wastewater networks

Computers and Chemical Engineering 35 (2011) 2853–2866

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Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng

Dual-objective optimization of integrated water/wastewater networks Raluca Tudor, Vasile Lavric ∗ University Politehnica of Bucharest, Chemical Engineering Department, RO-011061, Polizu 1-7, Bucharest, Romania

a r t i c l e

i n f o

Article history: Received 11 December 2010 Received in revised form 7 February 2011 Accepted 18 April 2011 Available online 23 April 2011 Keywords: Integrated wastewater network Fresh water minimization Costs optimization Multi-objective optimization Pareto front

a b s t r a c t The dual-objective optimization of an integrated water/wastewater network (IWWN) is addressed by targeting for minimum fresh water consumption at the same time with operating costs reduction. An IWWN is a recycle system composed of two oriented graphs, the first encoding the water-using units (WUs) and the second, the treatment units (TUs). Although internal recycles are forbidden ab initio for the WUs graph, external recycles from the appropriate TU to the WU whose inlet restrictions are met by the partially treated water are encouraged. The corresponding mathematical model was written. A synthetic example is proposed and analyzed under several scenarios with respect to the fresh water consumption, the magnitude of internal and treated water reuse and the investment/operating costs related to the active pipes network. A comparison is made regarding the differences in network topology and fresh water consumption implied by different points from the Pareto front (PF). © 2011 Elsevier Ltd. All rights reserved.

1. Introduction The excessive use and pollution of freshwater are called to give its way to alternative, efficient venues to exploit the water resources. The increased social awareness is combined with bigger operating costs scheduled to further rise, as environmental regulations become more stringent. Process integration enables the efficient use of water through water reuse, recycling and regeneration. Therefore, the development of design targets for the minimum freshwater demand with lower investments and operating costs becomes crucial to assess alternatives. Water system integration treats the water using processes in a plant as an organic whole, and considers how to distribute water both quantitatively and qualitatively to each WU, so that water reuse is maximized within the system concomitantly with wastewater minimization (Tudor & Lavric, 2010a). Wastewater can be reused for any purpose as long as adequate treatment is provided to meet the implied water quality requirements. In principle, the quality of reclaimed water can exceed potable water restrictions using today’s advanced treatment technologies. The problem is that the costs of such treatment become prohibitively large since they increase rapidly with water quality requirements. Therefore, the intended water reuse applications govern the degree of wastewater treatment required. A high degree of treatment would allow more wastewater reuse, which would in turn reduce costs associated with freshwater consumption and effluent disposal, but at the expense of increased treatment costs. Balancing these two require-

∗ Corresponding author. Tel.: +40 722142188. E-mail address: v [email protected] (V. Lavric). 0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2011.04.010

ments through an optimal degree of wastewater reuse is not trivial, since the objectives are competing (Tudor & Lavric, 2010b). Two main categories of methods are used to obtain good designs of water/wastewater networks (WWNs) in the recent literature: pinch technology and mathematical programming. The most recent comprehensive review of the various graphical techniques to design and retrofit continuous water networks has been published by Foo (2009). The analogous study of the mathematical programming approaches for continuous and batch water networks have been reviewed by Jezowski (2010). The studies of WWNs optimization based on mathematical approaches can be lumped into relatively few categories. Generally the main focus of researchers is on the optimization of singleor multiple-contaminant WWNs (Gomes, Queiroz, & Pessoa, 2007), but also there is an increased interest in the optimization of singleor multiple-contaminant IWWNs (Ku-Pineda & Tan, 2006; Ng, Foo, & Tan, 2007a, 2007b; Tudor & Lavric, 2010a, 2010b). Another researching direction is the use of regeneration units into water networks in order to further reduce external water demands as compared to systems with just direct water reuse/recycle. Regeneration systems enhance water recovery potential by improving stream quality to suit water demands within process plants (Iancu, Plesu, & Lavric, 2009; Tan, Manan, & Foo, 2007). But, still there are few papers published on this particular subject, i.e. IWWN optimization, which refer to multi-objective optimization of these networks. Insights of this latter approach will be summarized with focus on the most important aspects. The first complex mathematical optimization was introduced by Takama, Kuriyama, Shiroko, and Umeda (1980) who addressed the problem of optimal water allocation in a petroleum refinery (mass-transfer model for water-using processes, multiple contami-

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Nomenclature fresh water flow entering water-using unit “Ui ” (kg/h) U,in Cki contaminant “k” concentration entering waterusing unit “Ui ” (ppm) U,in,max maximum contaminant “k” inlet concentration Cki admitted by water-using unit “Ui ” U,out Cki contaminant “k” concentration leaving water-using unit “Ui ” (ppm) U,out,max Cki maximum contaminant “k” outlet concentration admitted by water-using unit “Ui ” mki load of pollutant “k” released in the water-using unit “Ui ” (kg/h) flow of water that is lost within the water-using unit Li “Ui ” (kg/h) Wi flow of wastewater leaving water-using unit “Ui ” (kg/h) T,in contaminant “k” concentration entering treatment Ckt unit “Tt ” (ppm) T,in,min Ckt minimum contaminant “k” concentration entering treatment unit “Tt ” (ppm) T,out Ckt contaminant “k” concentration leaving treatment unit “Tt ” (ppm)  mkt load of pollutant “k” removed in the treatment unit “Tt ” (kg/h) Lt flow of water that is lost within the treatment unit “Tt ” (kg/h) F fanning friction factor value Dij optimum economic diameter of the pipe linking the units i and j (m) Dr reference diameter (m) Fi

