Format And Type Fonts CCHHEEMMIICCAALL EENNGGIINNEEEERRIINNGG TTRRAANNSSAACCTTIIOONNSS VOL. 45, 2015 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Sharifah Rafidah Wan Alwi, Jun Yow Yong, Xia Liu Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-36-5; ISSN 2283-9216 DOI: 10.3303/CET1545012 Please cite this article as: Chang C., Wang Y., Feng X., Zhang P., 2015, Efficient solution strategy for stage-wise minlp model of interplant heat integration using heat recovery loop, Chemical Engineering Transactions, 45, 67-72 DOI:10.3303/CET1545012 67 Efficient Solution Strategy for Stage-wise MINLP Model of Interplant Heat Integration using Heat Recovery Loop Chenglin Chang, Yufei Wang*, Xiao Feng, Ping Zhang State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China wangyufei@cup.edu.cn Interplant Heat Integration using Heat Recovery Loop (HRL) is very different from intra-plant Heat Integration. As the heat sources and sinks are always separated in different regions, some additional factors should be focused on, i.e. capital cost of heat exchangers, installation cost of pumps and pipelines for long distance, and operation cost of pumping power and heat loss during the transportation. Based on economic criteria, this paper presents a stage-wise MINLP model for HRL designs considering the factors aforementioned. Unlike traditional heat exchanger networks (HENS), the flow rate of intermediate-fluid is considered as an important variable which results in a large complex, non-convex model. An efficient strategy is proposed for the problem by sequentially solving an MILP, an MINLP and a NLP. The distance plays a significant role in the design of HRL and it significantly affects the investment of pipelines. The optimum results show that the influence of pumps is relatively less. An industry case study is demonstrated to illustrate the efficiency of the strategy. 1. Introduction Heat Recovery Loop (HRL) is an indirect Heat Integration method using intermediate-fluids and it has been considered as a viable energy saving method for processing plants. Hui and Ahmad (1994) described indirect Heat Integration between separated plants. Their studies were all based on graphical targeting tools of Pinch Technology. Rodera and Bagajewicz (1999) found that a single plant can further improve energy efficiency by sharing energy with other plants. They developed an energy targeting procedure for interplant Heat Integration. Their studies showed that direct integration may achieve less energy savings than indirect integration using HRL, as there would be a large heat loss for process streams participated in direct Heat Integration across plants, so interplant Heat Integration using HRL is preferred. Rodera and Bagajewicz (2000) developed another procedure for interplant Heat Integration using HRL and developed an MILP model to determine the optimal location of the fluid circuits in interplant Heat Integration. Perry et al (2008) analysed heating and cooling requirements in an enlarged geographical area, which was referred as a Locally Integrated Energy Sector (LIES). Hot water was used as heat recovery loop (HRL) to reused industry waste energy for district heating in LIES. Their method showed that HRL can be successfully applied to integrate waste and renewable energy and consequently reduced the carbon footprint in an overall perspective. Walmsley and Atkins (2012) analysed interplant Heat Integration at a semi-continuous factory by the application of HRL. They examined the dynamic operation and variability of HRL in multi- plant site. Kapil et al (2012) suggested district heating to utilize this waste heat and alleviate the carbon footprint of the integrated energy system. There are still some significant factors ignored in conventional HRL design, i.e. the investment of pipeline heat exchangers, installation cost of pumps and pipelines, operation