View source for Semibatch esterification problem (TACO)

This page contains a model of the [[Semibatch esterification problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. 
The original model is due to <bib id="Kuehl2005" /> and <bib id="Milewska2006" />.
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

=== AMPL ===

This is the source file semibatch_taco.mod
<source lang="AMPL">
# ----------------------------------------------------------------
# Semibatch esterification problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
# ----------------------------------------------------------------
include OptimalControl.mod;

var t;

# propionic anhydride (species A, sd0) [mol]
var nA := 0.0, >= 0.0, <= 10.0;

# 2-butanol (species B, sd1) [mol]
var nB := 6.893955747436589, >= 0.0, <= 10.0 suffix scale 10.0;

# propionic acid (species C, sd2) [mol]
var nC := 0.0, >= 0.0, <= 10.0;

# reactor temperature change (sd3) [K]
var Tr := 0.0, >= -23.0, <= 30.0 suffix scale 10.0;

# accumulated dosing of propionic anhydride [mol]
var nK1 := 0.0, >= 0.0, <= 7.0 suffix scale 5.0;

# theoretical adiabatic temperature rise (DAE state) [degrees Celsius]
var xA := 293.15, >= 270.15, <= 363.15 suffix type "dae" suffix scale 300.0;

# dosing feed [kg/s]
var dF := 0.0002472, >= 0.0, <= 0.0005 suffix type "u0" suffix scale 1.0e-2;

# dosing temperature [K]
var Tdos := 298.15, >= 298.15, <= 298.15 suffix type "u0" suffix scale 100.0;

# ambient temperature [K]
var Tamb := 298.15, >= 298.15, <= 298.15 suffix type "u0" suffix scale 100.0;

# jacket temperature change [K]
var dTj := 0.0, >= 0.0, <= 0.0 suffix type "u0";

param TJ    := 313.15;
param Tr_sp := 313.15;
param MA    :=   0.13014;
param MB    :=   0.07412;
param MC    :=   0.07408;
param MD    :=   0.13011;
param U1    := 195; 
param U2    := 155;
param V1u   :=   0.8;
param V2u   :=   1.6;
param nS0   :=   5.01/98.08;
param N1    :=   1.58;
param N2    :=   0.76;
param EA    :=   9.14E+4;
param A1    :=   9.35E+10;
param A2    :=   9.22E+10;
param A3    :=   9.78E+10;
param R     :=   8.314;
param V1    :=   1;
param V2    :=   2;
param CpI1  := 117.3;
param CpI2  := 198.4;
param Amin  :=   0.0113;
param Vmin  :=   0.124;
param d     :=   0.155;
param alpha :=   0.1;
param HA    := 59458;

var Tr_   = Tr + Tr_sp;
var dens0 = 1000*0.13014/(0.46199*0.2166^((1-Tr_/630.0)^0.2857));
var dens1 = 1000*0.07412/(0.3199 *0.2088^((1-Tr_/536.01)^0.2857));
var dens2 = 1000*0.07408/(0.2848 *0.1993^((1-Tr_/611.0)^0.2857));
var dens3 = 1000*0.13011/(0.5078 *0.2265^((1-Tr_/578.01)^0.2857));
var V     = (nA*MA/dens0 + nB*MB/dens1 + nC*MC/dens2 + nC*MD/dens3) * 1000;
var Ua    = U1 + (U2-U1)/(V2u-V1u)*(V-V1u);
var xA_   = nA/(nA+nB+2*nC+nS0);
var r     = ( A1*exp(-EA/(R*Tr_)) + A2*exp(-EA/(R*Tr_)) 
          * (nC/V)^N1 + A3*exp(-EA/(R*Tr_)) * (nS0/V)^N2 ) * (nA/V) * (nB/V);
var Cpi   = CpI1 + (CpI2 - CpI1)/(V2-V1) * (V-V1);
var Area  = (Amin + 4*(V-Vmin)/(1000*d));
var cp0   = 683.7305 - 3.7009 * Tr_ + 9.6E-3 * Tr_^2 - 7.458E-6 * Tr_^3;
var cp1   = 242.5725 - 2.3128 * Tr_ + 1.07E-2 * Tr_^2 - 1.159E-5 * Tr_^3;
var cp2   =  94.8369 - 0.2432 * Tr_ + 2.2E-3 * Tr_^2 - 2.51E-6 * Tr_^3;
var cp3   = 206.162  + 0.1994689 * Tr_ - 3.55512E-4 * Tr_^2 - 1.03625E-6 * Tr_^3;
var cpm   = nA*cp0 + nB*cp1 + nC*cp2 + nC*cp3;
var qdil  = -(-2232.74201/0.13963 * exp(-xA_/0.13963)) * (dF/MA-r*V);

minimize Tracking: 
	integral (nB^2,3600) suffix scale 1.0E+3;

subject to 

ODE_nA:  diff(nA,t) = dF/MA - r*V;
ODE_nB:  diff(nB,t) = -r*V;
ODE_nC:	 diff(nC,t) = r*V;
ODE_Tr:  diff(Tr,t) = ( r*HA*V - qdil - Ua*Area*(Tr_-(TJ+dTj)) 
                        - alpha*(Tr_-Tamb) - dF/MA*cp0*(Tr_-Tdos) ) / (Cpi+cpm);
ODE_nK1: diff(nK1,t) = dF/MA;

DAE_xA: 0 = xA - (Tr_ + nA * 1000 * HA/(cpm * V * 900));

IC_nA:  eval(nA,0) = 0;
IC_nB:  eval(nB,0) = 6.893955747436589;
IC_nC:  eval(nC,0) = 0;
IC_Tr:  eval(Tr,0) = 0;
IC_nK1: eval(nK1,0) = 0;

option solver ...;

solve;

</source>

== Other Descriptions ==

Other descriptions of this problem are available in

* Mathematical notation at [[Semibatch esterification problem]]
 
== References ==
<biblist />

[[Category:AMPL/TACO]]