CHEMICAL ENGINEERING TRANSACTIONS VOL. 61, 2017 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš Copyright © 2017, AIDIC Servizi S.r.l. ISBN 978-88-95608-51-8; ISSN 2283-9216 Heat-Integrated Water Allocation Network Synthesis for Industrial Parks Haodong Song, Linlin Liu*, Jian Du Institute of Chemical Process System Engineering, School of Chemical Engineering, Dalian University of Technology, Dalian, 116024, Liaoning, China liulinlin@dlut.edu.cn Industrial parks can achieve the cooperative utilization of resource among multiple enterprises, and have become a major trend of process industry. Concerning the combined consumption issue of water and energy in industrial parks, this paper presents a methodology for interplant heat-integrated water allocation network (IHIWAN) synthesis, to explore the potential of water and energy conservation in industrial parks. The novel model proposed takes both direct and indirect schemes of cross-plant water reuse into consideration, and develops strategies for Heat Integration specific to industrial parks. The economically optimal overall IHIWAN is pursued by mathematical programming under the objective of minimum total annual cost (TAC). Based on superstructure, a non-linear programming (NLP) model is formulated containing two sub-networks: water allocation sub-network and heat exchanger sub-network. Regarding the two sub-networks, the overall network is synthesized in two solution approaches respectively: sequential design and simultaneous design. Through the comparison between these two approaches, it is indicated that simultaneous design presents preferable result, despite the higher requirement on solution process. The effectiveness of the proposed methodology is illustrated by a case study of an industrial park including three plants. 1. Introduction Over the past decades, considerable efforts have been made on the synthesis of water allocation network (WAN) and heat exchanger network (HEN), which are efficient means to reduce the consumption of water and energy respectively. In recent years, industrial parks have become a major trend due to the advantage in industrial symbiosis among multiple plants. Yet, most of the works on water and energy integration are carried out either separately or within a single plant, which limits the potential of resource conservation. Consequently, it is crucial to achieve the cooperative integration of water and energy in the scale of industrial parks. The study on individual synthesis of WAN and HEN in industrial parks started in the 1990s, with mathematical programming as the major approach. Chew et al. (2008) classified interplant water integration into two schemes: direct and indirect integration, wherein the former directly via cross-plant pipelines and the latter via a centralized utility hub. Liu et al. (2016) presented a plant-based mode of water allocation in industrial parks to restrict the number of interplant streams and thereby reduce complexity. As for Heat Integration, Chang et al. (2015) developed a two-step methodology for interplant Heat Integration via Heat Recovery Loop considering additional factors associated with distance between plants. Combining WAN and HEN, whilst utilizing the interactions between these two sub-networks, water and energy consumption can be further reduced. So far, heat-integrated water allocation network (HIWAN) synthesis has been widely studied and the optimization approaches mainly follow two routes: sequential design and simultaneous design. The former is a stepwise strategy, dividing the problem into two sub-problems (concerning water and energy respectively) and solving sequentially; while the latter takes the optimization problem as a whole, and all the trade-offs are balanced within the model, which is optimized under one objective covering both water and energy. However, most of the works only focus on the HIWAN synthesis within a single plant, whereas interplant HIWAN synthesis in the scale of industrial park has not been adequately investigated. Boix et al. (2011) addressed the water and energy management for an industrial park involving three plants, yet detailed issues such as network DOI: 10.3303/CET1761077 Please cite this article as: Song H., Liu