2 Using Microsoft Excel Solver

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CBB 4333

Process Optimisation

USING MICROSOFT EXCEL SOLVER

Dr Murni MelatiUniversiti Teknologi PETRONAS

Sept 2012


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OUTCOME

At the end of the lab session, one should be able to: appreciate the application of optimisation

2Copyright reservedMurni Melati Ahmad, UTP


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CASE STUDY ON

MAXIMISATION OF REFINERY PROFIT



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Volume percent yield maximum allowable

Crude 1 Crude 2 production (bbl/day)

Gasoline 80 44 24000

kerosene 5 10 2000

Fuel oil 10 36 6000

Residual 5 10

Processing cost ($/bbl) 0.5 1

Refinery

Cost($/bbl)24 crude #1

15 crude #2

Product Price($/bbl)Gasoline 36Kerosene 24Fuel oil 21

Residual 10

A schematic of a refinery is shown below, the objective isto maximise the profit of the refinery

OPERATION OF REFINERY



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Step 1- Define variables:

x1=bbl/day of crude 1 consumed

x2=bbl/day of crude 2 consumed

x3=bbl/day of gasoline producedx4=bbl/day of kerosene produced

x5=bbl/day of fuel oil produced

x6=bbl/day of residual produced

MODEL DEVELOPMENT



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0,,,,,

negativenonarevariablesallstated,explicitlynotAlthough

600036.01.0;6000oilFuel20001.005.0;2000Kerosene

2400044.08.0;24000Gasoline

:esInequalitib)

1.005.0Residual

36.01.0oilFuel

1.005.0Kerosene

44.08.0Gasoline

:Equationsa)

654321

215

214

213

621

521

421

321

xxxxxx

xxorxxxorx

xxorx

xxx

xxx

xxx

xxx

Step 2Formulate equations

MODEL DEVELOPMENT



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21

21

6543

216543

21216543

21

21

6543

8.101.8)(

andvariablestwoonlyleaving

s,constraintequalitytheviaand,,variablesgeliminatin

byreducedbecanproblemtheoflitydimensionatheObviously

165.2410212436)(

5.0152410212436)(

)/($5.0:costProcessing

)/($1524:costmaterialRaw

)/($10212436:Income

costprocessingcostmaterialrawincomeprofit)(Maximise

xxxf

xx

xxxx

xxxxxxxf

xxxxxxxxxf

dayxx

dayxx

dayxxxx

xf

Step 3

Formulate objective function

FORMULATION



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0,,,,,

6000

200024000

1.005.0

36.01.0

1.005.044.08.0

:

165.2410212436)(maximise

:

LPversionfullThe

654321

5

4

3

621

521

421

321

216543

xxxxxx

x

xx

xxx

xxx

xxx

xxx

toSubject

xxxxxxxf

Objective

LP model for the example problem



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ygraphicallmodelLPtherepresentusLet0,

600036.01.0

20001.005.0

2400044.08.0

:

8.101.8)(maximise

:

LPversionreducedThe

21

21

21

21

21

xx

xx

xx

xx

toSubject

xxxf

Objective



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Assignment 2

1. Plot the constraints and feasible region for theLP problem. Show the details of the working.

2. Solve for the maximum profit for the refinery .

3. Provide some analysis on the solution.

Copyright reserved Murni MelatiAhmad, UTP

10


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0

20

40

60

20 40 60

Crude2(in1

000bbl)

Crude 1 (in 1000 bbl)

x2

x1

Feasible

region

0,

)(600036.01.0

)(20001.005.0

)(2400044.08.0

21

21

21

21

xx

Cxx

Bxx

Axx

FEASIBLE REGION

Copyright reservedMurni Melati Ahmad, UTP


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2

3

1

4

000,1801 f

000,2432 f

740,2863

f

213 8.101.8 xxf

10

20 30

20

C

B

A

30

Crude2(in1000bbl)


10

Graphical solution to the problem indicates that optimum value of theprofit occurs roughly at x*1 = 26,000 bbl/day

x*2 = 7,000 bbl/day

f(x*) = 286,200 $/day

SOLVING USING CONTOUR PLOT

12Copyright reserved Murni Melati Ahmad, UTP

0,

)(600036.01.0

)(20001.005.0

)(2400044.08.0

..