nants) based on a superstructure described by a NLP model. Tsai and Chang (2001) were the first who solved the problem of an IWWN (mass-transfer model of water-using processes, multiple contaminants, treatment/regeneration modelled by fixed removal ratio) using genetic algorithms (GA) as optimizer. A mathematical programming model has been developed to identify the cost-optimal and least-consumption IWWN. The network configurations were generated on the basis of a superstructure embedded with the existing water-using units, the repeated water-treatment units, and the mixers. The benefits of using this model were demonstrated in the examples. Gunaratnam, Alva-Argaez, Kokossis, Kim, and Smith (2005) addressed the problem of total water systems with the option of elimination of the regeneration recycling possibilities. The optimization of the corresponding superstructure was performed using some approach characteristics: iterative procedure with relaxation of the material balance by fixing the outlet concentration at the maximum and introducing slack variables to the balance equation. Such a model was MINLP, with the objective of minimizing the cost of the network. Karuppiah and Grossmann (2006) used a modified model of mass-transfer water-using processes: fixed total flow rate, given mass loads and inlet concentrations fixed at the maximum. The problem considers multiple contaminants and no possibility for regeneration recycling elimination. The optimization model contains two versions of the model for two objective functions: NLP, because the objective function does not regard fixed charges on the apparatus and piping, and MINLP, because of the choice of treatment technology (treatment operations differ as for cost and removal ratio, but the objective function does not observe fixed charges on apparatus and piping). Erol and Thoming (2005) used a multi-objective optimization with a Pareto approach: total annual

cost and relative increase of the environmental aspects of the network, as a function of flow rates and concentration. The objective was to analyze various versions of the network, particularly, advantages and disadvantages of closed loop solutions and standard facilities without reuse. Mariano-Romero, Alcocer-Yamanaka, and Morales (2007) addressed the problem of multi-objective water networks optimization by extending the water pinch analysis with elements of capital costs of the required pipe work. Therefore the optimization is based on: minimization of freshwater consumption and minimization of infrastructure costs. A superstructure was generated which was described with a NLP model and solved by two optimization methods: (i) a reduced gradient search with a single goal function composed of the two criteria with weighting factors, and (ii) a metaheuristic approach called multi-objective distributed Qlearning. The effect of varying the regeneration concentration was analyzed against the amount of both freshwater consumed and wastewater regenerated, and the total costs. Feng and Chu (2004) presented cost-optimization models for water network that involved placement of the regeneration unit. They showed that the flow rate and the outlet concentration of a regeneration unit are the key parameters that determine the economic performance of an overall water network. They also concluded that the total cost of a water network can be minimized after the optimum regenerator outlet concentration is determined. The piping system within a process plant has a major impact upon overall plant design, and its contribution to the overall capital cost is often nontrivial. The piping costs in a fluid-process plant can run as high as 80% of the purchased equipment cost or 20% of the fixed-capital investment. The piping design must take into consideration not only economics and design simplicity, but also flexibility, support requirements, and other mechanical considerations, as well as safety needs and other various code requirements. In the designing process of an optimum wastewater network topology, the simplest and yet sufficiently precise economic objective function to be considered should be the sum of the fixed charges for the piping system and the pumping costs. Guirardello and Swaney (2005) reported a methodology for the optimization of chemical plant layout and piping design using a set of mathematical programming models. The main feature of the approach is the use of MILP subproblem models that can be solved using branch and bound algorithms. The models also provide a formal mechanism to incorporate the practical concerns of plant design constraints. Equipment layout and detailed pipe routing are determined sequentially. The equipment layout optimization employs surrogate costs based on separation distances to reflect the cost of the interconnecting piping, but does not explicitly determine a detailed piping layout. Later on, an optimization method for detailed piping system design is applied after the equipment positions have been determined. Lavric, Iancu, and Plesu (2007) proposed for a water network a cost-based objective function, which takes into consideration the on-field geometry of the network, through the distances between units, is used to look for the optimum topology of a given wastewater network. Moreover, in order to emphasize the optimality of the solution, every pipe of the wastewater system should have an optimum economic diameter, computed such as to minimize the friction losses due to the fluid velocity. To keep the computation as simple as possible, still preserving the main characteristics of the problem at hand, no adjacent costs were included in the objective function, like effluent disposal charges based on volume and/or contaminant loading, or on-site treatment costs to improve the water quality of the effluent for reuse, Iancu, Plesu and Lavric (2007). Faria, de Souza, Souza, and Arruda (2009) proposed alternatives to optimize water networks minimizing water consumption and/or reducing

R. Tudor, V. Lavric / Computers and Chemical Engineering 35 (2011) 2853–2866

LEGEND: Fresh water Partially decontaminated water Water complying environmental limits Contaminated water

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To environment

1

i

TUM j q

2

N-1

TU2

3 p FRESH WATER

N

TU1

Fig. 1. Abstraction of the IWWN as a system of two oriented graphs; the knots are either WUs (the first graph, with WUs ranked using some appropriate criterion) or TUs (the second graph), while the oriented arches are the pipes transporting the water reused internally. The TUs are ordered according to their inlet restrictions: TU1 , treats the most contaminated water, while the last one, TUM , treats the least contaminated water till it complies the limits to be discharged into the environment. The integration of WUs and TUs is done considering TUs as contaminated water supply sources for the suitable WUs. Thus, the water treated at different levels is recycled back into the system.

cost through wastewater reuse and/or recycling, through mathematical models. A superstructure was generated and solved by means of NLP. The problem of optimization of integrated wastewater networks was addressed also by Faria and Bagajewicz (2009a, 2009b). They concluded that all water allocation problems must at least include one treatment unit in which its treated stream can be reused/recycled. They proposed the term of “complete water system” for the process plants which are typically formed of 3 subsystems: water pre-treatment, water-using and wastewater treatment. The particular feature of the network proposed was the addition of the pre-treatment system. When many water supplies are available, the freshwater sources are not only competing with each other, but also with the regeneration units. The regeneration processes are not used for reuse/recycle purpose only, but also to condition the wastewater stream to be discharged; all wastewaters are mixed and send to end-of-pipe treatment. In the case of the complete water system, water pre-treatment and wastewater treatment become a unique set of regeneration processes, which are also allowed to receive freshwater. The same problem was addressed also by Tudor and Lavric (2010a) in which a detailed model of the IWWN was solved using genetic algorithms to obtain the best topology. The objective function aimed to pinpoint this particular topology of the complete network was the total fresh water consumption, which was minimized throughout maximization of internal and treated wastewater reuse. Different scenarios are used to generate the corresponding water network topologies which were analyzed and general conclusions were drawn for each case. In the present paper we propose a new approach on integrated water/wastewater networks optimization which is able to identify the equally optimal topologies of the network as identified from PF resulted when using a dual-objective function, i.e. fresh water consumption and total costs of the active piping system. Prior to the optimization process, the WUs and TUs are ordered according to some ranking criterion, thus ensuring a rather constant driving force throughout the IWWN (Iancu, Plesu, & Lavric, 2010). As a rule of thumb, freshwater consumption diminution is mainly done

