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fawley.gms : Platoform Example Refinery

This simple example refinery is taken from EXXONs Platoform monograph.
Three major units, a pipestill, a powerformer and a catalytic cracker
are present. the refinery has a choice of three crude oils and sells
four final products. The blending is done by recipe and quality
specifications. All product flows are measured by weight. the original
Platoform version does not give values for the research octane and
viscosity blending formulas because of its proprietary nature. A simple
functional form has been estimated from the Platoform results for
illustrative purposes and the lower specification of "ron" for motor-gas
had to be lowered from 99.3 to 99.0 in order to maintain feasibility.
Reference:
Small Model of Type: LP
$Title Platoform Example Refinery (FAWLEY,SEQ=65) $Ontext This simple example refinery is taken from EXXONs Platoform monograph. Three major units, a pipestill, a powerformer and a catalytic cracker are present. the refinery has a choice of three crude oils and sells four final products. The blending is done by recipe and quality specifications. All product flows are measured by weight. the original Platoform version does not give values for the research octane and viscosity blending formulas because of its proprietary nature. A simple functional form has been estimated from the Platoform results for illustrative purposes and the lower specification of "ron" for motor-gas had to be lowered from 99.3 to 99.0 in order to maintain feasibility. Palmer, K H, A Model Management Framework for Mathematical Programming, EXXON Monograph Series. John Wiley and Sons, 1984. $Offtext Sets c commodities / arabian-l crude arabian-h crude brega crude lv-naphtha light virgin naphtha v-heat-oil virgin heating oil iv-naphtha intermediate virgin naphtha vacuum-dst vacuum distillate vacuum-res vacuum residue res-arab-l vacuum residue - arabian light res-arab-h vacuum residue - arabian heavy res-brega vacuum residue - brega butane reformate cc-naph-l catalytic-cracked naphtha - low severity cc-naph-h catalytic-cracked npahtha - high severity cc-dist catalytic-cracked distillate fuel-imp imported fuel fuel-equiv fuel equivalent / cr(c) crude oils / arabian-l, arabian-h, brega / ci(c) components imported / fuel-imp / cf final products / motor-gas motor gasoline jet-fuel jet fuel heat-oil heating oil fuel-oil fuel oil / cfq(cf) final products quality blended cfr(cf) final products recipe blended k productive units / pipestill, reformer, c-cracker / p processes / d-arab-l distilling arabian light crude d-arab-h distilling arabian heavy crude d-brega distilling brega crude reform reforming ho-low-s cc of heating oil - low severity ho-high-s cc of heating oil - high severity vd-low-s cc of vacuum distillate - low severity vd-high-s cc of vacuum distillate - high severity / kuse(k,p) / pipestill .(d-arab-l,d-arab-h,d-brega) reformer .(reform) c-cracker .(ho-low-s,ho-high-s,vd-low-s,vd-high-s) / bposs(cf,c) blending possibilities for quality blends / motor-gas.