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/CET1545003 Please cite this article as: Ong B.H.Y., Pang Y.S., Wan J.Y., Yap A.K.S. , Ng W.P.Q., Foo D.C.Y., 2015, Water network optimisation with consideration of network complexity, Chemical Engineering Transactions, 45, 13-18 DOI:10.3303/CET1545003 13 Water Network Optimisation with Consideration of Network Complexity Benjamin H. Y. Ong a , Yoong Sze Pang a , Jian Yuan Wan a , Adrian K. S. Yap a , Wendy P. Q. Ng b , Dominic C. Y. Foo* a a Centre of Excellence for Green Technologies/Department of Chemical and Environmental Engineering, University of Nottingham Malaysia, Broga Road, 43500 Semenyih, Selangor, Malaysia b Eureka Synergy Sdn Bhd, No. 41-2, Jalan MPK 4, Medan Perdagangan Kepayang, 70300 Seremban, Negeri Sembilan, Malaysia Dominic.Foo@nottingham.edu.my This paper presents a superstructural model for the synthesis of water network, with the objective to reduce its complexity. A less complex network will ease its operation. Different constraints are added to the model, i.e. reduced piping length and number of piping connections. Literature case study comprises of ten water-using processes is used to demonstrate the approach. 1. Introduction Mass integration was extended by El-Halwagi and Manousiouthakis (1989) from heat integration (Linnhoff et al., 1982), following the analogy of heat and mass transfer. Water minimisation was then developed by Wang and Smith (1994) as a special case of mass integration. The main driving force for the developments of water minimisation is the awareness on environmental sustainability, which calls for the efficient use of water resources among industrial processes (Sueviriyapan et al., 2014). Insight-based pinch analysis and mathematical optimisation are the two major approaches developed rapidly in the past decades (Foo, 2012). Superstructural approach is one of the commonly-used mathematical optimisation technique for water minimisation. In recent years, some works on mathematical optimisation were reported for pre-treatment system (Ahmetović and Grossmann, 2011), as well as flexible network synthesis (Poplewski, 2014). In this paper, a superstructural model that incorporates different process constraints is proposed to synthesise a water network for the ease of process operation. When water minimisation is implemented for process plants with many water-using processes, it may lead to complex piping system. This may lead to controllability issue, due to the decrease in its degree of freedom. A less complex network is always desired as it will reduce operational and controllability issues of the process plant. Different model-size reduction techniques had been developed for different areas of process integration work. Lam et al. (2011) presented few model-size reduction techniques for large-scale biomass production and supply network. Amidpour and Polley (1997) presented decomposition approaches for heat exchanger network synthesis. Ng et al. (2012) on the other hand, decomposed an integrated heat exchanger network by dividing the integrated structure into two or more clusters. In this work, a superstructural model is developed to enable the synthesis of a less complex water network, which considers piping length and number of piping connections. 2. Model formulation In this section, the basic superstructural model for a water network is outlined. The objective function for the decomposition model is to minimise the total annual cost: Minimise TAC (1) For a water reuse/recycle network, this model has the following constraints: 14 i) Flowrate balance for process sources. Each process water source SRi may be allocated to the water sinks SKj, in which its allocated flowrate is denoted as FSRi,SKj. Unutilized source would be directed to waste disposal (WW), with flowrate term FSRi,WW. Eq(2) describes the overall flowrate balance for process source SRi, where FSRi denotes the total flowrate of source SRi. , ,SRi SKj SRi WW SRiSKj F F F  SRi SRI  (2) ii) Flowrate balance for process sinks. Each process water sinks have flowrate requirement, FSKj, which can be fulfilled by process sources (FSRi,SKj) or fresh resource (FW), with flowrate term FFW,SKj. Eq(3) describes the overall flowrate balance of process sink SKj. , ,SRi SKj FW SKj SKjSRi F F F  SKj SKJ  (3) iii) Contaminant load requirement. The amount of contaminant load from sources and fresh resource feed should not exceed the maximum limit of each process sinks, which is given by Eq(4). Source quality is denoted as qSRi and fresh resource quality is denoted as qFW. The maximum contaminant concentration of sink SKj is denoted as qSKj. , ,SRi SKj SRi FW SKj FW SKj SKjSRi F q F q F q     SKj SKJ  (4) In order to reduce the