CHEMICAL ENGINEERING TRANSACTIONS VOL. 52, 2016 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Peng-Yen Liew, Jun-Yow Yong, Jiří Jaromír Klemeš, Hon Loong Lam Copyright © 2016, AIDIC Servizi S.r.l., ISBN 978-88-95608-42-6; ISSN 2283-9216 A Superstructure Based Optimisation Framework for Batch Water Network Synthesis with Multiple Wastewater Treatment Models Shuming Wang, Xiong Zou, Hongguang Dong*, Lei Sun School of Chemical Engineering, Dalian University of Technology, NO. 2 Linggong Road, 116024, Dalian, P.R. China hgdong@dlut.edu.cn The existence of numerous water treatment/regeneration technologies capable of increasing the reuse opportunities for water–using network of batch processes calls for a systematic methodology to choose between them. Hence, this article aims to propose a new framework for the synthesis of total water network in batch plants when varieties of treatment units are available. First, a state space superstructure incorporating all feasible configurations for water reuse, recycle and treatment is proposed, which also accounts for the selection of different wastewater treatment technologies. Then, a mixed-integer nonlinear programming (MINLP) model embedded with the scheduling formulation of treatment subsystemis formulated based on the proposed superstructure. Furthermore, trade-off between treatment cost and fresh water consumptionis also taken into consideration in the formulation. In addition, five rules are developed in the pre-processing procedure to eliminate redundant water treatment technologies to simplify the topological structure of the synthesis problem. Two cases are presented to compare different categories of treatment units in total water network and demonstrate the effectiveness of the proposed methodology. 1. Introduction Increasing water requirement coupled with serious environmental crisis stimulate researchers to address the water network synthesis which aims to minimize the cost as well as exploit the opportunities for water reuse. Over the past decades, numerous methodologies have been developed to synthesize the water network for batch processes, which can be generally classed into two types: insights-based and mathematical optimization-based approaches (Pintarič et al., 2014). Exhaustive overviews of the approaches for water network synthesis can be found in review paper (Gouws et al., 2010). After the synthesis of batch water network through water reuse/recycle had been deeply delved, treatment process was also introduced to further reduce water consumption and wastewater generation. Li et al. (2010) introduced state-time-space superstructure including semi-continuous treatment/regeneration to simultaneously optimize production scheduling and water-allocation network for batch processes. Also, Adekola et al. (2011) considered semi- continuous treatment and achieved wastewater minimization and the scheduling of the batch plants through event-based model at the same time. Furthermore, Liu et al. (2009) synthesized batch water-using network with centralized semi-continuous treatment unit. However, these contributions ignored the investment of water network with different treatment units. Tokos and Pintarič (2009) developed a MINLP model to synthesize the water network in a brewery plant with batch/semi-continuous process. The addition feature of this work is the incorporation of batch/semi-continuous treatment, of which the removal ratio of contaminant and investment are different. But the research ignores the selection of various water treatment units. Cheng and Chang (2007) integrated water-using network and wastewater treatment subsystem for batch processes. However, this work fixed the beginning and end time of both batch and semi-continuous treatment units (CT), neglecting the schedule of these treatment operations. It is noteworthy that as a result of the existence of various treatment technologies, treatment