cost of pumping power and heat loss. Bade and Bandyopadhyay (2014) proposed a linear programming (LP) formulation to minimizing the flow rate of hot oil used as intermediate fluid for multiple plant Heat Integration. However, the formulation just considered the minimum total utilities requirement for interplant Heat Integration as a constraint. As mathematical programming can consider multiple factors aforementioned, this work presents a MINLP model with economic objective for interplant Heat Integration using HRL. The flow rate of intermediate-fluid needs to be large enough to recover the heat from heat source plant to heat sink plant, but the increased http://www.sciencedirect.com/science/article/pii/S0360544211008097 68 flow rate will directly increase the diameter of pipe and pump power so that both investment and operation cost will increase. This important variable results in nonlinear constraints with bilinear terms and a large complex, non-convex model, for which even finding a feasible solution is a challenge. An efficient strategy is developed for the complex problem by sequentially solving a MILP, a MINLP and a NLP. As the work focus on low temperature range, hot water is used as the intermediate-fluid medium. The solved results can give the mass flow rate of intermediate-fluid, diameter of pipeline, temperature of the intermediate-fluid circuit and the matches of heat exchangers networks (HENS) automatically. 2. MINLP model for inter-plant Heat Integration using HRL The superstructure of HRL in Figure 1 is modified from stage-wise MINLP model for heat exchanger networks (Yee, 1990). The model is fairly general and it allows both series and parallel decoupling of the exchangers, due to the stage-wise superstructure. . New Heat exchangers Existing Heatter H1 H2 Pump Stage k h =1 Stage k h =2 Stage k c =2Stage k c =1 Sink plant Source plant C2 C1 Existing Cooler Figure 1: Superstructure of interplant Heat Integration using HRL Energy balance of each additional heat exchanger is performed in order to define the outlet temperatures of heat exchanger, which leads to equations with bilinear terms:   1 h h h H H iik ik ik q F th th     i HPS , h k Sth (1)   1 h h h h H H H ik ik ik k q f t t     i HPS , h k Sth (2)  c c c cC C Cjk ik k jkq f t t   j CPS , c k Stc (3)  1c c c C C jjk jk jk q F tc tc     j CPS , c k Stc (4) Energy balance of each mixer defines the inlet temperatures of stages, which also leads to equations with bilinear terms: h h h H H ik ik k i HP f t Fcp t     h k Sth (5) 1 c c c C C jk jk k j CP f t Fcp t      c k Stc (6) Energy balances for final utility units define the utility loads: , (7)  hH outi i iikqcu F th Th   i HPS h k Lasth 69 , (8) In addition, big-M constrains are needed to ensure that the temperature approach if the heat exchangers exist. The parameter is an upper bound for the temperature difference.  1h h h h hH H H H ik ik ik ik ik dt th t z     i HPS , h k Sth (9)   1 1 1 1h h h h h H H H ik ik k ik ik dt th t z         i HPS , h k Sth (10)  1 1 1c c c c c C C C C jk jk jk jk jk dt t tc z        j CPS , c k Stc (11)  1h h h h hH H H H ik ik ik ik ik dt th t z     j CPS , c k Stc (12) Yes NLP model For given Configuration Optimal Grassroots Network obtianed NO Existence of heat exchangers MILP model w≥ xlo·y+ x·ylo-xlo·ylo w≥xup·y+x·yup-xup·yup w≥xlo·y+x·yup-xlo·yup w≥xup·y+ x·ylo-xup·ylo MINLP model Any Splits? Figure 2: Solution strategy for interplant Heat Integration using HRL (13) 3. Efficient solution strategy for the problem The model described here consists of a general straightforward formulation for a given stage-wise superstructure. It is a non-convex problem because of some equation constraints involving bilinear terms, and also the Eq.