Synthesis of Resource Conservation Networks with P-Graph Approach Direct Reuse/Recycle

Transcription

1 Process Integr Optim Sustain (2017) 1:69 86 DOI /s ORIGINAL RESEARCH PAPER Synthesis of Resource Conservation Networks with P-Graph Approach Direct Reuse/Recycle C. H. Lim 1 & P. S. Pereira 1 & C. K. Shum 1 & W. J. Ong 1 & R. R. Tan 2 & H. L. Lam 1 & D. C. Y. Foo 1 Received: 11 December 2016 /Revised: 5 March 2017 /Accepted: 5 March 2017 /Published online: 14 April 2017 # Springer Science+Business Media Singapore 2017 Abstract The need for climate change adaptation in industry has led to intensified research in industrial resource conservation, as well as waste reduction, to enable sustainable operations to be achieved even under conditions of declining water resources. Such sustainability initiatives can be facilitated using the systematic approach of process integration (PI). Of particular interest are resource conservation network (RCN) problems, which have been solved using pinch analysis or mathematical programming methods. On the other hand, other process system engineering (PSE) tools such as the process graph (or P-graph) framework offers potential alternative approaches to RCN problems. To date, P-graph methodology has been used for various process network synthesis (PNS) * D. C. Y. Foo Dominic.Foo@nottingham.edu.my 1 2 C. H. Lim chanheng9397@gmail.com P. S. Pereira petershaun92@gmail.com C. K. Shum chunkeat2@gmail.com W. J. Ong wenjie_ong0925@hotmail.com R. R. Tan Raymond.Tan@dlsu.ed.ph H. L. Lam HonLoong.Lam@nottingham.edu.my Department of Chemical and Environmental Engineering, University of Nottingham Malaysia Campus, Jalan Broga, Dahrul Ehsan, Semenyih, Selangor, Malaysia Chemical Engineering Department, De La Salle University, 2401 Taft Avenue, 0922 Manila, Philippines problems; however, no RCN synthesis applications have been reported thus far. This paper presents a novel implementation of P-graph for RCN synthesis. In addition to the inherent computational efficiency of its algorithms, P-graph allows the elucidation of optimal and near-optimal solutions, a feature which is potentially useful for practical decision-making. Capital and operating cost considerations can be incorporated easily. In this paper, direct reuse/recycle scheme is applied for in-plant RCN and inter-plant RCN (IPRCN). Keywords P-graph. Process integration. Resource conservation network. Optimisation. Waste minimisation Introduction Improving industrial resource efficiency is an important strategy for climate change adaptation in many parts of the world (Alkaya et al. 2015). Efficient use of resources such as water can be achieved through reuse, recycling and regeneration (Kumar et al. 2015). These measures can, in turn, be planned systematically using process integration (PI) for the synthesis of resource conservation networks (RCNs). El-Halwagi (1997) defined process integration as a holistic approach to process design and operation that emphasises the unity of the process. Using PI, both fresh resource consumption and waste generation can be reduced simultaneously. This technique was initially developed in the 1970s for enhancing industrial energy efficiency using heat exchange network systems (Hohmann 1971; Linnhoff and Flower 1978) and was later extended into various energy-intensive processes. In late 1980s, concept of mass exchange network (El-Halwagi and Manousiouthakis 1989) was reported, followed by other variants under the general family of mass integration systems in the 1990s (El-Halwagi 1997). Other PI tools have since been

