REACTORDESIGNFORNONCATALYTIC

THERMALHYDRODEALKYLATIONOFTOLUENE

SAEEDNUSRI-31923AMEERSIDDIQUE-30982ADNANNAJMI-32192

2

ExecutiveSummary

This report proposes the design of a noncatalytic adiabatic reactor that would produce 25000lbm/hr of benzene by the process of thermal hydrodealkylation of toluene. Plug Flow Reactor (PFR) was chosen to be the most appropriate type of reactor since the reaction is completely occurring in the gas phase. Simulations were carried out in HYSYS and Polymath and final volume of PFR was found out to be 566ft3 with 3ft-0inch internal diameter and 80 ft length. A single reactor of these dimensions was chosen.

3

TableofContentsAbstract.........................................................................................................Error!Bookmarknotdefined.

ListofFigures...............................................................................................................................................4

ListofTables.................................................................................................................................................4

Introduction.................................................................................................................................................5

Design...........................................................................................................................................................6

SectionA:Ratelaw.......................................................................................................................................6

SectionB:Thermodynamics(Temperaturedropdifferential).....................................................................7

SectionC:FluidFlow(Pressuredropdifferential)........................................................................................8

SectionD:CalculationofConstantsUsed..................................................................................................10

SectionE:AdditionalExplicitEquations:....................................................................................................12

SectionF:PolymathProgram.....................................................................................................................13

SectionG:HYSYSSolution..........................................................................................................................19

SectionH:ComparingHYSYSresultswithPolymath..................................................................................22

Conclusion..................................................................................................................................................23

References..................................................................................................................................................26

APPENDICES...............................................................................................................................................27

APPENDIXA-PolymathProgram–WithoutReverseReaction................................................................28

APPENDIXB-PolymathProgram–CASED-WithReverseReaction........................................................29

APPENDIXC–CASEBProfiles....................................................................................................................30

APPENDIXD–CASECProfiles....................................................................................................................31

APPENDIXE–CASEDProfiles....................................................................................................................32

4

ListofFiguresFigure1–PolymathSimulationforCaseA...................................................................................................4Figure2-PolymathSimulationforCaseB....................................................Error!Bookmarknotdefined.Figure3-PolymathSimulationforCaseC....................................................Error!Bookmarknotdefined.Figure4-Equilibriumconstantsforvariousreactionsintoluenedealkylation...........Error!Bookmarknotdefined.Figure5-PolymathSimulationofCaseD.....................................................Error!Bookmarknotdefined.Figure6-SettingupKineticReactioninHYSYS..........................................................................................19Figure7-InletSpecificationsinHYSYS.......................................................................................................22Figure8-PFRwith620ft3..........................................................................................................................20Figure9-PFRwith566ft3inHYSYS..........................................................................................................20Figure10-OutletstreamspecificationinHYSYS.......................................................................................21Figure11-HYSYSSimulationEnvironment................................................................................................22Figure12-PFRConversionProfile.............................................................................................................23Figure13-PFRTemperatureProfile..........................................................................................................24Figure14-PFRPressureDropProfile.........................................................................................................24

ListofTablesTable1-Heatofformation[5].....................................................................................................................7Table2-HeatCapacityCoefficients[5].......................................................................................................8Table3-ComparingCaseAB&C.............................................................................................................16Table4-Comparingforwardrxnwithreversiblerxn.................................................................................18Table5-ComparingHYSYSandPolymathsimulations..............................................................................22

5

Introduction

Design parameter are as stated below:

• Noncatalytic adiabatic reactor to facilitate the production of 25,000 lb/hr of benzene by the process of thermal hydrodealkylation of toluene.

• The inlet pressure of hydrogen is 550 psig (564.7 psia) • The reactor temperature should range from 1150-1350 oF • The selectivity to benzene (SB) is 98% along with a conversion of approximately 75%. • The ratio of H2 to toluene is kept at 2:1

The hydrodealkylation process proceeds according to the following reaction where toluene reacts with hydrogen to produce benzene and methane.