(13) is nonlinear. The flow rate of intermediate-fluid is considered as a variable which results in non-convex constraints Eq(2) and (3). In addition, energy balance around each mixer defines the inlet temperatures of stages, which also leads to Eq(5) and (6) with bilinear terms or non-convex constraints. To conquer the difficult, an efficient solution strategy is present in Figure 2. By assuming isothermal mixing of streams for stage-wise superstructure, which significantly simplifies the model formulation, the nonlinear heat balances around mixer can be eliminated. For each streams and intermediate-fluids, only an overall heat balance must be performed within each stage and variables ,  cC outj j j jkqhu F Tc tc   j CPS ck Firstc             1 1 0.3333 1 1 1 1 1 0.5 h h h h h h h h n i j n i HPS j CPS H i ikH ik H H H Hi HPS i HPSk Sth k Sth ik ik ik ik I I TAC Min CCU qcu CHU qhu Pumping Costpipe Costpump I h h q z dt dt dt dt                                                        1 1 0.3333 1 1 0.5 c c c c c c c c C j jkC jk C C C Cj CPS j CPSk Stc k Stc jk jk jk jk h h q z dt dt dt dt                                  h H ik f 70 , and are no longer needed in the model. The first step is a MILP problem with the McCormick convex envelope. The objection in this step encompasses operation cost of utility, fixed capital cost, number of heat exchanger and pipeline. The flow rate of intermediate-fluid is optimised through the trade-off between pipeline cost and energy recovery in this step. The second step is a MINLP problem and the result can offer the network configuration with the existence of each heat exchangers. If steams splits are needed, an additional NLP model with fixed structure can be solved to remove the isothermal mixing assumption and perform further optimisation of heat exchangers area. 4. Case Study The case is a Heat Integration project for two existing plants: an aromatic and a butadiene plant. The distance between two plants is 1.5 km. It is assumed that HENS within both plants are well established. Only the streams with cooler in aromatic and streams with heater in butadiene plant are considered to be integrated across plant. In this case, the aromatic is a heat source plant and the butadiene plant is a heat sink plant. The stream and cost data are shown in Table 1 and Table 2. In the table, Dout is the outer diameter of pipe, Din is the inner diameter of pipe, Wtpipe is the weight of pipe, Pcul is the cost of pipe. The HENS in each plant are showed in Figure 3. The Composite Curve of T-H profile of Heat Integration is showed as Figure 4. The minimised total annual cost is 772,613 $ and the heat recovered is 12,564 kW. The flow rate of intermediate-fluid is 143 t/h. In Table 3, the capital and operation cost of pump is about 12,172 $•y -1 and 4,246 $•y -1 and the heat loss is 200 kW, while the annualized pipe and additional heat exchanger cost is about 193,141 $•y -1 and 286,105 $•y -1 . The case study contains 164 continuous variables, 37 integer variables and 285 constraints. The problem is solved less than 1 min of CPU time on a desktop PC (Inter (R) Core (TM) i5 CPU 3.33 GHz, with 4.00 GB of RAM) using the GAMS 24.21. Table 4 is the computational performance of the model with different solvers. From the results, for Baron and Scip Solvers, without using the proposed strategy, no feasible solution can be obtained. And for Knitro and Dicopt Solvers, the solutions obtained by the proposed strategy are much better. Table 1: Streams data for case study Stream number Tin(℃) Tout(℃) ΔH(kW) h (W•m -2 •℃ -1 ) H1 (aromatic) 165 120 3,045 711 H2 (aromatic) 150 115 3,192 731 H3 (aromatic) 136 65 2,110 742 H4 (aromatic) 120 58 3,671 851 H5 (aromatic) 115 50 3,184 954 C1 (butadiene) 70 145 4,807 808 C2 (butadiene) 65 140 3,734 723 C3 (butadiene) 43 120 4,597 718 C4 (butadiene) 42 110 2,763 831 I=10 % n=4 yr Heat loss: 60 W/m Table 2: Cost data for case study Items Value HU 80,000 $•MW -1 •y -1 CU 10,000 $•MW -1 •y -1 Electric cost 120 $•MW -1 •h -1 Capital