identifying the opportunities for wastewater reuse, at the expense of increasing the complexity of the pipe network structure. Consequently, the two objectives are rather contradictory, leading to a set of alternative solutions equally optimal known as the Pareto front. A thorough analysis is done with respect to both the network topology and wastewater reused flows for some of the alternatives belonging to this PF. 2. Modelling the integrated wastewater network When searching for mass transfer driving force equipartition across a network, the constituting water/wastewater units can be ranked according to some appropriate criterion and thus the minimum entropy generation for certain operating conditions is ensured. Therefore an IWWN can be perceived as a system of two oriented graphs with respect to water flow (Fig. 1). The first graph starts with WUs with contaminant free constraints at their inlet, which are supplied with fresh water only. Any other WU, i, could collect streams from all WUs, j, preceding it (j = 1, 2, ..., i − 1), and could send streams to all succeeding WUs, j (j = i + 1, i + 2, ..., N). Due to the oriented nature of the graph, internal recirculation (water from the exit of a WU is recycled back to its entrance) and counter-current reuse (water from the exit of a WU cannot be sent to previous WUs) are avoided (Fig. 2). In an IWWN, the TUs constitute an oriented sub-graph as well: they are cascaded, starting with the least restrictive inlet TU which receives the heaviest contaminated wastewater streams and continuing with the more and more restrictive inlet TUs until the last one, which accepts the least contaminated wastewater streams and treats them until the environmental discharge requirements are fulfilled. The exit of any TU in cascade should not be lower than the inlet restrictions of the following one. The IWWN is designed in such a way as to recycle the water resulted from partially/complete treatment; each TU can be seen as a potentially contaminated supply water source, available for the appropriate WUs. When the contamination level of any wastewater stream reaches the inlet conditions of any of the TUs and cannot be reused by the next units in the network, then it enters this suitable TU and starts

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being decontaminated. The inlet restrictions of the last unit from the treatment cascade should match the lowest outlet restrictions of the WUs. This ensures that even the slightest polluted water stream from the WUs will be treated accordingly. Although it may seem that such an approach may impose some restrictions in the network topology, due to on-site location of the units or of the freshwater sources, the algorithm takes into account also the distances between the units so the ordering does not introduce new constraints. Moreover, the efficiency of such an integrated treatment system is twofold: on one hand, each polluted stream enters the correct TU, avoiding supplemental pumping costs and dilution of heavily polluted streams treated in the previous units, and on the other, allowing a possible reuse of each TU exit by a matching WU. It is also important to point out that the initial topology of the network, as encoded by the oriented graph, has the maximum number of virtual connections. The purpose of the optimization using appropriate objective functions is to eliminate those unnecessary virtual links and thus establishing the optimal topology of the network. 2.1. Mathematical model The complete mathematical model of the wastewater network, as resulted from total and contaminant species mass balances, together with the corresponding input and output constraints is given in Tudor and Lavric (2010a). In the present paper we will briefly review the mathematical model of an IWWN and then we will focus on the multi-objective optimization of the IWWN (Fig. 1). The mathematical model for the WUs (Fig. 2) sub-graph is: Total mass balance: Fi +

i−1 

Xji + Yti +

j=1

K 

N 

˙ ki = m

k=1

Xij + Wit + Li

(1)

j=i+1

Partial mass balance for the contaminant k:



=⎝

N 

⎞ WU,out Xij + Wit + Li ⎠ Cki

(2)

j=i+1

2.1.1. Constraints Inlet WUs concentrations: WU,in Cki

=

Fi +

i−1

X C WU,out j=1 ji kj Fi +

i−1 

TU,out + Yti Ckt

WU,in,max ≤ Cki

(3)

=

Fi +

TU,out X C WU,out + Yti Ckt j=1 ji kj N X + Wit + Li j=i+1 ij



˙ ki + m

≤

(4) The mathematical model for the TUs (Fig. 2) sub-graph is: Total mass balance: Wit + Zt−1 =

N  i=1

Yti + Zt+1 + Lt +

TU,in,min ≥ Ckt

K  k=1

˙ kt m

min[||CiWU,out ≥ CtTU,in,min ||]

∧

(7)

2.2. Derivation of the vector objective function An IWWN can have different topologies, each corresponding to the optimization of a particular objective function, which encodes the performance criteria envisaged. The optimality can be sought in different manners: either with respect to freshwater consumption, or to total costs which encapsulates both investment and operating charges. The latter objective function could address only a subsystem, like piping, or the whole network, including the WUs too. In the present study, we employ a double-objective function which accounts for freshwater consumption, on one hand, and investment and operating costs, on the other. The freshwater consumption as objective function has been completely derived in Tudor and Lavric (2010a), from the condition that each freshwater stream fed to WU i should ensure the simultaneous observation of both inlet and outlet restrictions with respect to the pollutant concentrations: i=1

in ), max(F out )] max[max(Fki ki k

k

(8)

F max

in represents the freshwater flow observing the inlet In Eq. (8), Fki out represents the freshwater restriction for the pollutant k, while Fki flow observing the outlet restriction for the pollutant k. Choosing the maximum of both maxima ensures the observation of all restrictions, both at inlet and at outlet, for WU i. The denominator represents the sum of the freshwater flows which should feed all WUs in the absence of any internal reuse. The total cost of the active pipe system, the second component of this dual-objective function, is based upon the costs of the unit length of a pipe linking two consecutive WUs and having the optimum economic diameter, and it was fully detailed in Lavric et al. (2007):

Dij



 · qaij · ˇ ·  · K · (1 + J) · Hy Dijı





+ B pumping

(9)

· KF

Dr

pipe

Eq. (9) has been derived considering one year as the time basis, the exponents of the pumping term depend upon the flow regime and the Fanning friction factor value, Dij stands for the optimum economic diameter of the pipe linking the units i and j, while Dr is the reference diameter. The flow regime gives the formula to compute Dij :



(5)

TU,out · Ckt

The last constraints mean that the stream Wit enters this TU if and only if the two conditions are met simultaneously: every pollutant has the concentration greater than the inlet limit of TU t and the distance between the WU i concentration vector and TU t inlet restriction vector is minimum. The last condition avoids feeding the TUs with lower inlet concentration restrictions with heavier than necessary polluted streams.