2 70 Process Integr Optim Sustain (2017) 1:69 86 developed, focusing on material resource conservation such as water (Wang and Smith 1994), industrial gases (Alves and Towler 2002) and solvents and solid wastes (Kazantzi and El-Halwagi 2005), amongst others. All these variants were characterised by a common underlying problem structure, which facilitated the development of solution techniques that were applicable to different industrial problems. Amongst the various recovery systems, water network synthesis (often known as water minimisation) has emerged as a special case in response to water scarcity issue. The techniques developed for water network synthesis may be categorised as the insight-based water pinch analysis and mathematical optimisation approaches. In the seminal work of water pinch analysis, Wang and Smith (1994) formally defined direct reuse as the recovery of material from one process to the other and not being sent to the process where it is generated originally. The latter is referred to as direct recycle scheme. Although the work of Wang and Smith (1994) contributes greatly towards water network synthesis, it is however limited to fixed load problems, where water-using units are treated as mass transfer operations. Later works in this area focused on fixed flow rate problems, where non-mass transfer processes such as cooling tower makeup and reactor byproduct formation are included (Hallale 2002; Manan et al. 2004). After two decades of development, various graphical (El-Halwagi et al. 2003; Prakash and Shenoy 2005) and algebraic tools (Manan et al. 2004) have been developed. Whilst most works made use of contaminant concentration as a principal measure of water stream quality, later works have also reported the use of physical properties (such as electrical resistivity or density), based on the concept of property integration (Kazantzi and El-Halwagi 2005; Foo et al. 2006). A detailed review for most of the established water pinch analysis methods is reported by Foo (2009). Apart from in-plant recovery, water pinch analysis techniques were also reported for inter-plant RCN (IPRCN). The seminal work using water pinch analysis technique for IPRCN was reported by Olesen and Polley (1996), who suggested that site geography must be considered when synthesizing a water network. Later works on IPRCN targeting were reported by Spriggs et al. (2004) and Foo(2008) utilizing graphical and algebraic method, respectively. However, both of these works do not guarantee rigorous targets for an IPRCN. Hence, systematic procedures for IPRCN targeting were later proposed by Chew et al. (2010a, 2010b), taking into consideration of assisted and unassisted integration schemes. Although water pinch analysis offers good insights for problem analysis, it has however several shortfalls, e.g. limited to single contaminant, not able to handle complex problems. Mathematical optimisation techniques, in contrast, are more convenient in handling complex problems such as those with multiple contaminant, as well as those that involve cost optimisation (Huang et al. 1999; Savelski and Bagajewicz 2003). Mathematical optimisation techniques were also extended for IPRCN. A mathematical optimisation model incorporating mass integration strategies was proposed to handle the multiple-contaminant water network in the problem pulp and paper by Lovelady et al. (2007). Later work was reported by Chew et al. (2008), who developed generic IPRCN model with direct and indirect integration; the latter features integration via a centralised utility hub. Apart from the conventional superstructure model, some later developments on hybrid techniques were also reported, where mathematical models are built on the concept of water pinch analysis. One such techniques is called the automated targeting model (ATM) developed for direct reuse/recycle (Ng et al. (2009a), regeneration (Ng et al. 2009b) and total water network (Ng et al. 2010). Extensions to property integration (Ng et al. 2009c; Ng et al. 2010) and IPRCN (Chew and Foo 2009) werealso reported. Downside to these approaches is that only a single solution will be shown until more constraints are specified. Besides, as the network size increases, so will be the difficulty in solving the mathematical model, as the solving of large superstructure model can be very time consuming. Not only that, these approaches can be very complicated as they require knowledge in coding to formulate the structure and to interpret the results. It has been shown that errors in formulating superstructure models may result in nominal optimal solutions that perform poorly in the context of the real engineering problem (Heckl et al. 2010). There is a need to seek for an alternative approach/technique to address these issues. This calls for the use of process graph (P-graph) framework. Whilst various techniques have been developed for RCN synthesis, to date, no attempt has been reported on the use of P-graph framework for this purpose. The latter is a powerful approach which utilises graph theory to perform an efficient search of the solution space of a special class of the so-called process network synthesis (PNS) problems (Friedler et al. 1992a, b, 1993). The P-graph framework provides a mathematically rigorous process of determining the superstructure (or maximal structure) of a given PNS problem. At the same time, it allows for a more computationally efficient search of the solution space compared to the conventional branch-andbound algorithm used to solve generic mixed integer linear programming (MILP) models. P-graph has been used for a broad range of applications with similar structures as the basic PNS problem, for instance, optimisation of process systems (Nagy et al. 2001), and identifying sustainable energy supply chains (Lam et al. 2013). Chong et al. (2014) applied the P-graph methodology for the suitability of carbon capture storage (CSS) facilities being retrofitted into existing plants, taking account into consideration of power cost. P-graph methodology has also been used to synthesise process networks, factoring more than one constraint. Ng et al. (2015) synthesised an optimal bioenergy supply chain process network, using P-graph methodology, whilst