4662356 CHHCHCHHC +↔+

which can also be represented as follows for simplicity:

A+ B ↔ C + D

This process also proceeds with other side reactions. These include hydrogenation of toluene and benzene to cycloparaffins, reactions of benzene and toluene to various diphenyls and hydro cracking of parrafins. For simplicity, these reactions have not been considered and the selectivity is assumed to be 100%. Therefore the rate law for the reaction will be as shown below:

5.02HToTo CCkr =− ,

sfttoluenelbmoles⋅3

Where,

-rTo is the rate of disappearance of toluene

CTo is the concentration of toluene

CH2 is the concentration of hydrogen

( )( ) slbmole

ftTREk

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−×= 5.0

5.0311 exp1018.7

E = 98,000 BTU/lbmole T in degree Rankine

6

Design

SectionA:RatelawThermal dealkylation of Toluene is found to occur most effectively between 1150 F - 1350F. Since this range is above the critical temperature of both benzene (552.6F) and toluene (605.84F), it can be assumed that the reaction is occurring in the gas phase .For simplicity, the species are assumed to be in ideal gas state. This assumption is convincing because the reaction is occurring at a high temperature.

Below are the equations used to derive the first differential equation which denotes the conversion with respect to the PFR volume:

Fao !"!"= −ra

4662356 CHHCHCHHC +↔+

For this reaction the rate law is given by:

-ra = k C!C!!.!

Since the reaction is occurring completely in the gas phase:

Ca = !"#(!!!)(!!Є!)

!!"

!!"

Cb = !"#(!!!!)(!!Є!)

!!"

!!"

Therefore,

−ra = k !"#(!!!)(!!Є!)

!!"

!!"

(!"#(!!!!)(!!Є!)

!!"

!!")!.!

For thermal hydrodealkylation of toluene

Є = δ y!"

δ = −1− 1+ 1+ 1 = 0

Є = 0

θ! = !"#!"#

= 2

Thus the rate law simplifies to

−ra = k Cao(1− X) !!"

!!"

Cao 2− X !!"

!!"

!.!

7

SectionB:Thermodynamics(Temperaturedropdifferential)A differential equation to track temperature change across the plug flow reactor is given by

𝑑𝑇𝑑𝑉 =

−𝑟! (−Δ𝐻!"# 𝑇 )𝐹!"( 𝜃! 𝐶!" + 𝑋ΔC!)

Where −𝑟! is the rate law

𝐹!" is the initial molar flow rate of Toluene

Δ𝐻!"#is the Heat of Reaction at T

𝐶!" is the Specific Heat Capacity of species i

ΔC! is sum of Specific Heat Capacity of products of species with respect to their stoichiometric coefficients

X fraction of conversion of Toluene

i. Heat of Reaction:

Literature review concluded that the ΔHrxn for the thermal dealkylation of toluene is negative which indicates that the reaction is exothermic. However ΔH◦rxn was calculated using the heat of formation of individual species that take part in the reaction with respect to their stoichiomeric coefficients. The values have been tabulated below.

Species ΔHf 298K (J/moles of substance formed) Toluene 50,170 Hydrogen 0 Benzene 82,930 Methane -74,520

Table1-Heatofformation[5]

4662356 CHHCHCHHC +↔+

Therefore the ΔHrxn was calculated to be:

Δ𝐻!"# = −74520+ 82730− 50170 = −107080 !!"#$

Δ𝐻!"# = −107080𝐽

𝑚𝑜𝑙𝑒 ∗9.47831 ∗ 10!!

1𝐽 ∗453.593 𝑚𝑜𝑙𝑒1𝑙𝑏𝑚𝑜𝑙𝑒 = −17953

𝐵𝑡𝑢𝑙𝑏𝑚𝑜𝑙𝑒

Δ𝐻!"# 𝑇 = Δ𝐻!"# 𝑇! + ΔC!(T− T!)

where T! is 536.4◦R.

