Multiperiod Planning of Optimal Industrial City ... - ACS Publications

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Multiperiod Planning of Optimal Industrial City Direct Water Reuse Networks Sumit Kr. Bishnu,† Patrick Linke,*,† Sabla Y. Alnouri,† and Mahmoud El-Halwagi‡ †

Department of Chemical Engineering, Texas A&M University at Qatar, P.O. Box 23874, Education City, Doha, Qatar The Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122, United States

‡

ABSTRACT: The minimization of the water footprint of industrial cities or parks requires the development of efficient water reuse strategies. Current methods for water integration do not consider industrial city planning horizons in the development of optimal water reuse and recycle strategies. This article presents a multiperiod planning approach for water integration within industrial cities. The initial formulation considers direct reuse of water between plants and involves water streams with several pollutants. A source−sink water mapping model was implemented such that available water sources can be either allocated to water sinks or discharged as wastewater streams. Freshwater streams were made available to mix with water sinks as necessary, to enable reuse between plants. The work presents two optimization models to determine the minimum freshwater use in the industrial city through maximum direct water reuse regardless of cost (model 1) and the lowest-cost design for direct water reuse (model 2). Several illustrative examples are presented to demonstrate the proposed methods. The results indicate great potential for achieving considerable savings of resources when integration strategies for plants are developed over an entire planning period rather than individual time periods. co-workers14,15 proposed mixed-integer linear programming (MILP) models for the plant-wide synthesis of water integration through recycle and reuse. Linear models considering topological constraints have been developed for solving the mass-exchangerbased formulation of the water-recycle problem.16 Gabriel and El-Halwagi17 developed a globally solvable optimization approach for the simultaneous synthesis of waste interception and material reuse networks. Chakraborty18 developed a source−sink equivalent of the same problem and proposed a mixed-integer nonlinear programming (MINLP) and MILP model. Chen et al.19 developed an MINLP problem for designing an interplant water network considering centralized and decentralized mains. Soo et al.20 considered water networks with distributed treatment units. Wang et al.21 designed a water network using the concept of concentration potential and linear programming. All of the research contributions mentioned so far consider water network integration within single plants. Additional research efforts have also been directed toward interplant integration problems, mostly relying on optimization methods. Klemes22 recently presented a review of water integration techniques and methodologies. Lovelady et al.23 applied the concept for integrating a pulp and paper plant water network that could handle multiple contaminants. Lovelady et al.24 also tackled the design of eco-industrial parks (EIPs) using a source− interceptor−sink representation. Chen et al.19 presented an MINLP problem for the interplant water integration of an industrial city considering recycle/reuse across plants. The objective of their formulation was the optimal selection of treatment

1. INTRODUCTION Many processes require water for various operations and utility applications. In addition to the need for water input, this typically results in significant amounts of wastewater being generated and discharged into the environment. With freshwater resources becoming scarcer and environmental regulations becoming tighter, there is a strong need for industries and their regulators to reduce the water footprints of industrial operations in terms of water intake and wastewater generation. Water integration within and across processes presents a practical approach to reduce water footprints of processing systems by exploiting synergies at the level of the processing system. Many strategies involving a single plant for a single period have been developed. Early works by El-Halwagi and Manuosiouthakis1 and Wang and Smith2 implement the concept of pinch analysis for the water treatment, exchange, and integration problems within a single plant. Alva-Argáez et al.3 introduced water-pinch decomposition to integrate the water-usage system of a petroleum refinery. El-Halwagi et al.4 developed the material recycle pinch diagram for the targeting and synthesis of recycle networks for various species (e.g., water, hydrogen, raw material). Additional approaches were developed and implemented to solve fixedflow-rate problems by Almutlaq et al.,5 Dhole et al.,6 Foo et al.,7 Hallale,8 Manan et al.,9 and Polley and Polley.10 Chen et al.11 utilized graphical techniques for synthesizing water networks in batch plants. Chung et al.12 developed a process-based graphical approach for the simultaneous targeting and design of water networks. Shenoy13 implemented graphical techniques together with a nearest-neighbor algorithm for solving fixed-flow-rate and fixed-contaminant problems. In terms of algebraic approaches, the case of a single plant has been considered. El-Halwagi et al.4 developed a rule-based approach for matching sources and sinks by applying dynamic-optimality conditions to the graphical targeting problem. Chakraborty and © 2014 American Chemical Society

Received: Revised: Accepted: Published: 8844

March 4, 2014 April 23, 2014 May 7, 2014 May 7, 2014 dx.doi.org/10.1021/ie5008932 | Ind. Eng. Chem. Res. 2014, 53, 8844−8865

Industrial & Engineering Chemistry Research

Article

Figure 1. Multiperiod representation of an industrial city.

units. Castro et al.25 focused on the optimal reconfiguration of a multiplant water network in an EIP with the help of an MINLP formulation. Montastruc et al.26 discussed the capacity of EIPs to sustain sudden variations in the concentration levels of pollutants. Boix et al.27 proposed a multiobjective optimization problem that involves minimizing freshwater, wastewater, and the number of stream connections. Takshiri et al.28 proposed optimal water allocation using the concept of “emergy”. Lee et al.29

developed a mathematical optimization model for an interplant water network for processes involving both batch and continuous units. Sabla et al.30 developed water integration model for an industrial city taking into account the spatial representation of plants. In addition to deterministic methods, approaches based on stochastic optimization methods employing metaheuristics have also been tried. Lavaric et al.31 utilized a genetic algorithm for the 8845

dx.doi.org/10.1021/ie5008932 | Ind. Eng. Chem. Res. 2014, 53, 8844−8865


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Figure 2. General representation of source−sink mapping.

