概要信息：

Catalytic Rates & Pressure Drop in PFR Reactors:  HYSYS 3.0 
By Robert P. Hesketh  Spring 2003 
 
Objectives:   
1. In this session you will learn how to convert a first order catalytic reaction rate for use in 
the PFR.   
2. In addition you will use the Ergun Equation to simulate the pressure drop within a PFR. 
(The reverse reaction or equilibrium will be ignored in this tutorial.) 
 
The references for this section are taken from the 2 HYSYS manuals: 
Simulation Basis:  Chapter 5 Reactions 
Operations Guide:  Chapter 9 Reactors 
 
Reactor Types in HYSYS 
1) CSTR model reactors – Well Mixed Tank-Type 
HYSYS Reactor Name Reaction Types (See above) 
Conversion Reactor Conversion ( ) 2
210% TCTCCX ++=
CSTR Simple Rate, Heterogeneous Catalytic, Kinetic 
Equilibrium Reactor ( )TfKeq = ; equilibrium based on reaction stoichiometry.   predicted 
from Gibbs Free Energy 
eqK
eqK  specified as a constant or from a table of values 
Gibbs minimization of Gibbs free energy of all specified components, 
option 1) no the reaction stoichiometry is required 
option 2) reaction stoichiometry is given 
 
2) Plug Flow Reactor:  Simple Rate, Heterogeneous Catalytic, Kinetic 
 
Taken from:  9.3 Plug Flow Reactor (PFR)  
 
The PFR (Plug Flow Reactor, or Tubular Reactor) generally consists of a bank of cylindrical 
pipes or tubes. The flow field is modeled as plug flow, implying that the stream is radially 
isotropic (without mass or energy gradients). This also implies that axial mixing is negligible.  
 
As the reactants flow the length of the reactor, they are continually consumed, hence, there will 
be an axial variation in concentration. Since reaction rate is a function of concentration, the 
reaction rate will also vary axially (except for zero-order reactions). 
 
To obtain the solution for the PFR (axial profiles of compositions, temperature, etc.), the reactor 
is divided into several subvolumes. Within each subvolume, the reaction rate is considered to be 
spatially uniform. 
 
You may add a Reaction Set to the PFR on the Reactions tab. Note that only Kinetic, 
Heterogeneous Catalytic and Simple Rate reactions are allowed in the PFR. 
 
 
 1
Reaction Sets (portions from Simulation Basis:  Chapter 5 Reactions) 
Reactions within HYSYS are defined inside the Reaction Manager. The Reaction Manager, 
which is located on the Reactions tab of the Simulation Basis Manager, provides a location from 
which you can define an unlimited number of Reactions and attach combinations of these 
Reactions in Reaction Sets. The Reaction Sets are then attached to Unit Operations in the 
Flowsheet. 
 
Summary of Reactions in HYSYS 
Reaction Type Description: 
Conversion Conversion% ( ) 2
210% TCTCCX ++=
Equilibrium ( )TfKeq = ; equilibrium based on reaction stoichiometry.   predicted or specified eqK
Gibbs minimization of Gibbs free energy of all components 
Kinetic γϕβα
SRrevBAfA CCkCCkr +−=  where the reverse rate parameters must be thermodynamically 
consistent and rate constants are given for both the forward and reverse rate constant by 
( )RTEATk n −= exp  
Heterogeneous 
Catalytic 
Yang and Hougen form: 
∑+






−
=−
i
ii
s
S
r
Rb
B
a
A
A CK
K
CCCCk
r γ1
 
This form includes Langmuir-Hinshelwood, Eley-Rideal and Mars-van Krevelen etc. 
Simple Rate 








−−=
eq
SR
BAfA K
CCCCkr
γϕ
βα  in which  is predicted from equilibrium data.   must 
be given as a Table of data or in the form of
eqK eqK
( ) ( ) DTTCTBAK +++= lnln   
 
 
HYSYS PFR Reactors using kinetic rates– Tutorial using Styrene 
 
Styrene is a monomer used in the production of many plastics.  It has the fourth highest 
production rate behind the monomers of ethylene, vinyl chloride and propylene.  Styrene is made 
from the dehydrogenation of ethylbenzene: 
 22565256 HCHCHHCHCHC +=−⇔−  (1) 
In this reactor we will neglect the aspect that reaction 1 is an equilibrium reaction and model this 
system using a power law expression.  In HYSYS this is called a Kinetic Rate expression.  The 
reaction rate expression that we will use in this tutorial is from Hermann1 and has been modified 
by removing the reverse reaction rate: 
 


















−×−= −
T
pr EBEB
K mol
cal1.987
molcal21874exp
kPa sg
EB mol10491.7
cat
2  (2) 
Notice that the reaction rate has units in terms of the mass of catalyst and that the concentration 
term is partial pressure with units of kPa. 
 
