MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

Transcription

1 Jiří Jaromír Klmš, Ptar Sabv Varbanov and Png Yn Liw (Editors) Procdings of th 24 th Europan Symposium on Computr Aidd Procss Enginring ESCAPE 24 Jun 15-18, 2014, Budapst, Hungary Elsvir B.V. All rights rsrvd. MINLP Modl for th Synthsis of Hat Exchangr Ntworks with Handling Prssur of Procss Strams Viviani C. Onishi a,b,c, *, Mauro A. S. S. Ravagnani a, José A. Caballro b a Dpartmnt of Chmical Enginring, Stat Univrsity of Maringá, Av. Colombo 5790, Maringá-PR , Brazil Abstract This papr introducs a nw mathmatical modl for th simultanous synthsis of hat xchangr ntworks (HENs), whrin th handling prssur of procss strams is usd to nhanc th hat intgration. Th proposd approach combins gnralizd disjunctiv programming (GDP) and mixd-intgr nonlinar programming (MINLP) formulation, in ordr to minimiz th total annualizd cost composd by oprational and capital xpnss. A multi-stag suprstructur is dvlopd for th HEN synthsis, assuming constant hat capacity flow rats and isothrmal mixing, and allowing for strams splits. In this modl, th prssur and tmpratur of strams must b tratd as optimization variabls, incrasing furthr th complxity and difficulty to solv th problm. In addition, th modl allows for coupling of comprssors and turbins to sav nrgy. A cas study is prformd to vrify th accuracy of th proposd modl. In this xampl, th optimal intgration btwn th hat and work dcrass th nd for thrmal utilitis in th HEN dsign. As a rsult, th total annualizd cost is also rducd du to th dcras in th oprational xpnss rlatd to th hating and cooling of th strams. Kywords: optimization, mixd-intgr nonlinar programming (MINLP), hat xchangr ntwork (HEN), hat intgration, handling prssur. 1. Introduction Optimizing nrgy us through th application of mor fficint procssing tchnologis is ssntial to improv th nrgy consrvation in industrial procsss (Onishi t al., 2013). Th incrasing global nrgy dmand allid with th currnt high cost of nrgy, and th tightning nvironmntal rgulations on gasous missions ar among th many driving forcs bhind th nd for nrgy consrvation (Razib t al., 2012) and fficincy in procssing plants. Th synthsis of hat xchangr ntworks (HENs) has bn xtnsivly studid ovr th past fw dcads (Huang and Karimi, 2012), du to th importanc of thrmal intgration in th rduction of nrgy consumption and fficint nrgy usag (Ravagnani and Silva, 2012). Amongst th major rsarch aras, mathmatical programming stands out for trating th HEN dsign as an optimization problm, in ordr to obtain an optimal ntwork in conomic and thrmodynamic trms. Although th simultanous mthods ar, gnrally, mor difficult to implmnt and solv, it can lad to largr conomic advantags (Kamath t al., 2012). Handling prssur is xtrmly important in many industrial plants, such as oil rfinris and cryognic procsss, du to bing rsponsibl for larg nrgy consumption. Dspit th numrous fforts to solv th problm of HEN synthsis, fw studis rlatd to procsss optimization involving prssur manipulation and hat