3 Process Integr Optim Sustain (2017) 1: factoring in constraints of cost and risk into the synthesis of the process network. In Tan et al. (2016), the P-graph methodology was also extended into determining optimal adjustments to allocation of resources during crisis conditions to minimise manufacturing losses. P-graph was used to synthesise multiple biomass corridor via decomposition approach (How et al. 2016). On the other hand, Lam et al. (2013) discusses the implementation of instructional P-graph modules in engineering degree programs in Malaysia and Philippines focusing on the design of green processes. Another recent work on footprint-constrained energy planning was also reported (Tan et al. 2017). Recent developments in P-graph methodology and applications are described by Lam et al. (2013) and Klemeš and Varbanov (2015). Whilst most work reported may focus on a specific constraint when synthesizing an optimum process network, no work has also been reported on synthesizing an optimum RCN with P-graph. In this paper, a novel application of P-graph methodology to RCN problems is developed. This framework brings distinct advantages over conventional mathematical and graphical approaches traditionally used for RCN synthesis. This paper focuses on both in-plant RCN and IPRCN with direct reuse/recycle scheme and is structured as follows. In the following section, formal problem statements for direct reuse/ recycle scheme for in-plant RCN and IPRCN are first given. This is followed by the basic formulations for both in-plant RCN and IPRCN in the following section. A brief overview of the P-graph framework is next illustrated. It will then be integrated into different scenarios featuring single- and inter-plant networks. A total of three examples will be used to supplement the proposed P-graph methodology. Each example features a unique character of itself and different incorporations of parameters to further prove the advantages of P-graph. Example 1 focuses on single-plant water network synthesis, whilst examples 2 and 3 will focus on inter-plant water networks. C max j is the maximum admissible concentration of sink j, whilst p min j and p max j are the specified lower and upper bounds on admissible properties of streams to sink j. Each source i (i =1,2,, m) has a given flow rate, F SRi, and a given impurity concentration C SRi or property P SRi (e.g. water resistivity and density). Also available for service is a fresh (external) resource with concentration C F or property P F (depending on property of choice) and can be purchased to supplement the use of process sources in sinks. Flow rate of the fresh resource (F R )istobedeterminedaspartofthe solution. For the case of direct reuse/recycle, it is desired to synthesise a RCN that features minimum flow rates/cost, whilst satisfying all process constraints. Figure 1a illustrates the SOURCE i = 1 i = 2 i = 3 i = N SR (a) SINK j = 1 j = 2 j = 3 j = N SK Problem Statement The problem addressed in this work can be formally stated as follows: Given a concentration- or property-based water network, with a number of process sinks (units) and sources (e.g. process and/or waste streams) that can be considered for possible reuse/recycle, it is desired to determine a network of interconnections amongst the process sinks and sources, so that the overall fresh resource and waste discharge flow rates are minimised, whilst the sink constraints are satisfied. Each sink j (j =1,2,, n) requires a feed with a given flow rate, F SKj, and an inlet concentration C in j,orpropertypin j, that satisfies the following constraints: C in j C max j or p min j p in j p max j ; where (b) Fig. 1 Superstructures for a direct reuse/recycle for RCN. b IPRCN with direct integration scheme (Foo 2012)

4 72 Process Integr Optim Sustain (2017) 1:69 86 superstructure representation for direct reuse/recycle for inplant recovery scheme. For an IPRCN, apart from in-plant RCN, material recovery is also carried out across different RCNs. Hence, the superstructural representations take the form as in Fig. 1b. Mathematical Model For the superstructure model for in-plant recovery scheme in Fig. 1a, the following constraints are used to describe for a concentration-based direct water reuse/recycle network. Equation 1 describes that the flow rate requirement of sink j is to be fulfilled by the flow rate allocated from process source i (F SRi, SKj ), as well as the fresh resource (F R, SKj ). F SKj ¼ i F SRi;SK þ F R;SKj ð1þ Equation 2 describes that the process sources and fresh resource being fed to a sink must fulfil the maximum impurity load of the sink, which is given by the first term of the equation. F SKj C SKj i F SRi;SKj C SRi þ F R;SKj C F j ð2þ The flow rate balance in Eq. 3 indicates that flow rate of each process source (F SRi ) may be allocated to sinks, whilst the unutilised source will be sent for waste discharge (F SRi, D ). F SRi ¼ F SRi;SKj þ F SRi;D i ð3þ Equation 4 indicates that all flow rate variables of the superstructural model should take non-negative values. F SKj ; F SRi;SKj ; F R;SKj 0 i; j ð4þ Note that the above model is also applicable for propertybased RCN, with impurity concentration (Eq. 2) being changed to property operators (Foo 2012). To incorporate cost considerations, capital and operating costs are to be included. To generate a water network with minimum total annualised cost (TAC), Eq. 5 is to be used. TAC ¼ AOC þ ACC ð5þ where AOC is the annual operating cost, which is the product of operating cost (OC) and annual operating time (AOT), given by Eq. 6. AOC ¼ OCðAOTÞ ð6þ The OC in Eq. 6 is contributed by the costs of fresh resource (with flow rate F R ) and waste discharge (with flow rate F D ), which are the product of their respective flow rates and unit costs (CT R for fresh resource; CT D for waste), given as in Eq. 7 that follows: OC ¼ F R CT R þ F D CT D ð7þ The last term in Eq. 5 is, i.e. the annualised capital cost (ACC), which is the product of capital cost (CC) with the annualised factor (AF). ACC ¼ CCðAFÞ ð8þ The basic form of piping cost is given in Foo (2012). CC ¼ ðafþbþd ð9þ where D is the distance between the water sink-source pairs. The annualising factor is given in Eq. 10 (Foo 2012). AF ¼ IR ð 1 þ IR ÞYR ð1 þ IRÞ YR 1 ð10þ where IR is the interest rate and YR is the operating life in years. For the superstructure representation for IPRCN in Fig. 1b, its model can also be simplified to the above model of the inplant RCN, when direct integration scheme is employed (Foo 2012). The optimisation objective can be set to determine the minimum total flow rate of fresh resource (F R ), given by Eq. 11. Minimise F R ð11þ where the total freshwater flow rate is given by the sum of its individual flow rate terms in Eq. 1. F R ¼ j F R;SKj ð12þ Alternatively, one may also set to minimise for TAC or AOC, given by Eqs. 5 and 6, respectively. Minimise TAC Minimise AOC ð13þ ð14þ The above model is a linear programme (LP) for which any solution found is globally optimal. P-Graph Framework A P-graph consists of a set of processes or operating units (Otype vertices), and a set of materials (M-type vertices), which represent the flows of material goods or energy in the system (Friedler et al. 1992a, b, 1993). Materials are categorised into raw materials (RMs), intermediates (Is) and products (Ps). O-