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ii. Specific Heat Capacity

Assuming ideality, the heat capacities were found as a function of temperature and were adopted from tabulated results presented by Smith et al (222). The species that were considered for heat capacities are toluene, hydrogen, methane and benzene. Since side reactions were not considered heat capacities of other species have been ignored.

The following table gives the heat capacities of each species as a function of temperature in Kelvin:

𝐶!𝑅 = 𝐴 + 𝐵𝑇 + 𝐶𝑇! + 𝐷𝑇!!

Where R is the gas constant in the specific units we require.

Species A 103 B 106 C D 10-5

Toluene 0.290 47.052 -15.716 … Hydrogen 3.931 1.490 … -0.232 Benzene -0.206 39.064 -13.301 … Methane 1.702 9.081 -2.164 …

Table2-HeatCapacityCoefficients[5]

iii. Sum of Heat Capacities (𝚫𝐂𝐩)

ΔC! = caC!" +

da C!" −

ba C!" − C!"

SectionC:FluidFlow(Pressuredropdifferential)

A differential for pressure drop was also used and it is given by,

𝑑𝑃𝑑𝐿 = −𝐺

𝑑𝑢𝑑𝐿 −

2𝑓𝐺!

𝜌𝐷

Where D is the pipe diameter

u is the average velocity of gas

f is fanning friction factor

G is ρ*u,

9

With the assumption that the pressure drop occurs at a constant temperature the above equation can be further simplified as

𝜌!𝑃𝑃!𝑑𝑃𝑑𝐿 − 𝐺

! 𝑑𝑃𝑃𝑑𝐿 −

2𝑓𝐺!

𝐷 = 0

− 2𝑓𝐺!

𝐷 = 𝑑𝑃𝑑𝐿 𝜌!

𝑃𝑃!− 𝐺!

𝑃

𝑑𝑃𝑑𝐿 =

− 2𝑓𝐺!

𝐷𝜌!𝑃𝑃!− 𝐺

!

𝑃

Further simplification and dividing by the cross sectional area Ac the differential becomes:

1𝐴!𝑑𝑃𝑑𝐿 =

1𝐴!∗

− 2𝑓𝐺!

𝐷𝜌!𝑃𝑃!− 𝐺

!

𝑃

𝑑𝑃𝑑𝑉 =

1𝐴!∗

− 2𝑓𝐺!

𝐷𝜌!𝑃𝑃!− 𝐺

!

𝑃

This differential equation accounts for the pressure drop in the PFR and it requires the following explicit equations:

i. 𝐴! = !!

𝐷!

ii. 𝜌! =!∗!"!"#

!∗! where R = 10.73 !"# !!

!

!"#$!% !

iii. 𝐺 = !!!!

Fanning friction factor for turbulent flow [1],

iv. f = !.!"𝑅𝑒0.25

10

SectionD:CalculationofConstantsUsed

4662356 CHHCHCHHC +↔+

A+ B ↔ C + D

i. Molecular Weights 𝑀𝑊!= 92 !"#

!"#$!%

𝑀𝑊!= 2 !"#!"#$!%

𝑀𝑊!= 78 !"#!"#$!%

𝑀𝑊!= 16 !"#!"#$!%

ii. Flowrates a. Flow rates at the inlet in which X denotes conversion

𝐹!! =𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶

𝑋 ∗𝑀𝑊!=

25000 𝑙𝑏𝑚ℎ𝑟0.75 ∗ 78 𝑙𝑏𝑚

𝑙𝑏𝑚𝑜𝑙𝑒 ∗ 3600𝑠ℎ𝑟

= 0.1187 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

𝐹!! = 𝑀𝑜𝑙𝑎𝑟 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐴 ∗ 2 = 0.1187 ∗ 2 = 0.2374 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

b. Flow rates at the exit

𝐹! = 𝐹!! ∗ (1− 𝑋) = 0.1187 ∗ (1− 0.75) = 0.0297 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

𝐹! = 𝐹!! ∗ (𝜃 − 𝑋) = 0.1887 ∗ (2− 0.75) = 0.1484 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

𝐹! = 𝐹!! ∗ 𝑋 = 0.1187 ∗ 0.75 = 0.089 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

𝐹! = 𝐹!! ∗ 𝑋 = 0.1187 ∗ 0.75 = 0.089 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

𝐹! = 𝐹! + 𝐹! + 𝐹! + 𝐹! = 0.3561 𝑙𝑏𝑚𝑜𝑙𝑒𝑠

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iii. Mole fractions 𝑥! = !!