2 2 V.C. Onishi t al. intgration of strams ar availabl in th litratur. Asplund t al. (2007) proposd an approach basd on Extndd Pinch Analysis and Dsign (ExPAnD) to study th xpansion of strams at sub-ambint conditions. In thir work, only a graphical intrprtation of prssur xrgy ar considrd to minimiz nrgy rquirmnts of th systm. Wchsung t al.(2011) prsntd a modl for th HEN synthsis with strams that ar subjct to comprssion and xpansion. Th authors combin pinch analysis, xrgy analysis and mathmatical programming in a formulation to minimiz th total irrvrsibility of th procss. Howvr, th costs involvd in th ntwork dsign as wll as th possibility of coupling quipmnt ar not valuatd, only th aspcts rlatd to huristics and xrgy analisys ar takn into account during th HEN synthsis. This papr introducs a nw mathmatical modl for th simultanous HENs synthsis, whrin th handling prssur of procss strams is usd to nhanc th hat intgration. Th proposd modl combins gnralizd disjunctiv programming (GDP) and mixdintgr nonlinar programming (MINLP) formulation, in ordr to minimiz th total annualizd cost composd by oprational and capital xpnss. Th suprstructur is basd on th modl of Y and Grossmann (1990), allowing for stram splits and assuming constant hat capacity flow rats and isothrmal mixing. Howvr, th strams prssur and tmpratur should b tratd as optimization variabls. In addition, th modl allows for coupling of comprssors and turbins, incrasing furthr its complxity. A cas study is prformd to vrify th accuracy of th proposd modl. Th rsults indicat that optimal intgration btwn th hat and work dcrass th total annualizd cost, du to rducd nd for thrmal utilitis in th HEN dsign. 2. Problm statmnt Givn a st of hot and cold procss strams with a known supply stat tmpratur and prssur and a targt stat in which som strams hav prssurs that diffr from th inlt conditions, nrgy supplis for hating and cooling, and prssur manipulation quipmnt, with thir rspctiv costs. Th main objctiv of th modl is to synthtiz an optimal HEN with handling prssur of strams that minimizs th total annualizd cost, considring th oprational xpnss and th capital invstmnt in th various units of th ntwork. In th proposd approach, som flows should follow a spcific rout of xpansion and comprssion via turbins and comprssors. This rout is slctd basd on th work of Wchsung t al. (2011), whrin th plus minus principl is usd to idntify th bst way of prssur manipulation of strams so that th nrgy rquirmnts may b rducd. Thus, considring a maximum of thr prssur manipulations, th hot strams can potntially b coold, comprssd, coold, xpandd, hatd, comprssd and coold. Similarly, th cold strams can b hatd, xpandd, hatd, comprssd, coold, xpandd and hatd. Th procsss of strams xpansion and comprssion ar formulatd as an isntropic procss, through th introduction of a constant fficincy factor to modl ral procsss. In addition, th proposd modl allows for coupling of turbins and comprssors as long as th costbnfit ratio is rspctd in ordr to sav nrgy. This fact, addd to th high nonlinarity and non-convxity of th cost corrlations, confr an vn highr dgr of complxity on th modl. For simplification, all strams should bhav as idal gass. 3. MINLP-basd modl Th proposd modl is dvlopd in gnralizd disjunctiv programming (GDP) and mixd intgr non-linar programming (MINLP) formulation. Th mathmatical modl

3 MINLP Modl for th Synthsis of HENs with Handling Prssur of Procss Strams 3 is basd on th MINLP modl for HEN dsign prsntd by Y and Grossmann (1990), assuming isothrmal mixing and constant hat capacity flow rats, and allowing for strams splits. Th suprstructur is rprsntd by stags according to tmpraturs. In ach of ths stags, a hot stram can xchang hat with all cold strams, and vic vrsa. Th numbr of stags is qual to th maximum numbr of possibl hat xchangs btwn hot and cold strams. Morovr, hatrs and coolrs ar allocatd in th nds of th strams. Th main diffrnc btwn th proposd modl and th Y and Grossmann (1990) suprstructur is that, in this modl, th strams ar subjctd to handling prssur, and thy must b connctd to th HEN through turbins and comprssors. Consquntly, th outlt tmpraturs of th HEN should corrspond to th tmpraturs of th inlt strams in th rspctiv prssur quipmnt. Thus, th procss conditions (i.., stram tmpratur and prssur) ar considrd as unknown variabls that must b optimizd in ordr to obtain an optimal dsign with a minimal cost. In consqunc, this proposd approach is significantly mor complx than th standard problm of hat intgration as formulatd by Y and Grossmann (1990). In fact, th strams can tmporarily chang thir idntity; as a rsult, a hot stram can bhav as a cold stram and, analogously, a cold stram can bhav lik a hot stram. Furthrmor, som procss strams can oprat as thrmal utilitis, mitigating problms rlatd to xcss or dficit of nrgy in th systm. Thrfor, thr is no clar distinction among hot and cold strams, nor btwn thrmal utilitis and strams. Morovr, th hat xchang among parts of th sam stram that assum othr idntity, lik as th placmnt of thrmal utilitis btwn stags of xpansion and comprssion should b forbiddn, through th implmntation of constraints in th modl that incrass furthr th difficult to solv it. As th convntional problm of HENs synthsis is xtndd to includ strams subjctd to handling prssur, a oprator for prssur manipulation and a GDP-basd oprator for th coupling of comprssors and turbins ar addd in th formulation: C lctricity yc, WCc WE CE WCc 0 Using th big-m rformulation, th disjunction may b xprssd as follows: WC WE M 1 y c 1 c, WC WE M 1 y c 1 c, C M 1 y lctricity 2 c, C CE WC M y lctricity c 2 c, (1) In which M is a positiv paramtr that is larg nough to validat th formulation (1). Th paramtr M 1 is calculatd as th diffrnc btwn th uppr bound of th xpansion work and th lowr bound of th comprssion work, and th paramtr M 2 is calculatd as th diffrnc btwn th uppr and lowr bounds of th lctricity cost. Th suprstructur is writtn in GAMS and solvd with th SBB solvr. As th modl is highly nonlinar and non-convx, it is vry difficult to solv it to global optimality with th availabl global solvrs du th larg CPU tim rquird. Nvrthlss, th us of a simpl branch and bound basd solvr, such as th SBB solvr, allows obtaining a

