757 A publication of CHEMICAL ENGINEERINGTRANSACTIONS VOL. 61 2017 Guet Editor:PetarSVarbanov Rongxin Su Hon Loong Lam Xia Liu Jiří J Klemeš Copyright 2017 AIDIC ServiziS.r.l. ISBN978-88-95608-51-8; ISSN 2283-9216 The Italian Aociation of Chemical Engineering Online at www.aidic.it/cet DOI: 10.3303/CET1761124 Simultaneou Synthei of Multi-Period Heat Exchanger Network for Multi-Plant Heat Integration Jiaze Ma Xiaolu Chen Chenglin Chang Yufei Wang* Xiao Feng State Key Laboratory of Heavy Oil Proceing China Univerity of Petroleum Beijing 102249 China wangyufei@cup.edu.cn Multi-Plant Heat Integration i an etablihed approach for improving energy efficiency in indutrial cluter. Current tudie motly focu on thi topic under a imple aumption that all plant are operating at a ame and ingle period. In reality proceing plant may operate at multiple period in which the operating condition of each plant vary with time. Proce tream parameter uch a ma flow rate upply and target temperature may change over a pecified range. So it i particularly neceary to deign multi-period heat exchanger network to improve the ytem flexibility. While multi-period operation problem ha been conidered in ome reearche of heat exchanger network ynthei within a ingle plant it i uually ignored in Multi-Plant Heat Integration tudie. In thi work we propoe a new methodology for Multi-Plant Heat Integration conidering multi-period operation. The methodology employ a novel repreentative upertructure to cover all poible network for Multi-Plant Heat Integration wherein the maximum area of a heat exchanger i required to achieve heat exchanging ervice in all period. The problem wa formulated a a mixed integer nonlinear programming (MINLP) problem. Trade-off among utility cot capital cot of heat exchanger piping cot and pumping cot were fully invetigated. An indutrial cae i employed to illutrate the effectivene of propoed model. 1. Introduction Multi-Plant Heat Integration can further improve heat exchanger network in proceing plant and ave large amount of energy in indutrial plant. Since the concept wa propoed in lat century Multi-Plant Heat Integration ha attracted countle attention from both academic reearcher and indutrial engineer. Generally peaking Multi-Plant Heat Integration can be implemented through either directly uing proce tream acro plant or indirectly uing intermediate fluid. Early attempt to achieve Multi-Plant Heat Integration acro plant were indirectly carried out through different level of team. Thi i becaue utility ytem i already in exitence the exiting team pipeline can largely implify overall network flexibility and ave on capital invetment. For example Dhole and Linnhoff (1993) initially tudied Indirect Heat Integration between individual plant and introduced Total Site Heat Integration wherein a et of plant were linked by a common utility ytem. By uing ite ource and ink profile they et target for the generation and utilization of team between plant. However the elimination of elf-ufficient pocket of the Intra-Plant Heat Integration zone alo call pocket heat reduced the opportunitie for energy recovery in certain cae. From then on many deign and methodologie have been propoed for thi ubject with extenive application to indutrial cae all around the world (Walmley et al. 2016). Neverthele hortcoming in Indirect Interplant Heat Integration uing intermediate fluid till exit. Firt Indirect Interplant Heat Integration methodology require twice heat tranfer between intermediate fluid and proce tream. The total number of heat exchanger intalled in Indirect Heat Integration i uually more than that needed in Direct Heat Integration uing proce tream acro plant (Nemet et al. 2016). Beide twice heat tranfer in Indirect Heat Integration lead to reduction on energy efficiency and the overall heating or cooling demand increae correpondingly. Becaue of thi more and more reearcher all around the world concentrate on Direct Heat Integration acro plant. For intance Ahmad and Hui (1991) initially introduced a ytematic method to generate heat recovery cheme for Direct Heat Integration acro plant. Their method emphaized that the interconnection among plant played a great role in the Heat Integration. A the interconnection ignifie the tranportation and ditribution of proce tream it reflect energy upply and Pleae cite thi article a: Ma J. Chen X. Chang C. Wang Y. Feng X. 2017 Simultaneou ynthei of multi-period heat exchanger network for multi-plant heat integration Chemical Engineering Tranaction 61 757-762 DOI:10.3303/CET1761124
