Synthesis and Design of Demethaniser Flowsheets for Low ...

Synthesis and Design of Demethaniser Flowsheets

for Low Temperature Separation Processes

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy

in the Faculty of Engineering and Physical Sciences

2011

Muneeb Nawaz

Under the supervision of

Dr. Megan Jobson

Prof. Robin Smith

Centre for Process Integration

School of Chemical Engineering and Analytical Science

2

TABLE OF CONTENTS

List of Figures ..........................................................................................................7

List of Tables ..........................................................................................................10

Abstract ...................................................................................................................12

Declaration .............................................................................................................13

Copyright Statement ...............................................................................................13

Dedication...............................................................................................................14

Acknowledgements .................................................................................................15

Nomenclature .........................................................................................................16

Publications and presentations ..............................................................................21

Chapter 1 Introduction ....................................................................................22

1.1 Background......................................................................................................22

1.2 Motivation and objective of the work............................................................27

1.3 Thesis outline ...................................................................................................28

1.4 Contributions of this work..............................................................................29

Chapter 2 Literature Review ...........................................................................31

2.1 Introduction .....................................................................................................31

2.2 Process synthesis..............................................................................................31

2.3 Separation process synthesis ..........................................................................35

2.3.1 Knowledge-based methods............................................................................................. 36

2.3.2 Optimisation based methods .......................................................................................... 38

2.4 Synthesis of low-temperature separation processes .....................................40

2.5 Commercial applications of demethaniser flowsheets..................................42

2.5.1 Demethaniser flowsheet design and optimisation .......................................................... 47

2.6 Design and simulation methods for distillation columns .............................49

2.6.1 Shortcut design methods ................................................................................................ 50

2.6.2 Rigorous simulation methods ......................................................................................... 51

2.6.3 Minimum reflux calculation........................................................................................... 54

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2.6.4 Distillation column design by boundary value approach................................................ 58

2.7 Conclusions ......................................................................................................63

Chapter 3 Demethaniser Column Design Method .........................................65

3.1 Introduction .....................................................................................................65

3.2 Model implementation ....................................................................................66

3.3 Product Composition Specification................................................................67

3.4 Boundary value method for multicomponent feed mixtures.......................69

3.5 Boundary value method with energy balance...............................................71

3.5.1 Calculation of rectifying section composition profile .................................................... 74

3.5.2 Calculation of stripping section composition profile...................................................... 75

3.6 Extended boundary value method for two phase feed .................................77

3.7 Double feed Column Design by Boundary Value Method...........................80

3.7.1 Composition profiles ...................................................................................................... 82

3.8 Extended boundary value method for column with side reboilers .............85

3.8.1 Composition Profiles for a column with side reboilers .................................................. 85

3.8.2 Illustrative example ........................................................................................................ 88

3.9 Extended boundary value design method for a reboiled absorption column

...........................................................................................................................91

3.9.1 Calculation of composition profiles ............................................................................... 92

3.10 Case studies ......................................................................................................94

3.10.1 Case study 1: HYSYS sample case (Turbo-expander plant) ........................................ 94

3.10.2 Case study 2: Multiple reflux stream hydrocarbon recovery process......................... 100

3.11 Conclusions ....................................................................................................105

Chapter 4 Demethaniser Flowsheet DESIGN AND Simulation Methodology.

.......................................................................................................107

4.1 Introduction ...................................................................................................107

4.2 Heat integration in demethaniser flowsheet................................................108

4.2.1 Heat recovery in multistream heat exchanger .............................................................. 110

4.2.2 Illustrative example ...................................................................................................... 111

4.3 Modelling of flowsheet units .........................................................................113

4.3.1 Demethaniser column model........................................................................................ 113

4.3.2 Flash unit model ........................................................................................................... 114

4

4.3.3 Turbo-expander Model................................................................................................. 115

4.3.4 Refrigeration cycle model ............................................................................................ 117

4.4 Flowsheet simulation and evaluation...........................................................125

4.4.1 Recycle loop convergence............................................................................................ 127

4.5 Case Study......................................................................................................129

4.5.1 Problem inputs.............................................................................................................. 130

4.5.2 Results .......................................................................................................................... 131

4.6 Conclusions ....................................................................................................134

Chapter 5 Fixed Structure Flowsheet Optimisation Using Nonlinear

Programming .......................................................................................................136

5.1 Degrees of freedom of demethaniser system - Optimisation variables .....136

5.1.1 Demethaniser operating pressure ................................................................................. 140

5.1.2 Flash temperature ......................................................................................................... 142

5.1.3 Split ratio of vapour from flash column ....................................................................... 144

5.1.4 Effect of side reboiler duty........................................................................................... 146

5.1.5 Summary of decision variables .................................................................................... 147

5.2 Process optimisation......................................................................................147

5.2.1 Objective function ........................................................................................................ 148

5.2.2 Process constraints ....................................................................................................... 150

5.2.3 Optimisation algorithm................................................................................................. 151

5.2.4 Fixed structure optimisation approach ......................................................................... 153

5.3 Case study ......................................................................................................154

5.3.1 Process constraints ....................................................................................................... 156

5.3.2 Optimisation variables.................................................................................................. 157

5.3.3 Results .......................................................................................................................... 158

5.3.4 Effect of feed and product price changes on optimisation............................................ 160

5.4 Conclusions ....................................................................................................163

Chapter 6 Demethaniser Flowsheet Synthesis by Stochastic Optimisation 164

6.1 Superstructure representation for demethaniser flowsheet ......................164

A. Use of a second flash unit ................................................................................................. 166

B. Side reboilers..................................................................................................................... 166

C. Internal reflux stream ....................................................................................................... 166

D. Use of external refrigeration cycle................................................................................... 166

6.1.1 Summary ...................................................................................................................... 166

6.2 Choice of optimisation method.....................................................................167

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6.3 Simulated annealing ......................................................................................170

6.4 Annealing schedule parameters ...................................................................173

6.4.1 Initial annealing temperature........................................................................................ 173

6.4.2 Acceptance criterion..................................................................................................... 173

6.4.3 Markov chain length..................................................................................................... 174

6.4.4 Cooling schedule .......................................................................................................... 174

6.4.5 Termination criterion.................................................................................................... 175

6.5 Simulated annealing moves ..........................................................................176

6.5.1 Flash unit move ............................................................................................................ 176

6.5.2 Side reboiler move ....................................................................................................... 177

6.5.3 Internal reflux stream move.......................................................................................... 177

6.5.4 Operating conditions move .......................................................................................... 177

6.6 Move probabilities .........................................................................................177

6.7 Stochastic optimisation framework .............................................................178

6.8 Case Study......................................................................................................180

6.8.1 Background .................................................................................................................. 180

6.8.2 Problem inputs.............................................................................................................. 181

6.8.3 Results .......................................................................................................................... 184

6.9 Conclusions ....................................................................................................188

Chapter 7 Conclusions and Future Work.....................................................190

7.1 Conclusions ....................................................................................................191

7.1.1 Discussion .................................................................................................................... 192

7.1.2 Limitations ................................................................................................................... 193

7.2 Future work ...................................................................................................195

References.............................................................................................................197

Appendix A: MATLAB-HYSYS Interface for physical properties and Vapour-

liquid equilibrium data.........................................................................................209

Appendix B: Cost Estimation...............................................................................213

B.1 Capital cost estimation..................................................................................213

B.1.1 Annualised capital cost ................................................................................................ 216

B.1.2 Capital cost estimation for distillation columns........................................................... 217

B.1.3 Capital cost estimation for heat exchangers................................................................. 218

B.2 Operating cost estimation .............................................................................218

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B.2.1 Steam cost.................................................................................................................... 219

B.2.2 Electricity Cost ............................................................................................................ 220

B.2.3 Cooling water cost ....................................................................................................... 220

Final word count 46788

7

List of Figures

Figure 1.1 World marketed energy use by fuel type (EIA 2011)..............................22

Figure 1.2 World natural gas consumption 2007-2035 (trillion cubic feet),.............23

Figure 1.3 UK gas production and demand to 2020 .................................................24

Figure 1.4 Total Ethane extraction from US gas processing (Fasullo, 2008) ...........26

Figure 2.1 Representation of onion model (Smith and Linnhoff, 1988)...................33

Figure 2.2 Case-based reasoning cyclic process (Farkas et al., 2003) ......................34

Figure 2.3 The interaction between process, HEN and refrigeration system (Wang, 2004)............................................................................................40

Figure 2.4 Gas subcooled process (Campbell and Wilkinson, 1981) .......................43

Figure 2.5 Cold residual reflux process (Pitman et al., 1998)...................................44

Figure 2.6 Recycle Split-Vapour process (Pitman et al., 1998) ................................45

Figure 2.7 Recycle Split-Vapour with Enrichment process (Campbell et al., 1999).........................................................................................................45

Figure 2.8 Enhanced NGL recovery process (Nasir et al., 2003) .............................46

Figure 2.9 Technip Cryomax Multiple Reflux Process (Barthe and Gahier, 2009).........................................................................................................47

Figure 2.10 A typical demethaniser column .............................................................50

Figure 2.11 Schematic diagram of an equilibrium stage (Seader and Henley, 1998).........................................................................................................53

Figure 2.12 Composition profiles in a ternary diagram (Doherty and Malone, 2001).........................................................................................................56

Figure 2.13 Schematic of the rectifying section of a distillation column .................59

Figure 3.1 Interlinking MATLAB with HYSYS ......................................................66

Figure 3.2 Schematic of the rectifying section..........................................................73

Figure 3.5 Feed mixing for feed injection between two stages.................................79

Figure 3.8 Schematic of the stripping section with lower feed.................................84

Figure 3.9 Schematic of column stripping section with side heaters ........................86

Figure 3.10 Molar flow profiles: new model (BVM) vs. HYSYS............................90

Figure 3.11 Composition profiles for key components: new model (BVM) vs. HYSYS ...............................................................................................90

Figure 3.13 HYSYS process simulation diagram of a typical expander plant..........95

Figure 3.14 Molar flow profiles: boundary value method (BVM) vs. HYSYS simulation results......................................................................................99

Figure 3.15 Liquid composition profiles: BVM vs. HYSYS simulation results........................................................................................................99

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Figure 3.16 Process flowsheet diagram of multiple reflux stream hydrocarbon recovery process (Patel and Foglietta, 2010) ....................101

Figure 3.17 Molar flow profiles: Boundary value method vs. HYSYS..................104

Figure 3.18 Liquid composition profiles (key components): Boundary value method vs. HYSYS ................................................................................104

Figure 4.1 Generalized gas processing scheme for ethane recovery (Yan et al., 2008).................................................................................................108

Figure 4.2 Composite curves for multistream exchanger (Hewitt and Pugh, 2007).......................................................................................................112

Figure 4.3 T-H curve for an isenthalpic expansion................................................115

Figure 4.4 Pressure-Temperature-Enthalpy Diagram (Wang, 2004) .....................116

Figure 4.5 A Simple vapour-compression refrigeration cycle: a)Flow diagram, b) Temperature-enthalpy diagram (Smith, 2005)....................118

Figure 4.6 Recommended operating temperature range of some refrigerants (Smith, 2005)..........................................................................................120

Figure 4.7 A cascade refrigeration cycle.................................................................122

Figure 4.8 The effect of partition temperature on the total shaftwork (Lee 2001).......................................................................................................123

Figure 4.9 Methods for recycle convergence a) Successive substitution method, b) Wegstein method (Smith, 2005). .........................................128

Figure 4.10 Molar flow profiles: Boundary value method vs. HYSYS..................133

Figure 4.11 Liquid composition profiles: Boundary value method vs. HYSYS...................................................................................................133

Figure 5.1 HYSYS process flowsheet diagram of a typical GSP demethaniser process for NGL recovery ......................................................................138

Figure 5.2 Effect of demethaniser operating pressure on power consumption.......141

Figure 5.3 Effect of demethaniser operating pressure on ethane recovery .............141

Figure 5.4 Effect of flash temperature on total power consumption.......................143

Figure 5.5 Effect of flash temperature on ethane recovery in NGL........................143

Figure 5.6 Effect of vapour split ratio on power requirement.................................145

Figure 5.7 Effect of vapour split ratio on ethane recovery......................................145

Figure 5.8 Effect of side reboiler duty on refrigeration power requirement ...........146

Figure 5.9 Price comparison of natural gas, crude oil , ethane and NGL (EIA 2011).......................................................................................................150

Figure 5.10 Optimisation framework for a fixed structure flowsheet.....................153

Figure 5.11 Process flowsheet diagram of multiple reflux stream hydrocarbon recovery process (Ohara et al., 2008)................................155

Figure 6.1 Superstructure for demethaniser flowsheet synthesis ............................165

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Figure 6.2 Flowchart for simulated annealing algorithm (Choong and Smith, 2004).......................................................................................................172

Figure 6.3 Flow of information in optimisation framework ...................................179

Figure 6.4 Process flowsheet diagram of a typical GSP demethaniser process (Chebbi et al., 2008) ...............................................................................182

Figure 6.5 Case study – Optimised flowsheet.........................................................187

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List of Tables

Table 1.1 Typical composition of natural gas (Mokhatab et al., 2006) ....................24

Table 1.2 UK NTS gas specifications (Jackson et al., 2006) ....................................25

Table 2.1 Hierarchy of decisions in design (Douglas, 1985) ....................................32

Table 3.1 Molar Feed Compositions .........................................................................88

Table 3.2 Validation results: Boundary value design results vs. HYSYS simulation results......................................................................................89

Table 3.3 Feed gas composition – from HYSYS source and simplified for this case study...........................................................................................96

Table 3.4 Column feed streams – flow rates and conditions ....................................96

Table 3.5 Molar compositions of demethaniser feed streams...................................97

Table 3.6 Column details from HYSYS....................................................................97

Table 3.7 Comparison of simulation results from HYSYS and the boundary value design method .................................................................................98

Table 3.8 Column inputs: Material streams (Patel and Foglietta, 2010).................101

Table 3.9 Column inputs: Material streams (Patel and Foglietta, 2010).................102

Table 3.10 Column inputs: Energy streams (from HYSYS simulation).................102

Table 3.11 Molar composition of column input streams ........................................102

Table 3.12 Comparison of simulation results: Boundary value design method vs. HYSYS. ............................................................................................103

Table 4.1 Stream data for multistream exchanger...................................................111

Table 4.2 Cascade refrigeration cycle vs. simple refrigeration cycle .....................125

Table 4.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for this case study ...................................................................................130

Table 4.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008).................................................................................................130

Table 4.5 Comparison of column simulation results: Boundary value design method vs. HYSYS. ...............................................................................132

Table 4.6 Simulation results: Shortcut model vs HYSYS ......................................134

Table 5.1 Feed gas composition - from Chebbi et al. (2008)..................................137

Table 5.2 Effect of demethaniser operating pressure on flowsheet performance............................................................................................140

Table 5.3 Effect of flash feed temperature on flowsheet performance ...................142

Table 5.4 Effect of vapour split ratio on flowsheet performance............................144

Table 5.5 Effect of side reboiler duty on flowsheet performance ...........................146

Table 5.6 Specified temperature and pressure of feed and products (Ohara et al., 2008).................................................................................................154

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Table 5.7 Feed gas composition from patent (Ohara et al., 2008) and simplified for this case study..................................................................154

Table 5.8 Values and bounds of optimisation variables.........................................157

Table 5.9 Simulation results of shortcut model and HYSYS..................................158

Table 5.10 Comparison of optimisation results with base case ..............................159

Table 5.11 Optimisation variables – Base case vs. optimised case.........................159

Table 5.12 Prices of feed and products ...................................................................161

Table 5.13 Comparison of optimisation results with base case ..............................162

Table 5.14 Optimisation variables – Base case vs. optimised case.........................162

Table 6.1 Design constants employed for case study..............................................180

Table 6.2 Simulated annealing parameters ............................................................181

Table 6.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for this case study ...................................................................................181

Table 6.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008).................................................................................................182

Table 6.5 Move probabilities and limits of optimisation variables.........................183

Table 6.6 Simulation results: Shortcut model vs HYSYS ......................................184

Table 6.7 Optimisation results of three solutions from a family of solutions .........185

Table 6.8 Decision variables for base case and best three cases.............................186

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Abstract

A demethaniser process is characterised by interactions between the complex distillation column and other flowsheet units, including the turbo-expander, flash units, multistream exchangers and refrigeration system. When a design problem dealing with demethaniser flowsheets is approached in a systematic way, the number of alternatives to be studied is generally very large. The assessment of all possible flowsheets with numerous options is a time consuming task with many simulations required to select the most economic option. This research presents a systematic approach for demethaniser flowsheet synthesis to generate cost-effective designs with minimal time and effort.

A demethaniser column has many degrees of freedom, including the operating pressure, multiple feeds, the number and duty of side reboilers and the flow rate of the external reflux stream. The additional feed and side reboiler streams enhance the efficiency of the process, but complicate process modelling. The number of design variables is also augmented by additional degrees of freedom such as the location and the order of feeds, the number of stages and the reflux ratio in the column. The complexity of the demethaniser column precludes the use of the Fenske–Underwood–Gilliland shortcut design method. A semi-rigorous boundary value method is proposed for the design of complex demethaniser columns for application within an optimisation framework for process synthesis and evaluation. The results of the proposed design methodology are shown to be in good agreement with those of rigorous simulation.

A simplified flowsheet simulation model based on a sequential modular approach is developed that is able to account for various configurations and inter-connections in the demethaniser process. Improved shortcut models for flash units, the turbo-expander, compressor and refrigeration cycle have been proposed for exploitation in a synthesis framework. A methodology accounting for heat integration in multistream exchangers is proposed. The simplified simulation model is applied for the optimisation of a flowsheet of fixed configuration. The nonlinear programming technique of sequential quadratic programming (SQP) is used as the optimisation method. A case study is presented to illustrate the application of the optimisation approach for maximising the annual profit. A generalised superstructure has been proposed for demethaniser flowsheet synthesis that includes various structural combinations in addition to the operational parameters. The various options included in the superstructure and their effects on flowsheet performance are discussed. A stochastic optimisation technique, simulated annealing, is applied to optimise the superstructure and generate energy-efficient and cost-effective flowsheets. The application of the developed synthesis methodology is illustrated by a case study of relevance to natural gas processing. The results allow insights to be obtained into the important trade-offs and interactions and indicate that the synthesis methodology can be employed as a tool for quantitative evaluation of preliminary designs as well as to facilitate evaluation, selection and optimisation of licensed demethaniser flowsheets.

13

Declaration

No portion of the work referred to in this thesis has been submitted in support of an

application for another degree or qualification of this or any other university or

other institution of learning.

Muneeb Nawaz

Copyright Statement

I. The author of this thesis (including any appendices and/or schedules to this

thesis) owns any copyright in it (the “Copyright”) and he has given The

University of Manchester the right to use such Copyright for any

administrative, promotional, educational and/or teaching purposes.

II. Copies of this thesis, either in full or in extracts, may be made only in

accordance with the regulations of the John Rylands University Library of

Manchester. Details of these regulations may be obtained from the

Librarian. This page must form part of any such copies made.

III. The ownership of any patents, designs, trade marks and any and all other

intellectual property rights except for the Copyright (the “Intellectual

Property Rights”) and any reproductions of copyright works, for example

graphs and tables (“Reproductions”), which may be described in this thesis,

may not be owned by the author and may be owned by third parties. Such

Intellectual Property Rights and Reproductions cannot and must not be

made available for use without the prior written permission of the owner(s)

of the relevant Intellectual Property Rights and/or Reproductions.

IV. Further information on the conditions under which disclosure, publication

and exploitation of this thesis, the Copyright and any Intellectual Property

Rights and/or Reproductions described in it may take place is available

from the Head of School of Chemical Engineering and Analytical Science.

14

Dedication

To

My mother for her love and prayers

15

Acknowledgements

I am in many ways indebted to my supervisor Dr. Megan Jobson for her guidance

and direction without which this project could not have been realized. She has

guided and supported me with her perfect mixture of competence, enthusiasm and

patience. Also, I would like to thank my co-supervisor, Prof. Robin Smith, for his

support and advice when most needed.

Special thanks to Paritta Prayoonyong for helping me during the early stages of

this research. I am grateful to all the students at process integration for providing a

stimulating and friendly environment. I want to thank Yanis, Bostjan, Ankur,

Imran, Anestis, Lu, Yongwen, Elias, Sonia and Michael for transforming the office

into a fun place to work in.

I would also like to thank to Salman, Atif, Babur and Bilal. Without their

friendship and company, my life in Manchester would not have been that

interesting and enjoyable.

I am grateful for the financial support provided by University of Engineering and

Technology, Lahore, Pakistan.

Last, but not the least, I want to express my gratitude to my brother Zuhaib and

sister Saba for all their love and support during all these years.

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Nomenclature

AC annualised capital cost of the equipment

B molar flow rate of bottom product

pC

Heat capacity,

c number of components

D Molar flow rate of the distillate in eq. 2.3

F molar flow rate of feed

E equality constraint functions

G flow rate capacity of utility in Eq. 5.8

h molar enthalpy flow rate

i component i

I inequality constraint functions

( )xH Hessian matrix of the Lagrange function in Eq. 5.11

( )xJ the Jacobian matrix of the constraint functions in Eq. 5.12

L molar flow rate of liquid

m coefficients fitted to the light key component recovery Eq. 3.1

n coefficients fitted to the heavy key component recovery Eq. 3.1

N number of stages

OC cost associated with the use of utility in Eq. 5.8

P pressure

P profit

q liquid fraction of feed stream

Q heating or cooling duty

Q& heat transferred in a zone in Eq. 4.1

r fractional recovery key component in Eq.3.2

17

R reflux ratio (molar)

Rmin minimum reflux ratio

s reboil ratio (molar)

T Temperature,

U Overall heat transfer coefficient between a process unit and the

surroundings,

minV minimum vapour flow in the top section of column

W Power

x vector of liquid mole fraction

y vector of vapour mole fractions

Greek letters

α relative volatility

iβ local volumetric heat transfer coefficient in Eq.4.1

ε pressure ratio, Pout/Pin in Eq. 4.11

θ root of the Underwood equation (2.1)

lmT∆

log mean temperature difference

η efficiency

µ vector of Lagrange multipliers for inequality constraint functions

in Eq. 5.10

ω random number

ρ density

σ standard deviation of the values of the objective function in Eq.

6.6 γ ratio of heat capacities CP/CV of refrigerant in Eq. 4.11

λ vector of Lagrange multipliers for equality constraint functions in

Eq. 5.10

18

Subscripts and Superscripts

0, 1, 2 stage number

1,2 side-reboiler number

a annealing

act actual

B bottom product

cond condenser

D distillate

e, E error, defined in eq. (3.13)

evap evaporator

F feed

HK heavy key

id ideal

in inlet

is isentropic

L, l liquid phase

L lower feed

LK light key

m, n stage number

M middle section

out outlet

op operating cost

prod product

R, rec rectifying section

reb reboiler

RM raw material

S, strip stripping section

sat saturated

U upper feed

19

ut utility

V, v vapour phase

Z error, defined in eq. (3.17) and

(3.33)

Acronyms

BVM boundary value method

CRR cold residue reflux

FUG Fenske-Underwood-Gilliland

GA genetic algorithm

GSP gas subcooled process

HEN heat exchanger network

HK heavy key

HHK heavier than heavy key

LK light key

LLK lighter that light key

LMTD log mean temperature difference

LP linear programming

LPG liquefied petroleum gas

MILP mixed integer linear programming

MINLP mixed integer nonlinear programming

MM million

20

NAG numerical algorithm group

NLP nonlinear programming

NGL natural gas liquids

OHR over head recycle process

OECD organisation for economic co-operation and development

RSV recycle split-vapour

RSVE recycle split-vapour with enrichment

SA simulated annealing

SQP successive quadratic programming

VLE vapour-liquid equilibrium

21

Publications and presentations

• Nawaz, M. and Jobson, M., ‘A new simplified method for design of complex

demethaniser columns’ Chemical Engineering Research and Design. 89

(2011) 1333-1347

• Nawaz, M., Jobson, M., and Smith R., ‘Process design and optimization of

complex demethanizer flowsheets’ AIChE 2010 Annual Meeting, Salt Lake

City USA

• Nawaz, M. and Jobson, M., ‘Synthesis and optimization of demethaniser

flowsheets for low temperature separation processes’ Distillation and

Absorption, Netherlands, (2010).

• Nawaz, M. and Jobson, M., ‘Boundary value design method for complex

distillation columns’ Distillation and Absorption, Netherlands, (2010).

• Nawaz, M. and Jobson “Modelling and optimization of demethaniser

flowsheets for sub-ambient separation systems”. Fluid Separation Subject

Group Event, IChemE. BP Sunbury, London (2010).

• Nawaz, M., Jobson, M., and Smith R., ‘Synthesis and optimization of low

temperature separation processes’. Process Integration Research Consortium

Annual Meeting Manchester, U.K, 2009.

• Nawaz, M., and Jobson M., ‘Design of sub-ambient complex distillation

columns’. 118th International Summer Course. BASF Aktiengesellschaft,

Ludwigshafen, Germany (2008).

Chapter 1 Introduction

22

CHAPTER 1 INTRODUCTION

1.1 Background

About one fifth of the world's primary energy demand is met by natural gas (EIA

2011). US Energy Information Administration (EIA) expects this share to rise over

the next twenty years. Figure 1.2 presents the energy consumption of various fuels

projected over the 2007-2035 period. Measured per energy unit, combustion of

natural gas is cleaner than other fossil fuels both concerning global emissions and

local pollutants (Balat, 2009). Therefore, it could be used to bridge the gap and

reduce emissions from coal before enough energy from renewable sources

becomes available (Mokhatab et al., 2006).

Figure 1.1 World marketed energy use by fuel type (EIA 2011)


23

According to EIA International energy outlook report 2010, natural gas

consumption will increase by 44 percent from 108 trillion cubic feet in 2007 to 156

trillion cubic feet in 2035 as shown in Figure 1.2. The natural gas demand is

expected to increase as the world economy rebounds from the recent economic

downturn. The largest projected increase in natural gas production is for the non-

OECD (Organisation for Economic Co-operation and Development) region, with

the major increments coming from the Middle East, Africa and Russia.

Figure 1.2 World natural gas consumption 2007-2035 (trillion cubic feet),

The UK relies on natural gas to provide energy for heating and electricity more

than any other primary energy source. 39% of the UK’s primary energy comes

from gas, compared with 35% from oil, 15% from coal, 9% from nuclear and 2%

from other sources (UK Parliament, 2003). Figure 1.3 presents the production and

demand of natural gas in UK. The supply gap is shown to increase by 100 bcm

(billion cubic meter) by 2020.


24

Figure 1.3 UK gas production and demand to 2020

The main constituent of natural gas is methane. The other constituents are

paraffinic hydrocarbons such as ethane, propane, and the butanes and impurities

such as nitrogen, carbon dioxide and hydrogen sulphide. Trace quantities of argon,

hydrogen, and helium may also be present. The composition of natural gas varies

depending on the field or reservoir from which it is extracted (Mokhatab et al.,

2006). Table 1.1 outlines the typical composition of raw natural gas before it is

refined.

Table 1.1 Typical composition of natural gas (Mokhatab et al., 2006)

Name Formula Volume (%) Methane CH4 > 85

Ethane C2H6 3-8

Propane C3H8 1-2

Butane C4H10 < 1

Pentane C5H12 < 1

Carbon dioxide CO2 1-2

Hydrogen sulphide H2S <1

Nitrogen N2 1-5

Helium He <0.5


25

After the separation of the impurities (H2S, N2), natural gas liquids (NGL) recovery

is the next step. NGL recovery refers to the process of extracting ethane, propane,

butane and other heavier hydrocarbon products from natural gas. These

hydrocarbons have a greater value as pure components than as a part of the sales

gas. Methane is mainly utilised as a residential and industrial fuel, ethane and

propane for petrochemical synthesis and C2+ components are used in auto fuels

(Fissore and Sokeipirim, 2011).

Worldwide, the gas processing industry meets a wide variety of economic and

recovery objectives, which range from meeting a specification for gas

transportation, to achieving high ethane recovery for providing feed to an ethylene

production plant (Mcmahon, 2004). In UK, the various issues regarding natural gas

include the gas quality from imports, depletion of existing offshore UK gas fields

and a drop in the number of new UK gas field developments (Jackson et al., 2006).

These issues have led to evaluation of more marginal (lower quality) gas fields that

would need special treatment and processing facilities to meet certain

specifications. In UK the natural gas is transported through the national

transmission system (NTS), by the National Grid. The required specifications for

the UK NTS are given in Table 1.2.

Table 1.2 UK NTS gas specifications (Jackson et al., 2006)

Specification Unit Limit

Wobbe Index MJ/sm3 47.2 – 51.41

Nitrogen mol % 5 (max)

carbon dioxide mol % 2 (max)

Oxygen ppmv 10 (max)

Hydrogen sulphide mg/sm3 5 (max)

Total sulphur ppmv 50 (max)

The Wobbe index is used as standard for calculating the heating value of the gas.

gravityspecificGas

HHVIndexWobbe =

where HHV is the higher heating value of the gas (MJ/m3)


26

The extent to which NGL are to be recovered is a balance between capital,

operating cost and the benefits of producing a range of products. It is important to

consider all the implications before any process is selected. The calorific value of

ethane is approximately 1.8 times that of methane (Poling et al., 2001). According

to Farry (1998), a typical natural gas stream with around 5% ethane content, will

have a 4% higher calorific value than a stream consisting of methane only. As a

result, the presence of ethane does not affect the properties of natural gas at low to

medium concentrations. Therefore, the decision to recover ethane from natural gas

is mainly governed by ethane market economics.

The main use of ethane is in ethylene production where it competing with other

NGL and petroleum feedstocks. On average, ethane constitutes 45% of the US

ethylene feedstock mix and it provides the highest ethylene yield of all the

feedstocks (Fasullo, 2008). A study was performed by Envantage Inc. (Fasullo,

2008) to access the outlook of US ethane production. The extraction of ethane from

the natural gas was shown to be dependent on the ratio of price of gas to crude oil.

When this ratio is higher the extraction of ethane is decreased as naphtha from

crude is used as the petrochemical feedstocks.

Figure 1.4 Total Ethane extraction from US gas processing (Fasullo, 2008)

250

300

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450

500

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Jan- 00

Jul- 00

Jan- 01

Jul- 01

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NG

L E

xtr

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PD

High Gas-to-Crude Ratios


27

1.2 Motivation and objective of the work

Ever since the discovery and recognition of natural gas as a desirable fuel, the need

for its transportation to markets has led to the development of treatment and

processing technologies. In order to be competitive in the global market, the

natural gas industry is trying to increase profits, reduce environmental impacts,

being safer and developing a commitment to sustainability in order to be

competitive. Such opportunities include energy savings, cost reductions, increasing

quality standards and eliminating bottlenecks (Sharratt et al., 2008).

Despite recent success of membrane separation and pressure swing adsorption in

natural gas industry, low-temperature processing remains the most important route

for the separation and purification of natural gas components, especially when high

recoveries are required (Mak, 2009, Bullin and Hall, 2000). These systems are

highly interactive and interlinked to each other. Due to the complex interactions

between the separation system and the refrigeration system, synthesis and

optimisation of low-temperature gas separation processes remains a major

challenge to process engineers (Tahouni et al., 2010) . The interactions between the

separation and refrigeration systems need to be considered at the early stages of the

design which affects the process heat integration decisions leading to energy

savings in the overall process (Yiqing et al., 2009).

