gasoil.gms : Catalytic cracking of gas oil COPS 2.0 #12

**Description**

Determine the reaction coefficients for the catalytic cracking of gas oil into gas and other byproducts. This model is from the COPS benchmarking suite. See http://www-unix.mcs.anl.gov/~more/cops/. The number of discretization points can be specified using the command line parameter --nh. COPS performance tests have been reported for nh = 50, 100, 200, 400

**References**

- Dolan, E D, and More, J J, Benchmarking Optimization Software with COPS. Tech. rep., Mathematics and Computer Science Division, 2000.
- Tjoa, I B, and Biegler, L T, Simultaneous Solution and Optimization Strategies for Parameter Estimation of Differential-Algebraic Equations Systems. Industrial and Engineering Chemistry Research 30, 2 (1991), 376-385.
- Averick, B M, Carter, R G, More, J J, and Xue, G L, The MINPACK-2 Test Problem Collection. Tech. rep., Mathematics and Computer Science Division, Argonne National Laboratory, 1992.
- Ascher, U M, Mattheij, R M M, and Russell, R D, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM, 1995.

**Large Model of Type :** NLP

**Category :** GAMS Model library

**Main file :** gasoil.gms **includes :** copspart.inc

```
$title Catalytic Cracking of Gas Oil COPS 2.0 #12 (GASOIL,SEQ=240)
$onText
Determine the reaction coefficients for the catalytic cracking of gas
oil into gas and other byproducts.
This model is from the COPS benchmarking suite.
See http://www-unix.mcs.anl.gov/~more/cops/.
The number of discretization points can be specified using the command
line parameter --nh. COPS performance tests have been reported for nh
= 50, 100, 200, 400
Dolan, E D, and More, J J, Benchmarking Optimization
Software with COPS. Tech. rep., Mathematics and Computer
Science Division, 2000.
Tjoa, I B, and Biegler, L T, Simultaneous Solution and
Optimization Strategies for Parameter Estimation of
Differential-Algebraic Equations Systems. Ind. Eng. Chem.
Res. 30 (1991), 376-385.
Averick, B M, Carter, R G, More, J J, and Xue, G L, The
MINPACK-2 Test Problem Collection. Tech. rep., Mathematics
and Computer Science Division, Argonne National
Laboratory, 1992.
Ascher, U M, Mattheij, R M M, and Russell, R D, Numerical
Solution of Boundary Value Problems for Ordinary
Differential Equations. SIAM, 1995.
Keywords: nonlinear programming, chemical engineering, catalytic cracking
$offText
$if not set nh $set nh 50
Set
ne 'differential equations' / ne1*ne2 /
np 'ODE parameters' / np1*np3 /
nc 'collocation points' / nc1*nc4 /
nh 'partition intervals' / nh1*nh%nh% /
nm 'measurements' / 1*21 /;
Parameter
bc(ne) 'ODE initial conditions' / ne1 1, ne2 0 /
tau(nm) 'times at which observations made'
/ 1 0.000, 2 0.025, 3 0.050, 4 0.075, 5 0.100, 6 0.125
7 0.150, 8 0.175, 9 0.200, 10 0.225, 11 0.250, 12 0.300
13 0.350, 14 0.400, 15 0.450, 16 0.500, 17 0.550, 18 0.650
19 0.750, 20 0.850, 21 0.950 /;
Table z(nm,ne) 'observation'
ne1 ne2
1 1.0000 0
2 0.8105 0.2000
3 0.6208 0.2886
4 0.5258 0.3010
5 0.4345 0.3215
6 0.3903 0.3123
7 0.3342 0.2716
8 0.3034 0.2551
9 0.2735 0.2258
10 0.2405 0.1959
11 0.2283 0.1789
12 0.2071 0.1457
13 0.1669 0.1198
14 0.1530 0.0909
15 0.1339 0.0719
16 0.1265 0.0561
17 0.1200 0.0460
18 0.0990 0.0280
19 0.0870 0.0190
20 0.0770 0.0140
21 0.0690 0.0100;
$batInclude copspart.inc nc4 21
Positive Variable theta(np) 'ODE parameters';
Equation
collocation_eqn1(nh,nc)
collocation_eqn2(nh,nc);
collocation_eqn1(i,j)..
Duc[i,j,'ne1'] =e= - (theta['np1'] + theta['np3'])*sqr(uc[i,j,'ne1']);
collocation_eqn2(i,j)..
Duc[i,j,'ne2'] =e= theta['np1']*sqr(uc[i,j,'ne1']) - theta['np2']*uc[i,j,'ne2'];
v.fx['nh1',s] = bc(s);
Model gasoil / all /;
$if set workSpace gasoil.workSpace = %workSpace%
solve gasoil minimizing obj using nlp;
```