Crude oil scheduling including the pipeline schedule connecting terminals and in-land refineries

Transcription

1 Crude oil scheduling including he pipeline schedule connecing erminals and in-land refineries Frederico S. de Paula, Valéria V. Muraa, Sérgio M. S. Neiro Federal Universiy of Uerlândia - Uerlândia - MG - Brazil frederico.eq@gmail.com, valeria@ufu.r, srgneiro@ufu.r Scheduling involving he crude oil supply is one of he mos challenging prolems in a refinery plan. The crude oil scheduling is of grea imporance o ensure ha disillaion columns operae coninuously and he qualiy of he crude mix always lies wihin desired range o mee operaing consrains and a he same ime guaranee high profiailiy of he process. Across he years, a grea numer of sudies concerning he crude oil scheduling prolem have een proposed in he lieraure. However, ime and logisics involving he crude ransfer eween erminals where he crude oil is unloaded and he in-land refineries is generally negleced in hese works. In he presen work, he pipeline connecing a erminal and an in-land refinery is included in he crude oil scheduling model. Three cases sudies were considered in order o sudy he ehavior of he sysem wih differen infrasrucure, namely: a single shared pipeline eween sorage anks and charging anks, wo shared pipelines eween sorage anks and charging anks. Finally,.a special case was also sudied in which a shor pipeline connecing vessels and sorage anks is also considered o capure he cases where he crude volume reained in ha pipeline canno e negleced. The models resuled in MINLP prolems due o he racking of mixure qualiies hroughou he resources, which were implemened in he GAMS sysem and solved wih decomposiion mehod, which he MILP prolem was solved using CPLEX and RMINLP was solved using CONOPT. For he hree sudied cases, he ojecive funcion was o maximize he gross profi margin. A comparison analysis of he resuls generaed considering insananeous ransfer and he shared pipeline is carried over o show he impac on he opimized soluions. Keyword: scheduling, in-land refinery, pipeline 1 Inroducion Across he years, peroleum indusries has suffered wih new challenges arising, as he compeiiveness increase, sric environmenal rules, price insailiy of crude oils and oil availailiy. Refinery planning opimizaion appeared as a grea soluion o face hese challenges. Refinery scheduling is responsile o deermine he volume of feedsock o e processed and he mix and amoun of produc o e produced over several monhs. Furhermore, scheduling deals wih ime in order o supply he marke and o ypass consrains prolems (CHANDRA PRAKASH REDDY e al., 2004). The oil-refinery scheduling is very complex, due o he grea numer of operaions involved, hus i is common o decompose refineries in hree pars. The firs par consiss on unloading of crude-oil from vessels, mixing and invenory conrol. Second par involves he producion unis, which includes oh fracionaion and reacion process. The hird prolem concerns aou he lending and disriuion of final producs y pipelines. The modeling and soluion of hese hree pars separaely, and he susequen inegraion of hese resuls has shown an effecive way o represen he overall operaion of a refinery. The crude oil cos represens 80% of he udge in a refinery operaion. Using a cheaper crude oil is a good way o reduce cos wih feedsock. However, disillaion unis operae coninuously and also he crude oil feeding hese unis mus e on a specified range of qualiy. Therefore crude oil scheduling has a grea imporance o ensure he operaion of a refinery wih high profiailiy. A large numer of sudies on he field of he crude oil scheduling have een proposed on he lieraure. The firs one was developed y Lee e al. (1996), which hey solved a prolem of invenory managemen of a refinery receiving several ypes of crude oil from differen vessels. They used a discree ime formulaion and he model proposed was a MILP generaed y linearizaion of ilinear equaions due o he mixing operaions. The linearizaion caused a composiion discrepancy hus ha was a grea limiaion on his approach. Pino e al.(2000) proposed a model o solve a invenory managemen prolem of a real-world refinery in Brazil, called RPBC. They developed a non-linear prolem, which he composiion discrepancy was solved, u he discree ime formulaion was a arrier due o he large numer of inary variales, which made he prolem compuaionally infeasile. Afer hey uil a MINLP, u using coninuous ime formulaion and herefore i was possile o schedule he RPBC operaion for a ime horizon of one week. The igges issue was he high compuaional requiremens. Jia e al. (2003) uil a coninuous ime MILP wih componen alance of Lee e al.(1996) arising o he same composiion discrepancy. They did no consider he coss relaed o crude class or ank changes feeding he disillaion unis, which are imporan operaional rules, resuling in producion losses. Furhermore ha approach, called even-ased model, alhough reducing he numer of inary variales, did no allow he inclusion of many operaional feaures such as muliple anks feeding muliples disillaion unis. Furman e al. (2007) presened a rous even-ased coninuous ime formulaion o represen he scheduling prolem of fluid ransfer in anks. They included ilinear equaions o calculae he componen fracion during he crude oil lending. In his approach, a he same even poin, anks could no e loaded and unloaded a he same ime. This assumpion allowed he model o calculae he fracion of each componen a he end of he even poin. New consrains developed o ensure his assumpion reduced he numer of inary variales, which improved he capaciy of he model o solve igger prolems. More e al. (2011) proposed a new approach, called MOS (muli-operaion sequence). In he MOS more han one operaion could e assigned o he same slo, as long as hey may overlap each oher. Operaion here is he volume ransferred eween wo anks, hus i is no inuiive he consrucion of he consrains for he resource. On he oher hand, his approach decreased he amoun of inary variales consideraly. Due o is grea efficiency, MOS is used o represen no jus crude oil scheduling prolems, u also single and muli-sages aches.