The recovery of heavier components from natural gas, employing a demethaniser

flowsheet is an example of low temperature gas separation process. The

demethanisation process is characterised by interactions between the complex

distillation column and other flowsheet components, including turbo expander,

flash units, multistream exchangers and external refrigeration system (Mehrpooya

et al., 2006).

The demethaniser is a low-temperature distillation column that makes a separation

between methane and heavier hydrocarbons, to provide pipeline quality methane

and recover natural gas liquids. The demethaniser has many degrees of freedom,

including the operating pressure, the location and the order of feeds, the number


28

and duty of side reboilers and the flow rate of the external reflux stream (Khoury,

2005). The complexity of the demethaniser column does not allow the use of the

Fenske–Underwood–Gilliland shortcut design method. Therefore, there is a need to

develop an appropriate design model for the demethaniser column which is

suitable for application within an optimisation framework for process synthesis and

evaluation.

The current approach for the design of the NGL recovery processes employing

expander based demethaniser column flowsheets is based on previous experience,

design heuristics and process simulation (Jibril et al., 2005). Despite the industrial

importance of the demethaniser process in natural gas separation processes, no

systematic method is available for the design of demethaniser processes (Chebbi et

al., 2010, Mehrpooya et al., 2009, Sharratt et al., 2008). Therefore, a

comprehensive approach for synthesis is required to generate effective and

economic design without excess requirements of engineering time and effort. In

this work, the objective is to develop a synthesis framework for demethaniser

flowsheets. This framework can systematically perform a screening and scoping of

integrated demethaniser flowsheets. In the framework, various possible options

available in these flowsheets are considered.

1.3 Thesis outline

Chapter 2 presents a critical review of relevant publications concerning various

aspects of this work. The challenges faced by design engineers for separation

process synthesis in general and specifically low-temperature separation processes

are highlighted. Various commercial applications and flowsheet options for the

demethaniser processes are also reviewed. Finally, a range of design methods for

distillation columns are discussed, along with their suitability for the design of

demethaniser column.

Chapter 3 presents a new simplified method for the design of demethaniser

columns based on the boundary value method. The design method accommodates

the use of complex column features such as multiple feeds, side heaters, external


29

reflux, etc. The validation of the proposed methodology against the rigorous stage

by stage calculation in a commercial simulation software is also presented.

Chapter 4 discusses a flowsheet design methodology based on a sequential

modular simulation approach. In this chapter, shortcut design models for various

units of the demethaniser flowsheet are developed. The validation of the new

integrated process model is performed by rigorous simulation of a typical

demethaniser process using the Aspen Tech simulation package HYSYS®.

Chapter 5 is dedicated to the optimisation of a flowsheet of fixed structure

flowsheet by employing a nonlinear technique, sequential quadratic programming,

where the design variables to be optimised are chosen following a sensitivity

analysis. Simultaneous optimisation of these variables is carried out to create cost-

effective design solutions while maintaining the performance specifications of the

process, as illustrated by a case study.

A systematic approach for the synthesis of demethaniser flowsheets based on

stochastic optimisation is proposed in Chapter 6. The structural options

incorporated in the superstructure are discussed. The use of simulated annealing, a

stochastic optimisation technique, to optimise the superstructure is proposed. A

case study is presented to demonstrate the applicability of the approach.

A summary of the research and conclusions are provided in Chapter 7.

Suggestions to extend the research are also discussed.

1.4 Contributions of this work

This thesis presents a novel optimisation-based synthesis of system consisting of

demethaniser flowsheets, i.e. to generate a few promising flowsheet configurations

with appropriate operating conditions. The main contributions of this work are

highlighted below:


30

� A novel extension of the established boundary value design method is

proposed in Chapter 3 for modelling demethaniser columns incorporating

o Multi-component feed mixtures

o Two-phase feed

o Columns with side reboilers

o Columns with an external reflux stream

� An novel integrated model for the demethaniser flowsheets is developed in

Chapter 4.

� A nonlinear constrained optimisation problem is formulated in Chapter 5

for fixed structure demethaniser flowsheets.

� In Chapter 6 a demethaniser flowsheet synthesis methodology is proposed

based on stochastic optimisation.

Chapter 2 Literature review

31

CHAPTER 2 LITERATURE REVIEW

2.1 Introduction

This chapter reviews relevant publications concerning different aspects of this

work. Process synthesis, including separation system synthesis, occupies a central

place in process engineering literature. Process synthesis plays a key role in the

identification of the best flowsheet structure to carry out a specific task, such as

conversion of raw material into a product, or separation of a multi-component

mixture.

This first section introduces the area of process synthesis along with the various

challenges faced by design engineers for process synthesis. The discussion is then

elaborated for separation processes and literature on separation process synthesis is

reviewed. Low-temperature separations are discussed in the next section. The

discussion of low-temperature synthesis is further extended for demethaniser

processes for NGL recovery. Various commercial demethaniser processes are also

reviewed.

Finally, shortcut and rigorous methods for the design of distillation columns are

reviewed. The suitability for these design methods for the demethaniser column

design is also discussed.

2.2 Process synthesis

Process synthesis is concerned with the activities in which the various process

elements are combined and the flowsheet of the process is generated so as to meet


32

design objectives. Hence, in process synthesis usually we know process inputs and

outputs but are either required to revamp the flowsheet or create a new flowsheet

(Barnicki and Siirola, 2004).

Traditionally, process synthesis methods can be classified into two groups:

heuristic methods and optimisation based methods. The heuristic methods are

based on the long-term experience of engineers and researchers. The main idea of

the optimisation-based approach is to formulate the synthesis of a flowsheet in the

form of an optimisation problem. It requires an explicit or implicit representation

of a superstructure of process flowsheets from among which the optimal solution is

selected (Westerberg, 2004).

Douglas (1985) has proposed a hierarchical heuristic procedure for chemical

process design where heuristic rules are applied at different design levels to

generate the alternatives. Shortcut calculations, based on economic criteria, are

carried out at every stage of process design. The hierarchy is shown in Table 2.1.

Table 2.1 Hierarchy of decisions in design (Douglas, 1985)

The hierarchical heuristic method of Douglas (1985) emphasizes the strategy of

decomposition and screening. However, the major limitation of this method, with

its sequential nature, is the difficulty to take into account the interactions between

different design levels. The inability to capture interactions also causes problems in

the systematic handling of multi-objective issues within hierarchical design. As a

result, the hierarchical heuristic method offers no guarantee of finding the best

possible design (Li and Kraslawski, 2004).

Level 1. Batch versus continuous

Level 2. Input-output structure of the flowsheet

Level 3. Recycle structure of the flowsheet

Level 4. General structure of the separation system

Level 5. Energy integration


33

Smith and Linnhoff (1988) proposed an ‘onion model’ for decomposing the

chemical process design into several layers (Figure 2.2). In the onion model, the

synthesis process begins at the centre of the onion with the synthesis of the

reaction system, and then proceeds outward. The reactor design affects the

separation and the recycle structures, which are designed next. The reactor, the

separator and the recycle system then dictate the heat recovery requirements.

Finally, the process utility system is designed to satisfy the heating and cooling

requirements of the process. The onion model is an example of sequential and

hierarchical nature of process flowsheet synthesis. Synthesis decisions are made at

each layer of the onion that ensures a feasible product flowsheet.

Figure 2.1 Representation of onion model (Smith and Linnhoff, 1988)

Another heuristic based approach involves the design of the process according to

the phenomena involved in the process. According to this method, reasoning for

design should be started at the level of phenomena occurring in the building

blocks. Gavrila and Iedema (1996) developed a design methodology based on

phenomena-driven process design. The methodology employs kinetic and

thermodynamic knowledge to propose structural and operational design

alternatives. Although the phenomena-based concept of Gavrila and Iedema (1996)

can be used to model conventional units, however, the methodology does not

support the modelling of complex and innovative designs.


34

More recently, a new approach has been developed for process synthesis which is

based on the case-based reasoning. This approach tries to solve new synthesis

problems by reusing solutions that were applied to similar problems in the past.

Farkas et al. (2003) described the main phases of the case-based reasoning

activities as a cyclic process (see Figure 2.2). During the first step, ‘Retrieval’, a

new problem is matched against problems of previous cases by calculating the

value of similarity functions, in order to find the most similar problem and its

solution. If the proposed solution does not meet the necessary requirements of the

new problem, case-based reasoning proceeds onto the next step, ‘Adaptation’, and

creates a new solution. The returned solution and new problem together form a

new case that is incorporated in the case base during the ‘Learning’ stage.

However, case-based reasoning has the disadvantage that the old design cases

strongly influence the approach and there are no methods available for adaptation

to support innovative design (Li and Kraslawski, 2004).

Figure 2.2 Case-based reasoning cyclic process (Farkas et al., 2003)

Grossmann and Daichendt (1996) discussed the major challenges in process

synthesis. They discussed that it is difficult to combine the heuristic search,

optimisation and targeting approaches in such a way that, on the one hand, the

integration is conceptually consistent and rigorous, and on the other it exploits the


35

strengths of each approach. A second issue raised by Grossmann and Daichendt

(1996) is that in most cases, mixed integer non-linear programming (MINLP) or

non-linear programming (NLP) models for process synthesis involve non-

convexities which may give rise to several local optimal solutions. The values of

the objective function differ largely between these solutions because of the large

number of structural alternatives in these process synthesis problems. As a result,

the optimisation algorithm can be trapped in local optima. Because of these

reasons, Grossmann and Daichendt (1996) suggested that there is a strong need for

developing global optimisation methods that are relevant to process synthesis.

In process synthesis, the separation system synthesis remains a very challenging

task (Koolen, 2001, Montolio-Rodriguez and Linke, 2011). Separation process

synthesis addresses a wide range of separation problems such as the selection and

identification of separation technologies, the sequencing of separation tasks and

the determination of appropriate conditions for unit operations (Seuranen et al.,

2005). The next section gives an overview of various approaches to separation

process synthesis.

2.3 Separation process synthesis

When a synthesis problem dealing with multicomponent mixtures and a variety of

separation technologies is approached in a systematic way, the number of

separation alternatives to be studied is generally very large. A screening tool can

reduce the number of design options in the early phases of design before a more

detailed study is undertaken. The tool can also provide a quick estimate of

alternatives without detailed simulation-based analysis, and can be used in the

conceptual process design phase (Caballero and Grossmann, 2004). Most of the

developed separation synthesis methods can be categorized into knowledge-based

and optimisation methods.


36

2.3.1 Knowledge-based methods

Sargent et al., (2004) noted that the current approaches for separation process

synthesis are not able to describe reliably every physical phenomenon and

engineering practice. They suggested that it is not possible to make all the rigorous

time consuming calculations at the early stages of synthesis for all process

alternatives. In practice, engineers rely on their experience and knowledge to select

the alternatives for further study. Thereafter, they usually proceed with more

advanced methods, for instance rigorous simulations.

Various heuristic rules have been proposed by different researchers, such as

heuristic functions (Lu and Motard, 1985) and vapour loads (Malone et al., 1985).

Siirola (1996) discussed that knowledge based generation methods involve a set of

unit operations, using process and thermodynamics constraints. These are used for

flowsheet synthesis by progressively transforming a given feed stream into

products.

Barnicki and Fair (1990), (1992) created a comprehensive rule-based system for

reducing the number of process alternatives in a separation process synthesis. Their

work contains a comprehensive set of heuristics for application to separations of

liquids and gas/vapour mixtures and offers an advice on separation technology

selection and sequencing. A range of separation technologies including

condensation, cryogenic distillation, physical and chemical absorption, membrane

separation were considered. They employed quantitative indicators to rank the feed

components in a list according to the physicochemical property exploited by the

separation technology. The relative position of key components in the ranked list

indicates whether a separation technology is suitable for a feed mixture. However,

the rule based system proposed by Barnicki and Fair (1990), (1992) is more

suitable for initial feasibility screening as compared to process design, as a design

methodology is required for the relevant separation unit.

Jaksland and Gani (1996) also presented an approach for the design and synthesis

of separation processes which employs physicochemical properties and their


37

relationships to separation techniques. For a specified multicomponent separation

problem, subsets of feasible separation techniques are first identified for a binary

mixture and user-specified separation tasks. The number of alternatives for each

separation task is then reduced by systematically analysing the relationships

between properties, separation technique and conditions of operation. After the

final step, an estimate of the final process flowsheet is produced with a list of

possible alternatives for the separation tasks.

Another knowledge based technique known as the attainable region (AR) was

developed by Glasser et al. (1987) for process synthesis. The initial work focused

on reaction systems and was based on the idea of Horn (1961). Horn defined the

AR as the set of all possible outcomes, for the system under consideration, that can

be achieved using the fundamental processes operating within the system, and that

satisfies all constraints placed on the system. Glasser et al. (1987) approached the

idea of the AR from a geometric perspective by considering a reactor as a system

comprising the only reaction and mixing processes.

Recently (Metzger et al., 2009) used attainable region analysis to optimise particle

breakage in a ball mill. The discussed that after the AR is known, a path between

the feed point and a point in the AR can be found. This path can be a combination

of reaction, mixing and other fundamental processes, which could in turn be

interpreted as a process layout with specified operating conditions. Hence by

finding the AR, the optimum process specifications to achieve points in the AR can

also be found.

As knowledge based methods are based on heuristics, they can ignore the potential

of alternative novel process configurations and operating strategies.


38

2.3.2 Optimisation based methods

The optimisation-based methods formulate the synthesis problem for a flowsheet

in the form of an optimisation problem and mostly involve mathematical

programming. These methods consist of an objective function and equality and

inequality constraints. In the separation process synthesis problem, both

continuous and discrete variables exist, which complicates the optimisation

procedure. Continuous variables are to represent states (temperature, pressure, etc.)

and flow rates. Discrete variables describe the topology of a process network or

represent the existence or non-existence of unit operations (Biegler et al., 1997).

Optimisation based process synthesis approach which involves systematic

generation of alternatives approach is highly combinatorial. Grossmann and

Biegler (2004) discussed that the main problem in using the approach of systematic

generation of alternatives is the inability of the algorithm to select wisely among

the alternatives at decision points. This shortcoming of pure systematic generation

algorithms can be solved by using superstructure optimisation (Caballero and

Grossmann, 2006) .

Superstructure optimisation is a process synthesis approach in which the structure

of a process and the operating parameters can be determined simultaneously.

Theoretically, the superstructure initially includes many redundant paths and

alternative units for achieving the design objectives. Then optimisation is

performed to remove the superfluous paths and equipment alternatives to find the

best solution (Grossmann and Biegler, 2004).

Andrecovich and Westerberg (1985) and Shah and Kokossis (2002) adopted

superstructure approaches while addressing the separation synthesis problem using

sequence of simple columns (a single feed and two product column). In their work,

a superstructure is first constructed, within which all possible sequences of simple

distillation columns are embedded. The synthesis problem is formulated as a mixed

integer linear programme (MILP) or a mixed integer non-linear programme


39

(MINLP) and an optimisation algorithm is implemented to obtain the solution. The

combinatorial characteristic of MINLP results in a large number of possible

combinations even for a modest number of binary variables (Floudas and

Gounaris, 2009).

The problem of global optimality in MINLPs have been solved by a number of

techniques: the Outer Approximation algorithm and its variants (Duran and

Grossmann, 1986, Caballero et al., 2005) handle MINLPs such that the binary

variables participate linearly and the continuous variables participate in a convex

manner; the Generalized Outer Approximation algorithm, (Fletcher and Leyffer,

1994), applies to problems with convex functions in the continuous and not

necessarily separable binary variables; the Generalized Benders Decomposition

algorithm, GBD (Floudas et al., 1989) is designed for problems with a convex

continuous part and binary variables in linear or mixed bilinear terms. A detailed

description of these methods is given by Biegler and Grossmann (2004).

Although modern tools such as the General Algebraic Modelling System (GAMS)

facilitate the implementation of different equation systems and provide solvers, the

correct implementation of the system of equations remains still a difficult task due

to the mere size and complexity of the problem (Henrich et al., 2008).

Stochastic optimisation methods are a potential alternative to conventional

methods for solving MINLP problems. These methods appear to overcome most of

the drawbacks suffered by their conventional counterparts. The stochastic methods

make random moves based on an algorithm to explore the solution space. The

search for the optimum is based on the values of the objective function at different

points of the search space. Consequently, discontinuous or non-differentiable

problems can also be optimised. In addition, most stochastic algorithms can avoid

becoming trapped at local optima, making these methods suitable for optimising

non-convex problems (Wang and Li, 2010).


40

2.4 Synthesis of low-temperature separation processes

A separation is considered low-temperature if it requires utility at sub-ambient

temperatures. Examples of processes involving low-temperature separation are

ethylene plants, natural gas liquids (NGL) recovery plants and air separation

plants.

A sub-ambient process usually comprises three major parts, namely: the separation

process, the heat exchanger network and the refrigeration system (Wang and

Smith, 2005), as shown in Figure 2.3. In a typical sub-ambient process, the feed

gas mixture, after compression, is cooled in a network of heat exchangers to the

desired pressure and temperature required for the separation. A sequence of

separation units is used to separate the feed mixture into the required products. The

separation process rejects heat at low-temperatures. This heat is removed by a

refrigeration system.

Figure 2.3 The interaction between process, HEN and refrigeration system

(Wang, 2004)

Refrigeration systems are typically more expensive than other utilities in terms of

energy per unit, because of the high operating cost and capital intensive

compressors associated with them. The operating costs for the refrigeration

systems are often dominated by the cost of shaft work to drive the compressors. In

ProductsFeed HE Network

Separation system

Refrigeration system

Compressor system


41

sub-ambient processes, the design of the refrigeration system dictates the energy

consumption and capital investment of the whole process (Mehrpooya et al., 2009).

Due to the complex interactions between the separation system and the

refrigeration system, synthesis and optimisation of low-temperature gas separation

processes remains a major challenge to process engineers. These systems are

highly interactive and interlinked to each other (Tahouni et al., 2010). Any

modifications in the separation process or in the heat exchanger network will have

a downstream impact on the shaft work requirement of the refrigeration system.

The different design considerations incur trade-offs between energy savings and

extra capital investment.

Wang and Smith (2005) presented a synthesis framework for screening low-

temperature heat-integrated separation systems based on separation task

representation. A separation task is defined as a sharp separation between two

adjacent (in volatility order) components. Their methodology is based on a

sequence superstructure where each separation task was further developed with

several device representations. Wang and Smith (2005) applied a stochastic

optimisation framework using genetic algorithm and further fine-tuned the results

using successive quadratic programming. They found that employing a hybrid

optimisation method results in a robust methodology for the optimisation of

complex low-temperature processes. However, a high computational time was

reported as a disadvantage in the research of Wang (2004). Moreover, the feed to

the distillation column is limited to the saturation conditions, thus not allowing a

two-phase feed.

Recently, Markowski et al. (2007) developed a new approach for energy

optimisation of a sequence of heat-integrated distillation columns for low

temperature processes. The adopted a sequential approach for the design of the

separation system, the refrigeration system and the heat exchanger network. Pinch

analysis was applied for heat integration within the separation sequence. However,

the refrigeration system is not heat integrated with the separation sequence.


42

In summary, the above discussion shows that there are still gaps in literature in the

area of low-temperature separation processes such as: accounting for various

interactions and structural options in the overall flowsheet, simultaneous

optimisation of key design variables in the separation and refrigeration system and

solving a nonlinear problem for flowsheet synthesis to generate practical designs

for commercial applications.

2.5 Commercial applications of demethaniser flowsheets

Among low-temperature separations, one of the important processes is the

recovery of natural gas liquids. Increase in the price of energy sources and global

economic problems have required cryogenic natural gas liquid recovery plants to

become more complex and efficient (Bullin and Hall, 2000, Chebbi et al., 2010).

NGL recovery plants commonly uses cryogenic or absorption processes. There is a

degree of overlap between the cryogenic process using a demethaniser, and the

enhanced absorption processes incorporating refrigeration for improved recovery.

Mehra and Gaskin (1999) compared the cryogenic and absorption processes for

ethane recovery from natural gas. According to them selection of the adequate

technology is dictated by a balance between various factors such as feed

compositions, feed pressure and recovery specifications of products.

In the case of cryogenic turbo-expander processes, a significant portion of the

refrigeration can be obtained via expansion of the feed stream. These processes

readily achieve very low-temperatures (down to around –100°C) and therefore

provide high recovery of the heavy hydrocarbons, with proprietary processes able

to achieve >90% ethane recovery and essentially complete recovery of propane

and heavier hydrocarbons (Mokhatab et al., 2006).

In the 1970’s Ortloff Engineers Inc. developed and patented various processes for

NGL recovery. Based on these patents, there are around 235 expander based NGL

recovery plants in the world (Ortloff, 2011). Pitman et al. (1998) described the

main features of these processes and compared them to the new generation


43

processes proposed by Ortloff Engineers Inc. in the 1980’s and later. Various

process schemes were compared by Pitman et al. (1998) in terms of recovery and

the relative compression power. They discussed that the main characteristic for

most of these processes is to split the vapour from the flash column and employ a

part of it to generate the reflux for the demethaniser tower. For the ethane

recovery, the most widely employed split-vapour-process is the gas subcooled

process (GSP) (Campbell and Wilkinson, 1981) shown in Fig. 2.4.

In a simplified version of the gas subcooled process, the high-pressure feed gas is

cooled, flashed and separated in a high pressure separator into vapour and liquid

streams. The vapour stream is expanded in a turbo-expander which drops the

pressure and partially liquefies it. The turbo-expander simultaneously produces

cooling/condensing of the gas and useful work which may be used to recompress

the sales gas. The liquid from the flash drum is throttled through a valve to about

the same pressure as the expander discharge and fed to an intermediate tray as

lower feed. The vapour from the expander is fed to the top of the demethaniser

column as top feed, and the valve outlet stream is fed to an intermediate tray as the

lower feed (Jibril et al., 2005).

Figure 2.4 Gas subcooled process (Campbell and Wilkinson, 1981)


44

The ethane recovery level in the GSP process is limited by the composition of the

stream acting as an external reflux for the column. In order to overcome this

restriction in recovery, new processes were developed by Ortloff Engineers Inc.

These include the cold residue reflux (CRR), the recycle split vapour (RSV), the

recycle split vapour with enrichment (RVSE) processes (Pitman et al., 1998).

The cold residue recycle (CRR) process is a modification of the gas subcooled

process to achieve higher ethane recovery levels (Figure 2.5). The process

flowsheet is similar to that of the GSP, except that a compressor and a condenser

have been added to the overhead system to take a portion of the residue gas and

provide additional reflux for the demethaniser. This process is attractive for high

ethane recovery (Wilkinson et al., 2002).

Figure 2.5 Cold residual reflux process (Pitman et al., 1998)

Figure 2.6 illustrates the Recycle Split-Vapour (RSV) (Pitman et al., 1998) process

which employs the split vapour feed as the external reflux stream for the

demethaniser. The external reflux stream is produced by withdrawing a small

portion of the residue gas, condensing and sub cooling and flashing it down to the

demethaniser pressure. The additional cost of adding a compressor in the CRR

process is avoided. Although there is a slight decrease in the ethane recovery as

compared to that of CRR process, the lower capital cost and process simplicity

justifies the slight loss of ethane recovery (Campbell et al., 1996).


45

Figure 2.6 Recycle Split-Vapour process (Pitman et al., 1998)

The Recycle Split-Vapour with Enrichment (RSVE) (Campbell et al., 1999)

process shown in Figure 2.6 is a variation of the RSV process, where the recycle

stream withdrawn from the residue gas is mixed with the split-vapour feed before

being cooled in an exchanger. The mixing, thus avoids the need of a separate

exchanger. The advantage of RSVE process is the result of lower capital

investment than RSV process. However, the ethane recovery in this process is

slightly lower than in the RSV process due to mixing the recycle stream with the

split-vapour feed.

Figure 2.7 Recycle Split-Vapour with Enrichment process (Campbell et al.,

1999)


46

Some other companies have developed competitive designs in order to improve

NGL recovery. (Nasir et al., 2003) explored the processes for NGL recovery

developed by Ortloff and compared them with that designed by International

Process Services (IPSI) Inc. (see Figure 2.8). The scheme proposed by IPSI uses a

side-draw taken from the bottom of the column which is used to cool the inlet gas.

The IPSI stripping gas process generates internal refrigeration by expanding a

liquid stream from the demethaniser. This arrangement eliminates the need of

external refrigeration. The flashed vapour is then compressed and returned to the

demethaniser as stripping gas while the flashed liquid combines with the

demethaniser bottom product.

Figure 2.8 Enhanced NGL recovery process (Nasir et al., 2003)

Barthe and Gahier (2009) discussed the CRYOMAX process from Technip France.

The process is known as multiple reflux ethane recovery. A high recovery of

ethane upto 95% can be achieved through this process by employing the multiple

reflux associated with a turbo-expander. The use of multistream exchangers also

enhances the energy efficiency of the process thorough heat integration the heat

integration. The process involves two vapour-liquid separators at different

pressures.


47

Figure 2.9 Technip Cryomax Multiple Reflux Process (Barthe and Gahier,

2009)

To summarize, processes for NGL recovery include a range of potential options.

The selection of an appropriate demethaniser flowsheet for the NGL recovery is

thus a difficult task. The choice of flowsheet structure and operating conditions

affect the recovery level. A systematic methodology for demethaniser flowsheet

synthesis for NGL recovery is thus required. Some of the previous work in the area

of design and optimisation of NGL recovery processes is discussed in the next

section.

2.5.1 Demethaniser flowsheet design and optimisation

There is a lack of academic research in the area of demethaniser process synthesis

and optimisation. One of the earliest studies for optimisation of demethaniser

process was performed by Bandoni et al. (1989), in which they divided the

demethaniser flowsheets into two sections; the compression and above-ambient

heat exchange section and the separation, expansion and below-ambient heat

exchange section. Cold tank temperature and demethaniser operating pressure were

studied as optimisation variables. Energy balance was also performed over the

second section which provided guidelines for the process selection.


48

Diaz et al., (1996) integrated a process simulator and a MINLP algorithm to

optimise the revamp design of an ethane recovery process. A range of natural gas

mixtures with 6–25% of heavy components is studied in order to determine the

optimal plant topology and operating parameters under different process conditions

However, their work was limited to a few configurations and the use of MINLP

algorithm does not guarantee a global optimum.

Mehrpooya et al. (2006) simulated an existing NGL recovery unit using HYSYS.

Two modifications were considered suitable for optimisation: turbo-expander and

turbo-expander exchanger configurations to find the best revamping alternative. A

genetic algorithm was used for optimisation to calculate the maximum profit. This

study however, is not useful in the conceptual design for process synthesis.

Two turbo-expander ethane recovery processes were analysed by Chebbi et al.

(2008): the conventional turbo-expander process (without external reflux) and the

gas subcooled process (GSP). They considered four different gas feeds with

varying proportions of ethane and heavier components. They noted the effect of

demethaniser operating pressure on ethane recovery for the two processes. The

GSP was shown to yield higher ethane recovery for a lean feed and at lower

demethaniser operating pressure compared to the conventional turbo-expander

process. The work by Chebbi et al. (2008) does not account for the complex

interactions between other flowsheet units and is restricted to only one

optimisation variable (column operating pressure).

In a more recent study by Chebbi et al. (2010), simulation of ethane recovery

employing a conventional turboexpander process was performed using Aspen

HYSYS. The use of external refrigeration was also studied in addition to the

column operating pressure. Both the capital and operating cost were calculated in

detail to compare a range of feeds with varying ethane composition. The study,

however, is focused only on comparing the use of refrigeration against the heat

recovery from top product for different operating pressures.


49

To summarize, market competition requires a constant development and

improvement in processing technologies. This is the case for demethaniser

processes; the complex nature of these flowsheets makes their design and

optimisation challenging. No systematic procedure has been described in the

literature to identify the appropriate process technology and operating conditions to

achieve an optimal design for particular product specifications. Therefore, a

flowsheet synthesis and design methodology for demethaniser flowsheets is

required which can be employed as a tool for quantitative evaluation of

preliminary designs as well as to facilitate evaluation, selection and optimisation of

licensed demethaniser flowsheets.

2.6 Design and simulation methods for distillation columns

In order to develop a systematic method for the synthesis and optimisation of

demethaniser flowsheets, a simplified design model for the complex demethaniser

column design is required. As this design model is to be integrated in an

optimisation framework for flowsheet synthesis, it is essential that it allows rapid

execution while offering a sufficiently accurate representation of the process. The

column design model should be able to predict realistically the separation

performance and the column energy requirements.

Demethaniser columns have complex features; including multiple feeds to the

column, side reboilers for heat recovery and an external reflux stream. A typical

demethaniser column is represented in Figure 2.10.


50

External reflux

Multip le feeds

Side reboilers

Figure 2.10 A typical demethaniser column

This section provides a description of some of the existing models for the design

and simulation of distillation columns. These models can be classified into shortcut

and rigorous models.

2.6.1 Shortcut design methods

Shortcut methods for distillation design rely on simplifying assumptions to solve

the column design equations. Analysing a distillation problem on the basis of these

methods is useful for preliminary estimations and for determining the column

operating limits. Shortcut methods are usually capable of calculating the required

number of stages for a given separation problem, whereas rigorous methods

usually assume a fixed number of stages and are more appropriate for simulation

of a column rather than the column design (Khoury, 2005).

The most common shortcut method for the design of distillation columns is the

Fenske-Underwood-Gilliland (FUG) method, as given by Seader and Henley,

(1998). The FUG method has two basic assumptions: constant molar flow within

each section of the column, and constant relative volatility throughout the column.

For a simple distillation column with one feed, one top product and one bottom


51

product, the method requires the specification of the feed conditions and

composition and the recoveries of light and heavy key components. The FUG

method gives reliable results for separation of relatively ideal mixtures and simple

columns. The FUG method, however, cannot be applied for the design of a

demethaniser column, as both the assumptions of constant molar overflow and

constant relative volatility are not applicable in this case.

Suphanit (1999) improved the standard FUG method, taking into account its

limiting assumptions, i.e., constant molar overflow within each column section and

constant relative volatilities throughout the column. At minimum reflux, there are

usually two pinches in a multicomponent distillation column. Constant vapour

flow can only be assumed in the section between the two pinches. Suphanit (1999)

applied the Underwood equations only in the pinch zones, rather than assuming

constant molar flow in the whole column, and applied an enthalpy balance around

the top section of the column to estimate the condenser duty and vapour flow rate

at the top of the column. The reboiler duty was calculated through an overall

enthalpy balance.

Although the method by Suphanit (1999) gives better results for the minimum

reflux compared to those from Underwood equations, the complex features of the

demethaniser column, including multiple feeds, side reboilers and an external

reflux stream, cannot be addressed by using the FUG with enthalpy balance.

Therefore there is a need to develop a new shortcut design method for the


2.6.2 Rigorous simulation methods

Rigorous simulation methods for distillation column design involve the

formulation and solution of a large number of linear and nonlinear equations that

represent material and energy balances and phase equilibrium relations (Khoury,

2005). The main assumptions in the rigorous method are that phase equilibrium is

achieved on each stage and that the entrainment of liquid drops in the vapour phase


52

and vapour bubbles in the liquid phase is negligible. Although rigorous solution

methods require fewer assumptions than shortcut methods, they require numerical

solution algorithms (Seader and Henley, 1998). In comparison, the short cut

models can be solved by employing simple calculations without the need of

complex numerical iterative methods.