facilities in different operation modes are considered in the aforementioned literatures. DOI: 10.3303/CET1652010 Please cite this article as: Wang S., Zou X., Dong H., Sun L., 2016, A superstructure based optimisation framework for batch water network synthesis with multiple wastewater treatment models, Chemical Engineering Transactions, 52, 55-60 DOI:10.3303/CET1652010 55 1, 1, , in in tu t tu c t m c 1, 1, out out tu t tu c m c Treatment unit 2 2, in in tu tu c f c 2 2, out out tu tu c f c Treatment unit Treatment unit 2 2, in in tu tu c f c 2 2, out out tu tu c f c 2 2, c c tu tu c f c (a) (b) (c) Figure 1: Three categories of regenerators: (a) BT, (b) SCT, (c) TCT And treatment units can be classified as: batch treatment units(BT) such as membrane bioreactor (MBR) and sequential batch reactor(SBR), single outflow semi-continuous treatment unit(SCT) like adsorption system and two outflows semi-continuous treatment unit(TCT) like reverse osmosis (RO) system (Figure 1). Nevertheless, less attention has been paid to the impact of different categories of treatment units on batch water network as well as the selection of various water treatment units. Accordingly, this article presents a general superstructure of total water network with different treatment units, so as to compare different treatment technologies and determine optimal technologies in the total water network in different cases. 2. Problem statement The problem addressed in this article is stated as follows: given a specific flowsheet; fresh water source f; a set of water-using tasks i ∈I with contaminant c ∈C; batch treatment units tu1∈TU1 and semi-continuous treatment units tu2∈TU2, before and after which storage tanks u1/v1 and u2/v2 are installed respectively; end-of-pipe treatment for effluent e . And it aims to achieve a cost-optimal total water network with treatment subsystem for the fixed-load problem of the batch processes. To simplify the formulation, several sets are defined: SR for all storage tanks, SR = { sr | u1, u2 , v1 , v2 }; tu1SO for water sources of batch treatment unit tu1, tu1SO = { tu1so | i , u1,v2}; tu1SI for water sinks of batch treatment unit, tu1SI = { tu1si | i , v1 , u2 }; tu1SO = { srso | water sources of storage tank}; srSI = { srsi | water sinks of storage tank}; TU = TU1 ∪ TU2 = { tu | treatment units}; T = { t | boundary points of identical time intervals achieved by dividing the time horizon}. It should be noted that the capital investment for water network will be taken into consideration in the objective function. The followings are the hypotheses for the synthesis problem. (1) Production schedule is predetermined and water-using processes operate in truly batch mode. (2) CTs with flowrate controlled to aspecific range are available immediately, while batch treatment units with featured treatment capacity are only available when the treatment is fully completed. (3) A pair of storage tanks is assigned, before/after the treatment unit, and stream must go through storage tanks when it is purified in the CT, while there exist direct connections between BT and water-using operations. TCT concentrate fresh water effluent end-of-pipe treatment V1 U2 V2 U1 BT tub1 tubn .. CT tuc1 tucn .. effluent PO DNP mixer s p iltte r TS .. .. .. Figure2: State Space superstructure for batch water network 3. Superstructure To design water network for batch process, a novel superstructure is proposed based on state-time-space superstructure (STS) (Li et al., 2010), as shown in Figure 2, which was consisted by process operator (PO), 56 distribution network of water-using process(DNP) and treatment subsystem(TS). PO represents water using process in truly-batch pattern wherein water is supplied from mixers of DNP at the start and wastewater is discharged to splitters of DNP at the end of its operation. Wastewater from DNP is intercepted by RS, which includes batch treatment units (BT), semi-continuous treatment units (CT), storage tanks installed for treatment. And the superstructure also accounts for the selection of treatment technologies. According to the proposed superstructure, total water network can be synthesized with optimal treatment technologies. 