duty (P2) in the reboiler. The in-signals are defined by: ,in L controlSignal level− = (3.39) and: , 1 23 23in Q control T reb X MP L T traySignal K T K X K level K T− −= ⋅ + ⋅ + ⋅ + ⋅ (3.40) The constants are either 0 or 1, depending on which variable is used as in-signal for control. They have been added to switch between in-signals manually. The level control will be coupled to the product removal from the reboiler. Initially however there is no product removal. The feed of the column may be light product and then it is desirable to evaporate the entire feed, otherwise the reboiler will overflow. For this reason the heat added may be coupled to the level in the reboiler. The heat added to the reboiler will be added to achieve a good separation and one would want to control the fraction of, for example, MP-1 or MP-2 in the reboiler. During startup these vary strongly and are not very good candidates for determining the heat input. Further, if one were controlling the fraction of MP-2 one would need to add heat to increase the fraction by decreasing the fraction of the lighter components. However, if most of the light components have been evaporated from the reboiler, MP-2 would be evaporated if more heat were added. To increase the fraction of MP-2 less heat would be needed. It can be seen that controlling the fractions in the reboiler is not the best solution for quality control. Controlling compositions could also be done by controlling the temperature in the reboiler, or by controlling the temperature on another tray, because a change in composition on a tray will lead to a change in temperature. In industrial practice compositions can not be measured directly at sufficiently small time intervals. Using the relationship between composition and temperature means one could measure the temperature to achieve the correct compositions. This can be done on-line.


30

Unfortunately it was found that the temperature in the reboiler did not vary sufficiently with different compositions and therefore it was not suitable as controller-input. Using the steady state temperature profiles it was decided to use the temperature on tray 23 to control the the reboiler duty, as the temperature change between trays 22, 23 and 24 was largest, corresponding to large changes in composition. This can be seen in the figure below.

Figure 3.5. Temperature difference between trays. The equation for the in-signal of the heat-input has to be situated in a higher level model, because the tray model is not a sub-model to the reboiler model. The rate of heat added will be given by:

0.42

min(1, max(0, )) min(1.25 , max(0, ))0.18reb

reb outlevelQ bias Signal−

= ⋅ ⋅ (3.41)

The reboiler is modeled as a kettle reboiler, where the heat is added directly to the base of the column. In practice the heating would take place by, for example, steam condensing in tubes, where the steam has a constant temperature. These tubes would need to be submerged for the heat to be added to the liquid. In steady-state the level in the reboiler is 0.88 m. It has been decided that 0.60 m is needed to submerge the tubes of the kettle and that if the level drops to 0.42 m no more heat can be added to the liquid. This explains the first min/max-section. The reboiler was further assumed to provide a maximum heating 25% larger than that for which it was designed (the controller bias). Also, it was assumed not to be able to give any cooling. For the design no vapor product is withdrawn: 0product

rebV = (3.42) The startup-line will be connected to a pump, so the flow can be controlled. For ease of notation and insight into the model, the startup-line has been named separately. For shutdown it was seen that the pressure dropped below atmospheric pressure and kept dropping. This is caused by the fact that the saturated vapor pressure of the lightest components are below atmospheric for the temperature of the surroundings. This would eventually cause the column to collapse. To save the column from this implosion nitrogen will be added during shutdown:

Temperature difference on trays

0

5

10

15

20

25

0 5 10 15 20 25 30

Tray (-)

Tem

pera

ture

diff

eren

ce

with

pre

viou

s tra

y (K

)


31

2 2

6 5max(0,3.56 10 (10 ))N N rebV K P−= ⋅ ⋅ ⋅ − (3.43) The factor 3.56*10-6 was added to cause the maximum in-flow of nitrogen to be 0.1 kmol/s with a 0.3 bar pressure difference. 3.3.4 Column model The column model combines the tray, condenser and reboiler models by connecting the streams. It was decided to use one stream-type, including the total molar flowrate, the molar fractions, the pressure, the temperature and the enthalpy of the stream. This means the temperature, or the enthalpy, and one molar fraction are extra, as they can be calculated from the other variables. Further, due to this choice of stream-type, not all streams can be connected. The dumping streams can not be completely connected, as they would give extra equations (the connections) without extra variables. This is due to the fact that the stream of the liquid flow over the weir already passes on the pressure and temperature. Within the connections with the condenser it can be seen that tray 1 does not have any liquid dumping into it. It also has no vapor escaping through the downcomer, as the top tray does not have a downcomer. Within the connections with the reboiler only the effective level needs to be redefined. Here it is defined as the level of liquid in the reboiler. For analysis of the behavior of the column it is desirable to be able to get an overview of various variables on all trays together. For this reason various profile-variables have been added, which have been defined in the profiles-section. The condenser and reboiler sections were not incorporated into these profiles. The equation for controlling the heat input to the reboiler was discussed in the reboiler section. 3.4 Reactor The other major piece of equipment is the reactor. The reactor consists of two parts. Both are basically shell-and-tube heat exchangers, in which the reaction takes place in the tubes. In the first part the reactants are heated in the shell, mixed with catalyst and allowed to react in the tube. In the second part the reaction continues in the tubes until all PO is converted. “All” in this context is a conversion above 0.999, as it is undesirable to condense PO in the condenser. The reactor differs significantly from the one developed in the conceptual process design. It was found that the adiabatic temperature rise with complete conversion of PO at (an estimated) 130°C was 269°C. The temperature rise in the shell of the conceptual process design was only 73°C. This can never take up the entire heat of reaction, especially if the tube-side temperature remains practically constant. The reactor from the conceptual process design, if modeled in one pass, would be 60 m long. If an estimated 73/269 part of the adiabatic temperature rise is cooled in the first part of the reactor it would be 16.3 m long. Therefore the first part was chosen to be this long. In the second part the other ~73% of the adiabatic temperature rise would need to be removed. To simplify programming (i.e. to not need to program the physical properties of a cooling medium) it was desirable to have a constant temperature on the shell side of the second part of the reactor. Further, it was estimated that if a lot of heat (about 5 MW) needs to be removed, at temperatures above 130°C, it would be advantageous to produce LP-steam. Here LP-steam is defined as being at 3 bar and 133.5°C. Therefore the second part of the reactor will produce LP-steam. This part will only be modeled as a tube, a wall and a constant shell temperature. These models are given the number 2. Of course the steam production could also have been the first section of the reactor. The stream entering the reactor, however, is at 127°C. This would mean that part of the shell


32

would be used for heating the tubes and part for cooling. The reason the steam production was added was to provide cooling, not heating. Therefore this option was not chosen. Due to the size of the reactor it will be placed horizontally. It will be modeled as one tube and one shell pass, as not to need to model the exact layout of the tubes. The reactor model has been sub-divided into: • shell, • wall, and • tube. The shell and tube-models have been sub-divided into: • boundary values, • balances, • hydrodynamics and definitions, • geometry, • physical properties, and • continuity equations. The wall-model only consists of an energy balance and a few other variables. Most of the variables used are distributed over the length of the reactor. For this reason the flow direction in the tube has been defined as positive from 0 to the length of the reactor (figure 2.4). The flow in the shell will be in the negative direction. The extra assumptions that will be made next to those from the literature are: • the dirt coefficients will be assumed constant, • the time scale of momentum transport is sufficiently small and the momentum balance is

assumed to not have any hold-up so that it is in a pseudo-steady-state, • the reactor will be placed horizontally, and • the reactor will be modeled as only one tube and shell pass. The complete derivations of the equations and the reasons for and influence of various assumptions can be seen in appendix B. 3.4.1 Shell model The shell is modeled as one large tube with 78 smaller tubes inside it. It has been sized by requiring the superficial velocity to be around 0.1 m/s, as this will cause the flow to be turbulent. With a volumetric flowrate of 8.69*10-3 m3/s flowing through the shell the effective area will be 8.69*10-2 m2 and the shell diameter can be found by:

2 21 ( )4s s tubes oA d N dπ= ⋅ ⋅ − ⋅ (3.44)

This means the shell diameter is 0.556 m. With the method for determining the shell diameter given in the literature (Sinnott, 1996) for one pass and a square pitch, a diameter of 0.738 m can be found. This could mean the clearance between the bundle of tubes and the shell will be too small. For modeling purposes this will not give any difficulties as turbulent flow will be assumed. Shell2 would be identical to shell one, except that due to time restrictions it was undesirable to model another set of physical properties. Therefore there is no shell2 model.


33

Boundary For the balances boundary conditions are required. These are the temperature, pressure and concentrations. All balances in the shell are valid from 0 to the length of the reactor, not including the final point. At this point the temperature, concentrations and pressure are known, as this is the point where the feed is added. The variables from the feed can be used as boundary values. Initially separate variables were added to be able to specify constant values for the feed. These could be removed. Balances As the energy is defined per unit volume the energy balance (equation (2.26)) becomes:

,, 2 2

4( )

( )( )z c cc i

tubes s i w cs tubes o

dD d

v HH N U T Tt z N− ⋅

∂ ⋅∂ ⋅= + ⋅ ⋅ ⋅ −

∂ ∂ (3.45)

As stated earlier energy and enthalpy will be used interchangeably, as changes in energy due to varying temperatures are significantly larger than changes in magnetic, electrical, kinetic, potential and “other” energy (see appendix B). Heat loss to the surroundings has been neglected, though this could be a significant amount. The molar component balance has been given by equation (2.25). The momentum balance given by equation (2.28) needs to be modified for the increased surface area of the tubes and the direction of the flow:

2( ),0 ,

v Pc c z c N gtubes w c c zz z

ρτ ρ

∂ ⋅ ∂= − − − ⋅ − + ⋅ −

∂ ∂ (3.46)

It must be remembered that the flow is in the negative direction and τw will be in the opposite direction to the flow. The gravitational acceleration in the axial direction will be zero, as the reactor is placed horizontally (figure 2.4). Hydrodynamics and definitions Because concentrations are used in the molar balances and fractions are required for the physical properties, concentrations need to be converted by:

1

n

i i ii

C x C=

= ⋅∑ (3.47)

The shell side heat transfer coefficient, the liquid film heat transfer coefficient, the Reynolds and Prandtl numbers, the shear force at the wall and the friction factor can be given by equations (2.31), (2.32), (2.33), (2.34), (2.37), and (2.38). Having assumed turbulent flow there is no difference between the viscosity at the wall and the viscosity in the rest of the liquid at a certain point and this part of equation (2.32) becomes unity. As Reynolds is a positive number the absolute superficial velocity must be taken, because the flow is contrary to the axial direction, and therefore negative. Geometry The hydraulic diameter of a shell encompassing N tubes has been given by equation (2.36). Continuity of mass For the momentum balance the velocity needs to be known. If the mass flowrate is assumed to be constant the velocity can be calculated from the mass flowrate entering the shell. Therefore, in the first equation in this section the mass flowrate is calculated from the molar flowrate entering the shell. The second equation is used to calculate the velocity at every


34

point in the reactor. The third equation is used to calculate the outgoing molar flowrate from the mass flowrate and the velocity. 3.4.2 Wall model The wall only consists of an energy balance, a couple of equations used as definitions and equations to view certain properties such as temperature difference over the wall and the temperature rise. The wall2-model is identical to wall-model, except that a constant shell-side temperature and heat transfer coefficient have been used. Balances Under the assumption that the density, heat capacity and conductivity of the metal wall are constant the energy balance becomes a temperature balance. This is equation (2.27). The wall was assumed to be iron and the constant physical properties of the wall were taken from Jansen and Warmoeskerken (1991). Other equations In the hierarchy of models several variables are shared between different models. In this case the temperatures of the wall and the cooling medium and the shell-side heat transfer coefficient are needed in both the wall and shell models. To check that the equipment is not heating up faster than 50°C/h (Luteijn, 2001) the temperature rise over time has been added as variable. 3.4.3 Tube model The tube is the highest model of the shell, wall and tube models. The tube2 model is identical to the tube model, except that its sub-model is wall2. Boundary As in the shell, boundary conditions are required for the tube-model as well. For the tube-model all balances are valid from 0 to the length of the reactor, not including the initial point, as the feed to the tubes is added here. Once again separate variables were added initially to be able to specify values for the feed. These too could be removed. Balances The energy balance, molar component balance and momentum balance are used exactly as described in the theory chapter. The equations are (2.26), (2.24) and (2.28) respectively. As in the shell, the gravitational acceleration in the axial direction will be zero, as the reactor is placed horizontally. Hydrodynamics and definitions The equations in the hydrodynamics section only differ in two ways from the shell-model: in the absence of an absolute velocity and a different equation for the heat transfer coefficient. No absolute velocity is used, as the velocity should always be positive. The equation for the heat transfer coefficient can be seen in equation (2.30), with the same assumptions as for the shell-model. Three equations have been added to share variables with the wall-model. This has been done, because the tube-model is a higher level model. The variables exchanged are the temperatures of the reactor and the wall and the heat transfer coefficient on the tube side. Geometry The hydraulic diameter of a tube is identical to the inner diameter of the tube. It has been given by equation (2.35).


35

Kinetics The reaction kinetics will be discussed in a subsequent section. Here it will be stated that a selectivity will be used for the formation of MP-1 and MP-2. This selectivity will be constant and has been taken up in the reaction coefficients. An equation has been added to calculate the conversion of PO. This is done by:

, ,5

,max(10 , )in PO in out PO out

POin PO in

F x F xF x

ξ −

⋅ − ⋅=

⋅ (3.48)

The max-statement has been added, as it is possible that xPO,in is zero. In dynamic operation this equation will not give correct results. This can be seen by the fact that the outflow of PO will still be zero when PO is first added to the column. This would give a conversion of 1. In steady-state it will function properly. Continuity of mass As has been done in the shell-model, three equations have been added to the tube-model for calculating the mass flowrate, the velocity and the molar flowrate exiting the reactor. 3.4.4 Reactor model The reactor model combines the tube, wall and shell models, with a mixer for catalyst addition and 4 conversion models for entering and exiting streams, as can be seen in figure 3.2. It also sets the flow-control for catalyst addition. Further the temperature-profiles over the two tubes and shells have been given. To connect distributed variables from more than one model with variables in one large array, auxiliary variables need to be introduced. Distributed variables can only be connected to arrayed variables of equal length. The temperature-change in the two wall models per unit of time has also been given. A profile of the steady-state conversion has also been added. 3.5 Reaction kinetics For catalysis there are several possible choices: • thermal, • acidic, • base, or • zeolite catalysis. Thermal catalysis is undesirable due to the high temperatures that are required, which may cause decomposition of products. Acidic catalysis is not selective, producing equal amounts of MP-1 and MP-2. Zeolites have a high selectivity, but a low conversion (40%) and are expensive. Base catalysis performs well. The reaction kinetics for the reaction of PO with methanol to MP-1 and MP-2 and the reaction of MP-1 and MP-2 with PO to MDP in a batch reactor, with a tertiary amine as catalyst, as given by Tao et al. (1997), are:

31.24

* *1 0 1 1130.3

EaR T R Tr k e C e C− −

⋅ ⋅= ⋅ ⋅ = ⋅ ⋅ (3.49)

36.55

* * * *2 0 1 3 4 1 3 44.05

EaR T R Tr k e C C e C C− −

⋅ ⋅+ += ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ (3.50)

Side-reactions, such as the reaction of PO with itself can also occur, but have been neglected in the expressions for the reaction kinetics.


36

The tertiary amine catalyzing the reaction remains unspecified. The results are verified by comparison to the acidic catalyst BF3. The reaction kinetics were based on experimental data and fit with a least-squares fit. For modeling purposes the reaction rate must be in the units kmol/(m3.s). This means the right hand side must be multiplied by mass of the catalyst and converted from minutes to seconds. This gives the following equations for the reaction rate:

31.24

1, 11130.360

R Tnew catr e C M

−⋅= ⋅ ⋅ ⋅ ⋅ (3.51)

36.55

2, 1 3 414.0560

R Tnew catr e C C M

−⋅

+= ⋅ ⋅ ⋅ ⋅ ⋅ (3.52)

Attention must be paid to the use of the correct units, as the pre-exponential factors have been given based on the number of grams of catalyst and based on a reaction rate per minute. The catalyst concentration can be given by:

,,6 1000

catcat batch

wt batch

MC

M V=

⋅ ⋅ (3.53)

The factor 1000 is introduced as the molecular weight will be given in kg/kmol and the mass is in grams. The volume of the reaction mixture in the literature reference is 4.95*10-4 m3. To make the reaction rate a function of the concentration it can be divided by the concentration of the catalyst in the batch reactor and multiplied by the concentration of the catalyst in the plug-flow reactor. This means that the reaction rate needs to be corrected by:

6,6 6

,

1000used new new wt batchcat batch

Cr r r M V C

C= ⋅ = ⋅ ⋅ ⋅ ⋅ (3.54)

The final reaction rates, as used in the design, are:

31.24

1, 1 6 ,61000130.3

60R T

used wt batchr e C C M V−

⋅= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (3.55)

36.55

2, 1 3 6 ,610004.05

60R T

used wt batchr e C C C M V−

⋅= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (3.56)

36.55

3, 1 4 6 ,610004.05

60R T

used wt batchr e C C C M V−

⋅= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (3.57)

In the article the concentrations of MP-1 and MP-2 are lumped. Here they have been taken separately. For the formation of MP-1 and MP-2 a selectivity factor will be used. The reaction conditions of the article are in a temperature range of 60-120°C and pressures ≤ 3 bar. Also, the reaction rate is assumed independent of the concentration of methanol as methanol is in excess (MeOH : PO = 5:1).


37

It will be assumed that: • There are no reactions besides the reactions of MeOH and PO to MP-1 and MP-2 and

the reactions of MP-1 and MP-2 with PO to MDP. • The amount of MP-2 and MP-1 formed will be calculated by a (constant) selectivity times

the amount of MeOH and PO that reacts. • Catalyst will be removed after the reactor. • The kinetics will still be valid up to temperatures of 190°C and up to pressures of 28 bar,

as no other kinetics could be found. • Though the excess in the article is specified at MeOH : PO = 5 : 1, the amounts will be

based on the conceptual process design. Here the amounts are about 3.36 : 1 mass based, or 6.09 : 1 mole based. Due to an error 3.95 : 1 mole based was used in stead and it will be assumed this is still a sufficient excess of MeOH that the reaction rate is independent of the concentration of MeOH.

Finally, a tertiary amine is suggested as catalyst, but not further specified. It will be assumed that this is N(OCH3)3. According to a patent by Schnurpfeil et al. (1997) the selectivity is not greatly influenced by the type of base catalyst. The selectivity is slightly above 90%. Therefore a selectivity of 90% MP-2 and 10% MP-1 will be assumed. 3.6 Other models 3.6.1 PIC As controller proportional-integral-controllers (PI-controllers) will be used. These can be defined by two equations: int inError Setpo Signal= − (3.58)

0( )

t

tout gain

Error dtSignal bias K Error

τ

⋅

= + ⋅ +∫

(3.59)

The integral action is especially useful in steady-state as a fine-tuning of the controller. In

startup situations integral control gain (1τ

) is usually set at about zero (Ratto and Paladino,

2001). Five controllers are used to control the reboiler level and duty, the condenser level and duty and the rate of catalyst addition. The steady-state controller parameters, as used in the model, are: Table 3.1. Controller parameters. Controller Setpoint bias Kgain τ Condenser level 1.1 0.0366 -1 15 Condenser heat removal

1.0 -7130 105 15

Reboiler level 0.88 0.0486 -1 105 Reboiler heat addition

362 8192 1000 105

Catalyst addition 420 2.5*10-3 2.5*10-4 1000 For the column models, the biases were determined from a steady-state run of the column with the feed from the conceptual process design. The gains on the level controls were determined by arbitrarily specifying flow-changes of 0.15 kmol/s due to level-differences of 0.15 meters. For the duty-controllers the gains were determined by allowing a change of 1 MW due to a pressure difference of 1000 Pa, or a temperature difference of 1°C. These are thought to be very strong controllers.


38

An unfortunate mistake which was made was forgetting to change the steady-state τ’s for the condenser. These should have been 105 like those in the reboiler during startup to reduce the overshoot of the out-signal. For the level controls this mistake does not give any problems. The pressure control caused the pressure to temporarily drop to 0.5 bar when the setpoint was changed from 4.6 to 1.0 bar, due to excessive cooling. This causes the need in the reboiler to generate more heat to keep the correct temperature, which in turn leads to fluctuations in the column. These could have been avoided. In any case this change in setpoint was too extreme and should have been ramped. For the catalyst addition to the reactor the parameters were determined by trial and error, as there was only a ruff estimate of how much catalyst would be needed for the “new” kinetics, as the physical properties of the catalyst were assumed to be those of MP-1. The setpoint of 420 K (at about 1/3 of the first part of the reactor) was chosen to keep the maximum temperature under the critical temperature of PO (482 K), yet give a high enough maximum temperature to have a high conversion. Once this was implemented the reactor never overheated. 3.6.2 XC/CX-converters The distillation column uses streams that contain the molar flowrate, the molar fractions, the pressure, the temperature and the enthalpy. For the reactor concentrations will be needed. Two equations can be used for calculating fractions from concentrations and concentrations from fractions:

1

n

i i ii

C x C=

= ⋅∑ (3.60)

and:

1 ,

ii n

i

i mol i

xC

xρ=

=∑

(3.61)

Equation (3.60) (also (3.47)) can only be used to calculate fractions from concentrations and equation (3.61) can only be used to calculate concentrations from fractions. Both equations can not be used in the other direction, because the variable in question would be divided by itself. This means the absolute value can not be determined, only a relative value. This is why there are two separate models for conversion between concentrations and fractions. The models XCins and XCint use equation (3.61), while the models CXouts and CXoutt use equation (3.60). The models using (3.61) also need to incorporate a section to determine the pure component molar densities. 3.6.3 Mixer The mixer-model is used when two liquid streams are combined. It uses simple mass and energy balances without accumulation: , ,1 , ,1 , ,2 , ,2 ,i in i in i in i in out i outF z F z F x⋅ + ⋅ = ⋅ (3.62) and: , ,1 ,1 , ,2 ,2i in in i in in out outF H F H Q F H⋅ + ⋅ + = ⋅ (3.63) In stead of the sum of the fractions equaling 1 the total mass balance has been added, because it was possible that one or both streams would be zero, which would make calculation of the resulting molar fractions impossible and irrelevant. For the energy balance the calculation of the enthalpies as function of the temperature has been added, to calculate the temperature of the out-going stream. The extra heat input in the


39

heat balance has been added to be able to specify a temperature and use the mixer as a heat exchanger. In the design no extra heat is added or removed in the mixers. 3.6.4 Connection breakers Connection breakers are used to manually specify one or more variables in a stream. A break in the pressure, for example, can be used to model an ideal, infinitely fast pump, which brings the liquid stream to a higher pressure. Two connection breaker models will be used: P_break and Con_break_liq. The P_break model is used to model an ideal pump and specify a new output pressure. It will also be used to remove part of the recycle stream during startup. In the model of the process it is called the break_recycle-model. The Con_break_liq model is used to remove catalyst, as the catalyst used is a salt and modeling the properties of a salt was not desirable. As the catalyst would end up in the bottom of the distillation column it was decided to remove it before the distillation column and avoid any difficulties due to catalyst interactions. Also part of the feed stream could be removed and the temperature of liquid leaving the connection breaker could be specified. For this reason it consists of simple mass and heat balances without accumulation, such as equations (3.62) and (3.63), and the equations for calculating the enthalpy of the mixture. As extra variables the catalyst, which is to be removed before the distillation column, has been added. In the model of the process it is called the breakT7feed-model. 3.7 The entire process The highest level model is the process model. It combines the reactor and column models with two feed-mixer models and the two connection breaker models. The process model consists of four subsections: • connections, • economics, • endpoint definition, and • in/out. Connections In the connections-subsection all streams are coupled and the feed-streams for the distillation column have been defined. Two equations besides the feed-streams are not simply connections of other streams. These define the amount of MeOH fed to the process and the amount removed in the break in the recycle. For MeOH removal from the recycle stream the equation is: max(0, 0.175)product

remove cond POL L F= + − (3.64) For MeOH addition via the feed the equation is: ,max(0,0.175 )MeOH recycle not removed POF L F= − − (3.65) Initially the reactor, condenser and part of the reboiler will be filled with MeOH. Though this is converted in steady-state it is always in excess. There will, however, be a physical maximum flow, which can be allowed to flow through the recycle loop. Also, it is undesirable to have the MeOH accumulate in the distillation column. This will cause all the MeOH to end up in the reboiler during startup and an overflow in the reboiler will cause the model to crash. To regulate the flowrate of MeOH it has been decided to allow the flowrate to the reactor to never be larger than the steady-state molar flowrate (0.175 kmol/s). If there is an excess of MeOH in the recycle stream it will be removed. If there is a shortage it will be added from the process feed. This means the initial mass-flowrate will be lower, as MeOH has a lower molecular weight than PO.


40

Unfortunately, as mentioned above, a ratio of MeOH : PO = 3.95 : 1 was used in stead of 6.09 : 1. This means the steady-state molar flowrate to the reactor was underestimated. The flowrate of 0.175 kmol/s should be a factor 6.09/3.95 higher. This would be 0.270 kmol/s, which agrees more closely with the conceptual process design (0.251 kmol/s). Due to this error the recycle flowrate will be smaller than in the design. For startup this is actually desirable, as smaller flowrates are more easily evaporated. For steady-state flowrates it is thought that the excess of MeOH is still sufficient as not to have any negative effect on the reaction kinetics. Economics The prices of feed and product, as used in the conceptual process design, can be seen in the following table. Table 3.2. Prices of feed and product.

Price Component (kfl/kton) (fl/kmol)

MeOH 342 11.0PO 1938 112.6Catalyst 950 101.8MP-2 1824 164.4MDP 1824 270.3

Though a different catalyst will be used, the same price will be used. The reboiler is heated with MP-steam. The MP-steam price can be calculated as shown in the table below, assuming the steam is not sub-cooled. Table 3.3. Calculation of MP-steam price.

Heat of vaporization

Price

(kJ/kg)** (kfl/kt) (fl/kg) (fl/kJ) MP-steam* 2013.595 27 2.7*10-2 1.341*10-5

* MP-steam is defined as being at 10 bar, 180°C (Grievink et al., 1998) ** from Smith and van Ness (1987) In comparison, the Webci (1999) gives the price as 28 kfl/kt. The cumulative costs and revenue per component can be given by: , ,PO cumulative PO cumulative PO POCosts F z price= ⋅ ⋅ (3.66) , ,MeOH cumulative MeOH cumulative MeOH MeOHCosts F z price= ⋅ ⋅ (3.67) , ,cat cumulative cat cumulative cat catCosts F z price= ⋅ ⋅ (3.68) , ,heat reb cumulative reb cumulative MP steamCosts Q price −= ⋅ (3.69)

2, 2,

, 2, 2

Re max(0, ( 0.88))MP cumulative MP reb

productreb cumulative MP reb MP

venue sign x

L x price− −

− −

= −

⋅ ⋅ ⋅ (3.70)

, , ,Re product

MDP cumulative reb cumulative MDP reb MDPvenue L x price= ⋅ ⋅ (3.71)


41

For a fair comparison MP-2 is assumed not to generate any revenue if the fraction of MP-2 in the reboiler is below 0.88, while the steady-state fraction is around 0.885. This underestimates the revenue due to MP-2, because in the complete process the reboiler product is fed to another column, which will extract almost all MP-2. The total of these costs and revenue will be the total cash flow. The costs of the condenser have been neglected, as it is an air cooler, which requires about 75 kW of electricity. With an energy price Hfl. 0.22/kWh this means an annual cost of about 0.14 million. Compared to annual costs of, for example, MeOH (11 million) or PO (121 million) this can be neglected. The costs of initially filling the reactor (and possibly any pipes) with MeOH were also neglected, though they run over Hfl. 6000. This was done as the main reason for adding economics was to compare process alternatives. All these alternatives would include the reactor being filled with MeOH initially. Endpoint definition For startup a point needs to be defined when the process is running in steady-state. It has been chosen to make this dependent on the holdup of MP-2 in the reboiler over time. The same equation is used as the component molar balance for MP-2 in the reboiler (equation (3.36)). In/Out At the end of a startup it will be interesting to note the cumulative in and out-flows. Variables have been added to show: • the amount of feed added, • the amount of catalyst added, • the amount of MeOH removed, • the volume of MeOH removed, • the amount of material purged, • the amount of N2 purged, • the amount of MeOH purged, • the amount of offspec product, • the volume of offspec product, and • the amount of onspec product produced. Onspec product has been defined as liquid product from the reboiler in which the molar fraction of MP-2 is above 0.88. Another check of the steady-state assumption is the total mass balance over the process. This has also been added. 3.8 Equipment sizing and parameter determination The equipment sizes used have, as much as possible, been taken from the conceptual process design mentioned above. Various pieces of necessary equipment were not included or sized in the design and needed to be designed for the model. This will be discussed below. The sizes of the equipment can be seen in the tables of appendix D. Distillation column (table D.1) For the number of trays the number of theoretical trays has been taken, as every tray is in complete equilibrium. As tray area the active tray area of the sieve tray has been taken. This means it has been assumed that no liquid occupies the space above the downcomer. The tray volume was calculated as the total volume between trays, including the downcomer. Using the weir length, the fraction of the total tray surface area that is part of the downcomer has been determined. This is about 27% and the surface area of a tray is 73% of the total surface area of a tray. In an older model the downcomer had been added. This model did not work and the downcomer was removed in an attempt to locate the problem. In this process increasing the surface area of the tray was forgotten, which means that the heat-loss per tray is underestimated by 37%. Heat loss is influenced by several factors, such as the temperature


42

difference between the column and the surroundings, the heat transfer coefficient and the surface area for heat transfer (equation (3.18)). The heat transfer coefficient is only an estimate and the outside temperature is chosen constant and independent of, for example, wind. The error made in underestimating the surface area of the tray will therefore lie within the accuracy of these assumptions and will not be of great influence to the process as modeled. The hole-size has been taken from the conceptual process design and is larger than 3/16 inch, so surface tension contributions are negligible (Prince and Chan, 1965). β and α, as used in equations (3.8) and (3.16), have been explained around these equations. Condenser (table D.2) Though the condenser was specified as an air-cooled cooling tower, the liquid collection drum was not specified. Based on a liquid hold-up of 5 minutes and 65% of the volume being liquid volume (Grievink et al. 1998) the total volume could be calculated. This was rounded up. As a length/diameter ratio of 1 is most economical (Webci, 1999), the height, diameter and surface area can be calculated. The cross-sectional area of the tube connecting tray 1 to the condenser was assumed to be about 10% of the tray area. α has been calculated using equation (3.30). For purge the “outside” pressure was specified as being 1 bar. Reboiler (table D.3) The volume of the reboiler was not specified in the design. Using the same method as for the condenser a total volume could be calculated. Given the column diameter this volume would result in a height of 0.30 m. This was thought to be too small and the reboiler would frequently overflow. The height of the reboiler was arbitrarily set to 1.5 m, giving a hold-up time of 38 minutes. With this level the apron height was set at 100 mm to eliminate the possibility of vapor flow through the downcomer. In industrial practice a seal-pan (Law, 2001 and Kister, 1990) would be used to achieve sealing without running the risk of liquid mal-distribution in the reboiler. For modeling purposes this is irrelevant as the liquid is assumed to be well mixed. The surface area of the reboiler was incorrectly defined as surface area of the sides + twice the surface area of the bottom. This causes an extra heat loss of approximately 69 kW in steady-state. It can be seen that this error, as well as the error due to the use of the incorrect surface area of the trays are smaller than 1% of the heat added in the reboiler or removed in the condenser. Therefore it is thought that the error introduced is negligible. Reactor (table D.4) The reactor from the conceptual process design has 466 tubes and 6 tube passes (78 tubes per pass). For the model this will be reduced to 78 tubes and 1 tube pass. The diameter of the shell and the lengths of the two reactors have been explained above. The dirt coefficients for organic liquids have been taken from Sinnott (1996) and the wall is assumed to be iron. Other parameters (table D.5) Using Sinnott (1996), a heat transfer coefficient between organics and air can be estimated. This was found to be 0.1 kW/m2.K. For boiling water the heat transfer coefficient can be estimated to be 1.8 kW/m2.K. The temperature of outside air was assumed to be 18°C and the temperature of the boiling feed water 133.5°C. As discussed above, the pre-exponential factors and activation energies were taken from Tao et al. (1997) and the selectivity of 90% MP-2 formed / PO reacted to MP-1 and MP-2 was taken from Schnurpfeil et al. (1997).


43

Controller parameters (table D.6) These have been explained above and were only added in the appendix to have all the parameters and set variables together. 3.9 gPROMS settings The simulations have been performed in gPROMS 1.8.4 for Linux. Besides choices in model-structure, choices in solver-options also need to be defined. These are grouped in the solution parameters. The following solution parameters were used: Table 3.4. Settings in gPROMS. Setting Value Absolute accuracy 10-7

Effective zero 10-6

Init. accuracy 10-5

Max. init. iterations 106

Max. iter. no improve 104

N. step reductions 105

LA Solver MA28 Though the accuracy may seem small it would have been preferable to have it be several orders of magnitude smaller. It was chosen a factor 10 smaller than the effective zero. The default value is 10-5. The effective zero was chosen as such, because the pressure differences seemed to cause problems when they were near zero. Estimating that a pressure difference of 0.1 Pa could be considered negligible the choice was made to have an effective zero of 10-6. All lower bounds of variables that were not allowed to be negative were put on the negative of the effective zero, as gPROMS may calculate a variable as -10-23 in stead of zero in which case it is undesirable for gPROMS to crash. The initialization accuracy was chosen a factor 10 higher than the effective zero. Once again this was determined by a reinitialization point which involved the pressure. This was a 4.6 bar setpoint, for which it was not thought to be very important if the initialization started at 1 Pa more or less. The number of maximum initial iterations, the maximum number of iterations without improvement and the number of step reductions were chosen extra high (factor 100 higher than standard). This was done with the idea that the stepsize may need to be reduced significantly to find a solution. Once the model was running these settings were irrelevant. The linear algebra solver MA28 was chosen, as it was the only one that worked. This may be due to the amount of elements that are zero, or change from zero to a value. An interesting point is that even when using MA28 the model in its most complete form would only run on gPROMS 1.8.4 for Linux and not on gPROMS 1.8.4 for Windows. Settings such as the reporting interval were varied during the entire process, depending on the rate of change and the need to see if the process was still running. Another important setting is the discretization method and number of discretization points chosen. There are four discretization methods: backward, forward and central finite difference methods and the method of orthogonal collocation. All these methods have various orders that can be used. The backward and forward methods can be used with first and second orders, the central method with second, fourth and sixth orders and the orthogonal collocation method with second, third and fourth orders. Using a simple tube-model, without reaction and only adding a PO/MeOH mixture to a tube filled with MeOH, all four were tried. Only the first order backward and forward methods and the second order central methods gave any results. The rest crashed due to bound violations. The second order central method showed oscillations, while the forward and backward methods showed the expected behavior. These oscillations can be expected due to the second order used, as this means that the path between the points can be approximated by a second order curve. This may show maxima and minima, which may exceed the bounds. It


44

must also be said that the choice of forward or backward methods depends on the direction of the flow. A method opposite to the direction of the flow must be chosen, otherwise no change will take place in any variables. To estimate the number of discretization points necessary part of a reactor startup was simulated in a tube. The wall temperature and inlet conditions were chosen to be constant. The variables chosen to examine the influence of the number of discretization points were two temperatures, one at 9/10 and one at 7/10 of the length of the first tube. These temperatures were determined at 50, 100 and 150 seconds into the run. Both temperatures are in the order of 45-55°C. The absolute deviations from 200 points as function of the number of deviation points can be seen in the figures below.