Rigorous methods have been developed for a fixed configuration column. Thus,

parameters such as the number of trays, feed tray location, and location of side

heaters and coolers are all fixed. Therefore, the column is completely specified by

defining a number of additional performance specifications equal to the number of

degrees of freedom of the column. The model is then solved to determine all the

other unknown variables.

Rigorous methods need good initialisation in order to converge. Moreover, more

computation time is required, compared with shortcut models.. For a sample

equilibrium stage, as shown in Figure 2.9 the mass balance equations, enthalpy

balance equations and equilibrium equations (known as MESH equations together

with summation equation) for the ith

component on stage j can be written as

(Seader and Henley, 1998):

Mass balance equation for each component i

( ) ( ) 0yVWxULzFxVxLM j,ijjj,ijjj,ij1j,i1j1j,i1jj,i =+−+−++= ++−− ( 2.1)

Energy balance equation for stage j

( ) ( ) 0QhVWhULhFhVhLH ivjjLjjFjV1jL1jjjjj1j1j

=−+−+−++=+− +− ( 2.2)

Phase equilibrium for each component i

0xKyE j,ij,ij,ij,i =−= ( 2.3)

Mole fraction summation for stage j

∑ =−= 01j,ij,y yS (Vapour mole fraction) ( 2.4)

∑ =−= 01j,ij,y xS (Liquid mole fraction) ( 2.5)


53

Figure 2.11 Schematic diagram of an equilibrium stage (Seader and Henley, 1998)

Equations 2.1 to 2.5 making up the generalized column model include nonlinear

equations. Their number increases with the number of components present in the

system. The analytical solution of these equations is not possible; numerical

iterative techniques are required. Many algorithms have been proposed for solving

the equations, a good description of which is presented by Seader and Henley

(1998). Due to the complexity of the equations, most solution algorithms are prone

to convergence difficulties in complex column situations. Contributing to these

difficulties is the large variation in the relative magnitudes of the variables round-

off errors. These equations also result in sparse matrices. Sparse matrices are

widely used in scientific computation, especially in large-scale optimization,

computational fluid dynamics and the numerical solution of partial differential

equations (Shah and Gilbert, 2004). The structure of sparse matrices can be

exploited in numerical techniques, however they require special algorithms for

solutions (Saad, 2003), which may not be necessarily available in commercial

simulation software packages.

1jV +

Vapour from

stage below

Liquid from

stage above

1jL −

Heat transfer

jQ Feed

jU

Vapour side

stream

jW

1

1

1

1

+

+

+

+

j

j

V

j,i

P

T

h

y

j

1j

1j

L

1j,i

P

T

h

x

1j

−

−

−

−

j

j

L

j,i

P

T

h

x

j

1j

1j

L

1j,i

P

T

h

x

1j

−

−

−

−

Stage j

Temperature Tj

Pressure Pj

j,F

j,F

F

j,i

P

T

h

z

F

j

j

jV

jL

Liquid side

stream


54

2.6.3 Minimum reflux calculation

One of the most decisive variables in the design of distillation column is the

minimum reflux ratio, which directly affects the reboiler and condenser duties, the

energy costs of which dominate the process economics in low-temperature

separation systems. For single columns, it is well known that minimum energy

requirements generally correspond to minimum reflux and/or boil-up ratios and an

infinite number of equilibrium stages, so that the column just performs the desired

separation and exhibits one or more pinch points. Most methods for determining

minimum energy requirements are based on either directly finding pinch points or

rigorous column simulations.

The best known method for the calculation of minimum reflux is the Underwood

method, as already explained in Section 2.6.1, which involves the calculation of

minimum vapour flow rate. The Underwood equation describes the minimum

reflux condition, i.e. the minimum allowable reflux for a specified separation

(King, 1980) and is used to find all the roots between the relative volatilities of

light and heavy key components:

qx

i

Fi i −=−

∑ 1θα

α

( 2.6)

Where: αi is the relative volatility of component i.

xF,i is the mole fraction of the component i in the feed stream.

q is the liquid fraction of feed stream.

θ is the root of the Underwood equation given by HKLK αθα <<


55

The minimum vapour flow in the top section and is determined by the following

equation:

min

i

DiV

xi =

−∑

θα

α

( 2.7)

Where xDi is the mole fraction of component i in the top product.

Vmin is the minimum vapour flow in the top section.

The minimum reflux ratio (Rmin) is calculated as:

1minmin −=

D

VR

( 2.8)

where D is the molar flow rate of the top product. The minimum vapour flow in

the bottom section ( '

minV ) is calculated using the following equation:

( )FqVV −−= 1min

'

min ( 2.9)

where F is the molar flow rate of the feed,

q is the quality of feed

However, as discussed in Section 2.6.1, the Underwood method fails to provide

accurate results when applied for the calculation of minimum reflux in the case of


For the calculation of the minimum reflux, Levy et al. (1985) presented the

boundary value method (BVM), based on finite difference approximations of

column composition profiles in the form of ordinary difference equations under the

assumption of constant molar overflow. In this method, the liquid composition

profiles of a ternary mixture can be plotted on a triangular diagram. Composition

profiles are calculated starting from the fully specified product compositions. The

specified product compositions are identified as feasible if the two composition


56

profiles intersect each other. For higher reflux ratios, the number of theoretical

stages can be counted from the composition profiles and the feed location is

indicated from the intersection between the two composition profiles (Figure 2.12).

A set of the product specifications is infeasible if the two compositions profiles do

not intersect for any reflux ratio.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Feed

Bottom

Distillate

Nonane Pentane

Hexane

Strippingprofile

Rectifyingprofile

product

Figure 2.12 Composition profiles in a ternary diagram (Doherty and Malone,

2001)

A similar method derived from the boundary value method called the ‘zero

volume’ method is presented by Julka and Doherty (1990). This method involves

the determination of the minimum reflux ratio by finding the pinch points without

calculating the liquid composition profiles. At minimum reflux, for direct splits,

the stripping node, the rectifying node, and the feed composition are aligned (Julka

and Doherty, 1990). Hence, the minimum reflux ratio can be determined by

varying the reflux ratio iteratively until any three of these points, i.e. the feed

composition, the saddle pinch point and stable node pinch are collinear.


57

Koehler et al. (1995) developed a method for the calculation of minimum reflux

ratio based on a reversible distillation model. This reversible distillation model

assumes that heat can be transferred to and from a column at zero temperature

difference and that no contact of non-equilibrium liquid and vapour streams is

allowed. The column material and equilibrium relations are used to derive the path

equations for reversible distillation. The solution of this reduced set of equations

requires the flow rates of the most and least volatile components to be specified at

the feed plate. According to Koehler et al. (1995), the concentration reached in a

reversible distillation column section for any given amount of energy is exactly the

same as the stationary concentration that is obtained in an adiabatic constant molar

overflow section, provided the same amount of energy is introduced only at the

ends of the column – this is the minimum energy requirement for the section.

Bausa et al. (1998) developed the rectification body method (RBM) for the

determination of minimum energy demands for multicomponent distillation. The

approach is based on geometrical analysis of plate-to-plate composition profiles.

After fixing all product compositions, the amount of the trace components is set to

a non-zero value, since all feed components have to appear in both products in a

finite column. The BVM requires checking all profiles for intersection. Rather than

calculating the manifold of plate-to-plate profiles, RBM approximates the manifold

using all available information. In this method, the accuracy of the minimum reflux

calculations is limited to the case where the composition profiles are not highly

curved, as the method is based on the linear approximation of the curved

concentration profiles.

In summary, most of the methods for calculating minimum reflux ratio have been

used for both ideal and non-ideal mixtures for simple distillation columns. At

present, there is no method for determining the minimum ratio for a complex

column such as a demethaniser. Rigorous simulation methods can be applied to

simulate the column at the expense of computational time. Furthermore, these

methods are mainly used for the simulation of the column of a fixed column


58

design. However, in this work, the distillation column model is to be used for

conceptual design and synthesis of demethaniser flowsheets.

The boundary value method proposed by Levy et al. (1985) is chosen for the

design of a demethaniser column because of its well established theoretical

background and its ability to generate the column design, given the feed and the

product recovery specifications, as do other shortcut distillation design methods.

However, the method needs to be modified and developed further to include the

various modelling and design issues associated with a demethaniser. A detailed

introduction to the original boundary value method for distillation column design

is provided in the next section.

2.6.4 Distillation column design by boundary value approach

The number of theoretical stages in the boundary value method can be counted

from the composition profiles and the feed location is indicated from the

intersection between the two composition profiles (Figure 2.12). A proposed

separation (i.e. a set of the product specifications) is infeasible if the two

composition profiles do not intersect for any reflux ratio.

The original boundary value method is based on the following key assumptions:

� Vapour-liquid equilibrium is achieved on each plate

� The molar flow rates are constant in each section of the column

� The feed enters the column as a saturated liquid

These assumptions simplify the model. The constant molar overflow assumption

allows the material and energy balances to be decoupled, thereby permitting the

composition profiles for the distillation column to be calculated using the material

balance and equilibrium equations (Levy et al., 1985). The assumption of a

saturated liquid feed calculates the reboil ratio from the given reflux ratio.

However, this assumption also limits the applicability of the method, as the method

cannot take into account two-phase or vapour feed conditions.


59

The boundary value method decomposes a single feed column into two sections,

i.e., rectifying section and stripping section. The composition profiles, which

represent the liquid mole fraction on each stage ( i,nx ) can be generated from both

the top and bottom product compositions. The composition profile for the

rectifying section is calculated by performing a mass balance around the rectifying

section. The calculation for the number of stages is started from the top of the

column. If a total condenser is used, the condenser is not counted as an equilibrium

stage, while in the case of a partial condenser, the vapour and liquid leaving the

condenser are in equilibrium, so it is counted as a stage.

Figure 2.13 Schematic of the rectifying section of a distillation column

Stage 1

yn+1,i

Vn+1

xn-1,i

Ln-1

xn,i

Ln

11 V,y i,

Stage n

D,x i,D ,

1V

y i,n

Condenser

Lo


60

Levy and Doherty (1986) calculated the overall and component mass balances

around the rectifying section (see Fig 2.13)

DLV n1n +=+ ( 2.10)

Dx Lx Vy iD,ni,ni1,ni,1n +=++ 11 −=∀ c,.....i ( 2.11)

The constant molar overflow assumption gives:

0-1nn L L L == ( 2.12)

Rearranging equations 2.10 to 2.12 we get:

i,Di,ni,n xR

xR

Ry

1

1

11

++

+=+ 11 −=∀ c,.....i

( 2.13)

where: xn,i is the mole fraction of component i in liquid phase leaving stage n.

yn+1,i is the mole fraction of component i in vapour phase entering stage n.

D

LR o= is the reflux ratio

The calculation of the rectifying composition profile starts from the given top

product specification. The reflux entering the top stage of column has the same

composition as the distillate in the case of a total condenser. In the case of a partial

condenser it can be calculated from the equilibrium calculations of the vapour

product leaving the partial condenser. The composition of the vapour (y1,i) leaving

the top stage is calculated from the mass balance (Eq. 2.13). The composition of

the liquid (x1,i) leaving that stage is calculated using the vapour-liquid equilibrium

calculation. This procedure of calculating (yn+1,i) from the mass balance and (xn,i)

from equilibrium relations continues and the liquid composition data points form

the rectifying composition profile.


61

.

The mass balance around the stripping section (Fig 2.14) gives

BVL m1m +=+ ( 2.14)

The component balance gives

iB,im,mi1,m1m BxyVxL +=++ 11 −=∀ c,.....i ( 2.15)

The constant molar overflow assumption gives:

11-mm VV V ==

( 2.16)

and m1m L L =+ ( 2.17)

B

Vs =

xm+1,i

Lm+1

ym-1,i

Vm-1

ym,i

Vm

xm+1,i

Lm+1

Reboiler B, xB,i

Stage m

x2,i, L2

Figure 2.14 Schematic of stripping section of a distillation column


62

Rearranging equations (2.14) to (2.16), we get,

i,Bi,mi,m xs

ys

sx

1

1

11

++

+=+ 11 −=∀ c,.....i

( 2.18)

where: x i1,m+ is the mole fraction of component i in liquid phase leaving stage m.

y im, is the mole fraction of component i in vapour phase leaving stage m.

B

Vs 1= is the boil-up ratio

In the column, the boil-up ratio is not an independent variable. The boil-up ratio

and reflux ratio are connected via the overall mass and energy balance equations

(Julka and Doherty, 1990).

( ) 1qxx

xxqRs

iD,iF,

iF,iB, −+

−

−+=

( 2.19)

where q is the feed condition and is defined by Eq. 2.20 (Doherty and Malone,

2001):

−

−=

sat,lF

sat,vF

Fsat,v

F

hh

hhq

( 2.20)

where: Fh is molar enthalpy of the feed calculated from the specified feed

composition and condition.

sat,v

Fh is the saturated vapour molar enthalpy of the feed

sat,l

Fh is the saturated liquid molar enthalpy of the feed


63

The feed quality thus indicates the liquid fraction of the feed: negative values of q

indicate a superheated vapour feed, a value of q = 0 indicates a saturated vapour

feed, a value of q = 1 a saturated liquid feed and values of q greater than unity

relates to a subcooled liquid feed.

The calculation of the stripping composition profile starts from the bottom product

specification. The vapour phase leaving the reboiler is assumed to be in

equilibrium with the liquid phase, therefore, the reboiler is counted to be an

equilibrium stage. Composition of the vapour leaving the reboiler is calculated

from the vapour liquid equilibrium calculation. Next, the liquid composition on the

bottom stage can be calculated through Eq. 2.18 while the vapour phase

composition (ym,i) is again calculated using bubble point calculation for given

liquid phase composition (xm,i.). This calculation yields the liquid composition data

points which then form the stripping composition profile.

The boundary value method requires the two composition profiles to intersect each

other to provide the column design details. The number of theoretical stages can be

counted from the composition profiles; the feed location is indicated from the

intersection point between the two composition profiles. This method has been

modified and extended in Ch. 3 to accommodate different design and modelling

issues associated with the demethaniser column.

2.7 Conclusions

This chapter introduces some challenges for separation process synthesis that have

been addressed in the literature. Generally, complete separation synthesis strategies

either do not exist; or the available quantitative approaches are restricted to one or

two separation technologies with connectivity constraints imposed between

different separations (Biegler et al., 1997).


64

Low-temperature separation processes are characterized by complex interactions

between the separation, heat recovery and refrigeration sections. These interactions

are prominent in the demethaniser flowsheets, where any change in one of the sub-

processes affects the others. For the synthesis of a demethaniser flowsheet,

flowsheet configurations and the associated operating conditions need to be

selected to achieve a good performance especially with respect to operating cost

and product value. There is a need for a systematic way to find the appropriate

separation technique and operating conditions for such processes to achieve an

optimal design for a particular feed and product specifications. This work presents

an approach to optimise and screen the various design options for their viability for

the process synthesis of demethaniser flowsheets.

Chapter 3 Demethaniser column design method

65

CHAPTER 3 DEMETHANISER COLUMN DESIGN

METHOD

3.1 Introduction

There is a need to develop a column design procedure that not only provides

reliable process screening, but also simultaneously generates good initialization for

simulation purposes. Given a separation task, before detailed sizing and device

selection, applying a shortcut model can help to make quick decisions about

equipment feasibility, approximate size and cost estimates (Barnicki and Siirola,

2004).

It was discussed in Chapter 2 that none of the existing short-cut design methods

could be applied for the design of a demethaniser column. This chapter presents a

new simplified design method for complex demethaniser columns. The new

method is an extension of the boundary value method which has been applied

previously to asses the feasibility of and to design azeotropic distillation columns

(Levy et al., 1985). As already explained in Section 2.6.4, the boundary value

method (BVM) utilizes composition profiles to design a column and calculate its

energy requirements.

The BVM method is extended to be applied to a multicomponent mixture. Energy

balance is included in the composition profiles calculation. The method is also

modified to include the other important characteristics of the demethaniser column

such as two feed streams, the side reboilers and an external reflux stream. Finally a

new model is developed where the demethaniser is modelled as a reboiled absorber

column. Case studies are presented to show the application of the new design


66

method; developed model results are validated by comparing against rigorous

simulation results in a commercial simulation package.

3.2 Model implementation

The links between various process simulation and physical property estimation

softwares in the wide area of computer aided process engineering led to the

development of CAPE-OPEN (Barrett & Yang, 2005). It is a standard developed

by the CAPE-OPEN Laboratories Network (CO-Lan) consortium (CAPE-OPEN,

2011) to create an effective integration of different modelling approaches. The

CAPE-OPEN standard divides the interchanging programmes into two software

components. The first is a process modelling environment (PME) represented by a

simulation engine, external software and external simulator (Jaworski and

Zakrzewska, 2011). The second group is called process modelling components

(PMC), which are normally databases for use within a PME. The PMC packages

can be used for computing thermo-physical properties and simulation of a

particular unit operation (Fermeglia and Pricl, 2009).

The boundary value method calculation procedure involving the mass and energy

balance equations has been written in MATLAB (version 7.5) which is a numerical

computing environment and programming language. In this work, MATLAB is

selected as the programming language as it provides a complete environment for

programming and interactive data analysis (The Mathworks, 2010).

Figure 3.1 Interlinking MATLAB with HYSYS

M A T L AB H Y S Y S

V L E an d E n th a lp y

M a ss a nd E n erg y

B a la n c e


67

This has been interfaced with AspenTech HYSYS 2006.5® for vapour-liquid

equilibrium and enthalpy calculations. HYSYS can be accessed from external

software, using a method called automation. By writing a code in the external

software, information of a stream or unit operation can be sent to and received

from HYSYS. This methodology is employed in this work for the calculation of

the physical properties, thus avoiding the complexity associated with the coding of

equations of state in MATLAB. This interface also exploits the robustness of

HYSYS physical properties databases and algorithms. The details of the interface

are provided in Appendix A.

3.3 Product Composition Specification

Usually, a separation problem involving a new design requires some design

specifications. These include the feed composition and condition, and the

separation objective in terms of the product recovery and/or purity. In the case of a

demethaniser, normally the product specifications are given in terms of methane

recovery in the top product and ethane in the bottom product. The feed mixture to

be separated the light key (LK) and heavy key (HK) components, and the non-key

components.

There is rarely any information on the product distributions in the first place

because at the conceptual design stage, the product distribution is typically not

available until a rigorous simulation is carried out. It is difficult to arbitrarily

specify the product distribution because it cannot be guaranteed that such product

compositions will be feasible. This is particularly true in multi-component

separations involving more than three components, as there is a considerable

uncertainty in product distribution. The estimation of non-key components in the

products is important as the product specification acts as the initial point for the

composition profiles to be generated (Castillo et al., 1998).

In this work the Hensgtebeck-Geddes correlation (See (King, 1980) references

within) is used to calculate the distribution of the non-key components in the

distillate and bottom product, given the relative volatility of the components and


68

the product specifications in terms of key components. Once the distribution of the

two products is specified, the composition of the overhead and bottom products

can be calculated. This satisfies one of the basic requirements of the boundary

value method which is to know the composition of all the components in the

products.

The Hensgtebeck-Geddes correlation assumes that there is an orderly pattern for

the distribution of the components into the overhead and bottom product with

respect to the relative volatility. In order to account for product distribution of the

non-key components at a finite reflux ratio, the product distribution is first

estimated at total reflux ratio (King, 1980). This is based on the assumption that

the non key components distribute according to following equation (Sinnott,

2003):

nln α mb

dln i

i

i +=

( 3.1)

where

id – distillate flowrate for component i

ib – bottom flowrate for component i

iα – relative volatility of component i relative to the heavy component

m and n - coefficients fitted to the light and heavy key component recoveries

Equation ( 3.1) reveals that a plot of

i

i

b

dln vs. ilnα yields a straight line.

According to Yaws et al. (1981), the Hensgtebeck-Geddes equation for the light

and heavy key component can be can be formulated in terms of fractional recovery

as following:

nlnα mr1

rln LK

LK

LK +=

−

( 3.2)

nlnα mr1

rln HK

HK

HK +=

−

(3.3)


69

where

LKr – Fractional recovery of light key component in top product

LKα – Relative volatility for light key component relative to heavy key component

The two unknown variables, (m and n), will be determined by solving two linear

Eq. 3.2 and 3.3. The two equations correspond to the recoveries and the relative

volatilities of the LK and the HK components in the column respectively. Once m

and n values are established, then the above equations can be applied to estimate

the non-key recovery at a given relative volatility for each of the non-key

components.

3.4 Boundary value method for multicomponent feed mixtures

The boundary value design method was originally developed for ternary mixtures.

For ternary mixtures, intersection of the composition profiles can be visualised

easily on the two-dimensional triangular diagrams. In the case of demethaniser

flowsheets, the feed is seldom a ternary mixture, typically containing more than

five components. Therefore the boundary value method needs to be modified to be

applicable for multicomponent feed mixtures.

Previous work on multicomponent mixtures has addressed issues such as graphical

representation and profile intersection. Thong and Jobson (2001) used manifolds

(the sets of all possible composition profiles) to establish the intersection of

composition profiles in the case of multicomponent systems. This method requires

the specification of the mole fraction of key components, rather than full

specification of product compositions. The distribution of trace components is

allowed to vary. The set of all compositions satisfying this partially specified

product with a specific purity is called the product region. For a given product

region, composition manifolds can be generated for given values of the reflux ratio

and stage number.

The composition manifold is similar to a point on a composition profile.

Composition profiles are, however, calculated for a fully specified product

composition, whereas the composition manifolds are generated for a product


70

region. Composition manifolds have the advantage that they can be used in

multicomponent mixtures. Intersection is achieved when either the rectifying

composition manifold and the stripping stage composition line intersect, or the end

point of the stripping stage composition line lies inside the volume formed by the

rectifying composition manifold and the top product mole fraction (Thong and

Jobson, 2001). Every intersection of a rectifying composition manifold and a

stripping stage composition line will indicate potentially feasible operating

parameters.

In another method to approximate the intersection between the stripping and

rectifying profiles, Amminudin et al. (2001) used a ‘minimum distance’ criterion.

In this method, the rectifying and striping profiles are constructed in the usual way,

starting from the product compositions for the given reflux and reboil ratios. The

intersection of profiles is assessed by calculating the shortest distance in mole

fraction space between the two profiles. If any two points on a pair of profiles are

within this specified minimum distance, the lines are considered to ‘intersect’.

The composition manifold and minimum distance techniques are used to identify

the intersection numerically, rather than graphically. The ‘composition manifold’

method results in multiple solutions for a range of different product compositions

and reflux and boil up ratios. Thus the method can lead to different column

designs. The column design is optimised in the overall flowsheet optimisation. So

at this stage in the development of a design model the minimum distance method

(Amminudin et al., 2001) is used to approximate the profile intersection. This

method is also easier to formulate within the overall synthesis framework.

The intersection between the rectifying and the stripping section according to the

‘minimum distance’ criterion is calculated by the following equation.

Distance = ( )2

∑ −stripn,irecn,i xx

c,...,i 1=∀

( 3.3)

where:

=recn,ix Mole fraction of component i in the rectifying composition profile

stripn,ix = Mole fraction of component i in the stripping composition profile


71

The distance between the liquid composition profiles is calculated for every pair

of stages, one from the rectifying and other from the stripping section. The

difference can be interpreted as the geometrical distance in mole fraction space

between one point on the rectifying profile and another point on the stripping

profile in the composition space. Therefore, the pair of stages that gives the

smallest value of the sum of difference is selected as the candidate for the profile

intersection. If the least sum of difference is the same or smaller than some

'minimum distance', it is approximated that the profiles intersect. In practice, a

value of 0.1 for the 'minimum distance' is found suitable for mixtures containing 6

to 10 components (Amminudin et al., 2001). The feed stage location will be the

stage on the stripping section that corresponds to this minimum difference. At this

minimum difference, the non-integer number of stages is rounded up to obtain an

integer number of stages.

3.5 Boundary value method with energy balance

The original boundary value method introduced by Levy et al. (1985) is limited by

the assumption of constant molar overflow which means that the vapour and liquid

flows are constant from plate to plate in each section of the column. The key

underlying assumption for this condition is that the molar heats of vaporisation of

all components are equal and do not depend on temperature (Doherty and Malone,

2001). In the case of a demethaniser these assumptions are not applicable: due to

the large difference in the size of the methane and ethane molecules, there is a

significant difference between their latent heats of vaporisation.

Knight and Doherty (1986) incorporated the heat effects in the calculation of the

composition profiles, avoiding the constant molar overflow assumption. In this

work, their approach is further explored to include the heat balance in the boundary

value method. The heat balance equations are integrated with the original set of

mass balance Equations (2.11 and 2.15) and then solved simultaneously.


72

Equation ( 3.4) gives the overall energy balance for an adiabatic simple column

condBDrebF QBhDhQFh ++=+ ( 3.4)

where: F is the feed flowrate

rebQ is the duty of reboiler

D is the distillate flowrate

fh is the specific molar enthalpy of the feed

Dh is the molar enthalpy of top product

Bh is the molar enthalpy of reflux stream

condQ is the duty of condenser

Throughout this work, the pressure is assumed to be constant along the column as

well as other unit operations in the overall flowsheet. Although, in reality, a

pressure profile is developed along the column as a result of liquid loading in the

stages and the pressure drop due to friction. The pressure profile in a column may

affect the separation efficiency and the reboiler and condenser duties due to the

dependence of the relative volatilities and the enthalpy of vaporisation on the

pressure.

However, as the design methodology proposed in this work is aimed at conceptual

design and process synthesis, pressure drop in the column can be neglected. This

argument is also supported by the uniformity of column pressure profiles across

the different flowsheets, which is linked to a minimal propagation of the pressure

factor to the comparison of alternative demethaniser flowsheets. The effect of

pressure drop in the demethaniser column design calculations is also shown to be

negligible as illustrated by an example in Section 3.8.2.


73

Figure 3.2 Schematic of the rectifying section

The individual heat loads can be evaluated by performing energy balances across

the appropriate units. The energy across the condenser (Fig 3.2) is given by

( )( )DhRhhRQ DL,rV,r

cond −−+= 121 ( 3.5)

where: R is the reflux ratio

V,rh2 is the molar enthalpy of vapour stream entering the condenser

Dh is the molar enthalpy of top product

L,rh1 is the molar enthalpy of reflux stream

Similarly, the reboiler duty ( rebQ ) is determined from the energy balance over the

column:

condFBDreb QFhBhDhQ +−+= ( 3.6)

DD h,x,D

Qcond

rV,rr y,h,V 222

r1

Lr,1

r1 x,h,L

r

nV 1+

V,rnh 1+ r

ny 1+

rnL

L,r

nh r

nx

Stage n

Stage 1


74

3.5.1 Calculation of rectifying section composition profile

The rectifying section composition profile is calculated by solving material and

energy balances simultaneously along with vapour-liquid equilibrium. Equations

( 3.7) and ( 3.8) are the material and energy balances for the rectifying section

respectively (Figure 3.2).

( ) 01 =−−+ + i,Dr

i,nrn

ri,n

rn DxxLyDL c,.....i 1=∀ ( 3.7)

( ) 01 =+−−+ + condD

L,r

n

r

n

V,r

n

r

n QDhhLhDL ( 3.8)

where condQ is determined from Eq. 3.5.

The calculation starts with the given top product specification (xD,i). The vapour-

liquid equilibrium and the enthalpy data for different streams are calculated using

HYSYS as explained in Section 3.2. For a given reflux ratio, the rectifying liquid

composition profile is calculated starting from the reflux composition ( r

i,nx ) using

the set of Equations ( 3.7) and ( 3.8) and vapour-liquid equilibrium. For the

calculation of liquid flow in the rectifying section Ln, the error in the energy

balance (E) is calculated, starting from the top of the column and proceeding down

stage by stage.

( ) condD

r

n

r

n

V,r

nn QDhhLhDLE +−−+= +1 ( 3.9)

This error is minimized by using Broyden's method with the value of nL being

updated every iteration. Broyden's method is a Quasi-Newton method for the

numerical solution of nonlinear equations in more than one variable (Eyert, 1996).

For solving an equation, Newton's method uses the Jacobian matrix and its

determinant, at every iteration. However, this computation is a difficult and

expensive operation. The Broyden's method computes the Jacobian only at the first

iteration, and to do a rank-one update at the other iterations (Sorensen and Asterby,

2009).


75

The final value of rnL is computed and the energy balance is then applied over the

whole rectifying section in the same manner. The calculation is continued to the

next stage down the column by solving material and energy balances (Equations

( 3.7) and ( 3.8)), for r

i,ny 1+ and r

nL , simultaneously with vapour-liquid equilibrium

for r

inx , . The calculation is stopped when the composition profile reaches its pinch

point where there is no change in composition from one stage to the next. These

data points, calculated from the above calculation are then connected to plot the

rectifying section composition profile.

3.5.2 Calculation of stripping section composition profile

The stripping section composition profile is calculated by performing material,

energy and equilibrium calculations across the stripping section (Figure 3.3) in a

similar manner to the rectifying section.

Stage 2

Stage m

Bi,B h,x,B

V,ssi,

sh,y,V 111

Stage 1

s

mL 1+

si,mx 1+

V,smh 1+

s

mV

si,my

V,smh

L,ssi,

sh,x,L 222

Figure 3.3 Schematic of the stripping section


76

The material and energy balances are:

( ) 01 =−−+ + i,Bi,m

s

m

s

i,m

s

m BxyVxBV c,.....i 1=∀ ( 3.10)

( ) 01 =+−−+ + rebBV,s

ms

mL,s

ms

m QBhhVhBV ( 3.11)

where rebQ is calculated from rearranging Equation ( 3.11).

( )( )BhhsshQ BL,sV,s

reb ++−= 21 1 ( 3.12)

when BVs s

1= , is specified; otherwise, if the feed condition is specified, rebQ is

calculated from Eq. ( 3.6).

For a given bottom product composition ( i,Bx ) and reboil ratio (s), the liquid

composition profile of the stripping section is calculated starting from the bottom

product composition. The vapour composition from the reboiler ( sy1 ) in

equilibrium with the bottom product is determined from the bubble point

calculation. The liquid composition entering the reboiler ( si,x2 ) is then calculated

from the set of equations ( 3.10) and ( 3.11).

The calculation is continued to the next stage up the column by solving the

material and energy balances (equations ( 3.10) and ( 3.11)), for si,mx 1+ and s

mV ,

together with vapour-liquid equilibrium for si,my . For the calculation of vapour flow

in the stripping section s

mV , the error in the energy balance between the two stages

in the stripping section ( Z ) is calculated and minimized by applying the Broyden’s

method as before.

( ) rebBV,s

ms

mV,s

ms

m QBhhVhBVZ +−−+= ( 3.13)

The stripping section composition profile is plotted by calculating the liquid

composition ( mi,sx ) at each of the stripping stage. The calculation is continued until

the composition profile either reaches its pinch point or intersects the rectifying

profile.