4. Mathematical model For water-using processes in PO, mass balances around the inlet/outlet and overall balances can refer to the constraints in water reuse/recycle module in the literature of Chen et al. (2011). 4.1 Constraints in TS Resources balance of batch treatment unit:                  1, 1 1 1, 1 1 1, ', 1, , ' ' ' ' ' R0 | | 1 TU1, Ttu t tu t tu t t tu t t tu t t t T t T t bt t t t t t bt R R y y tu t (1) where tu1,tR is the resource of tu1 at time point t ; tu1,t,t'y is a binary variable that denotes the usage of tu1 . Wastewater mass and contaminant balances around inlet and outlet ofbatch treatment unit:      1 1 1 1, , 1, 1 TU1, Ttu tu tu in tu t so tu t so SO m m tu t (2)      1 1 1 1, 1, , 1 TU1, Ttu tu tu out tu t tu si t si SI m m tu t (3)       1 1 1 1 1, 1, , , 1, , , 1 TU1, C, Ttu tu tu tu in in out tu t tu c t so tu t so c t so SO m c m c tu c t (4) where in tu1,tm / out tu1,tm are the amount of inlet/outlet water in tu1, tu1so ,tu1,t m amount of water flow from water source sotu1 to tu1, tu1tu1,si ,t m amount of water flow from tu1 to water sink tu1si ; in tu1,c,tc , tu1 out so ,c,tc denote inlet and outlet concentration of contaminant c in tu1 and tu1so . Overall water and contaminant balances for batch treatment unit:             max max 1, ' tu1 1, , ' 1 1, 1, ' tu1 1, , 'cap (1 ) cap (1 ) 1 TU1, , ' T , ' bt out in out tu t tu t t tu tu t tu t tu t tm y m m y tu t t t t t (5)             max max 1, , ' tu1,c 1, , ' 1, 1, , 1, , ' tu1,c 1, , 'c (1 ) c (1 ) 1 TU1, , ' T , ' bt out in out tu c t tu t t tu c tu c t tu c t tu t tc y c c y tu t t t t t (6) Where: out tu,c,tc represents contaminant concentration in tu1at time point t ; min tu1cap / max tu1 cap ,minimum /maximum amount of wastewater purified by tu1, max tu1,cc maximum concentration of contaminant c in tu1 ,  tu1,c removal ratio for contaminant c ,  tu1 recovery ratio of water in tu1. Water and contaminant balance in semi-continuous treatment unit:  tu2α = 2 TU2 in out tu2 tu2f f tu (7)       2, 2, , 2, 2, , 2, , 2 TU2, , C, T out in out tu c u c t tu c tu c t tu c tc c c tu c t (8) Where: in tu2f / out tu2f are inlet/outlet flow rate, in tu2,c,tc / out tu2,c,tc inlet/outlet concentration, tu2,t,t+1mu amount of wastewater purified in tu2 ,  tu2,c removal ratio for contaminant,  tu2 recovery ratio of water. For semi- continuous treatment unit with fixed outlet concentration fx,out tu2,cC : out fx,out tu2,c,t tu2,cc =C                1 1 1 1max max 2, , 1 2, , 1 2, , 1F (1 ) F (1 ) t t t t t t t t T T T Tin in tu2 tu2 tu t t tu t t tu2 tu2 tu t tT T T T f dt dt ux mu f dt dt ux (9) where: tT time at time point t , tu2,t,t+1ux binary variable denoting the usage of tu2 , max tu2F maximum flow rate. Installation of the treatment units: 57                 1 1, , ' 2 2, , 1 ' 0 ' 1 1 1 TU1 2 TU2 nmax nmax tu tu t t tu tu t t t T t T t T t t t bt y tu ux tu (10) where  tu1 ,  tu2 denote binary variables that denote the selection of treatment unit. The mass balances around specific storage tank sr ∈SR in TS:                  , , 1 , 2 , 2, 1, 2 tu2 2, 1, 2 2 2 2 2 α SR, T, t1| | |in outsr t sr t sr t sr v sr t tu t t sr u tu t t sr v tu TU tu TU q q m m mu mu sr t t (11)                       , , , , 1 , , 1 , , , 2 , , , 2, 1, , , 2 2 2 tu2 2, 1, 2, , 1 2 2 2 α SR, C, T, t1 | | | out out in in out out out sr t sr c t sr t sr c t sr t sr c t sr v sr t sr c t tu t t sr c t sr u tu TU out tu t t tu c t sr v tu TU q c q c m c m c mu c mu c sr c t t (12)     , s , , s SR, 2, T sr sr sr in sr t o sr t o S m m sr sr v t (13)     , , , , , , , SR, C, Tsr sr sr sr in in out sr t sr c t so sr t so c t so S m c m c sr c t (14)    , , , SR, Tsr sr sr out sr t sr si t si SI m m sr t (15) where: sr,tq represents the amount of water stored, in sr,tm / out sr,tm amount of inlet/outlet water, in sr,c,tc / out sr,c,tc inlet/outlet concentration of contaminant c in sr , srso ,sr,t m amount of water flow from water source srso to sr , srsr,si ,t m amount of water flow from sr to water sink srsi , sr out so ,c,tc outlet concentration of contaminant c in srso . 