!! = 0.083

𝑥! = !!!!= 0.4167

𝑥! = !!!!

= 0.25

𝑥! =!!!!= 0.25

iv. Viscosity

µ! = 4.18 ∗ 10!! !"# !".!

[2]

µ! = 3.93 ∗ 10!! !"# !".!

[3]

µ! = 4.8 ∗ 10!! !"# !".!

[3]

µ! = 3.93 ∗ 10!! !"# !".!

[3]

µ = ∑𝑥!µ! = 𝑥!µ! + 𝑥!µ! + 𝑥!µ! + 𝑥!µ!

= 0.083 ∗ 4.18 ∗ 10!! + 0.4167 ∗ 3.93 ∗ 10!! + 0.25 ∗ 4.8 ∗ 10!! + (0.25 ∗ 3.93 ∗ 10!!)

= 4.167 ∗ 10!! !"# !!!!

𝑀𝑊!"# = 0.3333 ∗ 92+ 0.6666 ∗ 2 = 32𝑙𝑏𝑚

𝑙𝑏𝑚𝑜𝑙𝑒

v. Initial concentration of Toluene (A) 𝐶!! = !"

!" = !.!!!∗!"#.!

!".!"#$∗!"!# = 0.0109

vi. Initial volumetric flow rate

Vo = !!!!!!

= !.!!"#!.!"!#

= 10.89 !!!

!

vii. Initial Temperature (TO ) 𝑇! = 1150+ 460 = 1610 𝑅

viii. Gas Constant (R) R = 1.9858 !"#

!"#$!% !

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SectionE:AdditionalExplicitEquations:

i. Total mass flowrate (m0)

ii. Velocity (vel) Vel = !!

!!

iii. Reynolds number (Re)

Re = !!∗!"#∗!!

iv. Density of feed

𝜌! =𝑃 ∗𝑀𝑊!"#𝑅 ∗ 𝑇

v. Fanning friction factor f = !.!"

!"!!

vi. Cross sectional Area

A = !!

!

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SectionF:PolymathProgram

After defining the equations the simulation was carried out in POLYMATH

CASE A – Diameter = 3ft

Since the differential equations have V (Volume) as a dependant variable, V was varied and trial and error was implemented until a conversion of 75% was achieved. In this case, a PFR volume of 620 ft3 gave a conversion of 75.5%. With a diameter of 3ft, the pressure drop is 0.201psia, which is negligible. Refer to Appendix A for the program details.

Figure1–PolymathSimulationforCaseA

14

Case B – Diameter 2ft

In this case all the variables were kept constant except (Diameter) , which was changed to 2ft. It was noted that the pressure drop increased from -0.201 to to -3.17psi.

Refer to Appendix C for the profiles.

Figure2-PolymathSimulationforCaseB

15

Case C – Diameter 1.14711 ft

In this case all the variables were kept constant except D, which was chnaged from 2ft to 1.1477ft. It was noted that the pressure drop increased from 3.17 psi to 305.87 psi. This is a fairly noticeable increase in the pressure drop. It was also observed that the conversion dropped from 0.749 to 0.3937, which is a significant change.

Refer to Appendix D for the profiles.

Comparison of varying diameters

Decreasing the diameter, caused an increase in pressure drop along the PFR which in turn reduced the reaction rate. This reduction in the reavtion rate reduces the conversion. Correspondingly, this decrease in conversion caused the temperature to increase by 109.54 which is lower than the temperature increase in case A and B. This decrease in tenperature change further contributed to reduction in the reaction rate.