 2
HYSYS Reaction rates must be given in units of volume of gas phase.  For example, to convert from units of kgcat 
given in equation 3 to the units required by HYSYS given in equation 4, you must use equation 5.   
 
 [ ]
gcats
mol
k
r =  (3) 
 [ ] 3
gasms
mol
=HYSYSr  (4) 
 
( )
φ
φρ −
=
1
cHYSYS rr  (5) 
From the source of the original reaction rate studies1 the properties of the catalyst and reactor are 
given as: 
 445.0=φ  (6) 
 3
catcat mkg2146=catρ  (7) 
 mm7.4=pD  (8) 
In many of the rates in your reaction engineering text the units of mol/(Lreactor s) are used.  Take 
out a piece of paper and write down the conversion from gcat given in Equation 2 to HYSYS 
units. 
 
( ) ( )
=






×−= −
EBnew
EBnew
A
A
kPa sg
EB mol10491.7
cat
2
 (9) 
 
Verify with your neighbor that you have the correct reaction rate constant.   
 
Please note that if you change the void fraction in your simulation you will need to also 
change the reaction rate that is based on your void fraction. 
 
In this simulation the pressure drop will be calculated by using the Ergun Equation given in the 
Steady-State Simulation manual Section 9.4.1 and is identical to that given by Fogler as equation 
4-22 in a slightly modified form 
 ( )








+
−





 −
−= G
DD
GP
pp
75.111501
dz
d
3
µφ
φ
φ
ρ
 (10) 
where 
[ ] ( )
 viscosityanddensity  fluid are  and
mkg  velocity,mass lsuperficia 2
µρ
s=G
 
 3
Procedure to Install a Kinetic Reaction 
Rate: 
 Start a New Case 1. Start HYSYS 
2. Open a new case by clicking on the blank 
white page OR use the commands File New.   
Press Add 
button 
3. Since these compounds are hydrocarbons, use the Peng-Robinson thermodynamic package.  
(Additional information on HYSYS 
thermodynamics packages can be 
found in the Simulation Basis 
Manual Appendix A: Property 
Methods and Calculations.  Note an 
alternative package for this system is 
the PRSV)  
3.1. Select the Fluid Pkgs menu tab 
and Press the Add button 
3.2. Select the EOS filter radio 
button to see only Equations of 
State (EOS) 
3.3. Then select the Peng Robinson 
Equation of State. 
tate – This will be discussed in thermodynamics or you 
e 
3.4. Notice that you have a choice in 
calculating the enthalpies.  You 
can either use the equation of s
can use a prediction method called the Lee-Kesler Method which is an extension of th
Pitzer method.  For thi
tutorial we will use th
equation of state method
Press the View button to 
start adding chemical 
compounds 
s 
e 
. 
3.5. 
Press to add 
components
 4
 
4. Install the chemicals for a styrene reactor:  ethylbenzene, styrene, and hydrogen.  If they are 
not in the order given below then use the Sort List… button feature.  
5. Let’s look at one of the components 
ponent 
5.3.  the temperature 
 on the 
5.4. the ideal gas enthalpy 
and see some of the physical 
properties that it is using.  
5.1. Select Ethyl benzene 
5.2. Click on the View Com
button  
Examine
dependent properties given
Tdep page 
Notice that 
has been correlated using a 5th 
order polynomial. 
 5
6. Now return to the Simulation Basis Manager by closing the Component List View window.  
Press the Close button or X   
7. Select the Rxns tab 
and then press the 
Simulation Basis 
Mgr… button.  Press here to 
start adding 
rxns 
8. The Reaction 
Component Selection 
view will appear.  
9. Press the Add Rxn 
button 
10. To install a reaction, 
press the Add Rxn 
button.  
 