+ (1 + F) · X · WU,out,max Cki

Yti

Constraints – inlet concentrations: WU,out Cki



i−1



(6)

Cij∗ = ([C ∗ ]pumping + [C ∗ ]pipe )ij =

Outlet WUs concentrations:

Lt + Zt+1 +

N  i=1



Xji + Yti

j=1

WU,out Cki

WU,out TU,out ˙ ki = Wit Cki + Zt−1 Ck,t−1 − m

˚=

WU,out TU,out ˙ ki Xji Ckj + Yti Ckt + m

j=1

⎛



N

i−1

Fi +

Partial mass balance for the contaminant k:

turbulent flow : Dij =

6.04 · 10−4 Drn · q2.84 · 0.84 · 0.16 · K · (1 + J) · Hy c ij

1/(4.84+n)

n · (1 + F) · X · E · KF

(10)

R. Tudor, V. Lavric / Computers and Chemical Engineering 35 (2011) 2853–2866

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Fig. 2. The abstraction for the main units of the IWWM, WU and TU (mixer – all the incoming streams are mixed then fed to the unit, splitter – the streams leave the unit with the same concentration). (a) Xji is the wastewater reused from the previous WUs j(j < i) to the WU i; likewise Xij is the wastewater reused from WU i to the next WUs j(i < j ≤ N); Fi is the fresh water flow entering the WU i; Yti is the treated water coming to WU i from the TU t; Wit is the stream sent to TU t, when its concentrations are ˙ ki is the k pollutant flow (load) released in WU i. (b) Zt−1 is the wastewater partially treated from the previous TU, which appropriate; Li is the possible flow loss and m cannot be reused internally; Yti , is the partially treated wastewater stream going from TU t to WU i; Zt+1 is the partially treated wastewater stream going from TU t to the ˙ kt is the k pollutant flow removed in TU t. next TU (the last TU is the only one being able to dispose water to environment, complying the legal limits) and m

 laminar flow : Dij =

0.1628 · Drn · q2ij · c · K · (1 + J) · Hy

1/(4+n)

n · (1 + F) · X · E · KF (11)

The total cost of the active pipe system is given by the topology of the network, which is represented by the grid of the active pipes (non-zero throughput flows):

N j=1

   =

∗ ∗ C0,j · l0,j +



 

supply pipes

N 

j=1

N N

∗ C0,j · l0,j +

i=1

j=i+1



∗ ∗ Ci,j · li,j +

 

internal pipes



N 

active N

i=1

j=i+1



N

∗ Ci,j · li,j +

j=1

∗ ∗ CN+1,j · lN+1,j





pipes to treatment



N j=1

∗ CN+1,j · lN+1,j



overall

(12)

It should be pointed out that the denominator in Eq. (12) is computed using the largest diameter value as resulted from applying (9) with the highest freshwater inflow for all the pipes of the IWWN, regardless if they are active or virtual (their presence is not necessary, since no water will flow through them). This ensures lower than unity values for the dimensionless total cost of the active pipes even when all the pipes of the grid are active, but for sure the flows will be lower than this highest value. The dimensionless dual-objective function is obtained considering the vector whose components are the freshwater consumption (8), and total cost of the active pipes (12):



fob =

˚ 



(13)

The optimization consists in searching the minimum of this dual-objective function; the solution is not trivial since the complete model is fully non-linear. We chose as optimization tool the genetic algorithm as implemented in MatlabTM , which uses each internal flow as a gene, defining a chromosome from all these flows (Tudor & Lavric, 2010a). The restrictions are dealt with during the population generation by simply eliminating these individuals outside the feasible domain. The individuals are interbreeding according to their selection frequency, using one-point crossover method, and then mutation is applied to randomly selected ones. 3. The case study A synthetic case study was used to perform a thorough analysis to emphasize the influence of TUs integration upon the WN optimal topology when using a dual-objective function to be minimized. Taking into account the antagonistic behaviour of the freshwater consumption and total cost of the active grid, a PF is expected, as a set of alternative solutions equally optimal. The chosen synthetic case study has six WUs, dealing with four contaminants (Tables 1 and 2 display the characteristics of the WUs), and three TUs (the information regarding the inlet and outlet restrictions of these latter are presented in Table 3). The spatial configuration of the units in the field, given by distances between the supply source of freshwater, the WUs and the TUs is specified in Table 4. These distances are to be taken into consideration when computing the total cost of the active pipes. Analyzing the inlet restrictions and the outlet concentrations of the TUs, it is readily observed that the outlet of one TU corresponds to the inlet restrictions of the next TU, while the last TU in series has the outlet contaminants concentration matching the environmental regulations for disposing the treated water. More, when a stream exiting a particular WU and heading towards treatment has

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Table 1 Inlet and outlet restrictions of the water-using units of the network. Contaminant

Cin,max (ppm) WU1

C1 C2 C3 C4

0 0 0 0

Cout,max (ppm)

WU2 20 8 4 5

WU3

WU4

WU5

WU6

WU1

12 10 22 15

15 25 16 17

17 14 10 18

8 18 25 20

35 40 25 30

WU2 100 85 40 60

WU3

WU4

WU5

WU6

85 75 65 80

75 65 95 110

115 95 100 150

75 95 135 115

Table 2 Mass load of contaminants. Mass load of contaminants, mki (g/h)