Figure 3.6. and 3.7. Influence of the number of discretization points (9/10 and 7/10). From these two figures it can be seen that at least more than 100 discretization points will be required. But doubling the number of discretization points will lead to doubling or even quadrupling the calculation time, due to the fact that many more equations need to be solved. For example, running the entire model with 30 discretization points in all the models takes 2.3 hours of simulation time. Running the entire model with 60 discretization points in all the models takes 6.0 hours. For speed 30 discretization points will be used.

Temperature at 9/10 of reactor length at various times

-5-4-3-2-1012

0 100 200 300

Number of discretization points (-)

Devi

atio

n in

tem

pera

ture

(K)

t=50 st=100 st=150 s

Temperature at 7/10 of reactor length at various times

-1-0.5

00.5

11.5

22.5

3

0 100 200 300

Number of discretization points (-)

Devi

atio

n in

tem

pera

ture

(K)

t=50 st=100 st=150 s

Modeling results

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4 Modeling results The model developed has been used to simulate the steady-state of the process, as well as shutdown and startup behavior. In this chapter the results obtained for the steady-state, shutdown and startup will be presented, as well as for a simplified optimization of the startup-procedure used. The ease in which the model can be adapted to be used for simulating other processes will also be touched upon. 4.1 Steady-state The best comparison of the process would be to check the steady-states of the process and that of the actual plant. The next best comparison would be to check the steady-states of the process and the conceptual process design. Unfortunately, no actual plant data are available and the incorrect MeOH : PO-ratio was used. This means only the production can be compared. To be able to make a comparison the distillation column was modeled in ASPEN PLUS 10.0, with the input data as given in appendix EXX, table E.1. The reactor has not been modeled in ASPEN. Setting the vapor fraction to 10-8 was done because the feed would partially flash when it is reduced in pressure from 27.5 bar to 1 bar. This was not modeled and for a fair comparison should not be included in ASPEN. The result was a feed-pressure of 1.009 bar. Besides the data above the heat loss per tray has been supplied to ASPEN. The reboiler chosen was a kettle reboiler. RK-ASPEN was the thermodynamic model used. The values used for comparison were from the basic model, which had run for 38 249 seconds. The fraction MP-2 in the reboiler, will still go down 10-4 and the temperature on tray 23 0.7 K. The difference, however, was thought to be sufficiently small, as the true steady state would not be reached until about 100 000 seconds. This may cause a data storage problem for the complete model. The results can be seen in the figures of appendix E. Below, the comparisons have been given for molar fractions of MeOH and MP-2 in the condenser and reboiler, as well as the heat flows in the condenser and reboiler. Table 4.1. Comparison of fractions MeOH and MP-2 in gPROMS and ASPEN.

Liquid Vapor Difference (%) Component ASPEN gPROMS ASPEN gPROMS Liquid Vapor

MeOH 0.9999 0.9999 0.9995 0.9338 0.00 6.58 Condenser MP-2 2.73*10-5 3.39*10-6 3.93*10-6 3.86*10-7 87.58 90.19 MeOH 0.0046 0.0042 0.0291 0.0269 7.87 7.54 Reboiler MP-2 0.8848 0.8852 0.8965 0.8967 0.04 0.02

Table 4.2. Comparison heat input and removal in gPROMS and ASPEN.

Heat input / removal ASPEN gPROMS

Difference (absolute)

Difference (%)

Condenser -4894.12 -4420.42 473.7 9.68Reboiler 5172.74 5359.08 186.3 3.60

From the figures in appendix E it can be seen that the ASPEN and gPROMS models are in good agreement. All deviations are within 10%. Only the pressure-profile (figure E.2) shows a mismatch, as ASPEN uses an identical pressure drop per tray. Supplying the entire pressure-profile can make these identical. This lowers the temperature (figure E.1) and flowrate (figures E.3 and E.4) profiles to match the trend of the gPROMS model exactly. The deviations still remain < 10%. This has not been presented, because it is undesirable to place all data in ASPEN, as this does not allow for a fair comparison. It was done to check the assumption that the largest deviations in the liquid and vapor flowrates are caused by the fact that ASPEN uses a linear pressure drop. In the

Modeling results

46

gPROMS model the pressure drop per tray in the bottom of the column is larger than in the top. This causes the vapor flow to be higher and by the assumption of equilibrium the liquid flow must also be higher. This was confirmed. The trends in the profiles of the MeOH and MP-2 fractions (figures E.5-E.8) follow each other nicely. The fraction of MeOH in the condenser of the gPROMS model differs, as can be seen in table 4.1. This is due to the fact that not all the N2 is purged from the condenser in the dynamic model. A fraction of 0.066 remains, which is the exact difference between the fractions as found with ASPEN and gPROMS. The fraction of MP-2 also differs. This is due to the fact that the fraction is practically zero and below the error tolerance in ASPEN. The values are in the range 10-6 and 10-5, which explains the large percentile difference found. In table 4.2 it can be seen that the duties of the condenser and reboiler are also within 10%. The temperature in the condenser calculated by gPROMS is lower than that calculated by ASPEN. Judging by the fact that it shows the same jump as the fraction of MeOH in the vapor phase it is reasonable to assume that this is caused by the presence of the N2. This can be verified by using Raoult’s law (equation (3.21)) and assuming, as seen in the comparison, that the pressure and liquid fractions of MeOH are identical in the condenser. Dividing these with each other, gives:

, ,

, ,

satMeOH ASPEN MeOH ASPEN

satMeOH gPROMS MeOH gPROMS

y Py P

= (4.1)

If the ASPEN temperature is used to calculate the saturated vapor pressure for ASPEN, the saturated vapor pressure for gPROMS can be calculated. Iteratively the temperature for the gPROMS model can be found. This will be 337 K, which is still slightly higher than the 336 K found in the model, but shows that the dip in temperature could indeed be due to the presence of N2. This may also be the cause that less cooling is necessary in the gPROMS model, as N2 does not condense. As described above the pressure profile in gPROMS is not linear. This causes a greater vapor flow from the reboiler. To supply this larger vapor flow the reboiler in gPROMS will need a higher reboiler duty. The difference in reboiler duty may also be an indication of the accuracy of the model in steady-state. In both cases the pressure on tray 19 is larger than the pressure of the feed. In practice this means the pressure drop before the column will be slightly lower. In appendix E, table E.1, an overview of the steady-state streams can be found. The numbering is according to the conceptual process design. For an overview of the process modeled the reader is referred to figure 3.2. In the table below a comparison of the production has been given: Table 4.3. Comparison of reboiler flows. Molar flowrates (kmol/s)

Conceptual process design

Model

PO 0 3.57*10-11

MeOH 7.63*10-6 1.47*10-4 MP-1 3.29*10-3 3.44*10-3 MP-2 3.15*10-2 3.10*10-2 MDP 2.43*10-4 4.31*10-4 N2/cat 0 0 Total 0.0350 0.0350

The molar fraction of MP-2 in the reboiler is 0.8852. In the conceptual process design the molar fraction (neglecting all heavies which were not modeled) is 0.8988. This causes a 1%

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47

smaller molar flowrate of MP-2. It can be conclude that the difference is due to better reaction kinetics in the conceptual process design, where less MP-1 and MDP is formed. This means the selectivity in the conceptual process design is slightly better and the reaction to MDP is slower, so less MP-2 is converted to MDP. Also, in the conceptual process design less MeOH is in the reboiler than in ASPEN. With the data presented above it can be said that the model gives a reasonable approximation of the process in steady-state, with an estimated accuracy of the steady-state simulation of about 5-10% in comparison with ASPEN. 4.2 Shutdown Shutting down the reactor basically means stopping PO and catalyst addition, while possibly continuing to add MeOH to prevent overheating of the reactor. As this was not as interesting, shutdown has only been performed on the distillation column, as this was the most complex and numerically challenging. The shutdown was mainly performed to reach initial values for startup. The shutdown procedure is very simple: • stop steady-state feed to reactor, switch to infinite reflux and cut all heat to the reboiler,

and • start emptying the reboiler. During this it is important not to empty the reboiler completely. This is due to the fact that the outflow is controlled. This means that there could be an outflow even if the level is zero, as the stream exiting the reboiler is only liquid. The simulation will crash if the level drops below zero. The shutdown of the distillation column can be characterized by the eight figures given in appendix F. It must be noted that the flows in the 3D-figures are the flows entering the trays. In these figures the simulation was first run for 2000 s in steady-state, as the initialization was not completely steady-state. This can be seen in figure F.4, where initial flows deviate significantly. The reboiler was slowly drained from 2200 s onwards, with the level set at 5 cm for the flow controller. At the end the reboiler level was 1.4 cm. Figure F.4 shows the trend for the liquid flowing over the weir and the vapor flowing through the holes. These cease almost immediately. This is due to the drop in pressure once the reboiler is turned off (figure F.6), while a little reflux is returned to the column and the (liquid) feed has stopped. The drop in pressure is reversed by adding N2 to the column to stop it from imploding (figure F.7). It can be seen that the temperature profile (figure F.5) decreases as well until it is at the temperature of the surroundings. The levels (figure F.1) remain constant until vapor escapes through the downcomer (figure F.3) and causes liquid to dump through the holes (figure F.2). This initially happens on trays 1-3, as they do not have much liquid holdup. When the vapor flow through the holes ceases, the effective level drops below the apron height. That trays 1-3 start dumping at 2000 s cannot be seen in figure F.2, because the dumping is in the order of 10-4, which is sufficient to drain the trays. When the liquid from the upper trays dumps down it causes the other trays to dump and all liquid levels decrease to 10-3 m, where dumping becomes zero. Due to the small flowrates and the assumption of equilibrium on the trays, this process takes a long time. The figures show that a “steady-shutdown-state” has been reached. In figure F.8 the fractions of MP-2 in the liquid and MeOH in the vapor can be seen during steady-state and shutdown. It must also be noted that these results were obtained with an older model. This model has slightly different equations for example for dumping and the effective level, wherefore the results must not be taken quantitatively.

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4.3 Startup In the conceptual process design startup of the process was not considered. Heat integration in the sense that the reaction heats up the feed to the reactor was applied, meaning an extra heat source would be necessary to start up the reactor. As not to change the design by adding an extra startup heater it was decided to attempt to start up the process using the reboiler of the distillation column as process heater. This means the distillation column would need to be operated at a higher pressure to attain a higher temperature of liquid leaving the condenser. A pressure of 4.6 bar was found to be sufficient and Luteijn (2001) suggested this could be possible with the column as designed. If the process were not connected by a recycle an extra heat source would be necessary. If it is also decided to send the stream between the reactor and distillation column to an offspec-tank then the units could be started up completely independent of each other, as the column could be started up under total reflux. This would cause more simple startup procedures, but would also result in more waste. In practice it is likely that an electric pipe heater would be used. Furthermore, the steady-state values of the condenser and reboiler duties were determined in an early model. These were significantly higher than the duties required eventually, due to the use of the exact steady-state feed from the conceptual process design. This feed was higher and more MeOH needed to be evaporated, meaning the condenser and reboiler have been significantly over-designed. In the following paragraphs the startup schedule and characteristics of startup will be discussed. The figures can be found in appendix H. 4.3.1 Startup schedule The startup procedures in the literature (chapter 2.4) are valid for an independent distillation column or reactor. In the model these two are coupled. Due to this fact, and instability problems, the startup procedure from the literature will be adapted slightly. The major changes are in the initial conditions. In the distillation column the trays and condenser will start with values obtained from shutdown. The reboiler will be filled with MeOH and MP-2. The initial pressure and temperature will approximately be that of the surroundings, i.e. 1 bar and 18°C, except for the reboiler, which will be at 43°C. This is done to ensure the pressure is identical, though different materials are used. The reactor is assumed to be filled with MeOH at a pressure of 27.5 bar and a temperature of 20°C. This is the pressure and temperature of the MeOH fed to the process. The basic procedure used, is: • 0 s - Purge N2 and heat column. • 185 s - Bring column up to higher pressure. • 362 s - Heat reactor with condenser effluent. • 10881 s - Add PO when temperature is sufficiently high. • 10999 s - Start all controls at steady-state values when MP-2 starts entering column. • 14096 s - Start steam production when the temperature is sufficiently high. The entire schedule can be seen in appendix H, table H.1. The numbers in bold are the values which have changed. The figures have been divided into the distillation column and the reactor. The figures of the distillation column have been sub-divided into the discontinuous phase and the total startup. 4.3.2 The discontinuous phase of the distillation column The discontinuous phase denotes the period from 0 to about 1200 s. This is the period before sealing of the downcomers has been achieved, as can be seen in figures G.1-G.9. Liquid feed to the column is added from the start. Initially this is pure MeOH. The reboiler is started with a constant 5 MW duty to heat the column and a small reflux is added to give all trays a small liquid holdup. The 5 MW duty is actually too large, as it would cause a temperature rise which

Modeling results

49

is greater than 50°C/hour, which is considered normal and safe in industrial practice (Luteijn, 2001). A smaller duty would result in a slower increase in temperature. If this is done it is important not to feed the entire MeOH feed to the column, as there will be insufficient duty to evaporate all MeOH entering the distillation column. As there was not much time available it was decided to allow a larger temperature rise here. In figure G.3 it can be seen that the feed leads to dumping on the lower trays. The reboiler duty causes a pressure buildup, which is sufficient to seal the dumping of the lower trays, cause the liquid to flow over the weir (figure G.1) and cause a vapor flow through the holes (figure G.2). In the upper trays this vapor flow mainly flows through the downcomers (figure G.4). N2 is slowly purged (figure G.9) from the bottom of the column upwards. This explains the initial rise of the fraction N2 on tray 25. Once 2.57 kmol of the N2 has been purged (185 s) the reboiler duty is increased, the reflux is increased and the pressure is raised to 4.6 bar. This amount has been chosen as it means practically all the N2 has been purged. The pressure was chosen to make the reflux warmer than 100°C. The reboiler duty is determined by controlling the level in the reboiler, as a reboiler overflow will cause the model to crash. This is inherent in the model. It can not handle the disappearance of one of the phases, which could mean the vapor flow exiting from the reboiler would actually be a liquid flow. The reflux is increased to cause a larger holdup on the upper trays. Initially all vapor in the upper trays flows through the downcomers (figure G.4), but the increased reflux causes dumping on these trays. This leads to an increased holdup on all upper trays (figure G.5) and seals the downcomers. The increasing pressure in the column causes dumping to stop and vapor to flow through the holes. Once the level and pressure setpoints for the controllers in the condenser have been reached (362 s) the flow and duty-controllers are turned on. This causes an initial increase in the reflux to the column and causes the levels to rise further, stopping vapor flow and causing dumping again. The result is an overshoot in the liquid levels, before the liquid starts flowing over the weir. The overshoot then cascades down the column to the feed-tray. Once the liquid starts flowing over the weir the trays have become sealed. The liquid flowing over the weir to the feed-tray causes the liquid flow in the bottom of the column to increase. The pressure is still rising slightly in the bottom of the column and this causes the vapor flow through the holes to increase as well. During this period the temperatures (figure G.6) and pressures (figure G.7) rise until the correct pressure setpoint in the condenser is reached. From this point on no major changes occur in the discontinuous phase. The pressure-drop per tray (figure G.8) follows the profiles of the liquid level and liquid flow over the weir. At the point when the downcomers are sealed (~1200 s) the discontinuous phase has ended. 4.3.3 The total startup Once the discontinuous phase has ended a steady state is reached (~3000 s) in the distillation column. This state is sustained until PO is added to the reactor. The reactor is slowly heated (figures G.25 and G.26) with light product from the column until the temperature difference between the condenser and the end of the first tube is 5°C and the temperature is about 100°C. During this time small amounts of MeOH are removed from the recycle stream (flows < 10-3 kmol/s). At this time (10881 s) PO is added to the shell, which causes an increase in mass flowrate through the reactor. This causes an increase in the Reynolds number, which initially is slightly over 4000, demonstrating equation 2.38 is valid. Also a small stream of catalyst is added. Once the PO reaches the entrance of the reactor (10999 s), the flow-control of the catalyst is added (figure G.31), causing a large initial amount of catalyst to enter the reactor to start the reaction. As can be seen in figure G.31 the controller is not well tuned. When the temperature at the point 32 m into the second tube (point 37 out of 62) is 5°C above the steam temperature, steam production is added (14096 s). For the material in the end of the tube it means it will suddenly be heated by the boiling feed water. This causes a great rise in the temperature, far greater than the 50°C/hour, as it has not been heated very

Modeling results

50

much yet. Since this only happens at this point in time and in practice this would not happen, it will be assumed that all other temperature-rises are lower than 50°C/hour. Better would have been to only turn on the steam production separately at each point where the temperature becomes 5°C warmer than the steam temperature. From this time onwards the temperature and composition profiles (figures G.27 – G.30) become established. The temperature profile over the tubes (figure G.25) has been given for the entire reactor. This gives a slightly distorted image, as the first tube-section of the reactor is 16 m long and the second section 161 m. The temperature profile over the shell (figure G.26) has only been given for the first section, as the temperature in the second shell-section is considered constant. Various plots in appendix G have been rotated 90° around the z-axis for better viewing. When PO enters the reactor-tubes, the pressure setpoint in the condenser is reset back to 1 bar and the control of the reboiler duty is switched to the temperature on tray 23. Both setpoint changes of the condenser and reboiler are very abrupt, which would never happen in industrial practice. The overshoot resulting after the setpoint change in the condenser even causes the entire pressure in the column to drop to 0.46 bar (figure G.16). This would never be allowed, meaning the setpoints would be changed more gradually and most likely manually. It also results in erratic behavior of the condenser and reboiler duties (figure G.24). Initially the reboiler duty decreases to zero until the temperature on tray 23 is below the setpoint. The large overshoot causes the reboiler duty to rise to its maximum, before returning to its steady-state. The condenser duty also hits its maximum to supply the cooling to reduce the pressure, before returning to its steady-state. Despite the large overshoots the control does not become unstable. The temperatures in the condenser and reboiler (figure G.23), as well as those in the rest of the column (figure G.15), follow the same trend. The vapor flow (figure G.11) increases during the pressure drop, resulting in a larger liquid flow (figure G.10), as a larger vapor flow results in a higher effective level. When the simulation nears the final steady-state the flows are lower than in the initial startup, as less material needs to be evaporated in the reboiler. It can be seen in figures G.12 and G.13 that dumping does not occur and sealing of the downcomers remains intact after the discontinuous phase. The levels, especially on the lower trays, increase slightly (figure G.14), as a larger mass-flow enters the system. The composition profiles (figures G.18-21) take approximately an hour to reach steady-state from the moment the steady-state feed enters the column (figure G.22). The endpoint is defined as the time when the accumulation of MP-2 in the reboiler is smaller than 2*10-6 kmol/s and the fraction of MP-2 is above 0.88, which occurs around 38 249 s. The simulation is continued till 60 000 s to demonstrate that a steady-state has been reached. It can be seen in all the figures, that, visually, the steady-state has been reached around 20 000 s. A clear endpoint was needed for simulation, though in practice small deviations will be within the operating range of the process. 4.3.4 Economics The process economics during startup were also considered. It was seen that these are overshadowed by two main factors: • the raw material price of PO, and • the product price of MP-2. The costs of MeOH, catalyst and steam as well as the revenue of MDP are practically negligible.

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The economics of the startup can be seen in the following three figures.

Figure 4.1. Cumulative cashflow. Figure 4.2. Cumulative costs, lower contributions.

Figure 4.3. Cumulative costs, larger contributions. The initial costs in figure 4.1 are due to the initial amount of MP-2 and MeOH in the reboiler. As mentioned earlier, the costs of initially filling the reactor have not been taken into account. From this point the curve slowly drops due to the costs of MP-steam in the reboiler and the small amount of MeOH added. Once PO is added the cumulative cashflow decreases sharply, as PO is a very valuable reactant. The downward trend is only reversed once MP-2 is produced, which more than compensates for the expenses of raw material. This is logical, because if this were not the case, the process would not be profitable. The break-even point for startup costs presented here will be around 70 000 s, or 19 hours. 4.3.5 Calculation times and computer dependencies Calculation times of the process are very large. Depending on the machine used for simulation (Athlon 700 Mhz with 520 Mb RAM operating under Unix or Pentium III 500 Mhz with 320 Mb RAM operating under Linux) simulation times were between 1.7 and 2.5 hours for a simulation of 60 000 s. Though this appears to be over six times real-time the majority of the speed is gained in the parts where the changes are minimal. In the beginning of the simulation and around the point where PO is added calculation times drop to 1/20 of real-time or even lower. This shows the reason a complete optimization was not attempted. Shutdown takes approximately 16 000 s to simulate 9200 s with stepsize 10 on a high output level. A disturbing fact is the inability to run the complete model on a Windows95 machine. The simulation would crash around the point that the new pressure setpoint in the condenser should be reached. Adjusting the accuracy settings did not have any effect. Shutdown only succeeded on the Linux-machine, though there was no time to investigate the cause. The separate models for distillation column and reactor did function on the Windows95 machine.

Base economics (I)

-30000

-25000

-20000

-15000

-10000

-5000

00 10000 20000 30000 40000 50000 60000

Time (s)

Cum

ulat

ive

cash

flow

(fl.)

Base economics (II)

02000400060008000

100001200014000160001800020000

0 10000 20000 30000 40000 50000 60000

Time (s)

Cum

ulat

ive

cost

s (fl

.)

Costs of MeOH Costs of catalyst

Costs of MP-steam Revenue of MDP

Base economics (III)

0

50000

100000

150000

200000

250000

0 10000 20000 30000 40000 50000 60000

Time (s)

Cu

mu

lati

ve c

ost

s (f

l.)

Costs of PO Revenue of MP-2

Modeling results

52

4.3.6 Validation As it is unknown if the conceptual process design has led to the construction of a plant and there are no startup or even steady-state data available a full validation is impossible. The next best thing is a face-validation of the results. To attempt this, the results, excluding the economics, were shown to an expert from industry (Law, 2001). Several remarks were in order: • Setpoint changes in the order used here for the condenser would never be done by

automatic controllers in industry. The change would be performed manually and the controller would be returned to automatic by the operator when the process had stabilized at the new setpoint.

• Setpoint switches such as in the reboiler would also never be done by automatic controllers. As above, this would give the controllers steps that are too large and may cause problems. This too would be done manually.

• Temperature rises are too large. • The reactor is not being used effectively. It would probably be economic to install a

jacketed pipe to preheat the feed entering the tube-side of the reactor after it had been preheated in the shell-side. As heating medium the LP-steam produced could be used.

Except for the aforementioned remarks it was agreed that the model could give a reasonable qualitative description of the actual situation with the controller tuning parameters selected and could be used to optimize controller parameters to achieve an even smoother startup. A good agreement with results produced by ASPEN was considered to be very important for validation of the model. 4.4 Optimization The goal of a model is to understand the process modeled and influence it in a desired direction. To optimize the startup a number of variables were determined, which were thought to be of some influence on the economics of the process. These were: • the temperature setpoint for catalyst addition, which controls the flow of catalyst to the

reactor, • the condenser pressure, which determines the temperature at which the reactor is

heated, • the initial level of material in the condenser, which determines the amount of reflux that

can be fed to the column and to the recycle, • the amount of MeOH being recycled, removed and fed to the process, which determines

the amount of heat being fed to the reactor, the amount of MeOH which is wasted and the amount of MeOH which needs to be purchased,

• the speed at which the PO is added, which determines the start of the reaction and the amount of PO added,

• the initial duty of the reboiler, which determines the speed at which the column is heated and the amount of heat that is added,

• the speed at which the reboiler is brought to its steady-state controller bias, which also determines the speed at which the column is heated and the amount of heat that is added,

• the initial fraction of MP-2 in the reboiler, which determines the purity and temperature in the bottom of the column,

• the initial level of the liquid in the reboiler, which determines the amount of MP-2 in the column and the amount of liquid that needs to be evaporated, and

• the reflux rate between the time the condenser reaches its high-pressure setpoint and the time that reaction starts.

These variables were increased and decreased to examine their effect on the cumulative cash flow. The variables, changes and results can be seen in the following table.

Modeling results

53

Table 4.4. Influence of different variables on the process economics – base. Variable Cumulative

cashflow Difference (%)

Catalyst, setpoint 430 K -2439 13 MeOH flow, factor 1.1 -2581 8 Reflux, 0.175 -2667 5 Reboiler, initial fraction MP-2 0.6 -2752 2 Condenser, level 1.1 -2756 2 Condenser, 4.8 bar -2766 2 Reboiler, level 0.95 -2814 0 Reboiler, 3 MW in 150 s -2816 0 Base -2819 0 Reboiler, 3 MW in 50 s -2823 0 Reboiler, 6 MW bias -2829 0 Reboiler, 4 MW bias -2831 0 Reboiler, initial fraction MP-2 0.4 -2842 -1 Condenser, 4.4 bar -2877 -2 PO-feed in 200 s -3042 -8 Reflux, 0.291 -3084 -9 MeOH flow, factor 0.9 -3204 -14 PO-feed in 400 s -3339 -18 Catalyst, setpoint 410 K -3454 -23 Reboiler, level 0.81 -3835 -36 Condenser, level 0.7 -4620 -64 It can be seen that the important variables in positive sense, are a higher setpoint for catalyst addition, a higher initial MeOH flowrate and a lower initial reflux ratio. In negative sense the important variables are a lower level in the condenser drum, a lower level in the reboiler, a lower setpoint for catalyst addition, ramping the PO addition and a lower initial MeOH flowrate. To increase the initial levels in the condenser and reboiler the schedule needs to be altered. In stead of purging 2.57 kmol of N2, purging will end when the fraction N2 in the condenser becomes 0.06. In the base schedule this is 0.0605. 2.55 kmol N2 will have been purged. A higher setpoint for catalyst addition is beneficial, as reaction rates are higher at a higher temperature and this means less catalyst needs to be added. This causes only an initial larger flow of catalyst to start the reaction and further a smaller flow is necessary. A higher initial MeOH flowrate causes more heat to be added to the reactor, which causes it to reach its initial temperature sooner. A lower reflux ratio means more MeOH is removed from the process, which is necessary to decrease the holdup of light product in the process, as MeOH can only leave in the initial startup. A higher initial condenser level also achieves this, as the top product stream will be larger initially. A higher initial fraction of MP-2 increases the holdup of heavy product, so the steady-state can be reached earlier. A higher pressure setpoint in the condenser allows a warmer stream to heat the reactor, causing the reactor to be heated earlier. A higher level in the reboiler, as well as different initial reboiler duties and ramping the reboiler duty has no noticeable effect on the process economics. For the initial duties this may be due to the extra costs of heat and a slightly faster startup compensating each other. This means a smaller reboiler duty could be used initially to cause the temperatures to rise at a slower rate. A lower level in the condenser causes a smaller flow to heat the reactor, causing the startup to take longer. A lower reboiler level, as well as a lower fraction of MP-2 in the reboiler, requires a longer time to generate a sufficiently large holdup of heavy components, and therefore requires a longer startup time. A lower catalyst setpoint eventually causes more catalyst to be added to achieve the correct temperature profile. Ramping the feed of PO causes the process to take longer to achieve steady-state and therefore has an undesirable impact on the economics. Possibly it causes more catalyst to be added to start the reaction. A

Modeling results

54

smaller initial flowrate of MeOH and a larger reflux ratio cause the recycle to be smaller and less heat to be added to the reactor. A lower pressure setpoint in the condenser has a similar effect. It is easy to see which variables have a large effect on the process. However, it was found that changing the condenser and reboiler levels could cause an overflow in the reboiler, which would cause the model to crash. A large factor for the flowrate had a similar effect. Ramping PO did not seem to be advantageous at all and in the end three variables were selected for optimization by factorial design. These were: • the temperature setpoint for catalyst addition, • the initial reflux ratio, and • the initial fraction of MP-2 in the reboiler. Of these three the initial fraction of MP-2 does not influence the path of the startup, though it is thought to influence the speed of the startup, as a higher initial fraction of MP-2 means more heavy product is present in the process. It also means higher initial costs, as MP-2 costs more than MeOH. The temperature setpoint for catalyst addition is only effective once catalyst is added, which is not immediately. A higher setpoint will cause less catalyst to be added and at lower costs. Of course sufficient PO will need to be converted, otherwise the profits due to the revenue of MP-2 will decrease. The initial reflux ratio directly influences the flow of light components in the process during startup and is thought to be most influential during startup. As stated above a larger reflux ratio will cause a smaller recycle and less heat to be added to the reactor, while a smaller reflux ratio will decrease separation in the column and cause MP-2 to enter the condenser. To generate the local profile of the cumulative cashflow small steps were taken in each of these variables. For factorial design it is generally a good idea to take steps in the order of twice the standard deviation of the controlled variable. Estimating that a temperature sensor could estimate accurately to about 0.1°C, steps of 0.5°C were taken in the temperature setpoint. Estimating that for small changes in flows the flow controller is accurate to 1 ml/s, or about 1%, the reflux ratio will be chosen to vary about 1% (and the inverse shown about 2*10-3). As the inverse reflux ratio will be used in optimization, it has been chosen to vary the natural log of the inverse reflux ratio by 0.01. The fractions have been varied by 0.005, though a gas chromatograph could probably reach a greater accuracy. To make a good comparison a “fingerprint” of each step was made, as mentioned in chapter 3.7. Besides these amounts it was also decided to view: • the run time, • the end time, • the cumulative cashflow, • the time at which xMP-2 entering the column was near steady state, • the conversion of PO, • the initial temperatures and pressures in the condenser and reboiler, • the accumulation of mass in the column, • the maximum temperature rise in the reactor, and • the duties of the condenser and reboiler. Although the amount of offspec product produced is included and the economic value of reboiler product with a fraction of MP-2 less than 0.88 is zero this is not a problem in practice. The process modeled is part of a larger process and the reboiler product is sent to a second distillation column. The literature (Gans et al., 1983 and Verwijs, 1994) agree that product finishing sections must always be started up first. Further a “stand alone” distillation column will be started up with more ease than an integrated one. The “fingerprints” for the variations of the base, as well as the optimized process (opt4), can be found in appendix H. Every pair of columns describes the sensitivity of both the base case (base) and the optimized case (opt4) to changes in the variables in table 4.5.

Modeling results

55

Initially the optimizations ran towards a longer startup time. This is caused by the fact that in steady-state the process is very profitable. The final part of the startup was near steady-state and being in that state longer will lead to a more profitable endpoint. As the steady-states occurred around 40 000 s, the endpoint was chosen significantly further at t = 60 000 s. Choosing a set end time was not done until after the first 4 optimization steps were completed. The results shown below, for the next 4 optimization steps, will therefore start at the end of the first 4 steps. The most optimal step per optimization (opt) has also been given, as well as the sensitivities according to equation 2.56 (bi). Table 4.5. Optimization steps.

Step Cum. Cashflow

Setpoint cat. add.