L., Du J., 2017, Heat-integrated water allocation network synthesis for industrial parks, Chemical Engineering Transactions, 61, 475-480 DOI:10.3303/CET1761077 475 structure and interplant distribution mode were not discussed. Zhou et al. (2012) presented the design of interplant water-allocation and heat-exchange network in a mixed integer nonlinear programming (MINLP) model based on multi-scale state-space superstructure, involving various scenarios of regeneration and redistribution. Still, relevant works are quite few and the methodologies are yet to be further explored. In this work, a methodology for the economically optimal design of IHIWAN is presented to reduce water and energy consumption in industrial parks. Based on superstructure approach, a mathematical model is presented and strategies for interplant integration specific to industrial parks are developed. It's worth noting that, to simplify the model and reduce the computation load, all the discrete variables are eliminated and the problem is formulated as an NLP model rather than an MINLP model. 2. Problem statement Given an industrial park including several plants, each plant containing a set of water generating and consuming units (assimilated as water sources and sinks) with specific flowrate, temperature and contaminant concentration, the objective is to synthesize an economically-optimal IHIWAN for the industrial park with minimum total annual cost whilst meeting all the process requirements. Regeneration operation is available with required operating temperature and fixed removal ratio of contaminant. 3. Superstructure The superstructure for IHIWAN synthesis in industrial park is shown in Figure 1. The solid blocks denote the single plants in the park, and the dotted blocks denote the water allocation and Heat Integration subsystems within each plant. As can be seen, plants are correlated by inter-plant water streams and a shared regeneration unit enables the centralized operation in the park. The water allocation subsystem is revised from the “plant- based” WAN superstructure in our recent work (Liu et al., 2016). All the possible intra-plant matches between water sources (including fresh water) and sinks (including waste effluent) are taken in, as well as inter-plant reuse opportunities in both direct and indirect scheme. Figure 1: IHIWAN superstructure for industrial park 476 As for Heat Integration subsystem, heat exchange is allowed among the streams within and entering/leaving the same plant. Specifically, streams of direct interplant reuse participate in the HEN of target plant. In each plant, the water streams to the same target unit (sinks/effluent/central regenerator) are non-isothermally mixed into one single stream before entering the HEN, to make the most of direct heat exchange and reach the minimum number of streams involved in Heat Integration subsystem. Consequently, utility consumption is lowered and the HEN structures are relatively less intricate. Detailed design of HENs is based on the modified stage-wise HEN superstructure. The existence and role (hot/cold/bypass) of the potential streams in HEN are identified in the synthesis procedure. Note that the inlet stream of waste effluent shall not be heated by hot utility if identified as cold stream, since only the upper temperature limit is required for effluent discharge. 4. Mathematical model Based on the superstructure, an NLP model is accordingly formulated to solve the problem. Compared with the generally used MINLP model, continuous variables u=f/(f+δ) and z=q/(q+δ) (δ is an infinitesimal number) are used to indicate the existence of potential water streams and heat exchangers respectively instead of binary variables, which significantly lowers computation complexity and facilitates the search for more desirable result. The model is divided into the following three sections. The objective function is the minimum TAC of the overall IHIWAN, which is the summation of the two subsystems.  