Optimization of Total Networks of Water-Using and ... - ACS Publications

Ind. Eng. Chem. Res. 2010, 49, 3715–3731

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Optimization of Total Networks of Water-Using and Treatment Units by Genetic Algorithms Raluca Tudor* and Vasile Lavric UniVersity Politehnica of Bucharest, Chemical Engineering Department, RO-011061, Polizu 1-7, Bucharest, Romania

The optimization of an integrated network of water-using (WU) and treatment (TU) units is addressed in this paper, by targeting for maximum treated water reuse as a considerably better alternative to fresh water consumption. An optimal integrated water network (WN) is an oriented graph, starting with inlet contaminant free WUs and then the other WUs ranked by a certain criteria. The outlet wastewater streams are either split to be reused by the next WUs in sequence or sent to treatment. The mathematical model of the integrated WN is based upon total and contaminant species mass balances for each and every WU/TU which is restricted with respect to the inlet and outlet contaminant concentrations. The performance of the approach is tested on a synthetic example. Several scenarios were used, the results being analyzed in connection with the reduction of fresh water consumption and the increase of internal and treated water reuse. I. Introduction The population growth and the progress of agricultural and industrial broad range of products have affected the freshwater supply around the world. Increasing freshwater demand at the same time with more and more restrictive environmental regulations has transformed it into a scarce commodity. As a consequence, it has generated greater awareness of the economic driving forces, local authorities, and public concern over environmental protection.1,2 Water is, probably, the vital component of the process industries, and it has been intensively used in abundant quantities by the chemical, petrochemical, petroleum refinery, food and drink, pulp and paper industries, and many others. Due to the fact that it is a potentially limiting element for industrial development, companies have become conscious of freshwaterrelated risks and of management approaches and tools available to lessen them. Thus, there is a growing emphasis on minimizing freshwater use in industry, through identification of reuse and recycle opportunities which, ultimately, lead to wastewater minimization. Minimization of freshwater usage and wastewater discharge has become one of the main targets of design and optimization of process systems.3 Among the many kinds of technologies for saving freshwater consumption, water system integration (WSI) shows significant effectivenes.2 Therefore, at present, the research on freshwater and wastewater minimization focuses, in essence, on WSI. Water system integration treats the water utilization processes in a plant as an organic whole, and considers how to distribute the water quantity and quality to each WU, so that water reuse is maximized within the system concomitantly with wastewater minimization.2 Typically, two main categories of methods are used to obtain good designs of these systems: 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.4 The water pinch analysis (PA) technique belongs to the class of graphical methods, which show simple solutions and beneficial results when applied to * To whom correspondence should be addressed. E-mail: r_tudor@ chim.upb.ro.

water-using networks. Besides making elementary changes for the process operations, options for reducing the water demand of a process may be done via water reuse, recycle, and regeneration.1–3 In the context of process integration, reuse means that the effluent from a water-using operation is sent to other operations and does not re-enter operations where it was emitted. On the other hand, a recycle scheme allows the effluent to re-enter the operations where it was generated. In regeneration schemes, effluent is partially treated by an appropriate water purification unit then reused or recycled.5 Since the introduction of PA,5,6 various significant development stages on targeting, design, and improvement of a maximum water recovery network have been accomplished. These include works on processes with fixed flow rate and fixed concentration,1,7 regeneration targeting,8 numerical water targeting,7 network design to attain water targets,1,5,6,9 problems with multiple contaminants,4 and water network retrofit.10–12 The concept of maximum water recoVery,4 related to maximum reuse, recycling and regeneration of spent water, has two limitations. First, it partly addresses the issue of water minimization which should holistically consider all conceivable methods to decrease water consumption through elimination, reduction, reuse/recycling, outsourcing, and regeneration. Second, since it focuses on water reuse and regeneration, it does not lead to the minimum water targets; these can only be achieved when all options for water minimization have been applied. Another approach in this area is by minimum waste targeting. Bandyopadhyay12 proposed a methodology to set a minimum waste generation target prior to the detailed network design. Later this study was developed to target the minimum waste treatment flow rate to satisfy environmentally discharge permits.13 The WN design is always regarded as the second stage of any conventional PA technique. Once the minimum flow rate targets are determined, a WN may be designed to achieve the established flow rate targets.4 It is also worth noting that most WN design techniques were originally developed for water reuse/recycle networks, which were then extended to cater to cases with regeneration and wastewater treatment. In contrast, there is also a design technique that is solely developed for wastewater treatment networks. Finally, once a network is

10.1021/ie901687z  2010 American Chemical Society Published on Web 03/23/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