model’s complexity, two aspects are considered, i.e. number of piping connections and piping length. To consider number of piping connections, a binary variable BSRi,SKj is introduced in the model. The binary variable is activated using Eq(5): , , SRi SKj SRi SKj F B M  (5) where M is an arbitrary large value. The total number of pipelines, NP, in the network is given by: ,SRi SKj NP B  (6) An upper bound for the total number of pipeline, NP UB , is introduced such that the total pipelines does not exceed the maximum limit, as the number of pipelines are used to measure the complexity of the network: UB NP NP (7) To limit the total length of piping connection in the network, PL. Eq(8) is used: , ,SRi SKj SRi SKj PL D B  (8) An upper bound for the total piping length, PL UB , is defined in which the synthesised network should not exceed the given upper bound, which will confine the area of the network. UB PL PL (9) It is important to consider the cost element of a water network. The estimation of piping cost (CC) and operating cost (OC) are used to calculate the total annualised cost (TAC) of the network. The piping cost correlation includes variation (a) and fixed (c), given as in Eq(10). The coefficient a accounts for the linear impact of flowrate on the capital cost of piping; whilst, the fixed term c is a constant value that describes the basic capital cost contribution. The capital cost is directly affected by the distance or length of the connections between the process sinks and sources, DSRi,SKj.  , ,SRi SKj SRi SKjSRiCC aF c D   (10) The distance between two unit operations is calculated as the modular sum of difference in each axis due to the piping characteristic defined: ,SRi SKj SRi SKj SRi SKj D X X Y Y    (11) where X and Y are coordinates of the sinks and sources. The distances are assumed to be straight lines in the x-axis and the y- axis. Operating cost takes into consideration of fresh water (with unit cost CTFW) and waste discharge (with unit cost CTWW), as shown in Eq(12): 15 , ,FW SKj FW SRi WW WWSKj SRi OC F CT F CT   (12) The total annual cost, TAC, is then calculated by Eq (13): TAC OC AOT CC AF    (13) where annual operating time (AOT) is taken as 8000 h and the annualising factor (AF) is then calculatedusing: (1 ) (1 ) 1 y y IR IR AF IR     (14) 3. Example A literature example is adapted from Savelski and Bagajewicz (2001), compromises of ten water-using processes is used to demonstrate the proposed approach. The streams data of the case study is presented in Table 1. A direct reuse/recycle network with minimum freshwater consumption and total cost was synthesised using the superstructural model. The mixed-Integer Linear programming (MILP) models are formulated and solved using LINGO v14.0. In this work, three cases are solved with constraints in Eq(2) toEq(4) and Eq(10) to Eq(14) and objective function in Eq(1): (i) case 1: a base case model that minimises fresh water flowrate, (ii) case 2: minimum flowrate constraint is embedded for the piping connections, the total number of pipelines and individual pipe lengths are then used in case 3 as the upper boundary; and (iii) case 3: with maximum total number of pipeline of 23 pipes and piping length of 700 m, which are the maximum predefined from Model 2. The capital cost is calculated using Eq(10), where constants a takes the value of 2 and c takes the value of 250. On the other hand, annual fractional interest rate, IR, of 5 % and 5 y is considered for Eq(14). The network designs of all cases are found in Figures 1-3, while the stream flowrates are tabulated in Table 2- 4, and their comparison in Table 5. Table 1: Stream data for case study Process Number ∆Mp (kg/h) Cin max (ppm) Cout max (ppm) Fp (t/h) x-coordinates (m) y-coordinates (m) 1 2.00 25 80 36.4 36.36 661.82 2 2.88 25 90 44.3 250.00 604.55 3 4.00 25 200 22.9 350.00 509.09 4 3.00 50 100 60.0 113.64 413.64 5 30.00 50 800 40.0 227.27 362.73 6 5.00 400 800 12.5 250.00 286.36 7 2.00 200 600 5.0 350.00 318.18 8 1.00 0 100 10.0 190.91 76.36 9 20.00 50 300 80.0 304.55 76.36 10 6.50 150 300 43.3 477.27 63.64 Total minimum flow rate 354.4 Wastewater 1 8 4 6 9 5 2 3 7 10 50 100 150 200 250 300 350 400 450 5000 100 200 300 400 500 600 700 Freshwater Legend from freshwater to wastewater Figure 1: Case 1 - Integrated Water Network 16 1 8 4 6 9 5 2 3 7 10 50 100 150 200 250 300 350 400 450 5000 100 200 300 400 500 600 700 Wastewater Freshwater Legend from freshwater to wastewater Figure 2: Case 2 - Integrated Water Network with Reduced Complexity 1 8 4 6 9 5 2 3 7 10 50 100 150 200 250 300 350 400 450 5000 100 200 300 400 500 600 700 Wastewater Freshwater Legend from freshwater to wastewater Figure 3: Case 3 - The Decomposed Water Network Table 