Episode 48 : Computer Aided Process Engineering Simulation Problem * Identify partitions * Identify recycle-loops * Determine tear-streams * Determine calculation order SAJJAD KHUDHUR ABBAS Ceo , Founder & Head of SHacademy Chemical Engineering , Al-Muthanna University, Iraq Oil & Gas Safety and Health Professional – OSHACADEMY Trainer of Trainers (TOT) - Canadian Center of Human Development

1. SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Episode 48 : Computer Aided
Process Engineering
Simulation Problem

2. Flowsheet for cyclohexane production - What are we solving?
C6 H6 =
100
C-1
T=422.2 K P = 33.3 atm
Recycle H2
T=330 K P = 34 atm
M-1
T=322 K P = 31.6 atm Purge gas
D-1
SP-1
E-2Isothermal
reactor
T=497.2 K
 P=1 atm
E-3
Other data: R-1 (heat of reaction, conversion,
reference compound), E-1 (U & A), SP-1
(purge rate)
Condition: H2/C6H6 in reactor feed=12
methane/H2 balance for purge
R-1
E-1
mixer
T=322 K
 P=0.5 atm
H2 = 97.5
CH =2.54
Cyclohexane
product

3. The objective is to fill-out all the stream summary table!
All stream is defined by NC+2 variables (component flows, T & P)
Variables Streams
S1 S2 S3 S4 S5 ……. S13
f1
f2
f3
f4
T
P

4. The objective is to fill-out the stream summary table! Which stream
variables are known? x indicate a specified variable.
Number of equations = 11 (NC+2); number of variables = 13 (NC+2); degree
of freedom = 2 (NC+2)
Variables Streams
S1 S2 S3 S4 S5 ……. S13
f1 x x
f2 x x
f3 x x
f4 x x
T x x
P x x

5. Steady State Simulation Approaches
E-1
E-2
E-3
R-1
SP-1
D-1
C-1
variables Solve
x
M-1
x
x
Equation Oriented
x
equations
x
x represents variables of
the connecting streamsx
x
x
M-1 E-1 E-2 R-1 E-3 D-1 SP-1 C-1

6. Flowsheet Decomposition
* Identify partitions
* Identify recycle-loops
* Determine tear-streams
* Determine calculation order
Equation Ordering
* Rearrange model equations
* Identify partitions
* Determine sparse pattern

7. Flowsheet decomposition & equation ordering
E-1
E-2
E-3
R-1
SP-1
D-1
C-1
variables Convergence procedure
*
M-1
x k+1 = x k -F / J
*
*
*
equations
*
the connecting streams
*
*
Calculation order
*
M-1 E-1 E-2 R-1 E-3 D-1 SP-1 C-1

8. How many partitions ?
How many recycle loops ?
How many tear streams and which are they ?
Flowsheet Decomposition

9. Flowsheet Decomposition
How many partitions ? 2
How many recycle loops ? 1
How many tear streams and which are they ? 1 ; any stream from 2,3,4,7
Solve, for tear-stream = 2, unit 2, unit 3, unit 4,
unit 1; after convergence,solve unit 5

10. Modularapproachversusequationorientedapproach
SequentialModularApproach EquationOrientedApproach
Simulateoneunitmodelatatime Solveallunitmodelstogether
Decomposeflowsheet Orderequations
Iterateintearstreams Updateallunknownvariables
simultaneously
Lessflexiblebutmorerobust Moreflexiblebutlessrobust
Initializationisimportant Initializationisveryimportant
Storagerequirement nothigh Storagerequirement canbeveryhigh

11. Flow-diagram for Sequential Modular Approach

12. Simultaneous Modular Approach
Generate
linear model
parameters
Solve with
rigorous model
Generate
new model
parameters
Check results
from inner-loop
with outer-loop

13. Determination of recycle-loops and
partitions
The first step is to determine the existence of recycle loops and partitions (algorithm
of Sargent and Westerberg) –
1) Trace from one unit to the next by following the direction of the unit output
streams, one after the other. Stop when,
a) Aunit reappears. In this case, collect all the units traced so far into one group.
b) Aunit with no linked output is encountered
2) Count the number of different groups of units. Each group of units represents a
partition.
3) Identify groups with a single unit. Add each of these groups to the list of
partitions.

14. Tear-stream determination and calculation order
• Algorithm2(Gundersen)
• Foreachpartition,performthefollowing,
1. Removeallstreamsthatarenotincludedinrecycleloops.
2. Calculatetheratioofnumberofvariablesper(outputstreams)/(inputstreams).
3. Tearallinput streamstotheunit(node)whichhasthelargestratioofnumberof
variablesper(outputstreams)/(inputstreams).
4. Repeatfromstep1untileveryloophasbeentorn.

15. Convergence Techniques (Modular)
Method J
Successivesubstitution I
Wegstein D=diag{d};djj =(yj –yj )/(hj –hj )
i i-1 i i-1
DominantEigen-value 1/(1-)I;=(wi
–wi-1
)/(yi
–yi-1
)
Broydon’srule FullmatrixQN–update(see3.2.3.3)
Newton [F(yi
)/y]–1
Table3.1:TheformofJthatcanbeusedinequations3.35–3.36fordifferentconvergencetechniques.
Equation for tear-
h (y) = y - w = 0
y i+l = y i – J h (y i)
stream convergence
Update method
Choice of the method defines J

16. Convergence Techniques (Equation Oriented)
Method J
Successivesubstitution I
Wegstein D=diag{d};djj =(yj –yj )/(hj –hj )
i i-1 i i-1
DominantEigen-value 1/(1-)I;=(wi
–wi-1
)/(yi
–yi-1
)
Broydon’srule FullmatrixQN–update(see3.2.3.3)
Newton [F(yi
)/y]–1
Table3.1:TheformofJthatcanbeusedinequations3.35–3.36fordifferentconvergencetechniques.
Mathematical model
F  A y - b = 0
y i+l = y i – J h (y i)
of process flowsheet
Update method
Choice of the method defines J

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