2 I is remarkale ha in lieraure mos of sudies are concenraed on represen he scheduling of crude oil for refineries locaed near he docs, where vessels unload he oil, so here is no considered in hese models a pipeline responsile o ranspor crude oil from sorage anks o charge anks. The represenaion of he pipeline is very imporan for he cases which refinery is locaed far from he docs, and he ranspor is made y pipelines, hus he volume reained is considerale. As i is shown in Figure 1, Brazil has a lo of in-land refineries. I is possile o see he exisence of one por receiving crude oil unloaded y vessels. This erminal is responsile for supplying four differen in-land refineries (RPBC, RECAP, REVAP and REPLAN). I is also possile o see ha a pipeline make he connecion eween he erminal and refineries, hus he ime ha crude oil spend eing ranspored and ype of crude oil ha can e unloaded is very imporan for he scheduling of hese real-world refineries. Figure 1: Scheme of he Brazilian refineries Due o he grea imporance of he pipeline for Brazilian refineries, his presen worked focused on including he model of a pipeline o schedule a crude oil supply and lending. Also evaluae he efficiency of his model. The formulaion MOS proposed y More e al. (2011) was used for represen he refinery, and for he pipeline, a large numer or sudies was developed, u focused on he field of final producs disriuion, so a approach creaed y Cafaro e Cerdá (2004) was adaped in his work. Three differen cases will e sudied here: a single shared pipeline eween sorage anks and charging anks; wo shared pipelines eween sorage anks and charging anks;.a special case was also sudied in which a shor pipeline connecing vessels and sorage anks is also considered o capure he cases where he crude volume reained in ha pipeline canno e negleced. The paper is organizer as follows. Secion 2 gives a descripion of he hree prolems and also ses he operaional rules of he prolems. Secion 3 presens he mahemaical formulaion wih paricular consrains necessary o represen he prolem. Secion 4 rings he sudy aou he numer of prioriy-slo necessary o give he maximum ojecive funcion, Gan chars and relevan discussions. Secion 5 is a conclusion aou he work and ideas for nex sudies. 2 Prolem descripion As i has already old, i will e sudied in his paper hree differen configuraions for he crude oil supply and lending prolem. For hese hree examples, he operaional rules are he same, and hey are presened elow: I. Jus one vessel per ime can e on he docs; II. Vessels can unload more han once during he ime horizon, u jus once in he same ank; III. Tanks eing loaded canno unload a he same ime; IV. The pipeline is compleely full a he eginning of he operaion; V. Jus one ank can load he pipeline, and he pipeline can load jus one ank; VI. Muliple anks can feed he CDUs; VII. The same ank can feed muliple CDUs; VIII. CDUs operae coninuously; Each example has is peculiariy herefore i will e presened in he nex susecions a deailed descripion of each case. 2.1 Example 1 For he example one, he operaion involves hree vessels, hree sorage anks, one shared pipeline hree charging anks, wo virual mixers and wo disillaion unis. Each vessel has is minimum arrival ime and is maximum deparure ime. Also hey can unload in any ank. A good poin o remark is ha mixers are no par of he operaion of real-world refineries, hey are presened in here jus o guaranee he properies of he mix feeding CDUs, in oher words, when more han one ank is feeding he CDU, mixers allow o calculae he properies of he feed sream. Figure 2 gives a perspecive of he prolem.