4.2 Objective function                                    , , , , 1, , ' 1 1 1 1 ' ' in in tu2 1 2 2 1 2 2 2 0 0 =[ cf ce] NTC IC mav OC NTC ICS (T T )OC NTC (1-α )(T T ) ce NTC f i t i e t tu tu tu t t tu tu t T i I t T i I tu TU tu TU t T t T t t t bt sr sr t t tu tu t t tu sr tu TU t T t T Cost m m y n f f (16) where: Cost is total annualized cost, srn represents the installation of storage tank, cf/ce fresh water/end-of- pipe treatment cost, tuIC / tuOC installation/operational cost, srICS annualized investment of storage tank; NTC is total number of batch cycle every year. 5. Rules in pre-processing procedure              1 2 1 1 2 2max max tu1 tu2 tu2 IC Δt IC Cp OC 1 TU1 Cp OC 2 TU2 H cap NTC α F H NTC tu tu tu tu tu tutu tu (17) To reduce the model complexity, five rules in the pre-processing procedure for the selection of proper technologies are developed when various treatment technologies are available, shown as the following. Rule 1: If one contaminant can only be purified by a certain treatment technology, choose this technology. Table 1: Comparison results for case I Treatment units BT(Δt = 1 h) BT(Δt = 0.5 h) SCT TCT( = 0.7) BT & SCT Fresh water consumption(t/cycle) 71.594 68.594 68.594 71.266 63.03 Rule 2: For CT/BT, treatment units with less costs for treated water per hour Cptu ( $ / ( )t h ) (shown as Eq(17) ) would be preferred when the contaminant concentrations of their outlet flows are identical. Rule 3: For CT/BT, if the costs for treated water per hour Cptu ( $ / ( )t h ) are equal, treatment units with lower outlet concentration would be preferred. Rule 4: For BT, when their unit costs Cptu1 and outlet concentrations are equivalent, choose the facility with shorter operation duration of single batch. 58 Table 2: Process parameters for TU in the RS of the example Technologies Outlet concentration Water recovery ratio Installation cost ($/y) Operation cost ($/t) Operation capacity Duration (h) TU1 Situ reactor 150 1 5,000 0.1 [5,12]t 1 SBR 70 1 15,000 0.15 [7.5,18]t 1.5 MBR 70 1 10,000 0.2 [5,12]t 1 TU2 RO 20 0.7 23,000 0.6 [5,12]t/h - Ultrafiltration 50 0.7 14,000 0.5 [5,12]t/h - Adsorption 50 1 15,000 0.4 [5,12]t/h - Rule 5: If unit cost of BTCptu1 is consistent with the counterpart of CTCptu2 and their outlet concentrations for contaminant are controlled to a similar range, the latter is preferentially selected to remove contaminant due to that the scheduling of batch treatment unit may limit the opportunities for further water reuse. 6. Example study An illustrative example from Liu et al. (2009) is introduced, which consists of five water-using processes merely involving single contaminant. Maximum capacity of storage tanks are determined as 70 t. Limiting data for water-using processes is taken from scenario 2 in the work of Liu et al. (2009). Two cases will be discussed to illustrate the proposed method for the synthesis of total network. The problem is solved by DICOPT in GAMS 23.4, using CPLEX as the MILP solver and CONOPT as the NLP solver. 