Table 1. Flow Rate Results of Multiperiod Freshwater Optimization for Case Study 1 Time Period 1 sinks (j) source (i)

back grinding (BG)

marking (MK)

wastewater (WW)

class 1−2 (C12) class 3−4 (C34) freshwater (FW)

440.25 0 559.75

209.75 490.25 0

0 109.75

Time Period 2 sinks (j) source (i)

back grinding (BG)

marking (MK)

wastewater (WW)


836.48 0 1063.52

463.52 1036.48 0

0 63.52


back grinding (BG)

marking (MK)

wastewater (WW)


1540.88 0 1959.12

759.12 1690.88 0

0 409.12


back grinding (BG)

marking (MK)

class 1−2 (C12) class 3−4 (C34) S1 S2 freshwater (FW)

858 0 1668.89 0 1473.11

2 2400 0 0 398

D6

0 0 2361.1 0 1888.9 Time Period 5

D8

D9

wastewater (WW)

1740 0 0 2840 0

0 0 1950 0 0

0 0 0 0 0

sinks (j) source (i)

back grinding (BG)

marking (MK)

D6

D8

D9

wastewater (WW)


2 0 1822.22 0 2575.78

2 2600 0 0 398

0 0 2777.8 0 2222.2

2796 0 0 3500 204

0 0 2400 0 0

0 0 0 0 0

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Figure 3. Multiperiod optimization minimizing freshwater usage for time periods 1−3 (case study 1).

industrializing nations, where the capacities of plants often expand and new plants are developed. To deal with this scenario, multiperiod water network design approaches would be required to determine the optimal utilization of water over the planning horizon and beyond. Burgara-Montero et al.39 developed an optimization approach that incorporates seasonal variations in the optimal treatment of industrial wastewater effluents. Liao et al.40 proposed an approach to the design of water networks in a single plant considering a single contaminant. They divided the main design problem into two subparts. The first part involved determining the amount of freshwater and the total number of connections required in the network using a trans-shipment model. The second part allowed optimal water network designs to be synthesized using the data obtained from the first model. The work dealt with fixed-contaminant and fixed-load operation. Outside the area of water network synthesis, multiperiod planning approaches have been proposed for many applications, including oil field development,41−43 heat- and mass-exchange

optimization of water consumption and wastewater network topology. Prakotpol and Srinophakun32 developed a genetic algorithm toolbox for water pinch analysis. Shafiei et al.33 used a genetic algorithm to synthesize an optimal water network for a pulp and paper mill, and Jezowski et al.34 employed a genetic algorithm for the optimization of water usage in the chemical industry. Tan and Cruz35 synthesized optimal water reuse network retrofits for single components. Aviso et al.36 developed a fuzzy mathematical programming model for synthesizing the optimal water network for an EIP. Hul et al.37 utilized particle swarm optimization (PSO) and mutation-enhanced PSO for the synthesis of near-optimal topologically constrained propertybased water networks. Tan et al.38 developed a methodology for the design of efficient resource conservation networks using adaptive swarm intelligence. So far, all of the research efforts that have been mentioned have focused on water integration with the assumption that a plant or industrial city will not change over time. However, this is certainly not the case in rapidly 8847



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• a number of contaminants to be considered across the industrial city, • a number of wastewater streams (sources) of known flow rate and composition in each plant, • a number of water-using operations (sinks) together with flow rate requirements and constraints on feedwater contamination, • existing connections between sources and sinks and their corresponding flow rate constraints, • a number of time periods over which to develop water reuse network designs, • a known expansion schedule detailing the addition of new plants and associated sources and sinks and alterations in existing plants of the corresponding sources and sinks in each time period, • lengths of the shortest connections between all sources and sinks in the industrial city, and • known topological constraints that restrict the number of pipes in a given time period, determine • the allocation of water between sources and sinks and the corresponding water flow rates over the entire planning

network design,44,45 batch reactor design,46 and hydrogen network design.47,48 This article is the first step to developing multiperiod planning approaches for water network design in industrial cities and considers cases that involve only direct water reuse within plants. Subsequent efforts that involve multiperiod optimization with water treatment considerations among plants will be the subject of future work. The next section presents the general problem statement, followed by the model formulation and implementation before four illustrative case studies are presented. The results illustrate that multiperiod planning aids in the more efficient utilization of water and allows for long-term network cost reductions.

2. PROBLEM STATEMENT The general problem addressed in this work is the mapping of water sources and sinks existing in an industrial city over a planning time horizon, through direct water reuse. The main objective is to determine the most water-efficient water reuse allocation, as well as the most economically efficient water network design. The problem is formally stated as follows: Given • an industrial city hosting a number of plants, 8848



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Table 2. Flow Rate Results of Freshwater Optimizations of Individual Time Periods for Case Study 1 Time Period 1 sinks (j) source (i)

back grinding (BG)

marking (MK)

wastewater (WW)


440.25 0 559.75

100 600 0

109.75 0


back grinding (BG)

marking (MK)

wastewater (WW)


836.48 0 1063.52

400 1100 0

63.52 0


back grinding (BG)

marking (MK)

wastewater (WW)


1540.88 0 1959.12

431.82 2018.18 0

327.29 81.82


back grinding (BG)

marking (MK)


0 0 3618.89 0 381.11

0 2400 0 0 400

D6

0 0 2361.1 0 1888.9 Time Period 5

D8

D9

wastewater (WW)

2600 0 0 1980 0

0 0 0 860 1090

0 0 0 0 0


back grinding (BG)

marking (MK)

D6

D8

D9

wastewater (WW)


0 0 0 3500 900

0 2600 0 0 400

0 49.25 1866.04 0 3133.96

1366.04 0 5133.96 0 0

1433.96 0 0 0 966.04

0 0 0 0 0

sinks, a source of freshwater, and a wastewater discharge. Each source can be split into several streams: (1) source-to-sink flows (Fi(p1),j(p2),t) representing the flow from the ith source of plant p1 to the jth sink of plant p2 in time period t (p1, p2 ∈ P) and (2) source-to-waste flows (Fi(p1),ww,t) representing the flow from each source of plant p1 to the environment for discharge. The freshwater source is split and allocated to different sinks as (Fj(p2),t). A constraint on the number of connections between sources and sinks is placed by the binary variable Xi(p1),j(p2),t, which represents the connection between the ith source of plant p1 and the jth sink of plant p2. X assumes a value of unity if the flow rate associated with the particular stream is nonzero and greater than a given minimum required value. As pipelines are major capital items with long lifetimes, any connections made within a particular time period will remain in subsequent time periods.