IHIWAN WAN HENobj minTAC TAC TAC  (1) 4.1 Water allocation subsystem The model for water allocation subsystem is basically revised from our recent work (Liu et al., 2016), including flowrate balance for water sources and sinks, contaminant concentration limit for water sinks, flowrate and contaminant load balance for inter-plant water streams, flowrate and contaminant load balance for centralized regenerator, and upper/lower bounds for flowrate. The TAC of water allocation subsystem consists of the cost of fresh water, regeneration and cross-plant pipeline, as shown in Eq(2).                                          WAN fresh water regeneration pipeline fw fw cap ind,out op ind,out , reg reg cp var pl ind,out ind,in dis fixed dir pl , ' ' 3.6 2 reg j p p p p j p p p p p p p p p p p TAC cost cost cost f uc AWH f AF f AWH f v AF D u u u                                 , , ' , ' p p j SK p SP p SP p p (2 ) where SP is the set of single plants in the park; SKp is the set of water sinks in plant p; f denotes the flowrate of water stream; uc denotes unit cost; Ddis denotes inter-plant distance; AWH denotes annual working hour. 4.2 Heat Integration subsystem The model for Heat Integration subsystem mainly includes overall heat balance for each stream, heat balance at each stage in superstructure, assignment of initial temperature in superstructure, feasibility constraints for temperatures, and constraints for heat transfer approach temperature. The TAC of Heat Integration subsystem consists of the cost of heat exchangers (fixed charge + area cost) and utilities, given by Eq(3).                                                 area he area area he he HEN heat exchangers utilities fixed hc HUc hCU he , , , , , hc , , , area he HUc hCU , , HU HUc CU hCU , , h c k p c p h p h c k c h h c k p h c k c p h p c h c p h p c h TAC cost cost z z z A A A uc q uc q                                      , , ,p p p h HS c CS p SP k ST (3) where HSp and CSp are the sets of hot and cold streams in the HEN of plant p; ST denotes the stages in HEN 477 superstructure; q denotes the heat load exchanged in each unit; A denotes the area of heat exchanger. Note that the cost of hot utility and heater related to waste effluent streams is excluded from TACHEN in practical solution process since it is invalid as stated in Section 3. 4.3 Interconnections between the two subsystems As mentioned in Section 3, according to the superstructure, the water streams to the same target unit are pre- mixed into one stream, which participates in the HEN to reach the required temperature before entering the target unit. The energy balance of the pre-mixing is shown by Eq(4) - Eq(7), from which the temperatures after mixing can be calculated and then assigned to the inlet temperatures of the streams in HEN in the order of sinks-effluent-regenerator, as shown in Eq(8). Whilst the outlet temperatures of the streams in HEN equal to the required temperature of corresponding units.  mix,cp cp sr exp, , ,p p i p i p p i T f T f i SR p SP       (4)  dir,in dir,in cp dir' , ' ' , , ' , ' p p p p p p p T f T f i SR p SP p SP p p          (5)  mix,sk sk sr in fw fw impd dir,in impi cr, , , , , , , , , ,j p j p i p i j p j p j p p j p p p i T F T f f T f T f T i SR j SK p SP               (6)  mix,e e impe sr impe cr, , , , e p i p p i p i p p p i i T f f T f f T i SR p SP                  (7) where SRp is the set of water sources in plant p; T mix,sk j,p , T mix,e p ,T mix,cp p are the inlet temperatures of the pre-mixed stream to sinks, effluent and centralized regenerator.                          mix,sk , in mix,e , mix,cp , , , , , 1 , , 2 j p p p p s p p p p p p p T s ES j SK p SP s j SK Ts T s ES p SP s SK T s ES p SP s SK (8) where ESp is the set of potential streams to be involved in the HEN of plant p, Ts in s,p is the inlet temperature of potential heat-exchange stream s in plant p; | SKp | is the number of sinks in plant p. When it comes to the simultaneous design of the two subsystems, the outlet temperature of pre-mixing nodes (i.e. inlet temperature in Heat Integration) is unknown before the HEN synthesis. The method from Yan et al. (2016) is adopted to identify the role (hot/cold/bypass) of the streams in HEN and allocate the corresponding rational value to their inlet temperatures, given by Eq(9) and Eq(10), which cooperate with the feasibility constraints of temperatures to guarantee the validity of the identification.    