5 Process Integr Optim Sustain (2017) 1: ratios in turn reflect process yield, thermodynamic efficiency, stoichiometry, etc. The P-graph methodology is based on the five axioms, as stated by (Friedler et al. 1992a): (EP) (a) (b) (EP) Fig. 2 Newly proposed P-graph structure for sink-source matching. a Block diagram representation. b P-graph representation type and M-type vertices are linked to each other by arcs. Relative flow rates of materials with respect to a given operating unit are described by fixed to input-output ratios; such 1. Every final product is represented in the graph. 2. A vertex of the M-type has no input if and only if it represents a raw material. 3. Every vertex of the O-type represents an operating unit defined in the synthesis problem. 4. Every vertex of the O-type has at least one path leading to a vertex of the M-type representing a final product. 5. If a vertex of the M-type belongs to the graph, it must be an input to or output from at least one vertex of the O-type in the graph. These five axioms provide the basis for rigorous and efficient solution of PNS problems. The P-graph methodology uses three main algorithms, namely Maximal structure generation (MSG) This algorithm essentially generates a mathematically rigorous superstructure, or maximal structure, which contains all combinatorially feasible solution structures (Friedler et al. 1993). The mathematical rigour ensures a complete superstructure, which is not guaranteed by ad hoc model-building approaches (Heckl et al. 2010). Solution structure generation (SSG) Fig. 3 P-graph superstructure representation of a two-sink and two-source matching