synthesized, the preliminary network is developed to yield a simplified network using an evolutionary technique. Mathematical programming approaches are more general and dominant and serve as an alternative tool to graphical PA in addressing more complex systems, with many WUs, single and multiple impurities,3 mass load uncertainty,14 water and utilities minimization,15,16 capital cost estimation,17–19 regeneration of internal streams,20 integration with interception network,21 as well as water treatment system, or evaluation of zero discharge possibility.22 Teles et al.3 studied the optimal design of industrial WNs with multiple contaminants by proposing a superstructure that accounts for all possible connections between water sources and WUs; during optimization, different structures are generated that consider all possible sequences of operations. The study focuses on the design of the WN without considering TUs, neither in an integrated way nor as a part of a downstream system required to lower the concentration of the WN streams down to the discharge limits. The model proposed was solved with a succession of linear programming techniques. The resulting WN, where the WUs are arranged in parallel, lacks the possibility of water reuse, which is exactly the responsible factor for most of the savings in freshwater consumption and wastewater generation. The same problem of optimization of single or multiple contaminants WNs was solved by the pinch multiagent genetic algorithm,23 inspired by multiagent system in artificial intelligence, which overcomes the computational time limitations to some extent. The problem of uncertainty in optimizing WNs was analyzed by Al-Redhwan et al.14 Due to the fact that wastewater flow rates and levels of contaminants can vary widely as a result of changes in operational conditions and/or feedstock and product specifications, optimal WN designs should be resilient and able to adapt to such changes. A stochastic programming approach able to accommodate uncertainties in designing and retrofitting industrial WNs was proposed, coping with both concentrations and temperatures.14 Sensitivity analyses revealed that accounting for uncertainty in operating conditions results in considerable changes in the connectivity of the WUs involved in wastewater reuse.14 In contrast with the previously mentioned tendency to focus on minimizing freshwater consumption of a WN with several contaminants, there are a number of papers that deal with minimizing cost objectives for investment, operating, or grassroots design.17–19 The cost-based optimization criterion17 is used to find the optimum WN topology with an improved genetic algorithm (GA) which reduces both the investment and operating costs, when water sources with or without multiple contaminants are used together. The topology found was compared against the best topology found using supply water minimization as optimization criterion. Another approach18,19 uses mathematical models to optimize a water network at the stage of grassroots design. Feng et al.19 proposed a superstructure for the total cost optimization of regeneration recycling WN, in order to determine the optimum postregeneration concentration. Later, Faria et al.18 focused on WNs retrofit projects, because of the need for capacity increase, product quality management, and complying with harsher environmental regulations, among others. Sometimes, there are economic incentives that come from cost reductions. While performing a retrofit to meet environmental targets could be mandated, retrofits to reduce freshwater costs as well as water treatment costs are not. In the latter case, profit drives the decision-making process. Setting aside the need to approach the retrofit problem trying to meet environmental

targets or maximize savings, the cost and finances management point of view (maximum profit) is still very important for the industrial competitive environment. This was why Faria and co-workers18 elaborated a procedure for the grassroots design and retrofit of single and multicomponent water network using cost, consumption, and profitability as objectives, considering regeneration too. The study focused on maximization of the net present value and/or return of investment instead of minimizing freshwater consumption. Feng et al.19 used mathematical programming coupled with a superstructure to optimize regeneration recycling WNs at the stage of grassroots design to reduce the capital cost. Water regeneration is a promising tool to be integrated into WN in order to further reduce external water demands as compared to systems with just direct water reuse/recycle. Regeneration systems boost water recovery potential by improving stream quality to suit delocalized water demands within process plants. Water regenerators are typically modeled as units that remove solute from a single stream of contaminated water20,24,25 the regenerators thus discharge a single stream of partially purified water for further reuse or recycle. For simplicity, regenerators are modeled either as having a fixed outlet concentration, or as removing a fixed ratio of the total contaminant in the stream. An automated targeting method has been developed that incorporates concepts of insight-based technique into the mathematical optimization model to determine the minimum flow rate or cost for a resource conservation network.24 A new class of waste interception processes termed partitioning regenerators is introduced in the context of linear programming-based technique that is equivalent to PA. They purify a contaminated water stream and split it into a lean regenerated stream (of much higher purity than the inlet stream) and a solute-rich reject stream (of much higher contamination than the inlet stream).24 Tan et al.25 proposed a superstructure-based optimization approach to be used for the design of WNs integrating partitioning regenerators, i.e. membrane-based processes (e.g., ultrafiltration, reverse osmosis), flotation systems, (e.g., dissolved air flotation, induced air flotation) and gravity settling systems (e.g., coagulation, flocculation, clarification). In most industrial applications, the reject stream is often disposed off due to its low quality. However, as it has been shown,25 the reject streams may still be valuable for recovery within the water network in some cases. The work presents a novel superstructure model, restricted to single-contaminant, for the synthesis of a WN with a single partitioning regenerator, while allowing for the possible reuse/recycle of both lean regenerated and reject streams from the regenerator. The contaminated streams are pooled before being sent for regeneration. Therefore, there will only be a single concentration for the purified and reject streams exiting the regenerator. Their approach is able to find the optimal solution, for fresh water minimization, while simultaneously generating a network configuration that achieves the optimal level of resource conservation.25 In the same framework lies the study of Iancu et al.26 aimed to reveal the topological impact of regeneration unit upon WN. For a better evaluation of the potential for internal regeneration, i.e. increasing the possibilities of water streams reuse as a supplementary asset for the optimization of complex WWNs, some new concepts have been introduced, i.e. regeneration of critical component, regeneration of bottleneck island, or partial/ total regeneration strategy.20,26,27 The influence of regeneration type upon the optimal WN topology was analyzed for three possible situations: critical component regeneration, partial