77

3.6 Extended boundary value method for two phase feed

The original boundary value model (Levy et al., 1985) makes two assumptions

regarding the feed; firstly, the feed is fed onto one stage, i.e. both liquid and vapour

fraction are fed to the same stage, and, secondly, the feed tray behaves as an

equilibrium stage, i.e. both mixing and equilibrium mass transfer occur on the

same tray. Under these assumptions the liquid composition of the last stage of the

stripping section profile has to be exactly the same as the liquid composition

calculated from the last stage of the rectifying section. For a feasible column

design, not only do the overall balances have to be satisfied, but also the section

profiles have to form a continuous profile between the bottom and the top product

(Julka and Doherty, 1990). The intersection of either the liquid or the vapour

composition profiles indicates a feasible design, irrespective of the feed quality and

the number of components.

The assumption that the feed is introduced to only one equilibrium tray can

practically be achieved if the feed is not in the two-phase region, i.e. if it is either a

saturated or subcooled liquid, a saturated or superheated vapour. In the case of a

demethaniser column, the feeds to the column are usually two-phase feeds. For the

case of two-phase feeds, the most practical solution is to inject the feed between

two stages (Kister, 1992), i.e. the liquid fraction of the feed is added to the stage

below and the vapour fraction to the stage above the injection point. Groemping et

al. (2004) developed a feasibility criterion for two-phase feeds, based on the

assumption that the feed stream mixes with the streams passing between the two

column sections. This approach is employed in this work for the design of columns

with two-phase feeds.

According to Julka and Doherty (1990), as described before, the profile is

continuous if the feed is introduced to one plate (Figure 3.4 ) and if the profiles of

stripping and rectifying section intersect. This reasoning is based on the equality of

the vapour stream leaving the feed stage, ( smV ) and the vapour entering the stage

above the feed, ( rnV 1+ ).


78

However, if a two-phase feed is introduced between the last stripping stage, and

the last rectifying stage, we have to take into account the mixing of the vapour

phase of the feed, vF with the vapour flow leaving the feed stage, smV and that of

the liquid phase of the feed, LF with the liquid entering from the feed stage r

nL as

shown in Figure 3.5. The material balance on the feed stage is performed by

assuming that the feed is entered above stage m , i.e. the liquid fraction of the feed

is introduced to the last stripping stage m and the vapour fraction to the last

rectifying stage n. Because the liquid and vapour streams do not exchange mass

between the stages (liquid is flowing through the down comer and the vapour

through the active column diameter), the balances over the two phases are

independent of each other (Groemping et al., 2004).

Fx,q,F

1-n stage

Rectifying

n stage

Rectifying

1-m stage

Stripping

m stage

Stripping

si,m

sm y,V 11 −−

ri,n

rn y,V 11 ++ r

i,nrn x,L

si,m

sm x,L

Figure 3.4 Feed mixing for feed injection completely onto feed stage (as in

(Julka and Doherty (1990))


79

Figure 3.5 Feed mixing for feed injection between two stages

The overall and component balances for the vapour phase are:

V

m

s

r

n FVV +=+1 ( 3.14)

i,FV

r

i,n

m

s

r

i,n

r

n vyFyVyV += +++ 111 11 −=∀ c,...,i ( 3.15)

The overall and component balances for the liquid phase balance are:

( 3.16)

i,FL

r

i,n

r

n

s

i,m

s

m LxFxLyL +=++ 11 11 −=∀ c,...,i ( 3.17)

It should be stressed that the feed stream mixing method employed in this work is

based on the assumption that the feed stream mixes with the streams passing

between the two column sections. If there is no mixing point, then the feasibility

test does not apply and the feasibility criterion by Julka and Doherty (1990) has to

i,Fx,q,F

ri,n

rn x,L

ri,n

rn x,L 11 −−

ri,n

rn y,V

si,m

sm x,L

1-n Stage

n Stage

1-m Stage

m Stage

s

i,m

s

m x,L 11 ++

vF

ri,n

rn y,V 11 ++

LF si,m

sm y,V

si,m

sm y,V 11 −−

L

r

n

s

m FLL +=+1


80

be used instead, which uses the assumption that the complete feed stream is fed to

a single stage. For a liquid feed added between two stages, the equations derived

by Julka and Doherty (1990) apply, i.e. the liquid and vapour composition profiles

intersect:

r

i,n

s

i,m xx 1+= ( 3.18)

and r

i,n

s

i,m yy 1+= ( 3.19)

Where a vapour feed is introduced between two stages, the stage index where the

liquid profiles intersect is one stage further up the column.

ri,n

si,m xx 11 ++ = ( 3.20)

ri,n

si,m yy 1+= ( 3.21)

For example, if for a saturated liquid feed, the liquid composition lines for n = 15

rectifying stages and 20=m stripping stages intersect, then there will be a feasible

design featuring 14115 =−=n rectifying stages and 20=m stripping stages.

Whereas, if the feed is a saturated vapour and the same stage composition lines

intersect, the feasible design will feature 15=n rectifying stages and

19120 =−=m stripping stages.

3.7 Double feed Column Design by Boundary Value Method

This section provides a detailed discussion of the boundary value method for

double-feed columns for multicomponent mixtures. Normally, in the case of

demethaniser columns, the upper feed is the turboexpander outlet while the lower

feed is the liquid product from a separator (flash unit) after being expanded in a

Joule- Thomson valve (Fig. 3.6). The boundary value method needs to be modified

for a double feed column design.


81

Levy and Doherty (1986) extended the boundary value design method to double-

feed columns. The divided the column into three sections, namely the rectifying

section, middle section, and stripping section (Figure 3.7). The specifications for

the double-feed column design by the boundary value method are: column

pressure, which is assumed constant throughout the column; upper and lower feed

compositions and flowrates; top and bottom product compositions and flowrates;

lower feed condition; reflux ratio; either reboil ratio or upper feed condition. The

product specifications are chosen to satisfy the product purity requirements and

material balance over the column.

In this work the method by Levy and Doherty (1986) is applied to introduce a

second feed in the column. The method starts with the column specifications. The

composition profiles of all column sections are then generated according to the

column specifications using material and energy balances along with phase

equilibrium calculations. The intersection of composition profiles identifies the

separation feasibility and is used to obtain the column design parameters, such as

the number of theoretical stages, feed stages, and feed condition.

Figure 3.6 A basic demethaniser flowsheet with external reflux

External reflux

stream Reflux heat exchanger


82

The overall mass balance gives:

BDFF LU +=+ ( 3.22)

and from the component balance

( )

i,Bi,D

i,BLUFLFU

xx

xFFxFxFD

i,Li,U

−

+−+=

( 3.23)

3.7.1 Composition profiles

Once all specifications of the double-feed column are given, the rectifying,

stripping and middle section profiles of the column are calculated using material

and energy balances and phase equilibrium of the mixture. The rectifying and

stripping composition profiles for a double-feed column are generated in the same

way as for a single-feed column as explained in Section 3.5. However, the

rebQ

LL F,F,L hxF

UU F,F,U hxF

i,Dx,D

Rectifying section

BB h,x,B

Middle section

Stripping section

Figure 3.7 Schematic of the two-feed section

condQ


83

composition profile of the middle section can be calculated by performing a mass

balance around the middle section. Prayoonyong (2009) showed that the

calculation of the middle section profile can be done in two ways. In the first

method, which is the top-down approach the number of stages in the middle

section is calculated in the downward direction. The composition profile is

calculated starting from the upper feed stage specification and terminates where the

profile intersects the stripping section composition profile, which indicates the

lower feed stage. The second method, the bottom-up approach, calculates the

number of stages starting from the specified lower feed stage and terminates at the

upper feed stage where the middle section composition profile intersects the

rectifying section composition profile (Prayoonyong, 2009)

In this work, the bottom-up approach is applied. The procedure for the middle

profile calculation according to the bottom-up approach can be summarized as:

� A stage in the stripping profile is arbitrarily chosen as the lower feed

location e.g. stage m in Fig 3.8. The location of the stage is an additional

degree of freedom.

� The vapour composition of stage m is determined by a bubble point

calculation for the liquid composition of stage m (xm,i). The value of xm,i is

already known from the stripping composition profile.

� The liquid composition of the next stage m+1 is calculated from the

material and energy balances (the set of Eq. ( 3.24) and ( 3.25)).

The calculation is continued by solving the material, energy and vapour-liquid

equilibrium calculations until the intersection between the middle and rectifying

section composition profiles occurs at the upper feed point.

( ) 01 =−−−−+ + i,FLi,BM

i,mM

mM

i,mLM

m LxFBxyVxFBV ( 3.24)

( ) 01 =++−−−+ + rebFLBV,M

mM

mL,M

mLM

m QhFBhhVhFBVL

( 3.25)

where ( )( )BhhsshQ BL,sV,S

reb ++−= 21 1 ( 3.26)

when B

Vs 1= is specified, otherwise, when the upper feed condition is specified:

condFLFUBDreb QhFhFBhDhQLU

+−−+= ( 3.27)


84

Figure 3.8 Schematic of the stripping section with lower feed

For given feed qualities and the reflux ratio, all stripping stages can be selected as

potential lower feed stages. The number of stages for the middle section is counted

as the number of stages from one stage above the lower feed stage to the stage

where the middle section composition profile intersects the rectifying section

composition profile. The number of stages for the rectifying section is counted

from the top of the column to the stage at the intersection between the middle and

the rectifying section composition profiles. At the intersection, the fractional

number of stages is calculated and rounded up to obtain an integer number of

stages.

The design variables of a double-feed column include the thermal conditions of

upper and lower feeds, reflux ratio, reboil ratio, and the ratio of upper-to-lower

feed rate. To apply the column design procedure, the lower feed condition must be

specified; otherwise, the middle section profile cannot be calculated continuing

Stage 2

Stage m

Bi,B h,x,B

V,ssi,

sh,y,V 111

Reboiler (stage 1)

L,ss

i,

sh,x,L 222

s

s

m

i,my

,V

1

1

−

−

vs

mh,

1−

s

im

s

m

x

L

,

,

Ls

mh,

LL FFL h,x,F

M

Mm

i,my

,V

V,Mmh

Mi,m

Mm

x

,L

1

1

+

+

L,Mmh 1+


85

from the stripping section of the column. The design procedure also requires the

ratio of upper-to lower feed rate to be specified. As a result, there are three

variables remaining, i.e. reflux ratio, reboil ratio and upper feed condition, of

which two degrees of freedom are chosen and the other variable is calculated from

the overall energy balance of the column.

Many feasible designs may be found, as several middle section profiles are

obtained, corresponding to various lower feed locations. Searching for feasible

designs using trial and error is tedious and time consuming. In this work, finding

feasible designs is performed systematically where the feed stage location is

optimised locally to minimise the number of stages, whereas the other design

variables are optimised globally, i.e. through flowsheet optimisation. Local

optimisation of the lower feed stage location is sufficient, i.e. by minimising

number of stages, as the number of stages is independent of reboiler and condenser

duties.

3.8 Extended boundary value method for column with side

reboilers

Side reboilers in low-temperature distillation columns are particularly important

because they enable heat recovery at temperatures lower than the temperature of

the column reboiler. The use of a side reboiler in the demethaniser provides greater

energy efficiency and reduces the duty of the main reboiler. The main benefit is

that the side reboiler provides a below-ambient heat sink, so reduces the

requirement for external refrigeration to pre-cool the feed to the desired

temperature in the cold separator as shown in Fig. 3.6 This heat recovery is likely

to be cost effective, as the cost of refrigeration increases as the temperature is

decreased (Elliot et al., 1996).

3.8.1 Composition Profiles for a column with side reboilers

Side reboilers are normally placed in between a lower feed and the main reboiler

(Foglietta and Patel, 2007). In addition to the specifications required for the

double-feed column design by the boundary value method as explained in Section

3.7.1, the duty and location of the side reboilers must also be specified.


86

Similar to the double feed column design, the column is divided into the rectifying,

middle and stripping sections. The calculation of the rectifying section is

performed as explained in Section 3.5. The calculation of the stripping section

composition profile needs some modifications to account for the side reboilers. In

order to avoid complexity in the model, the side reboilers are modelled as side

heaters, where heat is input to the specified stages in the column as shown in

Figure 3.9. The flow rate, condition, composition and stream temperatures of the

side reboiler draw and return are thus not explicitly modelled.

Figure 3.9 Schematic of column stripping section with side heaters

The stripping section composition profile in this case is calculated by performing

material, energy and equilibrium calculations across the stripping section (Figure

3.9. In order to explain the procedure, two side heaters having a duty of (Q1) and

(Q2) are entered at specified stages (m/) and (m//) respectively. The stage (m)

represents the lower feed location. The first step is to calculate the reboiler duty

Side Reboiler 2

Duty Q2

Side Reboiler 1

Duty Q1

L,sss h,x,L 222

Stage 2

Stage m

Bi,B h,x,B

v,sss h,y,V 111

Qreb

,x,F

LFL FLh

Stripping Section 1

Stripping Section 2

Stripping Section 3

Stage m//

Stage m/


87

(Qreb) from an overall balance of the column. This is obtained by introducing the

side heaters duties into Eq. 3.6 which yields

( ) 21 QQQFhBhDhQ condFBDreb −−+−+= ( 3.28)

The stripping section is further divided into three sections. The first section from

the bottom starts from the bottom product and finishes at /m stage. The

composition profiles in this section are calculated by a similar procedure as

explained in Section 3.5.2 by equations ( 3.10) and ( 3.11).

For a given bottom product composition, i,Bx and a reboil ratio s, the liquid

composition profile of the first stripping section is calculated starting from the

bottom product composition. The vapour composition from the reboiler ( si,y1 ) in

equilibrium with the bottom product is determined from the bubble point

calculation. The liquid composition entering the reboiler ( si,x2 ) is then calculated

from the set of equations ( 3.10) and ( 3.11). The calculation is continued to the next

stage up the column to the first side heater location (stage m/). For the calculation

of vapour flow in the first stripping section ( s

mV ), the error in the energy balance

between the two stages (Z) is calculated and minimized by applying Broyden’s

method

( ) rebB

v,s

m

s

m

v,s

m

s

m QBhhVhBVZ +−−+= ( 3.29)

For the second section, between the two side heaters, the equations for the energy

balance and the error in the energy balance (equations ( 3.10) and ( 3.11)) are

modified to include the duty of first side heater Q1:

( ) 011 =++−−+ + QQBhhVhBV rebB

v,s

m

s

m

L,s

m

s

m ( 3.30)

( ) 11 QQBhhVhBVZ rebB

v,s

m

s

m

v,s

m

s

m ++−−+= ( 3.31)

Similarly for the third section between the second heater location m// and the lower

feed location, the two equations are updated accordingly.


88

( ) 0211 =+++−−+ + QQQBhhVhBV rebBv,s

ms

mL,s

ms

m ( 3.32)

( ) 212 QQQBhhVhBVZ rebB

v,s

m

s

m

v,s

m

s

m +++−−+= ( 3.33)

The stripping section composition profile is plotted by calculating the liquid

composition xs on each stripping stage in all three sections. The intersection of the

profiles is then identified by the minimum distance criterion as explained in

Section 3.4.

3.8.2 Illustrative example

The design procedure of a double-feed column with side reboilers is demonstrated

by example: a five-component mixture of methane, ethane, propane, i-butane and

n-butane is to be separated in a demethaniser column. The upper feed flow rate is

2200 kmol/h while the lower feed flow rate is 800 kmol/h. Both the feed are

saturated liquids. The feed compositions are given in Table 3.1.

Table 3.1 Molar Feed Compositions

Component Upper Feed Lower Feed

Methane 0.865 0.65

Ethane 0.06 0.16

Propane 0.04 0.09

i-Butane 0.02 0.06

n-Butane 0.015 0.04

Total (kmol/h) 2200 800

The separation is carried out at a uniform pressure of 30 bar in the column. The

recovery of ethane in the bottom product is specified as 98%, while the mole

fraction of methane in the top product is specified as 99.5%. Side heater 1 with a

duty of 900 kW is introduced at eight stage above the reboiler of the column while

side heater 2 with duty of 600 kW is introduced at fourth stage above the reboiler.

A column with a partial condenser is employed in HYSYS for validation of the

boundary value model, results of which are presented below. The calculations were


89

performed on an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB RAM.

The shortcut model takes 1.12 seconds to solve while the HYSYS simulation for

column model takes around 2 seconds to converge. However, the time required to

setup a column simulation in HYSYS in this case is not accounted, which can vary

from 3 to 5 minutes depending on the column features.

Table 3.2 Validation results: Boundary value design results vs. HYSYS

simulation results

Results Boundary Value Method

HYSYS HYSYS with pressure drop

Number of stages 24 24* 24*

Upper feed location (from top)

6 6* 6*

Lower feed location (from top)

12 12* 12*

Reboiler duty (kW) 3580 3654 3646

Condenser duty (kW) 646 662 668

CPU time (sec) 1.12 2.0 2.0

*indicates specified values

The column flow and composition profiles for the key components are also

compared with the composition profiles obtained from HYSYS. The two profiles

are shown in Fig. 3.10 and Fig. 3.11, which demonstrate that the new model can

represent a complex demethaniser column with sufficient accuracy for the purpose

of conceptual design. It is evident from Fig. 3.11, that molar flows are not constant

in each column section, supporting the use of energy balances in calculating the

composition profiles. The third column in Table 3.2 presents the column

simulation results from HYSYS considering a pressure drop of 30 kPa over the

column. The condenser and reboiler duties are shown to vary by less than 1% in

the two cases, which shows that the assumption of neglecting the pressure drop

does not affect the design results significantly.


90

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30

Stage number (from top to bottom)

Mo

lar

flo

wra

te (

km

ol/

h)

Vapour (BVM)

Liquid (BVM)

Vapour (HYSYS)

Liquid (HYSYS)

Rectifying

section

First

stripping

section

Second

stripping

section

Third

stripping

section

Middle

section

Figure 3.10 Molar flow profiles: new model (BVM) vs. HYSYS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30


Mo

le f

ract

ion

Methane (BVM)

Ethane (BVM)

Methane (HYSYS)

Ethane (HYSYS)

Rectifying

section

First

stripping

section

Middle

section

Third

stripping

section

Second

stripping

section

Figure 3.11 Composition profiles for key components: new model (BVM) vs.

HYSYS


91

3.9 Extended boundary value design method for a reboiled

absorption column

As mentioned in Section 2.6, the top product from the demethaniser, methane, is

withdrawn as a vapour product and most commercial flowsheets do not have a

conventional condenser. The need for liquid in the upper section of the column is

fulfilled by introducing an external reflux stream to the top tray of the column.

This external reflux stream originates from the vapour stream of the flash column.

Before entering the column it is typically condensed in a reflux heat exchanger

which exchanges heat with the demethaniser top product as shown in Fig 3.6.

For the purpose of design using the boundary value method, the demethaniser is

treated as a reboiled absorber, with the external reflux stream analogous to the

solvent stream in an absorber. On the top tray, components that are volatile at the

tray temperature will exit the column with the overhead product. The rectifying

section uses a mass separating agent (external reflux) to remove heavy components

from the overhead, while the stripping section uses an energy separating agent (the

reboiler) to remove light components from the bottom product. The external reflux

rate affects the recovery of the heavy key component in the bottoms and the purity

of the light key component in the overhead, while the reboiler duty affects the

recovery of the light key in the overhead and the purity of the heavy key in the

bottoms.

In addition to the usual specifications for the reboiled absorber column design by

the boundary value method (i.e. column pressure, upper and lower feed

compositions and flowrates, top and bottom product compositions and flowrates,

lower feed condition, reboil ratio or upper feed condition), the flowrate and the

composition of the external reflux stream must also be specified.


92

3.9.1 Calculation of composition profiles

The composition profiles for the different sections in a reboiled absorption column

are calculated based on the mass and energy balances along with the vapour-liquid

equilibrium. The column is divided into three sections as discussed in Section 3.7.

The stripping and middle section calculations are performed in a similar manner as

for the double-feed distillation column. The absorption section calculation in this

case differs from rectifying section calculations.

An external reflux stream with a flow Lo, composition xo,i and enthalpy Lh0 enters

at the top of the column stage as shown in Figure 3.12. The composition profile for

the absorption section is started from the distillate composition that leaves the top

of the column.

The overall balance on the top stage is

The overall material balance on the top stage is given by:

DLVLo +=+ 12 ( 3.34)

1+nV

i,ny 1+ vnh 1+

Stage 1

nV

i,ny ,

Vnh

Stage n

V2i2,2 h,y,V

VDiD, h,y,D L

oL

i,oo h,x,L

L

,i

h

x

L

1

1

1

Ln

i,n

n

h

x

L

1

1

1

−

−

−

Ln

i,n

n

h

x

L

Figure 3.12 Schematic of the top stage with external reflux stream


93

while the component balance gives

i,DLi,i,

Li,oo DyxLyVxL +=+ 1122 11 −=∀ c,...,i ( 3.35)

Rearranging Eq. 3.35

( ) ( ) 01122 =+−+ i,DLi,

Li,ooi, DyxLxLyV 11 −=∀ c,...,i ( 3.36)

The energy balance on the top stage gives:

( ) ( ) 01122 =+−+ VD

LLoo

VDhhLhLhV ( 3.37)

Vapour-liquid equilibrium compositions and enthalpy are calculated using HYSYS

as explained in Section 3.2. The top stage calculations start from the external reflux

and the top product composition. Equilibrium is assumed to be achieved in the top

stage and the composition of the liquid leaving the stage is calculated assuming

vapour-liquid equilibrium. There are two remaining unknowns V2 and y2 which are

calculated by solving equations (3.36) and (3.37) simultaneously.

Similarly for the section from stage 1 to stage n, the balance equations can be

written as

( ) ( ) 011 =+−+++ i,Di,nnL

i,oonn DyxLxLyV ( 3.38)

( ) ( ) 011 =+−+

++VD

Lnn

Loo

Vn DhhLhLhV

n ( 3.39)

For the calculation of vapour flow in the absorption section, Vn+1, the error in the

energy balance e between the two stages in the absorption section is calculated as

follows:

( ) ( )D

L

nnLo

v

n DhhLhLhVeon

+−+=++ 11 ( 3.40)

This error is minimised using Broyden's method where the value of Vn+1 is updated

at every iteration. The final value of 1+nV is computed and the energy balance is

then applied over the whole rectifying section in the same manner.


94

The calculation continues to the next stages down the column by solving material

and energy balances, Equation (3.38), (3.39) and (3.40), for i,ny 1+ and 1+nV ,

simultaneously with vapour-liquid equilibrium, for i,nx . The calculation stops

when the composition profile reaches its pinch point, where there is no change in

composition from one stage to the next. The liquid compositions obtained

comprise the absorption section composition profile. Having calculated the

composition profiles for the absorption, middle and the stripping section (including

side heaters), the profiles intersection is identified by the minimum distance

method.

3.10 Case studies

Two case studies are presented to illustrate application of the new column design

method presented in this work to different column configurations.

3.10.1 Case study 1: HYSYS sample case (Turbo-expander plant)

The first process is a typical turbo-expander flowsheet model, presented in the

library of sample cases in HYSYS (version 2006.5), “G-3: Turbo-expander plant”.

Figure 3.13 presents the HYSYS process flow diagram. The demethaniser column

is represented by T-100. The feed gas (1) passes through a series of coolers, shown

as a sub-flowsheet (FLOW-1), where it is cooled to the required temperature of

stream 13. The duties for these coolers are supplied by side reboilers (represented

as energy streams) of the demethaniser. Streams 80, 81 and 82 represent the duties

of the main reboiler and two side reboilers, respectively.

Stream 13 is fed to a flash separator (V-100), where it is separated into equilibrium

liquid and vapour fractions. The liquid fraction (16) feeds the demethaniser, while

the vapour passes through an expander (E-100) that generates power to drive the

compressor (K-100). The expander outlet stream (17) is then sent to a second flash

separator (V-101), the liquid product of which (18) feeds the top of the


95

demethaniser as the external reflux, while the vapour bypasses the demethaniser

and is mixed with the demethaniser top product to form the final sales gas.

3.10.1.1 Problem inputs

The feed condition, and other options related to the thermodynamics (Peng-

Robinson equation of state, enthalpy-calculation options, etc.) are the same as used

in the original sample file. The process feed gas (1) is at a temperature of 37.8°C

and a pressure of 58.6 bar, with a molar flow rate of 4981 kmol/h. In this work,

components heavier than hexane as well as nitrogen and carbon dioxide, are

artificially eliminated from the feed in order to reduce the complexities that arise in

the presence of trace components in the calculations for establishing intersection of

profiles. This limitation of the design method is discussed further in Chapter 7. The

simplified composition of the feed for Case Study 1 and the original composition

from HYSYS are presented in Table 3.3.

Figure 3.13 HYSYS process simulation diagram of a typical expander plant


96

Table 3.3 Feed gas composition – from HYSYS source and simplified for this

case study

Component HYSYS feed composition Simplified feed composition

Nitrogen 0.0055 0.00

Carbon dioxide 0.0091 0.00

Methane 0.8457 0.8605

Ethane 0.0820 0.0834

Propane 0.0340 0.0346

isobutane 0.0058 0.0059

n-Butane 0.0086 0.0088

isopentane 0.0028 0.0028

n-Pentane 0.0021 0.0021

n-hexane 0.0018 0.0018

n-Heptane 0.0012 0.0000

n-Octane 0.0005 0.0000

n-Nonane 0.0004 0.0000

n-Decane 0.0005 0.0000

Total Flow (kmol/h) 4981 4981

The demethaniser column in this example is a reboiled absorption column with

stream 18 providing reflux at the top of the column, while stream 16 is the only

other feed to the column. Table 3.4 and Table 3.5 present data for the demethaniser

feed streams.

Table 3.4 Column feed streams – flow rates and conditions

Stream Flow rate (kmol/h) Temperature (oC) Vapour fraction

Feed (16) 1187 -80.7 0.41

Reflux (18) 438 -92.8 0.0


97

Table 3.5 Molar compositions of demethaniser feed streams

Component Feed (16) External reflux (18)

Methane 0.6414 0.58438

Ethane 0.1707 0.29594

Propane 0.1068 0.09607

i-Butane 0.0211 0.00953

n-Butane 0.0326 0.01085

i-Pentane 0.0113 0.00182

n-Pentane 0.0086 0.00105

n-hexane 0.0075 0.00036


Table 3.6 presents the column details obtained from the simulated flowsheet and is

used as specification to the BVM. Although there is a pressure drop in the HYSYS

simulation of the column, the pressure is assumed constant (19 bar) in the

boundary value design method. The feed flow rates and compositions, as well as

the side reboiler specifications (duty and locations) are used as inputs to the BVM.

The top and bottom product compositions are also needed for the BVM to calculate

the composition profiles. In this case study, the product composition specifications

are derived from the HYSYS simulation results.

Table 3.6 Column details from HYSYS

Molar ratio of methane to ethane in bottom product 0.02

Feed flow rate (kmol/h) 1189

Reflux flow rate (kmol/h) 440.7

Side heater 1 (stream 81) 698.2 kW

Side heater 2 (stream 82) 698.2 kW

3.10.1.2 Results and discussion

Table 3.7 presents the results of the boundary value design method and the

HYSYS simulation. It may be seen that the results are very similar with respect to


98

overall flows, duties and internal flows and compositions. Some discrepancies in

the molar flow profiles and composition profiles may be attributed to the

assumption made in the boundary value design method of constant pressure in the

column. The simulation of the column is also performed with the actual feed

composition in HYSYS. The third column in Table 3.7 presents the results with the

actual feed composition. The reboiler duty without the feed simplification is shown

to be around 1% lower in this case compared to the results using the simplified

feed.

Table 3.7 Comparison of simulation results from HYSYS and the boundary

value design method

Results Shortcut design

method

HYSYS

(Simplified feed)

HYSYS

(Actual feed)

Number of Stages 12 12* 12*

Feed Location (from top of

column)

3 3* 3*

Distillate flow rate (kmol/h) 1043.7 1044.0 1031

Bottoms flow rate (kmol/h) 585.3 587.0 600

Reboiler Duty (kW) 965.2 938.1 922

CPU time 1.35 1.9 1.9



99

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12 14


Mola

r fl

ow

(k

gm

ol/h

)

Vapour (HYSYS)

Liquid (HYSYS)

Vapour (BVM)

Liquid (BVM)

Rectifying

section

First strippping

section

Second strippping

section

Third strippping

section

Figure 3.14 Molar flow profiles: boundary value method (BVM) vs. HYSYS

simulation results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14


Mole

fra

ctio

n

Methane (HYSYS)

Ethane (HYSYS)

Propane (HYSYS)

Methane (BVM)

Ethane (BVM)

Propane (BVM)

Rectifying

section

First strippping

section

Second strippping

section

Third strippping

section

Figure 3.15 Liquid composition profiles: BVM vs. HYSYS simulation results


100

It may be concluded that the boundary value design method provides results that

are sufficiently accurate to provide column design parameters for initialising

rigorous simulations. Nevertheless, complete agreement with simulation

approaches using different inputs and specifications is not expected. It is known

that the composition profiles are sensitive to trace components in the products and

to the approximation introduced by the tolerance used in the minimum distance

criterion applied for the estimation of profile intersection for multicomponent

mixtures. To improve agreement between HYSYS simulation results and those of

the design method, input variables, such as the specified product compositions,

column pressure and feed condition, may be manually adjusted by the user.

3.10.2 Case study 2: Multiple reflux stream hydrocarbon recovery process

This case study is based on the US patent no 7818979, “Multiple reflux stream

hydrocarbon recovery process”, assigned to ABB Lummus Global Inc. (Patel and

Foglietta, 2010). Figure 3.16 illustrates the process.

The ABB Lummus process differs from the turbo-expander process described in

Case Study 1 in that two multistream exchangers are employed to pre-cool the

feed. The first uses the demethaniser top product as the cooling medium, while the

second uses the side reboilers for cooling the feed gas. The demethaniser involved

in this process has three feed streams in addition to the reflux stream entering the

top of the column.

3.10.2.1 Problem inputs

The process feed gas is at a temperature of 32°C and a pressure of 55 bar. This

work neglects the presence of nitrogen and carbon dioxide in the feed, as in first

case study. The feed composition data from the patent application and simplified

for this case study are presented in Table 3.8.


101

Figure 3.16 Process flowsheet diagram of multiple reflux stream hydrocarbon

recovery process (Patel and Foglietta, 2010)

Table 3.8 Column inputs: Material streams (Patel and Foglietta, 2010)

Component HYSYS feed

composition

Simplified feed

composition

Nitrogen 0.00186 0.00


Methane 0.8567 0.86160

Ethane 0.0756 0.07603

Propane 0.0332 0.03339

isobutane 0.0048 0.00483

n-Butane 0.00984 0.00990

isopentane 0.00274 0.00276

n-Pentane 0.00294 0.00296

n-hexane (used for C6 +) 0.00849 0.00854



102

The required data for the boundary value design of the demethaniser are given in

Table 3.9 and 3.10. The compositions of the external reflux and the three feed

streams to the column are presented in Table 3.11. The patent application provides

details of the material streams fed to the column, but the feed and side reboiler

locations are not specified explicitly. Therefore, a simulation of the process was

performed in HYSYS to provide reasonable values of unknown design data.