horizon so as to maximize direct water reuse and minimize freshwater requirements (target) and • the cost-optimal direct water reuse network that connects sources and sinks within the industrial city, together with its evolution over the time periods (design). Figure 1 illustrates the expansion of an industrial city over three time periods. The changes within the city over time are summarized in an industrial city development plan, which, in turn, specifies all information pertaining to all plants involved, as well as the corresponding water sources and sinks present in each time period. This includes any capacity expansion of existing plants that results in capacity changes of individual sources and sinks over the time periods, as well as information on the addition of new plants in different time periods, with corresponding new sources and sinks. A number of sets are defined as a basis for our problem formulation: I {i = 1, 2, ..., Nsources | I is a set of process sources} J {j = 1, 2, ..., Nsinks | J is a set of process sinks} T {t = 1, 2, ..., N time | T is a set of time periods} P {p = 1, 2, ..., Nplant | P is a set of plant} B {b = 1, 2, ..., Ncontaminants | B is a set of contaminants} Figure 2 illustrates a source−sink mapping for direct water reuse in a single time period, showing p plants with i sources and j

3. PROBLEM FORMULATION Two multiperiod optimization problems for direct water reuse in industrial cities have been formulated: (1) a model to target the direct reuse strategy that requires the minimum amount of water over the planning horizon and (2) a model to determine the cost-optimal direct reuse network design and its evolution over the planning horizon. Model 1 allows the development of 8849



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Table 3. Flow Rate Results of Multiperiod Cost Optimization for Case Study 1 Time Period 1 sinks (j) source (i)

back grinding (BG)

marking (MK)

wastewater (WW)


440 0 559.75

100 600 0

109.75 0


back grinding (BG)

marking (MK)

wastewater (WW)


836.48 0 1063.52

400 1100 0

63.52 0


back grinding (BG)

marking (MK)

wastewater (WW)


1540.88 0 1959.12

350 2100 0

409.12 0


back grinding (BG)

marking (MK)


381.11 0 3618.89 0 0

478.89 2321.11 0 0 0

D6

0 0 2361.1 0 1888.9 Time Period 5

D8

D9

wastewater (WW)

1740 0 0

0 0 0 0 1950

0 78.9 0 0 0

0


back grinding (BG)

marking (MK)

D6

D8

D9

wastewater (WW)


2 0 4234.58 0 163.42

2 2598 0 0 400

0 2 2765.4 0 2232.6

2796 0 0 3500 204

0 0 0 0 2400

0 0 0 0

criteria that the user deems worth exploring during the solution of a case study. The objective function is minimized subject to a number of constraints. The source and sink mass balance constraints are described by the equations

information on the maximum possible water savings in the city over time regardless of cost. Results from model 1 constitute the minimum water footprint possible for the system using direct reuse. Model 2 allows the development of cost-optimal designs that would strike a balance between the value of water saved and the capital investment made in the direct reuse network. The two model formulations are presented in detail in the next two subsections. 3.1. Model for Minimum Freshwater Targeting. The optimization formulation developed for the targeting of freshwater used during the planning time horizon is presented below. The objective function involves the minimization of freshwater used, as described by the equation min ∑

Fi(p ),ww, t + 1

1

2

∀ i ∈ I ; p1 , p2 ∈ P

1

(2)

Ffw, j(p ), t + 2

∑ Fi(p ), j(p ), t + Fj(p ), t , 1

2

∀ j ∈ J ; p1 , p2 ∈ P

2

(3)

Water sources can be either discharged to the environment (Fi(p1),ww,t) or sent to a sink (Fi(p1),j(p2),t).Here, p1 and p2 can be the same plant or two different plants. Moreover, sinks are able to receive contaminant-rich water from sources (Fi(p1),j(p2),t) and/or freshwater (Ffw,j,t). A purity constraint ensuring that the maximum contamination levels tolerable by the sink processes are not exceeded was used, as provided by the equation

∑ ∑ wtFfw, j(p), t

t∈T p∈P j∈J

∑ Fi(p ),j(p ), t = Fi(p ), t ,

(1)

Here, wt is the weight assigned to period t, and Ffw,j(p),t is the freshwater flow rate to sink j of plant p in time period t. The weights are specified by the user in the context of the particular case under investigation. Criteria to determine the setting of the weights might include the relative net water demand in a given period over the maximum demand, the expected continuation of industrial city operation beyond the last planning period, or other

Ffw, j(p ), t C b,fw, t + 2

∑ Fi(p ), j(p ), tC b, i(p ), t ≤ Fj(p ), tC b, j(p ), t ,

∀ j ∈ J ; p1 , p2 ∈ P 8850

1

2

1

2

2

(4)



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Figure 5. Multiperiod optimization minimizing cost for time periods 1−3 (case study 1).

if ϵ≤Fi(p ), j(p ), t ≤ U ,

where Cb,fw,t is the concentration of contaminant b in freshwater, Cb,i(p1),t is the concentration of contaminant b in source i of plant p1 in time period t, and Cb,j(p2),t is the concentration of contaminant b in sink j of plant p2 in time period t. The number of connections can be limited to a maximum acceptable number, to maintain simple designs as necessary. Equation 5 imposes a constraint on the number of pipelines that can be constructed between sources and sinks

1

1

2

1

2

1

1

2

(6b)

2

1

2

1

(7)

2

According to this equation, if Fi(p1),j(p2),t < ϵ, then Fi(p1),j(p2),t and Xi(p1),j(p2),t are forced to be zero to satisfy the constraint, and if Fi(p1),j(p2),t lies between ϵ and U, then Xi(p1),j(p2),t is forced to be 1. Any connection made in time period t is carried forward into future time periods according to the expression

(5)

then Xi(p ), j(p ), t = 0

2

ϵXi(p ), j(p ), t ≤ Fi(p ), j(p ), t ≤ UXi(p ), j(p ), t

Xi(p1),j(p2),t denotes the existence of flow between source i of plant p1 and sink j of plant p2 in time period t. Interconnections with flow rates (Fi(p1),j(p2),t) below a minimum threshold (ϵ) can be discarded for economic reasons. This constraint is satisfied by the following if−then conditions if Fi(p ), j(p ), t ≤ ϵ,

1

where U is an upper bound on the acceptable flow rate, Fi(p1),j(p2),t. The if−then conditions of eqs 6a and 6b can be implemented with the help of the equation

∑ ∑ ∑ Xi(p ), j(p ),t ≤ Nt p∈P i∈I j∈J

then Xi(p ), j(p ), t = 1

2

Xi(p ), j(p ),(t + 1) − Xi(p ), j(p ), t ≥ Xi(p ), j(p ), t − 1 1

2

1

2

1

2

(8a)

An alternative formulation to handle the requirement of eq 8a that future period connections are enforced is the expression Xi(p ), j(p ), t = Xi(p ), j(p ),(t + 1) ,

