reaction.gms : Logical Inference for Reaction path synthesis
Given a set of possible chemical reactions, we must verify
whether a chemical can be synthesized from a given set of
raw materials and catalysts.
References:
- Morari, M, and Grossmann, I E, Eds, Chemical Engineering Optimization Models with GAMS. Computer Aids for Chemical Engineering Corporation, 1991.
- Raman, R, and Grossmann, I E, Relation between MINLP Modeling and Logical Inverence for Chemical Process Synthesis. Computers and Chemical Engineering 15, 2 (1991), 73-84.
Small Model of Type: MIP
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$Title Logical Inference for Reaction Path Synthesis (REACTION,SEQ=121)
$Ontext
Given a set of possible chemical reactions, we must verify
whether a chemical can be synthesized from a given set of
raw materials and catalysts.
Morari, M, and Grossmann, I E, Eds, Chemical Engineering Optimization
Models with GAMS. Computer Aids for Chemical Engineering Corporation,
1991.
Raman, R, and Grossmann, I E, Relation between MINLP Modeling and
Logical Inverence for Chemical Process Synthesis. Computers and
Chemical Engineering 15, 2 (1991), 73-84.
$Offtext
Sets v system variables (chemicals) /
y01 ch3co2c2h5
y02 naoc2h5
y03 c2h5oh
y04 ch3coch2co2c2h5
y05 h3o-hydronium ion
y06 ch3coch3
y07 co2
y08 ch3cn
y09 ch3mgi
y10 c2h5oc2h5
y11 ch3c(nmgi)ch3
y12 h2o
y13 hcl
y14 ch3cho
y15 ch3ch(oh)ch3
y16 cro3
y17 h2so4
y18 ch2=c(ch3)2
y19 o3
y20 hco2h
y21 ch3i
y22 mg
y23 ch3co2ch3
y24 hoc(ch3)3
y25 ch4
y26 i2
y27 hi
y28 o2
y29 cr2o3
y30 ch3cl
y31 nacn
y32 nacl
y33 cl2
y34 ch3cooh /
rx logical conditions / rxn01 * rxn22 /
Alias (v,vv)
Set logic(rx,v,vv) mathematical representation of chemical reactions /
rxn01.y04.(y01,y02,y03)
rxn02.y06.(y04,y05)
rxn03.y07.(y04,y05)
rxn04.y03.(y04,y05)
rxn05.y11.(y08,y09,y10)
rxn06.y06.(y11,y12,y13)
rxn07.y15.(y14,y09,y10,y05)
rxn08.y06.(y15,y16,y17)
rxn09.y06.(y18,y19,y12)
rxn10.y20.(y18,y19,y12)
rxn11.y09.(y21,y22)
rxn12.y24.(y09,y23)
rxn13.y18.(y24,y17)
rxn14.y21.(y25,y26)
rxn15.y27.(y25,y26)
rxn16.y14.(y03,y28,y29)
rxn17.y32.(y30,y31,y12)
rxn18.y08.(y30,y31,y12)
rxn19.y30.(y25,y33)
rxn20.y13.(y25,y33)
rxn21.y01.(y34,y03)
rxn22.y34.(y14,y28) /
rxv(rx,v) rx to v mapping;
rxv(rx,v) = sum(vv, logic(rx,v,vv));
Binary Variable y(v); variable totsum
Equations obj minimize y06 to determine if acetone can be produced
leq(rx,v) logic constraints ;
obj.. totsum =e= y('y06') ;
leq(rxv(rx,v)).. sum(logic(rxv,vv), 1 - y(vv)) =g= 1 - y(v);
Sets yavail(v) available raw materials and catalysts /
y02,y03,y05,y10,y12,y13,y17,y22,y25,y26,y28,y31,y33 /
ynotavail(v) raw materials and catalysts not available /
y16,y19 /;
y.fx(yavail) = 1;
y.fx(ynotavail) = 0;
Model rulebase / all /;
Solve rulebase minimizing totsum using mip;
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