Water-using units

C1 C2 C3 C4

WU1

WU2

WU3

WU4

WU5

WU6

3150 2100 2480 2150

3200 2900 1850 1300

4500 3800 2730 3600

2800 2100 3400 3500

4100 3200 3800 4250

2100 3150 3750 3350

Table 3 Inlet restrictions and outlet settings of the treatment units of the network (TU1 is the first unit in series, for the heaviest polluted wastewater, TU3 is the last unit in series, for the slightest polluted wastewater). Contaminant

C1 C2 C3 C4

Cin,min (ppm)

Cout,max (ppm)

TU1

TU2

TU3

TU1

TU2

TU3

85 85 90 105

60 45 40 60

10 10 15 20

60 45 40 60

12 12 15 20

2 4 5 3

the contaminants concentrations below the exit of the last TU in series, it will be sent directly to the environment. When its concentrations will be higher than the aforementioned exit, but lower than the inlet restrictions of the last TU in series, it will be sent however to be treated in this TU. The first step in designing an optimal IWWN is to rank the WUs of the WN according to a given criterion. The suboptimal topology thus found represents the starting point for the iterative process of finding the optimal IWWN’s associated oriented graph. Four ranking criteria, all conforming to the principle of driving force equipartition (Iancu et al., 2010), are used to order the WN: outlet maximum allowable concentrations (OMC), inlet maximum permitted concentrations (IMC), maximum fresh water consumption (FWC) and maximum contaminant load (MCL). From the aforementioned criteria, FWC is not self explanatory; it means the maximum freshwater flow feeding a WU such to observe all restrictions, both at inlet and outlet, in the absence of any internal wastewater reuse. Disregarding which of these ranking criteria is used, the inlet-contaminant free WUs will always be placed first (in this case study, WU1 ) since it is not possible to feed them with internally reused wastewater. TUs are ordered according to their inlet/outlet

restrictions: the primary treatment unit (TU1 ) ensures the heaviest decontamination of the most polluted streams until the level required for admittance in the next TU or to be reused in WN, the secondary treatment unit (TU2 ) removes the pollutants such that the outlet wastewater stream either fits the inlet restrictions of a WUs or feed the tertiary treatment unit. The last treatment unit (TU3 ) eliminates the pollutants up to the level of complying with the environmental limits for discharge. Of course, the water resulted from the final treatment can and will be also used to feed the WUs whose inlet concentration restrictions accommodate its contaminants level. The rest of the paper will envisage some aspects related to the dual-objective optimization of this IWWN and how is the optimal topology affected by pre-optimizing the sub-network of WUs with different ranking criteria. The analysis will focus on the spread of the PF for each scenario, computing the mean and standard deviation for the freshwater flows in the equally optimal solution set, on one hand. On the other hand, three most representative solutions from the PF will be investigated with respect to the possible differences which could exist in the IWWN topology for each scenario: minimum, maximum and average freshwater inflows points.

Table 4 Distances between the points of interest in the water and wastewater network (m). Units

Freshwater source TU1 TU2 TU3 WU1 WU2 WU3 WU4 WU5

Water-using units WU1

WU2

WU3

WU4

WU5

WU6

1130 490 640 630

540 1310 1430 1410 820

1320 300 310 380 360 1140

840 850 820 640 580 850 560

1210 1030 1250 1380 650 690 1010 1110

1360 530 720 950 320 940 590 900 500

R. Tudor, V. Lavric / Computers and Chemical Engineering 35 (2011) 2853–2866

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• the upper part, where the freshwater consumption decreases over a smaller variation in the total cost; • the remaining solutions are then distributed over a proportional range of values in which the relationship between the decrease of the total cost and the increase in the freshwater consumption is almost linear;

Fig. 3. Pareto front of the dual-objective optimization of the IWWN (OMC used as ranking criterion).

3.1. Scenario 1: WUs sub-network ranked by outlet maximum allowable concentrations When pre-optimizing the sub-network of WUs using OMC as ranking criterion, the dual-objective optimization of the IWWN gives a set of 175 equally optimal solutions presented in Fig. 3. The range of the two objectives show, on one hand, that the freshwater consumption diminished with an average of 45.5%, and in the other hand, that the topology of the IWWN is not so complex, which reflects in the values of the dimensionless total cost of the active pipe system. For this scenario, the averages of freshwater inflows into the optimized IWWN and of the contaminated water reused inflows are presented in Table 5, together with their corresponding standard deviations. The range between the highest and the lowest values proposed in the PF represents 1.86% of the average. On the other hand, the reused contaminated water has a much higher contribution to the process, up to 55.2% more than the freshwater consumption (Table 5, OMC column). It must be pointed out that, although a decrease of freshwater consumption means an increase of the contaminated water reuse, this relationship is not linear. Thus, the lowest contaminated water reuse inflow does not correspond to the highest freshwater consumption, but to a value rather close to the lowest freshwater consumption, i.e. 176.42 t/h. At the same time, the highest contaminated water reuse inflow corresponds to a flow of 179.73 t/h freshwater consumed, far from the lowest value presented in Table 5, OMC column. The PF shows two main regions of interest (Fig. 3):

What is quite remarkable is that despite the multitude of solutions in the PF, the topology of the optimized IWWN ranked according OMC criterion remains the same (Fig. 4). The only changes are the internal flows and the diameters of the pipes, accordingly. A detailed presentation of the freshwater and reused wastewater flows is given in Table 6, where we choose the points corresponding to the extreme values of the freshwater consumption and, supplementary, to the closest value to the average of the same freshwater inflow (see Table 5 for these values). It should be pointed out that, although the WU2 is not inlet contaminant free, its inlet constraints are not matched by the exit of the last TU (see Tables 1 and 3), from which the treated water could be released to the environment (the third pollutant in the exit of TU3 has a higher concentration than the inlet restriction of WU2 ). Consequently, freshwater is the only feed for WU2 . Another interesting case is WU4 , which has more relaxed inlet constraints (see Table 1). Thus, the freshwater consumed is used for diluting the wastewater streams coming from the previous WUs (Table 6 and Fig. 4). What particularizes WU4 is that although it could receive water from TU3 , as do the other three WUs having relaxed inlet restrictions, it does not, thus increasing the total freshwater consumption. The answer to this question is twofold: (a) there is not enough treated wastewater exiting TU3 to be split between WU3 to WU6 (any attempt to increase it would simply mean a raise in the freshwater consumption in WUs 1 and 2) and (b) feeding any of the aforementioned three WUs with freshwater, instead of WU3 , would mean an increase in the total fresh water consumption. So, the solving methodology had chosen the correct alternative, producing the result with the minimum freshwater consumption.