4 4 V.C. Onishi t al. solution nar th global optimum. To solv th modl, on must impos limits (i.., uppr and lowr bounds) on all variabls, and provid initial valus with physical maning. 4. Cas study A cas study is prformd to vrify th applicability of th dvlopd MINLP modl, for obtaining an optimal HEN synthsis with handling prssur of strams at subambint conditions. Th xampl was xtractd from Wchsung t al. (2011), considring a two-fold flow in all strams. On hot stram H1 and on cold stram C1 ar at constant prssur, whras a scond cold stram C2 is xpandd from 0.4 to 0.1 MPa. Th prssur manipulation rout for C2 includs th stags of xpansion, comprssion and xpansion, and rquirs hat intgration in th HEN btwn ach of ths stags. Thus, C2 bhavs as C3 aftr th first xpansion, as H2 aftr comprssion, and finally, as C4 aftr th last xpansion. Th hat capacity and flow rats of all strams ar known constants. Th problm data ar prsntd in Tabl 1. A suprstructur with four stags, and th possibility of stram splits is considrd for th HEN synthsis.th unknown inlt tmpraturs can vary btwn K, th prssur of th C3 stram is rstrictd to MPa, and th prssur of th H2 stram is rstrictd to MPa. Th individual hat transfr cofficints for all strams ar maintaind at 0.1 kw/m 2 K, and a hot and cold utility cofficint of 1.0 kw/m 2 K is considrd. An annualizd capital cost factor of f = 0.18 (10 % intrst rat ovr 8 yars) is assumd. In addition, T h U = 383 K, T c U = 93 K, and ΔT min = 4 K. Th HEN synthsis considrs th possibility of coupling quipmnt with an fficincy of η= 0.7 and κ= 1.51 for both th turbin and th comprssor. Tabl 1. Problm data for th cas study. Stram F s Cp s (kw/k) T s,in (K) T s,out (K) p s (MPa) H C C C H C Cost data: CC = 1,000 US$y -1 kw; CE = US$y -1 kw; CH = 337 US$y -1 kw Firstly, th HEN is dsignd without handling prssur of stram C2, i.., all strams ar at constant prssur. Th optimal HEN is obtaind with two hat xchangrs (A = m 2, Q = kw; and A = m 2, Q = 371,64 kw), two hatrs with aras of A = m 2 (Q = kw), and A = m 2 (Q = kw) locatd at th nds of strams C1 and C2, and on coolr placd at th nd of H1 (A = m 2, Q = kw). In this cas, no comprssion and/or xpansion work is producd in th ntwork. Th total annualizd cost of th HEN with this configuration is 866,171 US$y -1, in which 690,634 US$y -1 drivs from th hot and cold srvics, and 175,537 US$y -1 is rlatd to th capital invstmnt in quipmnt. Scondly, th proposd MINLP modl is usd to solv th problm.th rsults indicat that th optimal HEN is obtaind with four hat xchangrs (A = m 2, Q = kw; A = m 2, Q = kw; A = m 2, Q = kw; and A = m 2, Q = 300 kw), on coolr locatd in th nd of H1 (A = 25.57m 2, Q = kw), and on hatr with ara of 7.74 m 2 (Q = kw) placd at th nd of stram C4. In this scond cas, two turbins and on

