alkyl.gms : Simplified Alkylation Process
This model describes a simplified alkylation process. Note the
modeling of error bounds on the estimated equations. This formulation
is very efficient in terms of problem comprehension and solution. The
additional nonlinearities are bounded in a narrow range and
introduce no additional computational burden.
Reference:
- Berna, T, Locke, M, and Westerberg, A W, A New Approach to Optimization of Chemical Processes. American Institute of Chemical Engineers Journal 26, 1 (1980), 37-43.
Small Model of Type: NLP
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$title Simplified Alkylation Process (ALKYL,SEQ=165)
$Ontext
This model describes a simplified alkylation process. Note the
modeling of error bounds on the estimated equations. This formulation
is very efficient in terms of problem comprehension and solution. The
additional nonlinearities are bounded in a narrow range and
introduce no additional computational burden.
Berna, T, Locke, M, and Westerberg, A, Simplified Alkyaltion Process.
AIChE Journal 26 (1980), 37.
$Offtext
variables
F Objective variable
OlefinFeed Olefins Feed
IsobutRec Isobutane Recycle
AcidFeed Acid Feed
AlkylYld Alkylate Yield
IsobutMak Isobutane Makeup
AcidStren Acid Strength
Octane Octane Number
Ratio iC4 olefin Ratio
AcidDilut Acid Dilution Factor
F4Perf F4 Performance Number
alkerr, octerr, aciderr, F4err;
equations
Objective Objective Function
AlkylShrnk Alkylate Volumetric Shrinkage Equation
AcidBal Acid Material Balance
IsobutBal Isobutane Component Balance
AlkylDef, OctDef, AcidDef, F4Def;
Objective.. F =e= - 6.3*AlkylYld*Octane + 5.04*OlefinFeed + 0.35*IsobutRec
+ AcidFeed + 3.36*IsobutMak;
AlkylShrnk.. AlkylYld =e= (OlefinFeed+IsobutMak)/1.22;
AcidBal.. 0.98*AcidFeed =e= AcidStren*((AlkylYld*AcidDilut)/100.0+AcidFeed);
IsoButBal.. 10.0*IsobutRec + IsobutMak =e= OlefinFeed*Ratio;
AlkylDef.. AlkylYld*AlkErr =e= OlefinFeed*(1.12+0.13167*Ratio-0.0067*Ratio*Ratio);
OctDef.. Octane*OctErr =e= 0.8635+(1.098*Ratio-0.038*Ratio*Ratio)/100 + 0.325*(AcidStren-0.89);
AcidDef.. AcidDilut*AcidErr =e= 35.82-22.2*F4Perf;
F4Def.. F4Perf*F4Err =e= -1.33+3*Octane;
alkerr.lo = .99; alkerr.up = 1/.99; alkerr.l = 1;
octerr.lo = .99; octerr.up = 1/.99; octerr.l = 1;
aciderr.lo = .90; aciderr.up = 1/.90; aciderr.l = 1;
F4err.lo = .99; F4err.up = 1/.99; F4err.l = 1;
F.L = -0.90;
OlefinFeed.lo = 0; OlefinFeed.up = 2.00; OlefinFeed.l = 1.745;
IsobutRec.lo = 0; IsobutRec.up = 1.60; IsobutRec.l = 1.2;
AcidFeed.lo = 0; AcidFeed.up = 1.20; AcidFeed.l = 1.10;
AlkylYld.lo = 0; AlkylYld.up = 5.00; AlkylYld.l = 3.048;
IsobutMak.lo = 0; IsobutMak.up = 2.00; IsobutMak.l = 1.974;
AcidStren.lo = 0.85; AcidStren.up = 0.93; AcidStren.l = 0.893;
Octane.lo = 0.90; Octane.up = 0.95; Octane.l = 0.928;
Ratio.lo = 3; Ratio.up = 12; Ratio.l = 8;
AcidDilut.lo = 1.2; AcidDilut.up = 4; AcidDilut.l = 3.6;
F4Perf.lo = 1.45; F4Perf.up = 1.62; F4Perf.l = 1.45;
model m /all/;
$ONTEXT optimal solutions
OlefinFeed.fx = 1.70368 ;
IsobutRec.fx = 1.58449 ;
AcidFeed.fx = .543165;
AlkylYld.fx = 3.03581 ;
IsobutMak.fx = 2.0 ;
AcidStren.fx = .90133 ;
Octane.fx = .950 ;
Ratio.fx = 10.4743 ;
AcidDilut.fx = 1.56164 ;
F4Perf.fx = 1.53535 ;
m.holdfixed=1;
$OFFTEXT
solve m using nlp minimizing f;
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