(1)

Reflux ratio (2)

Initial xMP-2, reboiler

(3)

Sensitivity to (1)

Sensitivity to (2)

Sensitivity to (3)

base -2819 420.00 0.2180 0.5000 1 -2728 423.16 0.2317 0.4687

opt 1 -2697 423.66 0.2293 0.4737 21.83 8.60 0.80

2 -2579 424.92 0.2191 0.5600 opt 2 -2550 425.42 0.2169 0.5650

18.23 8.28 2.88

3 -2357 427.87 0.2007 0.6340 opt 3 -2330 428.37 0.1987 0.6390

13.56 7.83 5.03

4 -2059 432.72 0.1766 0.7135 opt 4 -2038 433.22 0.1749 0.7185

6.37 7.65 7.64

It can be seen that in four steps the loss of the process during startup has been reduced 28%. Of course this is only Hfl. 781, but it shows that optimization can lead to more profitable startups, especially because this is only a simple optimization of only three variables. To illustrate the method used the optimization from step 3 will be shown. Eight points were determined around the base of step 3. These were fit to equation 2.56, where x1 is the setpoint for catalyst addition, x2 is the natural log of the inverse of the reflux ratio and x3 is the initial fraction of MP-2 in the reboiler. All these x were normalized. The X matrix, identical in all four cases as seen in the figure below, is:

1 0 0 01 1 1 11 1 1 11 1 1 11 1 1 11 1 1 11 1 1 11 1 1 11 1 1 1

X

− − = − −

− − −

− − − − −

(4.2)

Figure 4.4. Definition of normalized points chosen in optimization. This gave a function (the sensitivities in table 4.6): 1 2 3-2356.92 13.56 7.83 5.03Y x x x= + ⋅ + ⋅ + ⋅ (4.3)

(1,1,1)

(-1,1,1)

(1,1,-1)

(-1,1,-1)

(1,-1,-1)

(-1,-1,-1)

(-1,-1,1)

(1,-1,1)

(0,0,0)

x

y

z

Modeling results

56

It shows that all variables considered should be increased in the positive direction to improve process economics. Generally this was true for all of the final four optimization steps. The data collected was used to fit four functions of the sets (1,1,1), (0,0,0) and (-1,-1,-1), (-1,1,1), (0,0,0) and (1,-1,-1), (1,1,-1), (0,0,0) and (-1,-1,1), and (1,-1,1), (0,0,0) and (-1,1,-1). This gave four practically first order curves for every variable. Second order curves were drawn through them with excel, which gave identical coefficients in front of the second order term, while the other terms for each set of curves differed in sign. Of course a perfect fit was found, as second order curves were fit through three points. Four coefficients in front of the second order terms were found. Their average is -0.23, which means the average second derivative is -0.46. The 5% deviation from the cumulative cashflow, as seen in equation 2.63, was chosen as the influence of the variables on the cashflow is assumed to be non-linear and large steps may cause an optimum to be overlooked. This resulted in the fractions 0.184, 0.319 and 0.497, according to equation 2.62. The new xi were 9.69, 12.75 and 15.91, meaning the new values used were 432.72 K, (1/5.661=) 0.1766 and 0.7135, with the variations as mentioned above. In table 4.5 it can be seen that the steps for the first two variables keep increasing. The steps in the third variable are decreasing. This is due to the fact that initially the sensitivity to the fraction MP-2 in the reboiler was small and therefore a large step had been taken. After four steps the sensitivities are in the same order and therefore all normalized steps are also in the same order. As the steps are still taken in the same direction, the optimum has not yet been found. As can be seen in step one only the temperature setpoint has been altered in the correct direction with respect to the base case. Because the initial optimizations would increase the time for startup, it can be seen that only the initial reflux ratio and the initial fraction of MP-2 in the reboiler actually influence the startup time, as expected. After four optimization steps there was no time left to continue optimization, as calculation of nine points, at 2.5 hours per point, takes over 22 hours, excluding processing of the data. To show that the same sensitivities as above are still present in the optimized case (opt4), the deviations of all variables, as shown above, were calculated using the optimized values for the setpoint for catalyst addition, the initial reflux ratio and the initial fraction of MP-2 in the reboiler. The results can be seen in the table below, with deviations both from the optimized, as from the base process. Table 4.6. Influence of different variables on the process economics – optimized. Variable Cumulative

cashflow Difference opt4 (%)

Difference base (%)

Reboiler, level 0.95 -1478 28 48 MeOH flow, factor 1.1 -1842 10 35 Condenser, 4.8 bar -1959 4 31 Reboiler, 3 MW in 150 s -2036 0 28 Opt 4 -2039 0 28 Reboiler, 3 MW in 50 s -2042 0 28 Reboiler, 6 MW bias -2046 0 27 Reboiler, 4 MW bias -2050 -1 27 Condenser, 4.4 bar -2125 -4 25 Condenser, level 1.1 -2206 -8 22 MeOH flow, factor 0.9 -2318 -14 18 PO-feed in 200 s -2344 -15 17 PO-feed in 400 s -2763 -36 2 Reboiler, level 0.81 -3026 -48 -7 Condenser, level 0.7 X - -

Modeling results

57

The run with an initial condenser level of 0.7 m crashed due to the condenser becoming empty. To solve this problem a different schedule would need to be adapted, allowing the flow-control in the condenser to start earlier. This has not been done. Basically the same order in sensitivities has been found and in table H.1 the base case and the optimized case can be seen side by side. The savings are mainly due to less offspec product from the reboiler, as more MP-2 was added initially, and the smaller amount of catalyst needed. Due to the fact that more MP-2 was present, less MeOH needed to be purged. Unfortunately, initially a higher price is paid. Though in the end 8% less catalyst is added, initially more catalyst is required, showing this might be achieving more a steady-state optimum, than a dynamic one. Also, the choice of the temperature setpoint may not have been the best one, as the maximum temperature becomes 184°C, in stead of 173°C. This is undesirable as the saturated vapor pressure of PO becomes 33.3 bar and a larger pressure may be required in the reactor. Further, it can be seen that the cumulative cashflow at the end-point may not be the best optimization variable, as it does not take into account extra investments along the way. For a simple optimization as performed above, however, it should suffice. These drawbacks are thought to be outweighed by the fact that this optimization is only an optimization of one schedule and for three variables. If there were sufficient time an optimization of many schedules and many variables could be attempted. But even this simple optimization shows that dynamic modeling can be advantageous, though further research would be needed to show the full extent of it. 4.5 Adaptability The usefulness of a model is greatest if it can be used for many different processes, i.e. that it is a generic model. For the model developed this is only partially true. The non-generic parts are: • the physical properties, which, besides in the physical property models, are partially

incorporated in the XC-conv, mixer and con_break_liq models, • the different equations used for N2, as it does not enter the liquid phase, • the kinetics in the reactor, which are specific to the reaction performed, • the fact that the cooling takes place in a shell surrounding all tubes, • the friction coefficients on the tray, which should be a function of tray layout, • the coefficients on the tray used for switching between vapor flow and dumping (such as

equation 3.10), which for columns with smaller internal flowrates must be smaller, • the controllers with their min/max functions, where the range of operation has been

defined within the model, • the highest process model, in which specific economics and feeds are defined, and • the entire process section, but this is self evident. For a person with some experience in modeling in gPROMS the changes for a new process, for which all physical properties, kinetics, dimensions, etc. are known, should only take a matter of hours. Initializing the model and debugging errors, such as crashes, which will occur, may take significantly longer. Only time and experience will tell.

Conclusion and recommendations

58

5 Conclusion and recommendations Having demonstrated the capabilities of the model it is time to return to the goals of the project. 5.1 Conclusion The goals of the project were to build a model that will describe the startup and shutdown behavior of a process and to perform a simplified optimization of a specific startup procedure. A dynamic model has been built for an interconnected reactor and distillation system capable of describing a startup from a practically empty column to steady-state conditions. Features of the model are: • an equilibrium tray model, • liquid flows from the trays, both over the weir and dumping through the holes, • vapor flows from the trays, both through the holes and through the downcomer, • inert, which is added and purged, and • a single phase, plug-flow reactor of the shell-and-tube-type, operating under turbulent

flow conditions. The downcomer of the distillation column, liquid weeping and liquid entrainment have not been modeled. This model has a maximum deviation from ASPEN in the steady-state of 10%. As all trends in the profiles follow each other nicely it is thought to be about 5-10% accurate in steady-state, with respect to ASPEN. The model is capable of describing a shutdown, as long as vapor escapes through the downcomer from the reboiler. It is also capable of describing a startup in which the column is heated, inerts are purged, the reactor is heated, reactants are added and the steady-state is reached, without external heating source. These results have not been verified experimentally. Errors made include an incorrect excess of MeOH in the reactor, incorrect surface areas for heat loss on the tray and in the reboiler, small reset rates for controllers in the condenser, large setpoint changes and high rates of temperature rise in the system. The excess of MeOH is still 3.95:1 in stead of 6.09:1 and the heat loss neglected is smaller than 1% of the duties of the reboiler or condenser. The incorrect reset rates and large setpoint changes cause excessive overshoots during startup, which could have been avoided, but do not cause instability. The high temperature rises are caused by a sudden addition of the steam production, which should have been more gradual, and an initially too high duty of the reboiler. Most of these errors have little influence or can be corrected with increased calculation times. Drawbacks of the model are the long calculation times (2.5 hours) and numerical instabilities. These occur especially when a regime is entered for which the model was not constructed, such as an overflow of the reboiler or temperatures above 482 K, where the model will crash. Also, the model developed is not completely generic, but could be adapted for other systems. A full optimization of startup was not performed due to limitations in time. During a simplified optimization by factorial design of the startup-schedule used, only four optimization steps were needed to reduce the loss at the end-point by 28% (Hfl. 781). Though the absolute value is small, this demonstrates that optimization can lead to significant increases in profitability. Overall the model provides valuable insight in the processes that take place during dynamic operation of an interconnected reactor and distillation system.

Conclusion and recommendations

59

5.2 Recommendations Recommendations can be divided into two parts: Recommendations for the design and modeling and recommendations on the operational side. Design and modeling For a model to be trusted it needs to be verified experimentally. This could be done with the current process, but data on startup seem to be rare and therefore any startup data that can be obtained for such a process should be used. If necessary the equations should be adjusted to give a more realistic description of reality. Especially equations with factors for numerical stability may need to be reevaluated. The model should also be expanded with models for the downcomer, as liquid sealing is an important factor in dynamic as well as steady-state operation, and for adding a mixture of liquid and vapor to the distillation column, which has not been done here. Liquid entrainment and weeping can be disastrous to separation efficiency and should be included for a more realistic model. As the time necessary for all profiles in the column to reach the steady-state makes a large contribution to the total startup time, the assumption of equilibrium on the tray may not hold. Incorporating a non-equilibrium model in the distillation column will make the model more realistic. For a non-equilibrium model the physical properties would need to be reevaluated. Pressure dependencies are also desirable in the process, so the model would be applicable to a wider range of operating conditions. For the reactor the equations should be expanded to non-turbulent flow to be able to startup the reactor with smaller flowrates. For the reactor to be applicable to a wider variety of situations equations for the formation of vapor need to be added. The reaction kinetics were determined under other circumstances than for which they were used. Therefore the reaction kinetics need to be verified and improved. Overall, the speed of the model should be increased, especially the speed in the beginning of the startup and shutdown, so a full optimization will be possible. Operation Due to the limited amount of time available and the large calculation times there was no possibility to examine other startup schedules. Other startup schedules could include startup with strongly reduced flowrates or use of the startup-line. Examining different startup schedules is what the model was designed for and this will lead to greater understanding of the process of startup. Complete optimization of different startup schedules can also improve understanding and especially the profitability of a process and should be performed.

References

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Smith, J.M. & Ness, H.C. van (1987). Introduction to Chemical Engineering Thermodynamics, 4th ed, Singapore: McGraw-Hill.

Sinnott, R.K. (1996). Coulson & Richardson’s Chemical Engineering, Volume 6, Chemical Engineering Design, revised 2nd edition, Oxford: Butterworth-Heinemann.

Tao, L., Jingen, Y. & Zhiguang, Y. (1997). Study in homogeneous Catalytic Synthesis of Propylene Glycol Monomethyl Ether, Journal of East China University of Science and Technology, 23(1), 39-43 (Chinese).

Vargaftik, N.B., Vinogradov, Y.K. & Yargin, V.S. (1996), Handbook of Physical Properties of Liquids and Gases, Pure substances and mixtures, 3rd ed. New York: Begell House.

Verwijs, J.W. (1994). Reactor Start-up and Safeguarding in Industrial Chemical Processes, Ph.D. Thesis, Enshede.

Verwijs, J.W., Kösters, P.H., Berg, H. van den & Westerterp, K.R. (1996). Startup Strategy Design and Safeguarding of Industrial Adiabatic Tubular Reactor Systems, AIChE J., 42, 503-515.

Webci (1999). DACE-pricebooklet, 20th ed., Vorden: Weevers.

Yaws, C.L. (1999). Chemical properties handbook: physical, thermodynamic, environmental, transport, safety, and health related properties for organic and inorganic chemicals, New York: McGraw-Hill.

Appendices

Appendices

Appendix A: The conceptual process design

Appendix B: Derivation of equations



Appendix E: Steady-state values



Appendix H: Optimizations

Appendix I: gPROMS model

Appendix A. The conceptual process design

A-1

Appendix A: The conceptual process design Design basis The process is based on a conceptual process design performed by van den Eijnden, IJsebaert, Regenbogen and Wieland (1998). The goal of the design is geared to produce methoxy-propanol and methoxy-propoxy-propanol from propylene oxide (PO) and methanol (MeOH). Its main objective is to design a process producing 85,000 t/a 1-methoxy-2-propanol (MP-2) and 15,000 t/a methoxy-propoxy-propanol (MDP). This is performed in two reaction sections. The product specification for MP-2 is > 99.9 %w with < 0.01 %w methanol and < 0.1 %w of its isomer 2-methoxy-1-propanol (MP-1). The purity of MDP has to be > 99.0 %w with < 0.1 %w MP-1. The reaction is catalyzed by sodiummethylate (NaOCH3), which has a selectivity towards MP-2 of over 90%. During the reaction the main by-product is MP-1, which reacts with PO to MDP in the second reaction section. Reason for production Propylene glycolethers are used in solvents, inks, paints, as heat transfer fluids or anti-icing agents. More commonly ethylene oxide (EO) based glycolethers are used. PO based glycolethers are replacing EO based glycolethers due to (suspected) toxicity of EO based glycolethers. At least methoxy-ethanol is toxic and better replaced by methoxy-propanol. This can be used in pharmaceuticals, cosmetics, cleaning agents, degreasing agents, crop protection agents, inks and coatings. Process flow scheme The process flow scheme for the entire process can be given by the figure below.

Figure A.1. Process flow scheme of the entire process. The process flow diagram has been given in the second figure in this appendix. Reaction mechanism The reaction mechanism is: NaOCH3 Na+ + H3CO-

H3CO- +O O

O- ][ MeOH OH

O

MeOH[ ]O-O

OH3CO- + OHO

MP-1

MP-2

+ H3 CO-

+ H3 CO-

R1 T1 T2 T3 T4 R2

MeOH recycle MP-1 recycle

MP-2

MDP

Waste PO

PO, cat, MeOH

Appendix A. The conceptual process design

A-2

Figure A.2. Process flow diagram

Appendix B. Derivation of equations

B-1

Appendix B: Derivation of equations In this appendix various assumptions will be explained and accounted for. The equations for the reactor will be derived and used to demonstrate the validity of the assumptions for both reactor and distillation column. An overview of all assumptions made will be given. The energy balance Energy within a control volume can be defined as (Coulson and Richardson, 1997):

2,

2i j

i i i i

vE U P V g z

magnetic energy electrical energy other energy

= + ⋅ + + ⋅

+ + + (B.1)

in which:

Ei = Energy of component i [kJ/kmol i] Ui = Internal energy of component i [kJ/kmol i] P = Pressure within the control volume [Pa] Vi = Specific volume [m3/kmol i] vi,j = Velocity of component i in direction j [m2/s] g = Gravitational acceleration [m/s2] zi = Height above a given level [m]

Magnetic, electrical and other energies are usually neglected (Coulson and Richardson, 1997) and will be neglected here in light of other, larger energies. By definition: i i iH U P V= + ⋅ (B.2) in which:

Hi = The enthalpy of component i [kJ/kmol i] Given a sufficiently high pressure in the reactor to ensure no change from liquid to gas phase, a constant pressure or an enthalpy independent of the pressure (Smith and Van Ness, 1987), and with the minimum temperature rise in the reactor being in the order of 10 to 100 K, we can approximate the change in enthalpy in the reactor by: 3 4 3( ) 10 1 10 10 /out inH Cp T T kJ mρ∆ = ⋅ ⋅ − ≈ ⋅ ⋅ = (B.3) in which:

∆H = Change in enthalpy [kJ/m3] ρ = Density [kg/m3] Cp = Heat capacity [kJ/(kg.K)] Tout,in = Temperature of liquid exiting/entering control volume [K]

Here we have filled in the enthalpy in kJ/m3 in stead of kJ/kmol i and have a low guess for the change in enthalpy. In the distillation column temperatures range from approximately 65 to 130°C, giving an even larger temperature difference and there is evaporation and condensation. Given a fluid velocity of 0.015 m/s in the reactor, a small pressure difference (∆P≈300 Pa) and a maximum height difference of 10 m (if the reactor is placed vertically), then we can see that:

2 3 2 2, 3 4 310 (10 ) 10 10 /

2 2i jv

kJ mρ −

− −⋅ ⋅= ⋅ ≈ (B.4)


B-2

and: 3 3 2 310 10 10 10 10 /g z kJ mρ −⋅ ⋅ ∆ ≈ ⋅ ⋅ ⋅ = (B.5) Given the fact that the velocity was used in stead of the change in velocity we can see that the kinetic term can be neglected. In the distillation column the flows are in the order of 1 m/s. Therefore the kinetic term will be in the order 1, which can also be neglected. The contribution of the potential energy due to differences in height is also far below that the enthalpy, and this is only if the reactor would be place vertically. The estimated height of the distillation column is about 17 meters, so the same order of magnitude will be found. Therefore the contribution of potential energy due to differences in height will also neglected and the energy will be represented by the enthalpy: E H= (B.6) This, of course, is independent of the unit assigned to it. The energy balance becomes:

,in out in s outdE E E Q Wdt

= − + − (B.7)

in which:

Qin = Energy added to the system [W] Ws,out = Shaft work performed by the system [W] t = Time [s]

Within the reactor and the distillation column there is no shaft work, so Ws.out = 0. The only external heat exchange is the cooling supplied by the cooling water. The enthalpy balance One assumption that will be made immediately is that the reactor is symmetrical. This means there are no variations in the θ direction (figure 2.4). This can be done as there is no reason to assume a shell-and-tube heat exchanger would be made with tubes of varying diameter, as this is complex in construction and unnecessary. Deriving the energy balance, without shaft work, and with substitution of E = H (where H is in J/m3) for a slice of the reactor dr, dz, we find:

, , , ,( )

( ) ( )

( ) ( )

V z V z V r V rz z dz r r dr

r rr r dr

z zz z dz

d H V H H H Hdt

dT dTA Adr drdT dTA Adr dr

φ φ φ φ

λ λ

λ λ

+ +

⊥ ⊥+

⊥ ⊥+

⋅ = ⋅ − ⋅ + ⋅ − ⋅

+ ⋅ − ⋅ − ⋅ − ⋅

+ ⋅ − ⋅ − ⋅ − ⋅

(B.8)

in which:

V = Volume under consideration [m3] ϕV,i = Volumetric flowrate into slice in direction i [m3/s] λ = Thermal conductivity [kW/(m.K)] i = Contribution evaluated at place i A⊥ i = Area of slice in direction i [m2] i = Direction under consideration (r or z)


B-3

The r-direction is the radial direction and the z-direction is the axial direction. Many terms can be simplified by using: zV A dz⊥= ⋅ (B.9) ,V i i iA vφ ⊥= ⋅ (B.10) 2rA R dzπ⊥ = ⋅ ⋅ (B.11) and 2 2( ) 2zA r dr r rdrπ π π⊥ = ⋅ + − ⋅ ≈ (B.12) in which:

vi = Velocity in the i direction [m/s] R = Inner radius of the tube [m] ⊥ = Denotes direction perpendicular to the direction of the flow.

Filling this in we get:

( 2 ) 2 2

2 2

2 ( ) 2 ( )

2 ( ) 2 ( )

z zz z dz

r rr r dr

r r dr

z z dz

d H r dr dz H v rdr H v rdrdt

H v rdz H v rdz

dT dTR dz R dzdr dr

dT dTr dr r drdr dr

π π π

π π

π λ π λ

π λ π λ

+

+

+

+

⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ − ⋅ ⋅

+ ⋅ ⋅ − ⋅ ⋅

+ ⋅ ⋅ ⋅ − ⋅ − ⋅ ⋅ ⋅ − ⋅

+ ⋅ ⋅ ⋅ − ⋅ − ⋅ ⋅ ⋅ − ⋅

(B.13)

Taking the limit of dr and dz to zero and dividing by dr and dz we get:

2 2

2 2

( ) ( ) ( )2 2 2

( )2 2

z rH r H v r H v rt z r

T r TRr z

π π π

π λ π λ

∂ ⋅ ∂ ⋅ ⋅ ∂ ⋅ ⋅⋅ = − ⋅ − ⋅∂ ∂ ∂

∂ ∂ ⋅+ ⋅ ⋅ ⋅ + ⋅ ⋅∂ ∂

(B.14)

For the model this is too detailed. Assuming turbulent flow, meaning no variations in the r direction (no convective heat transport in the r direction) and no conductive heat transport in the z direction, the equation can be derived slightly differently:

2

2 2

2 2

2 2

1( ) 1 144 4

1 1 ( )( ) ( )4 41 1 ( )( ) ( )4 4

i

z i z iz z dz

zi i i i w

zi i i i w

d H d dzH v d H v d dQ

dtH v Hd dz d dz U d dz T Tt z

H v Hd d U d T Tt z

ππ π

π π π

π π π

+

⋅ ⋅ ⋅= ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅ +

∂ ∂ ⋅⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ − + ⋅ ⋅ ⋅ ⋅ −∂ ∂

∂ ∂ ⋅⋅ ⋅ = ⋅ ⋅ − + ⋅ ⋅ ⋅ −∂ ∂

(B.15)

Leading to the enthalpy balance:


B-4

( ) 4 ( )z

i wi

H v H U T Tt z d

∂ ∂ ⋅= − + ⋅ ⋅ −∂ ∂

(B.16)

in which:

Ui = Heat transfer coefficient, based on inside area of the tube, up to middle of tube [kW/(m2.K)]

Tw = Temperature of wall (assumed independent of r) [K] di = Tube inside diameter [m]

This is the enthalpy balance that will be used for a reactor tube. From it the temperature in a reactor tube will be calculated. It must be realized that the enthalpies used are the unit kJ/m3. This means the enthalpies in the physical property database must be converted from kJ/kmol to kJ/m3. For the coolant the differences will be in the heat added, which will be positive and therefore will include (Tw-Tc) as driving force, and the fact that heat will be added from many tubes to the cooling liquid. Once again no variations in the r direction will be included (assuming turbulent flow). The z direction is equal to that of the tubes. This means the velocity in the shell will be negative. This is not desirable for calculation of e.g. Re numbers. The balance can be derived as:

2 2

2 2,

2 2,

,2 2 2 2

,

1( ( ) ) 14 ( )

41

( )4

( )1 1( ) ( )

4 4

shell tubes o

z c shell tubes oz

z c shell tubes oz dz

z cshell tubes o shell tubes o

s i tubes

c

c

c

cc

d H D N d dzH v D N d

dt

H v D N d dQ

v HHD N d dz D N d dz

t zU N d

ππ

π

π π

π

+

⋅ ⋅ − ⋅ ⋅= ⋅ ⋅ ⋅ − ⋅

− ⋅ ⋅ ⋅ − ⋅ +

∂ ⋅∂⋅ − ⋅ ⋅ ⋅ = − ⋅ − ⋅ ⋅ ⋅

∂ ∂+ ⋅ ⋅ ⋅ ( )w ci dz T T⋅ ⋅ −

(B.17)

2 2

,,

4( )

( )( )

shell tubes o

z c cc itubes s i w c

dD N d

v HH N U T Tt z − ⋅

∂ ⋅∂ ⋅= − + ⋅ ⋅ ⋅ −

∂ ∂ (B.18)

in which:

Us,i = Heat transfer coefficient, based on inside area of the tube, middle of tube onwards [kW/(m2.K)]

Hc = Enthalpy of coolant [kJ/m3] Tc = Temperature of coolant [K] Ntubes= Number of tubes [-] vz,c = Velocity of coolant in -z direction [m/s] do = Tube outside diameter [m] Dshell = Diameter of shell [m]

It is important to realize that the z direction of the coolant is opposite to the z direction of the reactants in the tubes and that the overall heat transfer coefficient should be based on the inside area of the tube. Definition of U For both equations it is necessary to have a relation for the overall heat transfer coefficient (U), based on the inside area of the tube. The general equation, based on the outside area of the tube, is given by (Sinnott, 1996):


B-5

,

ln1 1 1 1 1

2

oo

i o o

o o o od w i id i i

ddd d d

U h h d h d hλ

⋅

= + + + ⋅ + ⋅⋅

(B.19)

in which:

Uo,o = Overall heat transfer coefficient based on the outside diameter [kW/(m2.K)] ho = Outside fluid film coefficient [kW/(m2.K)] hod = Outside dirt coefficient [kW/(m2.K)] hid = Inside dirt coefficient [kW/(m2.K)] hi = Inside fluid film coefficient [kW/(m2.K)] λw = Thermal conductivity of the tube wall material [kW/(m.K)]

If we wish to have the overall heat transfer coefficient based on the inside area of the tube, the relation becomes:

,

ln1 1 1 1 1

2

oi

ii i

o i o o o od w id i

dddd d

U d h d h h hλ

⋅

= ⋅ + ⋅ + + +⋅

(B.20)

in which:

Uo,i = Overall heat transfer coefficient based on the inside diameter [kW/(m2.K)] Sinnott gives several estimates for fouling factors. For organic liquids the typical value is 5 kW/(m2.K). This can be used on both the shell and tube sides as constant dirt coefficient. Up till now, however, two U’s have been defined in the enthalpy balances: Ui and Us,i. These are only a part of the overall heat transfer coefficient based on the inside diameter and are given by:

ln1 1 1

4

oi

i

i w id i

ddd

U h hλ

⋅

= + +⋅

(B.21)

and

,

ln1 1 1

4

oi

ii i

s i o o o od w

dddd d

U d h d h λ

⋅

= ⋅ + ⋅ +⋅

(B.22)

Both are based on the inner diameter of the tube and reach to the middle of the tube wall. To calculate U the inner and outer fluid film coefficients need to be evaluated. In Sinnott (1996) it is given that:

0.14

0.8 0.33, 0.023 Re Pri e ii i i

w

h DNu η

λ η⋅

= = ⋅ ⋅ ⋅

(B.23)

0.140.8 0.33,

,

0.023 Re Pro e o co o o

c w c

h DNu η

λ η ⋅

= = ⋅ ⋅ ⋅

(B.24)

The Reynolds number is defined as:


B-6

,Re z e ii

v Dρη

⋅ ⋅= (B.25)

, ,Re c z c e oo

c

v Dρη

⋅ ⋅= (B.26)

The Prandtl number is defined as:

Pr pi

C ηλ⋅

= (B.27)

,Pr p c co

c

C ηλ

⋅= (B.28)

The hydraulic diameter is defined as:

4

eCrosssectional areaDWetted Perimeter

⋅= (B.29)

,e i iD d= (B.30)

( )2 2

2 2

,

144 shell tubes o

shell tubes oe o

shell tubes o shell tubes o

D N d D N dDD N d D N d

π

π π

⋅ ⋅ ⋅ − ⋅ − ⋅= =⋅ + ⋅ ⋅ + ⋅

(B.31)

in which:

De,i = Hydraulic diameter inside tubes [m] De,o = Hydraulic diameter in shell [m] λ = Thermal conductivity of the fluid [kW/(m.K)] λc = Thermal conductivity of the coolant [kW/(m.K)] Nui/o = Nusselt number, inner/outer [-] Rei/o = Reynolds number, inner/outer [-] Pri/o = Prandtl number, inner/outer [-] η = Viscosity of the fluid in the reactor[Pa.s] ηc = Viscosity of the coolant [Pa.s] ηw = Viscosity at the wall in the reactor [Pa.s] ηw,c = Viscosity at the wall of the coolant-side [Pa.s] Cp = Heat capacity of fluid in the reactor [kJ/(kg.K)] Cpc = Heat capacity of coolant fluid [kJ/(kg.K)]

These equations hold for both shell and tube sides. With the assumption of turbulent flow there will be no variations in viscosity in the radial direction in a tube or in the shell. Therefore the viscosity-ratio term will disappear and the equations will become:

0.8 0.33, 0.023 Re Pri e ii i i

h DNu

λ⋅

= = ⋅ ⋅ (B.32)

0.8 0.33, 0.023 Re Pro e oo o o

c

h DNu

λ⋅

= = ⋅ ⋅ (B.33)


B-7

Tube wall enthalpy balance Under the assumptions as above the energy balance becomes an enthalpy balance. There is no flow, only conductive transport and the equations for the area of a slice dr, dz are the same. Along with the assumption of symmetrical tubes, this gives us:

( 2 ) 2 ( ) 2 ( )

2 ( ) 2 ( )

r r dr

z z dz

d H r dr dz dT dTr dz r dzdt dr dr

dT dTr dr r drdr dr

π π λ π λ

π λ π λ

+

+

⋅ ⋅ ⋅ ⋅ = + ⋅ ⋅ ⋅ − ⋅ − ⋅ ⋅ ⋅ − ⋅

+ ⋅ ⋅ ⋅ − ⋅ − ⋅ ⋅ ⋅ − ⋅ (B.34)

The density and heat capacity of the wall will be assumed to be constant, as the wall is a solid. This means the enthalpy can be approximated by: pH C Tρ= ⋅ ⋅ (B.35) Using this and once again taking the limit of dr and dz to zero and dividing by dr, dz , r (as it is not a function of the time or dz) and 2π gives:

2 2

2 2

1( )pT T T TCt r r r z

ρ λ∂ ∂ ∂ ∂⋅ ⋅ = ⋅ ⋅ + +∂ ∂ ∂ ∂

(B.36)

in which r ranges from the internal to the external radius. The extra distribution domain (r) of the tube will be neglected, as not to cause excessive calculation times and to use an overall equation in the form UA∆T for the heat transferred. This will give two added dQ’s, as above, but the volume considered for the enthalpy is 0.25*π*(do

2-di2)*dz. Therefore the balance is derived as:

2 2

o i2 2 2 2

o i o i

,i i

( (d d ) dz)(d d ) ( ) (d d ) ( )

d ( ) d ( )

11 144 4z z dz

i w s i c w

d HdT dT

dt dz dz

U dz T T U dz T T

ππ λ π λ

π π+

⋅ ⋅ − ⋅= ⋅ − ⋅ − ⋅ − ⋅ − ⋅ − ⋅

+ ⋅ ⋅ ⋅ ⋅ − + ⋅ ⋅ ⋅ ⋅ −

(B.37)

2

,, 2 2 2 2 2

o i o i

4 d4 d( ) ( )

(d d ) (d d )s i iw w i i

w p w w w c w

UT T UC T T T Tt z

ρ λ⋅ ⋅∂ ∂ ⋅ ⋅

⋅ ⋅ = ⋅ + ⋅ − + ⋅ −∂ ∂ − −

(B.38)

in which:

ρw = Density of tube wall [kg/m3] Cp,w = Heat capacity of tube wall [kJ/(kg.K)] Tw = Temperature of tube wall [K] λw = Thermal conductivity of the wall [kW/(m.K)]

In this equation the wall temperature at place z is calculated, which is assumed to be constant with respect to r. Actually what is done is that the wall temperature in the middle of the wall is taken and this is assumed to be the temperature in the whole wall at place z. To check this we assume the initial temperature of the heat exchanger as 18°C and the maximum temperature as 170°C. If we assume the heat exchanger, as all metal solids used in the process, is made of iron (ρ = 7870 kg/m3, Cp = 0.469 kJ/kg.K, from Jansen and Warmoeskerken (1991)) the maximum amount of heat that can be absorbed by the tubes is given by:


B-8

max

2

( )

468 10 0.25 (0.05 0.044) 7870 0.469 (170 18) 74tubes pQ n L A C T

MJ

ρ

π

= ⋅ ⋅ ⋅ ⋅ ⋅ ∆

= ⋅ ⋅ − ⋅ ⋅ ⋅ − = (B.39)

This is a high assumption, as not the whole tube will achieve the 170 °C level. Comparing this to the amount of heat transferred per second (with a ϕm of 9 kg/s and a Cp of 3 kJ/(kg.K)):

9 3 (140 54) 2.3 /MQ Cp T MJ sϕ ρ•

= ⋅ ⋅ ⋅ ∆ = ⋅ ⋅ − = (B.40) This shows that assuming a constant temperature is actually not permissible. Only if the time-scale under consideration is larger than the residence time (11 minutes) then the heat absorbed (74 MJ) far less than the heat transferred (1500 MJ). It will be assumed that it will give a good average. Another assumption made by assuming the density and heat capacity independent of the temperature is neglecting expansion of the tubes. With a linear expansion coefficient of 12*10-6 m/m.K (for iron), a length of 10 m and a maximum temperature rise of (170-18)°C, the expansion can be approximated by: 612 10 10 (170 18) 2L cm−∆ = ⋅ ⋅ ⋅ − = (B.41) This calculation has been made to show that there is expansion, even though it will be neglected. It is part of the bouncing ball view of modeling: understanding the levels of more detail beneath the one actually chosen. The heating of the distillation column itself will not be modeled. The distillation column consists of approximately 2 m3 of metal. Assuming it is made out of iron and it is heated up from the temperature of the surroundings to 100°C would need approximately 7 MJ of heat. Comparing this to a reboiler that produces 8 MW of heat in steady-state, it can be seen that neglecting this amount does not give a big error. Expansion will be in the order of that of the reactor and as such will also be neglected. The mass balance The same way as the heat balance is derived, a mass balance can also be derived. Here it will immediately be assumed that the tube and shell are symmetrical and there is only one distribution domain (z). Choosing to derive a molar balance, as component balance of a plug-flow reactor, over a slice of the reactor, gives:

,1

,1

22 2

,1

( )

ji

mol i mol i i j jz z dz

ji

v i v i i j jz z dz

ji z i

i j j

dN r dVdt

dV C C C r dVdt

d R dz C v CR dz r R dzdt z

ϕ ϕ ν

ϕ ϕ ν

π π ν π

+

+

= − + ⋅

⋅ = ⋅ − ⋅ + ⋅

⋅ ⋅ ∂ ⋅= − ⋅ ⋅ + ⋅ ⋅∂

∑

∑

∑

(B.42)

,1

( ) mi z i

i j jj

C v C rt z

ν=

∂ ∂ ⋅= − +∂ ∂ ∑ (B.43)

in which:

Ni = Amount of component i [kmol] ϕmol i = Molar flowrate of component i [kmol/s] νi,j = Reaction coefficient of component i in reaction j [-] rj = Reaction rate of reaction j [kmol/(m3.s)]


B-9

Ci = Molar concentration of component i [kmol/m3] From this equation the concentrations will be calculated. The choice for using concentrations in stead of molar fractions was made as concentrations were used in the reaction kinetics. Of course this mass balance can also be used on the shell side, without the reaction term. Once again assuming turbulent flow, and realizing the velocity is in the –z direction, it would be:

, , ,( )i c z c i cC v Ct z

∂ ∂ ⋅= −

∂ ∂ (B.44)

in which:

Ci,c = Molar concentration of component i in the coolant [kmol/m3] vz,c = Velocity of the coolant in the z direction [m/s]

Momentum balance Deriving the momentum balance for a slice of the reactor, with only one distribution domain (z), on the tube side and using the macroscopic τw, gives:

( )

2( ) ( )2 2 2 2 2

d v Vz v v P A P A dA g Vz z dzv z v z w zz z dzdt

v v Pz zR dz R dz R dz R dz R dz gw zt z z

ρϕ ρ ϕ ρ τ ρ

ρ ρπ π π τ π π ρ

⋅ ⋅= ⋅ ⋅ − ⋅ ⋅ + ⋅ − ⋅ − ⋅ + ⋅ ⋅++

∂ ⋅ ∂ ⋅ ∂⋅ ⋅ = − ⋅ ⋅ − ⋅ ⋅ − ⋅ + ⋅ ⋅ ⋅

∂ ∂ ∂

(B.45)

Dividing by the area and dz gives:

2( ) ( )

0v v Pz z gw zt z z

ρ ρτ ρ

∂ ⋅ ∂ ⋅ ∂= = − − − + ⋅∂ ∂ ∂

(B.46)

in which:

P = Pressure [Pa] A = Area [m2] gz = Gravitational acceleration in z direction [m/s2] τw = Shear force at the wall [kg/(m.s2)]

These variables, as far as possible, are all on the tube side. As the time scale of momentum transport is far smaller than that of e.g. enthalpy (i.e. momentum transport occurs at great speed), the momentum balance can be considered to be in a pseudo-steady state and therefore the zero is added. This equation will be used to calculate the pressure-profile. τw is defined for turbulent flow as (Beek and Muttzall):

212w zf vτ ρ= ⋅ ⋅ ⋅ (B.47)

in which:

f = Fanning friction factor [-] <vz> = Average velocity in the z direction [m/s]

Assuming turbulent flow and smooth walls, the Fanning friction factor is found as a function of the Reynolds number:


B-10

0.254 0.316 Reif −= ⋅ (B.48) For the shell side the same equations holds, with directions opposite to the axial direction for τw,c and gz:

2( ) ( ), ,0 ,

v v Pc z c c z c c N gtubes w c c zt z z

ρ ρτ ρ

∂ ⋅ ∂ ⋅ ∂= = − − − ⋅ − + ⋅ −

∂ ∂ ∂ (B.49)

2, ,

12w c c c z cf vτ ρ= ⋅ ⋅ ⋅

(B.50) and 0.254 0.316 Rec of −= ⋅ (B.51) in which:

ρc = Density of coolant [kg/m3] vz,c = Velocity in the z direction on the shell side [m/s] Pc = Pressure shell side [Pa] τw,c = Shear force at the wall on shell side[kg/(m.s2)] fc = Fanning friction factor, shell side [-] Reo = Reynolds number on shell side [-] De,o = Hydraulic diameter in shell [m] ηc = Viscosity on shell side [Pa.s]

For the Reynolds number the absolute value of the velocity should be used. List of assumptions made In deriving the equations above, and in modeling the process assumptions have been made. To give an overview of all assumptions made, they have been listed below. Reactor • There is no shaft work in the system. • The system is symmetrical. • There is no conductive heat transport in the z direction in fluids. • There is no heat flux to the surroundings (infinitely thick insulation). • The flow in both the shell and tube-sides is turbulent, so the physical properties will not

vary in the radial direction. • The dirt coefficients are constant. • There is no temperature profile in tube wall in the radial direction. • The enthalpy of the wall is to be approximated by H = ρ*Cp*T. • There is no evaporation. • The time scale of momentum transport is sufficiently small and the momentum balance is

assumed to not have any hold-up so that it is in a pseudo-steady-state. • All walls are considered to be smooth. • The reactor is placed horizontally. • The reactor is modeled as only one tube and shell pass. • There are no reactions besides the reactions of MeOH and PO to MP-1 and MP-2 and

the reactions of MP-1 and MP-2 with PO to MDP. • The amount of MP-2 and MP-1 formed is calculated by a selectivity times the amount of

MeOH and PO that reacts. • N(OCH3)3 is the tertiary amine used as catalyst. • The selectivity towards MP-2 is 90%, the selectivity towards MP-1 is 10%. • Catalyst is removed after the reactor. • The kinetics are valid up to temperatures of 180 °C and pressures up to 28 bar. • The reaction rate is independent of concentration of MeOH.


