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Wilcox home ChE design home Profession General Properties Equipment Separation HYSYS andUniSim Costs Safety Case studies Excel MATLAB

Use of HYSYS/UniSim to calculate the equilibrium constant

and reverse reaction kinetics for a chemical reaction

The numbered equations below are from general treatments ofequilibrium constants and of

reverse reaction kinetics. The same numbers are used here.

Consider a general chemical reaction:

iiA0 = (1)

wherei is the stoichiometric coefficient for component A i, withi > 0 for products and i > 0 forreactants. Here, to illustrate the equations and the methods in HYSYS/UniSim, we will use the

gas-phase catalytic dehydrogenation of isopropanol (IPA) to produce acetone (Ac) and hydrogen(H2), as described in Appendix B.3 ofAnalysis, Synthesis, and Design of Chemical Processes:

IPA Ac + H2 (a)

Thus, A1 = IPA and 1 = -1; A2 = Ac and 2 = +1; A3 = H2 and3 = +1; i = 1; and equation (1)becomes 0 = -IPA+Ac+H2.

Following is the relationship between Gibbs free energies Gi0 of the components in their standard

states (ai = 1) and the equilibrium constant Ka using activities ai:

RT/Gia

0i eaK

= (5)

where G0 = iGi0 and ai is the activity of the ith component. (For a gas the activity is replacedby the fugacity.) Applying this to the IPA reaction (2) and assuming the reaction mixture is an

ideal gas, we have:

Py

yy

p

ppPypKK

IPA

2HAc

IPA

2HAciipa

ii ==== (b)

where pi = yiP is the partial pressure of the ith component, y i is its mole fraction, and P is the

total pressure.

The equilibrium reaction section of the basis in HYSYS/UniSim computes G0 from its database of component properties and uses equation (5) to find the equilibrium constant.

(HYSYS/UniSim has equilibrium constants for a few reactions in its data base.) Unfortunately,HYSYS/UniSim does not display the equilibrium constant, so we must find it by creating a feed

stream, attaching it to an equilibrium reactor, and using the effluent compositions to calculate it.

We now give the steps required to do this for the IPA reaction above. Assume a vapor feedstream in which some water is present, so that water must be included as a component.

1. Open HYSYS/UniSim and click on the new case icon.2. Pull down Tools and select Preferences, Variables and EuroSI. Close the preferences

window.

3. Add the following components: Hydrogen, Acetone, 2-Propanol (IPA), and H2O.

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4. To examine HYSYS/UniSims data base for IPA, select 2-Propanol, click on ViewComponent, then click on each of the tabs at the bottom. For T Dep, click on Gibbs Free

Energy. This shows the coefficients for the temperature dependence of the Gibbs Free

Energy of formation of IPA relative to its elements as ideal gases at 1 bar and 25oC. These

will be used by HYSYS later to calculate the equilibrium constant of the reaction versustemperature.

5. Close the IPA Properties window and Component window, then click on the Fluid Pkgs tab

and Add.6. Select PR-Twu with Equation of State, HYSYS/UniSim and Smooth Liquid Density for the

Property Package.7. Close the Fluid Package Set Up page and click on the Reactions tab.

8. Add an Equilibrium Reaction with a Stoich Coeff (i) of -1 for IPA and +1 for acetone andhydrogen.

9. For a Basis select Partial Press (in bar), Vapour Phase, and Gibbs Free Energy. Change thename from rxn-1 to equilibrium. Note that HYSYS has calculated the standard heat of

the reaction, H0, as 5.5x104 kJ/kgmol = 5.5x104 J/gmol. (In step 32f you will compare thiswith the value obtained by fitting lnKp to 1/T.)

10. The Keq tab shows that HYSYS will use equation (5) to calculate the equilibrium constant,using the free energies of formation of the compounds (see step 4 above).

11. Set the Approach to 100% and DeltaT to 0 so that the product exiting the reactor will be at

equilibrium.12. Close the reaction setup page and click on Add to FP.

13. Enter the Simulation Environment and create a stream named reactor feed with the

following properties: T=150oC, P = 2 bar, Molar Flow 100 kgmole/h, 0 mole fractionHydrogen, 0.01 Acetone, 0.70 IPA and 0.29 H2O.