758 demand relationhip between plant. While they mainly focued on minimizing total energy conumption the related capital invetment were ignored in their tudy. A a continuou work Hui and Ahmad (1994) developed a new procedure to deal with the overall cot tradeoff among energy aving heat exchanger area and the number of interconnection for Direct Interplant Heat Integration. The procedure baically decompoed deigning interplant heat exchanger network into everal tep. But they kipped the elf-ufficient pocket within plant. Conidering thi drawback Rodera and Bagajewicz (1999) tudied Multi-Plant Heat Integration and propoed the concept of Aited and Unaited Heat Integration. Such concept indicated that both the heat tranfer between pinch point of different plant and external region could led to effective energy aving for Interplant Heat Integration. Baed on mathematical programming methodologie a linear programming model (LP) and a mixed-integer linear programming model (MILP) model were etablihed to optimize multiplant heat exchanger network for the integration. But energy aving and capital invetment were not conidered holitically due to the limitation of their model. Recently Zhang et al. (2016) tudied Direct Interplant Heat Integration by uing feed and dicharge proce tream between plant. A mixed-inter nonlinear programming model (MINLP) model wa preented to invetigate trade-off between utility cot and capital cot of heat exchanger. Becaue only feed and dicharge tream were conidered and piping cot wa ignored the obtained configuration might be not optimal. Engineer have to conider a variety of factor imultaneouly when they deign multi-plant heat exchange network uch a utility cot capital cot of heat exchanger piping and pumping cot. In the above-mentioned literature all plant are aumed to be running and operating at a ingle or conitent period. In practice however thi aumption i not uitable ince different plant may operate at their own production rate. The working condition of proceing plant may fluctuate due to change in environmental condition change in product quality demand tartup or hutdown chedule and other diturbance (Ahmad al. 2015). In thi cae it i neceary to deign multi-period heat exchanger network for Multi-Plant Heat Integration. Baed on thi idea a new methodology wa propoed for Direct Interplant Heat Integration conidering multi-period operation. The methodology employed a novel upertructure to cover all poible connection for both Intra-Plant and Interplant Heat Integration. Like other tudie proce tream are directly tranported between plant and the maximum area of a heat exchanger i ued to deign multi-period heat exchanger network in all plant (Iafiade et al. 2016). In thi work the maximum area approach i employed. The contact area of ame pair of matching tream in different period are compared the larget one i choen a the repreentative heat exchanger for the final multi-period heat network. Given thee background a Multi- Plant Heat Integration problem wa formulated a a mathematical programming problem. A MINLP model i etablihed to manage trade-off among utility cot capital cot of heat exchanger piping cot and pumping cot. An indutrial cae tudy i illutrated to verify the capability of our methodology. Stage k = 2 Stage k = 1 C1 C1 H1 H1 H2 Stage k = 2 Stage k = 1 H2 C2 C2 Figure 1: Supertructure for Multi-Plant Heat Integration conidering multi-period operation 2. Methodology and formulation The propoed methodology in thi work employed a repreentative upertructure hown in Figure 1. It can be een that all proce tream are tranported and ditributed between plant for both Intra-Plant and Interplant Heat Integration. For each hot proce tream it can be poibly driven from original plant into any other plant. After releaing heat the hot proce tream will be tranported back to original plant to keep fixed ma flowrate. Similarly each cold proce tream in Figure 1 i firtly tranported to any other plant to aborb heat.