B-11

Distillation column: • Both liquid and vapor are well-stirred. • Liquid and vapor are in equilibrium with each other. • Liquid and vapor are ideal. • The change in energy due to varying temperatures and evaporation/condensation is

significantly larger than change in energy due to changes in energy potential and impulse. • The influence of surface tension is negligible. • There is no entrainment of liquid in the vapor and no holdup of vapor in the liquid. • The bottom of the column is cylindrical. • The temperature is the same in both liquid and vapor phase. • There is no vapor flow from the top of the column to bottom. • There is no liquid flow from the reboiler to the tray above it. • All liquid is above the plate area. • The downcomers are not modeled and are therefore assumed to have no accumulation of

mass or heat. • With respect to heat transfer, the condenser and reboiler are over-designed by 25%. • Liquid density is not a function of the pressure. • Friction loss is mainly due to contraction of the flow path. • Trays are sieve trays. • The holes in the sieve trays of the column were punched, leaving a rim of 1 mm. • The temperature on the steam side of the reboiler is constant. • The outside temperature is constant (18°C). • The reboiler heat is fed directly to the liquid in the bottom of the column. • The liquid stream leaving reboiler is level controlled. • The liquid stream leaving condenser drum is level controlled. • No N2 enters the liquid. • The condenser is a cooling tower. • The cooling tower will operate normally above 45°C and not at all below 40°C. • Cooling tower cannot give heat, and reboiler can not provide cooling. • The reboiler is a kettle-type reboiler. • The reboiler can not add any heat if level is below 42 cm, and only partially add heat if the

level is under 60 cm. • The reboiler can not provide any cooling. • LP-steam is at 3 bar and 133.5°C. • MP-steam is at 10 bar and 180°C. • Steam production will not be modeled. • The area of tube connecting tray 1 to the condenser is about 10% of tray area. • The outside pressure and pressure of N2 is 1 bar. General • Energy dissipation is zero or negligibly small with respect to the amount of mechanical

energy that changes from one form into another. • Changes in energy due to varying temperatures are significantly larger than changes in

magnetic, electrical, kinetic, potential and “other” energy. • Physical properties may be extrapolated outside the given temperature domain. • The density and heat capacity of all solids is constant. • All thermal expansion is neglected. • All metal is iron. • The ratio of MeOH : PO is 3.95 : 1. • The economics from the conceptual process design are valid. • MP-2 only generates revenue if fraction > 0.88. • The condenser costs are negligible.


Comparison with MeOH Temperature range 293 - 450

Table C.1. Saturated vapor pressures, MeOH.Aspen, RK-AspenRef. 1 Ref. 2 Ref. 3 error

T PLXANT-1K Pa Pa Pa Pa % % %

293 1.28E+04 1.27E+04 1.28E+04 1.29E+04 0.36 0.15 -1.11300 1.85E+04 1.85E+04 1.85E+04 1.87E+04 0.35 0.15 -0.74350 1.61E+05 1.61E+05 1.61E+05 1.62E+05 0.24 0.03 -0.21400 7.70E+05 7.69E+05 7.71E+05 7.74E+05 0.04 -0.17 -0.57450 2.53E+06 2.53E+06 2.54E+06 2.54E+06 0.00 -0.22 -0.28

Range:Tmin 175.47 175.47 175.47 288Tmax 512.5 512.58 512.58 512.6

Table C.2. Heat of vaporization, MeOH.Aspen, RK-AspenRef. 1 Ref. 4 Ref. 2 error

T DHVLDP-1 avg. measuredK kJ/kmol kJ/kmol kJ/kmol kJ/kmol % % %

293 3.79E+04 3.83E+04 3.83E+04 -0.93 -0.92298 3.77E+04 3.80E+04 3.74E+04 3.80E+04 -0.83 0.68 -0.82300 3.75E+04 3.78E+04 3.78E+04 -0.79 -0.79

323.2 3.61E+04 3.62E+04 3.62E+04 3.62E+04 -0.32 -0.20 -0.31337.9 3.51E+04 3.51E+04 3.53E+04 3.51E+04 0.01 -0.45 0.02363.2 3.33E+04 3.31E+04 3.35E+04 3.31E+04 0.66 -0.44 0.65393.2 3.09E+04 3.04E+04 3.10E+04 3.04E+04 1.57 -0.08 1.55

400 3.03E+04 2.98E+04 2.98E+04 1.80 1.79416.9 2.87E+04 2.80E+04 2.85E+04 2.80E+04 2.46 0.73 2.43443.4 2.57E+04 2.48E+04 2.52E+04 2.48E+04 3.75 1.97 3.71476.9 2.06E+04 1.93E+04 1.96E+04 1.93E+04 6.33 4.82 6.27

Range:Tmin 175.47 175.47 175.47Tmax 512.5 512.58 512.58

Table C.3. Liquid heat capacity, MeOH.Aspen, RK-AspenRef. 1 Ref. 5 Ref. 2 Ref. 6 error

T CPLDIPK kJ/kmol.K kJ/kmol.K kJ/kmol.K kJ/kmol.K kJ/kmol.K % % % %

293 80.2 79.5 79.7 80.1 80.1 0.87 0.61 0.07 0.10298 81.1 79.9 80.6 81.1 1.52 0.64 0.03300 81.5 80.1 81.0 81.5 1.79 0.64 0.01320 85.9 82.0 85.5 86.1 4.62 0.55 -0.15340 91.1 84.1 91.0 91.4 7.62 0.12 -0.34360 96.9 86.7 97.7 97.5 10.62 -0.73 -0.53380 103.6 89.6 105.7 104.3 13.48 -2.02 -0.73400 111.0 93.1 115.1 112.0 16.10 -3.75 -0.93450 132.7 104.5 145.9 134.6 21.27 -9.94 -1.40

Range:Tmin 175.47 176 175.45 175.47Tmax 400 461 337.80 400

Table C.4. Liquid density, MeOH.Aspen, RK-AspenRef. 1 Ref. 2 Ref. 6 error

T DNLDIP-1K kmol/m3 kmol/m3 kmol/m3 kmol/m3 % % %

293 24.8 24.7 24.7 24.7 0.33 0.33 0.32298 24.6 24.6 24.6 0.30 0.30300 24.6 24.5 24.5 0.29 0.29400 21.1 21.2 21.2 -0.39 -0.39450 18.7 18.8 18.8 -0.84 -0.84

Range:Tmin 175.47 175.47 175.47Tmax 512.5 512.58 512.58

Table C.5. Liquid conductivity, MeOH.Aspen, RK-AspenRef. 2 Ref. 6 Ref. 1 Ref. 5 error

T KLDIP-1 (selected values)K W/m.K W/m.K W/m.K W/m.K W/m.K % % % %

293 0.2014 0.2014 0.2020 0.2026 0.00 -0.31 -0.61298 0.2000 0.2000 0.2011 0.00 -0.58300 0.1994 0.1994 0.2005 0.2020 0.00 -0.56 -1.30400 0.1713 0.1713 0.1668 0.1760 0.00 2.63 -2.74480 0.1488 0.1488 0.1266 0.1620 0.00 14.93 -8.86

Range:Tmin 175.47 175.47 175Tmax 337.85 337.85 487

Table C.6. Viscosity, MeOH.Aspen, RK-AspenRef. 2 Ref. 6 Ref. 1 Ref. 5 error

T MULDIP-1 (selected values)K Pa.s Pa.s Pa.s Pa.s Pa.s % % % %

273.15 7.77E-04 8.07E-04 7.82E-04 7.93E-04 -3.78 -0.58 -2.01278.15 7.17E-04 7.43E-04 7.21E-04 7.30E-04 -3.57 -0.43 -1.75

293 5.77E-04 5.91E-04 5.84E-04 5.78E-04 -2.51 -1.27 -0.21298.15 5.38E-04 5.49E-04 5.39E-04 5.42E-04 -2.00 -0.17 -0.74

300 5.25E-04 5.35E-04 5.26E-04 -1.80 -0.16400 2.14E-04 1.82E-04 1.85E-04 15.26 13.86450 1.66E-04 1.25E-04 1.09E-04 24.92 34.60

Range:Tmin 175.47 230 230Tmax 337.85 375 513

References1 Yaws, 19992 Daubert and Danner, 19893 Reid et al., 19884 Majer and Svodoba, 19855 Vargaftik et al., 19966 Jansen en Warmoeskerken, 1991


D-1

Appendix D: Equipment specification The following tables give the specifications of the equipment used. Table D.1. Distillation column. Design item Value Unit Trays (excl. reb/cond) 25 - Feed tray 19 - Reflux ratio 0.218 kmol/kmol Tray spacing 0.45 m Column diameter 2.80 m Column area (cross sectional) 6.16 m2 Downcomer cross-sectional area 0.74 m2 Net cross sectional area 5.42 m2 Active area (= tray area) 4.68 m2 Surface area 2.89 m2 Holes area 0.35 m2 Tray volume 2.74 m3

Weir length 2.10 m Weir height 45 mm Apron height 35 mm Hole diameter 5.0 mm Plate thickness 5.0 mm Width unperforated edge 50 mm Width calming zone 100 mm Area of calming zone 0.38 m2 Perforated area 4.1 m2 Number of holes 17875 - βset 0.6 - α 0.03 - Table D.2. Condenser. Unit Value Unit Mass flowrate (CPD) 7.05 kg/s Average density 748.6 kg/m3 Volumetric flowrate 9.42*10-3 m3/s Hold-up time 300 s Hold-up volume 2.82 m3 Total volume 4.34 m3 Chosen volume 4.50 m3 Chosen diameter 1.79 m Chosen height 1.79 m Area 2.52 m2

Surface area 15.1 m2 Tube area 0.5 m2

α 0.695 - Pset 1.0 bar


D-2

Table D.3. Reboiler. Unit Value Unit Mass flowrate (CPD) 3.18 kg/s Average density 786.8 kg/m3 Volumetric flowrate 4.04*10-3 m3/s Hold-up time 300 s Hold-up volume 1.21 m3 Total volume 1.87 m3 Chosen volume 9.24 m3 Diameter 2.80 m Chosen height 1.50 m Area 6.16 m2

Surface area 25.5 m2 Apron height 100 mm

Table D.4. Reactor. Unit Value Unit Number of tubes 78 - di 44 mm do 50 mm dshell 0.581 m hi,d 5 kW/m2.K ho,d 5 kW/m2.K λw 80.4*10-3 kW/m.K ρw 7870 kg/m3

cp,w 4.690 kJ/kg.K lengthtube 16.32 m lengthtube2 161 m

Table D.5. Other parameters used. Unit Value Unit Uair 0.100 kW/m2.K Ubfw 1.80 kW/m2.K Toutside 291 K Tbfw 407 K R = Rg 8.314 kJ/kmol.K g 9.81 m/s2

gz 0 m/s2

S 0.9 kmol/kmol k0,1 130.3 1/gcat.min k0,2 4.05 l/mol.gcat.min k0,3 4.05 l/mol.gcat.min Ea1 31.24*103 kJ/kmol Ea2 36.55*103 kJ/kmol Ea3 36.55*103 kJ/kmol

Table D.6. Controller parameters (also table 3.1). Controller Setpoint bias Kgain τ Condenser level 1.1 0.0366 -1 15 Condenser heat removal

1.0 -7130 105 15

Reboiler level 0.88 0.0486 -1 105 Reboiler heat added

362 8192 1000 105

Catalyst addition 420 2.5*10-3 2.5*10-4 1000

Appendix E. Steady-state values

E-1

Table E.1. Aspen input data. Variable Amount Unit Feed flowrate 0.1393 kmol/s xPO 6.29*10-5 - xMeOH 0.7496 - xMP-1 0.0247 - xMP-2 0.2225 - xMDP 0.0031 - Temperature of feed 344.05 K Vapor fraction of feed 10-8 - Stages 27 - Feed stage (on stage) 20 - Pcondenser (total condenser) 1 bar Reflux ratio 0.218 kmol/kmolReflux rate 0.02273 kmol/s Total pressure drop 0.09011 bar

Table E.2. Steady-state streams. Stream name MeOH-

recycle Catalyst feed

MeOH feed

PO feed Total MeOH

Shell feed Tube feed Reactor out

Stream number (CPD) 5 6 7 8 10 11 12 13 Molar fractions:

PO 8.40E-05 0 0 1 6.29E-05 0.2022 0.1987 6.15E-05 MeOH 0.9999 0 1 0 0.9999 0.7978 0.7839 0.7333 MP-1 8.26E-10 0 0 0 6.18E-10 4.93E-10 4.85E-10 0.0242 MP-2 3.39E-06 0 0 0 2.54E-06 2.02E-06 1.99E-06 0.2177 MDP 1.21E-23 0 0 0 9.08E-24 7.25E-24 4.03E-24 0.0030 N2/cat 0 1 0 0 0 0 0.0174 0.0218

Flowrate (kmol/s) 0.1043 0.0031 0.0350 0.0353 0.1393 0.1746 0.1777 0.1424 Pressure (bar) 27.5 27.5 27.5 27.5 27.5 27.5 27.5 27.5 Temperature (K) 335.63 295.25 295.05 295.25 324.84 316.08 389.41 406.67 Enthalpy (kJ/kmol) -234856 -449665 -238914 -122262 -235876 -212906 -209752 -283468 Phase (L/V) L L L L L L L L Stream name Column

feed Condenser product

Reflux to column

Purge Reboiler product

Catalyst removal

MeOH removal

Stream number (CPD) 14 15 - - 16 - - Molar fractions:

PO 6.29E-05 8.40E-05 8.40E-05 2.11E-04 1.02E-09 0 8.40E-05 MeOH 0.7480 0.99991 0.99991 0.9338 0.0042 0 0.9999 MP-1 0.0247 8.26E-10 8.26E-10 6.66E-11 0.0983 0 8.26E-10 MP-2 0.2225 3.39E-06 3.39E-06 3.86E-07 0.8852 0 3.39E-06 MDP 0.0031 1.21E-23 1.21E-23 9.20E-26 0.0123 0 1.21E-23 N2/cat 0 0 0 0.0660 0 1 0

Flowrate (kmol/s) 0.1393 0.1043 0.0227 n.n.f. 0.0350 0.0031 n.n.f. Pressure (bar) 1 1 1 1 1.09019 1 27.5 Temperature (K) 344.05 335.63 335.63 335.63 396.29 344.05 335.63 Enthalpy (kJ/kmol) -286513 -234856 -234856 -186307 -434171 -286513 -234856 Phase (L/V) L L L V L L L

Appendix E. Steady-state values

E-2

Figure E.1. Steady-state temperature profiles. Figure E.3. Steady-state liquid flowrates over the weir.

Figure E.2. Steady-state pressure profiles. Figure E.4. Steady-state vapor flowrates through the holes.

Temperature profile

330

340

350

360

370

380

390

400

0 10 20 30

Stage (-)

Tem

pera

ture

(K)

AspengPROMS

Pressure profile

9.80E+04

1.00E+05

1.02E+05

1.04E+05

1.06E+05

1.08E+05

1.10E+05

0 10 20 30

Stage (-)

Pres

sure

(Pa)

AspengPROMS

Liquid flowrates over the weir

0.00

0.05

0.10

0.15

0.20

0 10 20 30

Stage (-)

Flow

rate

(km

ol/s

)

AspengPROMS

Vapor flowrates through the holes

0

0.05

0.1

0.15

0 10 20 30

Stage (-)

Flow

rate

(km

ol/s

)

AspengPROMS

Figure E.5. Steady-state liquid fractions of MeOH. Figure E.7. Steady-state vapor fractions of MeOH.

Figure E.6. Steady-state liquid fractions of MP-2. Figure E.8. Steady-state vapor fractions of MP-2.

Liquid fractions of MeOH

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30

Stage (-)

Frac

tion

(-)

AspengPROMS

Vapor fractions of MeOH

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30

Stage (-)

Frac

tion

(-)

AspengPROMS

Liquid fractions of MP-2

0

0.2

0.4

0.6

0.8

1

0 10 20 30

Stage (-)

Frac

tion

(-)

AspengPROMS

Vapor fractions of MP-2

0

0.2

0.4

0.6

0.8

1

0 10 20 30

Stage (-)

Frac

tion

(-)

AspengPROMS


F-1

Appendix F: Shutdown data The results of shutdown will be presented here.

Figure F.1. Level profile during shutdown. Figure F.2. Dumping profile during shutdown.

Figure F.3. Vapor in downcomer-profile during shutdown.

Figure F.4. Vapor – liquid flows during shutdown.

-0.1

0.0

0.1

0.2

0.3

0.4

1000 2000 3000 4000 5000 6000 7000 8000

Flow

(km

ol/s

)

Time (s)

Normal vapor and liquid flows totrays 10 and 23 during shutdown

Liquid in tray 10 Liqu id in tray 23Vapor in tray 10 Vapor in tray 23


F-2

Figure F.5. Temperature profile during shutdown.

Figure F.6. Pressure profile during shutdown.

Figure F.7. Nitrogen fraction in vapor phase during shutdown.

Figure F.8. MP-2 in liquid and MeOH in vapor before and after shutdown.

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25

Frac

tion

(-)

Tray number (-)

Fractions of MP-2 in the liquid andMeOH in the vapor

XMP-2, st. st.XMP-2, sd.

YMeOH, st. stYMeOH, sd.

Feed PO Catalyst addition control

Reflux ratio

Time (s)

Description

flow, kmol/s

B (flow, kmol/s)

SP (Temp., K)

K Rset

Purge

0 Purge N2 and heat column 0 0 420 0 0 Yes 185 Increase pressure 0 0 420 0 0 Yes 362 Heat reactor 0 0 420 0 0.218 No

10881 Add catalyst and PO 0.0353 2.5E-03 420 0 0.218 No 10999 Start controls 0.0353 2.5E-03 420 2.50E-04 0.218 No 14096 Start steam production 0.0353 2.5E-03 420 2.50E-04 0.218 No 38249 Steady-state 0.0353 2.5E-03 420 2.50E-04 0.218 No

Reboiler controllers Condenser controllers Flow Heat added Flow Heat removed

Time (s)

Description

B (flow, kmol/s)

SP (level, m)

K B (Qreb, kW)

SP (level, m / Temp.(23), K)

K B (flow, kmol/s)

SP (level, m)

K B (Qcond, kW)

SP (P, bar)

K

0 Purge N2 and heat column 0 0.88 0 5000 0.88 0 0.01 1.1 0 0 1 0185 Increase pressure 0 0.88 0 8192* 0.88 -104 0.037 1.1 0 0 4.6 0362 Heat reactor 0 0.88 0 8192 0.88 -104 0.037 1.1 -10 -7130 4.6 105

10881 Add catalyst and PO 0 0.88 0 8192 0.88 -104 0.037 1.1 -10 -7130 4.6 105

10999 Start controls 0.05 0.88 -1 8192 362 103 0.037 1.1 -10 -7130 1 105

14096 Start steam production 0.05 0.88 -1 8192 362 103 0.037 1.1 -10 -7130 1 105

38249 Steady-state 0.05 0.88 -1 8192 362 103 0.037 1.1 -10 -7130 1 105

* in 100 s

Table G.1. Startup schedule.


G-2

Appendix G: Startup data The results of startup will be presented here. The distillation column: Discontinuous phase (0-2000 s):

Figure G.1. Liquid flow during startup (short). Figure G.2. Vapor flow during startup (short).

Figure G.3. Dumping during startup (short). Figure G.4. Vapor escaping through

downcomer during startup (short).


G-3

Figure G.5. Level profile during startup (short).

Figure G.6. Temperature profile during startup (short).

Figure G.7. Pressure profile during startup (short).

Figure G.8. Pressure-drop profile during startup (short).


G-4

Figure G.9. Nitrogen fraction in vapor phase during startup (short). Total startup:

Figure G.10. Liquid flow during startup (total). Figure G.11. Vapor flow during startup (total).

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

100 200 300 400

Frac

tion

(-)

Time (s )

Nitrogen fraction in vapor

Condens er Tray 10 Tray 19 Tray 25 Reboiler


G-5

Figure G.12. Dumping during startup (total). Figure G.13. Vapor escaping through

downcomer during startup (total).

Figure G.14. Level profile during startup (total).

Figure G.15. Temperature profile during startup (total).


G-6

Figure G.16. Pressure profile during startup (total).

Figure G.17. Pressure-drop profile during startup (total).

Figure G.18. Fraction of MeOH in the vapor phase (total).

Figure G.19. Fraction of MP-2 in the vapor phase (total).


G-7

Figure G.20. Fraction of MeOH in the liquid phase (total).

Figure G.21. Fraction of MP-2 in the liquid phase (total).

Figure G.22. Feed and product flows (total).

0.0

0.1

0.2

0.3

0.4

0 10000 20000 30000 40000 50000 60000

Feed

(km

ol/s

)

Time (s)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Fraction (-)

Feed and product of the column

Feed (left ) Product, condenser (left ) Product, reboiler (left )x ,MP-2, feed (right ) x ,MeOH, condenser (right) x,MP-2, reboiler (right)


G-8

Figure G.23. Temperatures in condenser and reboiler (total).

Figure G.24. Duties in condenser and reboiler (total).

-10000

-5000

0

5000

10000

15000

10000 20000 30000 40000 50000 60000

Dut

y (k

W)

Time (s)

Duties in condenser and reboiler

Qcond Qreb

250

300

350

400

450

0 10000 20000 30000 40000 50000 60000

Tem

pera

ture

(K)

Time (s)

Temperatures in condenser and reboiler

Condenser Reboiler


G-9

Reactor (total):

Figure G.25. Temperature profile in the tubes (total).

Figure G.26. Temperature profile in the first shell (total).

Figure G.27. Fraction of MP-2 in first tube (total).

Figure G.28. Fraction of PO in first tube (total).


G-10

Figure G.29. Fraction of MP-1 in first tube (total).

Figure G.30. Fraction of MeOH in first tube (total).

Figure G.31. Influence of catalyst flow on reaction rate (total).

-0.005

0.000

0.005

0.010

0.015

0.020

10000 20000 30000 40000 50000Reac

tion

rate

(km

ol/m

3.s)

Time (s) 0.000

0.005

0.010

0.015

Flow catalyst (km

ol/s)

Effect of catalyst flowrate on reaction rate

Reaction rate (1), 8 m (left ) Catalys t flowrate (right )

Description base opt4 Condenser, 4.8 bar Condenser, 4.4 bar Condenser, level 0.7 Condenser, level 1.1 Reboiler, 4 MW bias Based on true base

case optimized base case

base opt4 base opt4 base* opt4 base* opt4* base opt4

Runtime (s) 8083 8103 8333 8371 7852 8077 16320 X 16614 17624 6881 7285Endtime (s) 60000 60000 60000 60000 60000 60000 60000 60000 60000 60000 60000Cum. Cashflow (fl) -2819 -2039 -2766 -1959 -2877 -2125 -4620 X -2756 -2206 -2831 -2050Time column feed, xMP-2=0.15 (s)

13666 13652 13792 13776 13536 13524 13753 13685 13631 13664 13650

Conversion PO (-) 0.999750 0.999621 0.999752 0.999621 0.999752 0.999621 0.999861 0.99974 0.99964 0.99975 0.999621PO added (kmol) 1733.91 1733.52 1729.54 1729.23 1738.4 1737.95 1730.42 1733.27 1734.24 1733.98 1733.6MeOH added (kmol) 1708.73 1712.38 1704.18 1707.65 1713.51 1717.21 1706.67 1711.64 1715.37 1710.97 1715.11Catalyst added (kmol) 155.862 145.813 155.116 145.03 156.654 146.642 169.509 156.952 146.976 155.867 145.818MeOH removed (kmol) 222.216 209.563 222.184 209.172 222.286 209.899 208.058 238.539 224.361 224.538 212.349MeOH removed (m3) 5156.72 4860.45 5154.43 4849.79 5159.91 4869.81 4856.83 5512.5 5184.81 5207.39 4921.06Purged (kmol) 3.03816 3.1431 3.03816 3.1431 3.03816 3.1431 2.96636 2.98177 2.97828 3.04192 3.14626MeOH purged (kmol) 0.46794 0.572849 0.467938 0.572849 0.467938 0.572849 0.396155 0.42853 0.4283 0.47169 0.576004N2 purged (kmol) 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.55304 2.54978 2.57 2.57Bottoms onspec (kmol) 1602.49 1607.89 1598.7 1604.28 1606.38 1611.58 1597.18 1602.01 1608.35 1602.62 1608.06Bottoms offspec (kmol) 16.0987 13.1429 15.1313 12.2069 17.1441 14.1554 21.5398 15.6702 13.5785 15.8933 12.9336Bottoms offspec (m3) 212.216 144.245 198.059 132.289 227.646 157.326 291.436 206.088 149.668 209.237 141.617Initial T condenser (K) 291.368 291.368 291.368 291.368 291.368 291.368 291.368 291.368 291.368 291.368 291.368Initial T reboiler (K) 316.388 325.891 316.388 325.891 316.388 325.891 316.388 316.388 325.891 316.388 325.891Initial P condenser (Pa) 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4Initial P reboiler (Pa) 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9dMass/dt (kg/s) -2.92E-05 -1.88E-05 -2.82E-05 -1.77E-05 -3.03E-05 -2.01E-05 -2.50E-05 -2.97E-05 -1.82E-05 -2.91E-05 -1.86E-05dTw/dt,max, reactor wall (K/s)

1.35426 1.29442 1.38571 1.30517 1.33054 1.28739 1.31518 1.35787 1.29308 1.35448 1.29481

Qcond (kW) -4420.47 -4402.13 -4420.47 -4402.13 -4420.47 -4402.13 -4540.14 -4412.9 -4412.94 -4420.47 -4402.13Qreb (kW) 5358.41 5355.48 5358.41 5355.48 5358.41 5355.48 5377.36 5357.22 5357.19 5358.41 5355.48* Run parallel with other processes.

Table H.1. Optimization data.

Description Reboiler, 6 MW bias Reboiler, 3 MW in 50 s

Reboiler, 3 MW in 150 s

PO-feed in 2 PO-feed in 400 s Reboiler, level 0.81

Based on base opt4 base opt4 base opt4 base op base opt4 base* opt4* Runtime (s) 6297 6966 6920 6884 6692 7363 7044 8 7182 7562 14220 17470Endtime (s) 60000 60000 60000 60000 60000 60000 60000 0 60000 60000 60000 60000Cum. Cashflow (fl) -2829 -2046 -2823 -2042 -2816 -2036 -3042 -3339 -2763 -3835 -3026Time column feed, xMP-2=0.15 (s)

13671 13657 13669 13655 13664 13649 13763 7 13865 13484 13570 13572

Conversion PO (-) 0.99975 0.999621 0.999752 0.999621 0.999752 0.999621 0.999752 0.99975 0.99621 0.99983 0.999727PO added (kmol) 1733.74 1733.34 1733.81 1733.42 1734 1733.62 1730.38 9 1726.85 1726.46 1737.12 1736.17MeOH added (kmol) 1708.6 1711.73 1708.75 1712.25 1708.87 1712.58 1706.01 9 1704.08 1707.94 1716.28 1719.66Catalyst added (kmol) 155.848 145.797 155.854 145.804 155.87 145.819 156.526 8 157.615 148.337 165.353 153.756MeOH removed (kmol) 222.179 209.033 222.315 209.516 222.293 209.701 222.984 MeOH removed (m3) 5155.97 4848.98 5158.91 4859.42 5158.39 4863.4 5177.5 Purged (kmol) 3.03452 3.13683 3.03823 3.14319 3.03823 3.14319 3.03823 MeOH purged (kmol) 0.4643 0.566578 0.468005 0.572943 0.468005 0.572943 0.468005 N2 purged (kmol) 2.57 2.57 2.57 2.57 2.57 2.57 2.57 Bottoms onspec (kmol) 1602.28 1607.64 1602.38 1607.77 1602.59 1608 1598.62 Bottoms offspec (kmol) 16.2171 13.2677 16.1304 13.1761 16.0665 13.1091 16.5828 Bottoms offspec (m3) 213.951 145.816 212.687 144.663 211.756 143.82 218.931 Initial T condenser (K) 291.368 291.368 291.368 291.368 291.368 291.368 291.368 Initial T reboiler (K) 316.388 325.891 316.388 325.891 316.388 325.891 316.388 Initial P condenser (Pa) 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 Initial P reboiler (Pa) 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 dMass/dt (kg/s) -2.93E-05 -1.89E-05 -2.92E-05 -1.89E-05 -2.92E-05 -1.88E-05 -3.74E-05 -dTw/dt,max, reactor wall (K/s)

1.35413 1.29419 1.35422 1.29434 1.3543 1.2945 1.34281

Qcond (kW) -4420.47 -4402.13 -4420.47 -4402.13 -4420.47 -4402.13 -4420.47 Qreb (kW) 5358.41 5355.48 5358.41 5355.48 5358.41 5355.48 5358.41 * Run parallel with other processes.

Table H.1. Optimization data, continued.

00 s

t4 750

6000-23441374

0.999621729.91709.7146.77
210.422 224.518 211.907 219.518 208.4924883.04 5215.77 4919.95 5110.03 4852.843.14319 3.03823 3.14319 2.95509 2.968380.57294 0.46801 0.57294 0.3849 0.398182
2.57 2.57 2.57 2.57 2.571603.72 1594.62 1599.27 1601.8 1605.3714.0003 17.3127 15.3248 21.5269 19.4425154.926 229.705 172.269 306.667 242.487291.368 291.368 291.368 291.368 291.368325.891 316.388 325.891 316.388 325.89199703.4 99703.4 99703.4 99703.4 99703.499707.9 99707.9 99707.9 99707.9 99707.9

2.69E-05 -4.88E-05 -3.89E-05 -3.25E-05 -2.51E-051.28722 1.3275 1.27799 1.32648 1.28595

-4402.1 -4420.5 -4402.13 -4499.42 -4475.275355.48 5358.41 5355.48 5370.91 5367.07

Description Reboiler, level 0.95 MeOH flow, factor 0.9

MeOH flow, factor 1.1

Catalyst, setpoint 410 K

Cse43

Reflux, 0.291

Reflux, 0.175

Reboiler, initial fraction MP-2 0.4

Reboiler, initial fraction MP-2 0.6

Based on base* opt4* base opt4 base opt4 base* ba base* base* base* base* Runtime (s) 15343 18051 8008 8812 7702 7599 16906 6 16736 16560 15814 16730Endtime (s) 60000 60000 60000 60000 60000 60000 60000 0 60000 60000 60000 60000Cum. Cashflow (fl) -2814 -1478 -3204 -2318 -2581 -1842 -3454 -3084 -2667 -2842 -2752Time column feed, xMP-2=0.15 (s)

13608 13532 14887 14864 12680 12667 13689 6 13691 13656 13656 13677

Conversion PO (-) 0.99975 0.99965 0.999752 0.999621 0.999752 0.999621 0.999827 0.99975 0.99975 0.99976 0.999743PO added (kmol) 1735.97 1737.73 1690.75 1690.71 1768.76 1768.32 1733.91 1733.02 1734.26 1734.25 1733.53MeOH added (kmol) 1703.82 1707.04 1658.05 1661.74 1752.12 1755.77 1707.18 Catalyst added (kmol) 155.999 148.014 152.091 142.39 158.911 148.593 165.07 MeOH removed (kmol) 220.268 203.602 215.496 202.35 229.449 217.085 223.116 MeOH removed (m3) 5108.38 4722.54 5008.38 4699.89 5316.51 5027.94 5177.58 Purged (kmol) 3.02472 3.02161 3.03774 3.14189 3.03855 3.1436 3.0382 MeOH purged (kmol) 0.46708 0.466857 0.46752 0.571643 0.46833 0.573346 0.467983 N2 purged (kmol) 2.55742 2.55453 2.57 2.57 2.57 2.57 2.57 Bottoms onspec (kmol) 1607.26 1619.85 1560.39 1567 1636.22 1641.13 1604.29 Bottoms offspec (kmol) 14.4429 7.07746 14.1922 10.5729 18.5691 15.8112 12.8745 Bottoms offspec (m3) 177.537 75.7069 184.793 114.165 248.644 178.591 166.582 Initial T condenser (K) 291.368 291.368 291.368 291.368 291.368 291.368 291.368 Initial T reboiler (K) 316.388 325.891 316.388 325.891 316.388 325.891 316.388 Initial P condenser (Pa) 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 99703.4 Initial P reboiler (Pa) 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 99707.9 dMass/dt (kg/s) -2.20E-05 -1.01E-05 -3.15E-05 -1.88E-05 -2.79E-05 -1.93E-05 -2.19E-05 -dTw/dt,max, reactor wall (K/s)

1.35456 1.29239 1.35495 1.2941 1.35355 1.29471 1.47533

Qcond (kW) -4420.31 -4420.32 -4420.47 -4402.13 -4420.47 -4402.13 -4420.46 Qreb (kW) 5358.39 5358.36 5358.42 5355.49 5358.4 5355.47 5358.42 * Run parallel with other processes.