(lv-naphtha,butane,reformate,cc-naph-l,cc-naph-h) fuel-oil.(v-heat-oil,vacuum-dst,res-arab-l,res-arab-h,res-brega,cc-dist fuel-equiv,fuel-imp) / s product specification / rvp reid vapor pressure ron research octane number pct-212f percent distilled at 21 degrees f sulfur sulfur content vbn viscosity blending number / m product measure / volume, weight / ms(m,s) measure of specs / volume.(rvp, ron, pct-212f), weight.(sulfur, vbn) / cfm(cf,m) required measure l quality limits / lower, upper / r recipes / recipe-1*recipe-3 / tr transfer options / tr-1, tr-2 / Table crdat(cr,*) crude oil information table supply price transport gravity * (1000 tons) ($/bbl) ($/ton) (tons/m3) arabian-l 110 35 24.15 .858 arabian-h 165 34 24.15 .886 brega 80 42 10.05 .823 Table ddat(cf,*) demand data demand price * (1000 tons) ($/ton) motor-gas 40 430 jet-fuel 20 300 heat-oil 50 315 fuel-oil 145 250 Table kdat(k,*) capacity data capacity oper-cost oper-days * (1000bbl/d) ($/bbl f) (days/period) pipestill 65.0 .15 31 reformer 7.5 .60 28 c-cracker 8.0 .65 28 Table ap(c,p) process yields (proportion weight of crude feed) d-arab-l d-arab-h d-brega arabian-l -1.0 arabian-h -1.0 brega -1.0 lv-naphtha .035 .030 .045 iv-naphtha .100 .075 .135 v-heat-oil .390 .300 .430 vacuum-dst .285 .230 .280 res-arab-l .165 res-arab-h .335 res-brega .100 + reform ho-low-s ho-high-s vd-low-s vd-high-s iv-naphtha -1. v-heat-oil -1. -1. vacuum-dst -1. -1. butane .02 .02 .0325 .05 .06 reformate .90 cc-naph-l .275 .325 cc-naph-h .3775 .45 cc-dist .68 .555 .585 .44 fuel-equiv .08 .025 .035 .040 .050 Table recipes(cf,c,r) blending recipes (proportions of weight) recipe-1 recipe-2 recipe-3 heat-oil.v-heat-oil 1.0 heat-oil.cc-dist 1.0 jet-fuel.lv-naphtha .2 jet-fuel.iv-naphtha .3 .1 jet-fuel.v-heat-oil .7 .8 .1 jet-fuel.cc-dist .8 Table at(c,tr) transfer processes (proportion of weight) tr-1 tr-2 lv-naphtha -1 butane -1 fuel-equiv 1.11 1.07 Table specs(cf,l,s) product specifications for quality blend rvp ron pct-212f sulfur vbn motor-gas.lower 10 99 motor-gas.upper 60 fuel-oil.upper 3 37.5 Table prop(c,*) properties rvp ron pct-212f sulfur vbn gravity butane 75 101.6 100 .570 lv-naphtha 12 86.3 95 .650 iv-naphtha .737 reformate 6 102.5 35 .865 cc-naph-l 7 94.9 60 .730 cc-naph-h 9 99.1 64 .750 v-heat-oil 1.0 14.8 .886 vacuum-dst 1.7 21.8 .920 res-arab-l 4.0 48 res-arab-h 5.0 51 res-brega .6 44 cc-dist 1.5 18.0 fuel-imp 3.0 37.5 fuel-equiv 3.5 44 Scalars m3tob conversion of barrels to m3 (barrels per m3) / 6.29 / pbmg lead content in motor gas (gramms per liter) / .4 / ppb lead price ($ per kg) / 7.8 / ocpb lead cost ($ per m3 of gasoline) Parameters char(c,m) conversion for product balance bp(k,p) capacity utilization (m3 per ton) kp(k) capacity (1000 m3) oc(k) operating costs ($ per m3) pcr(cr) plantgate crude price ($ per ton) pimp(c) price of imported components ($ per ton) / fuel-imp 245 / invent(c) inventory change (1000 tons - buildup positive) / cc-naph-l -.58, reformate 1.65 / dir(l) sign of over-under specs / lower -1, upper +1 / ; cfr(cf) = sum((c,r)$recipes(cf,c,r), yes); cfq(cf) = not