8.101.8)(maximise

21

21

21

21

21

xx

Cxx

Bxx

Axx

ts

xxxf


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2

3

1

4

000,1801 f

000,2432 f

740,2863

f

213 8.101.8 xxf

10

20 30

20

C

B

A

30

Crude2(in1000bbl)


10

Graphical solution to the problem indicates that optimum value of theprofit occurs roughly at x*1 = 26,000 bbl/day

x*2 = 7,000 bbl/day

f(x*) = 286,200 $/day

SOLVING USING CONTOUR PLOT

13Copyright reserved Murni Melati Ahmad, UTP

0,

)(600036.01.0

)(20001.005.0

)(2400044.08.0

..

8.101.8)(maximise

21

21

21

21

21

xx

Cxx

Bxx

Axx

ts

xxxf


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Building Model in Excel



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Set Target and Changing Cells



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Solving using Solver

1

2



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CASE STUDY ON

MAXIMISATION OF PROFITFOR MULTI-PRODUCT PLANT

(mass balance)



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reactant s: A, B, C products: E, F, G process units: 1, 2, 3


OPERATION OF MULTI-PRODUCT PLANT

A schematic of a refinery is shown below, the objective is

to maximise the profit of the multi-product plant


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Step 1- Define variables:

Let

x1, x2, x3 - mass input flows of A to each process

x4,x5,x6, and x7 - individual reactant flows of B and Cx8, x9 and x10 - the three mass product flows (E, F, G)

x11 and x12 - total amounts of A and B and C is the same as x7A total of 12 variables


MODEL DEVELOPMENT


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MODEL DEVELOPMENT

107

106

95

84

103

92

81

65412

32111

333.0

167.0333.0

333.0

5.0

667.0667.0

xx

xxxx

xx

xx

xxxx

xxxxB

xxxxA



a) Linear mass balances:


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MODEL DEVELOPMENT

Suppose that the supply of reactant was limited

000,25000,30

000,40

7

12

11

xx

x

Constraints on production of E, F, and G in order to satisfy marketdemand or sales constraints.

000,30

000,25

000,20

10

9

8

x

x

x

21Copyright reserved Murni MelatiAhmad, UTP


a) Inequalities:


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712111098

1098

71211

1098

025.002.0015.0028.0028.0025.0)(

)/($01.0005.0015.0:costProcessing)/($025.002.0015.0:costmaterialRaw

)/($038.00033.004.0:Income

costprocessingcostmaterialrawincomeprofit)(Maximise

xxxxxxxf

dayxxxdayxxx

dayxxx

xf

Step 3Formulate objective function

FORMULATION



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000,5,000,25,000,20

000,25,000,30,000,40;333.0;167.0;333.0

;333.0;5.0;667.0

;667.0;;

:

025.002.0015.0

028.0028.0025.0)(maximise

:

LPversionfullThe

1098

71211

10710695

8410392

816541232111

71211

1098

xxx

xxxxxxxxx

xxxxxx

xxxxxxxxxx

toSubject

xxx

xxxxf

Objective

LP model for the example problem



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000,5,000,25,000,20

000,25,000,30,000,40

;333.0

;167.0333.0333.0

;5.0667.0667.0

:

025.002.0015.0

028.0028.0025.0)(maximise

:

LPversionreducedThe

1098

71211

107

109812

109811

71211

1098

xxx

xxx

xx

xxxx

xxxx

toSubject

xxx

xxxxf

Objective



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Building Model in Excel & Solving



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RECAP

appreciate the application of optimisation



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REFERENCES

1. Edgar T. F. and Himmelblau, Optimization of Chemical

Processes, McGraw Hill, 2001.2. Biegler, L.T., Grossmann E.I. and Westerberg, A.W.,

Systematic Methods of Chemical Process Design, PrenticeHall, 1997.

3. Lecture notes, MSc Process Integration, UTP-University ofManchester

27Copyright reserved Murni MelatiAhmad UTP

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