Table 3.9 Column inputs: Material streams (Patel and Foglietta, 2010)

Stream Flow rate

(kmol/h)

Temperature

(oC)

Vapour fraction

Reflux 4245 -90.12 0.00

Top feed 19520 -87.7 0.3

Middle feed 19520 -62.6 0.94

Lower feed 4812 -46.4 0.26

Table 3.10 Column inputs: Energy streams (from HYSYS simulation)

Table 3.11 Molar composition of column input streams

Component Reflux Top feed Middle feed Lower feed

Methane 0.975 0.909 0.909 0.470

Ethane 0.024 0.065 0.065 0.163

Propane 0.001 0.019 0.019 0.149

i-Butane 0.000 0.002 0.002 0.030

n-Butane 0.000 0.003 0.003 0.068

i-Pentane 0.000 0.000 0.000 0.022

n-Pentane 0.000 0.000 0.000 0.024

n-hexane 0.000 0.000 0.000 0.075

Stream Duty (kW)

Side reboiler at 18h stage 4894

Side reboiler at 21st stage 4027

Side reboiler at 24th stage 3452


103

3.10.2.2 Results and discussion

The complex column is divided into sections based on the locations of feeds and

side reboilers. The results from the boundary value design method, including the

location of feed stages in the column, compositions and temperatures along the

column, can be used as initial guesses to help the HYSYS algorithm converge to

the required specification.

Table 3.12 compares the boundary value design results and simulation results from

HYSYS. It may be seen that there is excellent agreement between the product flow

rates and reboiler heat duty predicted by the two approaches. Figures 3.17 and 3.18

compare the molar flow profiles and composition profiles in the column obtained

from the two simulation models. The validation of the boundary value simulation

results, with reference to HYSYS simulation results, is thus demonstrated; it may

be concluded that the model captures the process behaviour satisfactorily and is

therefore useful for application in demethaniser flowsheet synthesis framework.

Table 3.12 Comparison of simulation results: Boundary value design method

vs. HYSYS.

Results Boundary value

design method

HYSYS

Number of Stages 28 28*

Top feed 5 5*

Middle feed 11 11*

Lower feed 16* 16*

Ethane recovery in bottoms (%) 89.2* 89.4

Methane recovery in top product (%) 99.85* 99.85

Distillate flow rate (kmol/h) 42323 42316

Bottoms flow rate (kmol/h) 5778 5785

Reboiler Duty (kW) 1193 1151

CPU time 1.26 2.0



104

Figure 3.17 Molar flow profiles: Boundary value method vs. HYSYS

Figure 3.18 Liquid composition profiles (key components): Boundary value

method vs. HYSYS


105

3.11 Conclusions

In this work, a new simplified method for the initial design of complex

demethaniser column is presented. The method is an extension and modification of

the boundary value method that requires the feed and product compositions,

column pressure and reflux/reboil ratio to be specified as design parameters. The

proposed column design method allows rigorous simulation of the demethaniser

column to be carried out without trial and error.

Energy balance is included in the calculation of the composition profiles to

overcome the constant molar overflow assumption in the original method. The

method also takes into account two-phase feeds by introducing the feed between

two stages and considering mixing at the feed stage. A minimum distance criterion

is used to identify the near-intersection of composition profiles in order to apply

the design method to multicomponent feed mixtures.

In the case of double-feed columns, the model decomposes the column into three

sections, namely the rectifying, the middle and the stripping sections. For each

section, the composition profile is calculated in the same manner as for a single-

feed column. The rectifying and stripping section composition profiles are

calculated starting from top and bottom product composition, respectively. Using

the bottom-up approach, the middle section composition profile is calculated from

a specified lower feed stage. The intersection between the rectifying and the

middle section liquid composition profiles is used for the column design.

The model also accommodates intermediate heating using side reboilers. In this

case the duty and location of the reboilers need to be specified. The column energy

balance is extended to include the duties of the side reboilers. Finally the boundary

value method is modified to be applied to a reboiled absorber. The composition

profile in the rectifying section in this case is modified to account for the use of an

external reflux stream, as is common practice.


106

Two case studies are presented to illustrate the application of the design method to

a range of column configurations. The column design parameters obtained from

the boundary value method are used for initializing the rigorous simulation ion

HYSYS. HYSYS simulation results are shown to be in good agreement with those

of the proposed model. The extended boundary value method can be used for

assessing the feasibility of a proposed specification and generating designs for

finding the number of stages, feed stage locations and reboiler duty.

The design method developed in this work is useful for flowsheet design and

optimisation. The combination of this column design model and other models of

demethaniser flowsheet units will be employed in a synthesis framework. This will

also help in developing a systematic design method which will provide a powerful

tool for process design, selection and optimisation of demethaniser flowsheets.

Chapter 4 Demethaniser flowsheet design and simulation methodology

107

CHAPTER 4 DEMETHANISER FLOWSHEET

DESIGN AND SIMULATION

METHODOLOGY

4.1 Introduction

Numerous expansion processes are commonly used for NGL recovery in the gas

processing industry, particularly in the recovery of ethane from natural gas. Some

of these processes were discussed in Section 2.5 in detail. Mostly in the case of the

expander processes, the feed gas is cooled to a relatively low temperature to

achieve partial condensation, typically by heat exchange with the demethaniser

overhead vapour, side reboilers, and/or external propane refrigeration (Mokhatab et

al., 2006). In some process variations, a part of the demethaniser overhead product

is used to subcool a portion of vapour from flash unit to produce a low temperature

reflux, while a portion of the expander discharge is heated by the feed gas to form

a temperature-controlled column feed (Chebbi et al., 2010).

The cryogenic processes produce a liquid hydrocarbon stream through chilling the

feed gas. Low temperatures are needed when higher recoveries are required. The

low temperatures can be obtained through either mechanical refrigeration or via

turbo-expander processes. The use of turbo-expanders, combined with the

advantages of the plate fin multistream heat exchangers, also help to increase the

performance of these processes. Compression costs constitutes around 25 to 40%

of operating costs (Bai et al., 2006). Figure 4.1 shows the essential components of

a turbo-expander plant with a demethaniser column.


108

Figure 4.1 Generalized gas processing scheme for ethane recovery (Yan et al.,

2008)

In this chapter a flowsheet design and simulation model is developed in which the

individual sub-systems of the demethanisation process, namely the separation,

refrigeration and heat recovery systems, are modelled in order to capture the

overall picture and achieve optimal design of demethaniser flowsheets. The

developed model will be employed in a synthesis framework so that promising

design options are easily identified at an early stage and a wide range of major

design options are considered.

4.2 Heat integration in demethaniser flowsheet

The methodology for the systematic design and evaluation of demethaniser

flowsheets is not complete without considering opportunities for heat integration

between the heat sources and sinks of the process. By allowing individual hot

process streams to exchange heat with cold process streams, the operating costs

can be reduced. Thus, any systematic design approach must contemplate heat

integration opportunities. In the present methodology, heat integration is

Power recovery


109

considered at the very early stages to address demethaniser flowsheet synthesis

problem.

The heat integration methodology developed in this work considers the heat

recovery opportunities between the streams of the process and the background

process. In the present work, a refrigeration system may be present as a

background process. The heat recovery in the demethanisation process is carried

out in a multistream heat exchanger by setting recovery targets quantified using

pinch analysis.

The pinch analysis is widely used in the design and optimisation of heat exchanger

networks (HENs). Pinch analysis is a systematic methodology based on

thermodynamic principles to achieve utility savings by better process heat

integration and maximising heat recovery (Linnhoff and Boland, 1982). Three

important rules should be considered in the pinch design method. They are that

heat transfer should be avoided across the pinch, external heating should be

avoided below the pinch, and external cooling should be avoided above the pinch.

These requirements should be met in the process in order to reduce the external

utility loads.

Since the pinch analysis was introduced for the initial design of HENs by Linnhoff

and Boland (1982), it has been further developed significantly. Most of the

previous work focused on networks that consist of two-stream heat exchangers,

mostly shell and tube heat exchangers. However, multistream heat exchangers can

provide many advantages over conventional two-stream heat exchangers. A

multistream plate-fin heat exchanger is able to incorporate many streams and it is

characterized by compactness, flexibility and efficiency (Wang and Sunden, 2001).


110

4.2.1 Heat recovery in multistream heat exchanger

In this work, pinch analysis is applied to determine the maximum amount of heat

recovered in the multistream exchanger, where the heat source is the warm feed

gas and the heat sink consists of side reboiler and the column top product. A quick

method for heat recovery in exchangers based on pinch analysis, as discussed by

Hewitt and Pugh (2007) is adopted in this work. This method will be employed in

the demethaniser flowsheet simulation model.

The methodology starts by performing the energy balance for the process as if all

of the exchanger heat transfer sides were independent. The stream data is used to

construct the composite curves and determine enthalpy intervals. The composite

curves represent the heat balance of an entire process. They are composed of a hot

and a cold composite curve. The hot composite curve represents the total heat that

must be removed from all hot streams that take part in the process; and the cold

composite curve, represents the total amount of heat that must be added to all cold

streams present in the process (Smith, 2005). When both curves are superimposed,

the overlap between them indicates the amount of heat that can be recovered within

the process, whereas the overshoot on both ends indicates the amount of external

heating and cooling required for the process to be in thermal balance.

The method assumes constant physical properties, which results in the composite

curves formed by straight lines where each change in slope is related to the entry

and exit of a stream. If a vertical line is drawn whenever a change in slope occurs,

the whole heat recovery process is sectioned into enthalpy intervals and is

characterized by a temperature field (inlet and outlet temperatures), a heat load and

a stream population.

The heating and cooling loads in the multistream exchanger should be balanced by

separately summing the duties on each side of the exchanger. The residual duty is

then reduced to zero by refrigeration or a heat source. The method is illustrated in

the following example.


111

4.2.2 Illustrative example

Stream data are taken from Hewitt and Pugh (2007). There are six hydrocarbon gas

streams (three hot and three cold). The stream source and target temperatures along

with heat capacity are given in Table 4.1.

Table 4.1 Stream data for multistream exchanger

Stream Number pCM& (kW/K) Inlet Temperature

(K)

Outlet Temperature

(K)

Hot H1 10 300 150

Hot H2 5 250 100

Hot H3 8 200 150

Cold C1 15 90 130

Cold C2 5 120 210

Cold C3 20 170 250

The stream data are represented in terms of hot and cold composite curves using

the pinch analysis method. The resulting curves are shown in Figure 4.2. The pinch

temperature is 6 K. The composite curve is divided into zones corresponding to

linear sections of the hot and cold composite curves. Each of these zones

represents the actual heat transfer zones in the multistream exchanger and is

considered on its own.


112

Figure 4.2 Composite curves for multistream exchanger (Hewitt and Pugh,

2007)

A mean volumetric coefficient for a zone containing n streams can be estimated

from the expression

∑=

=n

i i

i

z

z Q

B

Q

1 β

&&

( 4.1)

Where zQ& is the total heat transferred in zone z, (kW)

Bz the mean volumetric coefficient for the zone, (m3K-1)

iQ& the heat lost or gained by the ith stream in the zone, (kW) and

iβ the local volumetric heat transfer coefficient for the ith stream (kW/m3K) , and

is given in Engineering Sciences Data Unit - Selection and costing of heat

exchangers manual (ESDU 1997). In this example a typical value of 80 (kW/m3K)

is chosen.


113

The log mean temperature difference (LMTD) is then calculated for each zone

(Tlm,z). The LMTD for a pure counter-flow exchangers with single phase streams of

constant specific heat capacity for a zone is given by:

( ) ( )( )

in,cout,h

out,cin,h

in,cout,hout,cin,hlm

TT

TTln

TTTTT

−

−

−−−=∆

( 4.2)

The multi stream exchanger is assumed to operate close to counter-current flow,

and Tlm,z can be calculated from Eq. 4.2, using the appropriate end temperatures of

the zone. The heat exchanger volume corresponding to the zone can then be

calculated using

z

z,m

z

z

TQ

Vβ

∆

&

=

( 4.3)

In this work, however the area of the exchanger is used for the calculation of the

cost of the heat exchanger as explained in Appendix B.

4.3 Modelling of flowsheet units

The mathematical models of the different units of the flowsheet are developed in

MATLAB. The physical properties are estimated by linking MATLAB with

HYSYS as explained in Section 3.2 and Appendix A. The models are developed so

that the output stream data including pressure, temperature, enthalpy, etc. can be

calculated for given input stream data and equipment operating parameters. The

shortcut models of the different units are explained below.

4.3.1 Demethaniser column model

The complex distillation column is simulated using a modified boundary value

method as explained in detail in Chapter 3. The method is employed for generating

the column design, verifying the separation performance and calculating energy

requirements.


114

4.3.2 Flash unit model

The flash unit model is used to estimate flowrate and composition of the vapour

and liquid fractions of a mixture of known composition for a given temperature

and pressure. In this work, an isothermal flash model is applied where the flash

temperature and pressure are known. The basic assumptions for the model are:

1. Equilibrium is achieved between the liquid and vapour leaving the column

2. There is no entrainment of liquid in the vapour

3. There is no carry over of vapour in the liquid.

The component material balance can be represented by the following equations

(Seader and Henley, 1998):

iii LxVyFz += ( 4.4)

where F is the molar flow rate of the feed, V and L are the molar flow rates of the

vapour and liquid from the flash unit respectively, zi, yi, and xi represent the mole

fraction of component i in the feed, vapour and liquid stream of the flash unit

respectively.

The vapour-liquid equilibrium relationship for each component is defined by

ii xKy = ( 4.5)

Where Ki represents the vaporisation equilibrium ratio of component i and is

calculated using HYSYS as discussed before. The composition of the vapour and

liquid streams of the flash unit are estimated using the following equations (Seader

and Henley, 1998):

i

i

i

KF

V

F

V

zy

11

−+

=

( 4.6)

( ) 11 +−

=

F

VK

zx

i

i

i

( 4.7)


115

where V/F is the fraction of the feed vaporised. The vapour fraction of the feed is

calculated by an iterative search using the following function:

( )( )

( )∑ =

+−

−=

N

ii

ii

KF

V

KzFVf 0

11

1/

( 4.8)

where N is the number of components in the mixture. A detailed account of flash

calculations can be found elsewhere (e.g. Walas, (1985); Seader and Henley,

(1998).

4.3.3 Turbo-expander Model

The use of a turbo-expander in the demethanisation processes is a widespread

industrial practice, where the work generated by the turbo-expander is used to

drive the compressors required for the final sales gas. Figure 4.3 indicates the

temperature and enthalpy relationship for a general expansion process. The line ab

shows the expansion of a saturated liquid fluid from pressure P1 to P2. The

temperature drop resulting from the stream pressure drop is employed to cool

down the feed gas and produce refrigeration.

Figure 4.3 T-H curve for an isenthalpic expansion


116

The power produced can be represented using the enthalpy-entropy graphs. Figure

4.4 shows an enthalpy-entropy graph for propylene in which the proplylene is

expanded from a pressure of 862 kPa to 138 kPa. Various efficiency curves are

plotted on the graph indicating the output enthalpy which then determines the

power produced by the expander.

Figure 4.4 Pressure-Temperature-Enthalpy Diagram (Wang, 2004)

The isentropic efficiency is given by:

id

actis

W

W=η

( 4.9)

and the work generated by the expander is

( )outinisoutinactual HHHHW −=−= η ( 4.10)

Eq. 4.10 is employed in this work to calculate the power produced by the turbo-

expander with 80 % isη . The temperature of the discharge stream from expander is

given by Smith (2005):

Entropy, kJ/(kg.K)

En

tha

lpy

, k

J/k

g


117

( ) n

n

inout TT1−

= ε ( 4.11)

The model thus requires the input conditions of the feed and the desired outlet

pressure to calculate the power produced by the expander.

4.3.4 Refrigeration cycle model

In the demethaniser processes, although most of the cooling of the feed gas is done

by internal heat recovery, any additional cooling requirement has to be fulfilled by

the use of external refrigeration cycles. Refrigeration cycles are highly energy

intensive; shaft power usually overwhelms capital investment and dominates the

final total cost of the cycle (Mehrpooya et al., 2009). Power consumption in the

refrigeration system is mainly based on the shaft power of the compressor. The

shaft power of a centrifugal compressor can be calculated with a simplified

formula derived from energy balance as explained by Smith (2005).

−

−=

−1

11

γ

γ

ηγ

γ

evap

cond

P

inevap

P

PFPW

( 4.12)

where W power required for compression (W)

Pevap, Pcond inlet and outlet pressures for the compressor (N⋅m –2)

Fin inlet volumetric flowrate (m3⋅s –1)

γ ratio of heat capacities CP/CV of refrigerant

ηis isentropic efficiency

ηP polytropic efficiency

Compression refrigeration cycles are the most common choices to provide the

required cooling. Figure 4.5(a) illustrates a typical simple compression

refrigeration cycle. Cooling required in the processes is provided through

evaporation of liquid refrigerant in an evaporator. Saturated refrigerant vapour

enters a compressor which increases the pressure of the refrigerant from the

evaporating pressure to the condensing pressure. Superheated vapour at high


118

pressure is condensed to saturated liquid and heat is rejected to external heat sinks

in a condenser. Liquid refrigerant at Point 1 enters the expansion valve, in which

the pressure of the refrigerant is reduced from the condensing pressure to the

evaporating pressure (neglecting the pressure drops in piping and heat exchangers).

Through expansion, liquid refrigerant is partially vaporised. The liquid passes

through the evaporator and absorbs heat from the process to provide refrigeration.

Figure 4.5(b) illustrates the cycle on a temperature-enthalpy program.

Figure 4.5 A Simple vapour-compression refrigeration cycle: a)Flow

diagram, b) Temperature-enthalpy diagram (Smith, 2005)

Smith (2005) discussed that simple refrigeration cycles can be used to provide

cooling at as low as -40°C, while for temperatures lower than -40°C and in

situations when there is more than one heat source or heat sink available, complex

refrigeration configurations of multiple levels or cascade arrangements should be

considered. This is consistent with the fact that shaft power requirements increase

with a larger temperature difference between evaporation and condensation in a

refrigeration cycle. This relationship becomes clear from inspection of the equation

that allows estimating the ideal power requirement of a refrigeration cycle

(Haselden, 1971):

1 4

2 3

Condenser

Compressor

Expansion valve

T

H

4

2 Evaporation 3

1

Condensation

Evaporator


119

−=

evap

evapcondevap

T

TT

η

QW

( 4.13)

Where

Qevap is the heat absorbed by the refrigerant from the heat source at

temperature Tevap,

Tcond is the temperature at which the refrigerant condenses, and

η is the mechanical efficiency of the compressor

The efficiency factor η is a function of refrigeration temperature. Typically a value

η can be set at 0.6 (ETSU 1992). In this work Eq. 4.13 is applied to calculate the

power requirement of a refrigeration cycle.

4.3.4.1 Selection of refrigerant

The refrigerant can be a pure component or a mixture of different components. A

pure refrigerant provides cooling at constant temperature when evaporating, while

mixed refrigerants provide cooling at a changing temperature even when

evaporating at constant pressure. In the present study, only pure refrigerant cycles

are considered, to avoid the complexity associated with the simulation and

optimisation of cycles with mixed refrigerants.

There are many factors affecting the choice of refrigerant for a compression

refrigeration cycle. Smith (2005) discusses the key points in the selection of the

refrigerants. These issues relate to the environmental impact, safety, corrosiveness,

economic analysis, and the physical properties affecting the operating parameters

of the refrigerants. In this section, the effects of freezing and normal boiling point,

latent heat, temperature-entropy curves of refrigerants are discussed and

suggestions for the operating temperature ranges of various refrigerants are

provided.

First of all, the freezing temperature of a refrigerant should be well below the

required cooling temperature to avoid the possibility of solid formation in the


120

refrigeration system. Secondly, the refrigeration process is normally required to be

operated above atmospheric pressure to avoid air ingression. This means that the

selected refrigerant should have a normal boiling temperature below the required

evaporating temperature. In addition to these two conditions the latent heat of the

refrigerant at evaporating conditions should be considered. It is desirable to have a

refrigerant with a high latent heat when evaporating. The higher latent heat leads to

a lower refrigerant flowrate in the cycle. This helps to reduce the power

requirement of the compressor (Smith, 2005).

IncreasingPowerRequirement

Nitrogen

Methane

Ethylene

Ethane

Propane

Propylene

i-Butane

n-Butane

Ammonia

Chlorine

80 100100 120 140 160 180 200 220 240 260 280200 32030060

77 118

112 178

169 264

185 286

231

225

261

273

240

239

Temperature (K)

Figure 4.6 Recommended operating temperature range of some refrigerants

(Smith, 2005)

Figure 4.6 presents operating ranges of a number of refrigerants. Typically

evaporating pressure of refrigerant is set at a value just above the atmospheric

pressure. This prevents air ingression into the refrigeration system. The latent heat

is reduced if the refrigerant operating temperature is far above that of the normal

boiling point, thus affecting the economics of the process. The upper boundary of

the operating temperature range is set at a temperature corresponding with a heat of

vaporization of 50% of that of atmospheric pressure. The lower boundary of

operating temperature range is set at refrigerant normal boiling point of


121

atmospheric pressure. More details discussion of selecting refrigerant for

compression refrigeration is given in Smith (2005).

Another factor to be considered in the choice of refrigerant relates to shape of the

two phase region on a temperature-entropy (T-S) diagram, as shown in Figure 4.8.

The steepness of the right-hand slope of the T-S curve affects the degree of

superheat of refrigerant after compression (Smith, 2005). The steeper the slope, the

less superheated the vapour after compressor. The less superheating results in the

increase of the coefficient of performance, as it decreases the average heat

rejection temperature. Thus the amount of cooling required for condensing the

refrigerant decreases.

Figure 4.8 Selection of refrigerant –Effect of two-phase curve shape

4.3.4.2 Choice of simple and cascade cycles

The decision whether to use simple or cascade cycles is based on the temperature

difference between evaporation and condensation. If the temperature difference is

relatively small, a refrigerant that is suitable for the simple cycle evaporation

temperature is selected. On the other hand, if the temperature difference between

evaporation and condensation exceeds the recommended temperature range of each

of the available refrigerants, a cascade cycle is selected.

A cascade refrigeration cycle is represented in Figure 4.7, the lower cycle extracts

heat at temperature T1,evap and lifts it to the upper cycle condenser temperature

T

S

T

S


122

T2,cond. The condenser of the lower cycle and the evaporator of the upper cycle are

combined into a single heat exchanger.

Figure 4.7 A cascade refrigeration cycle

Lee (2001) noted that the choice of the partition temperature is dependent on the

nature of refrigerants used and refrigeration duties of the upper and lower cycles.

For example in a propylene-ethylene cascade refrigeration system for ethylene

recovery plants, usually the total refrigeration duty of the propylene cycle is much

larger than that of the ethylene cycle.

Lee (2001) represented the problem of finding the optimal partition temperature by

a plot of shaftwork vs. partition temperature for the upper cycle and lower cycle.

As seen in Figure 4.6, the shaft work consumption of both the upper cycle and the

lower cycle depend on the partition temperature. A lower partition temperature

would reduce the shaft work of the lower cycle but increase that of the upper cycle.

The overall shaft work consumption curve is a convex function for which an

optimal partition temperature can be identified. In this work the approach

presented by Lee (2001) is employed for the selection of optimal partition

temperature.

Partition

Temperature

T2,cond

W2

W1 Lower cycle

Upper cycle

T1,evap,

T2,evap

T1,cond


123

Figure 4.8 The effect of partition temperature on the total shaftwork (Lee

2001)

The refrigeration system design approach adopted in this work is limited to simple

and cascaded refrigeration cycles. In practical design, it is frequent to encounter

single refrigerant multistage cycles featuring multiple evaporating stages and a

single condensing stage. According to Wang and Smith (2005) the difference

between the shaft power demand of simple cycles and the corresponding

multistage cycles is small; therefore, this work only incorporates the simple and

cascade refrigeration cycles.

In summary, in this study the decision making for refrigeration system selection

and calculation of power requirements is based on the temperature of the

evaporator. If Tevap> -36 oC a simple refrigeration cycle is employed with power

calculation by Eq. 4.14 with η = 0.6. If, however, Tevap< -36 oC, a cascade

refrigeration cycle is employed, where the optimal partition temperature is

estimated as discussed to calculate the power requirement of the cascade cycle.

In this work, propane is selected as the refrigerant for the simple cycle while i-

butane and ethane are chosen for the cascade refrigeration cycle. This choice of

refrigerant is based on two reasons, first is the availability of these refrigerants

within the process and second is the lower power consumption for the given range


124

of evaporation temperature as shown in Figure 4.6. However, the automatic

selection of refrigerant is not included within the synthesis framework and is

suggested as a future work in Chapter 7.

4.3.4.3 Illustrative example: Cascade cycle vs. Simple cycle

An example is shown to demonstrate the advantages of using a cascade cycle

instead of a simple cycle in the case of large temperature difference between the

heat sink and heat source. In this example, 4000 kW cooling is required at a

temperature of -65°C.

As the cooling temperature of -65°C is below the normal boiling point of

propylene, a simple cycle of propylene is incapable of providing the required

cooling above the atmospheric pressure. From Figure 4.6, other refrigerants such

as ethane or ethylene can be employed. Ethane is chosen in this case as it has a

normal boiling temperature of 88.73°C and requires less shaft power that ethylene.

The configuration of the cascade is illustrated in Figure 4.7. Ethane is the

refrigerant in the lower cycle and propylene is used in the upper cycle. Aspen

HYSYS is applied for simulation of the cycles with physical properties calculated

by choosing Peng-Robinson as the fluid package. The heat sink is assumed to be

available at 0 oC, to compare against a simple cycle, as explained later. In

simulation, the partition temperature between the two cycles is set at -45 oC which

is near the normal boiling point of propylene. The total shaft power requirement in

this case is 3300 kW.

On the other hand, if the temperature of the available heat sink is assumed to be

reduced to the operating range of ethane, at 0 °C, and the cooling temperature and

duty are kept the same, then a simple refrigeration cycle using ethane is possible

for the modified temperature range. The comparison is made by simulating a

simple ethane cycle at the new condensing temperature in HYSYS. The results are

listed in Table 4.2. The total shaft power requirement in the single ethane cycle is

4321 kW which is about 130% of that in the cascade cycle. It demonstrates that

when there is a big temperature difference between refrigerant condensing and

evaporating, using simple cycle can be of very low efficiency.


125

Table 4.2 Cascade refrigeration cycle vs. simple refrigeration cycle

4.4 Flowsheet simulation and evaluation

The flowsheet synthesis requires simulation of the process at given conditions

(optimisation variables) selected by the optimisation procedure. The two main

methods used for the flowsheet simulation are the sequential modular method and

the equation-oriented method. The sequential modular method performs the

calculations one block at a time in sequence, where a block typically represents a

unit operation. Process computations follow the material flow through the process,

which makes it easier to debug convergence failures (Biegler et al., 1997). The

known input streams and the known design parameters are generally required by

the block calculations to calculate the output streams. Recycle streams in this

approach are handled using tearing technique.

The main advantage of sequential modular approach relates to its robustness,

which ensures rigorous convergence, even in presence of extremely complex

modules that are treated in an autonomous way (Biegler et al., 1997). The

mathematical models of different modules can be developed and coded separately

Cascade Cycle

Ethane/propylene

Simple Cycle

Ethane

Cooling duty (kW) 4000 4000

Upper cycle -45

Evaporating Lower cycle -70

-70

Upper cycle 0

Temperature (°C)

Condensing Lower cycle -42

0

Upper cycle 7300 Condensing duty (kW)

Lower cycle 5558

8321

Upper cycle 1742 Shaft power consumption (kW)

Lower cycle 1558

4321

Total Shaft power consumption (kW) 3300 4321


126

with different solution algorithms. Due to the structured information flow in the

sequential-modular approach, the error checking is fairly easy and generally allows

for easy debugging in the case of program failure (Chen and Stadtherr, 1985).

The main problems affecting the efficiency of the sequential-modular approach,

includes the handling of design specifications and the presence of multiple nested

iteration loops (Bimakr et al., 2008). The handling of design specifications by the

introduction of additional iteration loops is an inefficient way to handle simple

equations. The second problem with the sequential modular approach is that it

requires iterative handling of the recycle streams and may require a large number

of iterations to converge (Turton et al., 2008).

The equation-oriented approach or simultaneous approach assembles the equations

from all the modules into one large set of equations, which are then solved

simultaneously using an appropriate method (Biegler et al., 1997). In the equation-

oriented approach, each equipment module contributes to the governing equations

to be solved. Tearing of streams is not necessary in the equation-oriented approach

since all the governing equations are solved simultaneously (Kisala et al., 1987).

The simultaneous method is computationally efficient as all equations are solved

simultaneously; there is no need for nested iteration loops, as in the case of the

sequential approach. The design specifications are easy to handle in this case as

they are represented by simple equations within the large system. The

simultaneous approach also offers a great potential for process optimisation as the

simultaneous equations can be used as constraints in a generalized nonlinear

programming problem (Ishii and Otto, 2011).

For large flowsheets the number of equations will be quite high which may cause

problems in convergence of the flowsheet models (Bimakr et al., 2008). Most of

the equations formed are nonlinear and require good initial guesses to obtain a

converged solution. However, it is difficult to provide a good initial guess for large

and complex nonlinear systems. (Grossmann and Daichendt, 1996).

In this work the sequential modular approach is selected for flowsheet simulation

because of the advantages mentioned before. The flowsheet simulation begins by

specifying conditions of the flash unit. The cooling duty required to meet these


127

operating conditions is evaluated based on the overall energy balance over the

whole flowsheet. If the feed cooling provided by ‘cold recovery’ from the top

product and the side reboiler is insufficient to achieve the flash temperature at the

selected pressure, external refrigeration is required; the refrigeration cycle

simulated with the short-cut model as explained in Section 4.4. The turbo-

expander, the compressor and the demethaniser are then simulated.

During the simulation of the flowsheet, the subroutines representing different units

are called sequentially, with the output of one unit serving as the input of the next.

The computation proceeds unit by unit from the feed to the product streams. The

recycle loops are torn at suitable points and estimated values are assigned to these

streams. Recycle loops are sequentially solved until the updated values of the tear

streams match the computed stream information. The recycle streams involved in

the flowsheet need to be solved iteratively in the sequential modular approach.

Some of the methods for the convergence of recycle loop are discussed in the next

section.

4.4.1 Recycle loop convergence

After various flowsheet subsystems have been modelled and partitioned, the next

step is to tear the recycle streams. This involves assigning values to the unknown

variables; then an iterative procedure is used, incorporating a suitable convergence

enhancement method to reduce the difference between the previous and currently

calculated values of the torn variables within a pre-assigned tolerance. Smith

(2005) notes that it is usual to specify a scaled error in the form:

Tolerancex

x)x(GTolerance ≤

−≤−

( 4.14)

where x is the initial estimate of the variable

G(x) is the resulting calculated value of the variable


128

It is unlikely that the estimated values for the recycle stream will be within

tolerance for the initial estimate. If the convergence criteria are not met then the

convergence block needs to update the value of the recycle stream. The simplest

approach to this is a direct substitution or a repeated substitution (Smith, 2005). In

this approach, the sequence is calculated from an initial estimate, while the

calculated value then becomes the value for the next iteration. This substitution is

repeated until all convergence criteria are met.

G(x) = x

FlowsheetResponse

G(x)

xInitial Guess

G(x) = x

G(x)

xInitialGuess

Solution byLinearInterpolation

(a) (b)

Figure 4.9 Methods for recycle convergence a) Successive substitution

method, b) Wegstein method (Smith, 2005).