3 Figure 2: Scheme for he example Example 2 For he example 2, he operaion involves hree vessels, four sorage anks, four charging anks, wo virual mixers and wo disillaion unis, u as addiion, here are wo shared pipelines connecing sorage anks and charging anks. Mixers have he same funcion as he example 1. Figure 3 shows a scheme for example 2. Figure 3: Scheme for he example Example 3 Example 3 was designed o include he crude oil scheduling of a special case where vessels canno reach he docs o unload oil direcly in sorage anks. Therefore vessels say on he sea and unload on a low volume pipeline, responsile o ranspor oil o sorage anks. This prolem includes herefore hree vessels, one shared low volume pipeline, hree sorage anks, one high volume pipeline, hree charging anks, 2 mixers and wo disillaion unis. Figure 4 represens he prolem descried

4 Figure 4: Scheme for Example 3 3 Mahemaical formulaion Firs of all, i is imporan o menion ha his paper propose a model capale o represen he crude oil supply and lending operaions considering he pipeline, hus i was necessary adap wo differen models. Firs i was used consrains uil y More e al.(2011) for he formulaion MOS where he pipeline does no exis. In a comparaive work made y Chen e al. (2012), MOS proved o have he es performance represening his ype of prolem. Afer a model proposed y Cafaro and Cerdá (2004) was adaped o represen he ranspor of crude oil, differen from ha proposed o final produc disriuion. A he end i was necessary include some consrains in order o connec hese wo models. I will e presened on he nex susecions jus addiional consrains for he formulaion MOS from More e al.(2011), addiional consrains adaped from Cafaro and Cerdá (2004), and he ones responsile for he connecion eween oh. 3.1 Ojecive funcion Ojecive funcions designed y More e al. (2011) was used on his work and i is represened y Eq(1). max G c. V ivc (1) i T r R D c C 3.2 Addiional Consrains for he formulaion MOS from More e al.(2011) Mixers does no exis on he process herefore i is necessary some consrains o ensure no accumulaion on mixers, in oher words, he volume feeding mixers mus e unloaded a he same ime. Wih ha said, Eq (2), Eq (3), Eq (4) and Eq(6) synchronize he saring and ending ime for he mixers operaion. Eq (5) and Eq (6) guaranee ha he same volumes are eing loaded and unloaded on mixers. S iv1 S iv H (1 Z iv ) i T, v I r, v 1 O r, r R M (2) S iv1 S iv + H (1 Z iv ) i T, v I r, v 1 O r, r R M (3) E iv1 E iv H (1 Z iv ) i T, v I r, v 1 O r, r R M (4) E iv1 E iv H (1 Z iv ) i T, v I r, v 1 O r, r R M (5) V iv = V iv i T, r R M (6) V ivc = V ivc i T, r R M, c C (7) 3.3 Addiional consrains adaped from Cafaro and Cerdá (2004) Cafaro and Cerdá (2004) proposed a formulaion capale of opimize he final produc ranspor, hus hey did no have producs mixes insides he pipeline. All equaions designed for mass alance should e adaped for he individual flow of each ype of crude oil ha is feeding he pipeline. Eq (8) shows he mass alance for slug B new when injecing for each ype of crude oil. Q cr = W rc + D rjc j J B, B new, r R, j J, c C (8)