in out in out, , , , 0 , , , ,h p s p c p s p p p pTh Ts Tc Ts h HS c CS s ES p SP h c s              (9) in in in out , , , , , , , , s p h p c p s p p p p Ts Th Tc Ts h HS c CS s ES p SP h c s             (10) where Th in h,p and Tc in c,p are the inlet temperatures of hot stream h and cold stream c in the HEN of plant p. 5. Case study To illustrate the application of the proposed method, a theoretical industrial park containing three plants is investigated. The process data are listed in Table 1. The centralized regenerator features a fixed removal ratio of 90 % and shall be operated at 30 °C, cost parameters α cap reg , β reg and α op reg are set at 12,600, 0.7 and 0.0067, respectively. Pipeline cost parameters α fixed pl and α var pl are set at 250 and 7,200. Fresh water (0.375 $/t) is supplied at 20 °C. Effluent shall be discharged at no higher than 30 °C. Inlet and outlet temperatures of cold utility are 10 °C and 20 °C, with unit cost 189 $/(kW·y); the temperature of hot utility (low pressure steam) is 120 °C, with unit cost 377 $/(kW·y). Heat exchanger cost parameters α fixed he , α area he and β area he are set at 8,000, 1,200 and 0.6; overall heat transfer coefficient is fixed at 0.833 and 0.5 kW/(m2·°C) for matches with/without steam. AWH, AF and Ddis are 8,000 h/y, 10 % and 180 m. The mentioned optimization approaches, namely sequential design and simultaneous design, are employed for the synthesis of the overall network. The problem is implemented in GAMS using BARON as solver. 478 Table 1: Process data for case study Plant Water Source Flowrate (t/h) Contaminant concentration (ppm) T (°C) Water Sink Flowrate (t/h) Contaminant concentration upper limit (ppm) T (°C) 1 1-1 72 100 40 1-1 72 0 40 1-2 360 100 100 1-2 360 50 100 1-3 144 800 75 1-3 144 50 75 1-4 36 800 50 1-4 36 400 50 2 2-1 360 100 100 2-1 360 50 100 2-2 144 800 75 2-2 144 50 75 2-3 600 1,100 100 2-3 600 800 100 3 3-1 68 250 40 3-1 209 20 44.8 3-2 169 100 43 3-2 972 20 43.9 3-3 1,130 150 46 3-3 190 20 43.1 3-4 436 150 48 3-4 36 20 81 3-5 832 160 46 3-5 432 148 49 3-6 1,332 20 44.8 5.1 Sequential design Sequential approach synthesizes the IHIWAN in two steps. First, water allocation sub-network is designed based on the WAN part of the superstructure and mathematical model, under the objective of minimum TACWAN. And an economically optimal WAN is obtained with the TACWAN of 2,299,729 $/y. On the basis of this WAN, the inlet temperatures of the pre-mixed streams to each target unit are obtained by Eq.(4)-Eq.(8). Comparing to the corresponding temperature specifications, the streams in demand for heat exchange are identified with determinate role, flowrate and temperature, which are to be involved in HENs. 4 hot streams and 12 cold streams are incorporated from 40 water streams. Then, the optimal heat exchanger sub-network with minimum TACHEN (34,985,946 $/y) is designed based on stage-wise HEN superstructure. Thereby, an IHIWAN for the industrial park with the TACIHIWAN of 37,285,675 $/y is eventually obtained. 5.2 Simultaneous design Sequential design is able to reduce the resource consumption and minimize the cost of the two sub-networks respectively, but the interaction between the two subsystems is not fully explored. Simultaneous design treats the whole system as one single problem and directly minimizes the overall TACIHIWAN. Accordingly, the economically-optimal IHIWAN with the minimum TACIHIWAN of 28,286,147 $/y is obtained, as shown in Figure 2. Detailed cost terms of the two approaches are listed in Table 2. Compared to sequential design, it is clear that simultaneous design presents preferable results, with a reduction of 24.14 % on TAC. This is mainly due to the instinct limitation of sequential approach that the internal trade-offs are not adequately processed, especially when Interplant Integration is involved. Although simultaneous design features higher fresh water consumption, yet the significantly lower utility consumption (especially for Plant 2) still leads to better overall performance, which implies that the optimal WAN might not be the most suitable one for Heat Integration. Yet, it should be noted that simultaneous design features much heavier computation load,and requires more appropriate initial points to search for solution. Table 2: Results of case