6 74 Process Integr Optim Sustain (2017) 1:69 86 Table 1 Limiting data for Polley and Polley (2000) Water sinks Flow rate (t/h) Concentration (ppm) Load (g/s) SK ,000 SK ,000 SK ,000 SK ,000 Water sources Flow rate (t/h) Concentration (ppm) Load (g/s) SR ,500 SR ,000 SR ,500 SR ,000 Table 3 Distances (meter) between sources and sinks for example 1 (scenario 2) SR i /SK j SK1 SK2 SK3 SK4 SR SR SR SR This algorithm enables generation of all combinatorially feasible solution structures, all of which are sub-sets of the maximal structure (Friedler et al. 1992b). Note that this algorithm utilises the five axioms to eliminate redundant search paths and is the basis for the relative computational efficiency of the P-graph framework. Furthermore, identification of alternative structures allows near-optimal solutions (corresponding to each elucidated network structure) to a given problem to be identified without needing additional steps. Accelerated branch and bound (ABB) From the identified solution structures, this algorithm will identify the most optimal solution structures based on externally specified objective function (e.g. cost, flow rates). The advantage of P-graph methodology is that compared to conventional branch-and-bound algorithm used to solve generic MILP models, the ABB algorithm incorporates solutions from the MSG and SSG algorithms to reduce the overall search scope of possible solutions due to the inherent information embedded in all PNS problems; hence, optimal solutions can be identified more rapidly in large-scale problems as seen in Friedler et al. (1996). Furthermore, a local optimum can be found corresponding to each of the previously elucidated network, thus allowing a finite set of ranked nearoptimal solutions to be determined for any given problem (however, the methodology cannot directly trace degeneracy of solutions within a given network structure, where an infinite number of solutions may exist). In practice, such n-best solutions may only have marginally worse performance than the nominal global optimum. The capability to easily identify these solutions is very useful for a broad range of engineering problems, since near-optimal alternatives may have qualitative or intangible advantages that are not accounted for in model objective functions or constraints (Friedler 2015). Relevant information about P-graphs, including online tutorials and free software, are available via The original software came as separate modules (PNS Draw and PNS Studio) that were unified into a single platform (Pgraph Studio) in These software are configured to model and solve conventional PNS problems but cannot be used directly to solve RCN synthesis problems. Thus, using P- graph methodology for RCN synthesis requires translating the latter into an equivalent PNS problem. This translation is described in the next section. P-Graph Model for Direct Reuse/Recycle Scheme In order to determine the minimum fresh resource and waste flow rates for a direct reuse/recycle scheme, the recovery scheme is represented by a new structure in P-graph. A simple example is in shown in Fig. 2, where Table 2 Sink-source matching matrix for example 1 F SKj (t/h) C SKj (ppm) F SRi (t/h) C SRi (ppm) SR i /SK j SK1 SK2 SK3 SK4 WW 70 0 FW SR SR SR SR Table 4 Sink-source matching matrix for example 1 (scenario 2) F SKj (t/h) C SKj (ppm) F SRi (t/h) C SRi (ppm) SR i /SK j SK1 SK2 SK3 SK4 WW 70 0 FW SR SR SR SR

7 Process Integr Optim Sustain (2017) 1: Table 5 Alternative solutions for example 1 Solution ranking FW (t/h) WW (t/h) Number of connections AOC ($/year) ACC ($/year) TAC ($) MILP a ,000 12, , ,000 12, , ,000 12, , ,000 18, , ,000 22, , ,088,000 20,936 1,108, ,120,000 23,251 1,143,251 a Solution obtained from the works of Foo (2012) a source is to be reused/recycled to a sink. The P-graph structure can be depicted in a block diagram representation in Fig. 2a, where the RM is linked to an operating unit. The sources are represented as RMs, whereas the sinks are represented as end products (EPs) in a P- graph model as shown in Fig. 2b. Note however that this RM will not be consumed by the operating unit, but rather, it serves as information regarding the material. For example, it is necessary for a RM to be linked to an imaginary operating unit in order to produce two EPs, in which they represent two different constraints. For the case of RCN, these correspond to flow rate (Eq. 1) and impurity load (Eq. 2) constraints of the sink, respectively. In other words, the operating unit represents the source that is directed to a particular sink. Hence, the number of operating units should be equal to the number of sinks in the RCN. This new representation overcomes the limitation of P-graph that does not allow more input information for a particular RM, e.g. composition, concentrations and temperature. In the construction of a P-graph superstructure, note that fresh resources with zero impurity will not have an edge attached to the end product for its load constraint, as the load for this source is always zero. Note also that the fresh resources are not linked to the waste, as to avoid the fresh resource from being directed to the waste stream. For the case in Fig. 2, the sink flow rate is set as a constant 1 kg/h, whereas the impurity load is set to a range, i.e kg/h. This indicates that the Table 6 Limiting data for example 2 Water network Sink SK j Flow rate F SK (t/h) Concentration C SK (ppm) Source SR i Flow rate F SR (t/h) Concentration C SR (ppm) A B C