Table H.1. Optimization data, continued.
atalyst, tpoint 0 K
se* 16676000-24391364

0.999671733.91
1710.96 1712.84 1706.93 1706.65 1710.2149.316 155.802 155.885 156.689 154.943221.893 225.662 220.961 228.845 216.479
5148.7 5233.59 5128.35 5310.08 5023.123.03816 3.03816 3.03816 3.02267 3.063570.46794 0.46794 0.46794 0.45245 0.493344

2.57 2.57 2.57 2.57 2.571600.84 1600.76 1603.37 1598.77 1605.7119.4198 18.4961 14.6652 18.4359 13.8053260.688 247.3 191.673 266.904 165.937291.368 291.368 291.368 291.368 291.368316.388 316.388 316.388 313.195 320.19999703.4 99703.4 99703.4 99703.4 99703.499707.9 99707.9 99707.9 99707.9 99707.9

3.63E-05 -3.09E-05 -2.81E-05 -4.05E-05 -2.07E-051.30102 1.35404 1.35426 1.35132 1.35781

-4420.5 -4420.5 -4420.47 -4427.05 -4412.95358.39 5358.41 5358.41 5359.45 5357.21

######################################################################## # # # Startup and Shutdown of a Glycolether process # # Constructed by J.R. Law # # April 2000 - April 2001 # # # ######################################################################## #----------------------------------------------------------------------- # Declarations #----------------------------------------------------------------------- DECLARE TYPE #----------------------------------------------------------------------- Coeff = -1 : -1E1 : 1E1 UNIT = "-" Concentration = 25 : -1E-6 : 1E2 UNIT = "kmol/m3" Conductivity = 2E-4 : -1E-6 : 1E2 UNIT = "kW/m.K" Density = 800 : 400 : 1200 UNIT = "kg/m3" Energy = -1E6 : -1E9 : 0 UNIT = "kJ" EnergyRate = -1E4 : -1E9 : 2E4 UNIT = "kJ/s" Energy_V = -1E6 : -1E9 : 1E9 UNIT = "kJ/m3" Enthalpy = -1E6 : -1E9 : 1E9 UNIT = "kJ/m3" EnthalpyDensity = -1E5 : -1E6 : 1E6 UNIT = "kJ/kmol" Fraction = 0.1 : -1E-8 : 1.00000001 UNIT = "-" Friction = 7E-3 : 1E-4 : 5 UNIT = "-" Heatcapacity = 1E2 : -1E-4 : 1E4 UNIT = "kJ/kmol.K" Heatcapacity_kg = 4E3 : -1E-4 : 1E4 UNIT = "kJ/kg.K" Heattransfer = 40 : -1E-4 : 1E4 UNIT = "kW/m2.K" Length = 0.1 : -1E-6 : 5 UNIT = "m" LiqDensity = 800 : 400 : 1200 UNIT = "kg/m3" LiqMolarVolume = 7E-2 : 1E-4 : 1E1 UNIT = "m3/kmol" Liquidmolardensity = 10 : 0.1 : 1E3 UNIT = "kmol/m3" MolarRate = 0.2 : -1E-4 : 20 UNIT = "kmol/s" MoleFlow = 0.2 : -1E4 : 100 UNIT = "kmol/s" #for test variables Moles = 1 : -1E-9 : 1E3 UNIT = "kmol" Molweight = 1E2 : 10 : 1E3 UNIT = "kg/kmol" NoType = 3E3 : -1E20 : 1E20 UNIT = "-" NoType_high = 3E3 : 1E2 : 1E7 UNIT = "-" NoType_low = 1 : 1E-4 : 1E3 UNIT = "-" Pressure = 1E5 : 0 : 8E6 UNIT = "Pa" Reaction = 1E-2 : -1E-6 : 1E2 UNIT = "kmol/m3.s" Shear = 2E-2 : 1E-5 : 1E2 UNIT = "kg/m.s2" Signal = 1 : -1e10 : 1e10 UNIT = "-" Temperature = 410.0 : 270 : 480 UNIT = "K" VapDensity = 1 : 1E-4 : 50 UNIT = "kg/m3" VapMolarVolume = 27 : 1E-1 : 1E2 UNIT = "m3/kmol" Vapormolardensity = 4E-2 : -1E-6 : 1E1 UNIT = "kmol/m3" Velocity = 0.1 : -1E-6 : 1E2 UNIT = "m/s" Velocity_neg = -0.1 : -1E2 : 1E-6 UNIT = "m/s" Viscosity = 1E-4 : -1E-4 : 1E2 UNIT = "Pa.s" STREAM DensityStream IS VapDensity,VapMolarVolume FlowStream IS MolarRate Heightstream IS Length MainStream IS MolarRate, Fraction, Pressure, Temperature, EnthalpyDensity MainStreamC IS MolarRate, Concentration, Pressure, Temperature, EnthalpyDensity ProdStream IS MolarRate, Fraction, Pressure, Temperature, EnthalpyDensity TPCFStream IS MolarRate, Concentration, Pressure, Temperature TPXFStream IS MolarRate, Fraction, Pressure, Temperature END # Declare #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # Physical Properties: PO, MeOH, MP-1, MP-2, MDP, catalyst (e.g. N(OCH3)3) #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODEL ASP_DATABASE PARAMETER NoComp AS INTEGER

R AS REAL VARIABLE Cpl_mdp AS Heatcapacity #kJ/kmol.K Cpl_meoh AS Heatcapacity #kJ/kmol.K Cpl_mix AS Heatcapacity #kJ/kmol.K Cpl_mp1 AS Heatcapacity #kJ/kmol.K Cpl_mp2 AS Heatcapacity #kJ/kmol.K Cpl_po AS Heatcapacity #kJ/kmol.K Cpv_n2 AS Heatcapacity #kJ/kmol.K dHvap_mdp AS EnthalpyDensity #kJ/kmol dHvap_meoh AS EnthalpyDensity #kJ/kmol dHvap_mp1 AS EnthalpyDensity #kJ/kmol dHvap_mp2 AS EnthalpyDensity #kJ/kmol dHvap_po AS EnthalpyDensity #kJ/kmol H_L_298_mdp AS EnthalpyDensity #kJ/kmol H_L_298_meoh AS EnthalpyDensity #kJ/kmol H_L_298_mp1 AS EnthalpyDensity #kJ/kmol H_L_298_mp2 AS EnthalpyDensity #kJ/kmol H_L_298_po AS EnthalpyDensity #kJ/kmol H_L_T_mdp AS EnthalpyDensity #kJ/kmol H_L_T_meoh AS EnthalpyDensity #kJ/kmol H_L_T_mixc AS EnthalpyDensity #kJ/kmol H_L_T_mp1 AS EnthalpyDensity #kJ/kmol H_L_T_mp2 AS EnthalpyDensity #kJ/kmol H_L_T_po AS EnthalpyDensity #kJ/kmol H_V_298_mdp AS EnthalpyDensity #kJ/kmol H_V_298_meoh AS EnthalpyDensity #kJ/kmol H_V_298_mp1 AS EnthalpyDensity #kJ/kmol H_V_298_mp2 AS EnthalpyDensity #kJ/kmol H_V_298_po AS EnthalpyDensity #kJ/kmol H_V_T_mdp AS EnthalpyDensity #kJ/kmol H_V_T_meoh AS EnthalpyDensity #kJ/kmol H_V_T_mix AS EnthalpyDensity #kJ/kmol H_V_T_mp1 AS EnthalpyDensity #kJ/kmol H_V_T_mp2 AS EnthalpyDensity #kJ/kmol H_V_T_n2 AS EnthalpyDensity #kJ/kmol H_V_T_po AS EnthalpyDensity #kJ/kmol Ldens_mass_mix AS Liqdensity #kg/m3 Ldens_mol_cat AS Liquidmolardensity #kmol/m3 Ldens_mol_mdp AS Liquidmolardensity #kmol/m3 Ldens_mol_meoh AS Liquidmolardensity #kmol/m3 Ldens_mol_mix AS Liquidmolardensity #kmol/m3 Ldens_mol_mp1 AS Liquidmolardensity #kmol/m3 Ldens_mol_mp2 AS Liquidmolardensity #kmol/m3 Ldens_mol_po AS Liquidmolardensity #kmol/m3 Liqmolvol_cat AS LiqMolarVolume #m3/kmol Liqmolvol_mdp AS LiqMolarVolume #m3/kmol Liqmolvol_meoh AS LiqMolarVolume #m3/kmol Liqmolvol_mix AS LiqMolarVolume #m3/kmol Liqmolvol_mp1 AS LiqMolarVolume #m3/kmol Liqmolvol_mp2 AS LiqMolarVolume #m3/kmol Liqmolvol_po AS LiqMolarVolume #m3/kmol MolWeight_avg_liq AS Molweight #kg/kmol MolWeight_avg_vap AS Molweight #kg/kmol MolWeight_cat AS Molweight #kg/kmol MolWeight_mdp AS Molweight #kg/kmol MolWeight_meoh AS Molweight #kg/kmol MolWeight_mp1 AS Molweight #kg/kmol MolWeight_mp2 AS Molweight #kg/kmol MolWeight_n2 AS Molweight #kg/kmol MolWeight_po AS Molweight #kg/kmol P AS Pressure #Pa T AS Temperature #K T0 AS Temperature #K Vapmolvol_mix AS VapMolarVolume #m3/kmol Vappres_all AS ARRAY(Nocomp) OF Pressure #Pa Vappres_mdp AS Pressure #Pa Vappres_meoh AS Pressure #Pa Vappres_mp1 AS Pressure #Pa Vappres_mp2 AS Pressure #Pa Vappres_po AS Pressure #Pa Vdens_mass_mix AS Vapdensity #kg/m3 Vdens_mol_mix AS Vapormolardensity #kmol/m3 X AS ARRAY(2,Nocomp) OF Fraction #-

EQUATION #Physical properties from Aspen #Liquid density Ldens_mol_po = (1.4855/0.2763^(1+(1-T/482.25)^0.29365));#kmol/m3 Ldens_mol_meoh = (2.3267/0.27073^(1+(1-T/512.5)^0.24713));#kmol/m3 Ldens_mol_mp1 = (0.92789/0.2728^(1+(1-T/566)^0.2052)) ;#kmol/m3 Ldens_mol_mp2 = (0.84648/0.24886^(1+(1-T/553)^0.3069)) ;#kmol/m3 Ldens_mol_mdp = (0.56992/0.26585^(1+(1-T/612)^0.28571)) ;#kmol/m3 Ldens_mol_cat = Ldens_mol_mp1; #kmol/m3, assume density catalyst = density MP-1 Liqmolvol_po = 1/Ldens_mol_po ;#m3/kmol Liqmolvol_meoh = 1/Ldens_mol_meoh;#m3/kmol Liqmolvol_mp1 = 1/Ldens_mol_mp1 ;#m3/kmol Liqmolvol_mp2 = 1/Ldens_mol_mp2 ;#m3/kmol Liqmolvol_mdp = 1/Ldens_mol_mdp ;#m3/kmol Liqmolvol_cat = 1/Ldens_mol_cat ;#m3/kmol Liqmolvol_mix = X(1,1)*Liqmolvol_po + X(1,2)*Liqmolvol_meoh+ X(1,3)*Liqmolvol_mp1 + X(1,4)*Liqmolvol_mp2 + X(1,5)*Liqmolvol_mdp + X(1,6)*Liqmolvol_cat ; #m3/kmol, with catalyst #X(1,6) for N2 will be 0 Ldens_mol_mix = 1/Liqmolvol_mix;#kmol/m3 Ldens_mass_mix = Ldens_mol_mix * MolWeight_avg_liq; #Vapor density Vdens_mol_mix = P/(R*T);# kmol/m3, watch unit of R, 8.314413E3 J/kmol.K! Vdens_mass_mix = Vdens_mol_mix * MolWeight_avg_vap; #kg/m3 Vapmolvol_mix = 1/Vdens_mol_mix; #m3/kmol #Vapor pressure Vappres_po = EXP(91.037-5976.3/T-10.686*LOG(T)+1.1993E-05*T*T); #Pa Vappres_meoh = EXP(82.718-6904.5/T-8.8622*LOG(T)+0.7466E-05*T*T); #Pa Vappres_mp1 = EXP(65.376-7185.1/T-6.0189*LOG(T)+2.2873E-17*T^6); #Pa Vappres_mp2 = EXP(62.333-6886.7/T-5.5896*LOG(T)+2.4555E-17*T^6); #Pa Vappres_mdp = EXP(64.266-8139.6/T-5.7434*LOG(T)+1.4556E-17*T^6); #Pa Vappres_all(1) = Vappres_po ; Vappres_all(2) = Vappres_meoh; Vappres_all(3) = Vappres_mp1 ; Vappres_all(4) = Vappres_mp2 ; Vappres_all(5) = Vappres_mdp ; Vappres_all(6) = 0;#Pa, no Vappres N2 #Heat of vaporization dHvap_po = ((39957)*(1-T/482.25)^(0.36659));#kJ/kmol dHvap_meoh = ((50451)*(1-T/512.5)^(0.33594)); #kJ/kmol dHvap_mp1 = ((53688)*(1-T/566)^(0.23092)); #kJ/kmol dHvap_mp2 = ((52022)*(1-T/553)^(0.22103)); #kJ/kmol dHvap_mdp = ((61013)*(1-T/612)^(0.19259)); #kJ/kmol #Liquid heat capacity Cpl_po = (167910-696.6*T+2.45*T*T-0.0021734*T^3)/1000; #kJ/kmol.K Cpl_meoh = (105800-362.23*T+0.9379*T*T)/1000; #kJ/kmol.K Cpl_mp1 = (67929+448.12*T)/1000; #kJ/kmol.K Cpl_mp2 = (154110+213.39*T)/1000; #kJ/kmol.K Cpl_mdp = (206590+420.21*T)/1000; #kJ/kmol.K Cpl_mix = X(1,1)*Cpl_po + X(1,2)*Cpl_meoh+ X(1,3)*Cpl_mp1 + X(1,4)*Cpl_mp2 + X(1,5)*Cpl_mdp ; #kJ/kmol.K #Vapor heat capacity Cpv_n2 = (29105 +8614.9*(1701.6/T/SINH(1701.6/T))*(1701.6/T/SINH(1701.6/T)) +103.47*(909.79/T/COSH(909.79/T))*(909.79/T/COSH(909.79/T))) /1000; #kJ/kmol.K #Enthalpies #Enthalpy of ideal gas @ 25 °C T0 = 298.15; #Reference temperature = 25 °C

H_V_298_po = - 93700;#kJ/kmol H_V_298_meoh = -200940;#kJ/kmol H_V_298_mp1 = -404300;#kJ/kmol H_V_298_mp2 = -403900;#kJ/kmol H_V_298_mdp = -607200;#kJ/kmol #Enthalpy of liquid @ 25 °C, HL_298 = HV_298-dHv_298 H_L_298_po = H_V_298_po -((39957)*(1-298/482.25)^(0.36659));#kJ/kmol H_L_298_meoh = H_V_298_meoh-((50451)*(1-298/512.5)^(0.33594));#kJ/kmol H_L_298_mp1 = H_V_298_mp1 -((53688)*(1-298/566)^(0.23092));#kJ/kmol H_L_298_mp2 = H_V_298_mp2 -((52022)*(1-298/553)^(0.22103));#kJ/kmol H_L_298_mdp = H_V_298_mdp -((61013)*(1-298/612)^(0.19259));#kJ/kmol #Enthalpy of liquid = Enthalpy of liquid @ 25 °C + integral(Cp.dT) H_L_T_po = H_L_298_po + (167910*(T-T0) -696.6 /2*(T-T0)*(T-T0)+2.45/3*(T-T0)^3-0.0021734/4*(T-T0)^4)/1000; H_L_T_meoh = H_L_298_meoh + (105800*(T-T0)-362.23/2*(T-T0)*(T-T0)+0.9379/3*(T-T0)^3)/1000; H_L_T_mp1 = H_L_298_mp1 + ( 67929*(T-T0)+448.12/2*(T-T0)*(T-T0))/1000; H_L_T_mp2 = H_L_298_mp2 + (154110*(T-T0)+213.39/2*(T-T0)*(T-T0))/1000; H_L_T_mdp = H_L_298_mdp + (206590*(T-T0)+420.21/2*(T-T0)*(T-T0))/1000; #Enthalpy of vapor = Enthalpy of liquid + Heat of vaporization H_V_T_po = H_L_T_po + dHvap_po ; H_V_T_meoh = H_L_T_meoh + dHvap_meoh; H_V_T_mp1 = H_L_T_mp1 + dHvap_mp1 ; H_V_T_mp2 = H_L_T_mp2 + dHvap_mp2 ; H_V_T_mdp = H_L_T_mdp + dHvap_mdp ; H_V_T_n2 = (29105*(T-T0)+8614.9*1701.6*COSH(1701.6/T)/SINH(1701.6/T) -103.47*909.79*SINH(909.79/T)/COSH(909.79/T) -8614.9*1701.6*COSH(1701.6/T0)/SINH(1701.6/T0) +103.47*909.79*SINH(909.79/T0)/COSH(909.79/T0))/1000; #Enthalpies of mixtures H_L_T_mixc = X(1,1)*H_L_T_po + X(1,2)*H_L_T_meoh+ X(1,3)*H_L_T_mp1 + X(1,4)*H_L_T_mp2 + X(1,5)*H_L_T_mdp ; #without catalyst H_V_T_mix = X(2,1)*H_V_T_po + X(2,2)*H_V_T_meoh+ X(2,3)*H_V_T_mp1 + X(2,4)*H_V_T_mp2 + X(2,5)*H_V_T_mdp + X(2,6)*H_V_T_n2 ; #without catalyst, with N2 #Molecular weights MolWeight_po = 58.081;#kg/kmol MolWeight_meoh = 32.042;#kg/kmol MolWeight_mp1 = 90.122;#kg/kmol MolWeight_mp2 = 90.122;#kg/kmol MolWeight_mdp = 148.202;#kg/kmol MolWeight_cat = 107.109;#kg/kmol, N(OCH3)3 MolWeight_n2 = 28.013;#kg/kmol MolWeight_avg_liq = X(1,1)*MolWeight_po + X(1,2)*MolWeight_meoh+ X(1,3)*MolWeight_mp1 + X(1,4)*MolWeight_mp2 + X(1,5)*MolWeight_mdp + X(1,6)*MolWeight_cat ;#kg/kmol, cat in liquid or no N2 MolWeight_avg_vap = X(2,1)*MolWeight_po + X(2,2)*MolWeight_meoh+ X(2,3)*MolWeight_mp1 + X(2,4)*MolWeight_mp2 + X(2,5)*MolWeight_mdp + X(2,6)*MolWeight_n2 ;#kg/kmol, N2 in vapor END #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # Physical Properties: N2

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODEL ASP_DATABASE_N2 VARIABLE H_V_T_n2 AS EnthalpyDensity #kJ/kmol T AS Temperature #K T0 AS Temperature #K EQUATION #Physical properties from Aspen #Enthalpies #Enthalpy of ideal gas @ 25 °C T0 = 298.15; #Reference temperature = 25 °C H_V_T_n2 = (29105*(T-T0) +8614.9*1701.6*COSH(1701.6/T)/SINH(1701.6/T) -103.47*909.79*SINH(909.79/T)/COSH(909.79/T) -8614.9*1701.6*COSH(1701.6/T0)/SINH(1701.6/T0) +103.47*909.79*SINH(909.79/T0)/COSH(909.79/T0))/1000; END #-------------------------------------------------------------------------- MODEL ASP_DATABASE_distribution PARAMETER NoComp AS INTEGER Reactorlength AS REAL # Reactor length DISTRIBUTION_DOMAIN Axial AS (0:ReactorLength) VARIABLE Cpl_mdp AS DISTRIBUTION(Axial) OF Heatcapacity #kJ/kmol.K Cpl_meoh AS DISTRIBUTION(Axial) OF Heatcapacity #kJ/kmol.K Cpl_mp1 AS DISTRIBUTION(Axial) OF Heatcapacity #kJ/kmol.K Cpl_mp2 AS DISTRIBUTION(Axial) OF Heatcapacity #kJ/kmol.K Cpl_po AS DISTRIBUTION(Axial) OF Heatcapacity #kJ/kmol.K Cpl_total_mass AS DISTRIBUTION(Axial) OF Heatcapacity_kg #kJ/kmol.K Cpl_total_mol AS DISTRIBUTION(Axial) OF Heatcapacity #kJ/kmol.K Eta_cat AS DISTRIBUTION(Axial) OF Viscosity #Pa.s Eta_mdp AS DISTRIBUTION(Axial) OF Viscosity #Pa.s Eta_meoh AS DISTRIBUTION(Axial) OF Viscosity #Pa.s Eta_mp1 AS DISTRIBUTION(Axial) OF Viscosity #Pa.s Eta_mp2 AS DISTRIBUTION(Axial) OF Viscosity #Pa.s Eta_po AS DISTRIBUTION(Axial) OF Viscosity #Pa.s Eta_total AS DISTRIBUTION(Axial) OF Viscosity #Pa.s H_L_298_mdp AS EnthalpyDensity #kJ/kmol H_L_298_meoh AS EnthalpyDensity #kJ/kmol H_L_298_mp1 AS EnthalpyDensity #kJ/kmol H_L_298_mp2 AS EnthalpyDensity #kJ/kmol H_L_298_po AS EnthalpyDensity #kJ/kmol H_L_T_mdp AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kmol H_L_T_meoh AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kmol H_L_T_mixr AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kmol H_L_T_mixrmass AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kg H_L_T_mp1 AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kmol H_L_T_mp2 AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kmol H_L_T_po AS DISTRIBUTION(Axial) OF EnthalpyDensity #kJ/kmol H_V_298_mdp AS EnthalpyDensity #kJ/kmol H_V_298_meoh AS EnthalpyDensity #kJ/kmol H_V_298_mp1 AS EnthalpyDensity #kJ/kmol H_V_298_mp2 AS EnthalpyDensity #kJ/kmol H_V_298_po AS EnthalpyDensity #kJ/kmol Lambda_cat AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Lambda_mdp AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Lambda_meoh AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Lambda_mp1 AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Lambda_mp2 AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Lambda_po AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Lambda_total AS DISTRIBUTION(Axial) OF Conductivity #kW/m.K Ldens_mass_mix AS DISTRIBUTION(Axial) OF Liqdensity #kg/m3 Ldens_mol_cat AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3 Ldens_mol_mdp AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3

Ldens_mol_meoh AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3 Ldens_mol_mix AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3 Ldens_mol_mp1 AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3 Ldens_mol_mp2 AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3 Ldens_mol_po AS DISTRIBUTION(Axial) OF Liquidmolardensity #kmol/m3 Liqmolvol_cat AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol Liqmolvol_mdp AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol Liqmolvol_meoh AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol Liqmolvol_mix AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol Liqmolvol_mp1 AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol Liqmolvol_mp2 AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol Liqmolvol_po AS DISTRIBUTION(Axial) OF LiqMolarVolume #m3/kmol MolWeight_avg_liq AS DISTRIBUTION(Axial) OF Molweight #kg/kmol MolWeight_cat AS Molweight #kg/kmol MolWeight_mdp AS Molweight #kg/kmol MolWeight_meoh AS Molweight #kg/kmol MolWeight_mp1 AS Molweight #kg/kmol MolWeight_mp2 AS Molweight #kg/kmol MolWeight_po AS Molweight #kg/kmol MolWeight_total AS ARRAY(NoComp) OF Molweight P AS Pressure #Pa T AS DISTRIBUTION(Axial) OF Temperature #K T0 AS Temperature #K X AS DISTRIBUTION(Nocomp,Axial) OF Fraction #kmol/kmol EQUATION #Physical properties from Aspen #Liquid density FOR z:=0 TO Reactorlength DO Ldens_mol_po(z) = (1.4855 /0.2763 ^(1+(1-T(z)/482.25)^0.29365));#kmol/m3 Ldens_mol_meoh(z) = (2.3267 /0.27073^(1+(1-T(z)/512.5)^0.24713));#kmol/m3 Ldens_mol_mp2(z) = (0.84648/0.24886^(1+(1-T(z)/553)^0.3069)) ;#kmol/m3 Ldens_mol_mp1(z) = (0.92789/0.2728 ^(1+(1-T(z)/566)^0.2052)) ;#kmol/m3 Ldens_mol_mdp(z) = (0.56992/0.26585^(1+(1-T(z)/612)^0.28571)) ;#kmol/m3 Ldens_mol_cat(z) = Ldens_mol_mp1(z); #kmol/m3, #assume density catalyst = density MP-1 Liqmolvol_po(z) = 1/Ldens_mol_po(z);#m3/kmol Liqmolvol_meoh(z) = 1/Ldens_mol_meoh(z);#m3/kmol Liqmolvol_mp1(z) = 1/Ldens_mol_mp1(z);#m3/kmol Liqmolvol_mp2(z) = 1/Ldens_mol_mp2(z);#m3/kmol Liqmolvol_mdp(z) = 1/Ldens_mol_mdp(z);#m3/kmol Liqmolvol_cat(z) = 1/Ldens_mol_cat(z);#m3/kmol Liqmolvol_mix(z) = X(1,z)*Liqmolvol_po(z) + X(2,z)*Liqmolvol_meoh(z)+ X(3,z)*Liqmolvol_mp1(z) + X(4,z)*Liqmolvol_mp2(z) + X(5,z)*Liqmolvol_mdp(z) + X(6,z)*Liqmolvol_cat(z); #m3/kmol, with catalyst Ldens_mol_mix(z) = 1/Liqmolvol_mix(z);#kmol/m3 Ldens_mass_mix(z) = Ldens_mol_mix(z) * MolWeight_avg_liq(z); #Vapor density #No Vapor #Vapor pressure #No Vapor #Heat of vaporization #No Vapor #Liquid heat capacity #kJ/kmol.K Cpl_po(z) = (167910-696.6 *T(z)+2.45 *T(z)^2-0.0021734*T(z)^3)/1000; Cpl_meoh(z) = (105800-362.23*T(z)+0.9379*T(z)^2)/1000; #kJ/kmol.K Cpl_mp2(z) = (154110+213.39*T(z))/1000; #kJ/kmol.K Cpl_mp1(z) = (67929 +448.12*T(z))/1000; #kJ/kmol.K Cpl_mdp(z) = (206590+420.21*T(z))/1000; #kJ/kmol.K Cpl_total_mol(z) = X(1,z)*Cpl_po(z) + X(2,z)*Cpl_meoh(z)+ X(3,z)*Cpl_mp1(z) + X(4,z)*Cpl_mp2(z) + X(5,z)*Cpl_mdp(z) + X(6,z)*Cpl_mp1(z);#kJ/kmol.K Cpl_total_mass(z)*MolWeight_avg_liq(z) = Cpl_total_mol(z);#kJ/kg.K for mass END #for z

#Vapor heat capacity #No Vapor #Enthalpies #Enthalpy of ideal gas @ 25 °C T0 = 298.15; #Reference temperature = 25 °C H_V_298_po = - 93700;#kJ/kmol H_V_298_meoh = -200940;#kJ/kmol H_V_298_mp1 = -404300;#kJ/kmol H_V_298_mp2 = -403900;#kJ/kmol H_V_298_mdp = -607200;#kJ/kmol #Enthalpy of liquid @ 25 °C, HL_298 = HV_298-dHv_298 H_L_298_po = H_V_298_po -((39957)*(1-298.15/482.25)^(0.36659));#kJ/kmol H_L_298_meoh = H_V_298_meoh-((50451)*(1-298.15/512.5)^(0.33594));#kJ/kmol H_L_298_mp1 = H_V_298_mp1 -((53688)*(1-298.15/566)^(0.23092));#kJ/kmol H_L_298_mp2 = H_V_298_mp2 -((52022)*(1-298.15/553)^(0.22103));#kJ/kmol H_L_298_mdp = H_V_298_mdp -((61013)*(1-298.15/612)^(0.19259));#kJ/kmol #Enthalpy of liquid = Enthalpy of liquid @ 25 °C + integral(Cp.dT) FOR z:=0 TO Reactorlength DO H_L_T_po(z) = H_L_298_po + (167910*(T(z)-T0)-696.6 /2*(T(z)-T0)^2 +2.45 /3*(T(z)-T0)^3-0.0021734/4*(T(z)-T0)^4)/1000; H_L_T_meoh(z) = H_L_298_meoh + (105800*(T(z)-T0)-362.23/2*(T(z)-T0)^2 +0.9379/3*(T(z)-T0)^3)/1000; H_L_T_mp1(z) = H_L_298_mp1 + ( 67929*(T(z)-T0)+448.12/2*(T(z)-T0)^2)/1000; H_L_T_mp2(z) = H_L_298_mp2 + (154110*(T(z)-T0)+213.39/2*(T(z)-T0)^2)/1000; H_L_T_mdp(z) = H_L_298_mdp + (206590*(T(z)-T0)+420.21/2*(T(z)-T0)^2)/1000; #Enthalpy of vapor = Enthalpy of liquid + Heat of vaporization #No Vapor #Enthalpies of mixtures H_L_T_mixr(z) = X(1,z)*H_L_T_po(z)+ X(2,z)*H_L_T_meoh(z)+ X(3,z)*H_L_T_mp1(z)+ X(4,z)*H_L_T_mp2(z)+ X(5,z)*H_L_T_mdp(z)+ X(6,z)*H_L_T_mp1(z); #with catalyst H_L_T_mixrmass(z)*MolWeight_avg_liq(z) = H_L_T_mixr(z); #Molecular weights MolWeight_avg_liq(z) = X(1,z)*MolWeight_po + X(2,z)*MolWeight_meoh+ X(3,z)*MolWeight_mp1 + X(4,z)*MolWeight_mp2 + X(5,z)*MolWeight_mdp + X(6,z)*MolWeight_cat ;#kg/kmol, cat in liquid #Viscosity Eta_po(z) = EXP(-3.08354472+2794.5/T(z)-0.9038*LOG(T(z)))*0.001; #Pa.s Eta_meoh(z) = EXP(-18.4092447+1789.2/T(z)+2.069*LOG(T(z)))*0.001; Eta_mp1(z) = EXP(-5.05924472+1143.5/T(z))*0.001; Eta_mp2(z) = EXP(-10.0442447+2821/T(z)+0.18833*LOG(T(z)))*0.001; Eta_mdp(z) = EXP(-8.58324472+3238.5/T(z)+0.00087166*LOG(T(z)))*0.001; Eta_cat(z) = Eta_mp1(z); Eta_total(z) = EXP(X(1,z)*LOG(Eta_po(z) )+ X(2,z)*LOG(Eta_meoh(z))+ X(3,z)*LOG(Eta_mp1(z) )+ X(4,z)*LOG(Eta_mp2(z) )+ X(5,z)*LOG(Eta_mdp(z) )+ X(6,z)*LOG(Eta_cat(z) )); #Pa.s #Conductivity Lambda_po(z) = (0.148859854-0.000287704*(T(z)-273.15))*1.163/1000; #kW/m.K Lambda_meoh(z) = (0.177940542-0.000241617*(T(z)-273.15))*1.163/1000; Lambda_mp1(z) = (0.155543877-0.000395193*(T(z)-273.15))*1.163/1000; Lambda_mp2(z) = (0.153604776-0.000304015*(T(z)-273.15))*1.163/1000; Lambda_mdp(z) = (0.146326677-0.000253852*(T(z)-273.15))*1.163/1000; Lambda_cat(z) = Lambda_mp1(z); #assume identical to MP-1 Lambda_total(z) = Lambda_po(z) *X(1,z)+ Lambda_meoh(z)*X(2,z)+

Lambda_mp1(z) *X(3,z)+ Lambda_mp2(z) *X(4,z)+ Lambda_mdp(z) *X(5,z)+ Lambda_cat(z) *X(6,z); END #for z MolWeight_po = 58.081;#kg/kmol MolWeight_meoh = 32.042;#kg/kmol MolWeight_mp1 = 90.122;#kg/kmol MolWeight_mp2 = 90.122;#kg/kmol MolWeight_mdp = 148.202;#kg/kmol MolWeight_cat = 107.109;#kg/kmol, N(OCH3)3 MolWeight_total(1) = MolWeight_po ; MolWeight_total(2) = MolWeight_meoh; MolWeight_total(3) = MolWeight_mp1 ; MolWeight_total(4) = MolWeight_mp2 ; MolWeight_total(5) = MolWeight_mdp ; MolWeight_total(6) = MolWeight_cat ; END #-------------------------------------------------------------------- # Conversion of fraction to concentration for reactor #-------------------------------------------------------------------- MODEL XC_conv PARAMETER NoComp AS INTEGER VARIABLE C AS ARRAY(NoComp) OF Concentration F AS MolarRate H AS EnthalpyDensity Ldens_mol AS ARRAY(NoComp) OF Liquidmolardensity P AS Pressure T AS Temperature X AS ARRAY(NoComp) OF Fraction STREAM Cstream : F, C, P, T, H AS MainStreamC Xstream : F, X, P, T, H AS MainStream EQUATION Ldens_mol(1) = (1.4855 /0.2763 ^(1+(1-T/482.25)^0.29365));#kmol/m3, PO Ldens_mol(2) = (2.3267 /0.27073^(1+(1-T/512.5)^0.24713)) ;#kmol/m3, MeOH Ldens_mol(3) = (0.92789/0.2728 ^(1+(1-T/566)^0.2052)) ;#kmol/m3, MP1 Ldens_mol(4) = (0.84648/0.24886^(1+(1-T/553)^0.3069)) ;#kmol/m3, MP2 Ldens_mol(5) = (0.56992/0.26585^(1+(1-T/612)^0.28571)) ;#kmol/m3, MDP Ldens_mol(6) = Ldens_mol(3); #kmol/m3, CATALYST, #assume density cat = density MP-1 FOR i:=1 to NoComp DO C(i) = X(i)/(SIGMA(X/Ldens_mol)); END #for i END #model XC_conv #-------------------------------------------------------------------- # Conversion of concentration to fractionfor reactor #-------------------------------------------------------------------- MODEL CX_conv PARAMETER NoComp AS INTEGER VARIABLE C AS ARRAY(NoComp) OF Concentration F AS MolarRate H AS EnthalpyDensity P AS Pressure T AS Temperature

