Structural Optimization of Process Flowsheets
minco
BARON
GAMS
short
| 2 |----->+ |
A | +-----+ | | B1 +-----+ C1
---->| +----+------->| 1 |-------->
| +-----+ | +-----+
+----->| 3 |----->+
A3 +-----+ B3
$Offtext
$Eolcom !
Positive Variables
a2 consumption of chemical a in process 2
a3 consumption of chemical a in process 3
b2 production capacity of chemical b in process 2
b3 production capacity of chemical b in process 3
bp amount of chemical b purchased in external market
b1 consumption of chemical b in process 1
c1 production capacity of chemical c in process 1 ;
Binary Variables
y1 denotes potential existence of process 1
y2 denotes potential existence of process 2
y3 denotes potential existence of process 3 ;
Variable
pr total profit in million $ per year ;
Equations
inout1 input-output for process 1
inout2 input-output for process 2
inout3 input-output for process 3
mbalb mass balance for chemical b
log1 logical constraint for process 1
log2 logical constraint for process 2
log3 logical constraint for process 3
obj profit objective function ;
* the original constraint for inout2 is b2 = log(1+a2)
* but this has been convexified to the form used below.
* the same is true for inout3. so b2 and b3 are the
* output variables from units 2 and 3 respectively
inout1.. c1 =e= 0.9*b1 ;
inout2.. exp(b2) - 1 =e= a2 ;
inout3.. exp(b3/1.2) - 1 =e= a3 ;
mbalb.. b1 =e= b2 + b3 + bp ;
log1.. c1 =l= 2*y1 ;
log2.. b2 =l= 4*y2 ;
log3.. b3 =l= 5*y3 ;
obj.. pr =e= 11*c1 ! sales revenue
- 3.5*y1 - y2 - 1.5*y3 ! fixed investment cost
- b2 - 1.2*b3 ! operating cost
- 1.8*(a2+a3) - 7*bp ; ! purchases
* demand constraint on chemical c based on market requirements
c1.up = 1;
Model process /all/ ;
Solve process maximizing pr using minlp ;
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Structural optimization of process flowsheets with 8 equations,
11 variables (3 discrete), and 26 non-zeroes.