8 76 Process Integr Optim Sustain (2017) 1:69 86 Table 7 Flow rate comparisons for various alternative solutions in P-graph vs. MILP model Solution ranking Total freshwater (t/h) Total wastewater (t/h) Cross-plant pipelines (N) Total cross-plant flow rate (t/h) MILP a a Solution obtained from the works of Chew et al. (2008) maximum load tolerated by this sink is kg/h. On the other hand, the wastewater flow rate and load are given a range of zero to infinity to accommodate any remaining flow rate not being reused/recycle to the sinks. Similarly, looking at Fig. 2b, a 1-kg/h source (labelled as RM ) is being directed to a sink (represented by the end products as below). Each end product represents one constraint. As for the case of Fig. 2, one of the end products is labelled as FLOW, indicating that the flow rate allocated to this sink constrained to 1 kg/h, whilst the other end product is labelled as LOAD. These two EPs are connected to operating unit 1. Note that a source (or RM) has to pass through an imaginary operating unit (which acts as cost input) to reach a single sink only. A more complicated case is shown in Fig. 3, where two sources are to be sent to two sinks. As shown, two operating units are required for each of the source, as each of them is linked to two different sinks. Three examples are next shown to demonstrate the P- graph model for in-plant and inter-plant water network synthesis. Illustrative Examples Three examples are used to illustrate how P-graph methodology is extended to solve RCN problems. Example 1 focuses on in-plant water recovery problem, whilst examples 2 and 3 Table 8 Cost comparison for alternative solutions in Table 7 Solution ranking Total freshwater cost (million $/year) Total wastewater cost (million $/year) Total cross-plant piping cost (million$/year) TAC (million$/ year) MILP a a Solution obtained from the works of Chew et al. (2008) focus on inter-plant water networks. For all examples, the piping parameters in Eq. 9 are given as 2 and 250. The AOT is set to 8000 h for all cases. Example 1: Polley and Polley (2000) The classical water recovery example of Polley and Polley (2000) is demonstrated here with the newly proposed P- graph structure. This plant consists of four process water sources and four water sinks, with their limiting data given in Table 1. Pure freshwater (0 ppm) is available when water sources are insufficient for use in the water sinks. Two scenarios will be analysed, i.e. minimum freshwater flow rate and minimum TAC. The P-graph network was constructed for all possible sinksource matches using the structure described in previous section (see P-graph representation in 'Appendix). The P-graph network is first solved to minimise freshwater flow rate (scenario 1; optimisation objective given as in Eq. 11), with the optimal water network represented by the sink-source matching matrix in Table 2 (see Appendix for the P-graph structure of the optimal solution). As shown, the network has a minimum freshwater flow rate of 70 t/h and wastewater flow rate of 50 t/h. These match the previously reported results in various literature (e.g. El- Halwagi et al. 2003; Manan et al. 2004). Note that the P- graph solutions also show all alternative solutions that are degenerate (i.e. same freshwater flow rate) or less optimal (with higher freshwater and wastewater flow rates). For scenario 2 (minimum TAC; optimisation objective in Eq. 12a), Table 3 provides the respective distance between the various sinks and sources of the example (Foo 2012). The P-graph superstructure for this case is similar to the maximal structure for direct reuse/recycle alone. The optimal network is shown in Table 4. ThePgraph superstructure and its associated result are shown in Figs. 6 and 7 in the Appendix. In Table 4, the water network has a freshwater flow rate of 70 t/h and wastewater flow rate of 50 t/h. With unit costs of freshwater and wastewater both set to $1/t, and assuming that the capital cost is annualised over a 5-year

9 Process Integr Optim Sustain (2017) 1: Table 9 Sink-source matching matrix for example 2 F SKj (t/h) F WWA = F WWB = F WWC = CSKj (ppm) F SRi (t/h) C SRi (ppm) SK j /SR i SK1 SK2 SK3 SK4 SK5 WWA SK6 SK7 SK8 SK9 SK10 WWB SK11 SK12 SK13 SK14 SK15 WWC F FWA = FWA SR SR SR SR SR5 10 FFWB = FWB SR SR SR SR SR FFWC = FWC SR SR SR SR SR

10 78 Process Integr Optim Sustain (2017) 1:69 86 Fig. 4 Superstructure for IPRCN with multiple contaminants in P-graph period, with a fixed interest rate of 5%, the minimum TAC can be calculated following Eq. 2, as $972,012. This value of TAC matches with that obtained using the mathematical-based superstructure model (Foo 2012). Optimisation results for both solutions are shown in Table 5 for comparison. As mentioned earlier, P-graph generates alternative solutions for a given problems. Table 5 shows the five Fig. 5 Process flow diagram for an integrated pulp mill and bleached paper plant (Lovelady et al. 2007)