5 Mass alance for each ype of crude oil should e done for slug B when injecing B new as i is showed y Eq (9). W rc ( = W 1) rc Drjc j J B, B new, >, r R (9) The oal amoun unloaded from he pipeline should e equal o he sum of each individual crude oil volume. D rj j J = D rjc j J c C B, i B new,, r R (10) Iniial condiions for he crude oil inside he pipeline are necessary, as well as iniial condiions for individual volumes of each ype of crude oil. Eq (11) and Eq (12) descrie his wo condiions respecively. ( W 1) r = 0 Wr ( W 1) rc = 0 Wrc B old, r R, = firs(b new ) (11) B old, r R, c C = firs(b new ) (12) Also he oal volume of a slug B should e he sum of individual volume of each ype of crude oil as showed in Eq (13). W r = W rc c C, B, r R, las(b old ) (13) Eq (14) presen he one of he mos imporan consrains for he model, ecause i guaranee he composiion of he volume unloaded from he pipeline is he same as he remaining porion reained inside he pipeline. W rc D rj = W r D rjc B, B new, r R, j J, c C (14) 3.4 Consrains connecing oh models Connecing oh models is imporan o ensure he model funcion herefore consrains was designed wih his proposal. As he pipeline operaes coninuously, Eq(15), Eq(16), Eq (17), and Eq(18) arise o ensure ha load and unload operaions occur a he same ime and wih he same volume. Z iv = Z iv i W, r R P (15) V iv = V iv i W, r R P (16) S iv = S iv i W, r R P (17) E iv = E iv i W, r R P (18) Eq (19) and Eq (20) was designed o define ha he volume of slug is he same of he volume he operaion v feeding he pipeline, oh oal volume and individual volume of each ype of crude oil. Q r = V iv i T, B new, r R P, i = (19) Q rc = V ivc i T, B new, r R P, c C, i = (20) Eq (21) and Eq (22) was designed o define ha he volume of slug is he same of he volume he operaion v eing unloaded he pipeline, oh oal volume and individual volume of each ype of crude oil.

6 D rj B D rjc B = V iv i T, r R P, B new, i = = V ivc i T, r R P, B new, c C, i = (21) (22) An imporan consrain is he one responsile for allocaing he loading and unloading operaions he pipeline susequenly. When he model decides no o use prioriy-slos, hey are lef y las. Z iv Z (i 1)v i T, r R P, i > 1 (23) 4 Soluions for examples proposed A CPU Inel Core i5-3210m, 2.5GHz processor, 6 GB, RAM memory and 64 i sysem. For he presen work, he hree models designed resuled in a MINLP prolem, hus i was solved using decomposiion mehod, which he MILP prolem used CPLEX as solver and RMINLP was solved using CONOPT. For MILP, gap used as a sop crierion was 2% and 3600 seconds of ieraions. In MOS formulaion, i is necessary o se efore sar solving he prolem, he numer of prioriy-slos, hus in his presen paper was used he addiive approach firs proposed y More e al. (2011), which consiss in seing a firs numer of prioriy-slos and solve he MILP prolem, han i is added 1 o he numer of prioriy-slos. When asolue variaion on he ojecive value is less han olerance (Δ ε), he search sops and he las numer of prioriy slos is se. This crierion does no guaranee he gloal opimaliy, u a local opimaliy. In his work, asolue olerance used was ε = Case 1 Tale 1 shows all he parameers used in example 1. Tale 2 presens resuls for he sudy of minimum prioriy-slos required in his prolem. For his firs prolem i is possile highligh ha he numer of slos was fixed on 6, since he asolue olerance was reached eween slos 6 and 7. Hence, he prolem couns wih 4383 equaions, 171 inary variales for a oal of 2931 variales. CPU ime demanded was 294,968 seconds. The ojecive funcion presened a value of $ 14756,853. Tale 1: Prolem 1 daa Time Horizon 12 hours Vessels Arrive ime Deparure ime Composiion Amoun of oil (Ml) Vessel % A 500 Vessel % B 500 Vessel % C 500 Sorage anks Capaciy Iniial composiion Iniial amoun(ml) TQS01 [10,1000] 40% D, 60%A 500 TQS02 [10,1000] 100% E 500 TQS03 [10,1000] 80% F, 20% B 500 Charging anks Capaciy Iniial composiion Iniial amoun(ml) TQR01 [10,1000] 100% G 500 TQR02 [10,1000] 100% E 500 TQR03 [10,1000] 100% F 500 Pipeline1 Iniial composiion Iniial amoun Slug 1 100% C 200 Slug % D 300 Crude Propery (sulfur concenraion) Gross margin ($/l) Crude A Crude B Crude C Crude D Crude E Crude F Crude G Crude mixure feeding CDU [0.01,0.085] (sulfur concenraion) Unload flowrae [5,500] Transfer flowrae [5,500] Disillaion flowrae [100,105]