X AS ARRAY(NoComp) OF Fraction STREAM Cstream : F, C, P, T, H AS MainStreamC Xstream : F, X, P, T, H AS MainStream EQUATION FOR i:=1 to NoComp DO C(i) = X(i)*SIGMA(C); # END #for i END #model CX_conv #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # MODEL OF PI CONTROLLER #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODEL PIC PARAMETER T AS REAL VARIABLE E AS Signal IntE AS Signal OuS AS Signal InS AS Signal K AS signal B AS signal SP AS signal EQUATION E = SP-InS; $IntE = E; OuS = B+K*(E+IntE/T); END #PIC #-------------------------------------------------------------------- # Model description of mixer #-------------------------------------------------------------------- MODEL Mixer PARAMETER NoComp AS INTEGER VARIABLE F AS MolarRate #kmol/s Fin AS ARRAY(2) OF MolarRate #kmol/s H AS EnthalpyDensity #kJ/kmol Hin AS ARRAY(2) OF EnthalpyDensity #kJ/kmol H_L_T_mdp AS EnthalpyDensity #kJ/kmol H_L_T_meoh AS EnthalpyDensity #kJ/kmol H_L_T_mp1 AS EnthalpyDensity #kJ/kmol H_L_T_mp2 AS EnthalpyDensity #kJ/kmol H_L_T_po AS EnthalpyDensity #kJ/kmol P AS Pressure #Pa Pin AS ARRAY(2) OF Pressure #Pa Q AS EnergyRate #kJ/s T AS Temperature #K Tin AS ARRAY(2) OF Temperature #K X AS ARRAY(NoComp) OF Fraction #- Zin AS ARRAY(2,NoComp) OF Fraction #- STREAM In1 : Fin(1), Zin(1,), Pin(1), Tin(1), Hin(1) AS MainStream In2 : Fin(2), Zin(2,), Pin(2), Tin(2), Hin(2) AS MainStream Out : F, X, P, T, H AS MainStream EQUATION #-------------------------Balances-------------------------------

# Component Molar Balances: IN = OUT FOR i:= 1 TO NoComp DO SIGMA(Fin( )*Zin( ,i)) = F*X(i); END # Heat Balance in the Mixer: IN = OUT SIGMA(Fin( )*Hin( )) + Q = F*H ; #Q added to use this as startup heater / cooler #Either Q or T can be specified. #-------------------------Definitions---------------------------- #Sum of fractions equals 1 #SIGMA(X) = 1; #Total mass balance SIGMA(Fin) = F; #not fractions = 1, easier equation because inflow may be zero #-------------------------Physprops------------------------------ #Enthalpy of liquid (see database model, kJ/kmol) H_L_T_po = - 93700 -((39957)*(1-298.15/482.25)^(0.36659)) + (167910*(T-298.15)-696.6 /2*(T-298.15)^2 +2.45 /3*(T-298.15)^3-0.0021734/4*(T-298.15)^4)/1000; H_L_T_meoh = -200940 -((50451)*(1-298.15/512.5)^(0.33594)) + (105800*(T-298.15)-362.23/2*(T-298.15)^2 +0.9379/3*(T-298.15)^3)/1000; H_L_T_mp2 = -403900 -((52022)*(1-298.15/553)^(0.22103)) + (154110*(T-298.15)+213.39/2*(T-298.15)^2)/1000; H_L_T_mp1 = -404300 -((53688)*(1-298.15/566)^(0.23092)) + ( 67929*(T-298.15)+448.12/2*(T-298.15)^2)/1000; H_L_T_mdp = -607200 -((61013)*(1-298.15/612)^(0.19259)) + (206590*(T-298.15)+420.21/2*(T-298.15)^2)/1000; #Enthalpies of mixture H = X(1)*H_L_T_po+ X(2)*H_L_T_meoh+ X(3)*H_L_T_mp1+ X(4)*H_L_T_mp2+ X(5)*H_L_T_mdp+ X(6)*H_L_T_mp1; #with catalyst having properties of MP1 #Pressure: Assume the streams are mixed at same pressure P = Pin(1); #Pin(1) arbitrarily chosen END #---------------------------------------------------------------- # Model description of reactor shell #---------------------------------------------------------------- MODEL Shell UNIT ADB AS ASP_DATABASE_distribution PARAMETER Din AS REAL # Inner diameter of tubes, m Dout AS REAL # Outer diameter of tubes # of the heat exchanger, m Dshell AS REAL # Diameter of the outer shell, m Gz AS REAL # Gravitational constant in z-direction, m/s2 Hod AS REAL # Outer dirt coefficient, kW/m2.K Lambdaw AS REAL # Thermal conductivity of the wall, kW/m.K NoComp AS INTEGER # Number of components, - NoDisc AS INTEGER # Number of discretisation points, - NoTubes AS INTEGER # Number of tubes, - Pi AS REAL # The number Pi Reactorlength AS REAL # Reactor length, m DISTRIBUTION_DOMAIN Axial AS (0 : ReactorLength) VARIABLE Cc AS DISTRIBUTION(NoComp,Axial) OF Concentration # Concentration of reaction mixture, kmol/m3 Cinc2 AS ARRAY(NoComp) OF Concentration # Concentrations in entering coolant, kmol/m3

Cpc AS DISTRIBUTION(Axial) OF Heatcapacity_kg # Heat capacity of coolant, kJ/kg.K Deo AS Length # Hydraulic diameter inside shell, m Ec AS DISTRIBUTION(Axial) OF Energy_V # Energy of reaction mixture, kJ/m3 Etac AS DISTRIBUTION(Axial) OF Viscosity # Viscosity of coolant, Pa.s Fc AS DISTRIBUTION(Axial) OF NoType_low # Friction factor in the reaction mixture, - Fiemass AS Notype # Mass flowrate in tube, kg/m3 Hc AS DISTRIBUTION(Axial) OF Enthalpy # Enthalpy of reaction mixture, kJ/m3 Hinc AS EnthalpyDensity # Enthalpy of entering liquid, kJ/kmol Ho AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient in the filmlayer # in the shell, kW/m2.K Houtc AS EnthalpyDensity # Enthalpy of exiting liquid, kJ/m3 Lambdac AS DISTRIBUTION(Axial) OF Conductivity # Thermal conductivity of the coolant, kW/m.K Ldensmoltot AS DISTRIBUTION(Axial) OF Liquidmolardensity # Molar density of mixture, kmol/m3 MolWeight AS DISTRIBUTION(Axial) OF Molweight # Molecular weight of liquid, kg/kmol Pc AS DISTRIBUTION(Axial) OF Pressure # Pressure in shell, Pa PhiMol2 AS MolarRate # Molar flowrate of the coolant entering, kmol/s PhiMol3 AS MolarRate # Molar flowrate of the coolant exiting, kmol/s Pinc2 AS Pressure # Pressure of entering coolant, Pa Pro AS DISTRIBUTION(Axial) OF NoType_low # Prandtl number of reaction mixture, - Reo AS DISTRIBUTION(Axial) OF NoType_high # Reynolds number of reaction mixture,- Rhoc AS DISTRIBUTION(Axial) OF Density # Density of coolant, kg/m3 Tauwc AS DISTRIBUTION(Axial) OF Shear # Shear force at wall, shell side, kg/m.s2 Tc AS DISTRIBUTION(Axial) OF Temperature # Temperature of reaction mixture, K Tinc2 AS Temperature # Temperature of entering coolant, K Tw AS DISTRIBUTION(Axial) OF Temperature # Temperature of wall, K Usi AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, transfer # coolant-wall, based on inside area # of the tube, up to the middle of the tube, kW/m2.K Vzc AS DISTRIBUTION(Axial) OF Velocity_neg # Velocity in z direction in the shell, m/s Vzc_abs AS DISTRIBUTION(Axial) OF Velocity # Absolute velocity in z direction in the shell, m/s Xcmol AS DISTRIBUTION(NoComp,Axial) OF Fraction # Molar fractions in shell, - STREAM Inlet : PhiMol2, Cinc2, Pinc2, Tinc2, Hinc AS MainStreamC Outlet: PhiMol3, Cc(,0), Pc(0), Tc(0), Houtc AS MainStreamC BOUNDARY # @ z = L Tc(Reactorlength) = Tinc2; FOR i:=1 TO NoComp DO Cc(i,Reactorlength) = Cinc2(i); END # for i Pc(Reactorlength) = Pinc2; # @ z = 0: not necessary, equations just continue here EQUATION #-------------------------Balances-------------------------------

# Energy balance FOR z:= 0 {|+} TO ReactorLength|- DO $Ec(z)= -PARTIAL(Vzc(z)*Ec(z),Axial) + NoTubes*Usi(z)*4*Din*(Tw(z)-Tc(z))/(Dshell^2-NoTubes*Dout^2); END #For z # Mass balance FOR i := 1 TO NoComp DO FOR z:= 0 {|+} TO ReactorLength|- DO $Cc(i,z)= -PARTIAL(Vzc(z)*Cc(i,z),Axial); END #For z END # For i #Momentum balance FOR z:= 0 {|+} TO ReactorLength|- DO 0 = -PARTIAL(Rhoc(z)*(Vzc(z))^2,Axial) -PARTIAL(Pc(z),Axial) -NoTubes*(-Tauwc(z))+Rhoc(z)*(-Gz); #tauw is contrary to z-direction!! END #For z #-------------------------Hydrodynamics and definitions---------- FOR z:= 0 TO ReactorLength DO FOR i:= 1 TO NoComp DO Cc(i,z) = Xcmol(i,z)*SIGMA(Cc(,z)); END # For i Ec(z) = Hc(z); Usi(z) = 1/(Din/(Dout*Hod)+Din/(Dout*Ho(z)) + Din*(LOG(Dout/Din))/(4*Lambdaw)); Ho(z) = Lambdac(z)*0.023*(Reo(z))^(0.8)*(Pro(z))^(0.33)/Deo; Vzc_abs(z) = ABS(Vzc(z)); Reo(z) = Rhoc(z)*Vzc_abs(z)*Deo/Etac(z); Tauwc(z) = Fc(z)*0.5*Rhoc(z)*(Vzc_abs(z))^2; 4*Fc(z) = 0.316*(Reo(z))^(-0.25); Pro(z) = Cpc(z)*Etac(z)/Lambdac(z); END # For z #-------------------------Geometry------------------------------- Deo = (Dshell^2-NoTubes*Dout^2)/(Dshell+NoTubes*Dout); #------------------------Database PhysProp---------------------- Tc = ADB.T; #K Pc(0) = ADB.P; #Pa Xcmol = ADB.X; #kmol/kmol Hc = ADB.H_L_T_mixr*ADB.Ldens_mol_mix; #kJ/m3 Houtc = ADB.H_L_T_mixr(0); #kJ/m3 Ldensmoltot = ADB.Ldens_mol_mix; #kmol/m3 Rhoc = ADB.Ldens_mass_mix; #kg/m3 Cpc = ADB.Cpl_total_mass; #kJ/kg.K Molweight = ADB.MolWeight_avg_liq;#kg/kmol Lambdac = ADB.Lambda_total; #kW/m.K Etac = ADB.Eta_total; #Pa.s #--------------------Continuity of mass-------------------------- Fiemass = Molweight(Reactorlength)*PhiMol2; Fiemass = Rhoc*0.25*Pi*(Dshell^2-NoTubes*Dout^2)*(-Vzc); Fiemass = Phimol3*Molweight(0); END # Model shell #----------------------------------------------------------------------------- # Model description of a reactor wall #----------------------------------------------------------------------------- MODEL Wall PARAMETER

Cpw AS REAL # Heat capacity of wall, kJ/kg.K Din AS REAL # Inner diameter of tubes, m Dout AS REAL # Outer diameter of tubes, m Lambdaw AS REAL # Thermal conductivity of the wall, kW/m.K NoDisc AS INTEGER # Number of discretisation points, - Reactorlength AS REAL # Reactor length, m Rhow AS REAL # Density of wall, kg/m3 DISTRIBUTION_DOMAIN Axial AS (0 : ReactorLength) UNIT Shell AS Shell VARIABLE dTwdt AS DISTRIBUTION(Axial) OF Notype # Temperature change over time, K/s T AS DISTRIBUTION(Axial) OF Temperature # Temperature of reaction mixture, K Tc AS DISTRIBUTION(Axial) OF Temperature # Temperature of shell, K Tdiff AS DISTRIBUTION(Axial) OF Notype # Temperature difference over wall, K Tw AS DISTRIBUTION(Axial) OF Temperature # Temperature of wall, K Ui AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, transfer reactor # fluid-wall, based on inside area of the tube, # up to the middle of the tube, kW/m2.K Usi AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, transfer # coolant-wall, based on inside area # of the tube, up to the middle of the tube, kW/m2.K EQUATION #-------------------------Balances------------------------------- # Energy balance FOR z:= 0 TO ReactorLength DO Rhow*Cpw*$Tw(z) = Lambdaw*PARTIAL(Tw(z),Axial,Axial) + Usi(z)*4*Din*(Tc(z)-Tw(z))/(Dout^2-Din^2) + Ui(z)*4*Din*(T(z)-Tw(z))/(Dout^2-Din^2); Tdiff(z) = T(z)-Tc(z); END #For z # Other relations # Definitions Tc = Shell.Tc; Usi = Shell.Usi; Tw = Shell.Tw; # dTwdt dTwdt = (Lambdaw*PARTIAL(Tw,Axial,Axial) + Usi*4*Din*(Tc-Tw)/(Dout^2-Din^2) + Ui*4*Din*(T-Tw)/(Dout^2-Din^2))/(Rhow*Cpw); END # Model Wall #----------------------------------------------------------------------------- # Model description of a tube in the reactor #----------------------------------------------------------------------------- MODEL Tube UNIT ADB AS ASP_DATABASE_distribution Wall AS Wall PARAMETER NoReac AS INTEGER # Number of reactions, - Din AS REAL # Inner diameter of tubes, m Dout AS REAL # Outer diameter of tubes, m Ea AS ARRAY(NoReac) OF REAL # ActivationEnergy, kJ/kmol Gz AS REAL # Gravitational constant in z-direction, m/s2

Hid AS REAL # Inner dirt coefficient, kW/m2.K K0 AS ARRAY(NoReac) OF REAL # ArrheniusConstant, various units Lambdaw AS REAL # Thermal conductivity of the wall, kW/m.K NoComp AS INTEGER # Number of components, - NoDisc AS INTEGER # Number of discretisation points, - NoTubes AS INTEGER # Number of tubes, - Pi AS REAL # The number Pi Reactorlength AS REAL # Reactor length, m Rg AS REAL # Gas constant, kJ/kmol.K S AS REAL # Selectivity, - DISTRIBUTION_DOMAIN Axial AS (0 : ReactorLength) VARIABLE C AS DISTRIBUTION(NoComp,Axial) OF Concentration # Concentration of reaction mixture, kmol/m3 Cin2 AS ARRAY(NoComp) OF Concentration # Concentrations in entering reactants, kmol/m3 Conversion AS NoType # Conversion of PO, - Cp AS DISTRIBUTION(Axial) OF Heatcapacity_kg # Heat capacity of reaction mixture, kJ/kg.K Dei AS Length # Hydraulic diameter inside tube, m E AS DISTRIBUTION(Axial) OF Energy_V # Energy of reaction mixture, kJ/m3 Eta AS DISTRIBUTION(Axial) OF Viscosity # Viscosity of reaction mixture, Pa.s F AS DISTRIBUTION(Axial) OF NoType_low # Friction factor in the reaction mixture, - Fiemass AS Notype # Mass flow of reactants, kg/s H AS DISTRIBUTION(Axial) OF Enthalpy # Enthalpy of reaction mixture, kJ/m3 Hi AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient in # the filmlayer in the tubes, kW/m2.K Hin AS EnthalpyDensity # Enthalpy of entering reactants, kJ/kmol Hout AS EnthalpyDensity Lambda AS DISTRIBUTION(Axial) OF Conductivity # Thermal conductivity of reaction mixture, kW/m.K Ldensmoltot AS DISTRIBUTION(Axial) OF Liquidmolardensity # Molar density of the reaction mixture, kmol/m3 MolWeight AS ARRAY(NoComp) OF MolWeight # Molecular weight of the species, kg/kmol Molweighttot AS DISTRIBUTION(Axial) OF MolWeight # Molecular weight of the mixture, kg/kmol Nu AS ARRAY(NoComp,NoReac)OF Coeff # Coefficient of species i in reaction j, - P AS DISTRIBUTION(Axial) OF Pressure # Pressure in tubes, Pa PhiMol4 AS MolarRate # Flowrate of the entering reactants, kmol/s PhiMol5 AS MolarRate # Flowrate of the exiting reactants, kmol/s Pin2 AS Pressure # Pressure of entering reactants, Pa Pri AS DISTRIBUTION(Axial) OF NoType_low # Prandtl number of reaction mixture, - Rate AS DISTRIBUTION(NoReac,Axial) OF Reaction # Reaction rate, kmol/s.m3 Rei AS DISTRIBUTION(Axial) OF NoType_high # Reynolds number of reaction mixture, - Rho AS DISTRIBUTION(Axial) OF Density # Density of reaction mixture, kg/m3 T AS DISTRIBUTION(Axial) OF Temperature # Temperature of reaction mixture, K Tauw AS DISTRIBUTION(Axial) OF Shear # Shear force at wall, tube side, kg/m.s2 Tin2 AS Temperature # Temperature of entering reactant, K Tw AS DISTRIBUTION(Axial) OF Temperature # Temperature of wall, K Ui AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, # transfer reactor fluid-wall, based on inside area # of the tube, up to the middle of the tube, kW/m2.K Vz AS DISTRIBUTION(Axial) OF Velocity # Velocity in z direction, m/s Xmol AS DISTRIBUTION(NoComp,Axial) OF Fraction

# Molar fractions in reaction mixture, - STREAM Inlet : PhiMol4, Cin2, Pin2, Tin2, Hin AS MainStreamC Outlet: PhiMol5, C(,Reactorlength), P(Reactorlength), T(Reactorlength), Hout AS MainStreamC BOUNDARY # @ z = 0 T(0) = Tin2; FOR i:=1 TO NoComp DO C(i,0) = Cin2(i); END # for i P(0) = Pin2; # @z=L, not necessary as equations are valid at z=L EQUATION #-------------------------Balances------------------------------- # Energy balance FOR z:= 0|+ TO ReactorLength {|-} DO $E(z)= -PARTIAL(Vz(z)*E(z),Axial)+Ui(z)*4/Din*(Tw(z)-T(z)); END #For z # Mass balance FOR i := 1 TO NoComp DO FOR z:= 0|+ TO ReactorLength DO $C(i,z)= -PARTIAL(Vz(z)*C(i,z),Axial)+ SIGMA(Nu(i,)*Rate(,z)); END #For z END # For i #Momentum balance FOR z:= 0|+ TO ReactorLength DO 0=-PARTIAL(Rho(z)*(Vz(z))^2,Axial)-PARTIAL(P(z),Axial)-Tauw(z)+Rho(z)*Gz; END #For z #-------------------------Hydrodynamics and definitions---------- FOR z:= 0 TO ReactorLength DO FOR i:= 1 TO NoComp DO C(i,z) = Xmol(i,z)*SIGMA(C(,z)); END # For i E(z) = H(z); Ui(z) = 1/(1/Hid+1/Hi(z)+ Din*(LOG(Dout/Din))/(4*Lambdaw)); Hi(z) = Lambda(z)*0.023*(Rei(z))^(0.8)*(Pri(z))^(0.33)/Dei; Rei(z) = Rho(z)*Vz(z)*Dei/Eta(z); Tauw(z)= F(z)*0.5*Rho(z)*(Vz(z)^2); 4*F(z) = 0.316*Rei(z)^(-0.25); Pri(z) = Cp(z)*Eta(z)/Lambda(z); END # For z T = Wall.T; Ui = Wall.Ui; Tw = Wall.Tw; #-------------------------Geometry------------------------------- Dei = Din; #-------------------------Kinetics------------------------------- # Reaction rates FOR z:= 0 TO ReactorLength DO #k*C1*C6*Mw6*Vbatch*1000(kg-->g)/60(s/min) Rate(1,z) = K0(1)*EXP(-Ea(1)/(Rg*T(z)))* C(1,z)* C(6,z)* MolWeight(6)*4.95E-4*1000/60; Rate(2,z) = K0(2)*EXP(-Ea(2)/(Rg*T(z)))* C(1,z)* C(3,z)* C(6,z)*MolWeight(6)*4.95E-4*1000/60; Rate(3,z) = K0(3)*EXP(-Ea(3)/(Rg*T(z)))* C(1,z)* C(4,z)* C(6,z)*MolWeight(6)*4.95E-4*1000/60; END #For z

FOR r:=1 TO NoReac DO Nu(1,r)=-1;# PO END # for r Nu(2,1)=-1; Nu(2,2)=0; Nu(2,3)=0; Nu(3,1)=1-S; Nu(3,2)=-1; Nu(3,3)=0; Nu(4,1)=S; Nu(4,2)=0; Nu(4,3)=-1; Nu(5,1)=0; Nu(5,2)=1; Nu(5,3)=1; Nu(6,1)=0; Nu(6,2)=0; Nu(6,3)=0; {Nu =[-1, -1, -1, # PO -1, 0, 0, # MeOH 1-S, -1, 0, # MP-1 S, 0, -1, # MP-2 0, 1, 1, # MDP 0, 0, 0];# Catalyst} Conversion = (PhiMol4*Xmol(1,0)-PhiMol5*Xmol(1,Reactorlength)) /MAX(PhiMol4*Xmol(1,0),1E-5); #------------------------Database PhysProp---------------------- T = ADB.T; #K P(0) = ADB.P; #Pa Xmol = ADB.X; #kmol/kmol Cp = ADB.Cpl_total_mass; #kJ/kg.K H = ADB.H_L_T_mixrmass*Rho; #kJ/m3 Hout = ADB.H_L_T_mixr(Reactorlength); Molweight = ADB.MolWeight_total; #kg/kmol Molweighttot = ADB.MolWeight_avg_liq ; #kg/kmol Rho = ADB.Ldens_mass_mix; #kg/m3 Ldensmoltot = ADB.Ldens_mol_mix; #kmol/m3 Lambda = ADB.Lambda_total; #kW/m.K Eta = ADB.Eta_total; #Pa.s #--------------------Continuity of mass-------------------------- Fiemass = Molweighttot(0)*PhiMol4; #kg/s Fiemass = Rho*0.25*Pi*Din^2*NoTubes*Vz; #kg/s Fiemass = Molweighttot(Reactorlength)*PhiMol5; #kg/s END # Model Tube #----------------------------------------------------------------------------- # Model description of a reactor wall #----------------------------------------------------------------------------- MODEL Wall2 PARAMETER Cpw AS REAL # Heat capacity of wall, kJ/kg.K Din AS REAL # Inner diameter of tubes, m Dout AS REAL # Outer diameter of tubes, m Lambdaw AS REAL # Thermal conductivity of the wall, kW/m.K Reactorlength AS REAL # Reactor length, m Rhow AS REAL # Density of wall, kg/m3 DISTRIBUTION_DOMAIN Axial AS (0 : Reactorlength) VARIABLE dTwdt AS DISTRIBUTION(Axial) OF Notype # Temperature change over time, K/s Tbfw AS Temperature

# Temperature of boiling feed water, K T AS DISTRIBUTION(Axial) OF Temperature # Temperature of reaction mixture, K Tc AS DISTRIBUTION(Axial) OF Temperature # Temperature of shell, K Tdiff AS DISTRIBUTION(Axial) OF Notype # Temperature difference over wall, K Tw AS DISTRIBUTION(Axial) OF Temperature # Temperature of wall, K Ubfw AS Heattransfer # Heat transfer coefficient of boiling # feed water, kW/m2.K Ui AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, transfer reactor # fluid-wall, based on inside area of the tube, # up to the middle of the tube, kW/m2.K Usi AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, transfer # coolant-wall, based on inside area # of the tube, up to the middle of the tube, kW/m2.K EQUATION #-------------------------Balances------------------------------- # Energy balance FOR z:= 0 TO Reactorlength DO Rhow*Cpw*$Tw(z) = Lambdaw*PARTIAL(Tw(z),Axial,Axial) + Usi(z)*4*Din*(Tc(z)-Tw(z))/(Dout^2-Din^2) + Ui(z)*4*Din*(T(z)-Tw(z))/(Dout^2-Din^2); Tdiff(z) = T(z)-Tc(z); Tc(z) = Tbfw; Usi(z) = Ubfw; END #For z # dTwdt dTwdt = (Lambdaw*PARTIAL(Tw,Axial,Axial) + Usi*4*Din*(Tc-Tw)/(Dout^2-Din^2) + Ui*4*Din*(T-Tw)/(Dout^2-Din^2))/(Rhow*Cpw); END # Model Wall2 #----------------------------------------------------------------------------- # Model description of a tube in the steam section of the reactor #----------------------------------------------------------------------------- MODEL Tube2 UNIT ADB AS ASP_DATABASE_distribution Wall2 AS Wall2 PARAMETER NoReac AS INTEGER # Number of reactions, - Din AS REAL # Inner diameter of tubes, m Dout AS REAL # Outer diameter of tubes, m Ea AS ARRAY(NoReac) OF REAL # ActivationEnergy, kJ/kmol Gz AS REAL # Gravitational constant in z-direction, m/s2 Hid AS REAL # Inner dirt coefficient, kW/m2.K K0 AS ARRAY(NoReac) OF REAL # ArrheniusConstant, various units Lambdaw AS REAL # Thermal conductivity of the wall, kW/m.K NoComp AS INTEGER # Number of components, - NoDisc AS INTEGER # Number of discretisation points, - NoTubes AS INTEGER # Number of tubes, - Pi AS REAL # The number Pi Reactorlength AS REAL # Reactor length, m Rg AS REAL # Gas constant, kJ/kmol.K S AS REAL # Selectivity, - DISTRIBUTION_DOMAIN Axial AS (0 : Reactorlength) VARIABLE

C AS DISTRIBUTION(NoComp,Axial) OF Concentration # Concentration of reaction mixture, kmol/m3 Cin2 AS ARRAY(NoComp) OF Concentration # Concentrations in entering reactants, kmol/m3 Conversion AS NoType # Conversion of PO, - Cp AS DISTRIBUTION(Axial) OF Heatcapacity_kg # Heat capacity of reaction mixture, kJ/kg.K Dei AS Length # Hydraulic diameter inside tube, m E AS DISTRIBUTION(Axial) OF Energy_V # Energy of reaction mixture, kJ/m3 Eta AS DISTRIBUTION(Axial) OF Viscosity # Viscosity of reaction mixture, Pa.s F AS DISTRIBUTION(Axial) OF NoType_low # Friction factor in the reaction mixture, - Fiemass AS Notype # Mass flow of reactants, kg/s H AS DISTRIBUTION(Axial) OF Enthalpy # Enthalpy of reaction mixture, kJ/m3 Hi AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient in # the filmlayer in the tubes, kW/m2.K Hin AS EnthalpyDensity # Enthalpy of entering reactants, kJ/kmol Hout AS EnthalpyDensity Lambda AS DISTRIBUTION(Axial) OF Conductivity # Thermal conductivity of reaction mixture, kW/m.K Ldensmoltot AS DISTRIBUTION(Axial) OF Liquidmolardensity # Molar density of the reaction mixture, kmol/m3 MolWeight AS ARRAY(NoComp) OF MolWeight # Molecular weight of the species, kg/kmol Molweighttot AS DISTRIBUTION(Axial) OF MolWeight # Molecular weight of the mixture, kg/kmol Nu AS ARRAY(NoComp,NoReac)OF Coeff # Coefficient of species i in reaction j, - P AS DISTRIBUTION(Axial) OF Pressure # Pressure in tubes, Pa PhiMol4 AS MolarRate # Flowrate of the entering reactants, kmol/s PhiMol5 AS DISTRIBUTION(Axial) OF MolarRate # Flowrate of the exiting reactants, kmol/s Pin2 AS Pressure # Pressure of entering reactants, Pa Pri AS DISTRIBUTION(Axial) OF NoType_low # Prandtl number of reaction mixture, - Rate AS DISTRIBUTION(NoReac,Axial) OF Reaction # Reaction rate, kmol/s.m3 Rei AS DISTRIBUTION(Axial) OF NoType_high # Reynolds number of reaction mixture, - Rho AS DISTRIBUTION(Axial) OF Density # Density of reaction mixture, kg/m3 T AS DISTRIBUTION(Axial) OF Temperature # Temperature of reaction mixture, K Tauw AS DISTRIBUTION(Axial) OF Shear # Shear force at wall, tube side, kg/m.s2 Tin2 AS Temperature # Temperature of entering reactant, K Tw AS DISTRIBUTION(Axial) OF Temperature # Temperature of wall, K Ui AS DISTRIBUTION(Axial) OF Heattransfer # Heat transfer coefficient, # transfer reactor fluid-wall, based on inside area # of the tube, up to the middle of the tube, kW/m2.K Vz AS DISTRIBUTION(Axial) OF Velocity # Velocity in z direction, m/s Xmol AS DISTRIBUTION(NoComp,Axial) OF Fraction # Molar fractions in reaction mixture, - STREAM Inlet : PhiMol4, Cin2, Pin2, Tin2, Hin AS MainStreamC Outlet: PhiMol5(Reactorlength), C(,Reactorlength), P(Reactorlength), T(Reactorlength), Hout AS MainStreamC BOUNDARY # @ z = 0 T(0) = Tin2; FOR i:=1 TO NoComp DO C(i,0) = Cin2(i); END # for i

P(0) = Pin2; # @z=L, not necessary as equations are valid at z=L EQUATION #-------------------------Balances------------------------------- # Energy balance FOR z:= 0|+ TO Reactorlength DO $E(z)= -PARTIAL(Vz(z)*E(z),Axial)+Ui(z)*4/Din*(Tw(z)-T(z)); END #For z # Mass balance FOR i := 1 TO NoComp DO FOR z:= 0|+ TO Reactorlength DO $C(i,z)= -PARTIAL(Vz(z)*C(i,z),Axial)+ SIGMA(Nu(i,)*Rate(,z)); END #For z END # For i #Momentum balance FOR z:= 0|+ TO Reactorlength DO 0=-PARTIAL(Rho(z)*(Vz(z))^2,Axial)-PARTIAL(P(z),Axial)-Tauw(z)+Rho(z)*Gz; END #For z #-------------------------Hydrodynamics and definitions---------- FOR z:= 0 TO Reactorlength DO FOR i:= 1 TO NoComp DO C(i,z) = Xmol(i,z)*SIGMA(C(,z)); END # For i E(z) = H(z); Ui(z) = 1/(1/Hid+1/Hi(z)+ Din*(LOG(Dout/Din))/(4*Lambdaw)); Hi(z) = Lambda(z)*0.023*(Rei(z))^(0.8)*(Pri(z))^(0.33)/Dei; Rei(z) = Rho(z)*Vz(z)*Dei/Eta(z); Tauw(z)= F(z)*0.5*Rho(z)*(Vz(z)^2); 4*F(z) = 0.316*Rei(z)^(-0.25); Pri(z) = Cp(z)*Eta(z)/Lambda(z); END # For z T = Wall2.T; Ui = Wall2.Ui; Tw = Wall2.Tw; #-------------------------Geometry------------------------------- Dei = Din; #-------------------------Kinetics------------------------------- # Reaction rates FOR z:= 0 TO Reactorlength DO #k*C1*C6*Mw6*Vbatch*1000(kg-->g)/60(s/min) Rate(1,z) = K0(1)*EXP(-Ea(1)/(Rg*T(z)))* C(1,z)* C(6,z)* MolWeight(6)*4.95E-4*1000/60; Rate(2,z) = K0(2)*EXP(-Ea(2)/(Rg*T(z)))* C(1,z)* C(3,z)* C(6,z)*MolWeight(6)*4.95E-4*1000/60; Rate(3,z) = K0(3)*EXP(-Ea(3)/(Rg*T(z)))* C(1,z)* C(4,z)* C(6,z)*MolWeight(6)*4.95E-4*1000/60; END #For z FOR r:=1 TO NoReac DO Nu(1,r)=-1;# PO END # for r Nu(2,1)=-1; Nu(2,2)=0; Nu(2,3)=0; Nu(3,1)=1-S; Nu(3,2)=-1; Nu(3,3)=0; Nu(4,1)=S; Nu(4,2)=0; Nu(4,3)=-1; Nu(5,1)=0;

Nu(5,2)=1; Nu(5,3)=1; Nu(6,1)=0; Nu(6,2)=0; Nu(6,3)=0; {Nu =[-1, -1, -1, # PO -1, 0, 0, # MeOH 1-S, -1, 0, # MP-1 S, 0, -1, # MP-2 0, 1, 1, # MDP 0, 0, 0];# Catalyst} Conversion = (PhiMol4*Xmol(1,0)-PhiMol5(Reactorlength)*Xmol(1,Reactorlength)) /MAX(PhiMol4*Xmol(1,0),1E-5); #------------------------Database PhysProp---------------------- T = ADB.T; #K P(0) = ADB.P; #Pa Xmol = ADB.X; #kmol/kmol Cp = ADB.Cpl_total_mass; #kJ/kg.K H = ADB.H_L_T_mixrmass*Rho; #kJ/m3 Hout = ADB.H_L_T_mixr(Reactorlength); Molweight = ADB.MolWeight_total; #kg/kmol Molweighttot = ADB.MolWeight_avg_liq ; #kg/kmol Rho = ADB.Ldens_mass_mix; #kg/m3 Ldensmoltot = ADB.Ldens_mol_mix; #kmol/m3 Lambda = ADB.Lambda_total; #kW/m.K Eta = ADB.Eta_total; #Pa.s #--------------------Continuity of mass-------------------------- Fiemass = Molweighttot(0)*PhiMol4; #kg/s Fiemass = Rho*0.25*Pi*Din^2*NoTubes*Vz; #kg/s FOR z:= 0 TO Reactorlength DO Fiemass/Molweighttot(z) = PhiMol5(z); #kg/s END #for z END # Model Tube2 #------------------------------------------------------------------- # Model description of the reactor #------------------------------------------------------------------- MODEL Reactor UNIT XCins , XCint AS XC_conv CXouts, CXoutt AS CX_conv Tube AS Tube Tube2 AS Tube2 Mix AS Mixer Tcontrol AS PIC PARAMETER NoReac AS INTEGER # Number of reactions, - Din AS REAL # Inner diameter of tubes, m Dout AS REAL # Outer diameter of tubes, m Ea AS ARRAY(NoReac) OF REAL # ActivationEnergy, kJ/kmol #Eta AS REAL # Viscosity of reaction mixture, Pa.s Gz AS REAL # Gravitational constant in z-direction, m/s2 Hid AS REAL # Inner dirt coefficient, kW/m2.K K0 AS ARRAY(NoReac) OF REAL # ArrheniusConstant, various units #Lambda AS REAL # Thermal conductivity of liquid, kW/m.K NoComp AS INTEGER # Number of components, - NoDisc AS INTEGER # Number of discretisation points, - NoTubes AS INTEGER # Number of tubes, - Pi AS REAL # The number Pi Rg AS REAL # Gas constant, kJ/kmol.K S AS REAL # Selectivity, - VARIABLE

