episode 54 : cape problem formulations

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


ADJUST D, Qr

STOP

Given: Feed compositions, feed flowrates, target product compositions


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


ADJUST D, Qr

STOP

Given: Feed compositions, feed flowrates, target product compositions


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 ?

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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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