14. Create an Equilibrium reactor (General Reactor E; ERV-100). Use the reactor feed stream

for the inlet, molten salt for the energy stream, reactor product for the vapour outlet, and

fictitious liquid for the liquid outlet (although there is no liquid product unless the reactorT is too low to be practical).

15. On the Design Parameters page set the Delta P to 0.

16. On the Reactions Details page select your reaction set and equilibrium reaction that you

created.17. Go to the Worksheet and set the reactor product temperature to 350oC. This should cause

HYSYS to calculate the product composition, which should be about 40% hydrogen and 41%acetone. Reaction Results shows a conversion of approximately 98% and an equilibrium

constant of about 34. Write down your values for comparison with the results to be found in

steps 22 and 23. How are compositions expressed in this equilibrium constant and what areits units?

Next you will find Kp and conversion under the conditions above.

18. From the Object Palette add a Spreadsheet to the pfd and then open it.

19. Rename the spreadsheet Conversion & K calculator.20. Add Import the following variables:

Cell A1: reactor feed, Phase Comp Molar Flow, Vapour Phase, 2-Propanol, OK.

Cell A2: reactor product, Phase Comp Molar Flow, Vapour Phase, 2-Propanol, OK.

Cell A3: reactor product, Phase Comp Mole Frac, Vapour Phase, Hydrogen, OK.Cell A4: reactor product, Phase Comp Mole Frac, Vapour Phase, Acetone, OK.

Cell A5: reactor product, Pressure, OK.

Cell A6: reactor product, Phase Comp Mole Frac, Vapour Phase, 2-Propanol, OK.

21. Click on the Spreedsheet tab and confirm the values shown.

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22. Click on cell A7 and enter =1-A2/A1 to get the fractional conversion, which should agreewith the percent conversion found in step 17. If they dont agree, you made a mistake

somewhere and must correct it before proceeding. In the Variable box, type Fractional

conversion.

23. Click on cell A8 and enter =A3*A4*A5/A6 to get Kp, which should agree with that foundin step 17 and has units of bar.1 In the Variable Type box type select Pressure and in the

Variable box type Equilibrium constant.

Next you will prepare a plot of Kp and conversion versus T.

24. Click on Tools/DataBook.25. Insert the reactor product pressure and temperature, and the fractional conversion and

equilibrium constant from the Conversion & K calculator. Alternately Equilibrium Constant

and Percent Conversion from ERV-100 could be used, in which case it would not have been

necessary to create the Conversion & K calculator.26. Click on the Case Studies tab, Add a case study and name it Reactor T effect at 2 bar.

Make Temperature the Independent variable and conversion & Kp the Dependent variables.

27. Click on View. Set the Low Bound at 150oC, the High Bound at 400oC and the Step Size at25oC.

28. Click on Start for HYSYS/UniSim to calculate conversion and Kp versus T.

29. Click on Results and Graph to see the results. Note that the equilibrium conversion decreasesas the temperature decreases, reaching about 1/3 at 150oC. This indicates that one must

account for the reverse reaction in HYSYS/UniSim when performing calculations for a plug-

flow reactor. (It is thermodynamically impossible to exceed the equilibrium conversion.)30. Right click on the graph and select Graph Control in order to format the graph to suitable

form. Print the result out.

Next you will fit the Kp versus T results using equation (9). This is necessary to determine thereverse reaction rate constants from the forward reaction rate constants for use in

HYSYS/UniSim. If this is not of interest, you can skip to step 33 to continue examining the

influence of pressure and temperature on the equilibrium constant and conversion of the IPA

reaction.

31. Continuing from step 18, Click on Table, highlight the results and copy them onto theclipboard (e.g., with Ctrl C).

32. Open Excel and do the following, in order to fit ln(Kp) versus 1/T to equation(9). This fit is

needed in order to determine the constants for reverse reaction kinetics in HYSYS/UniSim

for plug flow reactors.a. Paste the data from HYSYS/UniSim into Excel. Move the data so that they are all in one

row.

b. Create a new row consisting of temperature in K (you can use Excels convertcommand).

c. Create new rows for ln(Kp) and 1/T with T in K.d. Plot ln(Kp) versus 1/T and format it. Especially, change the x-axis so that it begins at

about 0.0015/K and ends at about 0.0025/K.

e. Right click on the data and create a linear trendline with equation. By comparison with

equation (9)this should give a value of about 7000 K forH0/R and 15 forS0/R.