11 Process Integr Optim Sustain (2017) 1: Table 10 Limiting data for integrated pulp mill and bleached paper plant (Lovelady et al. 2007) Plant Unit Sink SK j Flow rate F SK (t/h) Mass load, m j (t/h) Unit Source SR i Flow rate F SR (t/h) Mass load, m j (t/h) Cl K Na Cl K Na Pulp (A) Washer 1 13, Stripper 1 1 8, Screening 2 1, Screening 2 1, Washer/filter 3 5, Stripper 2 3 1, Paper (B) Bleaching 4 30, Bleaching 4 30, alternative sub-optimal water networks, in an ascending order of TAC. Solutions 1 and 2 both utilise the same minimum freshwater and wastewater flow rates. However, network in solution 2 has higher piping cost and hence is a sub-optimal solution. The other solutions in Table 5 are networks that incur water penalties and have higher TAC as compared to the optimal solution. Having these alternative solutions is the advantage of P- graph, as it is always desired to have alternative solutions in industrial practises (and with known deviation from the best objective). Example 2: Interplant Water Minimisation (Olesen and Polley 1996) Example 2 features an interplant water integration (IPWI) problem with single contaminant, taken from Olesen and Polley (1996). Its limiting data is shown in Table 6.Inthis example, a few assumptions are made: (1) freshwater contains no contaminant; (2) equal Manhattan distance of D = 100 m between all water networks; (3) the capital cost for the cross-plant pipelines were annualised to a 5-year period, assuming a fixed interest rate of 5%; (4) difference of piping cost for different reuse or recycle schemes within each plant is negligible; and (5) unit cost for freshwater and effluent treatment areassumedat$0.13/tand $0.22/t, respectively (Kazantzi and El-Halwagi 2005). These assumptions are made in order to have comparable results with MILP work of Chew et al. (2008). The model is solved for minimum TAC (optimisation objective in Eq. 12a), with result comparisons summarised in Tables 7 and 8. InTable7, four alternative solutions generated by P-graph are shown, whilst Table 8 summarises the cost associated to the alternative solutions in Table 7. Optimisation results in Tables 7 and 8 show a comparison between the minimum annualised cost solution obtained by using the MILP model in Chew et al. (2008) and the proposed P-graph methodology. Both models agree that minimum freshwater does not ensure minimum total annualised cost. P-graph also verified that higher freshwater flow rate will reduce total cross-plant flow rate. Besides, minimum freshwater required is t/h when N is 1. Solutions between two models are identical for N = 2 with a total annualised cost of $0.896 million, with both minimum freshwater and wastewater flow at t/h. Optimum network obtained via P-graph is shown using the sink-source matching matrix in Table 9, where values in italics indicate crossplant streams. The P- graph superstructure and the results for this example are shown in Figs. 8 and 9 in the Appendix. IPRCN with Multiple Contaminants (Constraints) Whilst some processes may focus on a particular contaminant, there are also processes with stringent requirements for more than one contaminant. This section will Table 11 Sink-source matching matrix for example 3 F SKj (t/h) 13,995 1,450 5,762 30,990 30,291.5 M SKj Cl (t/h) M SKj K + (t/h) M SKj Na + (t/h) F SRi (t/h) M SRi Cl (t/h) M SRi K + (t/h) M SRi Na + (t/h) SR/SK SK1 SK2 SK3 SK4 WW 40, FW 9, ,973 8, SR1 3,400 5,501 1, SR2 1, , SR , SR ,291

12 80 Process Integr Optim Sustain (2017) 1:69 86 Table 12 Near-optimal solutions for example 3 Solution ranking AOC ($/year) Total freshwater (t/h) Total wastewater (t/h) 1 563,316,800 40, , ,320,000 40, , ,497,600 40, , ,776,000 40, ,320.0 detail the incorporation of the P-graph methodology into processes featuring multiple contaminants of concern. The P-graph superstructure for IPRCN with multiple contaminants is shown in Fig. 4. For a direct integration scheme, apart from in-plant reuse/recycle to sinks in the local network, water sources may also be integrated with sinks from another network. Similar to the previous example, freshwater is the external source to be considered after all available water sources are fully utilised. All costing setup for respective sinks, sources, freshwater and wastewater are identical. As an example, source 1 have concentrations of 10 ppm for load A and 12 and 15 ppm for loads B and C correspondingly. It is worth noting that the values are regardless of unit. Maximum value for different kind of loads can be specified as maximum flow of product in P-graph. Also, P-graph will be able to show other important information such as lesser number of cross-plant pipes and reduced cross-plant flow. Example 3: IPRCN with Multi-Contaminant (Lovelady et al. 2007) This example illustrates the IPRCN of an integrated pulp mill and a bleached paper plant as found in Lovelady et al. (2007). Figure 5 shows the process flow diagram of an integrated plant. The main objective for this example is to minimise freshwater and wastewater costs. The costs for freshwater and wastewater are given as $1 and $1, respectively. In order to have fair comparison with the original work, the objective is set to minimise AOC (Eq. 12b). Table 10 summarises the limiting data for both plants. As shown, this is a multiple contaminant problem and water recovery will be bounded by the concentrations of three ions, i.e. chlorine, potassium and sodium. Concentration of ions in freshwater is given as 3.7, 1.1 and 3.6 ppm for Cl,K + and Na +, respectively (Lovelady et al. 2007). It is worth noting that the load of water sources is changed to concentrations in terms of ppm, similar to previous examples. Hence, loads for water sinks are multiplied by 10 6.As long as both sources and sinks load unit correspond to each other, there will be no effect caused by units that are used. P- graph yields an AOC of $563.3 million, with overall minimum freshwater flow rate of 40,123.6 t/h and wastewater flow rate of 30,291.5 t/h, which is identical with the results published by Lovelady et al. (2007). The IPRCN is shown using the sink-source matching matrix in Table 11, whilst the nearoptimal solutions are shown in Table 12. The P-graph superstructure and the results for this example are shown in Figs. 10 and 11 in the Appendix. Conclusion In this work, a P-graph-based approach to RCN synthesis has been developed. The methodology has been demonstrated with three literature case studies, for which the results match those reported previously. However, one important feature of this P-graph approach is the capability of identifying alternative optimal and near-optimal solutions corresponding to the network structures generated within the embedded algorithms; this feature can facilitate practical implementation of RCNs, especially if the near-optimal solutions have intangible or qualitative advantages over the nominal optimum. P-graph models are developed once and can be then used for different applications by specifying only the related data inputs. Hence, future works on water and property-based network synthesis with P-graph are able to use the framework and methodology proposed in this paper (Figs. 6, 7, 8, 9, 10 and 11).