3.2. Scenario 2: WUs sub-network ranked by inlet maximum allowable concentrations When pre-optimizing the sub-network of WUs using IMC as ranking criterion, the dual-objective optimization of the IWWN gives, again, a set of 175 equally optimal solutions presented in Fig. 5. The average values of fresh water consumption and contaminated water reused of each of the same three solutions of interest advocated in the previous scenario are presented in Table 5, column IMC.

Table 5 The synthesis of the results of the dual-objective function optimization process under different ranking criteria imposed to the WUs sub-network (the lowest and highest values for the contaminated water which is reused do not correspond to the lowest and highest values for the freshwater inflows, coming from different solutions belonging to the PF, but the middle values do). Optimized IWWN performances

Freshwater inflow, t/h

Contaminated water reused inflow, t/h

Scenario

Average Std. dev., ± Lowest Middle Highest Average Std. dev., ± Lowest Middle Highest

OMC

IMC

FWC

MCL

178.36 0.82 176.42 178.37 179.73 276.85 5.45 274.25 275.24 304.3

179.4 1.74 176.32 179.45 182.18 255.10 5.41 238.78 256.88 260.10

177.57 5.87 170.99 176 190.32 258.33 24.51 234.95 253.15 364.86

176.5 2.68 171.24 178.19 178.94 279.95 8.52 265.85 283.02 305.21

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Fig. 4. The topology of the dual-objective optimized IWWN using OMC as ranking criterion; the numbers on each arrow stand for the standardized diameters (m), for the lowest, middle and highest freshwater inflows.

The variation between the highest and the lowest value found in the PF is of 3.26% of the average. The flows of fresh water and contaminated water supply are slightly higher than in the first scenario. The PF shows in this case a piece-wise linear dependency of one objective against the other (Fig. 5). In contrast with the previous scenario, there are three regions that highlight some important variations: the left most part which shows a rapid decrease of the total cost at almost constant freshwater consumption, the middle part till the second gap, for which the total cost

is quasi-constant but there is a sharp increase in the freshwater consumption and the lower part where the linear variation is quite remarkable. This might be explained admitting that in the region with a sharp decrease in the total costs the flow is laminar for a significant part of the active network – slowly increasing the flow means decreasing the friction, at a rate higher than the rate of flow raise, thus decreasing the energy costs. At the same time, the pipes being standardized, their diameter does not vary continuously. Consequently, from a particular value of the flow, the optimum diameter of the

Table 6 The internal flows for the optimized IWWN corresponding to the lowest, middle and highest freshwater inflows with OMC as ranking criterion (on the main diagonal are the supply flows for each unit, normal for freshwater, bold for wastewater reused from TU3 ).

Ranked WUs WU1

WU2

WU3

WU4

WU6

WU5

Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest

WU1

WU2

99.1901

0

46.2407

Internal flows, t/h WU3 WU4 2.5573 10.347 2.2144 7.6069 2.2175 5.3382 2.2767 4.9255 1.5057 1.6645 1.4525 1.5137 52.1277 0.14813 52.4945 0.99095 1.2914 52.5026 30.9937 32.9385 34.2983

WU6 4.035 1.9042 1.8922 4.0135 1.6168 1.5844 3.7407 1.5694 1.5134 4.0299 1.5072 1.5101 149.9116 60.9988 59.9351

WU5 3.0162 2.225 2.2187 2.9087 2.9923 2.9651 1.4423 4.6675 4.6828 3.1671 3.5942 3.5752 3.6789 3.6346 3.6907 102.1082 161.3061 162.6521

To TU 3 79.245 85.2495 87.5334 32.1255 38.4707 38.7342 51.6451 52.4945 48.6996 39.228 38.1113 37.3682 162.0641 63.9743 62.7569 116.3367 178.435 179.8

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Fig. 5. Pareto front of the dual-objective optimization of the IWWN (IMC used as ranking criterion).

Fig. 7. Pareto front of the dual-objective optimization of the IWWN (FWC used as ranking criterion).

pipe jumps to the next standardized value where it remains for a certain range of flows – there could start the second part of the PF. Thus, the investment does not change, while the friction losses stabilize. The third part could correspond to constant investments due to constant pipes diameters, but a linear decrease of friction losses, thus pumping costs, due to the linear increase in flow (still laminar regime). As in the previous case, we chose the same representative sets of solutions for our network topological analysis (Fig. 6). It is important to notice that the topology of the IWWN changed in comparison with the previous scenario, but remained the same for all the solutions from the Pareto front. Of course, the main changes are in the flows of wastewater/treated water and their corresponding pipe diameters. The freshwater and reused wastewater flows are presented in Table 7. Although in this scenario the pre-optimizing ranking by IMC placed WU4 on the fifth position, it still receives freshwater only, since again, there is not enough fully treated wastewater com-

ing from TU3 to feed it too. The algorithm assigns freshwater supply for it, thus increasing the freshwater consumption, but this is the least increase, when compared to the freshwater needs of WU3 , WU5 and WU6 . 3.3. Scenario 3: WUs sub-network ranked by inlet maximum fresh water needed The analysis of the third scenario was performed in the same manner as in the previous two situations. This time the PF is defined by a set with fewer equally optimal solutions (141 only) which are dispersed over a somehow larger range of values of the corresponding two objective functions (Fig. 7). The equally optimal solutions found by the methodology can be clustered into several regions which are clearly separated by gaps. The optimization using FWC as ranking criterion for the WU’s offers some new and interesting perspective. Using this approach,

Fig. 6. The topology of the dual-objective optimized IWWN using as ranking criterion the IMC; the numbers on each arrow stand for the standardized diameters (m), for the lowest, middle and highest freshwater inflows.