1 It is believed that the equilibrium constant found in step 17 is for the compositions expressed as fugacities. Thatfound in 23 is for partial pressures. Under the temperature and pressure used here, this gas mixture should be very

near ideal, and so the fugacities are very close to the partial pressures and the two equilibrium constants should be

essentially the same.

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f. Using the value of the gas constant R in J/mol.K, calculate the standard heat of the

reaction H0 and entropy S0. The resulting value ofH0 should be approximately thesame as found in step 9. If not, you have made a mistake somewhere.

33. You will now use the values ofH0 and S0 just found to determine the reverse reactionkinetics for the IPA to acetone reaction, using the kinetic coefficients for the forward reactiongiven in Appendix B.3 ofAnalysis, Synthesis, and Design of Chemical Processes:

sreactorm

kmolC

RT

Eexpkr

3IPAa

0IPA

= (c)

where rIPA is the rate of conversion of IPA, Ea = 72.38 MJ/kmol is the activation energy for

the forward reaction, k0 = 3.51 x 105 m3gas/m3reactor s is the pre-exponential rate constant,

and CIPA is the molar concentration of IPA in kmol IPA/m3gas. In HYSYS/UniSim the

Kinetic Reaction Basis permits us to choose molar concentration in the Vapour Phase as abasis, but then requires that the rate units be in kgmole/m3-s. The m3 here is m3gas. To

convert from the given kinetics with m3bulk catalyst to m3gas we must divide ko by the void

fraction m3gas/m3reactor. If we choose = 0.5, and use the symbols in the KineticReaction Parameters of HYSYS/UniSim we have k0 = A = 7.02e+005/s, E = Ea = 72,380

kJ/kgmole, and = 0. Now you need to combine this with your relationship between Kp and

T to get the constants for the reverse reaction kinetics required by HYSYS.34. Since the HYSYS/UniSim basis is molar concentration, we must use KC rather than Kp. This

requires a different relationship with H0 and S0, i.e., equation(10). Equation (25)is thegeneral relationship for reverse reaction kinetics with molar concentrations as the bases,

giving the following for the reverse reaction rate coefficients required by HYSYS:

i0

i bareAR'A R/S = E' = E - H0 += i' (d)

Calculate these quantities for the IPA reaction using the values of A, E and given in step33. You should get approximately 3e-2 m3/kmol.K.s for A', 1.6e4 J/mol for E', and 1 for '.If not, you have made a mistake somewhere (if in A', probably in the units). It would be

instructive at this point to compare the performance of a plug flow reactor for IPA to acetone

calculated without and with the reverse reaction included. That exercise is left to the reader.

Continuing from step 28 in HYSYS/UniSim, you will now determine the influence of pressure

on conversion and equilibrium constant, using the IPA reaction as an example.

35. Change the reactor product temperature to 250oC and delete the specification for the reactor

feed Pressure.

36. On the DataBook Case Studies page, click on Add, change the name to Reactor P effect at250C, make the reactor product Pressure the Independent variable and Fractional conversion

and Equilibrium constant the Dependent Variables.

37. Click on View and vary the pressure from 1 to 10 bar in steps of 1 bar. Click on Start andthen Results. Format the resulting graph and print it out. How does Kp vary with pressure?

38. Finally, will examine the combined influence of varying pressure and temperature on the

equilibrium conversion. On the Case Studies page Add a new study named Influence of Pand T on conversion, with T and P as Independent variables and conversion as the sole

Dependent variable.

39. Click on view and vary the temperature from 150 to 400oC and the pressure from 1 to 10 bar.

Print out the graph. Explain how you could have anticipated the influences of pressure andtemperature from Le Chateliers Principle.

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Last revised July 2, 2009. Created by W.R. Wilcox atClarkson University.

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