5 MINLP Modl for th Synthsis of HENs with Handling Prssur of Procss Strams 5 comprssor ar also rquird, in which th xpandr EX1 is coupld to CO1 (WC = WE = kw); thrfor, th cost of lctricity is zro. Th xpansion work producd by EX2 is qual to kw. Th rsults obtaind for th dcision variabls and optimal HEN configuration ar prsntd in Figur 1. Th total annualizd cost of th HEN with this configuration is 603,844 US$y -1 (composd by C oprational = 179,924 US$y -1 and C capital = 423,920 US$y -1 ), which rprsnts 30 % of savings in th total annualizd cost of th HEN ovr that obtaind in th first cas, i.., without prssur manipulation of th stram C2. Th mathmatical modl has 322 continuous variabls, 25 discrt variabls, and 460 constraints with 1,411 Jacobian lmnts (non-zros), of which 200 ar nonlinar. Th CPU tim is 57 s with th SBB solvr undr th softwar GAMS (vrsion ). Th problm was solvd using a prsonal computr with an Intl Cor 2 Duo 2.40 GHz procssor and 3.00 GB RAM running Windows 7 Ultimat. 5. Conclusions A nw MINLP modl for HEN synthsis with handling prssur of strams is proposd to optimiz th intgration btwn hat and work. Th dvlopd approach, involvs gnralizd disjunctiv programming (GDP) and mixd-intgr nonlinar programming (MINLP) formulation. Th convntional HEN synthsis problm is xpandd to harnss nrgy from strams that undrgo prssur manipulation. As a rsult, intrmdiat prssurs and tmpraturs ar tratd as unknown variabls that must b optimizd. Th strams subjctd to handling prssur should b connctd to th HEN via comprssors and turbins. Th hot and/or cold strams should follow a spcific prssur manipulation rout to rduc th nrgy rquirmnts. Th possibility of coupld quipmnt is studid to optimiz th HEN dsign by minimizing th total annualizd cost, composd by oprational and capital xpnss of th ntwork. Figur 1. Optimal HEN configuration obtaind for th cas study. Th rsults indicat that th handling prssur of strams nhancs th hat intgration, dcrasing significantly th amount of ncssary thrmal utilitis in th HEN dsign. Consquntly, th total annualizd cost is rducd in 30 % du th diminution of

6 6 V.C. Onishi t al. oprational xpnss rlatd to hating and cooling of procss flows. Th total annualizd cost also dcrass in 8 % whn comprssors and turbins ar coupld, to allow th xpansion work to satisfy th nrgy rquirmnt of th comprssors. In this cas, th oprational xpnss associatd to lctricity ar zro. In th xampl, up to thr prssur manipulations of strams ar allowd. Howvr, a largr numbr of prssur changs can asily b implmntd in th modl through th us of a largr quantity of comprssors and turbins in ach stram subjctd to prssur manipulation. Nomnclatur A hat xchangr ara C cost CC cost paramtr for cooling CE cost paramtr for lctricity CH cost paramtr for hating Cp hat capacity F strams flow rat p prssur Q hat duty T tmpratur ΔT min minimal approximation of tmpratur WE xpansion work WC comprssion work y binary variabl that dfin th coupling quipmnt η isntropic fficincy κ polytrophic xponnt Subscripts xpandr (turbin) c comprssor s strams U utility Acknowldgmnts This study was financd by th Brazilian agncy Coordnação d Aprfiçoamnto d Pssoal d Nívl Suprior CAPES (procss nº10758/12-7), and th Spanish Ministry of Scinc and Innovation and Ministry of Economy and Comptitivnss (projct CTQ C02-02). Affiliation of José A. Caballro is Dpartmnt of Chmical Enginring, Univrsity of Alicant, Ap Corros 99, Alicant03080, Spain. Viviani C. Onishi also has th following affiliation: CAPES Foundation, Ministry of Education of Brazil, Brasília-DF , Brazil. pg51551@um.br/viviani.onishi@hotmail.com Rfrncs A. Asplund, D.O. Brstad, T. Gundrsn, 2007, An xtndd pinch analysis and dsign procdur utilizing prssur basd xrgy for subambint cooling, Applid Thrmal Enginring, 27, A. Wchsung, A. Asplund, T. Gundrsn, P.I. Barton, 2011, Synthsis of hat xchangr ntworks at subambint conditions with comprssion and xpansion of procss strams, Procss Systms Enginring, 57, 8, K.F. Huang, I.A. Karimi, 2012, Hat xchangr ntwork synthsis using a hyprstructur of stagwis stram suprstructurs, Computr Aidd Chmical Enginring, 31, M.A.A.S. Ravagnani, A.P. Silva, 2012, Rtrofit of hat xchangr ntworks including th dtaild quipmnt dsign, Computr Aidd Chmical Enginring, 31, M.S. Razib, M.M.F. Hasan, I.A. Karimi, 2012, Prliminary synthsis of work xchang ntworks, Computrs and Chmical Enginring, 37, R.S. Kamath, L.T. Biglr, I.E. Grossmann, 2012, Modling multistram hat xchangrs with and without phas changs for simultanous optimization and hat intgration, AIChE Journal, 58, T.F. Y, I.E.Grossmann, 1990, Simultanous optimization modls for hat intgration. II. Hat xchangr ntwork synthsis, Computrs and Chmical Enginring, 14, 10, V.C. Onishi, M.A.S.S. Ravagnani, J.A. Caballro, 2013, Mathmatical programming modl for hat xchangr dsign through optimization of partial objctivs, Enrgy Convrsion and Managmnt, 74,