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Table 7 The internal flows for the optimized IWWN corresponding to the lowest, middle and highest freshwater inflows with IMC as ranking criterion (on the main diagonal are the supply flows for each unit, normal for freshwater, bold for wastewater reused from TU3 ).

Ranked WUs WU1

WU2

WU5

WU3

WU4

WU6

WU1 Lowest Middle Highest

99.1901

Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest

WU2 0

46.2407

Internal flows, t/h WU5 WU3

WU4

WU6

2.2837 2.0757 1.6424

2.1765 1.9092 1.6266

11.021 6.0157 1.2933

2.6409 1.3849 1.4677

To TU 3 81.0783 87.8145 93.1701

2.1754 1.0603 1.1753 36.807 37.6755 37.9449

2.967 1.3904 0.97762 2.4786 0.97761 0.93744 61.3257 52.9558 53.2057

2.9467 1.8107 2.295 0.35893 0.55585 0.60878 1.1328 0.6281 0.7564 30.8869 34.0236 36.7479

2.7552 2.6694 2.6831 3.7712 3.7609 3.7911 1.7875 2.294 2.4872 3.5983 3.7835 3.6984 160.5598 165.621 168.1088

35.4057 39.3193 39.1189 34.6728 35.5325 35.4407 66.042 54.3256 53.5184 42.7595 39.2623 38.0148 175.1253 179.5259 182.2486

we observed that the network consumes the smallest flow of freshwater and the highest flow of the reused wastewater coming from TU3 , this being the expected result when the fresh water consumption decreases (Table 6). Although the topology of the network changed, there are still only three WU’s feed with freshwater: the first two which have the most restrictive inlet concentrations and the forth unit which is now placed on the forth position in the rank (Table 8 and Fig. 8). From this point of view, this topology resembles with the topology found in the first scenario, i.e. the forth WU placed

on the fourth position in the rank. This could be a good hint in specific situations when due to on-site constraints the fresh water source has a fixed position, i.e. a well. There is also another important aspect, the fact that the minimum fresh water flow determines a very high value of contaminated water inflows for WU5 . When the WU4 freshwater inflow increases, the wastewater inflows reused by WUs 3 and 5 sharply decrease, while the inlet of WU5 increases significantly. Compared to the previous cases, WU5 has a dramatic increase in the inlet flow, between 46% and 160%.

Table 8 The internal flows for the optimized IWWN corresponding to the lowest, middle and highest freshwater inflows with FWC as ranking criterion (on the main diagonal are the supply flows for each unit, normal for freshwater, bold for wastewater reused from TU3 ).

Ranked WUs WU1

WU2

WU6

WU4

WU5

WU3

Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest

WU1

WU2

99.1901

0

46.2407

Internal flows, t/h WU6 WU4 5.0599 10.896 1.4885 10.979 1.8691 3.8052 8.5308 1.9896 1.0986 1.9147 1.051 2.4691 8.0497 107.0307 1.9333 33.0049 6.4879 32.713 25.5621 30.5667 44.886

WU5 4.4606 2.5105 2.5756 3.6942 3.0148 3.063 4.5766 3.4894 4.1969 5.2333 3.4442 4.4282 143.564 150.2815 169.4927

WU3 2.1612 1.2683 1.7951 1.2553 1.4073 1.2685 3.1495 0.9098 1.096 2.24 1.7333 2.4343 1.0585 0.6264 0.46008 49.6255 52.2827 51.5175

To TU 3 76.6228 82.9537 89.1549 30.7801 38.8147 38.3983 104.8579 29.2719 23.8647 39.0354 40.2279 50.7975 160.4856 162.1294 183.3118 59.5046 58.2424 58.5862

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Fig. 8. The topology of the dual-objective optimized IWWN using FWC as ranking criterion; the numbers on each arrow stand for the standardized diameters for the lowest, middle and highest freshwater inflows.

3.4. Scenario 4: WUs sub-network ranked by maximum load The last optimization scenario is represented by the IWWN in which the WUs’ sub-network is ranked according to their maximum concentration load. The PF of the corresponding equally optimal solutions has this time a set of 133 points (Fig. 9). The PF is divided into two sub-sets with rather sharp variation of total cost, for the first region, and freshwater, for the second. In the upper part there is a sharp decrease of the total cost at rather small variation of the freshwater consumption while in the next part, the value of the total cost stabilizes in a very narrow range at freshwater flow increase. From the topological point of view, the network shows a specific characteristic: the first three WUs are fed only with freshwater while the last three with water coming from TU3 (Fig. 10). Although the freshwater consumption is equal to the previous case and distinctively lower against the first two scenarios, the reused fully

Fig. 9. Pareto front of the dual-objective optimization of the IWWN (MCL used as ranking criterion).

treated water inflow is the lowest (Table 5). This would be a sign that the internal flows are used better, being charged more than in the previous scenarios (Table 9). WU3 has a large range of inflows (Table 9) in the PF (over 60%), which might be a problem if the internal structure could not accommodate high flow rates, for example. This restriction is not taken into consideration in this optimizing methodology, but could be an argument in discriminating amongst the equally optimal solutions of the PF. 3.5. Analysis of overall mean availability An IWWN is completely optimized when each and every WU is operated as such that the concentration of at least one of the contaminants of the stream passing through attains one of the inlet or outlet constraints, or better both (Iancu et al., 2009). In order to commensurate how far the stream is from making the WU optimal, the concept of mean availability was introduced (Iancu et al., 2009), defined as the overall mean pseudo-driving force of the mass transfer of the contaminant k, defined as the average of concentration differences computed at the entrance and at the exit of each WU unit. Using this definition, the mean availabilities corresponding to all the units were computed, together with the overall mean availabilities, at the WUs sub-net level. These latter are presented in Table 10 for each contaminant of the system. For each scenario and the chosen equally optimal solutions within, the values of the critical contaminants, which control either the supply water consumption or part of the internal reuse due to the mass transfer bottlenecking, are highlighted. In the case of the first scenario – first set of data C1 is the critical component, its corresponding overall mean availability having the lowest value irrespective of the solution. For the second set of data of the first scenario, C1 is both a critical component and the constituent of the bottleneck island together with C3 . The existence of the latter implies that neither of the two constituents could be regenerated solely in order to increase the performance of the IWWN. Instead, they should be regenerated simultaneously, thus insuring