7 Tale 2: Tale 2: Analyses for he numer of prioriy slos for case 1 Gap slos MILP soluion CPU ime 2% ,579 50,857 2% , ,164 2% , ,031 2% , ,487 Figure 5 presens Gan char for example 1.The volume ransferred in each operaion occurring is locaed aove he ars. I is remarkale ha he model proposed wih 6 prioriy-slos is capale o schedule he crude oil supply and lending prolem. The pipeline operaion was well represened and CPU ime was no high. Also i is imporan o highligh ha despie he ojecive funcion does no conemplae penalies for changes on anks feeding CDUs, he opimizaion choose o use almos he enire volume of he ank aligned wih he CDU. This decision is imporan, ecause i represen a real operaional rule of real-world refineries. An imporan operaional rule ha is no considered in his presen work is he waiing ime of vessels a sea. In his case, as he ojecive funcion jus maximizes gross profi wihou penalies for he waiing ime of vessels, he unloading of vessel 1 sared afer is arrival ime, as i is possile o see on he saring ime of operaion v3. Figure 5: Gan Char for case Case 2 For prolem 2, daa are he same used on prolem 1. However i is necessary add some parameers due o he inclusion of a new shared pipeline and also he addiion of a sorage ank and charging ank. Tale 3 shows he addiional parameers used in example 2. Tale 4 presens resuls for he sudy of minimum prioriy-slos required in his prolem. CPU ime increased and he search for he numer of slos sopped ecause ojecive value sared degrading herefore numer of slos was se as 6. Prolem 2 is composed y 6958 equaions, 5151 variales, which are 294 inary variales CPU ime demanded o solve he prolem was 313,952 seconds. The soluion of RMINLP was $ 15026,267 Tale 3: Addiional daa for case 2 Sorage anks Capaciy Iniial composiion Iniial amoun(ml) TQS04 [10,1000] 100% A 500 Charging anks Capaciy Iniial composiion Iniial amoun(ml) TQR04 [10,1000] 100% B 500 Pipeline2 Iniial composiion Iniial amoun Slug 1 100% C 100 Slug 2 100% D 100

8 Tale 4: Analyses for he numer of prioriy slos for case 2 Gap slos MILP soluion CPU ime 4,27% , ,00% , ,429 2,00% , ,952 2,00% , ,294 Figure 6 shows he Gan char for case of sudy 2. This prolem proved o e more complex due o he addiion of a second shared pipeline and consequenly, increase on he operaions numer. CPU ime demanded was higher han he firs prolem, u a he end i could find a good soluion wih an accepale ime. Gan char showed ha he waiing ime of vessels also occurred in his case. Also here were no many changes on anks feeding CDUs despie he ojecive funcion does no conemplae penalies for hese changes. Figure 6: Gan char for case Case 3 For prolem 3, daa are he same used on prolem 1. However i is necessary o add some parameers due o he inclusion of a new shared pipeline eween vessels and sorage anks. Tale 5 depics he addiional parameers used in example 3. Tale 6 shows resuls for he sudy of minimum prioriy-slos required in his prolem. The numer of prioriy slos for case 2 is equaions, 186 ineger variales for a oal of 3641 variales compose case of sudy 2. Prolem was solved wih a CPU ime of 38,001. RMINLP prolem reurned an ojecive funcion value of $ ,862.