Add 
Reaction 
11. From the Reactions view, highlight the Kinetic reaction type and 
press the Add Reaction button.  Refer to Section 5 of the Simulation Basis 
Manual for information concerning reaction types and the addition of reactions.  
12. On the Stoichiometry tab select the first row of the Component 
column in Stoichiometry Info matrix. Select ethylbenzene from 
the drop down list in the Edit Bar. The Mole Weight column 
should automatically provide the molar weight of ethylbenzene. In 
the Stoich Coeff field enter -1 (i.e. 1 moles 
of ethylbenzene will be consumed).  
 6
13. Now define the rest of the Stoichiometry tab 
as shown in the adjacent figure.   
14. Go to Basis tab and set the Basis as 
partial pressure, the base component as 
ethylbenzene and have the reaction 
take place only in the vapor phase.   
 
 
 
15. From your previous hand calculation 
given by equation 9 you should have 
converted the reaction rate given in 
equation 2 by using the following: 
 
( )
kPa sL
mol48.200
L 10
m 1
m 0.445
m
m
m 445.01
m
kg 2146
kg
g10
kPa sgcat 
mol10491.7
gas
gas
3
3
gas
3
gas
3
R
3
R
3
cat
3
cat
cat
cat
cat
3
2
=







−












×= −A
(11) 
The new reaction rate expression is then given by Equation 12 which should agree with the 
calculation: 
 


















−−=
T
pr EBEB
K mol
cal1.987
molcal21874
exp
kPa sL
EB mol48.200
gas
 (12) 
16. The pressure basis units should be kPa and the units of the reaction rate given by equation 12 
is mol/(L s).  Since the status bar at the bottom of the property view shows Not Ready, then 
go to the Parameters tab.    
17. Add the pre-exponential which is assumed to give the units given in the basis tab.  Then enter 
the activation energy – with units of cal/mol (which is transformed to kJ/kmol after entry.)  
Leave β blank or place a zero in the cell.  Notice that you don’t enter the negative sign with 
the pre-exponential.  
18. Close the Kinetic Reaction Window 
 
 7
Add Set Button 19. By default, the Global Rxn 
Set is present within the 
Reaction Sets group when 
you first display the Reaction 
Manager. However, for this 
procedure, a new Reaction 
Set will be created. Press the 
Add Set button. HYSYS 
provides the name Set-1 and 
opens the Reaction Set 
property view.  
20. Open the drop down list in 
the Edit Bar and select the name of the 
Reaction. The Set 
Type will correspond to the type of Reaction 
which you have added to the Reaction Set. 
The status message will now display Ready. 
(Refer to Section 5.4 – Reaction Sets for details 
concerning Reactions Sets.)  
Enter Simulation Environment 
21. Press the Close button to return to the 
Reaction Manager. 
22. To attach the reaction set to the Fluid 
thermodynamics), highlight Se
Reaction Sets group and press the Add 
to FP button. When a Reaction Set is 
attached to a Fluid Package, it become
available to unit operations within the 
Flowsheet using that particular Fluid 
Package.  
Package (your peng robinson 
23. The Add ’Set-1’ view appears, from 
24. Press the Close button. Notice that the name of the Fluid Package (Basis-
25.
t by 
n in 
 
t-1 in the 
s 
Add to FP (Fluid Package)
which you highlight a Fluid Package 
and press the Add Set to Fluid Package 
button.  
1) appears in the Assoc. Fluid Pkgs group when the Reaction Set is 
highlighted in the Reaction Sets group. 
 Now Enter the 
Simulation 
Environmen
pressing the butto
the lower right hand 
portion  
 8
PFR
 
26. Install a PFR reactor.  Either through the 
26.1. Flowsheet, Add operation 
26.2. f12 
26.3. or icon pad.  Click on PFR, then release left mouse button.  
Move cursor to pfd screen and press left mouse button. Double click 
on the reactor to open.  
27. Add stream names as shown.  
28. Next add the reaction set by selecting the reactions tab and choosing Reaction Set from the 
drop down menu. 
 
 9
29. Go to the Ratings Tab.  Remember in the case of distillation columns, in which you had to 
specify the number of stages?  Similarly with PFR’s you have t specify the volume.  In this 
case add the volume as 160 m3, 3 m length, and a void fraction of 0.445 as shown in the 
figure.  Notice that the volume of gas in the reactor or void volume has been calculated. 
   