study Sequential design Simultaneous design Cost terms (M$/y) Plant 1 Plant 2 Plant 3 Total Plant 1 Plant 2 Plant 3 Total Fresh water 0.216 0 1.392 1.608 1.494 0.761 0 2.256 Regeneration - - - 0.556 - - - 0.502 Cross-plant pipeline - - - 0.136 - - - 0.124 TAC, WAN subsystem - - - 2.300 - - - 2.881 Heat exchangers 0.422 0.504 0.578 1.503 0.419 0.455 0.535 1.409 Hot utility 3.512 7.212 13.352 24.076 3.163 2.714 12.200 18.078 Cold utility 1.602 3.616 4.189 9.406 0.487 0.530 4.901 5.918 TAC, HEN subsystem 5.536 11.331 18.119 34.986 4.069 3.700 17.636 25.405 TAC, overall IHIWAN - - - 37.286 - - - 28.286 479 82.3, 75 18.9, 40 7145 Plant 1 SR1-1 72 100 40 SR1-2 360 100 100 SR1-3 144 800 75 SR1-4 36 800 50 CR 498 296.35 30 SK1-1 72 0 40 SK1-2 360 50 100 SR1-1 72 100 40 SR1-4 36 800 50 SK1-3 144 50 75 SK1-4 36 400 50 Fresh 498 0 20 E 1-1 E 1-2 E 1-3 C 1-1 H 1-1 H 1-2 24661 8925 435 2578 Centralized Regenerator 180, 100 Plant 2 SR2-1 360 100 100 SR2-3 600 1100 100 SR2-2 144 800 75 Waste 215.87 885.72 30 SK2-1 360 50 100 SK2-2 144 50 75 Spl-Ind 250.20 20 30 SK2-3 600 800 100 Fresh 253.80 0 20 E 2-1 C 2-1 H 2-1 9735 14580 1250 CR 268.59 389.60 30 E 2-2 C 2-2 1555 1244 7200 8406 1073 Plant 3 SR3-1 68 250 40 SR3-4 436 150 48 SR3-5 832 160 46 CR 2222.54 155.50 30 SK3-4 36 20 81SK3-5 432 148 49 SR3-2 169 100 43 SK3-6 1332 20 44.8 SR3-5 832 160 46 E 3-1 E 3-2 C 3-1 H 3-4 H 3-5 9665 25930 2142 9300 SK3-1 209 20 44.8 SK3-2 972 20 43.9 SR3-1 68 250 40SK3-3 190 20 43.1 Spl-Ind 2739 20 30 H 3-1 H 3-2 6462 3608 H 3-3 2903 13333 H 3-6 Spl-Dir 19.54 389.6 92.86 50 Source number flowrate t/h concentration ppm temperature °C Sink number flowrate t/h concentration ppm temperature °C 1.6, 100 4.3, 75 18.9,40 358.3, 100 18.9, 40 93 72, 20 53.1,40 291, 20 15.9, 50 135, 20 9, 50 24.27 21.88 420, 100 61.7,100 154.2,75 180,100 25.8, 100 19.5, 92.86 92.86 92.86 100 181.3, 20 72.5,20 178.7,30 71.5,30 19.5, 92.9 209, 30 972, 30 190, 30 36, 30 1332, 30 5.2, 40 169, 43 238.2, 46 SR3-3 1130 150 46 62.8,40 1130, 46 436, 48 593.7, 46 46.22 46.8 7 E 2-3 24.96 24.96 Flowrate t/h, Temperature °C E 1-1 Heat transfer load kW Temperature °C Figure 2: Optimal IHIWAN design of industrial park for case study 6. Conclusions This paper addresses a methodology for the optimal design of IHIWAN in the scale of industrial park. A combined superstructure specific to industrial parks is presented capturing all the intra-plant and inter-plant possibilities for integration, in which synthesis strategies are incorporated. An NLP model is correspondingly formulated, which is more computational friendly compared to conventional MINLP model. The effectiveness of the method is validated by a case study. Comparing the results v two approaches, it can be concluded that simultaneous design surpasses sequential design with TAC lower by 24.14 %. The method can promote the symbiotic system in industrial parks and contribute to the sustainable development of process industry. Acknowledgments The authors gratefully acknowledge the financial support from Natural Science Foundation of China (No. 21406026) and the Fundamental Research Funds for Central Universities of China (DUT16RC(4)07). References Boix M., Montastruc L., Pibouleau L., Azzaro-Pantel C., Domenech S., 2011, Eco-industrial Parks for Water and Heat Management, Computer Aided Chemical Engineering, 29, 1175-1179. Chang C., Wang Y., Feng X., Zhang P., 2015, A Two Step Methodology for Inter-Plant Heat Integration Design, Chemical Engineering Transactions, 45, 1759-1764. Chew I.M.R., Tan R., Ng D.K.S., Foo D.C.Y., Majozi T., Gouws J., 2008, Synthesis of Direct and Indirect Interplant Water Network, Industrial & Engineering Chemistry Research, 47, 9485-9496. Liu L., Wang J., Song H., Du J., Yang F., 2016, Synthesis of water networks for industrial parks considering inter-plant allocation, Computers and Chemical Engineering, 91, 307-317. Yan F., Wu H., Li W., Zhang J., 2016, Simultaneous optimization of heat-integrated water networks by a nonlinear program, Chemical Engineering Science, 140, 76-89. Zhou R., Li L., Dong H., Grossman I.E., 2012, Synthesis of Interplant Water-Allocation and Heat-Exchange Networks Part 1: Fixed Flowrate Processes, Industrial & Engineering Chemistry Research, 51, 4299-4312. 480