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Fig. 10. The topology of the dual-objective optimized IWWN using as ranking criterion the MCL; the numbers on each arrow stand for the standardized diameters for the lowest, middle and highest freshwater inflows.

a decrease of the overall mean availability for all the pollutants. In the case of the second scenario, C1 keeps being the critical component, but does not belong to the bottleneck island anymore, to which C2 and C3 fit in. This means that C1 could be regenerated alone to improve the performance of the IWWN, but any further enhancement would imply simultaneous regeneration of C2 and C3 . In the next scenario C3 the critical contaminant in all cases, in the first case together with C1 (both forming also the bottleneck island), while for the next two scenarios there is no bottlenecking. The last

scenario offers an interesting perspective on these two evaluation criteria because in the first case the optimization algorithm reveals no critical contaminant and no bottleneck island, while for both the next two cases the critical contaminants that also form the bottleneck islands are C2 and C3 . The only common thing in all scenarios and all cases is that C4 is never critical. However, there are some notable differences amongst all scenarios: C2 is a critical contaminant only in the last two cases and never in the previous ones, in the rest of the cases the critical contaminants are either C1 or C3 (or

Table 9 The internal flows for the optimized IWWN corresponding to the lowest, middle and highest freshwater inflows with MCL as ranking criterion (on the main diagonal are the supply flows for each unit, normal for freshwater, bold for wastewater reused from TU3 ).

Ranked WUs WU1

WU2

WU4

WU6 WU5

WU3

Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest

WU1

WU2

99.1901

0

46.2407

Internal flows, t/h WU4 WU6 2.7368 19.834 7.6754 1.7816 6.3614 2.1928 0.99653 2.3647 1.8259 0.87853 1.9211 1.0371 25.808 1.9928 32.7543 0.61347 33.5046 0.80839 57.2034 32.5839 32.1119

WU5 2.7478 2.3758 1.8429 2.5811 1.4914 1.9298 2.8323 1.8605 1.8621 3.725 2.1413 2.1429 108.9976 88.6409 89.8119

WU3 3.5408 1.7695 1.8736 3.2681 3.1066 3.1092 5.0704 4.3029 4.3246 7.0871 6.3014 6.3148 2.2404 1.5596 1.5634 139.0077 161.1998 161.8082

To TU 3 70.3411 85.5977 86.9294 37.0395 38.9476 38.2527 36.7545 35.4905 34.8039 53.4978 27.4271 27.7049 118.6587 94.9657 96.0415 160.2292 178.2544 179.0085

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Table 10 Overall mean availabilities for each scenario and the chosen cases within (bold highlights critical contaminants, italic highlights the bottleneck islands). Scenario

Case

OMC

Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest Lowest Middle Highest

IMC

FWC

MCL

Mean availability C1

C2

C3

C4

9.1939 9.7931 9.8093 6.5907 5.9168 5.9615 10.0113 10.9744 12.2643 12.3231 13.1363 12.8803

12.9217 12.2417 12.2371 10.3414 11.1152 11.1693 12.3341 8.1863 8.5907 11.5284 8.0390 8.0414

11.1646 9.5926 9.5776 11.1609 11.0065 11.1388 9.6032 5.8050 4.8022 10.4331 8.2059 8.1620

20.1606 19.0823 19.0540 17.2144 17.0857 17.2203 19.3561 15.8528 16.0007 19.8303 17.5128 17.5086

both of them). These observations interfere with the way regeneration would be used to improve the performances of the studied IWWN.

through the Financial Agreement POSDRU/88/1.5/S/60203. Professor Vasile Lavric gratefully acknowledges the financial support of UEFISCSU Project no. 663/19.01.2009.

4. Conclusions References dual-objective optimization of an integrated The water/wastewater and treatment network was performed with the aim of establishing the optimal topology which ensures the total costs and freshwater minimization. The nonlinear mathematical model resulted from total and partial mass balances together with the relationships to compute the pipe diameter observing optimal investment and operating costs. The associated dual-objective function was minimized using the genetic algorithm method implemented in MatlabTM . Due to the contradictory nature of the components of the dual-objective function, freshwater consumption and total cost of the active pipes, a Pareto front was obtained for each of the four cases taken into consideration according to the chosen ranking criterion: OMC, IMC, FWC and MCL. The TUs are assimilated with potential partial contaminated water sources, the methodology allowing their assignation to the proper WU according to the closeness between their outlet and inlet concentration restrictions. The optimal topology depends on the order in which the WUs are ranked and, also, on the TUs performances (Tudor & Lavric, 2010a). Analysing the topologies resulted from the optimization of the IWWN in each scenario we observed that the internal wastewater reuse is complete, meaning that there is not a single inactive link between WUs. This means that the only differences given by the scenarios at hand are in the directions in which the streams move between the interlinked WUs. Remarkably, the WUs fed with freshwater are the same, irrespective of the scenario. A further reduction in the freshwater consumption is through local regeneration. To support this decision, the overall mean availability analysis was done, pointing to the critical components and bottleneck islands for each scenario; regeneration of these contaminants only could be the next successful step. Nevertheless, a debate could be opened regarding the utility of the local regeneration when there are three TUs whose performances could be adjusted in such way as to minimize the overall mean availability; this will be our further development. Acknowledgements The work of Raluca Tudor has been funded by the Sectoral Operational Programme Human Resources Development 2007–2013 of the Romanian Ministry of Labour, Family and Social Protection

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