Lindo Systems
! Oil refinery model based on:
Aronofsky, J., J. Dutton, and M. Tayyabkhan(1978),
Managerial Planning with Linear Programming: in
Process Industry Applications, John Wiley & Sons;
! There are two main entities: materials and processes.
Each process takes one or more materials and converts
them to one or more other materials in fixed proportions.
In a final step, materials are blended into finished
products in proportions to be determined so as to satisfy
certain quality requirements.
Each process may use resources of limited time availability.
! Keywords: Process industry, refinery, petroleum refining, blending;
SETS:
matl: buy, octanem, vaporpm, densitym, sulfurm;
canbuy(matl): pricep, ur;
fprod: pricef, octanefl, vaporpfu, densityfu, sulfurfu, x;
process: costp, z;
resource: cap;
rxp(resource, process): uses;
! cxm(crude,matl): ur, octanem, vaporpm, densitym, sulfurm, ;
mxp(matl,process): rate;
mxf(matl,fprod): w;
ENDSETS
! Variables:
buy(m) = barrels(bbl) purchased of material type m,
z(p) = units of process p run,
w(m, cf) = bbl of material m blended into finished product cf,
x(cf) = bbl blended and sold of finished product cf,
Parameters:
rate(m,p) = bbl of material m produced per unit of process p.
Negative means input or used;
DATA:
! These data model a refinery that can process two crude oil
types: Mid-continent and West-Texas.
Crude is first processed through an atmospheric distiller, where
the crude is split into(light to heavy): fuel gas, naptha, gasoline,
light distillate, heavy distillate(gas-oil), and residual bottoms.
Naptha can be further processed through a reformer to produce:
fuel gas and reformed gasoline.
Distillate can be processed through the cracker to produce:
fuel gas and cracked gasoline.
Gas-oil can be processed through the cracker to produce:
fuel gas and cracked gasoline.
Residual can be processed through the hydro treater to produce
hydro treated residual that has lower sulfur content.
In the final step, the various materials can be blended into
premium gasoline, regular gasoline, distillate, and fuel oil
so as to satisfy quality requirements on octane, vapor pressure,
density, and sulfur content. Fuel gas is sold directly without
blending.
Butane may be bought to blend into gasoline to increase octane;
! Here are all the material types, excluding finished products;
matl = mccrude mcsrgas mcsrnap mcsrdist mcsrgasoil mcsresid
mcgasrf mcfuelgas mccgas mccgasoil
wtcrude wtsrgas wtsrnap wtsrdist wtsrgasoil wtsresid
wtgasrf wtfuelgas wtcgas wtcgasoil, wthyres
butane;
!The quality features of the above materials;
octanem = 0 78.5 65 0 0 0
104 0 93.7 0
0 78.5 65 0 0 0
104 0 93.7 0 0
91.8;
vaporpm = 0 18.4 6.54 0 0 0
2.57 0 6.9 0
0 18.4 6.54 0 0 0
2.57 0 6.9 0 0
199.2;
densitym= 0 0 272 292 295 343
0 0 0 294.4
0 0 272 297.6 303.3 365
0 0 0 299.1 365
0;
sulfurm = 0 0 .283 .526 .980 4.7
0 0 0 .353
0 0 1.48 2.83 5.05 11
0 0 0 1.31 6
0;
! (Subset of) Materials we can buy from outside:
Mid-continent and West-texas crude + butane;
canbuy = mccrude wtcrude butane;
! Availabilities of materials we can buy;
ur = 200 200 9999;
pricep= 7.50 6.50 6.75;
! The finished products to be blended, prices, and
quality requirements;
fprod = gasprm gasreg distlt fueloil fuelgas;
pricef = 10.50 9.10 7.70 6.65 1.50;
octanefl = 90 86 0 0 0;
vaporpfu = 12.7 12.7 999 999 999;
densityfu= 999 999 306 352 999;
sulfurfu= 999 999 0.5 3.5 999;
! The processes that convert materials;
process = mcadist mcnreform mccrackd mccrackg
wtadist wtnreform wtcrackd wtcrackg wthydro;
costp = .10 .15 .08 .08
.10 .15 .08 .08 .10;