(6a)

1

8851

2

1

2

{t : Xi(p ), j(p ), t = 1} 1

2

(8b)



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This equation ensures that, if a connection is not required in the previous period (Xi(p1),j(p2),t−1 = 0) and is required in the current period, values of all X in future periods will be set to 1. Finally, all flows must be non-negative

Ffw, j(p ), t ≥ 0

(9)

Fi(p ),ww, t ≥ 0

(10)

Fi(p ), j(p ), t ≥ 0

(11)

2

1

1

2

Table 4. Cost Chart of Multiperiod Optimization for Case Study 1 (×107 $) sinks (j)

Equations 1−11 constitute the optimization model for minimum freshwater targeting. Because a water network would develop over time and run beyond its development horizon, the relative importance of the different time periods might not be considered equal. Therefore, the objective function has a weight wt assigned to each time period t. The weights allow for the option to emphasize individual time periods. For instance, the importance of the individual time periods can be rated so that there is more emphasis on water savings in the last time period that would

source (i)

back grinding (BG)

marking (MK)

D6

D8

D9


1.15 0 2.99 0 2.48

0.59 0.78 0 1.05 1.23

0 0.17 1.03 0 2.12

2.46 0.72 0 1.56 0.65

0 0 0 0 1.82

wastewater (WW) 0.37 0.20 0 0

extend beyond the planning horizon. Time periods can be rated in different ways. The weighting could be done on the basis of flow rates in individual periods or on the total load being handled. The time periods can also be assigned equal weights if the industrial city is mature and is not going to expand significantly in the future. The setting of weights is user-dependent and should reflect the specific needs of a given case study. Apart from the minimization of freshwater, wastewater minimization can 8852



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Table 5. Flow Rate Results of Individual-Period Cost Optimizations for Case Study 1 Time Period 1 sinks (j) source (i)

back grinding (BG)

marking (MK)

wastewater (WW)


440 0 559.75

100 600 0

109.75 0


back grinding (BG)

marking (MK)

wastewater (WW)


836.48 0 1063.52

463.52 1036.48 0

0 63.52


back grinding (BG)

marking (MK)

wastewater (WW)


1540.88 0 1959.12

350 2100 0

409.12 0


back grinding (BG)

marking (MK)


2 0 3998 0 0

0 2400 0 0 400

D6

0 0 0 1634.61 2615.38 Time Period 5

D8

D9

wastewater (WW)

2598 0 1982 0 0

0 0 0 1205.38 744.61

0 0 0 0


back grinding (BG)

marking (MK)

D6

D8

D9

wastewater (WW)


0 0 900 3500 0

0 2079.78 920.22 0 400

0 0 2777.78 0 2222.22

2800 520.22 2 0 3177.78

0 0 2400 0 0

0 0 0 0 0

be set as an alternative objective function for the optimization problem. 3.2. Model for Cost-Optimal Network Design. The optimization formulation developed for minimizing the total cost used during the planning time horizon is presented next. The objective is to minimize the total cost of the network, both piping and freshwater cost utilization, as described in the equation min ∑

sinks (j)

wt [∑ ∑ a(DIic(p ), j(p ))b di , j

∑

t ∈ T p1 , p2 ∈ P

+

Table 6. Cost Chart of Individual-Period Optimization for Case Study 1 (×107 $)

1

i∈I j∈J

2

∑ a(DIcfw,j(p ))b dfw, j + ∑ a(DIic(p ),ww)b di ,ww j∈J

2

i∈I

+ H yC fresh ∑ ∑ Ffw, j(p ), t ] i∈I t∈T

2

1

source (i)

back grinding (BG)

marking (MK)

D6

D8

D9


2.09 0 2.99 2.28 4.49

1.47 1.34 0.6 0 1.23

0 0 1.03 1.02 2.11

3.34 0.97 1.67 0 2.06

0 0 2.31 1.3 1.11

wastewater (WW) 0.37 0.20 0 0

hours of operation in a time period, Cfresh is the cost of freshwater per ton, and a and b are cost parameters. The capital cost is a function of the diameters of interconnecting pipes, which, in turn, is calculated based on the flow rate through the interconnection as explained below. The number of connections are limited to a maximum acceptable number, to allow the user control to maintain simple designs as appropriate. Equation 13 imposes a constraint on the number of pipe connections that can be constructed between sources and sinks

(12)

where wt represents the weight associated with time period t, d represents the distance between two facilities, DIci(p1),j(p2) is the diameter of the pipe between source i of plant p1 and sink j of plant p2, DIcfw,j(p2) is the diameter of the pipe between the freshwater source and sink j of plant p2, DIci(p1),ww is the diameter of the pipe between source i of plant p1 and the wastewater discharge point, Ffw,j(p2),t is the flow rate between the freshwater source (Fw) and sink j of plant p2 in time period t, Hy denotes the 8853



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Table 7. Flow Rate Results of Multiperiod Freshwater Optimization for Case Study 2 Time Period 1 sinks (j) source (i)

P1D1

P1D2

wastewater (WW)

P2S2 P2S1 freshwater

43.71 2 74.28

39.18 0 40.82

37.1 78


P1D1

P1D2

P3D1

P5D1

wastewater (WW)

P2S2 P2S1 P3S1 P6S2 freshwater

10.82 25.36 0 0 83.82

39.18 0 0 0 40.82

0 27.83 0 0 52.17

70 0 70 0 0

0 26.81 70 80


P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)

P2S2 P2S1 P3S1 P6S2 P6S1 P4S1 freshwater

2 27.55 0 0 0 5.76 84.7

26.06 0 0 0 0 13.12 40.82

0 12.38 0 0 0 21.75 45.87

57.36 0 73.92 0 0 0 8.72 Time Period 4

34.61 0 18.36 2 0 25 0

0 40 47.71 78 0 0 29.22

0 0 0 0 195 34.34

source (i)

P1D1

P1D2

P3D1

P5D2

P4D1

wastewater (WW)


2 27.53 0 0 0 5.76 84.70

65.16 0 0 0 0 32.79 102

0 20.89 0 0 0 36.7 77.4

37.9 0 36.4 23.73 0 2 0

0 51.53 3.6 108.34 0 0 31.54

0 0 0 57.93 195 42.78 0

source (i)