Figure4-PolymathSimulationforCaseC

Figure3-PolymathSimulationforCaseC

16

The results of the three scenarios have been tabulated

Case Volume (ft3) Diameter (ft)

Conversion Pressure Drop (psi)

ΔT (R)

A 620 3 0.755 -0.201 209.02 B 620 2 0.749 -3.17 207.30 C 620 1.1477 0.3937 -305.87 109.54 Table3-ComparingCaseAB&C

As the diameter was decreased the pressure drop increased till the system became stiff below 1.1477ft diameter. Comparing the results shown above, it can be concluded that 3 ft diameter would be sufficient to have a negligible pressure drop across the PFR. Using a higher diameter would unnecessarily increase the cost and increase surface area for heat transfer which is undesired in this case. Therefore a diameter of 3ft was chosen as the basis for all further calculations.

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Case D – With Reverse Reaction (D = 3ft)

The simulation was then carried out considering the hydrodealkylation of toluene as a reversible reaction to study the effects of the backward reaction. It was assumed that the backward reaction is elementary. Hence the rate law becomes

−𝑟! = 𝑘(𝐶!𝐶! − 𝐶!𝐶!𝐾!

)

The equilibrium constant is given by:

𝐾! =𝐶!𝐶!𝐶!𝐶!

Literature value of K [4]

K= 200 at 1150 F

Figure4-Equilibriumconstantsforvariousreactionsintoluenedealkylation

18

𝒓𝒂𝟏 = 𝑘 Cao(1− X) !!"

!!"

Cao 2− X !!"

!!"

!.!

𝒓𝒂𝟐 = 𝑘 C!"! ∗ !!

!!∗ ( !

!"∗ !!")!

𝒓𝒂 = 𝒓𝒂𝟏 + 𝒓𝒂𝟐

Case Volume (ft3) Diameter (ft) Conversion Pressure Drop (psi) T (R) With Reverse Rxn 620 3 0.7552328 -0.2071643 1818.6349 Wthout Reverse Rxn 620 3 0.7554231 -0.2010053 1818.6869

Table4-Comparingforwardreactionwithreversiblereaction

From the table, it can be seen that accounting for the reverse reaction does not change the conversion, pressure drop and temperature increase in the PFR. This is due to the high value of K. Therefore, ignoring the reverse reaction is an acceptable assumption.

Refer to Appendix F for the profiles

Figure5-PolymathSimulationofCaseD

19

SectionG:HYSYSSolution

A simulation of the process was carried out on HYSYS in order to compare the results with the Polymath solution.

To start off, four components were added to the Component List:

1. Toluene 2. Hydrogen 3. Benzene 4. Methane

Next, since hydrocarbons are the main components of the process, Peng-Robinson was chosen as the Fluid Package. Then, in the “Reactions” tab, a kinetic reaction was selected and the components were added with their corresponding stoichiometric coefficients, keeping reactants as negative and products as positive. The orders of the forward reaction were specified as 1 with respect to Toluene and 0.5 with respect to Hydrogen, which is given according to the rate law. The reverse reaction was not considered for this simulation.

Figure6-SettingupKineticReactioninHYSYS

In the “Basis” tab, the basis units were selected to be lbmol/ft3 and rate units were lbmol/ft3-s because these are the units in which the rate law is given. Then the values for Frequency Factor (A) and Activation Energy (Ea) were specified in the “parameters” tab as 7.18*1011 and 98000 Btu/lb-mole, respectively.

The reaction was then added to the Global Rxn Set, which was then added to the Fluid Package. With this, the conditions were set for the simulation environment.

20

Simulation Environment

In the Simulation Environment, two flows (IN and OUT) and one PFR were added to the system. The initial conditions of Temperature, Pressure and flow rates of each component were specified at the inlet flow labeled “IN”

Figure7-InletSpecificationsinHYSYS

Next, the PFR conditions were specified with respect to the results from Polymath. First, the reaction set was added and Ergun Equation was selected for calculating pressure drop. A volume of 620 ft3 and a diameter of 3 ft were specified as the dimensions of the PFR. This was enough information for HYSYS to do all the other calculations and provide the results.