regeneration (with subtypes: limited or unlimited treatment), and total regeneration (zero discharge opportunity). Every case was compared against the optimal WN topology obtained minimizing the total supply water flow rate. Later, the study was extended to optimization of WN for simultaneous minimization of the fresh water consumption and optimal placement of the regeneration unit, through minimization of active pipes’ length.27 The next step of these study was to focus on the regeneration of internal streams.20 Different regeneration scenarios are presented, aiming to obtain the best WN topology for minimum water supply flow rate. These scenarios allow also to highlight the relationship between supply water saving, internal regeneration, increased water reuse, and WWN topology optimization. The problem of optimal synthesis of an integrated WN (IWN) where WU processes and water treatment operations are combined into a single network was studied also by Karuppiah and Grossmann.2,28 Their initial study was aimed to prove that in an IWN the total cost of obtaining freshwater for use in the WU operations and treating wastewater is globally minimized. They proposed a superstructure which comprised all the feasible design alternatives for water treatment, reuse, and recycle formulated as a mixed integer nonlinear programming (MINLP) problem. Later, they extended the previous study to take into account uncertainty features.28 A superstructure of an IWN is constructed with various interconnections between all the WUs, which are globally optimized to obtain a minimum cost. The WUs have fixed water demand, which is met by a freshwater source or wastewater coming from other processes, while the common restrictions on inlet and outlet concentrations apply. The wastewater is treated in a set of TUs from where it is either discharged into the environment, when the contaminant levels are always below some specified limits, or recycled back for use in the WUs. The IWN is subjected to significant uncertainties (taking on different values at different points of time during network operation) in the contaminant loads generated inside the WUs and the contaminant removals in the TUs. Due to the high interconnectivity, changes in the uncertain parameters can adversely affect all parts of the network, to the point where it may not be possible to operate the network without violating the discharge restrictions or the limits on the contaminant levels in the inlets to the WUs.28 The objective was to construct a WN such that the total cost of designing and the expected optimal operational cost over the complete interval are globally minimized. The superstructure was optimized with a multiscenario nonconvex mixed integer nonlinear programming (MINLP), which can grow in size with the number of scenarios and often require exponential computational effort to be solved to rigorous global optimality. Luo et al.29 considered that the performance of an integrated water and treatment network (WTN) will be more easily characterized in terms of fixed outlet concentration. Again, a superstructure that incoporates all feasible design options for wastewater treatment, reuse, and recycle was proposed, which is synthesized as a NLP model, optimized with an improved particle swarm algorithm. The main drawback is its limitation to the cases where the kinds and number of the units for WUs and for TUs are known. For the WN synthesis, however, the selection and the number of the WUs should be simultaneouly optimized which will lead to MINLP problems.29 Synthesis of distributed wastewater treatement plants (WTPs) has been studied also by Lim et al.30 in order to reduce capital and operating costs associated with wastewater treatment. The environmental and economic fesability of a total wastewater treatment network system including WTPs was estimated using

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life cycle assessment (LCA) and life cycle costing methods. A terminal WTP was included in a superstructure model used for the retrofiting existing WTPs to reveal real wastewater treatment scenarios, since the direct discharge of untreated and diluted wastewater into sea or surface water (previously employed for the distributed wastewater treatment network systems in the former studies), is prohibited by environmental regulations in some countries, even though the quality of the final effluent meets discharge permits.30 Later, Lim et al.31 continued their study focusing mainly on reduction of environmental impacts. A mathematical model was developed to retrofit existing distributed and terminal WTPs into an environmentally friendly system from the life cycle perspective. The objective function was formulated based on principal contributors to environmental impacts in all life cycle stages. The methods used for solving the problems of water and/or network optimization are in the recent years dominated by evolutionary algorithms, such as genetic algorithms,26,27,32–34 ant colony optimization algorithms,35 or particle swarm optimization.29,36–38 In this paper, an IWN combining WUs and TUs is optimized based upon GA by targeting for maximum treated water reuse and thus minimum fresh water consumption. Different scenarios are used to generate the corresponding WN topologies, which are analyzed and general conclusions are presented for each case. II. Abstraction of the Wastewater Network An optimal WN, in agreement to the principle of driving force equipartition across the process, can be perceived as an oriented graph, with respect to water flow, starting from unit operations with contaminant free constraints at their entrance, which are supplied with fresh water only (Figure 1a). Any other WU, i, could receive streams from any WU, j, behind it (j ) 1, 2, ..., i - 1) and could send streams to any subsequent WU, 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 countercurrent reuse (water from the exit of a WU cannot be sent to WUs behind) are lacking ab initio. If there are several water supply sources with different contaminant levels, the WUs are clustered according to the match between their inlet restrictions and the supply water characteristics, as in Figure 1b. The fresh water feeds only the inlet contaminant-free units, grouped into the first cluster. The next cluster will be formed by the units having moderately inlet restrictions, dealt with by the slightly contaminated supply water source (fresh water is avoided, since it is expensive). The considerably contaminated water supply can be, eventually, used to feed the last cluster, gathering the units with relaxed inlet restrictions. The distribution of contaminated sources across the wastewater topology is also in accordance with the principle of driving force equipartition. For an integrated WU and TU network (Figure 1c), the TUs are included into the previous graphs as well, but using a slightly different criterion. They are cascaded, starting with the most relaxed inlet TU which receives the heaviest contaminated wastewater streams and continuing with the less and less relaxed inlet TUs until the last one which receives the least contaminated wastewater streams and treats them until the legal conditions to be disposed off in nature are met. The exit of any TU in cascade should not be lower than the inlet of the next one (Figure 1c). The WTN is designed to recycle the water resulted from partially/totally decontamination; each TU can be assimilated to a contaminated supply water source, available for the WUs. When the contamination level of any wastewater

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Figure 1. Abstraction of the network as an oriented graph; the knots are WUs; the oriented arches are the pipes transporting the water reused internally. Two ranking procedures are envisaged: by load and by fresh water demand. (a) Only fresh water is available as supply. (b) Several contaminated water sources are available, with different levels of contamination. The WUs are lumped according to the match with the water supply sources. (c) Integrated WUs and TUs network (TUs can be seen as contaminated water supply sources as well). New knots (TUs) and arches are added to the network. The TUs are ordered according to their inlet restrictions (TUM, treats the least contaminated water complying the limits to be discharged in environment, while TU1, treats the most contaminated one). The treated water is recycled back in the system, TUs acting like contaminated water supply for the WUs.

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 TU and starts being decontaminated. The inlet restrictions of the last unit from the treatment cascade should accommodate

the lowest outlet restrictions of the WUs. This ensures that even the slightest polluted water stream from the WUs will be treated accordingly. The efficiency of such an integrated treatment system is 2-fold: on one hand, each polluted stream enters the


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Figure 2. Matrix of the wastewater network having N water-using units and M wastewater treatment units. The water-using units lay on the main diagonal; the uppermost positions are reserved for the members of the inlet contaminated streams, while in the downward part lay the outlet recycled streams. In this representation, it is assumed that, due to inlet restrictions, units U1 and U2 accept only freshwater. The last column of the matrix is reserved for the outlet contaminated streams of each water-using unit, which go directly to the treatment units.

the second, to the destination, so the element Xij is the stream coming from unit i and heading to unit j. The elements below the main diagonal are related to the treated streams, reused by WUs from the TUs, seen as contaminated water supply sources. As in the previous case, the first index of Ytj corresponds to the source, which this time is the TU, while the second is the sink, the WU. The sparsity of the matrix is the result of match between the exit of the TU and the inlet of WUs belonging to the same cluster.