After extracting heat from other hot proce tream it ha to be tranported back to original plant to keep the fixed flowrate. Supertructure in Figure 1 cover mot of poible network for both Intra-Plant and Interplant Heat Integration. The outlet temperature of all proce tream leaving each heat exchanger are aumed to be mixed iothermally at each tage. The following ection preent the MINLP formulation for the upertructure. For a repreentative hot (cold) proce tream i (j) in Figure 1 it can be tranported to any other plant. Binary variable x i ued to define the exitence of a repreentative hot (cold) proce tream i (j) the dijunctive formulation can be written a the following equation where NS NH and NC are et for operating period hot and cold proce tream. xi p 1 i NH NS (1) pnp x j p 1 j NC pnp NS If a proce tream i (j) wa ent from original plant to plant p tream inlet temperature tinx hould be equal to upply temperature Tin. Otherwie there will be no contraint of that tream. Baed on Big-M formulation Eq (3) - (6) expre temperature contraint. The parameter i the upper bound of correponding temperature. tinx Tin x 1 NS (3) 1 1 p i i p i i tinx Tin x p i i p i i tinx Tin x p j j p j j tinx Tin 1 x p j j p j j pnp pnp pnp pnp i NH i NH j NC j NC NS NS NS Beide when the proce tream i (j) i tranported back to original plant tream outlet temperature toutx hould be equal to inlet temperature tu of the available cooler (heater). Eq (7)-(10) are employed. toutx tu x 1 p NP i NH NS (7) 1 1 p i i p i i toutx tu x p NP i NH NS (8) p i i p i i toutx tu x p NP j NC NS (9) p j j p j j toutx tu 1 x p NP j NC NS (10) p j j p j j (2) (4) (5) (6) 759 Plant p Stage k = 2 Stage k = 1 tui Tini Tinj tuj Tinj tuj tui Tini Figure 2: Supertructure of heat exchanger network Figure 2 i a tage-wie upertructure for heat exchanger network which can repreent all poible configuration for both Intra-Plant and Interplant Heat Integration. Therefore the inlet temperature (tinx) of a repreentative hot (cold) proce tream i (j) ha to be equal to initial temperature ti 1 (tj K) when it enter the upertructure. Similarly tream outlet temperature (toutx) i equal to final temperature ti K (tj 1) in the upertructure. Eq(11)-(14) are ued to how the contraint. Variable t define the temperature of a proce tream at each tage in the upertructure. t tinx p NP i NH NS (11) t t t p i1 p i toutx p NP i NH NS (12) p i K p i tinx p NP j NC NS (13) p j K p j toutx p NP j NC NS (14) p j1 p j
760 In Figure 2 all ub-flow of a proce tream leaving each heat exchanger are aumed to be mixed iothermally at each tage in the upertructure. In thi cae the energy balance of all mixer are not required ince the outlet temperature of the ub-flow leaving heat exchanger at a tage k are ame. Only the overall energy balance at each tage are needed. Eq(15) and (16) are ued to how thi relationhip. F Tin Tout q qu NS (15) i NH i i i p i j k i jnc knk pnp F Tout Tin q qu j j j p i j k j inh knk pnp j NC NS In Eq. (17) - (20) everal Big-M contraint are ued to enure the temperature approache dt and dtu only exit when heat exchanger were preented. In thee equation parameter and denote the upper bound for the related temperature difference. dt t t 1 z k NK NS (17) p i j k p i k p j k p i j k i j dt t t 1 z p i j k 1 p i k 1 p j k 1 p i j k i j dtu tu tuin 1 zu u i i i i i j j j j j pnp pnp i NH i NH j NC j NC u (16) k NK NS (18) i NH NS dtu tuout tu 1 zu u j NC NS (20) In Eq. (21)-(24) everal Big-M contraint are ued to enure the temperature approache dt and