30. Return to the Reactions tab.  Notice that additional data must be entered since you specified a 
void fraction.  Add the particle size and density of catalyst from equations 7 and 8.   Notice 
that the bulk density of the catalyst is calculated for you.  This has units mass of catalyst per 
volume of reactor. 
 
 10
Comp 
Molar 
Flow
Add 
Button 
Give it a new 
name such as 
Compositions
31. Go to the Design Tab and select heat 
transfer.  To make this reactor 
adiabatic you need to set the heat 
duty to zero.  For this tutorial we 
will have an isothermal reactor so 
leave this unspecified.  The yellow 
note at the bottom is a warning and 
is letting you know that the pressure 
drop has not been specified.  We will 
add this later. 
32. Close the PFR Reactor  
33. Open the workbook 
 
Workbook 
34. Isn’t it strange that you can’t see the molar flowrate in the composition window?  Let’s add 
the molar flowrates to the workbook windows.  Go to Workbook setup. 
35. Press the Add button on the right side 
36. Select Component Molar Flow and then press the All radio button.  
37. To change the units of the variables go 
to Tools, preferences 
38. Then either bring in a previously 
named preference set or go to the 
variables tab and clone the SI set and 
give this new set a name.   
39. Change the component molar flowrate 
units from kmol/hr to gmol/s. 
40. Change the Flow units from kmol/hr 
to gmol/s 
41. Next change the Energy from kJ/hr 
to kJ/s. 
42. Save preference set as well as the case.  
Remember that you need to open this 
preference set every time you use this 
case. 
 11
43. Now add a feed composition of pure ethylbenzene at 217.5 gmol/s, 2610 gmol/s of water, 
880 K, and 1.378 bar.  Whoops!  We forgot to add the water.  Water is used in this reaction 
to drive the conversion to higher values.  You will see the utility of adding water after you 
complete the equilibrium tutorial.   
43.1. Go back to the fluid Property package by clicking on the Erlenmeyer flask or 
selecting Simulation, Enter Basis Environment. 
Return to Fluid Property 
Package. 
43.2. Go and view Component List-1  
43.3. Add water and then return to the 
simulation environment by pressing on 
the green arrow. 
43.4. It will put you in “holding mode” 
which stops all calculations.  If you 
answer yes, then press the Green light 
to return to the automatic calculation 
mode.  Be careful that you have added 
water to the correct list.  You should be 
able to see water in the workbook 
component list. 
44. Next set the outlet reactor temperature to 
880K and the outlet reactor pressure to 
1.378 bar to obtain an isothermal and 
isobaric reactor.  Remember you can type 
the variable and then press the space bar and 
type or select the units.  
Return to 
simulation
 12


Polymath Solution to Isothermal & Isobaric Reactor 
POLYMATH Results 
Styrene irreversible rate - volume reactor  2003  02-20-2003,   Rev5.1.230  
 
Calculated values of the DEQ variables 
 
 Variable  initial value  minimal value  maximal value  final value 
 VR          0              0              160           160       
 FEB         217.5          18.779137      217.5         18.779137 
 FS          0              0              198.72086     198.72086 
 FH          0              0              198.72086     198.72086 
 FW          2610           2610           2610          2610      
 P           137.8          137.8          137.8         137.8     
 rho_cat     2146           2146           2146          2146      
 T           880            880            880           880       
 FT          2827.5         2827.5         3026.2209     3026.2209 
 pEB         10.6           0.8551144      10.6          0.8551144 
 void_frac   0.445          0.445          0.445         0.445     
 k           0.3292753      0.3292753      0.3292753     0.3292753 
 rEB        -3.4903181     -3.4903181     -0.281568     -0.281568  
 XEB         0              0              0.9136591     0.9136591 
 
ODE Report (RKF45) 
 
 Differential equations as entered by the user 
 [1] d(FEB)/d(VR) = rEB 
 [2] d(FS)/d(VR) = -rEB 
 [3] d(FH)/d(VR) = -rEB 
 
 Explicit equations as entered by the user 
 [1] FW = 2610 
 [2] P = 137.8 
 [3] rho_cat = 2146 
 [4] T = 880 
 [5] FT = FEB+FS+FH+FW 
 [6] pEB = FEB/FT*P 
 [7] void_frac = 0.445 
 [8] k = 7.491e-2*rho_cat*(1-void_frac)*exp(-21874/1.987/T)*1000 
 [9] rEB = -k*pEB 
 [10] XEB = (217.5-FEB)/217.5 
 