Conversion AS ARRAY(NoDisc+1) OF NoType # Conversion of PO, - dTdt1 AS ARRAY(NoDisc+1) OF Notype # Temperature change over time, tube, K dTdt2 AS ARRAY(NoDisc+1) OF Notype # Temperature change over time, tube2, K dTdtprofile AS ARRAY(NoDisc*2+2) OF Notype # Total temperature change over time, K Fmolsi AS MolarRate # Molar flow rate, entering shell, kmol/s Fmolso AS MolarRate # Molar flow rate, exiting shell, kmol/s Fmolti AS MolarRate # Molar flow rate, entering tube, kmol/s Fmolto AS MolarRate # Molar flow rate, exiting tube, kmol/s Hsi AS EnthalpyDensity # Enthalpy, entering tube, kJ/kmol Hso AS EnthalpyDensity # Enthalpy, exiting shell, kJ/kmol Hti AS EnthalpyDensity # Enthalpy, entering tube, kJ/kmol Hto AS EnthalpyDensity # Enthalpy, exiting shell, kJ/kmol PhiMol5 AS ARRAY(NoDisc+1) OF Notype # Molar flowrate exiting tube2, kmol/s Psi AS Pressure # Pressure, entering tube, Pa Pso AS Pressure # Pressure, exiting shell, Pa Pti AS Pressure # Pressure, entering tube, Pa Pto AS Pressure # Pressure, exiting shell, Pa TprofileS1 AS ARRAY(NoDisc+1) OF Temperature # Temperature profile, shell, K TprofileS2 AS ARRAY(NoDisc+1) OF Temperature # Temperature profile, steam, K TprofileStotal AS ARRAY(NoDisc*2+2) OF Temperature # Total temperature profile, shell, K TprofileT1 AS ARRAY(NoDisc+1) OF Temperature # Temperature profile, tube, K TprofileT2 AS ARRAY(NoDisc+1) OF Temperature # Temperature profile, tube2, K TprofileTtotal AS ARRAY(NoDisc*2+2) OF Temperature # Total temperature profile, tube, K Tsi AS Temperature # Temperature, entering tube, K Tso AS Temperature # Temperature, exiting shell, K Tti AS Temperature # Temperature, entering tube, K Tto AS Temperature # Temperature, exiting shell, K Xpo AS ARRAY(NoDisc+1) OF Fraction # Fraction of PO in tube2, - Xsi AS ARRAY(NoComp) OF Fraction # Molar fractions, entering shell, - Xso AS ARRAY(NoComp) OF Fraction # Molar fractions, exiting shell, - Xti AS ARRAY(NoComp) OF Fraction # Molar fractions, entering tube, - Xto AS ARRAY(NoComp) OF Fraction # Molar fractions, exiting tube, - STREAM ShellIn : Fmolsi, Xsi, Psi, Tsi, Hsi AS Mainstream ShellOut : Fmolso, Xso, Pso, Tso, Hso AS Mainstream TubeIn : Fmolti, Xti, Pti, Tti, Hti AS Mainstream TubeOut : Fmolto, Xto, Pto, Tto, Hto AS Mainstream EQUATION #-------------------------Connections---------------------------- #Shell Tube.Wall.Shell.Inlet IS XCins.Cstream; ShellIn IS XCins.Xstream; ShellOut IS CXouts.Xstream; Tube.Wall.Shell.Outlet IS CXouts.Cstream; #Tube TubeOut IS CXoutt.Xstream; Tube.Outlet IS Tube2.Inlet; Tube2.Outlet IS CXoutt.Cstream; TubeIn IS XCint.Xstream; Mix.Out IS XCint.Xstream; Tube.Inlet IS XCint.Cstream; ShellOut IS Mix.In2; #-------------------------Profiles------------------------------- TprofileT1 = Tube.T; TprofileS1 = Tube.Wall.Shell.Tc; TprofileT2 = Tube2.T; TprofileS2 = Tube2.Wall2.Tc; FOR z:=1 TO NoDisc+1 DO TprofileTtotal(z) = TprofileT1(z); TprofileStotal(z) = TprofileS1(z); END #for z FOR z:=1 TO NoDisc+1 DO TprofileTtotal(z+NoDisc+1) = TprofileT2(z); TprofileStotal(z+NoDisc+1) = TprofileS2(z); END #for z dTdt1 = Tube.Wall.dTwdt ;

dTdt2 = Tube2.Wall2.dTwdt ; FOR z:=1 TO NoDisc+1 DO dTdtprofile(z) = dTdt1(z); END #for z FOR z:=1 TO NoDisc+1 DO dTdtprofile(z+NoDisc+1) = dTdt2(z); END #for z #-------------------------Other equations------------------------ #T-control Tcontrol.InS = TprofileTtotal(10); Mix.Fin(1) = MAX(0,Tcontrol.OuS); #Conversion PhiMol5 = Tube2.PhiMol5; Xpo = Tube2.Xmol(1,); FOR z:=1 TO NoDisc+1 DO Conversion(z) = (Tube.PhiMol4*Tube.Xmol(1,0)-PhiMol5(z)*Xpo(z)) /MAX(Tube.PhiMol4*Tube.Xmol(1,0),1E-5); END #for z END # Model Reactor #------------------------------------------------------------------- # Connection breaker: P #------------------------------------------------------------------- MODEL P_break PARAMETER NoComp AS INTEGER VARIABLE Fin AS MolarRate # kmol/s Fout AS MolarRate # kmol/s Fremove AS MolarRate # kmol/s Hin AS EnthalpyDensity # kJ/kmol H_L_T_mix AS EnthalpyDensity # kJ/kmol Pin AS Pressure # Pa Pout AS Pressure # Pa T AS Temperature # K Tin AS Temperature # K Xin AS ARRAY(Nocomp) OF Fraction # - Xout AS ARRAY(Nocomp) OF Fraction # - STREAM Instream : Fin , Xin , Pin , Tin, Hin AS MainStream Outstream: Fout, Xout, Pout, T , H_L_T_mix AS MainStream Purge : Fremove, Xout, Pout, T , H_L_T_mix AS MainStream EQUATION #Connections Fout = Fin-Fremove; Xout = Xin; T = Tin; Hin = H_L_T_mix; END #------------------------------------------------------------------- # Connection breaker in liquid phase and catalyst removal #------------------------------------------------------------------- MODEL Con_break_liq PARAMETER NoComp AS INTEGER VARIABLE Fcat AS MolarRate # kmol/s Fin AS MolarRate # kmol/s Fout AS MolarRate # kmol/s Frem AS MolarRate # kmol/s Hin AS EnthalpyDensity # kJ/kmol

H_L_T_mdp AS EnthalpyDensity # kJ/kmol H_L_T_meoh AS EnthalpyDensity # kJ/kmol H_L_T_mix AS EnthalpyDensity # kJ/kmol H_L_T_mp1 AS EnthalpyDensity # kJ/kmol H_L_T_mp2 AS EnthalpyDensity # kJ/kmol H_L_T_po AS EnthalpyDensity # kJ/kmol Pin AS Pressure # Pa Pout AS Pressure # Pa Q AS Energyrate # kW T AS Temperature # K Tin AS Temperature # K Xcat AS Fraction # - Xin AS ARRAY(Nocomp) OF Fraction # - Xout AS ARRAY(Nocomp) OF Fraction # - STREAM Catout : Fcat, Xcat, Pout, T , H_L_T_mp1 AS MainStream Instream : Fin , Xin , Pin , Tin, Hin AS MainStream Outstream : Fout, Xout, Pout, T , H_L_T_mix AS MainStream Removal : Frem, Xout, Pout, T , H_L_T_mix AS MainStream EQUATION #Physical properties from Aspen #Enthalpies #Enthalpy of liquid (see database model) H_L_T_po = - 93700 -((39957)*(1-298.15/482.25)^(0.36659)) + (167910*(T-298.15)-696.6 /2*(T-298.15)^2 +2.45 /3*(T-298.15)^3-0.0021734/4*(T-298.15)^4)/1000; H_L_T_meoh = -200940 -((50451)*(1-298.15/512.5)^(0.33594)) + (105800*(T-298.15)-362.23/2*(T-298.15)^2 +0.9379/3*(T-298.15)^3)/1000; #kJ/kmol H_L_T_mp1 = -404300 -((53688)*(1-298.15/566)^(0.23092)) + ( 67929*(T-298.15)+448.12/2*(T-298.15)^2)/1000; H_L_T_mp2 = -403900 -((52022)*(1-298.15/553)^(0.22103)) + (154110*(T-298.15)+213.39/2*(T-298.15)^2)/1000; H_L_T_mdp = -607200 -((61013)*(1-298.15/612)^(0.19259)) + (206590*(T-298.15)+420.21/2*(T-298.15)^2)/1000; #Enthalpy of mixture H_L_T_mix = Xout(1)*H_L_T_po + Xout(2)*H_L_T_meoh+ Xout(3)*H_L_T_mp1 + Xout(4)*H_L_T_mp2 + Xout(5)*H_L_T_mdp + Xout(6)*H_L_T_mp1 ; #with catalyst having properties of MP1 #Connections Fcat = Xin(6)*Fin; Fout+Frem = Fin-Fcat; Xcat = 1; FOR i:= 1 TO NoComp-1 DO Xout(i)*(Fout+Frem)=Xin(i)*Fin; END Xout(6)=0; Q=H_L_T_mix*(Fout+Frem+Fcat)-Hin*Fin; END #=========================================================================== # # Model of a tray # #=========================================================================== MODEL Tray UNIT ADB AS ASP_DATABASE PARAMETER alpha AS REAL # Lumped friction and flow coefficients, -

beta_set AS REAL # Liquid holdup in liquid phase, - g AS REAL DEFAULT 9.81 # Gravitational acceleration, m/s2 hap AS REAL # Apron height, m Height AS REAL # Weir height, m HolesArea AS REAL # Areo of holes, m2 Length AS REAL # Weir length, m NoComp AS INTEGER # Number of components, - PlateArea AS REAL # Area of tray, m2 Stray AS REAL # Surface area of tray, m2 Toutside AS REAL # Outside temperature, K Uair AS REAL # Heat transfer coefficient to surroundings, kW/m2.K Vtray AS REAL # Volume of tray, m3 VARIABLE dP AS notype # Pressure difference with lower tray, Pa EffLevel AS Length # Effective liquid height, m EffLevel_below AS Length # Effective liquid height on level below Ffeed AS ARRAY(2) OF MolarRate # Feed flow rate, kmol/s Fholesv AS MoleFlow # Vapor flow rate, test, kmol/s Fholesw AS MoleFlow # Dumping flow rate, test, kmol/s Fin AS ARRAY(3) OF MolarRate # Feed flow rate of entering streams, kmol/s Fout AS ARRAY(3) OF MolarRate # Exiting molar flowrates, kmol/s Fvapdc AS MolarRate # Vapor exiting through downcomer, kmol/s Fvapdcin AS MolarRate # Vapor entering from downcomer, kmol/s Fvapdctest AS MoleFlow # Vapor entering from downcomer, test, kmol/s H AS ARRAY(3) OF EnthalpyDensity # Enthalpy in phases, kJ/kmol Hfeed AS ARRAY(2) OF EnthalpyDensity # Enthalpy of feed, kJ/kmol Hin AS ARRAY(3) OF EnthalpyDensity # Enthalpy in entering streams, kJ/kmol Level AS Length # Liquid height, m M AS ARRAY(NoComp) OF Moles # Moles of components in both phases, kmol MTOT AS ARRAY(2) OF Moles # Total moles in both phases, kmol P AS Pressure # Pressure on tray, Pa Pfeed AS Pressure # Pressure of feed, Pa Pin AS ARRAY(2) OF Pressure # Pressure in entering streams, Pa Pisat AS ARRAY(NoComp) OF Signal # Saturated vapor pressure, Pa Q AS EnergyRate # Heat loss, kW rho_liq AS Liqdensity # Liquid density, kg/m3 rho_vap AS Vapdensity # Vapor density, kg/m3 rho_vapin AS VapDensity # Vapor density of entering vapor, kg/m3 T AS Temperature # Temperature on tray, K Tfeed AS Temperature # Temperature of feed, K Tin AS ARRAY(2) OF Temperature # Temperature in entering streams, K UTOT AS Energy # Energy on tray, kJ V_liq AS LiqMolarVolume # Liquid molar volume, m3/kmol V_vap AS VapMolarVolume # Vapor molar volume, m3/kmol V_vapin AS VapMolarVolume # Vapor molar volume of entering vapor, m3/kmol X AS ARRAY(3,NoComp) OF Fraction # Fractions in both phases, - Zfeed AS ARRAY(2,NoComp) OF Fraction # Fractions in feed, - Zin AS ARRAY(3,NoComp) OF Fraction # Fractions in entering streams, - STREAM FeedStream : Ffeed(), Zfeed(,), Pfeed, Tfeed, Hfeed AS MainStream LiquidInlet : Fin(1), Zin(1,), Pin(1),Tin(1),Hin(1) AS MainStream VapourInlet : Fin(2), Zin(2,), Pin(2),Tin(2),Hin(2) AS MainStream LiquidOutlet : Fout(1), X(1,), P,T,H(1) AS MainStream VapourOutlet : Fout(2), X(2,), P,T,H(2) AS MainStream DensityStreamIn : rho_vapin, V_vapin AS DensitySTream DensityStreamOut : rho_vap, V_vap AS DensitySTream Weepingout : Fout(3), X(1,), P, T, H(1) AS mainstream # only link Fout(3)/Fin(3) and Zin(3,)/X(1,) Weepingin : Fin(3), Zin(3,), Pin(1), Tin(1),Hin(3) AS mainstream Vapordcout : Fvapdc AS flowstream #vapor exiting to tray above through downcomer Vapordcin : Fvapdcin AS flowstream

#vapor entering from tray below through downcomer levelsin : Efflevel_below AS heightstream levelsout : Efflevel AS heightstream EQUATION #-------------------------Balances------------------------------- # Component Molar Balances in Phase 1 and 2 FOR i:= 1 TO NoComp DO $M(i)= SIGMA(Ffeed()*Zfeed(,i)) +SIGMA(Fin( )*Zin( ,i)) -SIGMA(Fout*X(,i)) +Fvapdcin*Zin(2,i) -Fvapdc*X(2,i); #escape of vapor through downcomer END # Heat Balance in the Mixer $UTOT= SIGMA(Ffeed()*Hfeed())+SIGMA(Fin( )*Hin( )) -SIGMA(Fout*H)+ Fvapdcin*Hin(2) - Fvapdc*H(2)+ Q ; #------------------------Definitions----------------------------- SIGMA(X(1,))=1; SIGMA(X(2,))=1; X(3,)=X(1,); FOR i:= 1 TO NoComp DO M(i) = X(1,i)*Mtot(1) + X(2,i)*Mtot(2); END UTOT=Mtot(1)*H(1)+Mtot(2)*H(2); #------------------------Hydrodynamics--------------------------- Fout(1)=1.84*Length*(MAX(0,(EffLevel - Height)))^1.5 /V_liq ; EffLevel*(0.01+Fin(2))=level*(0.01+Fin(2)/beta_set); Fholesv=1.190664711*HolesArea/V_vapin/(SQRT(rho_vapin)) *(Pin(2)-P-g*rho_liq*(Level))/(SQRT(ABS(Pin(2)-P-g*rho_liq*(Level))+0.02)); Fholesw=1.190664711*HolesArea/V_liq/(SQRT(rho_liq)) *(Pin(2)-P-g*rho_liq*(Level))/(SQRT(ABS(Pin(2)-P-g*rho_liq*(Level))+0.02)); Fin(2) = MAX(0,Fholesv); #positive side of Fholesv Fout(3) = -1*MIN(0,Fholesw)*(level-1E-3)/0.045; #negative side of Fholesw Fvapdctest=(Pin(2)-P)/(109906-109478) #scaled /(SQRT(ABS(Pin(2)-P)+0.02))*(SQRT((109906-109478)+0.02)); Fvapdcin = Length/V_vapin/(SQRT(alpha*rho_vapin))*(109906-109478) *(Hap-EffLevel_below)/(SQRT((109906-109478)+0.02)) *MAX(0,SGN(Hap-EffLevel_below))*MAX(0,Fvapdctest); dP = (Pin(2)-P-g*rho_liq*Level); #------------------------Heat transfer--------------------------- Q=Uair*Stray*(Toutside-T); #------------------------Geometry-------------------------------- MTOT(1)*V_liq + MTOT(2)*V_vap = Vtray; Level = MTOT(1)*V_liq / PlateArea ; #------------------------Equilibrium------------------------ FOR i:=1 TO NoComp-1 DO P*X(2,i)=X(1,i)*Pisat(i); END X(1,NoComp)=0;# No nitrogen in liquid #------------------------Database PhysProp----------------------

T = ADB.T; #K P = ADB.P; #Pa X(1,) = ADB.X(1,); #- X(2,) = ADB.X(2,); #- H(1) = ADB.H_L_T_mixc; #kJ/kmol H(2) = ADB.H_V_T_mix; #kJ/kmol H(3) = H(1); #kJ/kmol Pisat = ADB.Vappres_all; #Pa V_liq = ADB.Liqmolvol_mix; #m3/kmol V_vap = ADB.Vapmolvol_mix; #m3/kmol rho_liq = ADB.Ldens_mass_mix; #kg/m3 rho_vap = ADB.Vdens_mass_mix; #kg/m3 END #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODEL Condenser UNIT ADB AS ASP_DATABASE P1,P2 AS PIC PARAMETER alpha AS REAL # Lumped friction and flow coefficients, - AreaCond AS REAL # Area of condenser, m2 AreaTube AS REAL # Area of tube between tray 1 and condenser, m2 NoComp AS INTEGER # Number of components, - Scond AS REAL # Surface area of condenser, m2 Toutside AS REAL # Outside temperature, K Uair AS REAL # Heat transfer coefficient to surroundings, kW/m2.K VolCond AS REAL # Volume of condenser, m3 VARIABLE dPcond AS NoType # Pressure difference between tray 1 and condenser, Pa Fcond AS ARRAY(2) OF MolarRate # Product flow rate, kmol/s Fin AS ARRAY(2) OF MolarRate # Feed flow rate of entering streams, kmol/s Fout AS ARRAY(2) OF MolarRate # Exiting molar flowrates, kmol/s Fpurge AS MoleFlow # Vapor purge, test, kmol/s Ftest AS MoleFlow # Vapor inflow from tray 1, test, kmol/s H AS ARRAY(2) OF EnthalpyDensity # Enthalpy in phases, kJ/kmol Hin AS ARRAY(2) OF EnthalpyDensity # Enthalpy in entering streams, kJ/kmol K AS NoType # On/off for purge, - KP AS NoType # Pressure control, - Ksd AS NoType # Increase in heat transfer for shutdown, - KT AS NoType # Temperature control, - Level AS Length # Liquid height, m M AS ARRAY(NoComp) OF Moles # Moles of components in both phases, kmol MTOT AS ARRAY(2) OF Moles # Total moles in both phases, kmol P AS Pressure # Pressure in condenser, Pa Pin AS ARRAY(2) OF Pressure # Pressure in entering streams, Pa Pisat AS ARRAY(NoComp) OF Signal # Saturated vapor pressure, Pa Ppumpset AS Pressure # Pressure setpoint for purge, Pa Qcond AS EnergyRate # Heat added to condenser, kW Qloss AS EnergyRate # Heat loss, kW rho_liq AS Liqdensity # Liquid density, kg/m3 rho_vap AS Vapdensity # Vapor density, kg/m3 rho_vapin AS VapDensity # Vapor density of entering vapor, kg/m3 Rset AS signal # 1/Reflux ratio, - T AS Temperature # Temperature in condenser, K

Tin AS ARRAY(2) OF Temperature # Temperature in entering streams, K UTOT AS Energy # Energy in condenser, kJ V_liq AS LiqMolarVolume # Liquid molar volume, m3/kmol V_vap AS VapMolarVolume # Vapor molar volume, m3/kmol V_vapin AS VapMolarVolume # Vapor molar volume of entering vapor, m3/kmol X AS ARRAY(2,NoComp) OF Fraction # Fractions in both phases, - Zin AS ARRAY(2,NoComp) OF Fraction # Fractions in entering streams, - STREAM DenInlet : rho_vapin, V_vapin AS Densitystream Inlet : Fin(1), Zin(1,),Pin(1),Tin(1),Hin(1) AS Mainstream ProdOutlet : Fcond(1), x(1,),P,T,H(1) AS ProdStream RefluxOutlet : Fout(1), x(1,),P,T,H(1) AS Mainstream Startupline : Fin(2), Zin(2,),Pin(2),Tin(2),Hin(2) AS Mainstream EQUATION # cond subscript: 1 Liquid product # 2 Vapor product (in case of partial Condenser) #-------------------------Balances------------------------------- # Component Molar Balances in Phase 1 and 2 FOR i:= 1 TO NoComp DO $M(i)= SIGMA(Fin*Zin(,i))-SIGMA(Fout*X(,i))-SIGMA(Fcond()*X(,i)); END # Heat Balance in the Mixer $UTOT= SIGMA(Fin*Hin)-SIGMA(Fout*H)-SIGMA(Fcond*H)+ Qcond + Qloss; #------------------------Definitions----------------------------- SIGMA(X(1,))=1; SIGMA(X(2,))=1; FOR i:= 1 TO NoComp DO M(i) = SIGMA(X(,i)*MTOT); END UTOT=SIGMA(MTOT*H); #------------------------Hydrodynamics--------------------------- P1.Ins=Level; P2.Ins=KT*T+KP*P/1e5; Fout(1)=MAX(0,P1.Ous); Qcond= MIN(1,MAX(0,(T-313.15)/5))*MAX(1.25*P2.B,MIN(0,P2.Ous)); #off if T=40°C, starting from T=45°C Fout(1)* Rset=Fcond(1); Ftest=AreaTube/V_vapin/(SQRT(alpha*rho_vapin))*(Pin(1)-P) /(SQRT(ABS(Pin(1)-P)+0.02));#see flow1-cond.xls Fin(1)=MAX(0,Ftest); #purge for N2, Fout(2)=purge. Fpurge=MAX(0,3.56E-5*(P-Ppumpset)); Fout(2)=K*Fpurge; #Purge only positive, K to turn it on/off manually. Fcond(2)=0;#No vapor product dPcond=Pin(1)-P; #------------------------Heattransfer---------------------------- Qloss=Ksd*Uair*Scond*(Toutside-T); #Ksd added to increase cooling down in shutdown, otherwise = 1 #------------------------Geometry-------------------------------- MTOT(1)*V_liq + MTOT(2)*V_vap = Volcond;

Level*Areacond = MTOT(1)*V_liq ; #------------------------Equilibrium------------------------ FOR i:=1 TO NoComp-1 DO P*X(2,i)=X(1,i)*Pisat(i); END X(1,NoComp)=0;# No nitrogen in liquid #------------------------Database PhysProp---------------------- T = ADB.T; #K P = ADB.P; #Pa X = ADB.X; #- H(1) = ADB.H_L_T_mixc; #kJ/kmol H(2) = ADB.H_V_T_mix ; #kJ/kmol Pisat = ADB.Vappres_all; #Pa V_liq = ADB.Liqmolvol_mix; #m3/kmol V_vap = ADB.Vapmolvol_mix; #m3/kmol rho_liq = ADB.Ldens_mass_mix; #kg/m3 rho_vap = ADB.Vdens_mass_mix; #kg/m3 END # Model Condenser #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODEL Reboiler UNIT ADB AS ASP_DATABASE ADB_N2 AS ASP_DATABASE_N2 #for N2 addition P1,P2 AS PIC PARAMETER Nocomp AS INTEGER AreaReb AS REAL VolReb AS REAL Toutside AS REAL Sreb AS REAL Uair AS REAL XMP2initial AS REAL initialLevel AS REAL initialLdensMP2 AS REAL initialLdensMeOH AS REAL VARIABLE Fin AS ARRAY(2) OF MolarRate # Feed flow rate of entering streams, kmol/s Fn2 AS MolarRate # Flow rate of entering N2, kmol/s Fout AS ARRAY(2) OF MolarRate # Exiting molar flowrates, kmol/s Freb AS ARRAY(2) OF MolarRate # Product flow rate, kmol/s Fsuline AS MolarRate # Flow rate of liquid in startup line, kmol/s Fvapdc AS MolarRate # Vapor exiting through downcomer, kmol/s H AS ARRAY(2) OF EnthalpyDensity # Enthalpy in phases, kJ/kmol Hin AS ARRAY(2) OF EnthalpyDensity # Enthalpy in entering streams, kJ/kmol Hinn2 AS EnthalpyDensity # Enthalpy of entering N2, kJ/kmol KL AS NoType # Level control, - KN2 AS NoType # On / off N2 inflow, - KT AS NoType # Temperature control, - KT23 AS NoType # Temperature control tray 23, -

KX AS NoType # Composition control, - Level AS Length # Liquid height, m M AS ARRAY(NoComp) OF Moles # Moles of components in both phases, kmol oles MTOT AS ARRAY(2) OF Moles # Total moles in both phases, kmol P AS Pressure # Pressure in condenser, Pa Pin AS ARRAY(2) OF Pressure # Pressure in entering streams, Pa Pisat AS ARRAY(NoComp) OF Signal # Saturated vapor pressure, Pa Qloss AS EnergyRate # Heat loss, kW Qreb AS EnergyRate # Heat added to reboiler, kW rho_liq AS Liqdensity # Liquid density, kg/m3 rho_vap AS Vapdensity # Vapor density, kg/m3 rho_vapinn2 AS Vapdensity # Vapor density of entering N2, kg/m3 T AS Temperature # Temperature in reboiler, K Tin AS ARRAY(2) OF Temperature # Temperature in entering streams, K UTOT AS Energy # Energy in condenser, kJ V_liq AS LiqMolarVolume # Liquid molar volume, m3/kmol V_vap AS VapMolarVolume # Vapor molar volume, m3/kmol V_vapinn2 AS VapMolarVolume # Vapor molar volume of entering vapor, m3/kmol X AS ARRAY(2,NoComp) OF Fraction # Fractions in both phases, - Zin AS ARRAY(2,NoComp) OF Fraction # Fractions in entering streams, - STREAM DenOutlet : Rho_vap, V_vap AS DensityStream Inlet : Fin(1), Zin(1,), Pin(1), Tin(1), Hin(1) AS Mainstream ProdOutlet: Freb(1), X(1,), P, T, H(1) AS ProdStream Startupline: Fout(1), X(1,), P, T, H(1) AS Mainstream Vapordcout: Fvapdc AS flowstream VBOutlet : Fout(2), X(2,), P, T, H(2) AS Mainstream Weepingin : Fin(2), Zin(2,), Pin(2), Tin(2), Hin(2) AS Mainstream EQUATION # 1 Liquid Reboiler subscript: 1 Liquid flow in # 2 Vapor 2 Liquid weeping in #-------------------------Balances------------------------------- # Component Molar Balances in Phase 1 and 2 FOR i:= 1 TO NoComp-1 DO $M(i)= SIGMA(Fin*Zin(,i))-SIGMA(Fout*X(,i))-SIGMA(Freb()*X(,i))-Fvapdc*X(2,i); END $M(6)= SIGMA(Fin*Zin(,6))+Fn2-SIGMA(Fout*X(,6))-SIGMA(Freb()*X(,6))-Fvapdc*X(2,6); # Heat Balance in the Mixer $UTOT= SIGMA(Fin*Hin)+Fn2*Hinn2 -SIGMA(Fout*H)-SIGMA(Freb*H) -Fvapdc*H(2)+ Qreb + Qloss; #------------------------Definitions----------------------------- SIGMA(X(1,)) =1; SIGMA(X(2,)) =1; FOR i:= 1 TO NoComp DO M(i) = SIGMA(X(,i)*MTOT); END UTOT = SIGMA(MTOT*H); #------------------------Hydrodynamics--------------------------- P1.Ins = Level; #P2.Ins is defined at higher level to control by T_tray(23) Freb(1) =MAX(0,P1.Ous); Qreb = MIN(1,MAX(0,50/9*(level-0.42)))* MIN(1.25*P2.B,MAX(0,P2.Ous) ); Fn2 = KN2*MAX(0,3.56E-6*(1E5-P));

Fout(1) = Fsuline;#for startup line. (No liquid outflow besides product) Freb(2) = 0;#No vapor product #------------------------Heat transfer--------------------------- Qloss = Uair*Sreb*(Toutside-T); #------------------------Geometry-------------------------------- MTOT(1)*V_liq + MTOT(2)*V_vap = Volreb; Level*Areareb = MTOT(1)*V_liq ; #------------------------Equilibrium------------------------ FOR i:=1 TO NoComp-1 DO P*X(2,i) = X(1,i)*Pisat(i); END X(1,NoComp) = 0;# Nitrogen not in liquid #------------------------Database PhysProp---------------------- T = ADB.T; #K P = ADB.P; #Pa X = ADB.X; #- H(1) = ADB.H_L_T_mixc; #kJ/kmol H(2) = ADB.H_V_T_mix; #kJ/kmol Pisat = ADB.Vappres_all; #Pa V_liq = ADB.Liqmolvol_mix; #m3/kmol V_vap = ADB.Vapmolvol_mix; #m3/kmol rho_liq = ADB.Ldens_mass_mix; #kg/m3 rho_vap = ADB.Vdens_mass_mix; #kg/m3 #-------------------N2------------------------------- 298.15 = ADB_N2.T; #K Hinn2 = ADB_N2.H_V_T_N2; V_vapinn2 = ADB.Vapmolvol_mix; rho_vapinn2 = ADB.Vdens_mass_mix; END # Model Reboiler #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODEL Column PARAMETER Feedtray AS INTEGER # Feedtray location, - Nocomp AS INTEGER # Number of components, - NoTrays AS INTEGER # Number of trays, - R AS REAL # Gas constant, J/kmol.K !!!!!! Stray AS REAL # Surface area of tray, m2 Toutside AS REAL # Outside temperature, K Uair AS REAL # Heat transfer coefficient to surroundings, kW/m2.K UNIT Tray AS ARRAY(NoTrays) OF Tray Condenser AS Condenser Reboiler AS Reboiler VARIABLE dPprof AS ARRAY(notrays) OF Notype # Pressure difference profile over the column, Pa Fcond AS MolarRate # Product flow rate of condenser, kmol/s Fdcprof AS ARRAY(notrays) OF MolarRate # Downcomer vapor flow rate profile over the column, kmol/s

Ffeed AS ARRAY(NoTrays,2) OF MolarRate # Molar flowrate of feed, kmol/s Flprof AS ARRAY(Notrays) OF MolarRate # Liquid flow rate profile over the column, kmol/s Freb AS MolarRate # Product flow rate of reboiler, kmol/s Fvprof AS ARRAY(Notrays) OF MolarRate # Vapor flow rate profile over the column, kmol/s Fwprof AS ARRAY(Notrays) OF MolarRate # Dumping flow rate profile over the column, kmol/s H AS ARRAY(2) OF EnthalpyDensity # Enthalpy in product streams, kJ/kmol Hfeed AS ARRAY(NoTrays,2) OF EnthalpyDensity # Enthalpy of feed, kJ/kmol Lprof AS ARRAY(Notrays) OF Length # Liquid level profile over the column, m P AS ARRAY(2) OF Pressure # Pressure in product streams, Pa Pfeed AS ARRAY(NoTrays) OF Pressure # Pressure of feed, Pa Pprof AS ARRAY(Notrays) OF Pressure # Pressure profile over the column, Pa T AS ARRAY(2) OF Temperature # Temperature in product streams, K Tfeed AS ARRAY(NoTrays) OF Temperature # Temperature of feed, K Tprof AS ARRAY(NoTrays) OF Temperature # Temperature profile over the column, K X AS ARRAY(2,Nocomp) OF Fraction # Fractions in product streams, - xprof AS ARRAY(Notrays,Nocomp) OF fraction # Fractions profile in liquid phase over the column, - yprof AS ARRAY(Notrays,Nocomp) OF fraction # Fractions profile in vapor over the column, - Zfeed AS ARRAY(NoTrays,2,Nocomp) OF Fraction # Fractions in feed, - STREAM BottomProduct : Freb, X(1,), P(1), T(1), H(1) AS ProdStream FeedStreams : Ffeed, Zfeed, Pfeed, Tfeed, Hfeed AS ARRAY(NoTrays) OF MainStream TopProduct : Fcond, X(2,), P(2), T(2), H(2) AS ProdStream # 1 Liquid or bottom product # 2 Vapor or top product EQUATION #-------------------------Connections---------------------------- #Tray connections FOR i :=1 TO NoTrays -1 DO Tray(i).LiquidOutlet IS Tray(i+1).LiquidInlet ; Tray(i+1).VapourOutlet IS Tray(i).VapourInlet ; Tray(i+1).DensityStreamOut IS Tray(i).DensityStreamIn; Tray(i).Fout(3) IS Tray(i+1).Fin(3); Tray(i).X(1,) IS tray(i+1).Zin(3,); Tray(i).H(1) IS tray(i+1).Hin(3); Tray(i).Vapordcin IS tray(i+1).Vapordcout; Tray(i).levelsin IS tray(i+1).levelsout; END #For i #Feedstreams FOR i:=1 To NoTrays DO Tray(i).FeedStream IS FeedStreams(i) ; END #For i #Connnections to condenser Tray(1).LiquidInlet IS Condenser.RefluxOutlet; Tray(1).VapourOutlet IS Condenser.Inlet; Tray(1).DensityStreamOut IS Condenser.DenInlet; Tray(1).Fin(3) = 0; Tray(1).Zin(3,)= 0; Tray(1).Hin(3) = Tray(1).Hin(1); Tray(1).Fvapdc = 0; #Connnections to reboiler Tray(NoTrays).LiquidOutlet IS Reboiler.Inlet ; Tray(NoTrays).VapourInlet IS Reboiler.VBOutlet ; Tray(NoTrays).DensityStreamIn IS Reboiler.DenOutlet; Tray(Notrays).Weepingout IS Reboiler.Weepingin; Tray(Notrays).Vapordcin IS Reboiler.Vapordcout; Tray(Notrays).EffLevel_below = Reboiler.level;