Figure 3. Generic unit operations abstraction for the IWM, each having a mixer, M, all the incoming streams are mixed then fed to the unit, and a splitter, S, the streams leave the unit with the same concentration. (a) Ui stands for a generic WU, Xji is the water flow from j (j < i) to i units; likewise Xij is the water flow from i to j (i < j < N) ones; Fi is the fresh water flow entering the unit Ui; Yti is the treated water coming from the treatment unit t to the unit operation i; Wit is the stream sent directly to TUt, if its concentrations are higher than and closest to this unit, LUi is the possible flow loss and ∆mki is the k pollutant flow (load) released in water in Ui. (b) Tt stands for a generic TU, and Wit represents the stream leaving Ui and heading to the treatment unit Tt since it fulfills the requirements to be admitted for treatment in this unit; Zt-1 is the wastewater partially treated in the previous unit, which cannot be reused internally; Ytj is the partially treated water stream going from treatment unit t to unit operation j; Zt+1 is the partially treated wastewater stream going from unit t to the next unit (the last TU is the only one being able to dispose water to environment, complying with the legal limits).

correct TU, avoiding supplemental pumping costs and dilution of heavily polluted streams treated in the previous units and, on the other, permitting a possible reuse of each TU exit by a matching WU. The topology of the IWN as encoded by the oriented graph (Figure 1c) can be adequately represented by a sparse nonsquare matrix as in Figure 2. The units lay on the main diagonal and could be fed with freshwater, (F1, F2, ..., FN). The elements above the main diagonal correspond to the internally reused water streams, the left uppermost positions being zero according to the number of WUs in the inlet contaminant-free units cluster. The first index of the element corresponds to the source unit,

It has to be pointed out that the initial topology, as encoded by the oriented graph and the associated sparse nonsquare matrix has the maximum number of virtual connections. The goal of the optimization using some convenient objective function(s) is to prune the unnecessary virtual links, thus establishing the final working IWN. III.1. Mathematical Model of the IWN. The mathematical model of the wastewater network is based upon the overall and partial mass balances around each WU and TU, separately. Let us consider two generic units, Ui for the WUs (Figure 3a) and Tt for the TUs (Figure 3b). The unit Ui is responsible for sending K pollutants into water; a total mass balance and K - 1 partial mass balances can be written for every one of them. Total mass balance i-1

Fi +

∑X

ji

j)1

K

+ Yti +

∑ ∆m

N

ki

)

k)1

∑X

ij

+ Wi + Li

j)i+1

(1) K ∆mki is rather low, it Although the unit load ∆mi ) ∑k)1 should be taken into consideration in the overall mass balance.

Partial mass balance for the contaminant k i-1

Fi +

∑X C

U,out ji kj

j)1

N

+ YtiCktT,out + ∆mki ) (

∑X

ij

+ Wi + Li)CkiU,out

j)i+1

(2)

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Analyzing the inequality 3, it should be observed that, for any k species, the equal sign is valid for some specific minimum contaminated water supply, dependent on the load level ∆mki:

Constraints: exit mixer concentration i-1

Fi + Cki )

∑X C

U,out kj

ji

+ YtiCktT,out + ∆mki

j)1

e CkiU,out,max

N

∑X

i-1

+ Wi + Li

ij

(

∑X C j)1

j)i+1

(3) FU,min | out ik

i-1

∑X C

U,out ji kj

+ YtiCT,out kt

j)1 i-1

Cin ki )

Fi +

∑X

ji

e CU,in,max ki

(4)

+ Yti + ∆mi

j)1

The unit Tt (see Figure 3b) is responsible for removing K pollutants from the wastewater; again, a total mass balance and K - 1 partial mass balances can be written for every one of them. The inlet flow represented by the term (Wi)t which is the outlet from the WU i gets to treatment since it reached the required level of contamination. In the case where the contamination of Xij streams is too high, rendering them nonreusable, the whole WU exit goes to TU t; otherwise, reusing internally some streams in the next WUs helps minimize the fresh water consumption and lowers the treatment costs. The outlet flow of the treatment unit is split into streams (denoted by Ytj) that can be reused only if the contaminants concentration complies to the WU’s inlet restrictions and Zt+1 stream, that will be further decontaminated by the next treatment unit in sequence (for the last treatment unit, that treats wastewater until the highest level of decontamination, the stream Zt+1 is the stream to be discharged into environment). So, the reusable outlet flow of each treatment unit could be seen as a contaminated water source, thus taking part in the total and partial mass balances of the WUs, together with the fresh water Fi, aiming to completely remove the latter as influent. For the depletion of contaminant k, ∆m′kt, removed by each treatment unit, the following statement stands: no matter the flow entering TU, it is assumed that the treatment is done until the specified outlet concentration, CT,out kt , is reached. Total mass balance N

Wit + Zt-1 ) Lt +

∑Y

tj

i-1

(

Constraints: outlet splitter concentration Fi +

+ YtiCT,out + ∆mki) kt

U,out ji kj

+ Zt+1

(5)

)

∑X

+ Yti + ∆mki)CU,out,max ki

ji

j)1

(8)