P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


2 27.53 0 0 0 5.76 84.75

65.16 0 0 0 0 32.8 102

0 18.58 0 0 0 39.96 76.46

95 0 95 0 0 0 0

38 0 36 24 0 2 0

0 53.76 4 107.63 0 0 29.6

0 0 0 58.36 195 39.5

sinks (j) P5D1 95 0 95 0 0 0 0 Time Period 5 sinks (j)

Finally, a non-negative constraint was imposed on all flows within the network, described by the equations

∑ ∑ ∑ Xi(p ), j(p ),t ≤ Nt 1

2

(13)

p∈P i∈I j∈J

Equation 14 imposes a constraint on the minimum flow rate requirement enforced on a connection to avoid connections with very small flow rates and therefore diameters ϵXi(p ), j(p ), t ≤ Fi(p ), j(p ), t ≤ UXi(p ), j(p ), t 1

2

1

2

1

2

Ffw, j(p ), t ≥ 0

(16)

Fi(p ),ww, t ≥ 0

(17)

Fi(p ), j(p ), t ≥ 0

(18)

2

1

(14)

1

where U is a very large number and ϵ is the minimum value of the flow rate. Any connection made in time period t is carried forward into future time periods according to the equation

2

The pipe size (DI) is calculated as DI = 0.363(M 0.45ρ0.13 )

(19) 49

Xi(p ), j(p ),(t + 1) − Xi(p ), j(p ), t ≥ Xi(p ), j(p ), t − 1 1

2

1

2

1

2

This expression was taken from Peters et al., where M represents the volumetric flow rate given in m3/s and ρ is the

(15) 8854



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a planning horizon in determining water networks. In terms of results for the freshwater minimization model, we expect the amounts of freshwater required in both multiperiod optimization and single-period optimization over all time periods to be identical. This is because the model does not take into account the network cost and, therefore, can achieve optimal allocations for water in each period with additional connections and adjusted flows that might not be cost-effective. On the other hand, we expect the multiperiod model for cost optimization to determine lower-cost networks as compared to the single-period optimization. The MINLP model formulation given by Chakraborty18 was used to solve the freshwater and total cost minimization problems using single-period optimization.

density of the stream. The pipe diameter obtained using the expression is rounded off to one decimal place. The assumption of rounding up to the next highest decimal number is justified, as this gives a standard pipe size value (in meters) that satisfies the requirement of the flow and makes selection of the pipe easier. 3.3. Implementation and Case Study Development. The two MINLP formulations for multiperiod water minimization and cost-optimal network design were implemented using the “What’sBest 9.0!”50 global solver for MS-Excel 2007 on a laptop with an Intel Core 2 Duo processor T6400, 2 GHz, 4 GB RAM, and a 32-bit operating system. In addition to the multiperiod solutions developed for the case studies in section 4, results were also developed using single-period optimization. In single-period optimization, we do not take into consideration future supplies and demands when establishing connections between facilities. Each period is optimized with information for that period only while retaining connections made in previous periods. The single-period optimization results resemble the use of existing methods, which do not take into consideration

4. CASE STUDIES Two case studies illustrating the advantages of multiperiod planning over individual-period planning are presented in the following subsections. The case studies were solved separately 8855



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case studies are used only for instances of commissioning of plants, the expansion-plan data are artificial data and were generated under the assumptions that the contaminant level in the streams of the individual plants was constant for all time periods and that the ratios of the flow rates of sources to sinks did not vary much. The data for flow rates and concentrations that have been provided represent a mixture of real instances and hypothetical scenarios. The case study input data are presented in the Appendix. Freshwater Minimization. The flow rate results of multiperiod optimization for this example are provided in Table 1, and Figures 3 and 4 depict the development of the water network over time. By minimizing the weighted sum of the freshwater flow rates over five time periods, the minimum value obtained was 12742 tons/h. Weights were assigned on the basis of amount of flow handled during a period. The ratios of the total flow rates in individual periods to the total flow rate handled in all periods were made the basis for assigning the weights. Periods 1−5 were assigned weights of 5, 5, 15, 30, and 45, respectively, on a scale of 100. The ratios of the sum totals of the flow rates of all streams in

for both multiperiod and individual-period optimizations, the results of which were compared. In all case studies, the values of a, b, and ρ were set to 3114.86, 1.0532, and 1000 kg/m3, respectively. Hy was set to a value of 8760 h/year, and the cost of freshwater, Cfresh, was set to $0.13/ ton. The lower bound for the flow rate (ϵ) was set to 2 tons/h. 4.1. Case Study 1. This example is based on two case studies involving the Malaysian Textile Company (Ujang et al.51) and a thermomechanical pulp and newsprint mill (Jacob et al.52). The original case study of the Malaysian Textile Company consists of two sources and two sinks. The planning is done for 10 years divided into five time periods of two years each. The initial setup consists of only a bleaching section textile plant with two sources and sinks involving one type of contaminant. This setup expands in capacity for three time periods, with concentration levels of the contaminant staying the same in all time periods. In the fourth time period, the pulp and news print mill is commissioned, thereby adding another type of contaminant to the system. This system expands in capacity until the fifth period. Although the data available in the original 8856



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Table 8. Flow Rate Result of Individual-Period Freshwater Optimization for Case Study 2 Time Period 1 sinks (j) source (i)

P1D1

P1D2

wastewater (WW)


46.53 0 73.47

36.37 2 41.63

37.1 78


P1D1

P1D2

P3D1

P5D5

wastewater (WW)


46.53 0 0 0 73.47

0 27.82 0 0 52.18

0 27.83 0 0 52.17 Time Period 3

73.47 0 66.53 0 0

0 24.35 73.47 80


P1D1

P1D2

P3D1

P5D5

P5D2

P4D1

wastewater (WW)


0 29.09 0 0 0 5.58 85.33

23.1 0 0 0 0 13.84 43.06

14.63 0 0 0 0 24.54 40.82

50.59 0 0 63 0 0 26.42 Time Period 4

7.26 50.92 0 0 21.81 0 0

24.4 0 140 17 0 0 13.58

0 0 0 0 173.19 56.03

source (i)

P1D1

P1D2

P3D1

P5D5

P5D2

P4D1

wastewater (WW)


0 29.08 0 0 0 5.58 85.34

0 55.12 0 0 0 20.35 124.54

0 0 18.1 0 0 33.25 83.65

85.62 15.8 87.56 0 0 0 1 Time Period 5

39.38 0 29.34 31.28 0 0 0

75 0 0 120 0 0 0

0 0 0 38.72 195 60.83

source (i)