cfr(cf); cfm(cf,m) = sum((l,s)$specs(cf,l,s), ms(m,s)); cfm(cf,"weight") = yes; char(c,"weight") = 1 ; char(c,"volume")$prop(c,"gravity") = 1/prop(c,"gravity"); prop(cr,"gravity") = crdat(cr,"gravity"); bp(k,p)$kuse(k,p) = 1/sum(c$(ap(c,p) lt 0), -ap(c,p)*prop(c,"gravity")); kp(k) = kdat(k,"capacity")*kdat(k,"oper-days")/m3tob; ocpb = pbmg*ppb; oc(k) = kdat(k,"oper-cost")*m3tob ; pcr(cr) = crdat(cr,"price")*m3tob/crdat(cr,"gravity"); Display cfr, cfq, cfm, char, bp, kp, oc, ocpb, pcr; Variables u(c) crude purchase (1000 tons) z(p) production levels (1000 tons) cap(k) capacity use (1000 m3) trans(tr) transfer activities (1000 tons) import(c) import of components (1000 tons) bq(c,cf) quality blending activity (1000 tons) rb(cf,r) recipe blending activity (1000 tons) q(cf,m) final product measure (1000 tons) ov(cf,l,s) over or under blending (1000 units) sales(cf) final product sales (1000 tons) revenue final product revenue (1000 $) recurrent operating cost (1000 $) purchase external product purchase (1000 $) transport transport cost (1000 $) profit operating profit (1000 $) Positive Variables u, cap, z, bq, rb, q, sales, ov, trans, import Equations mbal(c) component balance (1000 tons) kbal(k) capacity constraints (1000 m3) dbal(cf) demand balance (1000 tons) qsb(cf,l,s) quality constraint (1000 units) pbal(cf,m) product balance (1000 units) drev revenue definition (1000 $) doper recurrent cost definition (1000 $) dpur purchase cost definition (1000 $) dtran transport cost definition (1000 $) dprof profit definition (1000 $); mbal(c).. u(c)$cr(c) + sum(p, ap(c,p)*z(p)) + sum(tr, at(c,tr)*trans(tr)) + import(c)$ci(c) =e= sum(cfq$bposs(cfq,c), bq(c,cfq)) + invent(c) + sum((cfr,r), recipes(cfr,c,r)*rb(cfr,r)) ; kbal(k).. cap(k) =e= sum(p, bp(k,p)*z(p)); dbal(cf).. sales(cf) =e= q(cf,"weight")$cfq(cf) + sum((c,r), recipes(cf,c,r)*rb(cf,r))$cfr(cf) ; qsb(cfq,l,s)$specs(cfq,l,s).. sum(c$bposs(cfq,c), prop(c,s)*sum(m$ms(m,s), char(c,m)*bq(c,cfq))) + dir(l)*ov(cfq,l,s) =e= sum(m$ms(m,s), specs(cfq,l,s)*q(cfq,m)) ; pbal(cfq,m)$cfm(cfq,m).. q(cfq,m) =e= sum(c$bposs(cfq,c), char(c,m)*bq(c,cfq)); drev.. revenue =e= sum(cf, ddat(cf,"price")*sales(cf)); doper.. recurrent =e= sum(k, oc(k)*cap(k)) + ocpb*q("motor-gas","volume"); dpur.. purchase =e= sum(cr, pcr(cr)*u(cr)) + sum(ci, pimp(ci)*import(ci)) ; dtran.. transport =e= sum(cr, crdat(cr,"transport")*u(cr)); dprof.. profit =e= revenue - recurrent - purchase - transport; Model exxon /all/; u.up(cr) = crdat(cr,"supply"); sales.fx(cf) = ddat(cf,"demand"); cap.up(k) = kp(k); Solve exxon maximizing profit using lp; Parameter fblend summary of blending operation for fuel oil; fblend(c,"weight") = bq.l(c,"fuel-oil"); fblend("**total**","weight") =q.l("fuel-oil","weight"); fblend(c,"percent") = fblend(c,"weight")/fblend("**total**","weight")*100; fblend("**total**","percent") = 100; fblend(c,"sulfur")$bposs("fuel-oil",c) = prop(c,"sulfur") ; fblend("**total**","sulfur") = sum(c, fblend(c,"percent")*fblend(c,"sulfur"))/100; fblend(c,"vbn")$bposs("fuel-oil",c) = prop(c,"vbn"); fblend("**total**","vbn") = sum(c, fblend(c,"percent")*fblend(c,"vbn"))/100; Display fblend;