 Comments 
 [1] d(FEB)/d(VR) = rEB 
     V in L of reactor and P in kPa  
 [6] k = 7.491e-2*rho_cat*(1-void_frac)*exp(-21874/1.987/T)*1000 
     mol/(s kPa m^3 reactor)  
 [9] P =     137.8 
     kPa  
 
 Independent variable  
 variable name : VR 
 initial value : 0 
 final value : 160 
 
 Precision  
 Step size guess. h = 0.000001 
 Truncation error tolerance. eps = 0.000001 
 
 15
46. Comparision to POLYMATH Solution: 
46.1. Actual Conversion from HYSYS is 90.09% whereas the POLYMATH solution 
gives 91.36%.   
 
46.2. Compare the reaction rates from the hand calculation to that in HYSYS.  HYSYS 
does not give the initial reaction rate.  Instead it gives the reaction rate at the first 
iteration of Length.  With the default conditions this is at 0.075 m in length.  The last 
line of the hand calculations given on the previous page was adjusted using the 
ethylbenzene molar flowrate at 0.075 m of 192.922 mol/s and the total flowrate at 2852 
mol/s.  These results are found in the performance tab.  The hand calculation gives 
6.895×10-3 mol/(Lgas s) compared to 6.904×10-3 mol/(Lgas s) given by HYSYS below. 
 
 16
47. Plots can be obtained from 
the Performance tab by 
pressing the Plot button. 
And selecting the 
components that you would 
like to plot. 
48. To improve the 
performance of HYSYS 
you need to increase the 
number of steps used to 
solve the differential 
equations.  Increase the 
number of steps to 40 
segments.  This results in 
an actual conversion of 
90.74% compared to 91.36% from POLYMATH.  Believe it or not POLYMATH is a more 
powerful ordinary differential equation solver than the default used by HYSYS.  Increasing 
to 200 segments gives a HYSYS conversion of 91.28%.  If your simulation is very complex 
this number of segments could slow the computer down considerably.  You should always 
examine reactor behavior at low segment values and then increase the number to check your 
solution. 
17 
 
49. Now let’s add the pressure drop equation.   
49.1. Change the number of segments back to 20. 
49.2. Delete the outlet reactor pressure in the worksheet or workbook 
49.3. Next go to the Parameters portion of the Design window.  Click on the radio 
button next to the pressure drop calculation by the Ergun equation.  Voila! 
 
50. The rule of thumb for reactors is that the inlet pressure drop should be less than 10% of the 
inlet pressure.  If the pressure drop is higher than this value then you should do something to 
decrease the pressure drop.   
 01.0 PP ≤∆  (13) 
Write the ways that you can decrease the pressure drop given by equation 10: 
 
50.1._______________________________________________________________________  
50.2._______________________________________________________________________  
50.3._______________________________________________________________________  
 18
The answers are:  G, Dp and z or reactor length.   
Making the reactor shorter will decrease the pressure drop.   
Decreasing the superficial mass velocity, G, will decrease the pressure drop, but if you 
have a production rate that is based on your reactant flowrate how do you decrease G?.  
Remember that 
cA
00G
ρυ
=
kPa8.13=
.  If you have found a volume of reactor that gives a desired 
conversion then you need to increase Ac and decrease L (length of reactor) such that the 
volume remains constant V   HYSYS does this automatically!  Try this.  The 
inlet pressure in 137.8 kPa.  A 10% loss in pressure would give an outlet pressure of 
124.02 or a .  If you get tired of switching back and forth then you could try the 
adjust function.   
LAc=
∆P
Adjust 
51. Add the adjust function.  (F4 or Flowsheet palette). 
51.1. Select the adjusted variable of reactor tube length and the target variable (the 
variable you would like to find) product pressure.   
51.2. Go to the Parameters page and change the step size to 0.2 m and set the minimum 
to 0.5 m and the maximum to 3 m.  Why did you pick these values?  You know that 3 m 
is gives too large a pressure drop!  If you give a really large value of reactor length 
HYSYS will yell at you and do strange things!  To fix this turn the adjust off by clicking 
the ignored box on the connections page.  Then go back to the PFR reator and reset the 
value of the reactor tube length.  Then find out what you did wrong! 
51.3. Now you may need to increase your volume to obtain the 90% conversion. 
 