cost of heat exchanger 4,000+200•Area 0.83 $•y -1 Capital cost of pump 450(q•H 0.5 ) 0.2 $•y -1 Cost of pipeline: Dout(m)=1.052 Din+0.005251 Wtpipe(kg•m -1 )=644.3 Din 2 +72.5 Din+0.4611 Pcul($•m -1 )= 0.82 Wtpipe+185 Dout 0.48 +6.8+265 Dout c C jk f h H ik t c C jk t 71 Table 3: Annual cost and profit of the project Items Solved result Annualized pipe cost 193,141 $•y -1 Annualized pumps 12,172 $•y -1 Heat loss 200 kW Pump power cost 4,246 $•y -1 Annualized heat exchanger cost 286,105 $•y -1 Energy saving benefit 12,564 kW Table 4: Computational result of the model without and with the strategy Solver Model without the strategy Model with the strategy Obj. Function ($•y -1 ) TAC ($•y -1 ) Obj. Function ($•y -1 ) TAC ($•y -1 ) Baron * * 776,650 773,624 Scip * * * * Knitro 100,269 99,869 777,636 774,629 Dicopt 97,542 93,269 775,642 772,613 C1 Source plant Sink plant C2 C3 C4 H1 H2 H3 H4 H5 2,040kW 2,875kW 1,966kW 3,192kW 3,045kW 3,896kW 3,258kW 2,647kW 1,368kW 1,950kW 134.5℃ 143.9t·h -1 143.9t·h -1 135.4℃ 60.6℃ 60℃ 143.9t·h -1 143.9t·h -1 Figure 3: The heat exchanger networks in source and sink plants 5. Conclusions Interplant Heat Integration using HRL is an efficient way to improve energy and economic efficiencies. An MINLP model based on economic objective is established for HRL designs. The flow rate of intermediate- fluid is an important variable and this results in a large complex, non-convex model, for which even finding feasible solution is a challenge. An efficient strategy is developed for the complex problem by solving a MILP, a MINLP and a NLP sequentially. The solved results can give the mass flow rate of intermediate- fluids, diameter of pipeline, temperatures of the intermediate-fluid circuits and the matches of HENS automatically. The proposed methodology can be used by industrial clusters to explore energy and cost 72 savings opportunities. The solved results give the mass flow rate of intermediate-fluid, diameter of pipeline, temperature of intermediate-fluid circuits and matches of HENS automatically. The solution strategy has been illustrated with a case study for two plants within one industrial cluster. Figure 4: Composite Curve and intermediate fluid T-H profiles of Heat Integration Acknowledgements Financial support from the National Basic Research Program of China (973 Program: 2012CB720500) and the National Natural Science Foundation of China under Grant No. 21476256 is gratefully acknowledged. References Hui C., Ahmad S., 1994, Minimum cost heat recovery between separate plant regions, Computers & Chemical Engineering, 18(8), 711-728. Rodera H., Bagajewicz M.J., 1999, Targeting procedures for energy savings by heat integration across plants, AIChE Journal, 45(8), 1721-1742. Bagajewicz M., Rodera H., 2000, Energy savings in the total site heat integration across many plants. Computers & Chemical Engineering, 24(2-7), 1237-1242. Bagajewicz M., Rodera H., 2002, Multiple plant heat integration in a total site, AIChE Journal, 48(10), 2255-2270. Atkins M.J., Walmsley M.R.W, Neale J.R., 2012, Process integration between individual plants at a large dairy factory by the application of heat recovery loops and transient stream analysis, Journal of Cleaner Production, 34, 21-28. Kapil, A., Bulatov, I., Smith, R., Kim, J., 2012, Process integration of low grade heat in process industry with district heating networks, Energy, 44(1), 11-19. Walmsley M.R.W., Walmsley T.G., Atkins M.J., Neale J.R., 2013, Methods for improving heat exchanger area distribution and storage temperature selection in heat recovery loops, Energy, 55, 15-22. Bade, M.H., Bandyopadhyay, S., 2014, Minimization of thermal oil flow rate for indirect integration of multiple plants, Industrial & Engineering Chemistry Research., 53(33), 13146-13156. 30 50 70 90 110 130 150 170 0 3,000 6,000 9,000 12,000 15,000 18,000 12,564 kW 12,364 kW T (°C) H (kW)