CU,out,max ki

In eq 8, FU,min |out is the fresh water needed to be mixed with the ki wastewater coming from the previous units and, possibly, from one of the treatment units, so that the outlet restrictions to be observed. Due to the cascade nature of the network, all the information associated with the preceding units are already and CT,out are fixed. In computed, i.e. Xji and Ckj while CU,out,max ki ki order for inequality 3 to hold for the worst case of the k pollutant species, the maximum value given by eq 8 should be chosen, since it guarantees the strict observation of conditions by the rest of the contaminants’ concentration: ) max(FU,out,min ) FU,out,min i ik k

(9)

As in the case of inequality 3, the equal sign in (4) is valid for any k species, given some specific level of the supply water: i-1

( FikU,min | in )

∑

i-1

XjiCkjU,out + YtiCktT,out) - (

j)1

∑X

ji

+ Yti + ∆mi)CkiU,in,max

j)1

CkiU,in,max

(10) |in has the same meaning as FU,min |out, except it is In eq 10, FU,min ki ki computed based upon the inlet restrictions. Analogously, the maximum flow among all k found will guarantee the full observation of the inlet restrictions. ) FU,in,min ) max(FU,in,min i ik k

(11)

In order for both inlet and outlet restrictions to hold true, the maximum from eqs 9 and 11 should be kept, thus the feed for WU i should be

j)1

FU,min ) max(FU,in,min , FU,out,min ) i i i in,out

Partial mass balance for the k contaminant N

T,out ∆mkt′ ) (WitCU,out + Zt-1Ck,t-1 ) - (Lt + Zt+1 + ki

∑ Y )C tj

T,out kt

j)1

(6) Constraints: inlet concentration T,out WitCki + Zt-1Ck,t-1 CT,in ) g CT,in,min kt kt Wit + Zt-1

(7)

III.2. Deriving the Objective Function. Solving this optimization problem is not simple, since the independent variables determine the equations’ number and the objective function including the constraints is not easy to find. The total number of unknowns, considering the constraint values, , CU,out,max , CT,in,min , and CT,out,min , together with the load for CU,in,max ki ki ki ki each unit operation ∆mki, as imposed, is N(N + 3)/2 + M: the internal reused streams for WUs, N(N - 1)/2 elements, F and W each with N elements, while Z has M elements.

(12)

Analyzing again the total and partial mass balances (1-4), we observe that in order to increase the treated water reuse, which is the main goal of the present paper, the fresh water flow should be as low as possible. When all the fresh water flow is zero, the zero discharge case is obtained. According to this observation, the objective function permitting to maximize the treated water reuse is simply: N

F)

∑F

U,min i

(13)

i)1

meaning that the total amount of the supplied fresh water is minimized. III.3. Optimization Algorithm. The optimization problem is solved using the objective function (13) derived in the previous chapter. The network’s optimization, i.e. finding the water network topology and the minimum water supply guarantying the maximum reuse and recycle, was solved using

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 33,34

GA as implemented in Matlab. Like in any standard GA, the elements of the matrix (Figure 2), i.e. internal and external flows, are the genes encoded in a chromosome through direct storage. Considering the overall mass balance (1), the effluents to the treatment section can be expressed with respect to the influents and internal streams, while using the partial mass balance (2), the influents can be expressed with respect to the internal flows only. So, the solution should be iterative in nature; first, start with a guessed topology, in terms of internal flows, then verify if the mathematical model, including the constraints, holds: if not, modify the topology in a suitable manner to obtain a better approach, under the imperative of minimum fresh water and maximum treated water consumption, as expressed by the corresponding objective function. GA governs the task of finding the optimal topology through suitable modifications of an initial population of topologies. The algorithm can be expressed in the following basic steps: 1. Order the WU by a criterion (i.e., FWC or MCL) observing their restrictions. 2. Assign from which TU the WUs will receive their feeding. 3. Compute the upper limits of the internal flows. 4. Generate the initial population pool. 5. For each individual, solve the mathematical model and compute the objective function. 5.1. Compute the wastewater flow for unit Ui according to eq 1 and then compute the contaminants’ concentration for each and every unit. 5.2. Compute the wastewater flow for unit Tt according to eq 5 and calculate the contaminants’ concentration. 6. Make a new generation using genetic operators like selection, crossover, and cloning. 7. Apply mutation to arbitrarily selected individuals. 8. If the minimum objective function is attained, stop the algorithm; otherwise, restart from the fifth step. The software written in Matlab starts by generating a population of chromosomes for which the mathematical model is solved and the objective function is computed. Four genetic operators are used to improve the first population: selection (choose randomly the parents to be recombined in order to produce better offsprings, among the fittest ranked individuals from the population), crossoVer (recombine genes of selected pairs of individuals), mutation (randomly change genes in the chromosomes with a very small probability, thus keeping the population diverse and preventing from early convergence onto a local optimum), and cloning (duplicate the individuals from the previous to the next generation). IV. Case Studies A synthetic example was used to study both the optimal topology of an IWN and which are the effects of the integration of TUs upon the subnetwork of WUs. An integrated network of six WUs and three contaminants (the information regarding each unit’s load and associated restrictions are presented in Table 1) and three TUs (the inlet and outlet concentration restrictions are presented in Table 2) is analyzed under different scenarios having as objective to find the optimum topology which reduces fresh water consumption while increasing internal wastewater reuse and treated wastewater use. This topology is compared against the optimal topology found for the WN given in Table 1 when using supply water minimization as optimization criterion, but without the treatment network integrated. The first step in designing an optimal IWN is to rank the WUs of the WN according to a given criterion. The suboptimal topology thus established (this can be seen as a superstructure

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Table 1. Primary Data (Mass Loads, Inlet, and Outlet Restrictions) of the Water-Using Units of the Integrated Network inlet concentration restrictions (ppm)

load (kg/h) contaminant

outlet concentration restrictions (ppm)

contaminant

contaminant

unit no.

