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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 of equilibrium constants and of
reverse reaction kinetics. The same numbers are used here.
Consider a general chemical reaction:
0   i A i
(1)
where i is the stoichiometric coefficient for component Ai, with i > 0 for products and i > 0
for reactants. 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 of Analysis, Synthesis, and Design of Chemical
Processes:
IPA ― Ac + H2
(a)
Thus, A1 = IPA and 1 = -1; A2 = Ac and 2 = +1; A3 = H2 and 3 = +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:
0

K a  a i i  e  G / RT
(5)
where G0 = iGi0 and ai is the activity of the ith component. (For a gas the activity is replaced
by the fugacity.) Applying this to the IPA reaction (2) and assuming the reaction mixture is an
ideal gas, we have:
p p
y y
K a  K p  pi i  yi P   i  Ac H 2  Ac H 2 P
p IPA
y IPA
(b)
where pi = yiP is the partial pressure of the ith component, yi is its mole fraction, and P is the
total pressure.
The equilibrium reaction section of the basis in HYSYS/UniSim computes G0 from its data
base 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 feed
stream 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.
window.
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Close the preferences
3. Add the following components: Hydrogen, Acetone, 2-Propanol (IPA), and H2O.
4. To examine HYSYS/UniSim’s data base for IPA, select 2-Propanol, click on View
Component, 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 versus
temperature.
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 and
hydrogen.
9. For a Basis select Partial Press (in bar), Vapour Phase, and Gibbs Free Energy. Change the
name 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 this
with 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 fraction
Hydrogen, 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 reactor
T 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 are
its 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 agree
with the percent conversion found in step 17. If they don’t 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 found
in 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 at
25oC.
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 decreases
as 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 plugflow 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 the
reverse 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 the
clipboard (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 Excel’s convert
command).
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 for H0/R and 15 for S0/R.
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It is believed that the equilibrium constant found in step 17 is for the compositions expressed as fugacities. That
found 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 of H0 should be approximately the
same as found in step 9. If not, you have made a mistake somewhere.
33. You will now use the values of H0 and S0 just found to determine the reverse reaction
kinetics for the IPA to acetone reaction, using the kinetic coefficients for the forward reaction
given in Appendix B.3 of Analysis, Synthesis, and Design of Chemical Processes:
kmol
 E 
 rIPA  k 0 exp  a  C IPA
3
 RT 
m reactor  s
(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 a
basis, 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 Kinetic
Reaction 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 the
general relationship for reverse reaction kinetics with molar concentrations as the bases,
giving the following for the reverse reaction rate coefficients required by HYSYS:
A'  AR   i e  S
0
/R
bar   i
E' = E - H0
'      i
(d)
Calculate these quantities for the IPA reaction using the values of A, E and  given in step
33. 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 at
250C,” 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 and
then 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 P
and 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 and
temperature from Le Chatelier’s Principle.
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Last revised July 2, 2009. Created by W.R. Wilcox at Clarkson University.
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