P1D1

P1D2

P3D1

P5D5

P5D2

P4D1

wastewater (WW)


0 29.08 0 0 5.58 85.34 0

59.32 5 0 0 0 31.68 104

0 0 15.96 0 0 37.14 81.9

95 0 95 0 0 0 0

0 65.98 24.04 10 0 0 0

45.68 0 0 128.15 0 0 21.17

0 0 0 51.88 195 45.59

sinks (j)

sinks (j)

in which only the existence of the pipe is fixed whereas it is diameter is determined by considering the entire time period. In this case, both the existence of a connection and its size are fixed after solving for a particular period. This approach gives a water network that is more complex. Moreover, the total number of interconnections required from multiperiod planning was found to be eight. The sum total of freshwater flow rates that was obtained by independently optimizing in individual time periods was 12742 tons/h. The total number of interconnections required to achieve this objective was 11. As expected, the amounts of freshwater required were equal in the two cases, but multiperiod planning provided a less complex piping layout.

a single period to the sum total of the flow rates of all streams in the entire period of planning were taken as the basis for these ratings. The fact that later periods provide a more developed picture of the industrial city was also taken into account. Based on these two facts, the periods were assigned ratings in multiples of five. The last period was assigned extra weight as it presents the most developed layout of the city. The five time periods were also solved individually for a comparison of the results. Table 2 presents the results for case study 1 from single-period optimizations minimizing the freshwater requirements. The flow rates obtained in a particular period form the basis of the selection of pipes without taking into account the needs of future periods, unlike the multiperiod planning approach, 8857



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Table 9. Flow Rate Results of Multiperiod Cost Optimization for Case Study 2 Time Period 1 sinks (j) source (i)

P1D1

P1D2

wastewater (WW)


46.53 0 73.47

39.18 0 40.82

34.29 80


P1D1

P1D2

P3D1

P5D1

wastewater (WW)


46.53 0 0 0 73.47

39.18 0 0 0 40.82

0 0 21.57 0 58.42

2 0 2 0 136

32.29 80 116.48 80


P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


37.55 0 0 0 0 8.98 73.47

26.06 0 0 0 0 13.11 40.82

0 0 10.73 0 0 19.7 49.57

9.73 0 88.7 0 0 0 41.56 Time Period 4

0 31.23 40.57 2 0 0 6.19

46.65 48.76 0 78 21.58 0 0

0 0 0 0 173.42 58.2

source (i)

P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


37.55 0 0 0 0 8.98 73.47

65.16 0 0 0 0 32.8 102.04

0 0 18.1 0 0 33.24 83.65

82.44 0 98.89 0 0 0 8.66 Time Period 5

0 2 18 49.71 0 0 30.28

14.84 98 0 80.15 2 0 0

0 0 0 60.13 193 44.97

source (i)

P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


37.55 0 0 0 0 8.98 73.47

65.16 0 0 0 0 32.8 102.04

0 15.95 0 0 0 37.14 81.9

95 0 95 0 0 0 0

0 65.98 24 9.97 0 0 0

2.28 34 0 119.19 2 0 37.5

0 0 0 60.13 193 41.08

sinks (j)

sinks (j)

Table 10. Cost Chart of Multiperiod Optimization for Case Study 2 (×107 $) sinks (j) source (i)

P1D1

P1D2

P3D1

P5D5

P5D2

P4D1

wastewater (WW)


0.31 0.21 0 0 0 0.35 0.66

0.28 0 0 0 0 0.63 0.59

0 0 0.12 0 0 0.55 0.49

0.57 0 0.45 0 0 0 0.65

0 0.56 0.54 0.41 0 0 0.42

0.23 0.29 0 0.25 0.13 0 0

0.15 0.2 0.53 0.42 0.66 0.49

and Figures 5 and 6 present the flow rate results, and Table 4 provides the cost chart, which gives the capital cost for piping.

Total Cost Minimization. Artificial data for an industrial city layout were generated and utilized for this example. Table 3 8858



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five in time period 2, four in time period 3, 10 in time period 4, and seven in time period 5. Because the periods are optimized independently, pipes are laid whenever the capacity increases. A multiperiod scenario allows for the flexibility of choosing the flow rates between two facilities by examining the entire period of planning and then selecting the maximum flow rates that can be handled. Selecting the maximum value of the flow rate ensures that the pipe diameter satisfies the need in all time periods, hence also ensuring a single-time pipe installation. Conversely, future periods are not taken into consideration in individual-period optimization. The flow rate in the pipe is determined as the optimization is done for a single period. This flow rate provides a pipe diameter that might fulfill the need for the current time period but probably will not be able to satisfy the need in future time periods. Therefore, extra pipes need to be installed between the facilities, and this results in increases in the cost and complexity of the water network. 4.2. Case Study 2. This case study considers planning of an industrial setup for five time periods of two years each. The initial setup consists of two sources and two sinks. This number increases to four sources and four sinks in the second time period, while the flow rates and concentration values of the

This example was also solved by considering the periods independently. Tables 5 and 6 present the flow rate and cost data, respectively, for case study 1 from single-period optimizations minimizing the total network cost. The capital cost of the network obtained using multiperiod planning was found to be $21.33 × 107, and the total cost of freshwater required within the fifth time period was $2.92 × 107. When the periods were solved independently, the capital cost of the network was increased to $34.03 × 107, and the cost of freshwater calculated was $2.92 × 107. Comparing the two results, one can see that the total cost calculated using multiperiod planning is 35% cheaper than that obtained by individual-period planning. The cost of freshwater was almost the same in both cases. The total number of connections required was found to be 15 for multiperiod planning and 30 for individual-period planning. The water networks in the multiperiod and single-period optimizations developed differently through time. In multiperiod optimization, five connections were made in time period 1, seven in time period 4, and three in time period five. Because the connections were made keeping in mind the future plan of the city, only single connections were required between two facilities. When single-period optimization was considered, four connections were made in time period 1, 8859



