SAJJAD KHUDHUR ABBASCeo , Founder & Head of SHacademyChemical Engineering , Al-Muthanna University, IraqOil & Gas Safety and Health Professional – OSHACADEMYTrainer of Trainers (TOT) - Canadian Center of Human Development
Episode 54 : CAPE Problem Formulations
Computer Aided Process Engineering
Lecture 2: CAPE Problem Formulations
* Four types of CAPE problemsFlowsheeting
Specification (Design) Optimization (Design) Synthesis (& Design)
Flowsheeting Problem
INPUT TFLOWSHEET OUTP
U
OPERATING CONDITIONS
3
EQUIPMENT PARAMETERS
Given - all incoming information
Determine - all outgoing information plus internal variables
Flowsheeting Problem V1
Qc
VN + 1F, xF
All incoming information is specified while all outgoing and intermediate data is calculated
Given - F, x F, N, NF, Reflux ratio, D (or B), & Qr (or Qc), P
Determine - V, L, T,x , x D, x B, etc.p
1
D, x D
4
Lo
NF
N
Qr
B, x B
Specification (Design) Problem
INPUT
5
OUTPUT
OPERATING CONDITIONS
EQUIPMENT PARAMETERS
Compared to the flowsheeting problem, instead of all incoming information, some outgoing data is specified.
Note that the degree of freedom remains the same !
FLOWSHEET
Specification (Design) Problem V1
VN + 1
F, xF
Instead of all incoming information being specified, two outgoing data are specified !Thus, the same number of in- going information need to be determined.
Given - F, x F, N, NF,
x1 , x2 , reflux
ratio, P Determine - V,
L, T, xp,
D B
x D (not x1 ), x (notD B
x B), D, B, Q ,Q , etc2 c r
Qc
6
D, x DLo
reflux ratio = L0/D
Qr
B, x B
1
NF
N
GUESS D, Qr
SOLVE THE FLOWSHEETING PROBLEM
ADJUST D, Qr
STOP
Given:
7
Feed compositions, feed flowrates, target product compositions
Product flowrates, heating dutiesFind:
Calculation procedure for specification problem
ARE TARGET PRODUCT COMPOSITIONS SATISFIED ?
Optimization Problem
GivenFeed composition, feed flowrate
ChooseTarget product composition Number of trays, feed tray location
Minimize
Objective = f (yield, energy, capital cost, ….)
8
Optimization Problem V1
QcGiven - F, x F, N, NF, x1
, x2 , reflux ratio, P
Determine - V, L, T, xp,
x D (not x1 ), x (notD B
x2 ), D, B, Qc ,Qr, etc
Subject to,
(xD, xB, Qr, Qc, cost data) = minimum, and, x1 > 0.98 & x2 > 0.95
1
VN + 1
D, xLo
9
NF
D B
N
Qr
B, x B
Calculation procedure for optimization problem
GUESS D, Qr
SOLVE THEFLOWSHEETINGPROBLEM
ARE TARGET PRODUCT COMPOSITIONS SATISFIED ?
ADJUST D, Qr
STOP
Given: Feed compositions, feed flowrates, target product compositions
Product flowrates, heating dutiesFind:
Is
minimum ?
NLP solver
10
Synthesis (& Design) Problem
?INPUT
11
OUTPUT
Inputs and outputs are known but flowsheet, equipment parameters and condition of operation are unknown !
Synthesis/Design Problem
INPUT OUTPUT
methanol, water
separation technique?
how many, design
12
methanol
water
Separation technique - distillation, flash, extraction, membrane-based separation?How many unit operations are needed? What is the design of each equipment?
F, xF
1 2
Determine - optimalseparation unit operation.
Assume distillation has been selected & only one needed
Determine, N, NF, P, reflux ratio, V, L, T, xp, x D
(not x1 ), x (not x2 ), D, B, Qc ,Qr, etc
D B B
Subject to, (xD, xB, Qr, Qc, cost data) = minimum,and, x1 > 0.98 & x2
> 0.95D B
Qc
Synthesis/Design ProblemV1Given - F, x F, x D, x B
VN + 1
Lo D
reflux ratio = L0/D
Qr
B13
1
NF
N
Calculation procedure for synthesis problem
GUESS D, Qr
SOLVE THEFLOWSHEETINGPROBLEM
ARE TARGET PRODUCT COMPOSITIONS SATISFIED ?
ADJUST D, Qr
STOP
Given: Feed compositions, feed flowrates, target product compositions
Product flowrates, heating dutiesFind:
Is
minimum ?
MINLPsolver
N, NF,reflux ratio,
etc
14
15
A Simple Example : problem formulationConsider: A benzene feed stream & a hydrogen
feed stream with methane as an impurity !We know:
benzene + hydrogen = cyclohexane reaction takes place in vapor phase & there is99.9 % conversion of benzene; reactor
operatesat 497.2 K
We would like to obtain: pure cyclohexane Which simulation problem do we have ?
16
A Simple ExampleConsider: A benzene feed stream & a hydrogen feed
stream with methane as an impurity !We know: benzene + hydrogen = cyclohexane
reaction takes place in vapor phase & there is 99.9 % conversion of benzene; reactor operates at 497.2K
We would like to obtain: pure cyclohexane
we need, a mixer, a reactor, a separator, a divider, plus utility units (pumps, compressors,
& heat exchangers) - we have a flowsheet!Which simulation problem do we have ?
17
A Simple ExampleConsider: A benzene feed stream & a hydrogen feed stream
with methane as an impurity !We know: benzene + hydrogen = cyclohexane
reaction takes place in vapor phase & there is 99.9 % conversion of benzene; reactor operates at
497.2 KWe would like to obtain: pure cyclohexane
we need, a mixer, a reactor, a separator, a divider, plus utility units (pumps, compressors, & heat exchangers) - we have a
flowsheet!
We have the found the equipment parameters and the design of reactor, purge, distillation column, heat
exchangers, & compressors
Which simulation problem do we have ?
Flowsheet for cyclohexane production
C6 H6 = 100
C-1T=422.2 K P = 33.3 atm
Recycle H2
T=330 K P = 34 atm T=322 K P = 31.6 atm Purge gas
D-1
SP-1
E-2Isothermal reactor
T=497.2 K
P=1 atm
R-1
E-1
mixer
E-3 T=322 K
P=0.5 atmOther 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
H2 = 97.5 CH4=2.5
Cyclohexane product
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