9 Tale 5: Addiional daa for case 3 Pipeline2 Iniial composiion Iniial amoun Slug 1 100% A 200 Slug 2 100% B 300 Tale 6: Analyses for he numer of prioriy slos for case 3 Gap slos MILP soluion CPU ime 2% ,148 2% , ,163 2% , ,331 2% , ,729 Gan char is presened on figure 7. For his example, he model proposed was also capale of represening he prolem. There were no many changes on he anks feeding CDUs and he opimizaion chose o use almos all he volume of a ank wih a good crude oil mixure. Jus in he case, he vessels waiing ime on sea did no occur, despie no having penalies on ojecive funcion, as i was already discussed. 5 Conclusion Figure 7: Gan char for case 3 The presen work had as main ojecive propose a model ale o generae a crude oil scheduling for in-land refineries, which exiss a pipeline connecing erminal and charging anks. Three cases of sudy were conemplaed on his paper in order o evaluae he efficiency of he model. MOS formulaion draw y More a al.(2011) linked wih a model designed y Cafaro and Cerdá (2004) was used o represen crude oil operaions and pipeline operaions. The choice of MOS linked wih model from Cafaro and Cerdá (2004) proved o e correc due o he model s ailiy o generae a soluion for he prolems in such a low CPU ime. Case of sudy 2 showed o e he mos complex case as resul of he increase on he operaions numer, leading o an increasing on inary variale numer. A naural exension for his work is o adap he ojecive funcion wih he aim of conemplaing penalies for decisions aken y he opimizaion ha in real-world refineries would have a cos, such as a cos for he waiing ime of vessels a sea and coss on changing anks feeding CDUs. Also use he model designed in his work o schedule a real scenario of a real-world refinery operaion.

10 Nomenclaure Ses Variales T se of all prioriies slos S i,v sar ime of operaion v in ime slo I W se of all operaions D i,v duraion of operaion v in ime slo I W u unloading operaions E i,v end ime of operaion v in ime slo I W m mixer inle operaions V i,v oal volume ransferred y operaion v in ime slo I R se of all resources V volume of crude c ransferred y operaion v in ime slo i,v,c i R p pipeline V value of key-propery k for operaion v in ime slo i i,v,k R m mixers Z i,v 1 if operaion v is acive in ime slo i R d disillaion unis Q r original volume of he new slug on pipeline r I r inle operaions of resource r Q rc original volume of crude c he new slug on pipeline r O r oule operaions of resource r ( ) W r volume of slug a ime C C ype of crudes ( ) W rc volume of slug for each ype of crude c a ime C B slugs (Iold Inew) ( ) D rj volume of slug ransferred from he pipeline r o B new B old J Parameer W 0 r W 0 rc H Acknowledgmens References old slugs inside he pipeline a he sar of he ime horizon new slugs o e poenially injeced during he ime horizon exis among pipeline iniial volume on he pipeline iniial volume of each ype of crude c on he pipeline ime horizon D rjc ( ) The auhors would like o acknowledge he financial suppor from FAPEMIG. while injecing slug volume of slug of each ype of crude c ransferred from he pipeline r o while injecing slug 1 P. Chandra Prakash Reddy, I.A. Karimi, R. Srinivasan, A new coninuous-ime formulaion for scheduling crude oil operaions, Chemical Engineering Science, 2004, 59, Heeman Lee, Jose M. Pino, Ignacio E. Grossmann, and Sunwon Park, Mixed-Ineger Linear Programming Model for Refinery Shor-Term Scheduling of Crude Oil Unloading wih Invenory Managemen, Indusrial &Engineering Chemical Research, 1996, 35, J.M. Pino, M. Joly, L.F.L. Moro, Planning and scheduling models for refinery operaions Compuers and Chemical Engineering, 2000, 24, Z. Jia, M. Ieraperiou, J.D. Kelly, Refinery Shor-Term Scheduling Using Coninuous Time Formulaion: Crude-Oil Operaions,, Indusrial &Engineering Chemical Research, 2003, 42, K.C. Furman, Z. Jia, M.G. Ieraperiou, A Rous Even-Based Coninuous Time Formulaion for Tank Transfer Scheduling, Indusrial &Engineering Chemical Research, 2007, 46, S. Moure,, I.E. Grossmann, P. Pesiaux, Time represenaions and mahemaical models for process scheduling prolems, Compuers and Chemical Engineering, 2011, 35, D.C. Cafaro, J. Cerdá, Opimal scheduling of muliproduc pipeline sysems using a non-discree MILP formulaion, Compuers and Chemical Engineering, 2004, 28, 2053,2068.