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utilized for this example. Table 9 present the flow rates from period 1 to period 5, and Table 10 present the capital cost chart. Figures 9 and 10 show the pipe network over the time periods. Tables 11 and 12 present the flow rate and cost data for case study 2 from single-period optimizations minimizing the total network cost. The capital cost of the network obtained using multiperiod planning was found to be $10.63 × 107, and the total of the cost of freshwater required in all periods was $0.24 × 107. When the periods were solved independently, the capital cost was calculated to be $12.91 × 107, and the cost of freshwater was calculated as $0.26 × 107. Comparing the two results, the total cost calculated using multiperiod planning was 17.68% lower than that obtained by individual-period planning. A total of 26 connections were required for the multiperiod planning case, as opposed to 36 connections for the individual-period planning case. In the case of multiperiod optimization, six connections were made in time period 1, four in time period 2, and 16 in time period 3. Only a single connection was established between the facilities, and the network satisfied the requirements in all time periods. When the periods were optimized independently, six connections were made in time period 1, six in time period 2, 14 in time period 3, eight in time period 4,

previous two sinks are kept the same. In the third time period, the numbers of sources and sinks become six by addition of two more sources and sinks with the flow rate, while the concentration data associated with the previous four facilities remain constant. In the fourth period, the capacities of sources and sinks expand, but the concentrations of the contaminants remain the same. In the fifth time period, the flow rate from the fourth time period is maintained, but the concentrations of the contaminants change. Three different contaminants were assumed to be present in the streams. The input data for case study 2 are presented in the Appendix. Freshwater Minimization. The total amount of freshwater required in multiperiod planning was found to be 1089 tons/h, and the number of connections required was 27. The results for multiperiod optimization are provided in Table 7 and Figures 7 and 8. Table 8 presents the results for case study 2 from singleperiod optimizations minimizing the freshwater requirements. For individual-period planning, the total flow rate required was 1089 tons/h, with 33 pipeline connections. Therefore, as expected, the water requirements in the two cases were identical, but the number of required connections was lower in the case of multiperiod optimization. Total Cost Minimization. Similarly to the previous case study, artificial data for an industrial city layout were generated and 8860



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Table 11. Flow Rate Results of Individual-Period Cost Optimizations for Case Study 2 Time Period 1 sinks (j) source (i)

P1D1

P1D2

wastewater (WW)


46.53 0 73.47

39.18 0 40.82

34.29 80


P1D1

P1D2

P3D1

P5D5

wastewater (WW)


46.53 0 0 0 73.47

39.18 0 0 0 40.82

0 0 0 0 80

0 32.69 59.06 0 48.27

34.29 44.33 80.94 80


P1D1

P1D2

P3D1

P5D5

P5D2

P4D1

wastewater (WW)


0 29.08 0 0 0 5.58 85.34

24.05 0 0 0 0 13.61 42.33

14.63 0 0 0 0 24.55 40.81

0 50.92 0 48.36 0 0 40.72 Time Period 4

32.82 0 25.14 0 22.04 0 0

48.49 0 114.86 31.64 0 0 0

0 0 0 0 172.95 56.25

source (i)

P1D1

P1D2

P3D1

P5D5

P5D2

P4D1

wastewater (WW)


0 29.08 0 0 0 5.58 85.34

0 38.93 14.02 0 0 17.66 129.38

0 12.87 6.94 0 0 35.38 79.8

85.44 19.11 85.44 0 0 0 0 Time Period 5

42.25 0 16.9 40.84 0 0 0

72.3 0 11.68 111.01 0 0 0

0 0 0 38.14 195 61.37

source (i)

P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


0 29.08 0 0 0 5.58 85.34

46.09 12.19 3.4 0 0 28.5 109.8

0 0 15.96 0 0 37.14 81.9

95 0 95 0 0 0 0

5.25 58.73 20.64 15.38 0 0 0

53.65 0 0 125.93 0 0 15.42

0 0 0 48.68 195 48.77

sinks (j)

sinks (j)

Table 12. Cost Chart of Individual-Period Optimization for Case Study 2 (×106 $) sinks (j) source (i)

P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


0.31 0.21 0 0 0 0.35 0.66

0.28 0.18 0.11 0 0 0.63 0.59

0.22 0 0.12 0 0 0.53 0.49

0.57 0.47 0.45 0.32 0 0 0.42

0.66 0.56 0.54 0.41 0.17 0 0

0.23 0 0.58 0.25 0 0 0.13

0.15 0.2 0.53 0.42 0.66 0.49

and two in time period 5. These connections were not necessarily single connections, and multiple connections were

needed when connecting the freshwater source to P1D2 and source P6S2 to P4D1. 8861



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5. CONCLUSIONS

total cost, or both can be reduced. A reduction in the number of connections means a less complex water network. This work clearly shows the deficiencies of individual-period optimization without considering future periods. Moreover, multiperiod planning enables the rating of time periods, for which the last time period in any case gives the most developed water network. The ratings can be made on several bases. In this work, the periods were rated according to the flow rates handled in them. They can also be rated on the basis of the load handled in a particular period. Thus, water resources were found to be utilized more often during the planning phase for a given city. Moreover, because this work involves only recycle and reuse as a water integration option, the multiperiod planning methodology can certainly be expanded to further look into treatment scenarios. Also, more components of costs such as operating costs can be analyzed. Therefore, future work will certainly look into

This work involved the use of direct recycling water integration strategies to obtain an optimal network for an industrial city considering the fact that its layout changes with time. The shortest source-to-sink distances associated with the provided layout and arrangement of the different plants within the industrial city were provided. The results indicate that network design planning for an entire time period (multiperiod) yields enhanced performance compared to the solutions obtained from solving individual time periods for most of the cases that have been illustrated. The former method shows that either the number of connections, the Table A1. Flow Rate and Contaminant Data for Sources in Case Study 1 source

flow rate (tons/h)

class 1−2 (C12) class 3−4 (C34)

650 600

class 1−2 (C12) class 3−4 (C34)

1300 1100

class 1−2 (C12) class 3−4 (C34)

2300 2100

class 1−2 (C12) class 3−4 (C34) S1 S2

2600 2400 5980 2840

class 1−2 (C12) class 3−4 (C34) S1 S2

2800 2600 7000 3500

contaminant 1 (kΩ cm)−1

Time Period 1 7.14 × 10−5 8.33 × 10−5 Time Period 2 7.14 × 10−5 8.33 × 10−5 Time Period 3 7.14 × 10−5 8.33 × 10−5 Time Period 4 7.14 × 10−5 8.33 × 10−5 − − Time Period 5 7.14 × 10−5 8.33 × 10−5 − −

contaminant 2 (%)

