A publiation of VOL. 29, 2012 CHEMICAL ENGINEERINGTRANSACTIONS Guest Editors: Petar Sabev Varbanov, Hon Loong Lam,Jiří Jaromír Klemeš Copyrigt 2012, AIDIC ServiziS.r.l., ISBN 978-88-95608-20-4; ISSN 1974-9791 Te Italian Assoiation of Cemial Engineering Online at: www.aidi.it/et DOI: 10.3303/CET1229057 Simultaneous Heat Integration and Bat Proess Seduling Tibor Holzinger a, Máté Hegyáti a, Feren Friedler* a a Department of Computer Siene and Systems Tenology, University of Pannonia, Egyetem u. 10, H-8200, Veszprém, Hungary friedler@ds.uni-pannon.u Heat integration of ontinuous proesses is a widely studied resear area, were many approaes ave been developed to minimize old and ot utility usage. Bat proesses require additional onsideration for te planning of te eat exanger network: sine te flows are not always present in te system, teir timing as to be onsidered as well. Bot eat integration and seduling of bat proesses are igly omplex, teir ombination is expeted to be even iger. Several papers ave already addressed te integrated problem in te last deade (Majozi, 2006, Cen and Cang, 2009, Halim and Srinivasan, 2011). Adonyi et. al. (2003) as presented an algoritm to minimize te utility usage for a given time orizon. Teir approa assumed, owever, tat eat exangers are present for all of te ot-old stream pairs. Moreover, ea ot or old stream was allowed to be mated wit only one ot or old stream, respetively, furter eat demands of te stream ad to be satisfied from utilities. Te aim of tis work is to present an extension of Adonyi et. al.'s approa by allowing te streams to ave eat exanges wit multiple oter streams. Te newly presented approa also takes into aount te limitation on te number of available eat exangers and teir seduling. 1. Introdution Heating and ooling are among te most signifiant energy demands of a emial plant. Linoff made an enormous ontribution to redue te energy requirements of a emial proess by introduing and developing te Pin tenology for te syntesis of Heat Exanger Networks (HENS) starting in te 80 s of te 20 t entury. Altoug, HENS gained te fous of te emial engineering literature, and many approaes as been publised to takle tis type of problems (see e.g., Smit (2005), Klemeš et. al. (2010)), te problem is still far from being solved, espeially in te ase of bat proesses. Bat proesses pose an additional diffiulty for eat integration, sine te system is not steady state, i.e., te flows are present only for a sort period of time not te wole time orizon. As a result, te seduling deisions and eat integration need to be arried out simultaneously to aieve te energy optimal operation of te system. Some of te publised approaes rely on a deomposed metod, were a sedule is identified a-priori to eat integration. Altoug tese approaes an adapt teniques developed for ontinuous proesses, te optimality annot be guaranteed. Anoter lass of papers present MILP or MINLP based formulations for te simultaneous seduling and eat integration of bat plants, see e.g., Cen and Cang (2009), Georgiadis and Papageorgiou (2001), Halim and Srinivasan (2011), Majozi (2006), Peneva et. al. (1992). Tese approaes differ in addressing te eat integration, e.g., onsidering one-to-one eat exanges of streams, applying eat storage vessels. Please ite tis artile as: Holzinger T., Hegyáti M. and Friedler F., (2012), Simultaneous eat integration and bat proess seduling, Cemial Engineering Transations, 29, 337-342 337
Present work minimizes te utility usage for a given time orizon and te number of bates to be produed for ea produt. Note, tat te feasibility of te problem requires te time orizon to be at least te minimal makespan, wi is usually aieved by using only utilities to satisfy te eat demands. A old or ot stream may exange eat wit anoter ot or old stream, if tey are present at te same time, and tey an be assigned to one of te eat exangers. Unlike in te previous approa by Adonyi et. al. (2003), present approa simultaneously onsiders te seduling of eat exangers and te proessing units. If it is not pratially proibited, te algoritm an onsider oneto-many eat exanges as well. 2. Problem definition Te goal is to minimize te ot and old utility usage for a given prodution witin a given time orizon. Te seduling problem is given by a master reipe ontaining te set of produts, intermediate- and raw materials, tasks, and proessing units. Furter neessary parameters as bat numbers, bat sizes, proessing-, transfer-, and leaning times are also given. A proess material needs eating or ooling, wen its temperature is required to be different for being te input of te upoming task. For tis type of tasks te initial- and