1

2

3

1

2

3

1

2

3

1 2 3 4 5 6

0.35 0.15 0.35 0.45 0.25 0.15

0.25 0.35 0.45 0.15 0.45 0.45

0.15 0.25 0.55 0.45 0.35 0.85

0 15 15 25 45 35

0 20 35 45 35 20

0 25 0 45 55 25

35 70 75 95 90 85

45 90 95 85 100 80

55 120 125 135 120 95

Table 2. Primary Data (Mass Loads and Inlet and Outlet Restrictions) of the Wastewater Treatment Units of the Integrated Network inlet concentration restrictions (ppm)

outlet concentration restrictions (ppm)

Contaminant

Contaminant

treatment unit no.

1

2

3

1

2

3

1 2 3

45 25 15

45 35 20

55 45 25

30 20 2

40 25 4

50 30 5

already pruned of the ab initio useless links) represents the starting point for the iterative process of finding the optimal IWN. Two are the ranking criteria, both conforming to the principle of driving force equipartition, used to order WN: fresh water consumption (FWC) and maximum contaminant load (MCL). Both of them will be used since up to now, there is no clear evidence that one of them gives better results than the other one.20,26,27,32 Irrespective of the ranking criterion, the inlet contaminant-free units will always be placed at the beginning of the oriented graph, since there cannot be internal reuse for them. TUs are cascaded according to their inlet/outlet restrictions: the primary treatment unit (further denoted by 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 (further denoted by 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 (further denoted by TU3) eliminates the pollutants up to the level of complying with the legislation regarding environmental 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 present study will focus on three main directions: (1) optimization of the WN without TUs, using supply water as objective function, (2) optimization of the IWN using all the available treatment units; comparison of the WN subnetwork with the topology obtained in the first case; (3) analysis of the influence of the TUs availability (primary and final TUs, secondary and final TUs and eventually tertiary TU) upon the optimal topology of an IWN. The analysis of each network was done in terms of total water supply and treatment cost, i.e. the operating cost. A ratio between fresh water price (formed by actual fresh water price and the supply cost) and the cost of water treatment in each TU was proposed, considering a nonlinear increase with the exit level of purity. So, assuming that the price of fresh water is P mu/t (from now on, mu stands for monetary units), the cost of wastewater treatment in the primary TU is nP mu/t, in the secondary TU is mP mu/t, while in the last TU is qP mu/ tone.

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Figure 4. Optimal topology of the WN ranking criterion is FWC. The rank is given by the numbers in square brackets, while the initial arrangement is given by the plain figures. The dashed arrows represent the fresh water entering each WU, the numbers on the arrows stand for the flow (t/h), while the rest of the arrows give the internal flow distribution. The difference between the WN outlet and inlet comes from the total load removed from the WUs belonging to the network.

Figure 5. Optimal topology of the WN. The ranking criterion is MCL. For the rest of the notations, see Figure 4.

In order to have a clearer evaluation of each situation and the possibility to compare the cases with each other, some values were given to these ratios: n ) 10, m ) 20, and q ) 50. IV.1. Base Cases: WN Optimization, Treatment Not Included. The topologies obtained after WN optimization of the network from Table 1, minimizing the fresh water consumption in the absence of any treated water availability, are presented in Figures 4 and 5, for the two ranking criteria: fresh water consumption and maximum contaminant load. Both optimized network need almost the same feed of fresh water (26.8511 t/h FWC vs 26.8 t/h MCL). The total operating cost is 6.2% higher for the MCL case. The fresh water supply price represents around 1.5% from the operating cost in both cases. It has to be mentioned that since the WN should ultimately discharge the water into environment, the consumed fresh water

should be treated accordingly, dramatically increasing the operating cost. The topology of the two optimized WN differs according to the ranking criterion used. When ranked by FWC (Figure 4), there is an efficient water reuse because the outlet streams of WUs 1 and 3 feed the next units in the sequence. When the units are ranked according to MLC, the only outlet stream completely reused comes from the first WU (Figure 5). Another advantage of the WN from Figure 4 is that it is shorter compared to the one from Figure 5. The former uses a pipe less (unit 3 does not send water to treatment), thus less energy for pumping is consumed. In Tables 3 and 4 are listed the actual inlet and outlet values of contaminant concentrations, with emphasis on the critical components, i.e. when at least one of the contaminants has

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 a

Table 3. Concentrations for the Optimal WN from Figure 4 actual inlet concentration (ppm)

actual outlet concentration (ppm)

components

components

unit no.

1

2

3

1

2

3

unit 1 unit 2 unit 3 unit 4 unit 5 unit 6

0 1.31 0 20.86 33.62 22.4

0 1.15 0 44.87 34.19 19.86

0 0.99 0 32.34 28.65 13.38

32.49 29.37 73.89 95 70.18 36.8

23.21 66.61 95 69.58 100 63.07

13.93 47.75 116.11 106.48 79.84 95

a

The values written in bold represent the critical concentrations.

Table 4. Concentrations for the Optimal WN from Figure 5a actual inlet concentration (ppm)


components

components

unit no.

1

2

3

1

2

3


0 12.12 0 24.75 44.97 20.55

0 8.83 0 38.81 34.68 19.95

0 5.54 0 27 38.85 13.55

32.76 46.91 73.89 95 81.26 34.92

23.4 90 95 62.22 100 63.07

14.04 63.52 116.11 97.25 89.66 95

a

The values written in bold represent the critical concentrations.

reached the critical concentration. This means that the minimum possible fresh water has been allocated for this WU, still complying with the restrictions; more units with at least one critical concentration attained, less fresh water would be allocated to the WN. IV.2. IWN Optimization. The optimized networks of six water-using and three wastewater treatment units are represented in Figure 6, for the FWC criterion, and Figure 7, for the MCL criterion, respectively. Both networks use the same flow of fresh water (14.7347 t/h) meaning they discharge the same flow (14.7411 t/h) in the environment, the difference being given by