It was found that, under these conditions, the conversion obtained was 88.5%.

Figure8-PFRwith620ft3

This difference from the conversion obtained in the Polymath calculation can be due to many different factors and assumptions made in the Polymath part. It also showed no pressure drop while using Ergun Equation.

In order to obtain the required conversion of 75%, the volume of the reactor was changed and trial and error was used until 75% conversion was obtained. The results gave a volume of 566 ft3

at our required conversion.

21

Figure9-PFRwith566ft3inHYSYS

We also obtained our required output of about 25,000 lb-mole of Benzene per hour. However, the Temperature slightly exceeded the maximum temperature of 1350 oF.

Figure10-OutletstreamspecificationinHYSYS

22

The final Simulation Environment is as follows:

Figure11-HYSYSSimulationEnvironment

SectionH:ComparingHYSYSresultswithPolymath

Simulations Conversion Volume (ft3)

Diameter (ft)

Length (ft)

Pressure at the outlet (psi)

Temperature at the outlet (R)

Polymath 0.755 620 3 87.7 564.17 1818.7 HYSYS 0.7499 566 3 80.07 564.7 1828 Table5-ComparingHYSYSandPolymathsimulations

As stated in the table above Polymath and HYSYS provide results which are in the same range and are comparable at the same conversion and diameter. However, HYSYS simulation provided a PFR volume which was 54ft3 less than the Polymath solution (620 ft3). This may be due to the ideal gas assumption used in Polymath. The HYSYS was done using the Peng-Robinson fluid package which takes the non-ideality of gases at high pressure and temperature into consideration. This is also the reason for the temperature difference of 10 R between the two simulations. However, the pressure drop remained negligible in both the simulations.

23

Conclusion

FinalDesign

In order to produce 25,000 lbm/hr of benzene, we require an adiabatic PFR of volume 566 ft3 with a radius of 3ft-0inch. According to Rase (2011), 347 stainless steel can be used as the inner lining for the reactor [4]. The outer shell can be made of low alloy steel that should be painted with heat sensitive paint and insulated accordingly.

Discussion

This report has presented simulations done in Polymath as well as in HYSYS.

The conversion profile generated in Polymath is shown below

Figure12-PFRConversionProfile

24

The temperature profile is as follows:

Figure13-PFRTemperatureProfile

and the pressure drop across the PFR is shown below:

Figure14-PFRPressureDropProfile

25

Finally HYSYS generated solution is considered more accurate since it uses Peng-Robinson fluid package and corrects for non ideality of the gases at high pressure. It is also necessary to point out that tube bundles have not been used because the reactor being used is adiabatic. Generally tube bundles are used in order to increase surface area for heat transfer. Since heat transfer is negligible the use of tube bundles would just add to the cost.

That being said, the presented solution still has limitations such that it does not consider the possibility of side reaction. As mentioned before, hydrodealkylation of toluene occurs with many side reactions some of which include hydrogenation of toluene and benzene to cycloparaffins and reactions of benzene and toluene to various diphenyls. Selectivity of benzene would largely be affected if not accounted for.

Also, the simulation denotes a temperature range that exceeds the range specified in the design parameter (1609.7 – 1828 R). At high temperatures, the rates of side reactions increase. The final temperature can be brought down by decreasing the initial temperature. But this would affect the kinetics of the hydrodealkylation reaction and would eventually increase the PFR volume, hence adding to the cost. Therefore further optimization is required in terms of cost which is beyond the scope of this report.

26

References

[1] H.K. Fauske (2003). Process Safety (Vol 10, 1st ed.). Available: http://www.fauske.com/Download/Chemical/ProcessSafety/Vol10-No1.pdf

[2] Gas Viscosity Calculator (n.d.). Available: http://www.lmnoeng.com/Flow/GasViscosity.htm

[3] Perry’s Handbook, 8th ed., McGraw Hill,, NY, 2008.