 19
 
52. Changing the particle diameter Dp 
is dangerous (well you just need to 
be careful)!   
If you change the particle size then you 
will also change the void fraction of 
catalyst.  Figure 5-70 of the 5th Edition 
of the Chemical Engineers Handbook 
shows the relation between particle 
diameter and void fraction for various 
types of particles.   
 
In Figure 1 shown below is the curve 
that I have digitized for spherical 
particles.  The x-axis is the ratio of the 
particle size to the tube or reactor 
diameter.  This equation can be entered 
into a HYSYS spreadsheet so that the 
void fraction is automatically calculated 
when the particle diameter or reactor 
diameter change.  Notice that you must 
also include the void fraction in your 
reaction rate term! 
 
 
Figure 5-70 in Perry's 5th y = 0.4208x + 0.329
R2 = 0.9989
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6
Dp/Dtube
vo
id
 fr
ac
tio
n
void
Linear (void)
 
Figure 1:  Void Fraction for Spherical Particles 
 20
POLYMATH and Hand Calculations 
53. Now we will look at verifying what is going on in HYSYS.  Notice that HYSYS is a black 
box calculation.  You can’t see what it is doing.  Reading the help files will give an 
indication on how it is integrating the reactor.  To fully understand the PFR let’s go to some 
hand calculations given on the following page.  
53.1. For the comparison with POLYMATH reset the size of the reactor to the 
following a volume of 163 m3 and a length of 2.190 m.  You could also add a 
spreadsheet for ease in examining variables.  Remember that to quickly add variables 
you can right click on the variable that you want and drag it to the spreadsheet. 
21 



Construct a POLYMATH program to give the following: 
POLYMATH Results 
Pressure Drop in Isothermal Styrene Reactor   
 
Calculated values of the DEQ variables 
 
 Variable  initial value  minimal value  maximal value  final value 
 W           0              0              1.941E+08     1.941E+08 
 FEB         217.5          20.299645      217.5         20.299645 
 FS          0              0              197.20036     197.20036 
 FH          0              0              197.20036     197.20036 
 P           1.378E+05      1.236E+05      1.378E+05     1.236E+05 
 FW          2610           2610           2610          2610      
 T           880            880            880           880       
 k           2.765E-07      2.765E-07      2.765E-07     2.765E-07 
 FT          2827.5         2827.5         3024.7004     3024.7004 
 P0          1.378E+05      1.378E+05      1.378E+05     1.378E+05 
 pEB         10.6           0.8291809      10.6          0.8291809 
 rEB        -2.931E-06     -2.931E-06     -2.292E-07    -2.292E-07 
 FT0         2827.5         2827.5         2827.5        2827.5    
 Betacat     6.639E-05      6.639E-05      6.639E-05     6.639E-05 
 X           0              0              0.9066683     0.9066683 
 
ODE Report (RKF45) 
 
 Differential equations as entered by the user 
 [1] d(FEB)/d(W) = rEB 
 [2] d(FS)/d(W) = -rEB 
 [3] d(FH)/d(W) = -rEB 
 [4] d(P)/d(W) = -Betacat*P0/P*FT/FT0 
 
 Explicit equations as entered by the user 
 [1] FW = 2610 
 [2] T = 880 
 [3] k = 7.491e-2*exp(-21874/1.987/T) 
 [4] FT = FEB+FS+FH+FW 
 [5] P0 = 1.378e5 
 [6] pEB = FEB/FT*P/1000 
 [7] rEB = -k*pEB 
 [8] FT0 = 217.5+2610 
 [9] Betacat = 6.639E-05 
 [10] X = (217.5-FEB)/217.5 
 
 Comments 
 [6] k = 7.491e-2*exp(-21874/1.987/T) 
     mol/(gcat s kPa)  
 [8] pEB = FEB/FT*P/1000 
     kPa  
 [13] Betacat = 6.639E-05 
      Pa/g  
 
 Independent variable  
 variable name : W 
 initial value : 0 
 final value : 194137890 
 
 Precision  
 Step size guess. h = 0.000001 
 Truncation error tolerance. eps = 0.000001 
 