#Product streams BottomProduct IS Reboiler.ProdOutlet ; TopProduct IS Condenser.ProdOutlet ; #Startupline Condenser.Startupline IS Reboiler.Startupline ; #-------------------------Profiles------------------------------- FOR i:=1 TO NoTrays DO Tprof(i)=Tray(i).T; Pprof(i)=Tray(i).P; Lprof(i)=Tray(i).Level; Fvprof(i)=Tray(i).Fin(2); Flprof(i)=Tray(i).Fin(1); Fwprof(i)=Tray(i).Fin(3); Fdcprof(i)=Tray(i).Fvapdcin; dPprof(i)=Tray(i).dP; FOR j:=1 TO NoComp DO xprof(i,j)=Tray(i).x(1,j); yprof(i,j)=Tray(i).x(2,j); END #For j END #For i #-------------------------Reboiler control----------------------- Reboiler.P2.Ins= Reboiler.KT*Reboiler.T +Reboiler.KX*Reboiler.X(1,3) +Reboiler.KL*Reboiler.Level +Reboiler.KT23*Tray(23).T; #Temperature, quality control or level control END #000000000000000000000000000000000000000000000000000000000000000000000000000000 #000000000000000000000000000000000000000000000000000000000000000000000000000000 #000000000000000000000000000000000000000000000000000000000000000000000000000000 #000000000000000000000000000000000000000000000000000000000000000000000000000000 #------------------------------------------------------------------- # Model description of the process #------------------------------------------------------------------- MODEL Proc UNIT BreakT7feed AS Con_break_liq Break_recycle AS P_break Mix_MeOH_feed AS Mixer Mix_PO_feed AS Mixer R5 AS Reactor C AS Column PARAMETER Feedtray AS INTEGER # Feedtray location NoComp AS INTEGER # Number of components NoTrays AS INTEGER # Number of trays VARIABLE Bottoms_offspec AS NoType # Moles offspec bottom product, kmol Bottoms_offspecV AS NoType # Volume offspec bottom product, m3 Bottoms_onspec AS NoType # Moles onspec bottom product, kmol Cash_flow AS NoType # Cumulative cash flow, fl Cat_added AS NoType # Moles catalyst added, kmol Cost_Cat AS NoType # Cumulative cost of catalyst, fl Cost_MDP AS NoType # Cumulative cost of MDP, fl Cost_MeOH AS NoType # Cumulative cost of MeOH, fl Cost_MP2 AS NoType # Cumulative cost of MP-2, fl Cost_MPsteam AS NoType # Cumulative cost of MP-steam, fl Cost_PO AS NoType # Cumulative cost of PO, fl dMassdt AS NoType # Accumulatino of mass in process, kg dMdt AS NoType # Accumulation of MP-2 in reboiler, kmol/s Fmol AS MolarRate # Column feed, kmol/s H AS EnthalpyDensity # Enthalpy of feed, kJ/kmol

initmaterialcost AS NoType # Initial material costs, fl MeOH_added AS NoType # Moles MeOH added, kmol MeOH_purged AS NoType # Moles MeOH purged, kmol MeOH_removed AS NoType # Moles MeOH removed, kmol MeOH_removedV AS NoType # Volume of MeOH removed, m3 Mol_Cat_cost AS NoType # Price of catalyst, fl Mol_MDP_cost AS NoType # Price of MDP, fl Mol_MeOH_cost AS NoType # Price of MeOH, fl Mol_MP2_cost AS NoType # Price of MP-2, fl Mol_PO_cost AS NoType # Price of PO, fl MPsteam_cost AS NoType # Price of MP-steam, fl N2_purged AS NoType # Moles N2 purged, kmol P AS Pressure # Pressure of feed, Pa PO_added AS NoType # Moles PO added, kmol Purged AS NoType # Moles purged, kmol T AS Temperature # Temperature of feed, K X AS ARRAY(NoComp) OF Fraction # Fractions in feed, - STREAM T7Feed : Fmol, X, P, T, H AS Mainstream EQUATION #-------------------------Connections---------------------------- #T7 feed BreakT7feed.T = MIN(BreakT7feed.Tin, 273.15+70.9); #Due to drop in pressure, T drops to 70.9°C. BreakT7feed.Instream IS R5.TubeOut; BreakT7feed.Outstream IS T7Feed; BreakT7feed.Frem = 0; FOR j:=1 TO NoTrays DO T = C.Tfeed(j); P = C.Pfeed(j); X = C.Zfeed(j,1,); END #for j FOR j:= 1 TO Feedtray-1 DO C.Tray(j).Ffeed(1)=0; C.Tray(j).Ffeed(2)=0; C.Hfeed(j,1)= C.Hfeed(Feedtray,1); C.Hfeed(j,2)= C.Hfeed(Feedtray,2); END #for j C.Tray(Feedtray).Ffeed(1)= Fmol; C.Tray(Feedtray).Ffeed(2)= 0;#assume all feed liquid C.Hfeed(Feedtray,1) = H; C.Hfeed(Feedtray,2) = H; #no vapor, this is used for simplification FOR j:= Feedtray+1 TO NoTrays DO C.Tray(j).Ffeed(1)=0; C.Tray(j).Ffeed(2)=0; C.Hfeed(j,1)= C.Hfeed(Feedtray,1); C.Hfeed(j,2)= C.Hfeed(Feedtray,2); END #for j #Reactor feed Mix_MeOH_feed.Out IS Mix_PO_feed.In2; Mix_MeOH_feed.Fin(1) = MAX(0, 0.174598-Mix_MeOH_feed.Fin(2)-Mix_PO_feed.Fin(1)); Mix_PO_feed.Out IS R5.ShellIn; #Recycle Break_recycle.Outstream IS Mix_MeOH_feed.In2; Break_recycle.Fin = C.Condenser.Fcond(1); Break_recycle.Xin = C.Condenser.X(1,); Break_recycle.Pin = C.Condenser.P; Break_recycle.Tin = C.Condenser.T; Break_recycle.Hin = C.Condenser.H(1); Break_recycle.Fremove = MAX(0,C.Condenser.Fcond(1)-0.174598+Mix_PO_feed.Fin(1)); #Remove flow which is larger than in steady state as to prevent MeOH accumulation #-------------------------Economics------------------------------ #Component costs Mol_PO_cost = 112.6; #fl/kmol 112.561 Mol_MeOH_cost = 11.0; #fl/kmol 10.958 Mol_Cat_cost = 101.8; #fl/kmol 101.754

Mol_MP2_cost = 164.4; #fl/kmol 164.383 Mol_MDP_cost = 270.3; #fl/kmol 270.320 #Cumulative costs $Cost_PO = Mix_PO_feed.Fin(1) *Mix_PO_feed.Zin(1,1) *Mol_PO_cost ; $Cost_MeOH = Mix_MeOH_feed.Fin(1)*Mix_MeOH_feed.Zin(1,2)*Mol_MeOH_cost; $Cost_Cat = R5.Mix.Fin(1) *R5.Mix.Zin(1,6) *Mol_Cat_cost ; $Cost_MP2 = MAX(0,SGN(C.Reboiler.X(1,4)-0.88))*C.Freb*C.Reboiler.X(1,4)*Mol_MP2_cost ; $Cost_MDP = C.Freb*C.Reboiler.X(1,5)*Mol_MDP_cost ; initmaterialcost = (C.Reboiler.XMP2initial*Mol_MP2_cost+(1-C.Reboiler.XMP2initial) *Mol_MeOH_cost)*C.Reboiler.initialLevel*C.Reboiler.AreaReb *1/(C.Reboiler.XMP2initial/C.Reboiler.initialLdensMP2 +(1-C.Reboiler.XMP2initial)/C.Reboiler.initialLdensMeOH); #assume initial material costs are at constant temperater = 20°C #Steam MPsteam_cost = 1.3409E-5;#0.000013408853;#fl/kJ $Cost_MPsteam = C.Reboiler.Qreb * MPsteam_cost; #Total cumulative costs Cash_flow = - Cost_PO - Cost_MeOH - Cost_Cat + Cost_MP2 + Cost_MDP - Cost_MPsteam - initmaterialcost; #cumulative revenue #-------------------------Endpoint definition-------------------- dMdt = SIGMA(C.Reboiler.Fin*C.Reboiler.Zin(,4)) -SIGMA(C.Reboiler.Fout*C.Reboiler.X(,4)) -SIGMA(C.Reboiler.Freb()*C.Reboiler.X(,4)) -C.Reboiler.Fvapdc*C.Reboiler.X(2,4); #change smaller than certain value #-------------------------In / Out------------------------------- $MeOH_added = Mix_MeOH_feed.Fin(1); $PO_added = Mix_PO_feed.Fin(1); $Cat_added = R5.Mix.Fin(1); $MeOH_removed = Break_recycle.Fremove; $MeOH_removedV = Break_recycle.Fremove*C.Condenser.ADB.Ldens_mol_mix; $Purged = C.Condenser.Fout(2); $MeOH_purged = C.Condenser.Fout(2)*C.Condenser.X(2,2); $N2_purged = C.Condenser.Fout(2)*C.Condenser.X(2,6); $Bottoms_offspec = C.Reboiler.Freb(1)*MAX(0,SGN(0.88-C.Reboiler.X(1,4))); $Bottoms_offspecV = C.Reboiler.Freb(1) *MAX(0,SGN(0.88-C.Reboiler.X(1,4))) *C.Reboiler.ADB.Ldens_mol_mix; $Bottoms_onspec = C.Reboiler.Freb(1)*MAX(0,SGN(C.Reboiler.X(1,4)-0.88)); #Massbalance dMassdt = Mix_MeOH_feed.Fin(1)*R5.Tube.Molweight(2) #feed, kg/s +Mix_PO_feed.Fin(1)*R5.Tube.Molweight(1) +R5.Mix.Fin(1)*R5.Tube.Molweight(6) -BreakT7feed.Fcat*R5.Tube.Molweight(6) #-BreakT7feed.Frem* is always zero -Break_recycle.Fremove*C.Condenser.ADB.MolWeight_avg_liq -C.Condenser.Fout(2)*C.Condenser.ADB.MolWeight_avg_vap #purge -C.Reboiler.Freb(1)*C.Reboiler.ADB.MolWeight_avg_liq; END # Model Reactor #------------------------------------------------------------------- # Process Description #------------------------------------------------------------------- PROCESS Re UNIT Total AS Proc MONITOR Total.C.Reboiler.Qreb; Total.C.Reboiler.level;

Total.C.Reboiler.P; Total.C.Reboiler.T; Total.C.Reboiler.P1.*; Total.C.Reboiler.P2.*; Total.C.Reboiler.X(*,*); Total.C.Condenser.Qcond; Total.C.Condenser.level; Total.C.Condenser.P; Total.C.Condenser.T; Total.C.Condenser.P1.*; Total.C.Condenser.P2.*; Total.C.Condenser.X(*,*); Total.C.Xprof(*,*); Total.C.Yprof(*,*); Total.C.Fcond; Total.C.Freb; Total.C.Ffeed(*,*); Total.C.Tray(1).P; Total.C.Tray(1).T; Total.C.Tray(1).level; Total.C.Tray(5).P; Total.C.Tray(5).T; Total.C.Tray(5).level; Total.C.Tray(10).P; Total.C.Tray(10).T; Total.C.Tray(10).level; Total.C.Tray(15).P; Total.C.Tray(15).T; Total.C.Tray(15).level; Total.C.Tray(19).P; Total.C.Tray(19).T; Total.C.Tray(19).level; Total.C.Tray(22).P; Total.C.Tray(22).T; Total.C.Tray(22).level; Total.C.Tray(23).P; Total.C.Tray(23).T; Total.C.Tray(23).level; Total.C.Tray(25).P; Total.C.Tray(25).T; Total.C.Tray(25).level; Total.Mix_PO_feed.*; Total.Mix_MeOH_feed.*; Total.Break_recycle.*; Total.BreakT7feed.*; Total.R5.Conversion(*); Total.R5.TprofileTtotal(*); Total.R5.TprofileStotal(*); Total.R5.dTdtprofile(*); Total.R5.Fmolsi; Total.Cost_PO ; Total.Cost_MeOH ; Total.Cost_Cat ; Total.Cost_MP2 ; Total.Cost_MDP ; Total.Cost_MPsteam ; Total.initmaterialcost; Total.Cash_flow ; Total.MeOH_added ; Total.PO_added ; Total.Cat_added ; Total.MeOH_removed ; Total.MeOH_removedV ; Total.Purged ; Total.MeOH_purged ; Total.N2_purged ; Total.Bottoms_offspec ; Total.Bottoms_offspecV; Total.Bottoms_onspec ; Total.dMdt ; Total.dMassdt ; SET WITHIN Total DO

NoComp := 6; #PO, MeOH, MP-1, MP-2, MDP, Catalyst (N(OCH3)3) Notrays := 25; #Number of trays FeedTray := 19; #Feedtray location (1 is top tray) WITHIN C DO Uair := 0.100; #kW/m2.K Stray := 2.89; #m2 Toutside := 273.15+18; #18°C R := 8.314413E3; #J/kmol.K FOR i:=1 TO Notrays-1 DO Tray(i).Hap := 0.035; #height under apron on tray END Tray(Notrays).Hap := 0.10; #height under apron in reboiler FOR i:=1 TO FeedTray-1 DO WITHIN C.Tray(i) DO Height := 0.045; VTray := 2.7387; Beta_set := 0.6; Alpha := 0.03; HolesArea := 0.35; Length := 2.1; PlateArea := 4.68; END # within tray(i) END #for i FOR i:=1 TO NoTrays DO WITHIN C.Tray(i) DO g:=9.81; END # within tray(i) END #for i FOR i:=FeedTray TO NoTrays DO WITHIN C.Tray(i) DO Height := 0.045; VTray := 2.7387; Beta_set := 0.6; Alpha := 0.03; HolesArea := 0.35; Length := 2.1; PlateArea := 4.68; END # within tray(i) END #for i WITHIN Condenser DO AreaCond := 2.5165; VolCond := 4.5045; Scond := 3.14159*1.79*1.79+AreaCond*2; AreaTube := 0.5; Alpha := 0.695254401; WITHIN P1 DO T:=15; END #P1 WITHIN P2 DO T:=15; END #P2 END #within C.Condenser WITHIN Reboiler DO AreaReb := 0.25*3.14159*2.8*2.8; Sreb := 3.14159*2.8*1.5+2*areareb; VolReb := 9.23628;# has been increased, making level 1.5 m max XMP2initial := 0.5; initialLevel := 0.88; initialLdensMP2 := 10.25035; #kmol/m3, @20°C initialLdensMeOH := 24.79184; #kmol/m3, @20°C WITHIN P1 DO T:=10000; END #P1 WITHIN P2 DO T:=10000; END #P2

END #within C.Reboiler END #within C WITHIN R5 DO NoReac := 3; NoTubes := 78; Gz := 0; #horizontal reactor Din := 0.044; #m Dout := 0.05; #m Hid := 5.000; #kW/m2.K S := 0.9; # selectivity K0 := [130.3, 4.05, 4.05]; #see article for unit Ea := [31.24E3, 36.55E3, 36.55E3]; #kJ/kmol Rg := 8.3144; #kJ/kmol.K Pi := 3.141592654; Tcontrol.T := 1000; #just a guess WITHIN Tube DO Lambdaw := 80.4E-3; #kW/m.K WITHIN Wall DO Rhow := 7870; #kg/m3, iron Lambdaw := 80.4E-3; #kW/m.K, iron Cpw := 4.690; #kJ/kg.K, iron WITHIN Shell DO Hod := 5.000; #kW/m2.K Dshell := 0.581; Axial := [FFDM, 1, NoDisc]; #countercurrent END # Within Shell END # Within wall Axial := [BFDM, 1, NoDisc];#countercurrent Reactorlength := (1-0.728)*60;#m here 72.8% of dTadiabatic END # Within Tube NoDisc := 30; WITHIN Tube2 DO Reactorlength:= 161; #m Lambdaw := 80.4E-3; #kW/m.K Axial := [BFDM, 1, NoDisc]; WITHIN Wall2 DO Rhow := 7870; #kg/m3, iron Lambdaw := 80.4E-3; #kW/m.K, iron Cpw := 4.690; #kJ/kg.K, iron END #Within Wall2 END # Within Tube2 END # Within R5 END # Within Total ASSIGN WITHIN Total DO WITHIN C DO FOR j:=1 TO NoTrays DO WITHIN Tray(j) DO zfeed(2,1):= 0.000087; #no vapor feed! zfeed(2,2):= 0.776509; zfeed(2,3):= 0.020992; zfeed(2,4):= 0.200343; zfeed(2,5):= 0.002069; zfeed(2,6):= 0; END #WITHIN tray(j) END # for WITHIN Condenser DO Rset := 0;#1/0.218 in steady state; K := 1; Ppumpset:=1.0E5; #1 bar Ksd :=1; KT :=0; #Temperature control, or KP :=1; #Pressure control

WITHIN P1 DO SP:=1.1; K:=0;#-10 in steady state; B:=0.01;#3.658348052240710E-02 in steady state; END #P1 WITHIN P2 DO SP:=1.0; K:=0;#1E5 in steady state; B:=0;#-7.129896510057987E+03 in steady state; END #P2 END #within C.Condenser WITHIN Reboiler DO WITHIN P1 DO SP:=0.88; K :=0;#-10 in steady state; B :=0;#4.857770249660341E-02 in steady state; END #P1 KN2 :=0; Fsuline :=0; KT :=0; #T control of reboiler KT23 :=0; #T control on tray 23 KX :=0; #X(1,4) control KL :=1; #level control WITHIN P2 DO SP:=396.54;#Tcontrol added in stead of reb X(1,4), 0.898926; K :=0;#st st Tcontrol: 351.3665# off initially,for x(1,4) 1E6 B :=5E3;#8.192249419676275E+03 in steady state; END #P2 END #within C.Reboiler END #within C WITHIN R5 DO Tcontrol.Sp := 420; #chosen as it was highest without Tmax>443K Tcontrol.B := 0;#2.5E-3; Tcontrol.K := 0;#2.5E-4; WITHIN Tube2 DO WITHIN Wall2 DO Tbfw := 273.15+133.5; #K Ubfw := 0;#1.800; #kW/m.K, no cooling until temperature is high enough END # Within Wall2 END #within Tube2 WITHIN Mix DO Zin(1,) := [0, 0, 0, 0, 0, 1]; Pin(1) := 27.5E5;#Pa Tin(1) := 273.15+22.1;#K Hin(1) := -449664.6;#kJ/kmol, catalyst! Q :=0; #specify either Q or T END #Mix END # Within R5 WITHIN BreakT7feed DO Pout :=1E5; END #Within BreakT7feed WITHIN Break_recycle DO Pout :=27.5E5; END #Within Break_recycle WITHIN Mix_MeOH_feed DO Zin(1,) := [0, 1, 0, 0, 0, 0]; Pin(1) := 27.5E5;#Pa

Tin(1) := 273.15+21.9;#K Hin(1) := -238913.5;#kJ/kmol Q := 0; #kW END #WITHIN Mix_MeOH_feed WITHIN Mix_PO_feed DO Fin(1) := 0;#0.0353; Zin(1,) := [1, 0, 0, 0, 0, 0]; Pin(1) := 27.5E5;#Pa Tin(1) := 273.15+22.1;#K Hin(1) := -122262.2;#kJ/kmol Q :=0; #kW END #WITHIN Mix_PO_feed END # Within Total PRESET RESTORE "totalstst" INITIAL WITHIN Total DO Cost_PO = 0; Cost_MeOH = 0; Cost_Cat = 0; Cost_MP2 = 0; Cost_MDP = 0; Cost_MPsteam = 0; MeOH_added = 0; PO_added = 0; Cat_added = 0; MeOH_removed = 0; MeOH_removedV = 0; Purged = 0; MeOH_purged = 0; N2_purged = 0; Bottoms_offspec = 0; Bottoms_offspecV = 0; Bottoms_onspec = 0; WITHIN C DO WITHIN Condenser DO P1.intE = 0; P2.intE = 0; P = 0.997034E5; #gives Tinitial = 291.368 X(1,1) = 0.000114265;#sd values X(1,4) = 3.96E-06; #sd values X(1,3) = 9.26E-10; #sd values X(1,5) = 5.73E-26; #sd values X(2,6) = 0.882797535;#sd values Level = 0.9;#under sd value (=1.1) END WITHIN TRAY(1) DO T = 291.276; X(1,1) = 0.000344087; X(1,4) = 8.11E-14; X(1,3) = 1.09E-19; X(1,5) = 3.09E-22; X(2,6) = 0.883297; Level = 0.00100011; END WITHIN TRAY(2) DO T = 291.296; X(1,1) = 0.000291981; X(1,4) = 7.37E-14; X(1,3) = 9.91E-20; X(1,5) = -4.70E-23;

X(2,6) = 0.883189; Level = 0.00100026; END WITHIN TRAY(3) DO T = 291.319; X(1,1) = 0.000253755; X(1,4) = 6.81E-14; X(1,3) = 9.19E-20; X(1,5) = 1.27E-21; X(2,6) = 0.883062; Level = 0.00100043; END WITHIN TRAY(4) DO T = 291.344; X(1,1) = 0.000226079; X(1,4) = 6.38E-14; X(1,3) = 6.42E-20; X(1,5) = -1.84E-18; X(2,6) = 0.882912; Level = 0.00100064; END WITHIN TRAY(5) DO T = 291.375; X(1,1) = 0.000206296; X(1,4) = 6.02E-14; X(1,3) = -7.72E-19; X(1,5) = -3.45E-14; X(2,6) = 0.88272; Level = 0.0010009; END WITHIN TRAY(6) DO T = 291.414; X(1,1) = 0.000191797; X(1,4) = 5.70E-14; X(1,3) = 1.49E-14; X(1,5) = -4.03E-15; X(2,6) = 0.88247; Level = 0.00100122; END WITHIN TRAY(7) DO T = 291.465; X(1,1) = 0.000180636; X(1,4) = 5.41E-14; X(1,3) = 3.80E-17; X(1,5) = 3.15E-16; X(2,6) = 0.882145; Level = 0.00100161; END WITHIN TRAY(8) DO T = 291.53; X(1,1) = 0.00017154; X(1,4) = 5.14E-14; X(1,3) = -8.66E-17; X(1,5) = 3.23E-16; X(2,6) = 0.881724; Level = 0.0010021; END WITHIN TRAY(9) DO T = 291.614; X(1,1) = 0.000163715; X(1,4) = 4.89E-14; X(1,3) = -2.57E-17; X(1,5) = 1.12E-16; X(2,6) = 0.881178; Level = 0.00100271; END WITHIN TRAY(10) DO

T = 291.723; X(1,1) = 0.000156664; X(1,4) = 4.66E-14; X(1,3) = -1.45E-18; X(1,5) = -1.69E-15; X(2,6) = 0.880468; Level = 0.00100349; END WITHIN TRAY(11) DO T = 291.864; X(1,1) = 0.000150064; X(1,4) = 4.45E-14; X(1,3) = 6.03E-18; X(1,5) = 1.48E-16; X(2,6) = 0.87954; Level = 0.00100448; END WITHIN TRAY(12) DO T = 292.047; X(1,1) = 0.00014369; X(1,4) = 4.25E-14; X(1,3) = 7.22E-18; X(1,5) = 3.34E-13; X(2,6) = 0.87832; Level = 0.00100573; END WITHIN TRAY(13) DO T = 292.287; X(1,1) = 0.000137373; X(1,4) = 4.10E-14; X(1,3) = 6.35E-18; X(1,5) = -4.99E-14; X(2,6) = 0.876707; Level = 0.00100734; END WITHIN TRAY(14) DO T = 292.602; X(1,1) = 0.000130969; X(1,4) = 4.10E-14; X(1,3) = 5.38E-18; X(1,5) = -1.33E-14; X(2,6) = 0.874565; Level = 0.0010094; END WITHIN TRAY(15) DO T = 293.015; X(1,1) = 0.000124348; X(1,4) = 5.18E-14; X(1,3) = 6.68E-18; X(1,5) = -1.85E-15; X(2,6) = 0.871706; Level = 0.00101205; END WITHIN TRAY(16) DO T = 293.555; X(1,1) = 0.000117396; X(1,4) = 1.53E-13; X(1,3) = 1.87E-16; X(1,5) = -8.07E-16; X(2,6) = 0.867882; Level = 0.00101545; END WITHIN TRAY(17) DO T = 294.257; X(1,1) = 0.000110018; X(1,4) = 1.16E-12; X(1,3) = 4.82E-16; X(1,5) = 3.58E-16;

X(2,6) = 0.862771; Level = 0.0010198; END WITHIN TRAY(18) DO T = 295.156; X(1,1) = 0.000102162; X(1,4) = 1.21E-11; X(1,3) = 8.44E-15; X(1,5) = 9.80E-17; X(2,6) = 0.85597; Level = 0.00102537; END WITHIN TRAY(19) DO T = 296.287; X(1,1) = 9.38E-05; X(1,4) = 1.42E-10; X(1,3) = 1.54E-13; X(1,5) = -9.42E-17; X(2,6) = 0.847007; Level = 0.00103243; END WITHIN TRAY(20) DO T = 297.672; X(1,1) = 8.51E-05; X(1,4) = 1.77E-09; X(1,3) = 2.95E-12; X(1,5) = -1.61E-16; X(2,6) = 0.835389; Level = 0.00104128; END WITHIN TRAY(21) DO T = 299.308; X(1,1) = 7.62E-05; X(1,4) = 2.29E-08; X(1,3) = 5.77E-11; X(1,5) = 6.77E-17; X(2,6) = 0.820704; Level = 0.00105222; END WITHIN TRAY(22) DO T = 301.152; X(1,1) = 0.000067421; X(1,4) = 3.02E-07; X(1,3) = 1.14E-09; X(1,5) = 4.23E-14; X(2,6) = 0.802825; Level = 0.00106548; END WITHIN TRAY(23) DO T = 303.097; X(1,1) = 5.89E-05; X(1,4) = 3.94E-06; X(1,3) = 2.21E-08; X(1,5) = 4.83E-12; X(2,6) = 0.782347; Level = 0.00108113; END WITHIN TRAY(24) DO T = 304.939; X(1,1) = 5.10E-05; X(1,4) = 4.81E-05; X(1,3) = 4.00E-07; X(1,5) = 5.98E-10; X(2,6) = 0.761326; Level = 0.00110027; END WITHIN TRAY(25) DO

T = 306.322; X(1,1) = 4.29E-05; X(1,4) = 0.000722185; X(1,3) = 9.69E-06; X(1,5) = 5.00E-08; X(2,6) = 0.744581; Level = 0.0015; END WITHIN REBOILER DO P1.intE = 0; P2.intE = 0; #level chosen, X(2,6) kept at sd value, #X(1,4)/X(1,2) chosen @ 0.5, #NOT SD values. Startup needs an initial amount of MP-2 P = 0.997079E5;#gives 316.388. X(1,1) = 0; X(1,4) = XMP2initial; X(1,3) = 0; X(1,5) = 0; X(2,6) = 0.771483; Level = initialLevel; END END #within C WITHIN R5 DO Tcontrol.IntE =0; WITHIN Tube DO FOR z:=0|+ TO ReactorLength DO T(z) = 20+273.15; FOR i:=3 TO NoComp DO C(i,z) = 0; END #For i C(1,z) = 0; C(2,z) = 24.7918399935674;#kmol/m3 END #For z WITHIN Wall DO FOR z:=0 TO ReactorLength DO Tw(z) = 20+273.15; END #For z WITHIN Shell DO FOR z:=0 TO ReactorLength|- DO Tc(z) = 20+273.15; FOR i:=3 TO NoComp DO Cc(i,z) = 0; END #For i Cc(1,z) = 0; Cc(2,z) = 24.7918399935674;#kmol/m3 END #For z END # Within Shell END # Within Wall END # Within Tube WITHIN Tube2 DO FOR z:=0|+ TO Reactorlength DO T(z) = 20+273.15; FOR i:=3 TO NoComp DO C(i,z) = 0; END #For i C(1,z) = 0; C(2,z) = 24.7918399935674;#kmol/m3 END #For z WITHIN Wall2 DO FOR z:=0 TO Reactorlength DO Tw(z) = 20+273.15; END #For z END # Within Wall2 END # Within Tube2 END # Within R5 END # Within Total SOLUTIONPARAMETERS

MONITOR := ON; gRMS := "base -file -nogui -nooverwrite";#ON; #to write .gRMS to file without viewing it gPLOT := OFF; BlockDecomposition := ON; ReportingInterval := 5; OutputLevel := -1; AbsoluteAccuracy := 1e-7; EffectiveZero := 1e-6; InitAccuracy := 1e-5; Diagnostics := OFF; MaxInitIterations := 1000000; MaxIterNoImprove := 10000; NStepReductions := 100000; LASolver := "MA28"; SCHEDULE PARALLEL SEQUENCE CONTINUE UNTIL Total.BreakT7feed.Xout(4)>0.15; END #sequence PARALLEL SEQUENCE #reactor CONTINUE UNTIL #wait for Ttube to be about Tshell and Tshell to be above 370 K Total.R5.Tube.T(Total.R5.Tube.Reactorlength) > Total.R5.Tube.Wall.Shell.Tc(Total.R5.Tube.Wall.Shell.Reactorlength)-5 AND Total.R5.Tube.Wall.Shell.Tc(Total.R5.Tube.Wall.Shell.Reactorlength) > 370; REPLACE #@10881 Total.Mix_PO_feed.Fin(1), #add PO and cat-bias Total.R5.Tcontrol.B WITH Total.Mix_PO_feed.Fin(1):=0.0353; Total.R5.Tcontrol.B:=2.5E-3; #just a guess; END CONTINUE UNTIL #wait untill PO is in tube Total.R5.Tube.Wall.Shell.Xcmol(1,0) > 1E-3; REINITIAL #@10999 Total.R5.Tcontrol.IntE WITH Total.R5.Tcontrol.IntE = 0; END REPLACE Total.R5.Tcontrol.K WITH Total.R5.Tcontrol.K:=2.5E-3/10; END CONTINUE UNTIL Total.R5.TprofileTtotal(37)>Total.R5.Tube2.Wall2.Tc(0)+5; REPLACE #@14096 Total.R5.Tube2.Wall2.Ubfw WITH Total.R5.Tube2.Wall2.Ubfw:=1.800; #kW/m2.K END END #sequence reactor SEQUENCE #column { Model ScheduleSU this part has been added for easy access through function list} CONTINUE UNTIL Total.N2_purged > 2.57 MONITOR FREQUENCY 60 REINITIAL #make sure no IntE ever becomes too big. @185 Total.C.Condenser.P2.IntE,

Total.C.Reboiler.P2.IntE WITH Total.C.Condenser.P2.IntE = 0; Total.C.Reboiler.P2.IntE = 0; END REPLACE #@185 Total.C.Reboiler.P2.B, Total.C.Reboiler.P2.K, Total.C.Reboiler.P2.SP, Total.C.Condenser.K, Total.C.Condenser.P1.B, Total.C.Condenser.P2.SP WITH Total.C.Reboiler.P2.B:=MAX(0,MIN(8.192249419676275E+03, 3000/100*(Time-OLD(Time))+OLD(Total.C.Reboiler.P2.B))); Total.C.Reboiler.P2.K:=-1E4;#0.25 * 8.2E3 kW/-0.2m; Total.C.Reboiler.P2.SP:=0.88; Total.C.Condenser.K:=0; Total.C.Condenser.P1.B:=3.658348052240710E-02; Total.C.Condenser.P2.SP:= 4.6; END CONTINUE UNTIL Total.C.Condenser.P > Total.C.Condenser.P2.SP*1E5 REINITIAL #@362 Total.C.Condenser.P2.IntE WITH Total.C.Condenser.P2.IntE = 0; END REPLACE Total.C.Condenser.Rset, Total.C.Condenser.P2.K, Total.C.Condenser.P2.B WITH Total.C.Condenser.Rset:=1/0.218; Total.C.Condenser.P2.K:=1E5; Total.C.Condenser.P2.B:=-7.129896510057987E+03; END CONTINUE UNTIL Total.C.Condenser.Level > Total.C.Condenser.P1.SP REINITIAL #@362 Total.C.Condenser.P1.IntE WITH Total.C.Condenser.P1.IntE = 0; END REPLACE Total.C.Condenser.P1.B, Total.C.Condenser.P1.K WITH Total.C.Condenser.P1.B:=3.658348052240710E-02; Total.C.Condenser.P1.K:=-1; END CONTINUE UNTIL # wait untill PO is in tube, then 4.6 bar is # not necessary anymore #(PO is added after reactor is on temperature) Total.R5.Tube.Wall.Shell.Xcmol(1,0) > 1E-3; REINITIAL #@10999 Total.C.Condenser.P2.IntE, Total.C.Reboiler.P2.IntE WITH Total.C.Condenser.P2.IntE = 0; Total.C.Reboiler.P2.IntE = 0; END REPLACE #st st values Total.C.Condenser.Rset, Total.C.Reboiler.KL, Total.C.Reboiler.KT23, Total.C.Reboiler.P2.SP, Total.C.Reboiler.P2.K, Total.C.Condenser.P2.SP WITH

Total.C.Condenser.Rset:=1/0.218; Total.C.Reboiler.KL:=0; Total.C.Reboiler.KT23:=1; Total.C.Reboiler.P2.SP:=362;#396.54, reboiler, 362.000 is tray 23 Total.C.Reboiler.P2.K:=1000; Total.C.Condenser.P2.SP:=1; END CONTINUE UNTIL Total.C.Reboiler.Level > Total.C.Reboiler.P1.SP OR Time > 150000 REINITIAL #@10999 Total.C.Reboiler.P1.IntE WITH Total.C.Reboiler.P1.IntE = 0; END REPLACE Total.C.Reboiler.P1.B, Total.C.Reboiler.P1.K WITH Total.C.Reboiler.P1.B:=4.857770249660341E-02; Total.C.Reboiler.P1.K:=-1; END MONITOR FREQUENCY 1000 CONTINUE UNTIL (ABS(Total.dMdt) < 2E-6 AND Total.C.Reboiler.X(1,4) > 0.883) AND Time > 20000 CONTINUE UNTIL Time > 60000 END #sequence column END #parallel END #parallel END # Process Reactor

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Dynamic modeling for startup and shutdown

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