3723

the load removed in the IWN. The total supply and treatment cost, evaluated as presented above, is 7.2% higher for the MCL ranked network. The details of the operating cost computation are presented in Table 7. In Table 5 are listed the inlet and outlet actual contaminants concentrations, emphasizing the critical concentrations where they appear. WUs 4 and 5 are fed with partially decontaminated water which, mixed with upward streams, gives the maximum concentration admitted for one contaminant (Table 5). In Table 6 are presented the inlet and outlet actual contaminant concentration for the WUs of the INW represented in Figure 7. Like in previous cases, here there are also two WUs, 2 and 5, for which the inlet restrictions are met, when the partially decontaminated water supplied from the TUs is mixed with the upward streams. The outlet restrictions are reached as well, but for WUs 3, 4, and 6, ensuring this way the minimum fresh water consumption. In Table 7 is presented the detailed operating cost for the networks shown in Figures 6 and 7. A comparison in terms of the flows entering the TUs and the operating cost is made. The topology of the network changed significantly in comparison with the previous two cases (Figures 4 and 5). There is a lesser internal water reuse, coming from the WUs subnetwork, due to the fact that the WUs are primarily fed with treated water, according to their inlet restrictions. WUs 4 and 5, which have less restrictive conditions for the inlet concentration, accept secondary treated water as inlet (Figure 6). Consequently, less water coming from the previous WUs will be used to match the restrictions imposed for WUs 4 and 5 (WU 4 uses only streams from 1 and 3, while WU 5 gets streams from 3 and 4 only). When the decontaminated water comes from the final treatment unit, thus its level of contamination is close to the fresh water, there is a higher water reuse potential, and since more internal streams can be used to match the corresponding inlet restrictions (see WUs 3 and 6, for which the internal water reuse has significantly improved). The optimiza-

Figure 6. Optimal topology of the IWN ranked by FWC. The TUs are cascaded according to the match between their exits and inlets (the primary unit’s exit is equal to or higher than the secondary’s, secondary’s exit is equal to or higher than tertiary’s, which has its exit lower than the legal values permitting environmental discharge). It is worth mentioning that the exit flow from any TU could and should be reused in the WUs subnetwork (for the rest of the notations see Figure 4).

3724


Figure 7. Optimal topology of the IWN ranked by MCL (for the rest of notations see Figure 6). Table 5. Concentration Data of the Optimal IWN Represented in Figure 6 actual inlet concentration (ppm)


components

components

unit no.

1

2

3

1

2

3


0 8.41 0 25 24.87 9.92

0 10.35 0 36.78 35 13.08

0 11.43 0 37.01 33.24 13.16

35 32.04 73.89 47.39 42.13 24.36

25 65.49 95 44.24 66.06 56.41

15 50.81 116.11 59.4 57.4 95

Table 6. Concentration Data of the Optimal IWN Represented in Figure 7 actual inlet concentration (ppm)


components

components

unit no.

1

2

3

1

2

3


0 14.64 0 21.05 33.03 5.74

0 20 0 27.87 35 8.74

0 24.54 0 31.84 46.45 10.78

35 33.03 73.89 95 49.75 20.60

25 62.91 95 52.51 65.11 53.32

15 55.18 116.11 105.79 69.87 95

tion algorithm computes the contaminant concentration of each stream and divides the outlet stream such that to be used by the next units, still complying with the inlet restrictions of each of it, and then to assign each of the remaining streams to the corresponding treatment unit. The actual concentrations for each case and each WU are presented in Tables 5 and 6. In similar cases, when ranking by MCL, the operating cost of the IWN is 28.4% higher than the base-case cost (Figures 5 and 7 and Table 8). But the fresh water needed by the WN is 45% higher than for the IWN. When ranking by FWC, the operating cost of the IWN is only 27% higher than the basecase cost (Figures 4 and 6 and Table 8). On the contrary, the WN consumes 45% more fresh water. The detailed operating cost analysis of the previously presented cases is given in Table 8. Although the expenses when using fresh water supply are at

Table 7. Cost Analysis for the IWN When the Two Ranking Criteria Are Applied ranking criteria fresh water entering the system (t/h) price of fresh water entering the system flow of wastewater entering TU1 (t/h) cost of wastewater to be treated in TU1 flow of wastewater entering TU2 (t/h) cost of wastewater to be treated in TU2 flow of wastewater entering TU3 (t/h) cost of wastewater to be treated in TU3 total cost of treatment (mu) total operating cost (mu)

(mu) (mu) (mu) (mu)

FWC

MLC

14.74 14.73P 4.08 40.76P 34.9 698.00P 28.69 1434.28P 2173.04P 2187.77P

14.74 14.73P 20.78 207.76P 28.47 569.46P 31.03 1551.49P 2328.71P 2343.44P

Table 8. Cost Analysis: WN vs IWNa IWN ranking criteria fresh water used (t/h) primary treatment (t/h) secondary treatment (t/h) tertiary/final treatment (t/h) total operating cost (mu)

FWC 14.74 4.08 34.9 28.69 2187.77P

WN

MCL FWC MCL 14.74 26.8511 26.8 20.78 28.47 31.03 2343.44P 1736.75P 1852.23P

a In the case of WN only, the wastewater leaving the system should be treated as well, in order to be released to the environment.

most 28% lower than for the treated water reuse, the much higher fresh water need as supply may be a major drawback, e.g. in the case of placing this plant in a region with less fresh water availability, since WNs need 45% more fresh water. In such a situation, an IWN can cut-back almost half of the fresh water flow’s demand of this plant. IV.3. IWN Using Primary and Tertiary TUs. The next optimization scenario considers that only the primary and final TUs are available and emphasizes the effects of disregarding the secondary TU upon the IWN. This scenario takes into account an increase of the mass transfer driving force of the treated water, since more slightly contaminated water will be available from the final TU. As in the previous cases, FWC (Figure 8) and MCL (Figure 9) were the ranking criteria. Table 9 summarizes the actual inlet and outlet contaminant concentrations for the optimal IWN ranked by FWC with primary and


3725

Figure 8. Topology of the optimal IWN, ranked by FWC with primary (TU1) and final treatment (TU3) units only.