dtu only exit when the heat exchanger were preented (z and zu). In thee equation parameter and denote the upper bound for the related temperature difference. dt t t 1 z k NK NS (21) p i j k p i k p j k p i j k i j 1 dt t t z p i j k 1 p i k 1 p j k 1 p i j k i j 1 dtu tu tuout zu u i i i i i j j j j j pnp pnp i NH i NH j NC j NC u (19) k NK NS (22) i NH NS dtu tuout tu 1 zu u j NC NS (24) In thi work objective i to minimize total annual cot (TAC). The function in Eq. (25) i compoed of utility cot capital cot of heat exchanger piping and pumping cot. Dop Dop Min TAC CUi qu i CU j qu j inh NS Dop jnc NS Dop NS NS + Pipingcot Pumpingcot Af z p i j k zui zu j pnp inh jnc knk inh jnc Af Af Af pnp inh jnc knk inh jnc 3. Cae tudy qp i j k Max dt dt 0.5dt dt p i j k p i j k 1 p i j k p i j k 1 qui Max dtui touti tuini 0.5dtui touti tuin qu j Max dtu tuin tout dtu tuin tout i 0.5 j j j j j j The example preented in thi work i baed on a heat integration project for three exiting plant located in Northern part of China. All plant are aumed to be operated in two period due to environmental impact. The patial arrangement of three plant i an equilateral triangle with 0.25 km ide length. Table 1 how all data of tream in each operating period and the minimum temperature difference for heat tranfer unit are all 10 C. It can be een in Table 1 that H1 H2 C1 and C2 are in plant 1 H3 H4 C3 and C4 are in plant 2 and H5 H6 C5 and C6 are in plant 3. The purpoe i to deign multi-period heat exchanger network for both Interplant and Intra-plant Heat Integration. 0.3333 0.3333 0.3333 (23) (25)
761 Table 1: Stream data for the cae Stream number Period 1 Period 2 Tt( C) Tt( C) F(kW/ C) cp(kj/ kg) (kg/m³) Tt( C) Tt( C) F(kW/ C) cp(kj/ kg) (kg/m³) H1 (P1) 500 50 38 1.2 321 450 45 30 1.2 321 H2 (P1) 350 46 25 1.1 302 400 50 32 1.1 302 H3 (P2) 220 45 30 1.0 330 250 55 25 1.0 330 H4 (P2) 200 42 38 1.2 325 220 40 35 1.2 325 H5 (P3) 215 40 36 1.3 330 230 45 33 1.3 330 H6 (P3) 200 35 35 1.2 325 225 38 35 1.2 325 C1 (P1) 80 255 100 1.2 340 70 258 115 1.2 340 C2 (P1) 58 250 110 1.2 380 68 252 110 1.2 380 C3 (P2) 55 230 115 1.0 360 55 250 100 1.0 360 C4 (P2) 50 205 108 1.3 380 45 200 108 1.3 380 C5 (P3) 46 185 112 1.0 310 42 205 100 1.0 310 C6 (P3) 45 130 125 1.2 320 40 135 105 1.2 320 50 46 50 80 70 58 68 C1 C2 72.7 m2 57.4 m2 874.0 kw 1140.0 kw 675.0 kw 1056.0 kw 3550.0 kw 4141.9 kw 593.8 m2 485.4 m2 5112.0 kw 4851.0 kw 6958.0 kw 5245.0 kw 172.2 m2 409.4 m2 65.1 m2 3375.0 kw 6002.1 kw 9268.0 kw 5765.0 kw 8232.0 kw 15855.0 kw 2125.0 kw 0.0 kw 316.3 m2 82.9 m2 H1500 450 H2350 400 255 258 250 252 55 42 40 55 55 50 C3 C4 47.2 m2 600.0 kw 125.0 kw 68.4 m2 874.0 kw 700.0 kw 150.0 kw 260.4 kw 190.0 kw 500.0 kw 40.8 m2 49.8 m2 31.6 m2 515.7 m2 306.3 m2 4500.0 kw 4489.6 kw 501.9 m2 4940.0 kw 5100.0 kw 6135.0 kw 4500.0 kw 16225.0 kw 15615.0 kw 145.5 m2 453.4 m2 H3 220 250 H4 200 220 230 250 205 200 175.0 kw 364.6 kw 4550.0 kw 5410.4 kw 40 35 38 46 C5 42 C6 40 91.5 m2 97.9 m2 Plant 3 1188.0 kw 1254.0 kw 1050.0 kw 770.0 kw Plant 3 15568.0 kw 16300.0 kw 10625.0 kw 9975.0 kw Plant 3 397.9 m2 372.4 m2 H5 215 230 H6 200 225 185 205 130 135 Figure 3: Heat exchanger network for Multi-Plant Heat Integration. The MINLP model of thi example include 960 binary variable 3000 continuou variable 4800 contraint and an objective function. After olving the MINLP problem in about 2500 a locally optimal olution with a TAC of 4145291.1 $/y can be obtained. The detailed deign for our olution reult i preented in Figure 3. In thi figure