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54. Now let’s compare the solution of POLYMATH with that given in HYSYS.   
Volume  163 m3 
Catalyst Weight  1.941E+08 kg 
Length  2.19 m 
 HYSYS HYSYS HYSYS HYSYS HYSYS POLYMATH
Number of 
Segments 
20 200 300 400 500  
∆P/P0 (%) 10.01 10.06 10.06 10.07 10.07 10.30 
Conversion (%) 89.36 90.58 90.63 90.657 90.66 90.66 
Ethylbenzene 
Product Flow 
(mol/s) 
23.15 20.48 20.38 20.33 20.30 20.30 
 
 
The above values show that HYSYS is using the same equations as those that you entered in 
POLYMATH.  The 2 differences are in the calculation of pressure drop and the manner in which 
the ordinary differential equations are integrated.  The difference of 2% in the percent pressure 
drop is attributed to the value of viscosity that was used.  I assumed that the gases were all steam 
with a viscosity of 2.969e-5 kg/(m s).  HYSYS uses a value of 2.63E-05 kg/(m s).  Plugging the 
HYSYS value of viscosity into a spreadsheet to eliminate any round-off errors in the hand 
calculation and then placing the new pressure drop value of Betacat = 6.4428E-05 results in a 
pressure drop ratio to inlet pressure of 10.01!  The method of integration of ODE’s requires an 
adjustment of the number of segments to between 400 and 500 to have an precision equal to that 
of POLYMATH.  We will find in later calculations that a setting of number of segments this 
high will cause the HYSYS program to solve very slowly.  .
 26
At the end of this exercise submit 4 printouts (5 pages total).   
 
1) From a word document printout the following (2 pages):  (Paste all of your results into one 
word document.)  Make the following plots from your Conversion reactor simulation:   
a) The effect of reactor length on pressure drop for a constant volume of 163 m3.  Notice 
that diameter will vary.  You may have already done this above by trial and error for a 
fixed amount of catalyst to determine the pressure drop at 10% of the inlet pressure.  
Before you begin find the limits on the pressure drop – Find out when HYSYS says that 
the pressure drop is too big! 
b) The effect of reactor diameter on pressure drop for a constant volume of 160 m3.  Notice 
that length will vary. 
c) The effect of changing the particle diameter from 1.2 mm to 0.2 m (really big particles!) 
on the pressure drop given that the void fraction from Figure 5-70 in Perry’s 5th edition 
for spherical particles is 
 0.329  0.4208  
spherical
+=
tube
p
D
D
φ  (14) 
Notice that that the void fraction will be nearly constant for this problem and it will be much 
less than 0.445!  This means that this catalyst was not spherical!  To solve this problem just 
change the void fraction to the new value.  If you needed to change the void fraction as a 
function of particle diameter then you would need to do the following:   
i) Create a spreadsheet that you can import the particle diameter and the tube diameter.  
Then calculate the void fraction and export it to the reactor.   
ii) Now you must adjust the reaction rate pre-exponential!   
iii) Again make a calculation in the spreadsheet based on equation 5 and then export it 
the pre-exponential within the reactor.   
iv) To find the pre-exponential term you need to go to the reactor, select the reactions 
menu, and view the reaction.  See figures on this page for help.   
2) On a separate sheet printout the Reaction Summary Printout (See Below for instructions) 
3) On a separate sheet printout the Reactor Summary Printout  
 27
 
Reaction Summary 
1. Go back to the simulation Basis Manager by 
clicking on the Erlenmeyer flask.  
2. View the reaction  
3. Remove the pushpin 
4. Select File Print and use the preview feature to 
see the following:  
5. Print 
 
Reactor Summary: 
Double click on reactor  
Undo pushpin 
Select Print from main menu 
Then select the Datablock(s) shown in the 
Select Datablock(s) to Print for PFR figure: 
 
Workbook 
Select workbook and print. 
 
 
 
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Solutions: 
 
 
 29
 
 
Figure 2:  Effect of Particle Diameter on Pressure Drop for a reactor with spherical particles and a void fraction of 
0.33, volume of 163 m3, length of 2.19 m, diameter 9.73 m and pre-exponential in the rate expression of 
107.8 mol/(Lgas s kPa). 
Reference: 
                                                 
1 Hermann, Ch.; Quicker, P.; Dittmeyer, R., “Mathematical simulation of catalytic dehydrogenation of ethylbenzene 
to styrene in a composite palladium membrane reactor.”  J. Membr. Sci.  (1997),  136(1-2),  161-172. 
 30