Figure 4.9 (a) shows a schematic representation of the successive substitution

strategy. The problem with this approach is that convergence requires many

iterations and some problems might fail to converge to the required tolerance

(Smith 2005).

Wegstein's method can be employed to accelerate convergence when the method

of successive substitution requires a large number of iterations. Figure 4.9(b)

illustrates the Wegstein method. At each iteration, the previous two iterates of G(x)

and x are extrapolated linearly to obtain the next value of x as the point of

intersection with the 450 line. Two direct substitution iterations are linearized. A

straight line equation can be written for the two iterations as:


129

bax)x(G += ( 4.15)

Where a = slope of the line = 1

1

−

−

−

−

kk

kk

xx

)x(G)x(G

)(,)( 1−kk xGxG = calculated values of variables for iterations k and k-1

1, −kk xx = estimated values of variables for iterations k and k-1

Eq. (4.17) can be used for the calculation of the next estimate for recycle based on

the calculated value (G(xk)) and the previous value (xk).

[ ]kkkk x)x(G)q(xx −−+=+ 11 ( 4.16)

If q = 0 in Eq. (4.17), the method becomes direct substitution. If q < 0 acceleration

of the solution occurs. Bounds are normally set for the value of q to prevent

unstable behaviour (Smith, 2005).

In this work, the Wegstein method for the convergence of recycle streams is

employed as it requires fewer iterations for our system of demethaniser flowsheet.

4.5 Case Study

In this section the simulation model proposed in this chapter is applied to an

industrial demethanisation process. The case study has been adapted from Chebbi

et al. (2008). The main aim of this study is to validate the developed simulation

model to recover at least 98% of the methane to the top product and recover a

minimum of 70% of the ethane to the NGL product. The lean methane-rich sales

gas is used as fuel whereas the natural gas liquid (NGL) product serves as feed for

petrochemicals production.


130

4.5.1 Problem inputs

In this work, components heavier than butane, as well as nitrogen, are artificially

eliminated from the plant feed (Chebbi et al., 2008) in order to reduce the

complexities that arise by the presence of trace components in the calculation for

establishing intersection of profiles for column design. The simplified composition

of the feed and the original composition from Chebbi et al. (2008) are presented in

Table 4.3.

Table 4.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for

this case study

Component Actual feed* composition mole fraction

Simplified feed composition mol fraction

Nitrogen 0.01 0.000

Methane 0.76 0.784

Ethane 0.13 0.134

Propane 0.054 0.056

isobutane 0.026 0.027


n-hexane 0.01 0.000


The Peng-Robinson property prediction method, using the default parameters of

Aspen HYSYS 2006.5 is applied throughout. This equation of state is selected on

the basis of low to moderate pressure gas processing (Carlson, 1996). Table 4.4

provides the specified feed and product conditions.

Table 4.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008)

Products Feed gas

Sales gas NGL

Temperature 37 oC 40 25

Pressure 60 bar 60 30


131

The gas subcooled process (GSP) as given in Chebbi et al. (2008) is a typical

turboexpander based demethaniser process (Fig. 4.10). The feed gas is initially pre-

cooled by a side reboiler before entering a heat exchanger where it is cooled by the

top product from the demethaniser. The cold feed leaving the exchanger is further

cooled down by a chiller using an external refrigeration cycle. The exit stream is

fed to a flash unit, the liquid from which is sent to the demethaniser as the lower

feed, while the vapour is split into equal proportions. One portion is expanded and

sent as the upper feed to the demethaniser while the second portion is sent to the

top of demethaniser as an external reflux stream after being cooled by a heat

exchanger.

Figure 4.10 Process flowsheet diagram of a typical GSP demethaniser process

(Chebbi et al., 2008)

4.5.2 Results

The simulation of the process begins with the flash unit temperature, for which the

temperature and pressure are initially given (base case values). The cooling duty

required to meet the temperature is evaluated based on the overall energy balance

over the whole flowsheet.


132

The complex distillation column is simulated using the modified boundary value

method explained in Chapter 3. In this case study, a two-feed column with one side

reboiler is used. The pressure in the column is assumed constant at 30 bar.

The process is simulated in Aspen HYSYS with the available data from Chebbi et

al. (2008). The data required for simulation of the demethaniser column is not

explicitly specified in the paper. The results from boundary value method are used

to initiate the column simulation in HYSYS. The column design results are

presented in Table 4.5. Figures 4.11 and 4.12 compare the molar flow profiles and

composition profiles in the column obtained from the BVM and rigorous HYSYS

simulation.

Table 4.5 Comparison of column simulation results: Boundary value design

method vs. HYSYS.

Results Units Boundary Value Model

HYSYS

Number of Stages - 28 28*

Top feed - 12 12*

Lower feed - 22 22*

Side reboiler duty (4th from bottom) kW 1500* 1500*

Distillate flow rate (kmol/h) kmol/h 4043 4044

Bottoms flow rate kmol/h 937 936

Reboiler temperature oC 30.5 30

Reboiler duty kW 1828 1845

CPU time sec 0.84 1.0



133

0

1000

2000

3000

4000

5000

0 5 10 15 20 25 30

Number of stages (top to bottom)

Mola

r fl

ow

(k

mol/h

)

Vapour (HYSYS)

Liquid (HYSYS)

Vapour (BVM)

Liquid (BVM)

Rectifying

sectionMiddle

section

First

stripping

section

Second

stripping

Section

Figure 4.10 Molar flow profiles: Boundary value method vs. HYSYS

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0 5 10 15 20 25 30

Number of stages (top to bottom)

Mo

le f

ract

ion

Methane(HYSYS)

Ethane (HYSYS)

Propane (HYSYS)

Methane(BVM)

Ethane (BVM)

Propane (BVM)

Rectifying

section

Middle

section

Second

stripping

section

First

stripping

section

Figure 4.11 Liquid composition profiles: Boundary value method vs. HYSYS


134

The flowsheet simulation model predicts the recoveries of methane and ethane as

well as total power consumption. The simulation of the process in HYSYS

provides a rigorous basis for model validation. The simulation results for the

developed flowsheet model are in good agreement with those of the HYSYS, as

shown in Table 4.6. This indicates that the model accurately represents the overall

demethaniser process. The computation time for the simulation is 12.4 seconds on

an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB RAM). The simulation

time for HYSYS is also presented in Table 4.6, where the time for setting up the

flowsheet unit models is not considered (usually setting up time is around 20-30

minutes depending on flowsheet complexity).

Table 4.6 Simulation results: Shortcut model vs HYSYS

* indicates specified values

4.6 Conclusions

In this chapter, a demethaniser flowsheet simulation approach is presented which

will be employed in a systematic framework for design and optimisation of

demethaniser flowsheets. Shortcut design models for different units of a complex

demethaniser flowsheet are developed. An integrated process simulation model is

presented which considers the demethaniser column and the heat recovery system

utilising multistream exchanger. The integrated process model is able to account

for interactions between the different unit operations in the process flowsheet.

Results Units Shortcut model HYSYS

Ethane recovery in NGL % 76.43* 76.43

Methane recovery in sales gas % 99.54* 99.54

Residue compressor power kW 2055 2042

Refrigeration power kW 2980 2950

Total power consumption kW 5035 4992

CPU time sec 12.4 20


135

These interactions can be exploited for improving the performance of the overall

demethaniser system.

An industrially important process is simulated using the simplified models and

validated against rigorous simulation in HYSYS. The results show that the

developed model of the flowsheet is sufficiently accurate and is suitable for

applying in an optimisation framework for demethaniser flowsheet synthesis.

Chapter 5 Fixed structure flowsheet optimisation using nonlinear programming

136

CHAPTER 5 FIXED STRUCTURE FLOWSHEET

OPTIMISATION USING NONLINEAR

PROGRAMMING

Demethaniser flowsheets are normally proprietary designs. However, the majority

of these designs are based on similar flowsheet configurations with different

operating conditions. So this chapter discusses an approach for optimising a

demethaniser flowsheet with a fixed structure with the aim to optimise the

performance by appropriate choice of the operating conditions. A nonlinear

programming (NLP) technique is used for optimisation.

5.1 Degrees of freedom of demethaniser system - Optimisation

variables

The potential of a design variable to affect the performance of the process can be

identified using sensitivity analysis. The use of sensitivity analysis ascertains how

a given model output depends on the input parameters. The quantitative effects of

the design variable of interest on the key performance indicators can be identified.

If the value of the performance indicators varies significantly, it indicates that the

design variable of interest should be considered during optimisation.

In this work, sensitivity analysis is performed on the most commonly employed

demethaniser process for NGL recovery, the gas subcooled process (GSP). The

composition and condition of feed is obtained from Chebbi et al. (2008). The feed

gas is at 60 bar and 37 oC and its composition is given in Table 5.1. The sales gas


137

is required at a pressure of 60 bar and a temperature of 40 oC, while the NGL

product is required at 25 bar.

Table 5.1 Feed gas composition - from Chebbi et al. (2008)

Component Feed composition

(Mole fraction)

Nitrogen 0.01

Methane 0.76

Ethane 0.13

Propane 0.054

isobutane 0.026

isopentane 0.01

n-hexane 0.01

Total Flow (kmol/h) 4980

AspenTech simulation package HYSYS® has been used in this work for

performing the sensitivity analysis. In order to achieve accurate results over the

range of temperature and pressure required in the process, an appropriate choice of

fluid package is critical (Elliot et al., 1996). Peng-Robinson is selected as the

equation of state for this process due to its accurate prediction of the process

components at the process conditions.

The flowsheet for the GSP process is shown in Figure 5.1. Dry feed gas flows

through a pre-cooler, where it is cooled to about –5 oC with the help of the

demethaniser top product. This pre-cooled feed then passes through the side

reboiler and the refrigeration cooler respectively. The side reboiler is used to

provide sub-ambient cooling through heat recovery from the column and reduce

the external refrigeration requirement. A simple refrigeration cycle using propane

as the refrigerant is also simulated in HYSYS to calculate the power requirements

in the compressor of the refrigeration cycle. The cooler lowers the temperature of

the feed to about -22 oC.

138

Chap

ter 5 F

ixed

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ear pro

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min

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Figure 5.1 HYSYS process flowsheet diagram of a typical GSP demethaniser process for NGL recovery


139

The two phase stream produced as a result of cooling enters a vapour-liquid

separator where liquid and vapour are separated. The vapour product is split into

two streams (V1 and V2) in equal proportion, where stream V1 (acting as an

external reflux stream for the demethaniser) is then sent to the top of the

demethaniser after passing through a reflux cooler and a valve to reduce its

temperature and pressure to the desired conditions in the column. A reboiled

absorption column represents the demethaniser column with 30 stages including

the reboiler. The stream V2 is passed to an expander which reduces the pressure to

20 bar and enters the column as the top feed at the 12th stage. The power generated

by the expander is utilised in the compressor for sales gas.

The liquid from the vapour-liquid separator is sent directly to the column as the

lower feed on 23rd stage after passing through a throttle valve. Most of the heavier

components are recovered as NGL in the bottom product of demethaniser. The top

product, consisting mainly of methane, is used for cooling the reflux stream and

feed in the pre-cooler, and finally compressed to the required pipeline pressure of

60 bar in a recompressor.

The process flowsheet is reviewed to determine the available parameters, which

can be modified, i.e., to determine the number of degrees of freedom. Each of these

parameters is then taken one at a time, subjected to a case study (using the HYSYS

Databook tool) varying the selected parameter over a range which is usually

dependent on the process constraints. Once the effect of the parameter on the

performance indicators for the process has been noted, the parameter is reset to the

base case value. This process is then repeated for other decision variables.

The criteria that need to be met during the sensitivity analysis are listed below:

• Maximum methane to ethane ratio in the demethaniser bottom

product: 1.5% mol

• Minimum temperature approach in all heat exchangers: 2 °C

• 80% adiabatic efficiency for compressor and expander


140

The decision variables selected in this work are the demethaniser column pressure,

temperature of the flash unit, split ratio of the vapour from the flash column and

the duty of the side reboiler. These variables are chosen on the basis of heuristics

and previous research (Diaz et al., 1996, Bandoni et al., 1989, Mehrpooya et al.,

2006).Various indicators can be used for evaluating the flowsheet performance. In

this work the ethane recovery and the total power requirements are the main

performance indicators. The effect of various process parameters on these

indicators is discussed in following sections.

5.1.1 Demethaniser operating pressure

The demethaniser operating pressure has a significant effect on the process

economics. Operating the column at higher pressures reduces the sales gas

compression power requirements. However, recovery of ethane is reduced at high

pressure as a result of a decrease in the relative volatility between the key

components. Therefore, an optimum value of the operating pressure needs to be

determined. In this work, the pressure is varied in the range 10 bar to 35 bar to

consider its effect on the flowsheet performance indicators.

Table 5.2 Effect of demethaniser operating pressure on flowsheet performance

Demethaniser operating pressure bar 10 15 20+ 25 30 35

Refrigeration power kW 941 941 941 941 941 941

Compressor power kW 6736 4964 3798 2944 2278 1737

Total power consumption kW 7677 5905 4739 3885 3219 2678

Overall ethane recovery % 86.6 84.3 81.1 77.5 73.3 68.8

Reboiler duty kW 411 980 1460 1882 2261 2610

+ indicates base case value

Figure 5.2 shows the effect of pressure on the total power consumption which is

the sum of compressor and refrigeration power requirements. By increasing the

column pressure from 10 to 35 bar, the total power is decreased significantly by

65%. This decrease is mainly due to the decrease in the power requirement in the


141

sales gas compression. There is no change in the refrigeration power requirements

as evident from the results shown in Table 5.2.

Figure 5.2 Effect of demethaniser operating pressure on power consumption

Figure 5.3 illustrates that with the increase of column operating pressure from 10

to 35 bar, overall ethane recovery decreases from 86% to 68%, reflecting decrease

in the ease of separation, i.e. reduced relative volatility due to higher operating

pressure.

Figure 5.3 Effect of demethaniser operating pressure on ethane recovery

0

2000

4000

6000

8000

10000

0 5 10 15 20 25 30 35 40 Column operating pressure (bar)

To

tal

po

wer

co

nsu

mp

tio

n (

kW

)

50

60

70

80

90

0 5 10 15 20 25 30 35 40

Column operating pressure (bar)

Eth

an

e re

cov

ery

(%

)


142

5.1.2 Flash temperature

The vapour to liquid ratio changes with the flash temperature. As a result, the

amount of lower feed entering the demethaniser is altered. A temperature range of

-35°C to -15°C is considered in this work, where results are shown in Table 5.3.

The upper limit of -15°C is chosen in order to meet the minimum approach

temperature criterion in the heat exchanger, a value of 2°C is applied in line with

the industrial practice (GPSA 2004). The lower limit of -35 °C follows the

selection of propane as refrigerant in the external refrigeration cycle (Smith, 2005).

Table 5.3 Effect of flash feed temperature on flowsheet performance

Flash feed temperature oC -35 -30 -25+ -20 -15

Refrigeration power kW 1765 1343 941 554 378

Compressor power kW 3871 3831 3798 3771 3749

Total power consumption kW 5636 5174 4739 4325 3927

Overall ethane recovery % 83.3 82.3 81.1 79.8 78.3

Reboiler duty kW 1928 1677 1460 1271 1109


A decrease in the flash temperature mainly affects the power requirement of the

refrigeration cycle as the cooling load increases. The refrigeration power

consumption is shown to decrease by approximately 350% as the flash feed

temperature increases from -35 oC to -15 oC. There is also a slight decrease in the

power requirement of the recompressor with the decrease in the flash temperature

as shown in Table 5.3. The decrease of recompressor power is attributed to the fact

that the higher temperature results in more vapour being produced and hence, an

increase in the power produced in the turbo-expander. As the power produced by

the expander is used to drive the first compressor (Figure 5.1), so the net power

required by the recompressor to achieve the final specified pressure for sales gas is

decreased.


143

Figure 5.4 Effect of flash temperature on total power consumption

Ethane recovery decreases by increasing the flash temperature from 83% to 78% as

shown in Figure 5.5. As the flash temperature is raised, less liquid is separated in

the vapour-liquid separator; hence the amount of lower feed is decreased. This has

an adverse effect on the ethane recovery.

Figure 5.5 Effect of flash temperature on ethane recovery in NGL

78

80

82

84

-40 -35 -30 -25 -20 -15 -10 Flash temperature (oC) o

Eth

an

e re

cov

ery

(%

)

0

2000

4000

6000

-40 -35 -30 -25 -20 -15 -10

Flash temperature (oC)

To

tal

po

wer

co

nsu

mp

tio

n (

kW

)


144

5.1.3 Split ratio of vapour from flash column

The vapour from the flash column is divided into two streams as shown in Figure

5.1. The split ratio (external reflux to upper feed) is another important factor

affecting the flowsheet performance. In this work this ratio is increased from 0.2 to

0.7 as shown in Table 5.4.

Table 5.4 Effect of vapour split ratio on flowsheet performance

Flash vapour split ratio

(reflux/feed)

– 0.2 0.3 0.4 0.5+ 0.6 0.7

Refrigeration power kW 708 708 708 941 708 708

Compressor power kW 3517 3612 3699 3798 3862 3968

Total power kW 4225 4320 4407 4739 4570 4676

Overall ethane recovery % 50.3 60.8 71.0 81.1 88.6 92.1

Reboiler duty kW 1058 1154 1250 1460 1432 1716

Expander power generation kW 935 818 700 584 467 350


The effect of the vapour split ratio on the flowsheet performance indicators is

shown in Figure 5.6 and 5.7. There is an increase in the total power consumption

which is mainly due to the increase in the compression power as the refrigeration

power stays constant (Table 5.4). A higher split ratio means less vapour (upper

feed) goes in the expander which leads to less power being generated in the

expander. As the power from expander is utilised in the compressor, hence the

power requirement of the recompressor is increased.


145

Figure 5.6 Effect of vapour split ratio on power requirement

The ethane recovery is also shown to increase with the increase of the split ratio as

more reflux ensures a higher recovery in the bottom product. But this has a

penalty; a higher reboiler duty. The highest overall ethane recovery of 92% is

achieved at a vapour split ratio of 0.7, but at the cost of higher energy requirements

in both the column reboiler and the final compressor for the sales gas.

Figure 5.7 Effect of vapour split ratio on ethane recovery

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Split ratio

Eth

an

e re

cov

ery

(%

)

3000

3500

4000

4500

5000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Split ratio

To

tal

po

wer

co

nsu

mp

tio

n (

kW

)


146

5.1.4 Effect of side reboiler duty

The side reboiler in the demethaniser increases the overall energy efficiency by

reducing the main reboiler duty and pre-cooling the feed gas. The use of side

reboilers enables the heat recovery at temperatures lower than the temperature of

the column reboiler which consequently reduces the power required by the external

refrigeration system to pre-cool the feed to the desired temperature in the flash unit

(Figure 5.1).

For the sensitivity analysis, the side reboiler duty is increased from 0 to 2000 kW

and the effect of this increase on the performance indicators is shown in Table 5.5.

The refrigeration power is shown to decrease with the increase of side reboiler

duty (Figure 5.8). The compressor power and ethane recovery do not change with

the change in the duty of the side reboiler.

0

400

800

1200

1600

0 500 1000 1500 2000 2500

Side reboiler duty (kW)

Ref

rig

era

tio

n p

ow

er (

kW

)

Figure 5.8 Effect of side reboiler duty on refrigeration power requirement

Table 5.5 Effect of side reboiler duty on flowsheet performance

Side reboiler duty kW 0 500 1000+ 1500 2000

Refrigeration Power kW 1259 983 941 432 157

Compressor Power kW 3780 3780 3798 3780 3780

Total Power kW 5039 4763 4739 4212 3937

Overall ethane recovery % 80.3 80.3 81.1 80.2 80.2

Reboiler Duty kW 2342 1843 1343 845 347



147

5.1.5 Summary of decision variables

The key variables affecting the demethaniser process performance have been

identified by sensitivity analysis. The results show that there is a trade-off between

ethane recovery and the total compression power as an increase in one increases

the other when the selected parameters are varied. Therefore, an objective function

needs to be defined which can account for the trade-off between power consumed

and ethane recovery. The design variables are then varied to maximise the annual

profit or minimise the annualised cost.

Having identified the significance of each variable and its effect on the overall

processes performance, an appropriate optimisation technique can then be selected

to determine the optimal values of these variables to minimise or maximise the

objective function.

5.2 Process optimisation

The optimisation of a process involves the minimisation or maximisation of an

objective function by varying the process variables, subject to satisfying the

simulation model as well as some practical process-related linear and nonlinear

constraints. A suitable algorithm is also required to solve the optimisation problem.

Mathematically, the optimisation problem is represented as

( )z,ufMinz

( 5.1)

Subject to ( ) 0=z,uE ( 5.2)

( ) 0≤z,uI ( 5.3)

Where: ( )z,uf = nonlinear objective function

( )z,uE = equality constraints representing mass and energy balances, and

equilibrium expressions

( )z,uI = inequality constraints representing design specifications, operational and

safety restrictions and logical constraints

u = vector of dependent variables

z = vector of independent variables


148

5.2.1 Objective function

Mathematically, finding an optimal solution requires the minimisation or

maximisation a specified objective function. In the process design stage, the

energy and cost investment are more easily quantified and may be of overriding

significance than other factors (i.e. safety, reliability, etc) because the economic

viability is crucial (Smith, 2005). The goal of the optimisation process in this work

is to maximise the profit from the process while respecting certain constraints,

which involve the maximisation of the product throughputs and/or minimisation of

operating costs.

The objective function for a fixed structure flowsheet optimisation is

Max ( )x,uP ( 5.4)

where

P = Annual profit

u = Optimisation variables

x = Process constraints

The annual profit is defined as:

ACCCPRP opRM −−−= ( 5.5)

where PR is the annual revenues from products, RMC is annual cost of the raw

materials, opC is the annual operating costs and AC is the annualised capital cost of

the equipments involved.

The product revenues PR is defined by

kodPr

k

kodPr FPPR ∑= ( 5.6)

where kodPrP is the sale price of component k in the product stream and k

odPrF is

the flow rate of component k in the product stream.


149

The raw material cost is given by

kFeed

k

kFeedRM FPC ∑= ( 5.7)

where kFeedP refers to the material cost of component k in the feed stream and k

FeedF

is the flow rate of component k in the feed stream.

The operation costs (Cop) are defined as

∑=i

iutiop GOCC ( 5.8)

where, utiOC is the cost associated with the use of utility I and iG is the flow rate

capacity of utility i. The utilities include cooling water, electric power and LP

steam. The cost of these utilities cost is calculated in Appendix B. Annual

operating hours are 8600

Finally capital costs are defined as

∑=i

iACAC ( 5.9)

where ACi is the annualised capital cost for equipment i.

In this work, the capital cost of the equipments is calculated by the bare module

cost approach presented by Turton et al. (2008). A time period of 3 years and 5%

interest rate is assumed to estimate the annualised cost. The details of the method

to calculate the annualised capital cost is presented in Appendix B.

The volatility in the price of the natural gas and NGL over the last 5 years is a

significant issue facing the natural gas industry and energy companies. Price

volatility contributes to an uncertain climate for energy companies, consumers and

regulators. Figure 5.9 indicates the comparison of price movements of various

fuels over a three year period. The prices for natural gas and NGL are shown to

follow the same trend as that of crude oil. The ethane and NGL composite (C2+)

are higher than the raw natural gas from a wellhead.


150

Figure 5.9 Price comparison of natural gas, crude oil , ethane and NGL (EIA

2011)

5.2.2 Process constraints

The various constraints applied in the optimisation of the demethaniser process are

listed and discussed below:

- Purity specification of sales gas

- Maximum methane mole fraction in demethaniser bottom product

- A lower bound on ethane recovery in the overall process

- Minimum approach temperature in heat exchangers

- Minimum amount of the external reflux stream

Each of these constraints has its own significance. The purity specification of sales

gas is important as it directly affects the heating value of the product gas, which is

normally specified by the customer. The methane specification in bottom product

is used by the boundary value method for column design. The lower bound on

ethane recovery is employed as it is usually specified externally. A minimum

approach temperature of ensures a finite heat exchanger area and avoids a


151

temperature cross. Also, as the reflux to the column is provided by an external

stream from the flash column, another nonlinear constraint is imposed on the

minimum amount of the external reflux stream, as otherwise the top of the column

would dry up.

5.2.3 Optimisation algorithm

Successive quadratic programming (SQP) is selected as the optimisation algorithm

for a fixed structure demethanisation process. SQP is appropriate for solving

smooth nonlinear optimisation problems when the problem is not too large and

functions and gradients can be evaluated with sufficiently high precision (Hock

and Schittkowski, 1983).

For the SQP method, all the functions, including the objective function ( )xf and

constraints ( )xE , ( )xI must be continuously differentiable. The solution procedure

involves formulating and solving a quadratic sub-problem in each iteration. The

objective function and the constraints can be reformulated into one equation, which

is the Lagrange function, while the search direction is based on Newton's method.

The sub-problem is obtained by linearising the constraints and approximating the

Lagrangian function quadratically (Hock and Schittkowski, 1983).

Equations (5.1 to 5.3), representing the generic objective function and process

constraints, can be further rearranged into a Lagrange function (See Biegler 1997

references within):

( ) ( ) ( ) ( )( )2

2

1sxIxExf,,xL

TT −++= µλµλ ( 5.10)

Where:

µ,λ = vectors of Lagrange multipliers for equality and inequality constraint

functions respectively


152

=s vector of constants included in the Lagrange function to avoid discontinuities

when the inequality constraint functions are modified into equality constraint

functions .

The quadratic function ( )pQ is given by:

( ) ( )λλλ xHgpQ minimiseTT

2

1−=

( 5.11)

subject to ( ) 0=λxJ ( 5.12)

Where:

g = the gradient vector of ( )xf at current value of x

( )xH = the positive definite approximation of the Hessian matrix of the Lagrange

function given by ( )

2

2

x

,,xL

∂

∂ µλ

( )xJ = the Jacobian matrix of the constraint functions evaluated at current value of

x , given by ( ) ( )

x

xIand

x

xE

∂

∂

∂

∂

This QP subproblem solution is used to form a search direction dk for a line search

procedure. In other words, the solution is used to form the next iterate

kkkk dxx α+=+1 ( 5.13)

where ix and id are the vectors of the iteration and kα is the step length parameter

The step length parameter αk is determined by an appropriate line search procedure

so that a sufficient decrease in a ‘merit’ function is obtained. The merit function is

formed from the objective function and a weighted sum of the constraint

infeasibility functions (Biegler et al., 1997). The initial iteration sets the step length

to a moderate value when the optimisation is closer to the optimum, however, the

step length can be reduced to converge the optimisation problem rapidly. The

optimisation problem can be terminated when the convergence criteria are satisfied

and the objective function has been maximised or minimised within the specified

tolerance.


153

5.2.4 Fixed structure optimisation approach

The fixed structure optimisation of the flowsheet starts by defining a flowsheet

structure. The optimisation variables are then selected. The base case flowsheet is

simulated at initial conditions using the shortcut design models and sequential

modular approach as explained in Chapter 4. The size and cost of the flowsheet

equipments are calculated by functions developed in Matlab. The simulated

flowsheet is then evaluated in terms of the annual profit. For the SQP algorithm, an

optimisation function ‘‘fmincon’’ in Matlab is employed. The optimisation

framework is highlighted in Figure 5.10.

Figure 5.10 Optimisation framework for a fixed structure flowsheet

Objective function

Constraints

Variables

• Complex column model

• Heat recovery model in

multistream exchanger

• Refrigeration model

• Cost models

NLP optimiser

(SQP)

Flowsheet structure

Optimum flowsheet

Base case with

initial conditions


154

5.3 Case study

A case study is presented to illustrate the design of an optimised NGL recovery

system by the application of the proposed optimisation framework. This case study

is based on the US patent ‘‘Process and apparatus for separation of hydrocarbons’’,

number 7357003 assigned to Toyo Engineering Corporation (Ohara et al., 2008).

Figure 5.11 illustrates the process.

In this work, the trace components nitrogen and carbon dioxide are artificially

eliminated from the feed in order to reduce the complexity introduced in the

calculation for composition profiles. The resulting simplified composition of the

feed and the original composition from the patent are presented in Table 5.7.

Table 5.6 Specified temperature and pressure of feed and products (Ohara et al., 2008)

Products

Feed gas Sales gas NGL


Pressure 62.4 bar 38 30

Table 5.7 Feed gas composition from patent (Ohara et al., 2008) and simplified for this case study

Component Original feed

composition

Simplified feed

composition

Nitrogen 0.010 0.00


Methane 0.894 0.908

Ethane 0.049 0.049

Propane 0.022 0.023

isobutane 0.013 0.013



155

Chap

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min

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Figure 5.11 Process flowsheet diagram of multiple reflux stream hydrocarbon recovery process (Ohara et al., 2008)

113

Sales gas

Reboiler

NGL

C-102

SR1

SR2

112

111

110

109 108 106

105

104

107

103

E-103 R-101 C-100

B-100

V-101 V-100

E-101 R-100

Demethaniser

T-100 E-100

Feed gas

C-101


156

The feed gas is cooled down to around -26 oC in the first multistream exchanger

(E-100) by heat exchange with the residue gas (120) and the lower side reboiler

(SR1) which is at a temperature of approximately -23 oC. The outlet stream (101)

is then further cooled down by using propane refrigerant (R-100) to -37 oC before

entering the second multistream exchanger (E-101). This exchanger utilizes the

second side reboiler (SR2) and the residue gas as the cold media.

The outlet stream from E101 (103) is a two-phase mixture which is separated into

the liquid fraction (104) and the vapour fraction (105) in a separator (V-100). The

liquid fraction is sent to the demethaniser as the lower feed. The vapour stream is

sent to an expander (B-100) where the pressure is decreased to 30 bar and useful

energy is generated. The outlet stream from the expander (106) is partially

liquefied and is separated into vapour and liquid streams in the second separator

(V-101). The liquid (107) is delivered to the column as the middle feed while the

vapour (108) is split into two parts: 60 % of stream 108 forms the top feed of

demethaniser while the rest is compressed to 62 bar. The compressed stream (111)

is then cooled and condensed in E103 by external refrigeration and demethaniser

top product respectively. The liquid stream exiting the exchanger (E-103) is then

depressurised to 30 bar and sent to the top of the demethaniser as a reflux stream

(112). The demethaniser recovers the ethane in the bottom product, while

separating the methane in the top product (113).

In the case study, the sale price of the products are obtained from US Energy

Information Administration (EIA 2011). The prices used are for November 2010

data. The sale gas, ethane and NGL (excluding ethane) prices are 4 $/GJ, 8 $/GJ

and 12 $/GJ respectively. The price of well head natural gas is 3.80 $/GJ (EIA

2011).

5.3.1 Process constraints

Various linear and nonlinear constraints are included in the formulation of the

optimisation problem. The nonlinear constraints are the specification of the

maximum allowed methane in the NGL product, the minimum ethane recovery in


157

NGL and the limits of the optimisation variables, as shown in Table 5.8. The linear

constraints are the mass and energy balances of the process. The summation of

vapour split fractions to be equal to unity is also added as a linear constraint. These

constraints are:

• Ethane recovery in NGL %85≥

• Methane to ethane ratio in NGL 020.≤

• Minimum approach temperature in E-101, E102 and E-103 C.o51≤

• 1=+ ur xx

where xr is the fraction from the vapour splitter used as reflux and xu is the fraction

from splitter used as column feed.