target temperatures, and teir speifi eats are given. It is assumed, tat two streams an exange eat only if te differene between teir soure- and target temperatures is at least T min. Heat exanges take plae in one of te available eat exangers. Pysial and emial properties of te proess materials may set furter limitations on te pairs of streams an go troug te same eat exanger. If tere is a eat exange between two materials, te exanged eat is proportional to te time of te eat exange. Bat sizes and transfer times are fixed, tus te eat transfer oeffiient an be alulated based on te temperature and flowrate data. Due to operational onsiderations, a material an flow troug only at most one eat exanger. However, it may exanges eat wit several oter streams. If te exanged eat is not suffiient, ig pressure gas or ooling water an be utilized to fulfil te temperature demands of te upoming task. 3. Proposed approa Te proposed approa relies on bot te S-grap framework and linear programming tools. Te problem is formulated as a MILP model, owever, it is not diretly given to te MILP optimization tools. Te disrete deisions are arried out by an S-grap based Bran-and-Bound algoritm, and te bounds of te binary variables of te master MILP model are updated aordingly for ea subproblem. Te relaxation of tese MILP models are used to provide bounds at te internal nodes of te tree, and te value of a solution at te leafs. 3.1 MILP master problem Te basis of te MILP master problem is a so-alled general preedene based formulation, were binary variables are assigned to te alloation and sequening of tasks; and ontinuous variables represent te starting and finising time of a task or a material transfer. Tis part of te matematial model is omitted ere, similar models an be found in Mendez and Cerda (2003), Kopanos and Puigjaner (2010). Te basi formulation is extended by ontinuous variables TTS s and TTF s to represent te starting and finising of a transfer of material s, respetively. In te eat integration part of te model, indies and denote old and ot streams, and n is represents one of te available eat exangers. Binary variable A,,n, denotes te assignment of eat exanger n to te ot-old stream pair,. A eat exanger an be used for ompatible stream pairs, e.g., te streams of te same materials of different bates of te same produts, tus, a binary variable is needed for te sequening of tese exanges. Variable P,,n,,, takes te value of 1, if te eat exange between, takes plae earlier in n ten te exange between,. Continuous variables THS,, and THF,, represent te starting and finising time of eat exange between streams,, respetively. Te amount of exanged eat is denoted by Q,, tat is naturally proportional to te eat transfer oeffiient d, between te streams, and te sared time of te streams in te eat exanger: 338
Q, d, THF, THS, (1) Te starting and finising time of te eat exange is bounded by te starting and finising time of te transfers of materials and, as it is desribed in Eqs. 2-5 (H is a parameter for te time orizon). THS, TTS H 1 A n (2) nn THS, TTS H 1 A n (3) nn THF, TFS H 1 A n (4) nn THF, TFS H 1 A n (5) nn If two streams does not meet in any eat exangers, te orresponding THS,s and THF, variables are set to 0 by Eq. 6. THF, THS, 2 H A (6),, n nn After te possible eat exanges, te rest of te eat demand is fulfilled by utilities. Te time spent on using ot and old utilities to ool down or eat up streams is denoted by TU s. Te eat balane equation for stream s is given in Eqs. 7 and 8. q Q q S Q S,, d TU d TU (7) (8) Were parameter q s is te eat demand of a stream s, and d, d are te eat transfer oeffiients wit te old and ot utilities, respetively. Te objetive is to minimize te overall utility usage: S d TU d TU. S 3.2 S-grap based braning Te Bran-and-Bound proedure is driven by an S-grap based braning algoritm. Te approa is based on an extended S-grap representation of a proess, sown in Figure 1. 339
Figure 1: Extended S-grap representation Te standard S-grap representation as te tasks and produts as nodes. In tis simple example, produt PA is produed troug two onseutive steps TA1 and TA2. Te task, wose input needs eating is indiated by an upward arrow, as introdued in Adonyi et. al. (2003). In te extended presentation, additional nodes are added for te transfer of te materials: TRA for te transfer of raw material RA, TIA for te intermediate IA, and TPA for te produt. Additionally, if a material needs eating or ooling, a node is added for te utility stage. In tis example only te intermediate needs eating, so an additional node, UIA is added to te grap. Te weigt of te ars are te time demand of te previous operation, i.e., transfer