Table A3. Industrial City Layout (Distances, km) for Case Study 1

− −

sinks (j)

− − − − − − 0.5 0.49

back grinding (BG) marking (MK) back grinding (BG) marking (MK) back grinding (BG) marking (MK) back grinding (BG) marking (MK) D1 D2 D3 back grinding (BG) marking (MK) D1 D2 D3

flow rate (tons/h)

contaminant 1 (kΩ cm)−1

Time Period 1 1000 6.25 × 10−5 700 1.00 × 10−4 Time Period 2 1900 6.25 × 10−5 1500 1.00 × 10−4 Time Period 3 3500 6.25 × 10−5 2450 1.00 × 10−4 Time Period 4 4000 6.25 × 10−5 2800 1.00 × 10−4 4250 − 4580 − 1950 − Time Period 5 4400 6.25 × 10−5 3000 1.00 × 10−4 4600 − 5000 − 2300 −

marking (MK)

D6

D8

D9

wastewater (WW)

class 1−2 class 3−4 S1 S2 freshwater

5.4 3.6 9.6 8.2 11.6

5 3.2 4 7 10.4

8 6.2 4.2 4.8 8.6

10 8.2 7.8 5.6 7.4

11.6 9.8 9.4 7.2 7.4

2.6 3.6 9.2 7.4 7.6

Table A4. Flow Rate and Concentration Data for Sources in Case Study 2

− − 0.5 0.49

source

Table A2. Flow Rate and Contaminant Data for Sinks in Case Study 1 sink

source (i)

back grinding (BG)

contaminant 2 (%) − − − − − − − − 1 1 1 − − 1 1 1 8862

flow rate (tons/h)

P2S2 P2S1

120 80

P2S2 P2S1 P3S1 P6S2

120 80 140 80

P2S2 P2S1 P3S1 P6S2 P6S1 P4S1

120 80 140 80 195 100


200 100 135 190 195 120


200 100 135 190 195 120

C1 (ppm) Time Period 1 100 140 Time Period 2 100 140 180 230 Time Period 3 100 140 180 230 250 100 Time Period 4 100 140 180 230 250 100 Time Period 5 100 160 180 210 270 120

C2 (ppm)

C3 (ppm)

50 100

30 60

50 100 150 180

30 60 130 180

50 100 150 180 190 190

30 60 130 180 200 210

50 100 150 180 190 190

30 60 130 180 200 210

50 120 150 210 190 180

30 60 160 180 210 210



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with the industrial city. In the case study, weights were assigned to different periods in the objective function. The ratios of the total flow rate in individual periods to the total flow rate handled in all periods were the basis for assigning weights. Periods 1−5 were assigned weights of 5, 10, 15, 25, and 45, respectively, on a scale of 100. The last period was assigned extra weight as it presents the most developed layout of the city.

Table A5. Flow Rate and Contaminant Data for Sinks in Case Study 2 sink

flow rate (tons/h)

P1D1 P1D2

120 80

P1D1 P1D2 P3D1 P5D1

120 80 80 140

P1D1 P1D2 P3D1 P5D1 P5D2 P4D1

120 80 80 140 80 195


120 200 135 190 100 195


120 200 135 190 100 195

C1 (ppm)

C2 (ppm)

C3 (ppm)

60 50

30 80

60 50 70 100

30 80 100 100

60 50 70 100 120 130

30 80 100 100 130 150

60 50 70 100 120 130

30 80 100 100 130 150

60 50 85 100 120 145

30 80 120 100 140 150

Time Period 1 40 50 Time Period 2 40 50 50 140 Time Period 3 40 50 50 140 170 240 Time Period 4 40 50 50 140 170 240 Time Period 5 40 50 50 140 160 240

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This publication was made possible by NPRP Grant 4-1191-2468 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors.

■

investigating the impact of the presence of treatment plants on the cost and number of connections within the network design, from a multiperiod planning perspective. Apart from the inclusion of treatment plants, more water-consuming sinks such as irrigation and demands for potable water will also be included in future works. Inclusion of these water-consuming options will better describe the industrial city. This effort will be coupled with the development of multiperiod approaches for industrial city energy and cogeneration integration53,54 toward energy−water nexus integration.

■

APPENDIX This appendix summarizes the input data used in the two case studies. Tables A1 and A2 present the source and sink data for case study 1, and Table A3 presents the layout of the industrial city. Tables A4 and A5 present the source and sink data for case study 2, and Table A6 presents the distance information associated

■

NOMENCLATURE Cb,fw,t = Concentration of contaminant b in freshwater during time period t Ci(p1),t = concentration of the ith source of plant p1 during time period t Cj(p2),t = concentration of the jth sink during time period t DIi(p1),j(p2) = diameter of the pipe connecting the ith source in plant p1 to the jth sink in plant p2 Ffw,j(p2),t = flow rate between the freshwater source and the jth sink of plant p2 during time period t Fi(p1),j(p2),t = flow rate between the ith source in plant p1 and the jth sink in plant p2 during time period t Fi(p1),ww,t = flow rate from the ith source in plant p1 for wastewater discharge during time period t Nt = maximum number of connections allowed during time period t U = large number used in eqs 6b and 14 Vi(p1),j(p2),t = artificial variable used to linearize the bilinear terms Xi(p1),j(p2),t = binary variable representing the connection between the ith source and the jth sink during time period t ϵ = minimum value of flow rate

REFERENCES

(1) El-Halwagi, M. M.; Manuosiouthakis, V. Synthesis of Mass Exchanger Networks. AIChE J. 1989, 35, 1233−1244. (2) Wang, Y.-P.; Smith, R. Design of distributed effluent treatment systems. Chem. Eng. Sci. 1994, 49, 3127−3145.

Table A6. Industrial City Layout (Distances, km) for Case Study 2 sinks (j) source (i)

P1D1

P1D2

P3D1

P5D1

P5D2

P4D1

wastewater (WW)


5.4 3.6 9.6 8.2 8 12.6 11.6

5 3.2 4 7 6.8 11.4 10.4

8 6.2 4.2 4.8 3.8 9.6 8.6

10 8.2 7.8 5.6 4.6 10.4 7.4

11.6 9.8 9.4 7.2 6.2 11.2 7.4

4 5 10.2 4.4 4.6 5.6 4.6

2.6 3.6 9.2 7.4 7.6 8.6 7.6

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