5.3.2 Optimisation variables

The optimisation variables are selected on the basis of sensitivity analysis. The

objective function is the annual profit from the process as explained in Section

5.2.1. The decision variables which are manipulated for the optimisation of the

process are discussed in Table 5.8. The lower and upper bounds and the base case

values are also shown.

Table 5.8 Values and bounds of optimisation variables

Decision variable

Description Unit Lower bound

Upper bound

Base case

x1 Demethaniser operating pressure

bar 15 35 28

x2 First flash separator temperature

oC -40 -60 -40

x3 Split ratio (Reflux to upper feed)

0.2 0.8 0.5

x4 Side reboiler 1 duty kW 500 2000 1500

x5 Side reboiler 2 duty kW 1000 3000 1000

x6 Reflux compressor outlet pressure

bar 30 80 62


158

5.3.3 Results

The process is simulated using the methodology presented in Chapter 4. The

conditions from the base case are used as the initial value for the simulation and

subsequent optimisation. The flowsheet simulation model calculates the recovery

of key components and total power requirements. The validation of the flowsheet

model is done by simulating the process in Aspen HYSYS. Table 5.9 compares the

simulation results from the shortcut model and HYSYS. The computation time for

the simulation using the simplified model developed in Chapter 4 is 22.4 seconds

on an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB RAM). The

simulation time for HYSYS is also presented in Table 5.9, where the time for

setting up the flowsheet unit models is not considered.

Table 5.9 Simulation results of shortcut model and HYSYS

Results Unit Model HYSYS

Number of stages in column - 40 40*

Methane recovery in Sales Gas % 99.94* 99.95*

Ethane recovery in NGL product % 90.62 90.65


Reflux compressor power demand kW 2134 2155

Residue gas compressor power demand kW 1004 1028

Refrigeration system power demand kW 3585 3612

CPU time sec 22.4 30


The simulation model is then employed in the optimisation framework (Figure

5.9). The results of the optimisation are highlighted in Table 5.10. The overall

annual profit is shown to increase from 190 MM$ to 198 MM$. Thus the

optimised flowsheet shows an increase in annual profit of around 4%, compared to

the base case. The increase in profit is due to both the decrease in the total power

requirements of the flowsheet, and the increase in overall ethane recovery.


159

Table 5.10 Comparison of optimisation results with base case

Total shaft power required deceased from 6.7 MW to 4.5 MW (33%). As utility

cost mainly comprises the electric power cost, this reduction in power

requirements has a pronounced effect on the overall objective function. Reboiler

duty is shown to decrease by 60%, owing to increased heat recovery by side

reboilers (Table 5.11). As the capital cost of the compressors and drivers are

directly dependent on the shaft power, so a decrease in power requirement gives a

lower capital cost. This eventually lowers the annualised capital cost as shown in

Table 5.10. The computation time for the optimisation using SQP is 24 minutes

and 38 seconds on an Intel® Core 2 Duo CPU 2.93 GHz processor with 4 GB

RAM).

Table 5.11 Optimisation variables – Base case vs. optimised case

Results Unit Base case Optimised case Residue compressor power kW 1004 1810

Reflux compressor power kW 2134 1080


Total shaft power requirement kW 6723 4480

Ethane recovery in NGL % 90.62 94.20


Annualised capital cost MM$ 13.94 12.42

Utility cost MM$ 11.38 6.62

Annual profit MM$ 190.4 198.24

Decision variable Unit Base case Optimised case

Demethaniser operating pressure bar 24 28

First flash separator temperature oC -40 -48

Split ratio (Reflux to upper feed) - 0.5 0.35

Side reboiler 1 duty kW 1500 2800


Reflux compressor outlet pressure bar 62 54


160

Table 5.11 compares the values of optimisation variables for the base case and the

optimised case. The results indicate that operating the demethaniser at a lower

pressure enhances the separation efficiency and hence the recovery of ethane is

increased. However, this also results in a higher compression power in the sales

gas compressor. Another important optimisation variable is the outlet pressure of

the reflux compressor. Optimisation results in a lower outlet pressure of 54 bar,

which not only decreases the compression power requirements but also decreases

the external refrigeration requirement as the cooling duty is also decreased.

Table 5.11 also indicates a lower vapour split ratio in the optimum case compared

to the base case. This is contrary to the results obtained by the sensitivity analysis,

where both the ethane recovery and power requirements are shown to increase with

the increase of split ratio. However, in this case study an additional compressor and

refrigeration cooler is present compared to the gas subcooled process studied for

sensitivity analysis. The lower split ratio decreases the flowrate of reflux stream

entering the compressor and subsequent cooler, thus decreasing the overall power

requirements as shown in Table 5.10.

5.3.4 Effect of feed and product price changes on optimisation

As discussed in Section 5.2.1 the prices of feed gas and the NGL product is quite

volatile and varies generally with the price of crude oil. The calculation for the

price of electric power required for the plant is also based on natural gas fuel as

explained in detail in Appendix B. In order to study the effect of variation in prices

of raw materials, products and power, another range of data is selected based on

the historical prices as shown in Figure 5.9. The data for July 2008 is selected

which represents the values before the world’s economic recession. Table 5.12

indicates the prices.


161

Table 5.12 Prices of feed and products

Component Price ($/GJ)

Feed gas 10

Sales gas 12

Ethane 18

NGL 22

The price of power is computed from Eq. B12 (Appendix B) and is $ 0.153 /KW.

The cooling water and steam cost are computed in the same manner for the new

price of natural gas. Table 5.13 presents the optimisation results for the new values

of the raw materials and products. The annualised profit in this case is shown to

increase from 394.22 MM$/yr to 410.62 MM$/yr. Thus the optimised flowsheet

shows an increase in annual profit of around 4.2 %, compared to the base case.

This percentage increase is similar to the first case with lower prices of both the

feed gas and NGL product.

The values of optimisation variables for the base case and the optimised case in

this scenario with different prices are presented in Table 5.14. The values are

similar to the previous case which shows that the price variations in the feed,

products and utilities do not affect the optimisation results significantly.


162

Table 5.13 Comparison of optimisation results with base case

Table 5.14 Optimisation variables – Base case vs. optimised case

The case study successfully demonstrates that the developed optimisation

methodology for a fixed structure flowsheet is able to accommodate the complex

interactions among the various units and find the optimal values for the important

decision variables.

Results Unit Base case

Optimised case Residue compressor power kW 1004 1906

Reflux compressor power kW 2134 1034


Total shaft power requirement kW 6723 4260



Annualised capital cost MM$/yr 13.94 12.20

Annual utility cost MM$/yr 13.42 7.18

Product revenues MM$/yr 1512.4 1520.82

Annual profit MM$/yr 394.22 410.62

Decision variable Unit Base case Optimised case

Demethaniser operating pressure bar 24 27.5

First flash separator temperature oC -40 -46

Split ratio (Reflux to upper feed) - 0.5 0.35



Reflux compressor outlet pressure bar 62 54


163

5.4 Conclusions

In this chapter, an optimisation algorithm for demethaniser flowsheets of a fixed

structure is presented. Sensitivity analysis has been used to identify the potential of

a design variable for changing the objective function. From the sensitivity analysis

it can be seen that there are strong interactions between various decision variables

in the demethaniser flowsheet. Simultaneous optimisation of these variables is

needed to create cost-effective design solutions while maintaining the performance

specifications of the process.

The optimisation procedure uses a nonlinear programming technique, the

successive quadratic programming to maximise the annual profit of the process.

The results indicate that the proposed methodology offers an effective approach for

design and optimisation of demethaniser flowsheets with a defined structure. A

case study is presented that applies the developed optimisation approach to a

commercial process. The results indicate an increase of 4% in the annual profit.

The optimisation approach presented in this chapter, however, cannot take into

account the various structural options of the demethaniser flowsheet. Moreover,

NLP optimisation can get trapped in local optima and may not find the best

solution for the problem. So in order to avoid these conditions a stochastic

optimisation technique will be applied in Chapter 6 to accommodate the structural

options in the flowsheet and achieve a near global optimum solution.

Chapter 6 Demethaniser flowsheet synthesis by stochastic optimisation

164

CHAPTER 6 DEMETHANISER FLOWSHEET

SYNTHESIS BY STOCHASTIC

OPTIMISATION

The synthesis of process flowsheets involves the selection of the structure, which

for given reactants and product specifications, promises the best performance

typically in terms of highest profit or the lowest cost. In order to determine the

optimal structure of the flowsheet, a superstructure may be developed that shows a

wide range of the potential interconnections between flowsheet units. The optimal

configuration is then determined from many alternatives through structural and

parametric optimization of the superstructure.

6.1 Superstructure representation for demethaniser flowsheet

In this research work, a generalised superstructure is developed taking into account

the important features found in demethaniser flowsheets for NGL recovery. This

superstructure includes various process units, including one or more flash units

operating at various pressures, heat recovery from residual gas and side reboilers,

external refrigeration, and an internal reflux stream. The simultaneous optimisation

of these structural options along with operating conditions, such as column

pressure, flash temperature, etc., can lead to cost-effective and energy-efficient

flowsheets. Figure 6.1 shows a basic expansion-based demethaniser flowsheet

including a range of structural options indicated by dotted lines.

165

Chap

ter 6 D

emeth

aniser flo

wsh

eet synth

esis by sto

chastic o

ptim

isation

Figure 6.1 Superstructure for demethaniser flowsheet synthesis

D

C

B

A

Reflux exchanger

Flash unit (High pressure)

2nd Flash unit (Low pressure)

Internal reflux stream

NGL

Compressor

Sales gas

Demethaniser

Side reboilers

Splitter

Reboiler

Expander

Recompressor

Multistream exchanger

Feed gas

External refrigeration


166

The various structural options indicated in the demethaniser superstructure are

explained below.

A. Use of a second flash unit

The low pressure stream from the expander is normally sent to the demethaniser as

the top feed, but in some process variations, it can be sent to another flash unit

where it is separated into liquid and vapour fractions. The liquid is sent to the

column as a feed while the vapour is mixed with the stream coming from the first

flash unit and enters the top of the column as an external reflux stream.

B. Side reboilers

The use of a side reboiler in the demethaniser enhances the overall energy

efficiency by not only decreasing the main reboiler duty, but also reducing the

external refrigeration required to pre-cool the feed. In the superstructure, the dotted

lines in the multistream exchanger represent the presence of side reboilers in the

flowsheet.

C. Internal reflux stream

The liquid entering the top of the demethaniser is provided by an external reflux

stream obtained from a high pressure flash unit. In some cases, a portion of the top

product can also be used as an additional reflux stream as indicated in Figure 6.1.

D. Use of external refrigeration cycle

The use of an external refrigeration cycle for the cooling of the feed gas is also

embedded in the superstructure. The external refrigeration requirement depends on

the heat recovery within the process. The refrigeration system is designed

according to the shortcut method explained in Section 4.3.

6.1.1 Summary

The optimisation of demethaniser flowsheets is complicated by the interaction of

non-linear models for the different flowsheet units as discussed in Chapter 4. There


167

are both continuous decisions (operating variables), integer variables (number of

side reboilers) and binary integers (existence of units) in the flowsheet

superstructure. Demethaniser flowsheet synthesis problem can thus be formulated

as a mixed integer nonlinear programming (MINLP) problem. The MINLP

formulation accounts for both non-linear models and discrete variables describing

the process topology. MINLP problems are typically expressed as following

(Adjiman et al., 1998):

miny,x

( )y,xf ( 6.1)

Subject to

( ) 0=y,xh ( 6.2)

( ) 0≤y,xg ( 6.3)

where

- f(x, y) is a nonlinear objective function representing the performance criterion

- x is a vector of continuous variables representing flowrates, temperatures and

pressures of process streams and sizing of process units

- y is a vector of integer variables representing process alternatives

- ( )y,xh are the equality constraints representing mass and energy balances, and

equilibrium expressions

- g(x, y) are nonlinear constraints representing design specifications, operational

and safety restrictions and logical constraints

6.2 Choice of optimisation method

The solutions of integrated process synthesis problems needs to take into account

the limitations and applicability of optimisation technique. Generally, optimisation

tools start from an initial guess, search through the solution space, and converge to

an 'optimal' state. Deterministic methods in the form of MINLPs are most

frequently employed, where gradient information is used to evolve the search.


168

MINLP problems are considered to be one of the most difficult optimisation

problems, as discussed by Grossmann and Biegler (2004). The presence of non-

linear terms in the modelling equations for various units and the combinatorial

nature introduced by discrete variables results in a complex optimisation problem.

Bartfeld and Aguirre (2002) emphasized the importance of an efficient

initialization procedure to enhance the robustness of MINLP optimisation.

Conventional methods for solving MINLP problems involve the decomposition of

the problem into NLP and MILP sub-problems, which are then solved iteratively.

Among the conventional methods, the most commonly used are Branch and

Bound, Generalised Benders Decomposition and Outer Approximation methods. A

comprehensive review of these methods can be found in Grossmann and Daichendt

(1996), Biegler et al. (1997) and Grossmann and Biegler (2004).

The search algorithms used in the above methods for the NLP subproblems are

generally deterministic and need derivative calculations at each step. Grossmann

and Biegler (2004) noted that these search algorithm are likely to converge to a

local optimum instead of the global optimum. Moreover, NLP methods require a

good initial guess to ensure the convergence of the solution. These conventional

methods also require significant amount of computational time and memory; as for

every NLP subproblem solution, a linear approximation must be formulated and

solved as a MILP subproblem (Grossmann and Biegler, 2004). These shortcomings

of the traditional deterministic optimisation methods make them unsuitable for the

proposed synthesis framework. The use of gradient information limits the

application of these methods to problems with continuous and differentiable

functions.

An alternative for solving the problems associated with the conventional MINLP

methods is to use the stochastic optimisation methods, which were devised to

overcome non-convergence issues and reduce mathematical complexity (Hedar

and Fukushima, 2006). These methods do not require detailed problem formulation

or derivatives of the problem. The search for the optimum is based exclusively on

the values of the objective function at different points of the search space. Arora

(2004) showed that the stochastic optimisation techniques are effective in escaping

local optima by incorporating control mechanisms in the form of logical


169

conditions. They are also useful for finding globally optimal solutions for complex

non-linear and non-convex problems as compared to deterministic methods (Arora,

2004).

Stochastic methods perform a global search over all design options included in the

superstructure and the potential of the process with respect to a given objective

function is revealed. Paules and Floudas (1992) noted that although stochastic

optimisation will not converge on a local optimum, a solution within the global

solution space can be obtained that is close to the required ‘‘target’’ of the process.

If required, the resulting solution can be fine-tuned using gradient based

deterministic optimisation methods (Grossmann et al., 2000).

Commonly applied stochastic methods in process engineering problems include

Genetic Algorithms (GA) and Simulated Annealing (SA). GA methods use

techniques inspired by evolutionary biology such as inheritance, mutation,

selection, and crossover (Leboreiro and Acevedo, 2004). The search process of this

algorithm involves the selection of ‘individuals’ with highest ‘fitness’ generated by

a structured, yet random exchange of information (Mitchell, 2009). Various studies

have been reported in literature for the use of genetic algorithms for separation

system optimisation (Low and Sorensen, 2004, Boozarjomehry et al., 2009, Wang

and Smith, 2005). However, the drawback of GA is the large computational time

for estimating the required number of generations in order to obtain a solution to

within a certain level of accuracy (Wang et al., 2004).

Simulated Annealing (SA) is another stochastic optimisation algorithm, which has

been widely applied for process design due to its ease of implementation and its

robustness (e.g. Flouquet et al., 1994 ; Athier et al., 1997 ). However, simulated

annealing also requires a large computation time to search for solutions in the

vicinity of global optimum. Floquet et al. (1994) noted that SA will converge to a

globally optimal solution given an infinitely large number of iterations and a

temperature schedule that converges to zero sufficiently slowly.

The implementation of simulated annealing algorithm is relatively easier in a

systematic optimisation framework in comparison to other stochastic optimisation

methods (Zhong and Gang, 2009). SA offers flexibility with respect to the number


170

and type of optimisation variables, including continuous and discrete variables

(Vanlaarhoven and Aarts, 1987). In contrast to deterministic optimisation methods,

SA is less prone in converging to suboptimal solutions by not relying on local

gradient information. The robustness of SA makes it appropriate to account for

non-convex model equations. Therefore, in this work, stochastic optimisation is

carried out using simulated annealing. The simulated annealing algorithm is

described in detail in the next section.

6.3 Simulated annealing

The simulated annealing algorithms have been developed using an analogy to the

physical annealing of metals, where a metal in molten state at a very high

temperature is cooled down very slowly. In its molten state, metal atoms are

distributed randomly. When the system, i.e. the metal, is cooled, it reaches a state

of minimum energy. If the annealing process is carried out slowly such that at any

point in time the system is close to thermodynamic equilibrium, then the system

may reach a stable crystalline structure with minimum energy. However, if cooling

does not take place slowly enough or if the initial temperature is not high enough,

then the metal forms a glass-like metastable structure with higher energy than the

crystalline state. The analogy between the cooling process and the mathematical

optimisation become obvious when the undesirable metastable state and the

minimum energy crystalline structure are interpreted as a local and global

minimum, respectively (Kirkpatrick et al., 1983).

Metropolis et al. (1953) proposed an annealing algorithm to find the equilibrium

configuration of a group of atoms at a given temperature. In this algorithm, a

simulation is carried out at each step giving an atom a small random displacement

and computing the change in energy ( E∆ ). If the change in energy is negative,

then the displacement is accepted and used as starting point for the next step.

However, if the change in energy is positive, it is accepted with a probability given

by Eq.( 6.4):


171

=

aaTk

EexpP

∆

( 6.4)

Where Ta is the annealing temperature of the system.

ka is the Boltzman constant, 1.38 x 10-23 JK-1

Eq. 6.4 shows that with a decrease in temperature of the system, the probability of

accepting a positive change in energy also decreases. The system temperature

decreases according to the cooling schedule evaluating the new perturbations

during the cooling process. The algorithm terminates when the temperature of the

system reaches zero or the temperature of the solid state (Metropolis et al., 1953).

This work employs the simulated annealing algorithm of Kirkpatrick et al., (1983)

as given by Choong and Smith (2004), which is represented in Figure 6.2. The

simulated annealing process starts with an initial feasible solution at a reasonably

high value of the annealing temperature. The annealing temperature serves as a

control parameter for optimisation. The initial trial solution is modified by a

random change, known as a random move. The objective function of the new

solution is calculated and compared with that of the current trial solution. The

acceptance or rejection of the objective function depends on the magnitude of the

change and the current temperature in the cooling schedule. The modification

made to the current trial solution is then either accepted or rejected based on the

Metropolis acceptance criterion. This process of modification, simulation and

evaluation is repeated a number of times determined by the parameter known as

the Markov chain length, to obtain a set of sample solutions. Once several

candidate solutions have been obtained, the annealing temperature is reduced. This

cycle is continued until the termination criterion is satisfied.


172

Figure 6.2 Flowchart for simulated annealing algorithm (Choong and Smith,

2004)

Tem

per

atu

re l

oo

p

Mark

ov

loo

p

No

New Ta

Specify initial trial solution

Generate a new trial solution by making a random move

Evaluate objective function

Acceptance criterion met?

Final solution

Yes

Replace current state with modified state

Set initial annealing temperature

Termination criterion met?

Yes

No

Markov criterion met?

Apply cooling schedule

Yes

No


173

6.4 Annealing schedule parameters

The annealing schedule is described by the initial annealing temperature, the

cooling schedule, the acceptance criteria, the Markov chain length and the

termination criteria (Kirkpatrick et al., 1983). The selection of these parameters

affects the performance of simulated annealing. Guidelines for the selection of

annealing parameters selection are explained further below.

6.4.1 Initial annealing temperature

The initial annealing temperature depends on the nature of the problem and the

scale of objective function. Too high a temperature will unnecessarily increase the

algorithm convergence time. On the other hand, too low a temperature restricts the

number and magnitude of accepted uphill moves, thus limiting the ability of the

method to escape from local optima. Kirkpatrick et al. (1983) suggested that a

suitable initial temperature is one that results in an average acceptance probability

of about 0.8. Van Laarhoven and Aarts (1987) proposed an approach for selecting

initial annealing temperature.

o

ava

pln

fT

∆−=0

( 6.5)

Where avf∆ represent the average deterioration of the objective function for uphill

moves in a run where all the uphill moves are accepted, and po is the desired initial

acceptance probability.

6.4.2 Acceptance criterion

Any changes made by the simulated annealing algorithm to trial solutions are

accepted or rejected depending on the acceptance criterion chosen. An acceptance

criterion usually accepts a random move by the algorithm if it improves the

objective function. Many acceptance criteria are proposed in the literature

(Metropolis et al., 1953, Kirkpatrick et al., 1983, Hedar and Fukushima, 2006). In

this work, the original Metropolis acceptance criterion (Metropolis et al., 1953) has

been used, as this acceptance criterion has been observed to provide efficient

performance in simulated annealing algorithms (Zhong and Gang, 2009).


174

6.4.3 Markov chain length

The simulated annealing algorithm consists of two loops (Figure 6.2); the Markov

loop and the annealing temperature loop. The inner loop is the Markov loop while

the outer loop is formed by the annealing temperature. A sequence of moves

executed at each temperature corresponds to a Markov chain and the number of

these moves is known as the Markov chain length.

There is no systematic method to choose the length of the Markov chain. The

Markov chain length is dependent on the type and dimensionality of the problem

being solved (Marcoulaki and Kokossis, 1999). A balance between the quality of

the solution and computational time should be considered in selecting the value of

the Markov chain length. Too short a Markov chain length will lead to an

optimisation procedure converging to a local optimum; too long a Markov chain

length will increase the probability of finding the global optimum, however, at the

expense of an infinite computational time.

6.4.4 Cooling schedule

The reduction of the annealing temperature is controlled by the cooling schedule. It

is normal to let the temperature decrease until it reaches zero. However, this makes

the algorithm run for a lot longer, especially when a geometric cooling schedule is

being used (Van Laarhoven and Aarts 1987). In practice, it is not essential for the

annealing temperature to reach the temperature of the solid state as the chances of

accepting a worse move are almost the same as the temperature being equal to

zero.

The reduction of the annealing temperature must be slow enough to avoid being

trapped in a local optimum. However, too slow cooling will unnecessarily increase

the computational time. This work adopts the cooling schedule suggested by Van

Laarhoven et al. (1987), which is based on the statistical information gathered

during the previous Markov chain. According to Van Laarhoven et al. (1987),


175

annealing temperature at a given point on Markov chain, 1+k

aT is related to the value

of the previous iteration, kaT , by Equation ( 6.6):

( )1

1

3

11

−

+

++=

σ

θ k

ak

a

k

a

TlnTT

( 6.6)

Where:

θ is a parameter, indicative of the cooling rate, that is typically selected in the

range of 0 to 1.0; in this work the cooling parameter was set to 0.05.

σ represents the standard deviation of the values of the objective function

achieved at temperature .Tk

a A small value of σ results in a large annealing

temperature drop causing an early termination of the annealing process. The

following constraint is employed to overcome the above mentioned problem

(Vanlaarhoven and Aarts, 1987):

k

a

k

a

k

a T.TT 101 ≥≥ + ( 6.7)

The cooling schedule is applied at each temperature level until all the states in the

Markov chain have been evaluated. The number of moves at each temperature

level can be limited by imposing a condition to override the Markov chain length.

Marcoulaki and Kokossis (1999) proposed that a Markov process is finished when

the number of accepted configurations reaches half of the Markov chain length. In

this work, this criterion is chosen to determine the termination of a Markov

process.

6.4.5 Termination criterion

The decision to stop the search for the optimal solution in the simulated annealing

algorithm is made through the termination criterion being satisfied. Various criteria

are used to decide when to stop the search procedure. If any of these conditions is

met, the algorithm stops. These criteria are given below:


176

i. The annealing temperature reaches the lower boundary, Taf. (a value of 10-4 is

used in this work)

ii. No structure is accepted after a certain number of Markov loops. In this

work, this number is 10.

6.5 Simulated annealing moves

A move in simulated annealing refers to the process of generating a new candidate

solution from a current solution. The optimisation algorithm makes random moves

which depend on the nature of the optimisation problem and the variables

involved. Moves are provided to the current structure by changing the various

structural and operational parameters of the existing design. When a modification

is to be performed, a random number (ω) is generated. The random number, ω

takes a value between 0 and 1. The new value of a continuous variable is

calculated by the following expression (Knuth, 1981):

( )abax −+= ω ( 6.8)

where a and b are the lower and upper limits for the continuous variable x. The

new value of a discrete variable is calculated by:

( )[ ]1+−+= mnmy ω ( 6.9)

where m and n are the minimum and maximum allowable values for the discrete

variable y.

Randomly selected moves are performed to provide a new design for the

demethaniser flowsheet. Various simulated annealing moves employed in this

work are discussed below.

6.5.1 Flash unit move

The flash unit move controls the existence of a second flash unit in the process.

The existence of the second flash is a binary number, chosen randomly by

optimisation. The binary number 1 includes the additional flash on the process


177

stream from expander while 0 represents the non-existence of the second flash unit

(Fig 6.1).

6.5.2 Side reboiler move

The side reboiler move represents the addition or removal of a side reboiler to the

demethaniser column which affects the total heat recovery in the process. The use

of a side reboiler in the demethaniser provides greater energy efficiency and

reduction of the duty of the demethaniser bottom reboiler. The main benefit is the

reduction of the external refrigeration that is required to pre-cool the feed to the

desired temperature in the flash unit.

6.5.3 Internal reflux stream move

The reflux stream move indicates the presence of an additional reflux stream

obtained from the final sales gas (Figure 6.1).

6.5.4 Operating conditions move

The operating condition move changes the operating conditions related to

flowsheet such as demethaniser operating pressure, flash feed temperature, vapour

split ratio and side reboiler duty.

6.6 Move probabilities

During simulated annealing, the search is driven by random modifications. These

modifications are called perturbation moves, as they perturb the network from an

old state into a new state. All structural and operational parameters of the

superstructure can be changed across their associated range. The probability is

usually the same for each perturbation move, if unless additional information about

the process is available (Martin, 2009).


178

6.7 Stochastic optimisation framework

Figure 6.3 illustrates flow of information the stochastic optimisation framework.

The simulated annealing algorithm supplies the new trial solution as an input to the

simulation model of the process (developed in Chapter 4), and the simulation

model of the process returns the objective function (Eq. 5.4) for this trial solution.

The optimisation search changes the state of the superstructure and its effect on the

objective function.

During stochastic optimisation in the form of simulated annealing the discrete

options and continuous variables contained within the superstructure – i.e.

structural and operational parameters – are modified by the perturbation moves. A

perturbation move is performed on the initial structure, which is obtained from the

base case. This move is simulated and then either accepted or rejected based on the

acceptance criterion.

In cases, where the system performance is sensitive to a particular variable, a high

move probability can be allocated to this variable throughout the optimisation. As

these variables have a higher chance of being changed, less optimisation time is

spent on the variables having less significant effect on the objective function. Thus,

the optimisation framework can also accommodate heuristics in implementing the

optimisation.

A range of solutions are obtained for each SA run due to the annealing schedule

and the random nature of the search in simulated annealing. Therefore, multiple

runs of simulated annealing optimisation are implemented in this work. Once a run

is finished, its best solution becomes initial point to start the next run, with a

different random number seed. A total of three simulated annealing optimisation

runs is carried out to gain confidence in the optimised solution. The confidence in

the optimised solution is measured in terms of the standard deviation of final value

of objective function of optimisation runs.


179

Figure 6.3 Flow of information in optimisation framework

Input data

• Superstructure, initial structure

• Physical properties

Simulation of a specific structure

• Flowsheet simulation (Ch. 4)

• Objective function (Eq. 5.4)

Stochastic optimiser (Fig. 6.2)

• Simulated annealing

• Accept or reject SA moves

Simulated annealing moves

• Flowsheet structural changes

• Operational changes

Optimised flowsheet

• Flowsheet structure

• Operating parameters

• Objective function close to global optimum

Stochastic Optimisation

framework


180

6.8 Case Study

6.8.1 Background

A case study is presented in this section to illustrate the application and benefits of

the proposed synthesis methodology. The feed and products data is obtained from

Chebbi et al. (2008). The simulation of the process has been performed by the

developed model and validated against rigorous simulation data as discussed in

Chapter 4.

The main aim of this study is to apply the developed optimisation framework for

demethaniser flowsheet synthesis. The methodology aims to establish the optimal

configuration and operating conditions of the demethaniser flowsheet to recover at

least 98% of the methane to the top product and recover a minimum of 70% of the

ethane to the NGL product. The design constants employed in this case study are

given in Table 6.1.

Table 6.1 Design constants employed for case study

Annual operating hours 8600

Cost index factor CEPCI 560.4*

Column tray spacing 0.5 m

Column top and bottom spacing 10% of column height

Compressor/expander isentropic efficiency 0.8

* Dec. 2010 data (Marshall, 2011)

Table 6.3 presents the simulated annealing parameters employed in this work. As

discussed in Section 6.4, these parameters show the trade-off between the quality

of the final solution and the computational time required to reach the final solution.

For example, the algorithm may find a better solution in terms of the value of the

objective function by employing a longer Markov chain length at the expense of a

much longer time. Chen (2008) discussed that the performance of the final solution

increases only slightly after these parameters reach particular values, indicating

that the required computational time does not vary linearly with solution


181

performance. In this case study, these parameters are selected on the basis of

experience and trial and error.

Table 6.2 Simulated annealing parameters

Initial annealing temperature 41001 ×.

Final annealing temperature 41001 −×.

Cooling parameter 0.05

Markov chain length 20

Acceptance criteria Metropolis

6.8.2 Problem inputs

In this work, as in Chapter 4, components heavier than butane, as well as nitrogen,

are artificially eliminated in order to reduce the complexities that arise in the

presence of trace components in the calculations for establishing intersection of

profiles. The simplified composition of the feed and the original composition from

Chebbi et al. (2008) are presented in Table 6.3. The Peng-Robinson equation of

state, using the default parameters of Aspen HYSYS 2006.5 is applied in this case

study to estimate the physical properties and vapour liquid equilibrium. Table 6.3

provides the specified feed and product conditions.

Table 6.3 Feed gas composition - from Chebbi et al. (2008)* and simplified for

this case study

Component Actual feed*

composition mole fraction

Simplified feed

composition mol fraction

Nitrogen 0.01 0.000

Methane 0.76 0.784

Ethane 0.13 0.134

Propane 0.054 0.056

Isobutene 0.026 0.027

Isopentane 0.01 0.000

n-hexane 0.01 0.000



182

Table 6.4 Specified temperature and pressure of feed and products (Chebbi et al., 2008)

Products

Feed gas Sales gas NGL


Pressure 60 bar 60 30

Figure 6.4 Process flowsheet diagram of a typical GSP demethaniser process

(Chebbi et al., 2008)

The gas subcooled process (GSP) as given in Chebbi et al. (2008) is a typical

turboexpander based demethaniser process (Fig. 6.4). The feed gas is initially pre-

cooled by a side reboiler before entering a heat exchanger where it is cooled by the

top product from the demethaniser. The cold feed leaving the exchanger is further

cooled down by a chiller using an external refrigeration cycle. The exit stream is

fed to a flash unit, the liquid from which is sent to the demethaniser as the lower


183

feed, while the vapour is split into equal proportions. One portion is expanded and

sent as the upper feed to the demethaniser while the second portion is sent to the

top of demethaniser as an external reflux stream after being cooled by a heat

exchanger.