times (TT RA, TT IA, TT PA), proessing times (PT TA1, PT TA2), and time spent on using utility (UT IA). In ea step of te Bran-and-Bound proedure eiter a proessing unit or a eat exanger is seduled. In bot ases some additional ars are inserted to te grap. Te presene of a proessing unit assigned to a task is required from te starting of te transfer of te input materials until te end of te transfer of te output materials. If, for example, a unit is assigned to TA1, te sedule ar from te previously assigned task is direted to TRA and te sedule ar to te next seduled task will start from UIA. To illustrate te ars indued by te seduling of eat exangers, two bates of produts PA and PB are onsidered. Te reipe of PB is similar to te one of PA, exept for te intermediate, wi needs ooling instead of eating. Suppose tat a eat exanger is assigned to exange eat between tese two intermediates in te first bat, and ten it is assigned to exange eat between te same materials in te seond bat. Tis seduling deision for te eat exanger is denoted by te ars sown on Figure 2. In te ase if te transfer of te material TIB takes longer time, part of te stream may exange eat wit bot bates of TIA. Tis ase is represented on Figure 3. 3.3 Interation between te MILP master problem and te S-grap framework Wile te grap is being extended wit additional sedule-ars, te MILP model is also updated. Tis is arried out by setting te values of te binary variables tat as been deided by te deisions made so far. Te S-grap representation of a partial sedule an owever provide additional information for te MILP problem as well. As an example, if tere is a non-negative direted pat from UIA to TIB beause of some seduling deisions made on proessing units, TIA and TIB will obviously unable to exange eat. Following tis observation, all te orresponding eat exanger assignment variables, and eat exanger sequening variables an be set to 0. In a similar fasion, deisions made on eat exangers an influene te assignment and sequening variables of proessing units. Te interation between te modules is not one diretional. If an MILP relaxation finds an integer optimal solution, no furter braning is needed at tat part of te tree. Additionally, te MILP relaxations an be used to provide lower bounds on te time needed for utilities, wit wi values te weigt of te orresponding utility ars an be inreased. 340
Figure 2: Sedule-ars for eat exangers Figure 3: Sedule-ar for one side of te eat exanger 4. Conluding remarks A new approa as been presented for te simultaneous seduling and eat integration for multipurpose bat plants. Te proposed approa minimizes te utility usage witin a given time orizon applying bot MILP programming teniques and te S-grap framework. Unlike te formerly 341
publised S-grap based algoritm, tis approa onsiders te seduling of bot eat exangers and proessing units, and allows a stream to exange eat wit several oter streams. Aknowledgement Tis publiation/resear as been supported by te TAMOP-4.2.2/B-10/1-2010-0025 projet. Referenes Adonyi R., Romero J., Puigjaner L., Friedler F., 2003, Inorporating eat integration in bat proess seduling, Applied Termal Engineering, 23, 1743-1762. Cen C.-L., Cang C.-Y., 2009, A resoure-task network approa for optimal sort-term/periodi seduling and eat integration in multipurpose bat plants, Applied Termal Engineering, 29, 1195-1208. Georgiadis M. C., Papageorgiou L. G., 2001, Optimal seduling of eat-integrated multipurpose plants under fouling onditions, Applied Termal Engineering, 21, 1675-1697. Halim I., Srinivasan R., 2011, Sequential metodology for integrated optimization of energy and water use during bat proess seduling, Computers and Cemial Engineering, 35, 1575-1597. Klemeš J., Friedler F., Bulatov I., Varbanov P., 2010, Sustainability in te proess industry Integration and optimization. New York: MGraw-Hill., USA. Kopanos G. M., Puigjaner L., 2010, Simultaneous Bating and Seduling in Multi-produt Multi-stage Bat Plants troug Mixed-Integer Linear Programming, Cemial Engineering Transations, 21, 505-510. Majozi T., 2006, Heat integration of multipurpose bat plants using a ontinuous-time framework, Applied Termal Engineering, 26, 1369-1377. Mendez C. A., Cerda J., 2003, An MILP Continuous-Time Framework for Sort-Term Seduling of Multipurpose Bat Proesses Under Different Operation Strategies, Optimization and Engineering, 2003, 4, 7-22. Peneva K., Ivanov B., Banea N., 1992, Heat integration of bat vessels at fixed time interval. II. Semes wit intermediate eating and ooling agents, Hung. J. Ind. Cem., 20, 233-239. Smit R., 2005. Cemial proess design and integration, Ciester, Wiley,U.K. 342