2: Case 1 - Flowrates of Integrated Water Network Sink 1 Sink 2 Sink 3 Sink 4 Sink 5 Sink 6 Sink 7 Sink 8 Sink 9 Sink 10 Wastewater Fresh water 10.00 26.26 32.00 17.14 23.18 18.00 40.53 - - - - Source 1 - - - - - - - - - - - Source 2 - 10.10 - - - - - - - - - Source 3 - 12.31 - - - - - - - - - Source 4 - - - 5.71 - - - - - - - Source 5 36.36 - - - 0.45 - - - - - - Source 6 - - - - - 0.10 - - - - 79.90 Source 7 - - 34.92 4.29 - - 0.26 - - - 34.72 Source 8 - 21.90 25.08 - 17.4 - - 0.85 - - - Source 9 - - - - 5.00 - - - - - 40.00 Source 10 - - - - - - 8.35 4.15 - 0.76 12.50 Table 3: Case 2 - Flowrates of Integrated Water Network with reduced complexity Sink 1 Sink 2 Sink 3 Sink 4 Sink 5 Sink 6 Sink 7 Sink 8 Sink 9 Sink 10 Wastewater Fresh water 10.00 33.33 34.31 22.86 23.64 30 35.69 - 3.75 - - Source 1 - - - - - - - - - - - Source 2 - - - - - 3.03 - - - - - Source 3 - - - 10.00 - - - - - - 21 Source 4 - - - - - - - - - - - Source 5 36.36 - - - - - - - - - 12.86 Source 6 - - - - 10.00 - - - - - 76.97 Source 7 - 44.31 - - - - - - - - 30.83 Source 8 - - 39.00 - - - - 4.33 - - 0.67 Source 9 - - - - - - - - 1.25 - 38.75 Source 10 - - - - - - 12.50 - - - 12.5 17 Table 4: Case 3 - Flowrates of Decomposed Water Network Sink 1 Sink 2 Sink 3 Sink 4 Sink 5 Sink 6 Sink 7 Sink 8 Sink 9 Sink 10 Wastewater Fresh water 10.00 26.26 32.00 17.86 23.63 20.00 40.00 - - - - Source 1 - - - - - - - - - - - Source 2 - 10.1 - - - - - - - - 1.42 Source 3 - 12.31 - - - - - - - - - Source 4 - - - 5 - - - - - - - Source 5 36.36 - - - - - - - - - - Source 6 - - 20.00 - - - - - - - 80.00 Source 7 - - 40.00 - - - - - - - 30.83 Source 8 - 20.48 - - 22.86 - - - - - 5.00 Source 9 - - - 5.00 - - - - - - 40.00 Source 10 - - - - - - 12.50 - - - 12.50 Table 5: Comparison between different models Case 1 Case 2 Case 3 Freshwater, FFW (t/y) 167 194 170 Piping Cost, CC ($) 3,297,283 3,714,628 3,515,060 Operating Cost, OC ($/y) 2,673,909 3,097,227 2,716,098 Number of pipelines, NP 28 24 23 Total Annual Cost, TAC ($/y) 3,435,582 3,955,306 3,528,077 *The cost of supplying freshwater and treated wastewater is estimated to be 1 $/t/h. As shown in Table 5, the network in cases 2 and 3 have less piping connections as compared to that in case 1. By setting upper boundaries for the number of pipelines and piping length, the network is divided into subsystems as according to Figure 3. By dividing the network into subsystems, the disturbances arises within the processing units remain within the subsystems; hence, easier controllability can be achieved to amend the disturbances, Note however that the costs of these cases are higher than that of case 1. In other words, the reduced complexity is compensated with higher cost. The piping and total annual costs of Model 3 is higher than those in case 1 by 6.6 % and 2.7 % respectively. The increase in operating cost of Model 3 is resulted by 16 % increment in freshwater and wastewater flowrates. However, the piping cost, total annual cost and freshwater flowrate of case 3 is significantly lower than those in case 2. On the other hand, by 4. Conclusions This paper presented a superstructural model of water network that emphasises on reduced network complexity, based on the number of piping connections and piping length. Future research work can be carried out to develop clustering approach in reducing the complexity of water network, integration of regeneration unit, as simultaneous heat and water recovery. Nomenclature Sets Parameter SRi Set of process sources AF Annualising factor SKj Set of process sinks AOT Annual operating hour FW Set of fresh resources Cin max Maximum inlet concentration WW Set of waste disposals Cout max Maximum outlet concentration Variable CTFW Unit cost of fresh resource BSRi,SKj Binary variable for the existence of CTWW Unit cost of waste discharge piping connection from SRi to SKj DSRi,SKj Distance between SRi and SKj CC Capital cost IR Annual fractional interest rate FFW,SKj Flowrate from source FW to sink SKj NP UB Upper bound for number of pipeline FSKj Flowrate required at sink SKj PL UB Upper bound for piping length FSRi Total flowrate from source Sri qFW Quality for fresh resource FW FSRi,SKj Flowrate from source SRi to sink SKj qSKi Quality of sink SKi FSRi,WW Flowrate from source SRi to sink WW qSRi Quality of source SRi NP Total number of pipeline XSKi x-coordinate of sink SKi 18 OC Operating cost XSRi x-coordinate of source SRi PL Total piping length YSki y-coordinate of sink SKi TAC Total annual cost YSRi y-coordinate of source SRi References Amidpour M., Polley G.T., 1997, Application of Problem Decomposition in Process Integration, Chemical Engineering Research Design, 75(1), 53-63. 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