[4] H.F. Rase (n.d.). Chemical Reactor Design for Process Plants (Vol 2). Available: http://coecs.ou.edu/Richard.G.Mallinson/gradkinetics/pdf/Case%20Study%20104.pdf

[5] J.M. Smith, H.C. Van Ness, M.M. Abbott, “Appendices” in Introduction to Chemical Engineering Thermodynamics, 7th ed. New York, USA: McGraw Hill, 2005,,, pp. 677-687.

27

APPENDICES

28

APPENDIXA-PolymathProgram–WithoutReverseReaction

d(x)/d(V) = -ra / Fao # Design Equation d(T)/d(V) = (-ra) * (-deltaH) / (Fao * ((Cpa + 2 * Cpb) + x * (deltaCp))) # Temperature Profile d(P)/d(V) = ((-2 * f * (G ^ 2) / D) / (((RHOo * (P / Po)) - (G ^ 2 / (P*32.174*144)))) / (Ac))(32.174*144) # Pressure Drop (with conversion factors) ra = -k * (Cao ^ 1.5) * (1 - x) * ((2 - x) ^ 0.5) * ((A) ^ 1.5) * ((To / T) ^ 1.5) # Rate Law [lbmole A/ (ft^3).(s)] Cao = 0.0109 # Initial Concentration of A (lbmole/ft^3) k = 718000000000 * exp(-E / (R * T)) # Rate Constant [(ft^3)^0.5/(lbmole^0.5).(s)] E = 98000 # Activation Energy(BTU/lbmole) R = 1.98588 # Gas Constant (BTU/lbmole.R) vo = 10.89 # Initial volumetric Flow (ft^3/s) To = 1609.67 # Initial Temperature (R) Fao = Cao * vo # Initial Flow (lb mole/s) deltaH = -17953 + deltaCp * (T - 536.4) # Enthalpy change of reaction [Btu/lbmole] deltaCp = Cpc + Cpd - Cpa - Cpb # Overall Cp w.r.t Stoichiometric coefficients [Btu/(lbmole).(R)] Cpd = ((1.702) + (9.081 * 10 ^ (-3) * Tk) - (2.164 * 10 ^ (-6)) * (Tk ^ 2)) * R # Heat capacity for D (Btu/lb mole R) Cpb = (3.249 + (0.422 * 10 ^ (-3) * Tk) + (0.083 * 10 ^ 5) * (Tk ^ (-2))) * R # Heat Capacity for B (Btu/lb mole R) Cpc = (-0.206 + (39.064 * (10 ^ (-3)) * Tk) - (13.301 * (10 ^ (-6)) * Tk ^ 2)) * R # Heat Capacity for Benzene (Btu/lbmole R) Cpa = ((0.29) + (47.052 * 10 ^ (-3) * Tk) - (15.716 * 10 ^ (-6)) * (Tk ^ 2)) * R # Heat Capacity for Toluene (Btu/lbmole R) Tk = T / 1.8 # Temperature in Kelvin mo = 11.412 # Initial Mass Flow Rate [lbm/s] G = mo / Ac # Superficial velocity [(lbm)/(ft^2).(s)] D = 3 # Diameter [ft] Ac = (3.14/4) * (D ^ 2) # Cross sectional Area of the Reactor (ft^2) RHOo = (Po * MW) / (10.73 * To) # Density of the Feed (lbm/ft^3) Po = 564.17 # Initial Pressure (lbf/inch^2) MW = 32 # Average molecular weight of the feed [lbm/lbmole] f = 0.08 / Re ^ (1 / 4) # Fanning friction factor A = P / Po # Pressure fraction L = V / Ac # Length of the reactor [ft] deltaP = P - Po # [psia] Re = (RHOo * vel * D) / mew # Reynolds Number vel = vo / Ac # Velocity [ft/s] mew = 4.167 * 10 ^ (-7) # Viscosity [lbm/(ft).(s)] V(0) = 0 x(0) = 0 T(0) = 1609.67 P(0) = 564.17 V(f) = 620