! Here we describe the various processing of materials,
what the process uses(-) and what it produces(+);
mxp, rate=
! Mid continent crude thru the distiller;
mccrude mcadist, -1.0
mcsrgas mcadist, .236
mcsrnap mcadist, .223
mcsrdist mcadist, .087
mcsrgasoil mcadist, .111
mcsresid mcadist, .315
mcfuelgas mcadist, .029
! West Texas crude thru the distiller;
wtcrude wtadist, -1.0
wtsrgas wtadist, .180
wtsrnap wtadist, .196
wtsrdist wtadist, .073
wtsrgasoil wtadist, .091
wtsresid wtadist, .443
wtfuelgas wtadist, .017
! Mid continent based material thru naptha reformer;
mcsrnap mcnreform, -1.0
mcgasrf mcnreform, .807
mcfuelgas mcnreform, .129
! West Texas based material thru naptha reformer;
wtsrnap wtnreform, -1.0
wtgasrf wtnreform, .836
wtfuelgas wtnreform, .099
! Mid continent based distillate thru catalytic cracker;
mcsrdist mccrackd, -1.0
mcfuelgas mccrackd, .300
mccgas mccrackd, .590
mccgasoil mccrackd, .210
! West Texas based distillate thru catalytic cracker;
wtsrdist wtcrackd, -1.0
wtfuelgas wtcrackd, .360
wtcgas wtcrackd, .580
wtcgasoil wtcrackd, .150
! Mid continent based gas-oil thru catalytic cracker;
mcsrgasoil mccrackg, -1.0
mcfuelgas mccrackg, .310
mccgas mccrackg, .590
mccgasoil mccrackg, .220
! West Texas based gas-oil thru catalytic cracker;
wtsrgasoil wtcrackg, -1.0
wtfuelgas wtcrackg, .380
wtcgas wtcrackg, .600
wtcgasoil wtcrackg, .150
! West Texas based material thru hydro treater;
wtsresid wthydro, -1.0
wthyres wthydro, .970;
resource = atmstill reformer cracker;
cap = 100 20 30;
! Which process uses which resource;
rxp, uses =
atmstill, mcadist 1
reformer, mcnreform 1
cracker, mccrackd 1
cracker, mccrackg 1
atmstill, wtadist 1
reformer, wtnreform 1
cracker, wtcrackd 1
cracker, wtcrackg 1;
! Which materials can be used in which finished products;
mxf = butane, gasprm
mcsrgas,gasprm
mccgas, gasprm
mcsrnap,gasprm
mcgasrf,gasprm
wtsrgas,gasprm
wtcgas, gasprm
wtsrnap,gasprm
wtgasrf,gasprm
butane, gasreg
mcsrgas,gasreg
mccgas, gasreg
mcsrnap,gasreg
mcgasrf,gasreg
wtsrgas,gasreg
wtcgas, gasreg
wtsrnap,gasreg
wtgasrf,gasreg
mcsrdist, distlt
mcsrnap, distlt
mcsrgasoil,distlt
mccgasoil, distlt
wtsrdist, distlt
wtsrnap, distlt
wtsrgasoil,distlt
wtcgasoil, distlt
mcsrgasoil,fueloil
mcsresid, fueloil
mccgasoil, fueloil
wtsrgasoil,fueloil
wtsresid, fueloil
wtcgasoil, fueloil
wthyres, fueloil
mcfuelgas, fuelgas
wtfuelgas, fuelgas;
ENDDATA
! Maximize profit;
max = revenue - pcost - ocost;
! Compute cost of raw materials purchased;
pcost = @sum(canbuy(m): pricep(m)*buy(m));
! Operating cost of the processes;
ocost = @sum(process(p): costp(p)*z(p));
! Revenues;
revenue = @sum(fprod(f): pricef(f)*x(f));
! Cannot buy more of each material than is available;
@for(canbuy(m):
[buylim] buy(m) <= ur(m)
);
@for(matl(m) | #NOT# @in(canbuy, m):
[buylm0] buy(m) = 0
);
! For each material type m
sources >= uses, i.e. amount bought
+ net from processes >= amount to finished products;
@for( matl(m):
[mtlbal] buy(m) + @sum(mxp(m,p): rate(m,p)*z(p)) >=
@sum(mxf(m,cf): w(m,cf));
);
! For each resource, cannot use it more than it
has time available;
@for(resource(r):
[rcap] @sum(rxp(r,p): uses(r,p)*z(p)) <= cap(r);
);
! Blending step;
! For each finished good, sources = uses;
@for(fprod(cf):
[fpbal] @sum(mxf(m,cf): w(m, cf)) = x(cf)
);
! For each finished good, must meet quality requirements;
@for(fprod(cf):
[octlim] @sum(mxf(m,cf): octanem(m) *w(m, cf)) >= octanefl(cf) *x(cf);
[vaplim] @sum(mxf(m,cf): vaporpm(m) *w(m, cf)) <= vaporpfu(cf) *x(cf);
[denlim] @sum(mxf(m,cf): densitym(m)*w(m, cf)) <= densityfu(cf)*x(cf);
[slflim] @sum(mxf(m,cf): sulfurm(m) *w(m, cf)) <= sulfurfu(cf) *x(cf);
);