Table 6.5 presents the optimisation boundaries imposed for each move. These

bounds take into consideration practical constraints. The limits on the split fraction

ensure that there is a minimum amount of liquid entering at the top of the column

as reflux. Some of the simulated annealing moves can also result in the failure of

the simulation model to converge. In this work, a constraint value is set to the

infeasible region in the case of simulation failure. This results in the rejection of

the move by optimisation.

Table 6.5 Move probabilities and limits of optimisation variables

Variable

Type

Move decision Lower

bound

Upper

bound

Move

probability

Demethaniser operating

pressure (bar)

15 35 0.15

Flash unit temperature (oC) -20 -60 0.15

Split ratio (reflux to upper

feed)

0.2 0.8 0.15

Continuous

variables

Side reboiler duty (kW) 0 2000 0.15

Flash unit move 0 1 0.15

Internal reflux move 0 1 0.1

Discrete

Variables

Number of side reboilers 1 3 0.15


184

6.8.3 Results

The simulation begins with the heat recovery in the multistream exchanger for a

given temperature of the flash unit feed stream. The side reboilers and external

refrigeration duties are evaluated based on the overall energy balance over the

whole flowsheet. The complex distillation column is simulated using the modified

boundary value method explained in Chapter 3. In this case study, a two-feed

column with a side reboiler is used. The other flowsheet units are simulated using

the shortcut design models as explained in Section 4.3 and employing the

sequential modular approach for flowsheet simulation. The validation of

simulation model is performed by simulating the flowsheet in Aspen HYSYS. The

validation and results are presented in detail in Section 4.5. Table 6.6 presents

some of the important results as obtained in Ch. 4.

Table 6.6 Simulation results: Shortcut model vs HYSYS


Table 6.7 presents a summary of the final three optimisation solutions from a

family of solutions for the demethaniser synthesis problem for annualised profit

optimisation. The product revenues along with the capital and utility contributions

to the cost of each solution are provided. It is evident from the results that the

operating costs generally dominate the total costs of the process as the reduction in

the operating costs is significant. The capital cost of the optimised solutions which

are increased due to the addition of an extra flash unit and a side heater in the

Results Units Shortcut model HYSYS


Methane recovery in sales gas % 99.54* 99.54*

Residue compressor power kW 2055 2042


Reboiler temperature oC 30.3 30



185

optimised flowsheet configurations. The annual profit for the optimised flowsheet

is 139.8 MM$/yr compared to 129.6 MM$ in the base case. Thus the optimised

flowsheet shows over 8% increase in the annual profit compared to the base case.

Both structural and operational changes allow these savings to be achieved.

Table 6.7 Optimisation results of three solutions from a family of solutions

The best solution among a family of solutions is highlighted in Table 6.7. The

values of the optimisation variables of the final three solutions cases are presented

in Table 6.8. All the three solutions presented have the same structure, only the

operating conditions are different.

In the first solution, a lower pressure (25 bar vs 30 bar) in the demethaniser results

in higher power requirements (around 425 kW) in the recompressor. On the other

hand, the addition of a second side reboiler decreases the external refrigeration

power requirements by 1060 kW. So the total power requirements are shown to

Results Unit Base case First

solution

Second

solution

Third

solution

Ethane recovery in NGL % 76.43 82.22 82.14 81.8

Methane recovery in sales gas % 99.54 99.54 99.54 99.54

Residue compressor power kW 2055 2480 2560 2500

Refrigeration power kW 2980 1920 2035 2160

Total shaft power kW 5035 4400 4595 4680

Reboiler duty kW 1828 138 176 208

Annualised capital cost MM$/yr 6.0 6.2 6.25 6.29

Annual utility cost MM$/yr 8.53 5.25 5.52 5.64

Annual revenues MM$/yr 305.32 312.44 312.37 312.22

Annual profit MM$/yr 129.6 139.8 139.41 139.1


186

decrease by 13%. Moreover, the ethane recovery is enhanced by 5.8%, which

increases the revenue from product sales.

Table 6.8 Decision variables for base case and best three cases

Decision variables Units Base case

First solution

Second solution

Third solution

Demethaniser operating pressure bar 30 25 25.5 25.2

Flash unit temperature oC -35 -28 -30 -31

Split ratio (reflux to upper feed) - 0.5 0.65 0.65 0.60

First side reboiler duty kW 1500 1750 1700 1680

2nd side reboiler duty kW 0 1250 1250 1230

Number of flash units - 1 2 2 2

Internal reflux - 0 0 0 0

Number of side reboilers - 1 2 2 2

The optimised flowsheet for the first solution is shown in Figure 6.5. As seen from

the results listed in Table 6.5, in comparison with base case, the optimised

flowsheet has two flash units and two side reboilers. The addition of the second

flash unit is shown to increase the ethane recovery. The use of an additional side

reboiler reduces the external refrigeration requirement as evident from the lower

shaft work requirement for the refrigeration system (Table 6.7). The lower

refrigeration load also decreases the condenser load and hence less cooling water is

required. In addition to this, the main reboiler duty is also lowered. Therefore, the

overall operating cost is reduced.

The computation time for the design obtained using the proposed synthesis

approach for demethaniser process, using simulated annealing with three runs

optimisation is 94 minutes and 20 CPU seconds on an Intel® Core 2 Duo CPU

2.93 GHz processor with 4 GB RAM).

Figure 6.5 Case study – Optimised flowsheet

Chap

ter 6 D

emeth

aniser flo

wsh

eet synth

esis by sto

chastic o

ptim

isation


188

The developed synthesis methodology offers the user control over the optimisation

variables, the move probabilities in the case study can be adjusted to investigate

specific optimisation variables. External variables such as feed conditions and

composition, different product recoveries or change in price of power may also be

investigated by conducting parametric studies, which require successive

optimisation runs.

The profit calculation in the above case study is relatively simple, and the capital

and operating cost models employed in this work are not verified as accurate. The

flowsheet may need further analysis using more detailed cost models before being

accepted for investigation. The focus of this research is to develop a novel

synthesis approach aimed at conceptual design of demethaniser flowsheets.

Therefore, these issues are considered beyond the scope of this work.

6.9 Conclusions

In this chapter, a systematic methodology based on stochastic optimisation for the

synthesis and design of demethaniser flowsheets has been presented. A

superstructure is formulated for flowsheet optimisation which includes various

possible structural combinations. The superstructure-based approach allows one to

identify promising configurations systematically. Structural and operating issues

are addressed simultaneously to achieve the design specifications.

A stochastic optimisation algorithm, simulated annealing (SA), is employed in the

framework. Relevant parameters of the simulated annealing algorithm are

discussed; how these are chosen for demethaniser system design problem is

presented. The advantage of the simulated annealing optimisation algorithm is that

it does not need any derivative calculations, and it can accommodate the non-

linearity, non-differentiability and discontinuity of the problem formulation. The

SA algorithm can manage continuous and discrete variables simultaneously and

hence can optimise simultaneously both operating conditions and the structure of

the demethaniser system.


189

The developed optimisation approach is applied with the objective of maximising

profit of the process. The final optimised flowsheet shows considerable

improvement in annual profit, compared to the base case. The approach, however,

is generic; and is applicable to other objectives as well, e.g. minimising capital

investment, maximising throughput, etc. Although this new approach is developed

mainly for complex separations systems such as demethaniser flowsheets, the

approach can be applied more generally, with some modifications, to other heat-

integrated distillation systems such as ethylene production.

Chapter 7 Conclusions and future work

190

CHAPTER 7 CONCLUSIONS AND FUTURE WORK

Increasing energy costs and stricter gas purification specifications are creating a

challenge for the design and operation of gas treating processes with low operating

and capital costs. The recovery of natural gas liquids (NGL) is an important and

necessary part of the natural gas industry. Major challenges in NGL recovery

processes are, on one hand, the reduction of power consumption to reduce

greenhouse gas emissions and cost, and, on the other hand, maximising the

recovery of ethane and heavier components (Sharratt et al., 2008).

NGL recovery from natural gas offers an economic incentive due to the higher

value of the recovered components as feedstocks, over their fuel value as natural

gas components. The main market for ethane is ethylene production, where ethane

feeds are traditionally the most cost-effective due to the generation of fewer by-

products in comparison to naphtha feeds (Farry, 1998). The extent to which NGL

are to be recovered is a balance between capital, operating cost and the market for

range of products obtained used as feedstocks for other petrochemicals.

A large number of design alternatives are available for demethaniser processes

which must be evaluated when selecting an energy efficient process for a new gas

processing facility (Mehrpooya et al., 2006). Therefore, a comprehensive approach

for synthesis is required to generate effective and economic design without excess

requirements of engineering time and effort.


191

7.1 Conclusions

The new simplified models and optimisation-based approach presented in this

thesis are major contributions in the area of natural gas liquids recovery employing

demethaniser flowsheets. This work extends knowledge in this area by developing

a systematic procedure for grassroots design of demethaniser flowsheets. The new

short-cut model developed in this work for design of complex demethaniser

columns is a significant step forward in the modelling of these processes. The

optimisation-based approach presented in this thesis, which considers the

interactions between the demethaniser column and other flowsheet units same

time, overcomes a major limitation of the previous research work in this area, and

can achieve significantly better designs of demethaniser flowsheets compared to

designs achieved by previous approaches. The main contributions of this work are

highlighted below:

� A novel extension of the established boundary value design method is

proposed for modelling and designing demethaniser columns for

multicomponent mixtures. The proposed method represents the column

accurately, compared to alternative shortcut models, without compromising

the computation time excessively. The model accommodates complex

column features and can be used in the early stages of flowsheet design

with only basic information, such as feed properties and product

specifications. The model is validated against an equilibrium stage-by-stage

column model in AspenTech process simulation package HYSYS and is

shown to represent the process behaviour satisfactorily.

� A systematic representation of overall demethaniser flowsheet design and

simulation is developed. Opportunities for heat-integration and power

recovery are identified and exploited in the overall flowsheet to improve

the process economics.

� A nonlinear constrained optimisation problem is formulated for

optimisation of fixed structure demethaniser flowsheet. An industrial case

study is presented to illustrate the application of the fixed structure


192

optimisation approach, which can also be applied to compare various

licensed flowsheets for a specific objective function.

� A robust simulation and optimisation methodology based on superstructure

optimisation is proposed. The methodology applies a stochastic

optimisation technique to solve the superstructure to systematically

synthesize the flowsheet. The proposed approach is tested with an industrial

case study which gives a novel flowsheet design with an improvement in

annual profit of around 8%.

7.1.1 Discussion

Existing short-cut methods, for example based on the Fenske-Underwod-Gilliland

method, for modelling and design of distillation columns are not sufficiently

accurate to estimate the number of stages, reboiler duty and reboiler temperature of

a demethaniser column. A new design method for demethaniser columns is

developed, extending the established boundary value method (Levy and Doherty,

1986) for column design. The energy balance is included in the calculation of the

composition profiles to overcome the assumption of constant molar overflow in the

original boundary value method. The new design method takes into account two-

phase feeds by introducing the feed between two stages and considering mixing at

the feed stage. Multicomponent mixtures are represented without requiring

visualisation of the composition profiles, by the use of a minimum distance

criterion to indicate near-intersection of composition profiles. The model also

accommodates intermediate heating using side reboilers and the use of an external

reflux stream. Two case studies are presented to illustrate the application of the

design method to a range of column configurations.

A novel integrated process model for simulation of a demethaniser flowsheet is

presented; the model comprises shortcut design models for various units in the

demethaniser flowsheet. Heat recovery in a multistream exchanger is also

represented by the model. A typical process is simulated using the new process

model and validated against rigorous simulation results using HYSYS. The results


193

show that the shortcut model of the flowsheet is sufficiently accurate to be

employed in an optimisation framework for process synthesis.

The simplified simulation model takes into account interactions various flowsheet

units, as well as between process variables, and hence, can lead to energy-efficient

and cost-effective flowsheets. An approach is developed for process optimisation

of a flowsheet of fixed configuration. Important variables affecting the flowsheet

are extracted from a large number of process variables by sensitivity analysis. The

optimisation is carried out using a nonlinear programming technique, the

successive quadratic programming. A case study of industrial relevance is

presented to illustrate the application of the optimisation approach for maximising

the annual profit. A 4% increase in annual profit is obtained which indicates that

the proposed optimisation procedure for a fixed flowsheet structure offers an

effective way of design and optimisation of a demethanisation flowsheet of fixed

structure.

A superstructure is formulated for flowsheet synthesis to include various possible

structural combinations such as addition of a low pressure flash column, an

additional side reboiler and an internal reflux stream. The superstructure-based

approach allows one to identify promising configurations systematically.

Optimisation of structural and operating issues has been approached

simultaneously to achieve the design specifications and maximise the objective

function, in this case, annual profit. A stochastic optimisation methodology is used

to solve the superstructure to systematically synthesize the flowsheet. The

proposed approach is tested with a case study which gives a new flowsheet design

with around 8% improvement in annual profit, compared to the base case.

7.1.2 Limitations

The demethaniser design model used for the synthesis in this work is a simplified

model. The model is based on some assumptions that the vapour-liquid equilibrium

is achieved on every stage and the pressure drop over the column is zero. These


194

assumptions, however, have a minimal affect on the overall flowsheet design as the

optimisation framework is independent of the column model.

The application of boundary value approach to multicomponent systems is

accomplished by the 'minimum distance' criterion to approximate the intersection

of composition profiles. Complete agreement with simulation approaches using

different specifications will not be expected, given the sensitivity of the

composition profiles to trace components and the approximation introduced by the

minimum distance criterion applied in the boundary value method. To improve

agreement between HYSYS simulation results and those of the design method,

input variables, such as the specified product compositions, column pressure and

feed condition, may need to be manually adjusted.

The trace components present in the column feed are neglected and the feed is

simplified to overcome the complexity introduced by the presence of trace

components in the calculation of intersection of the composition profiles by

minimum distance approach. However, this assumption has a negligible affect on

the column design as discussed in Section 3.6.

Although the use of simulated annealing as the optimisation tool in this work

produces promising results, the long computational time required by its

implementation constitutes one of the weaknesses of this algorithm. As for any

other stochastic optimisation tool, the search for the solution space is random and

derivative free. This unique property is the primary merit of the strategy, but also

the cause for the long computational time. However, as the technology evolves

rapidly, the processing power of computers has increased exponentially in recent

years. Therefore it might not be a major issue of concern in the near future.

The superstructure optimisation approach can produce several near-optimal

designs with complex structures, some of which are likely to be impractical. In

order to improve the practical applicability of the framework, it is recommended to


195

include that sensitivity towards design variations should be considered, especially

in complex designs.

7.2 Future work

The side reboilers in the demethaniser column are modelled as side heaters in this

work where the duty and location of the heaters needs to be specified. This

approach simplifies the column design model by avoiding the mass and

equilibrium calculations that otherwise need to be performed. The boundary value

design model can be modified and updated further to overcome this limitation of

the model.

The superstructure presented in Chapter 6 can be extended to include more

demethaniser flowsheets options available in patents such as the addition of pre-

fractionator and inclusion of a stripping stream in the demethaniser stripping

section. Moreover, downstream columns for NGL fractionation like deethaniser,

depropaniser and debutaniser can also be included in the superstructure.

Heat integration in this work is performed by considering heat recovery in a

multistream exchanger. In some variations of demethaniser flowsheets, a network

of shell and tube heat exchangers are applied instead of a multistream exchanger

(Konukman and Akman, 2005). Heat integration with downstream NGL

fractionation columns can also be included in the overall synthesis framework. A

rigorous methodology for heat exchanger network design can be employed.

Another future research direction can involve the addition of the selection of

refrigerant for the external refrigeration cycle as an option in the synthesis

framework, where a database of different refrigerants can be developed. In addition

to the choice of refrigerant and the inclusion of complex refrigeration cycles in the

framework can also enhance its robustness.


196

The stochastic optimisation method offers higher chances to escape the local

optima of the objective function. This however, has the penalty of longer

computational time which can increases significantly with the complexity of the

problem. Therefore, it would be desired to speed up the optimisation process by

investigating hybrid processes (stochastic with deterministic) to achieve shorter

computational time. The use of hybrid optimisation can also help in fine tuning of

the results obtained from simulated annealing.

Finally, the capability of the proposed synthesis methodology to identify energy-

efficient and cost-effective configurations has been illustrated in Chapter 6. In

addition to economic efficiency (annual profit), some other industrially relevant

objectives for the demethaniser processes, such as system flexibility, controllability

and maintainability are also significant. It is challenging to accommodate these

factors in a systematic synthesis framework because of the lack of methods for

estimation these factors. Multi-objective optimisation is a challenging topic that

offers scope for future work.

197

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209

Appendix A: MATLAB-HYSYS Interface for physical properties

and Vapour-liquid equilibrium data

External software can be used to access Aspen HYSYS using a method called

automation (HYSYS 2006.5 Customization Guide1). Automation allows the user to

interact with an application through objects exposed by developers of that

application. By using an automation client such Visual Basic, the end user can

write the code to access these objects and interact with HYSYS.

Aspen HYSYS v 2006.5 is employed in this work to calculate the physical

properties and vapour-liquid equilibrium data. The procedure to link MATLAB

and HYSYS is not provided directly in the customization guide. Therefore an

interface is developed between MATLAB and HYSYS. The interface is explained

with the aid of an example below:

Example: Dew point calculation of a ternary mixture.

The example illustrates the calculation of the dew point of a saturated vapour

mixture having 60 mol% n-Hexane, 25 mol% n-Heptane and 15 mol% n-Nonane.

The method involves the following steps:

1. Start HYSYS with only one active file and flowsheet. Specify the

components in HYSYS and select fluid property package (Peng-Robinson

in this example)

2. Create a material stream (named ‘DEW’). The pressure, vapour fraction,

temperature and composition of this stream is provided by MATLAB.

1 Available from:

http://support.aspentech.com/Public/Documents/Engineering/Hyprotech/2006.5/As

penHYSYS2006_5-Cust.pdf

210

3. Create a spreadsheet (named ‘SPRDSHT’). This spreadsheet is used for

receiving mole fractions of the stream from MATLAB and sending them to

the material stream created in the previous step.

a) The mole fractions of the stream sent from MATLAB will be stored

in cells A1 (for n-Hexane), A2 (for n-Heptane) and A3 (for n-

Nonane).

b) Define the values in cells B1, B2 and B3 to be equal to those in cells

A1, A2 and A3, respectively.

c) Make connections between cells B1, B2 and B3 and mole fractions

of the material stream created in step 2 using ‘Exported Variables’

in ‘Connections’ tap of the spreadsheet.

MATLAB Code

%Specify molar composition of mixture

XF = [0.6 0.25 0.15];

%Start the MATLAB-HYSYS communication

hy = actxserver ('HYSYS.Application');

% Active the HYSYS document and flowsheet

hyActive = hy.ActiveDocument;

hFlowsheet = hyActive.Flowsheet;

% Connect to HYSYS solver

hSolver = hyActive.Solver;

% Link to the material stream 'DEW'

hDEW = hFlowsheet.Streams.Item('DEW');

% Link to the spreadsheet 'SPRDSHT'

hSprd = hFlowsheet.Operations.Item('SPRDSHT');

%Link to cells A1 to A3 in 'SPRDSHT'

211

hCellA1 = hSprd.Cell('A1');



% Set the pressure of 'STREAM' to be 1 atm

hDEW.Pressure.SetValue(1, 'atm');

% Set the vapour fraction of 'STREAM' as saturated vapour

hDEW.VapourFraction.SetValue(1);

% Turn HYSYS Solver off

hSolver.CanSolve = 0;

% Delete the current values in cells A1 to A3

hCellA1.Erase;

hCellA2.Erase;

hCellA3.Erase;

% Set the mole fraction of components as given by XF

hCellA1.CellValue = XF(1);



% Turn HYSYS Solver on (HYSYS automatically determines phase equilibrium)

hSolver.CanSolve = 1;

% Define ‘hDpl_DEW’ to use for retrieving phase equilibrium data

hDupl_DEW = hDEW.DuplicateFluid;

Get the molar enthalpy of given phase (kJ/kmol)

H_V = hDupl_DEW.MolarEnthalpyValue

% Get the composition of liquid phase in equilibrium with xF

x = hDupl_DEW.lightliquidPhase.MolarFractionsValue

212

% Get the molar enthalpy of liquid phase (kJ/kmol)

H_L = hDupl_DEW.lightliquidPhase.MolarEnthalpyValue

% Get the dew point temperature (oC)

T = hDupl_DEW.TemperatureValue

Results

Composition Feed (saturated vapour) Liquid phase

n-Hexane 0.6 0.23

n-Heptane 0.25 0.21

n-Nonane 0.15 0.56

Molar enthalpy -1.6794x105 -2.255x105

Dew-point 105.1 oC

213

Appendix B: Cost Estimation

The quantitative synthesis methodology developed in this work uses capital and

operating costs to establish a comparison between design options and to enable the

systematic optimisation of the problem.

A number of sources of equipment sizing and capital cost correlations are available

in the open literature (Peter and Timmerhaus, 2008, Walas et al., 2005, Turton et

al., 2008). Published capital cost data often derive from various sources of different

times. Such data need to be up to date and expressed on a common basis using cost

indexes.

The operating cost is assumed to be based solely on the utility requirement. After

the capital and operating costs are calculated, the total annualised cost of the

flowsheet can be determined from the sum of annualised capital cost and operating

cost. The total annualised cost is used for calculating the annual profit which is

used as an indicator for comparison among different flowsheets and quantitatively

analyse the optimisation results.

B.1 Capital cost estimation

The first step in the equipment cost estimation is to calculate the equipment size.

Once the equipment is sized, the capital cost can be estimated using correlations or

cost data from literature as appropriate.

In this study, the capital cost of flowsheet units is calculated by applying the

Module costing technique (Turton et al., 2008). The bare module cost, which is the

sum of direct and indirect cost for a unit is given by:

BMopBM FCC = (B.1)

214

where

BMC is the bare module equipment cost

opC is the purchased cost at ambient pressures using carbon steal as the material

of construction

BMF is the bare module cost factor, dependent on the material of construction

and operating pressure

Eq. B.1 can be further written as:

( )PMopBM FFBBCC 21 += (B.2)

where FM and FP are the material and pressure factor respectively.

The values of B1 and B2 are provided in the following table.

Table B.1 Constants for Bare module factor

Equipment Type B1 B2

Fixed tube Heat exchanger 1.63 1.66

Process vessel 2.25 1.82

The purchased cost of the equipments at ambient operating pressure and using

carbon steel as the material of construction is given by:

( ) ( )[ ]2103102110 AlogKAlogKKClogop ++= (B.3)

where A is the capacity or size parameter for the equipment. The data for K1, K2

and K3 along with maximum and minimum values used in the above correlation is

given in Table B.2.

215

Table B.2 Equipment cost data for Equation B.1

Equipment Type K1 K2 K3 Capacity Min

size

Max

size

Centrifugal

Compressor

2.2897 1.3604 -1.027 Fluid power,

kW

450 3000

Fixed tube Heat

exchanger

4.3247 -0.303 0.1634 Area, m2 10 1000

Process vessel 3.4974 0.4485 0.1074 Volume, m3 0.3 520

Tray column 3.4974 0.4485 0.1074 Volume, m3 0.3 520

Sieve trays 2.9949 0.4465 0.361 Area, m2 0.07 12.3

The cost obtained from Eq. B.2 is at the ambient pressure. To account for a higher

pressure in the pressure vessel the following equation is employed (Turton et al.,

2008):

( )( )[ ]

00630

0031501608502

1

.

.P.

DP

F vessel,p

++−

+

=

(B.4)

where D is the vessel diameter in meters, P the operating pressure in barg based on

ASME code for pressure vessel design (ASME 2000).

For other equipments, Eq. B.5 gives the pressure factor

( )2103102110 PlogCPlogCCFlog p ++= (B.5)

Table B.3 Pressure factors for process equipments (Turton et al., 2008)

Equipment Type C1 C2 C3 Pressure range (barg)

Centrifugal

Compressor

0.038 -0.112 0.082 5<P<140

Fixed tube Heat exchanger 0 0 0 5<P<140

216

Turton et al., (2008) obtained the data for the purchased cost of different

equipments in 2001. In order to account for inflation and to obtain current cost

estimates, it is necessary to update the original estimates with the adequate

economic indexes. This relationship is given by Eq. B.6

1

2

12I

ICC =

(B.6)

where C2 is the purchased cost at current time

C1 is the purchased cost at base time

I2 is the cost index at current time

I1 is the cost index at base time

Typical cost indexes for the chemical industry include the Chemical Engineering

Plant Cost Index (CEPCI), published monthly in Chemical Engineering magazine.

The Marshall & Swift Economic Index is also of general use for equipment

costing. In this work, CEPCI is used to account for inflation. A value of 397 for

CEPCI was used for year 2001 (Turton et al., 2008) while a value of 560.4 is used

December 2010 for this work which is obtained from Chemical Engineering

Magazine (Marshall, 2011).

B.1.1 Annualised capital cost

In this work, we assume that the capital is borrowed over a fixed period n (3 years)

at a fixed rate of interest i (5%). Capital cost is then expressed on an annual basis

according to

( )( )( )11

1

−+

+×=

n

n

i

iiCCAC

(B.7)

where AC is the annualised cost, CC is the capital cost, n is the number of years,

and i is an interest rate per year.

217

B.1.2 Capital cost estimation for distillation columns

The capital cost of a column consists of the costs of the shell, trays and installation

cost of equipment. The shell cost is proportional to the weight of column which

depends on the column diameter, height and material of construction. The cost of

trays is a function of column diameter, number of stages and column internals.

Sieve trays are assumed in this work, while the material of construction is carbon

steel. The height of a column is estimated based on the actual number of stages.

The height of the column (H) is given by Eq.B.8 (Peter and Timmerhaus, 2008).

( ) HHNH sact ∆+−= 1 (B.8)

where Nact is the actual number of stages, Hs is the trays spacing and H∆ is the

additional height for vapour and liquid disengagement at the top and bottom of the

column.

A tray spacing of 0.5 m and an efficiency of 100% is employed in this work. H∆ is

assumed to be 10% of the column height. To avoid flooding, the vapour velocity

must be operated below the flooding velocity, and the velocity will normally be

between 70 to 90 percent of the flooding velocity. The diameter of the column is

given by:

u.

VD

π

4=

(B.9)

where V is the volumetric vapour flow rate, and u is the vapour velocity, which is

is assumed to be 80% of flooding velocity (uf) in the column. The flooding velocity

is calculated from Equation B.10 (Sinnott, 2003):

v

vLf Ku

ρ

ρρ −= 1

(B.10)

where Lρ is the density of liquid, Lρ the density of vapour and K1 is a coefficient

dependent on the vapour liquid flowrates. The value of K1 is obtained from

Sinnott (2003).

218

The column diameter and the height of the column are used to determine the

volume of the column, which is then used in Eq. B.3 for estimating the purchased

cost of the column.

B.1.3 Capital cost estimation for heat exchangers

The purchase cost of shell and tube heat exchangers is estimated by the module

costing technique. However, the cost factors were not available for the multistream

plate fin heat exchangers. So the cost of plate-fin heat exchangers is obtained from

Peters and Timmerhaus (2003, Figure 14-27) for compact heat exchangers.

A preliminary area may be obtained from the heat exchanger load, Q, the inlet and

outlet temperatures and an approximate overall heat transfer coefficient, U, using

the following equation.

LMTU

QA

∆=

(B.11)

Where LMT∆ represents the logarithmic mean temperature of the heat exchanger.

The temperature of cooling water is taken to be 25oC. A minimum temperature

difference of 10oC is assumed. The overall heat transfer coefficient (U) is

estimated to be 600 W/m2 K for a shell and tube heat exchanger with the cooling

water in the tube side and light organics in the shell side (Peter and Timmerhaus,

2008). For the reboiler using steam, a value of 800 W/m2 K is used. For all other

heat exchangers using process streams U is assumed to be 400 W/m2 K.

B.2 Operating cost estimation

The consideration of utility cost is quite important as it projects the energy trade-

offs onto the synthesis process. In this work, operating costs are assumed to be the

equivalent of utility costs. The different process utilities used in the demethaniser

process flowsheet synthesis include the electricity, process steam, refrigerants and

cooling water. The calculation of the utility costs is a complex problem as the

utility prices can not be estimated from the conventional inflationary indexes

(Ulrich and Vasudevan, 2006). Moreover, the cost of utilities fluctuates due to the

219

volatility of energy costs and utility tariffs being determined on individual plant

basis.

The method presented by Ulrich and Vasudevan (2006) to estimate utility costs is

employed in this study. This method is based on empirical correlations. According

to this method, the cost of any utility may be correlated to the cost of fuel through

an equation of the form:

( ) fu bCCEPCIaC += (B.12)

Where

Cu is the cost of the utility, Cf is the price of fuel in $/GJ, CEPCI is the Chemical

Engineering Plant Cost Index, and coefficients a and b are functions of certain

utility specific variables are available from Ulrich and Vasudevan (2006).

B.2.1 Steam cost

Smith and Varbanov (2006) discussed that it is difficult to attribute a single

economic value for steam at a certain level. The cost of steam is dependent on the

cost of fuel utilised in the boiler. They discussed that the steam price depends on

the fuel price, fuel heat content, boiler efficiency, price of electricity and driver

mechanical efficiency.

In this study we only require steam at low pressure conditions for the demethaniser

column reboiler. Steam at 6 bar is assumed to be available for heating. The cost of

the steam is calculated based on steam generation in a boiler using natural gas as a

fuel. The boiler is assumed to have an efficiency of steam generation of 80%.

Boiler feed water is available at 100oC. The costs of steam at each pressure

determined from Equation (B.13).

efficiencyBoilerfeedwaterboilersteam

ofEnthalpyofEnthalpytcosFuelsteamofCost ×

−×=

(B.13)

220

For an average cost of natural gas at 5.0 $/GJ, the LP steam cost from this equation

is about 500 $/kWyr.

B.2.2 Electricity Cost

Equation B.10 is used to estimate the cost of electricity. For the electricity

purchased from outside the plant, a = 0.00013 and b = 0.010.

Based on the cost of natural gas for electric power generation of $5.6 /ft3($5.0/GJ)

(from U.S. Energy Information Administration, www.eia.doe.gov), gross calorific

value of 40 MJ/m3 and CEPCI of 560.4 in Dec. 2010 (Marshall, 2011), the cost of

electricity calculated from equation (B.12) is $ 0.123/kWh.

B.2.3 Cooling water cost

Cooling water is assumed to be available at 25oC with a target temperature of 30

oC. The cost of cooling water ($/m3) is also based on the Eq. B.11 where the

coefficient a and b are given by Ulrich and Vasudevan (2006):

15100300010 −−×+= q..a and 0030.b =

where q is the cooling water volumetric flowrate.

Solving the Eq. B.11 for an assumed capacity of 1 m3/sec comes out at $ 0.088/m3

($130/kWyr).

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