29

APPENDIXB-PolymathProgram–CASED-WithReverseReaction

d(x)/d(V) = -ra / Fao # Design Equation d(T)/d(V) = (-ra) * (-deltaH) / (Fao * ((Cpa + 2 * Cpb) + x * (deltaCp))) # Temperature Profile d(P)/d(V) = ((-2 * f * (G ^ 2) / D) / (((RHOo * (P / Po)) - (G ^ 2 / (P*32.174*144)))) / (Ac))(32.174*144) # Pressure Drop (with conversion factors) ra1 = -k * (Cao ^ 1.5) * (1 - x) * ((2 - x) ^ 0.5) * ((A) ^ 1.5) * ((To / T) ^ 1.5) # Rate Law [lbmole A/ (ft^3).(s)] ra2 = (k/K) * ((Cao ^ 2) * (x ^ 2) * (A ^ 2) * ((To / T) ^ 2)) # Rate Law [lbmole A/ (ft^3).(s)] Cao = 0.0109 # Initial Concentration of A (lbmole/ft^3) k = 718000000000 * exp(-E / (R * T)) # Rate Constant [(ft^3)^0.5/(lbmole^0.5).(s)] E = 98000 # Activation Energy(BTU/lbmole) R = 1.98588 # Gas Constant (BTU/lbmole.R) vo = 10.89 # Initial volumetric Flow (ft3/s) To = 1609.67 # Initial Temperature (R) K = 200 # Literature Value ra = ra1 + ra2 # Total Reaction Rate Fao = Cao * vo # Initial Flow (lb mole/s) deltaH = -17953 + deltaCp * (T - 536.4) # Enthalpy change of reaction [BTU/ lbmole] deltaCp = Cpc + Cpd - Cpa - Cpb # Overall Cp w.r.t Stoichiometric coefficients [Btu/(lbmole).(R)] Cpd = ((1.702) + (9.081 * 10 ^ (-3) * Tk) - (2.164 * 10 ^ (-6)) * (Tk ^ 2)) * R # Heat capacity for D (Btu/lb mol R) Cpb = (3.249 + (0.422 * 10 ^ (-3) * Tk) + (0.083 * 10 ^ 5) * (Tk ^ (-2))) * R # Heat Capacity for B (Btu/lb mol R) Cpc = (-0.206 + (39.064 * (10 ^ (-3)) * Tk) - (13.301 * (10 ^ (-6)) * Tk ^ 2)) * R # Heat Capacity for Benzene (BTU/lbmole R) Cpa = ((0.29) + (47.052 * 10 ^ (-3) * Tk) - (15.716 * 10 ^ (-6)) * (Tk ^ 2)) * R # Heat Capacity for Toluene (BTU/lbmole R) Tk = T / 1.8 # Temp. in Kelvin mo = 11.412 # Initial Mass Flow Rate [lbm/s] G = mo / Ac # Superficial Velocity [lbm/(ft^2).(s)] D = 3 # Diameter [ft] Ac = (3.14/4) * (D ^ 2) # Cross sectional Area of the Reactor (ft^2) RHOo = (Po * MW) / (10.73 * To) # Density of the Feed (lbm/ft^3) Po = 564.17 # Initial Pressure (lbf/inch^2) MW = 32 # Average molecular weight of the feed f = 0.08 / Re ^ (1 / 4) # Fanning friction factor A = P / Po # Pressure Ratio L = V / Ac # Length of PFR (ft) deltaP = P - Po # Pressure Drop (psia) Re = (RHOo * vel * D) / mew # Reynold's Number vel = vo / Ac # Velocity (ft/s) mew = 4.7 * 10 ^ (-7) # Viscosity [lbm/(ft).(s)] V(0) = 0 x(0) = 0 T(0) = 1609.67 P(0) = 564.17 V(f) = 620

30

APPENDIXC–CASEBProfiles

31

APPENDIXD–CASECProfiles

32

APPENDIXE–CASEDProfiles