6.1 Case I: Comparison of different types of treatment units Irrespective of economic cost for treatment, this case is intended to explore the discrepancies of different categories of treatment units that are incorporated into the total water network, as well as verify rules in the pre-processing procedure. Maximum inlet flow rates of both SCT and TCT are set to be 11.875 t/h, and the capacity of BT is 11.875 t/batch. The duration of BT is defined as one hour. Outlet concentration of the all the treatment units are set to be 100 g /g, and the recovery ratio of TCT is determined as 0.7. The results are shown in Table 1. Optimal fresh water requirement of 68.594 t/cycle is attained when only SCT is involved in the water network, the same as the result in the paper of Liu et al. (2009). Note that fresh water consumption for batch water network involving BT& SCT is the lowest, as a result of greater capacity of this treatment. SCT has advantage over BT (Δt = 1 h) in fresh water consumption with identical average treatment capacities, which tests the pre-processing rule 5. Similarly, BT (Δt = 0.5 h) is superior to BT (Δt = 1 h) in fresh water consumption while their average treatment capacities are equal, verifying the pre-processing rule 4. Since rules1, 2 and 3 are apparent, it is unnecessary to validate them in this paper. 6.2 Case II: Selection of proper treatment technologies This case aims to apply the proposed methodology to determine proper treatment units and optimize the total water network. Economic parameters for available treatment units are presented in Table 2. The annual cost for each storage tank is assumed to be 1,000 $/y. Process parameters for treatment units are shown in Table 2, and costs of fresh water and wastewater treatment are 1 $/t and 5 $/t, respectively. Total number of batch cycles every year is perceived as 1,000. To decrease computational efforts, pre-processing rules are exploited to eliminate redundant treatment technologies before solving the problem. 0 21 3 4 5 6 7 8 U 2 /t 10 20 30 40 T/h T/h0 21 3 4 5 6 7 8 10 20 30 40 V 2 /t Figure 3: Storage profiles of the storage tanks 59 fresh water effluent to end-of-pipe treatment V2 A 0 21 C 3 4 5 6 7 8 B D E MBR U2 adsorption 5 0 18 35.44 1 3 .5 3 .9 4 6 5 .9 4 1 2 57.1 t 57.1 t 9 0 2 4 86 0 2 4 86 BT CT 25.041 0 1 9 .5 1 8 12 5 0 1 8 6 .0 6 T/h T/h T/h Figure 4: Resulting total water network for the example According to the pre-processing rules, ultrafiltration and SBR are firstly removed from the synthesis framework. Then, the other four types of technologies are incorporated into the superstructure, based on which the problem can be efficiently solved. The total annual cost of 386,400 $/y and fresh water consumption of 57,100 t/y for the total water network are achieved, which corresponds to a 20 % reduction in annualized investment cost and a 29.07 % reduction in fresh water consumption as compared to the water-using network with central storage tank. And compared with water network with adsorption, it yieldsa 9.3 % reduction in annual cost and a 14.8 % reduction in freshwater consumption. The total water network structure is depicted as Figure 4, indicating MBR and adsorption are selected for treatment. Also, the variations of the amount of residual water in storage tank u2 and v2 are depicted in Figure 3. In addition, it can be noted that storage tank u1 and v1 designated as buffer vessels for BT are not installed, which can decrease the investment cost of storage tanks. 7. Conclusions This article introduces a superstructure to incorporate varieties of treatment facilities (BT, SCT/TCT) into the optimization framework of batch water network. On the basis of the proposed superstructure, a MINLP model is formulated which consists of the scheduling formulation of batch treatment units. Then, five heuristic rules are developed to eliminate redundant treatment technologies, which can simplify the topological structure of the synthesis problem. Two cases are introduced todemonstrate the application of the proposed method. Form case I, pre-processing rule 4 and 5 are clearly verified, while the result of case II illustrates that the proposed approach can achieve a good trade-off between treatment cost and fresh water consumption. Acknowledgments This work is supported by the National Natural Science Foundation of China (No.21276039). 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