13 Process Integr Optim Sustain (2017) 1: Future extensions of this work include extending the P-graph methodology to total network synthesis that incorporates pre-treatment schemes, regeneration schemes and waste treatment plant design. Furthermore, the synthesis framework can be broadened by including various approaches for selecting an RCN configuration from different alternatives, using such methods as Monte Carlo simulation, global sensitivity analysis (GSA) or multicriterion decision making (MCDM). Nomenclature Indices i Process sources (i = 1, 2,, m) p max j Variables ACC AF AOC AOT CC specified upper bound on admissible properties of streams to unit j Annualised capital cost Annualised Factor Annual operating cost Annual operating time Capital cost of piping j Process sinks (j = 1, 2,, n) Parameters C SRi Concentration of a source i C in j C max j Concentration of a sink j Maximum concentration of a sink D EP F R,SKj F SRi, SKj Distance between sink and source End Product Fresh resource flowrate to sink j Flowrate allocated from process source i to sink j F R F D CT R CT D F skj F SRi p in j P SRi P F p in j p min j Fresh resource flowrate Waste discharge flowrate Fresh resource unit cost Waste discharge unit cost Flowrate of process source i Flowrate of process sink j Property of process sinks j Property of process source Property of fresh resource Inlet property of process sinks Specified lower bound on admissible properties of streams to unit j F SRi, D IR IPRCN OC PC PI RC RCN RM TAC YR Flowrate allocated from process source i to waste discharge Annual fractional interest rate Interplant Resource Conservation Network Operating Cost Piping Cost Process Integration Recovery factor Resource Conservation Network Raw Materials Total Annual Cost Number of years considered in the analysis

14 82 Process Integr Optim Sustain (2017) 1:69 86 Appendix (P-Graph Superstructure and Their 1 Optimal Solution For Examples) 1 Fig. 6 P-graph superstructure for example 1 1 P-graph files are made available to readers by contacting the corresponding authors.

15 Process Integr Optim Sustain (2017) 1: Fig. 7 P-graph optimum solution structure for example 1 SR 1 SR 2 SR 3 SR 4 SR 11 SR 5 SR 12 SR 13 FW Load Constraint Flow Constraint SK 2 SK 1 SR 6 SK 4 SK 3 SR 7 SK 8 SK 6 SK 5 SK 7 SR 8 Fig. 8 P-graph superstructure for example 2 SK 10 SK 9 SR 9 SK 11 SK 13 SK 12 SR 10 SK 15 WW SK 14 SR 14 SR 15

16 84 Process Integr Optim Sustain (2017) 1:69 86 SR 1 SR 2 SR 3 SR 4 SR 5 SR 11 SR 12 SR 13 FW Load Constraint Flow Constraint SK 1 SK 2 SK 4 SK 3 SK 5 SK 6 SK 8 SK 10 SK 11 SK 13 SK 15 SK 7 SK 9 SK 12 SK 14 WW SR 6 SR 7 SR 8 SR 9 SR 10 SR 14 SR 15 Fig. 9 P-graph optimum solution structure for example 2 Fig. 10 P-graph superstructure for example 3

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