the maximum heat exchanger area are ued to achieve the heat exchanging ervice in different period. A howed in Figure 2 two proce tream involved in Interplant Heat Integration. The firt one i hot proce tream H5 which i tranported from original plant (plant 3) to plant 1. After releaing heat to cold proce tream C2 H5 i then tranported back to original plant. Similarly the econd one i hot proce tream H6 which i tranported to plant 2 and exchange heat with cold tream C4. It wa ent back to plant 3 finally. A the final reult the utility cot annualized cot of heat exchanger piping and pumping cot are 3698452.5 $/y 271117.2 $/y 62776.7 $/y and 104056.2 $/y. The overall operation cot of heating and cold utilitie account for a large proportion of TAC. A previou tudie of Interplant Heat Integration the capital cot of heat exchanger in thi cae i alo a coniderable cot item. 4. Concluion The baic idea of thi article i to provide a new methodology to deign flexible heat exchanger network for Multi-Plant Heat Integration conidering multi-period operation. Our methodology employed a novel
762 repreentative upertructure to cover all poible network for both Intra-Plant and Interplant Heat Integration. An MINLP model baed on economic criteria i etablihed for the integration. The model invetigate tradeoff between energy aving and capital invetment imultaneouly ince objective function include utility cot capital cot of heat exchanger piping and pumping cot. An indutrial cae i ued to demontrate the capabilitie of our methodology. From the reult it can be proved that multi-period heat exchanger network for Multi-Plant Heat Integration can be obtained through the propoed methodology. The obtained flexible network can atify heat tranfer in each operating period. Beide the piping and pumping cot account for about 1.5 % and 2.5 % of TAC which mean the ditance factor i a coniderable factor in Multi-Plant Heat Integration. Acknowledgement Financial upport from the National Natural Science Foundation of China (No. 21476256) and Science Foundation of China Univerity of Petroleum Beijing (No.2462017BJB03) are acknowledged. Reference Ahmad M.I. Zhang N. Jobon M. Chen L. 2012 Multi-period Deign of Heat Exchanger Network Chemical Engineering Reearch and Deign 90 1883-1895. Ahmad S. Hui D.C.W. 1991 Heat Recovery between Area of Integrity Computer & Chemical Engineering 15 809-832. Dhole V.R. Linnhoff B. 1993 Total Site Target for Fuel Co-generation Emiion and Cooling Computer & Chemical Engineering 17 S101-S109. Hui C.W. Ahmad S. 1994 Minimum Cot Heat Recovery between Separate Plant Region Computer & Chemical Engineering 18 711-728. Iafiade A. Bogataj M. Fraer D. Kravanja Z. 2015 Optimal Synthei of Heat Exchanger Network for Multiperiod Operation Involving Single and Multiple Utilitie Chemical Engineering Science 127 175-188. Nemet A. Čuček L. Kravanja Z. 2016 Procedure for The Simultaneou Synthei of Heat Exchanger Network at Proce and Total Site Level Chemical Engineering Tranaction 52 1057-1062. Rodera H. Bagajewicz M.J. 1999 Targeting Procedure for Energy Saving by Heat Integration Acro Plant. AIChE journal 45 1721-1742. Walmley T.G. Atkin M.J. Walmley M.R.W. Neale J.R. Philipp M. Schumm G.M. Peeel R.-H. 2016 Total Site Utility Sytem Optimiation for Milk Powder Production Chemical Engineering Tranaction 52 235-240. Zhang B.J. Li J. Zhang Z.L. Wang K. Chen Q.L. 2016 Simultaneou Deign of Heat Exchanger Network for Heat Integration Uing Hot Direct Dicharge/Feed Between Proce Plant Energy 109 400-411.