Figure 9. Topology of the optimal IWN ranked by MCL, with primary (TU1) and final treatment (TU3) units only. Table 9. Concentration Data for the Optimal Restricted IWN Represented in Figure 8

Table 10. Concentration Data for the Optimal Restricted IWN Represented in Figure 9

actual inlet concentration (ppm)


actual inlet concentration (ppm)


components

components

components

components

unit no.

1

2

3

1

2

3

unit no.

1

2

3

1

2

3


0 15 0 10.95 5.458 13.0

0 18.26 0 15.63 6.20 19.75

0 20.75 0 13.34 6.05 21.55

35 37.18 73.89 95 57.57 25.96

25 70.01 95 43.65 100 58.63

15 57.71 116.11 97.39 79.0 95


0 15 0 12.90 21.1 16.4

0 18.34 0 19.35 22.98 20

0 20.89 0 20.37 24.14 24.18

35 30.18 73.89 95 63.89 24.56

25 53.74 95 46.71 100 44.511

15 46.19 116.11 102.46 84.04 70.48

tertiary TUs only, pinpointing the critical situations. Likewise, but for the optimal IWN ranked by MCL, Table 10 presents the actual WUs inlet and outlet contaminant concentrations, here

too emphasis being made to the critical spots. The detailed operating cost analysis of both cases at hand is presented in Table 11.

3726


Table 11. Comparison between IWN in Terms of Inlet, Outlet, and Reused Flows (t/h) of the TUs and Operating Costs (P mu/t)a no. crt. 1 2 3 4 5 6 7 8

a

full IWN ranking criterion inlet WW flow TU1 (t/h) inlet WW flow TU2 (t/h) inlet WW flow TU3 (t/h) outlet WW flow reused in WWN (from TU1) (t/h) outlet WW flow reused in WWN (from TU2) (t/h) outlet WW flow reused in WWN (from TU3) (t/h) total WW flow (t/h) total WW reused in WWN (t/h) total treatment costs (× P-1) (mu)

FWC 4.08 34.9 28.69 0 23.37 13.94 67.66 37.31 2173.04

IWN with primary and tertiary TUs

MCL 20.78 28.47 31.03 0 17.51 16.29 80.28 33.80 2328.71

FWC 6.67

MCL 10.27

37.8 0

44.14 0

23.06 44.48 23.06 2549.15

29.4 54.42 29.40 2667.01

In the total flow line, upper values mean reused treated water, while lower values mean processed water.

Figure 10. Topology of the optimal restricted IWN ranked by FWC with secondary (TU2) and final treatment (TU3) units only.

Although the fresh water used in both topologies did not changed from the optimal full IWNs (14.7347 t/h), the cost analysis reveals that ranking by MCL of the current optimal IWN implies an increase of the operating cost of 37% only. The network with the WUs ranked by MCL reuses more wastewater: WU 4 uses all the upstream flows and makeup water coming from the tertiary treatment, unlike the optimal full IWN ranked by FWC, when WU 4 uses only one stream coming from WU 1. Further, FWC ranking ends up with a topology where the stream of the WU 2 is used by the WUs 3 and 6 only. Supplementarily, the corresponding IWN has a pipe more than the resulted network when applying MCL criterion (see Figures 8 and 9). Comparing the operating costs of the optimal full IWN (Figure 6) and the optimal restricted IWN (Figure 8), both ranked by FWC, we observe an increase of 24.8% for the former. This means that the removal of the secondary TU and redistribution of its duty to the primary and final TUs is beneficial with respect to the costs. There is also a significant change in topology. The network in Figure 8 is shorter because the pipes corresponding to TU 2 do not exist, which leads to less energy consumption for pumping and lesser investment cost. Also the local internal reuse of the wastewater increases for the WUs subnetwork, meaning a decrease of the treated water consumption. When the network has only primary and tertiary TUs (Figure 8), the supply water is 23.0603 t/h, provided by TU 3 only. Also the contaminated wastewater to be treated is

distributed between the two available TUs: the inlet wastewater for primary treatment is 6.6738 t/h, while for the tertiary treatment is 31.1277 t/h, instead of 4.0755 t/h for the primary treatment, 30.8246 t/h for the secondary treatment, and 28.6856 t/h for the tertiary treatment (see Figure 6 for comparison). The reduction in overall treated water flow is quite spectacular, with the aforementioned benefices for the operating cost. When MCL is used as ranking criterion, the operating cost of the optimal full IWN (Figure 7) is 37% than the one associated with the optimal restricted IWN (Figure 9). Again, the reduction is given by the decrease of the treated water flow in the latter case. The topology of the network has changed, fewer pipes being used for the optimal restricted IWN (Figure 9), thus lesser energy for pumping is consumed and smaller investment cost. Again, Table 12. Concentration Data for the Optimal Restricted IWN Represented in Figure 10 actual inlet concentration (ppm)


components

components

unit no.

1

2

3

1

2

3


0 14.64 0 25 27.635 11.394

0 20 0 31.88 34.27 16.77

0 24.54 0 37.81 40.91 15.99

35 29.7 73.89 63.85 64.15 25.34

25 55.14 95 44.82 100 58.6

15 49.63 116.11 76.65 92.03 95

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 Table 13. Concentration Data for the Optimal Restricted IWN Represented in Figure 11 actual inlet concentration (ppm)


components

components

unit no.

1

2

3

1

2

3


0 2 0 25 29.19 12.38

0 4 0 31.19 35 17.23

0 5 0 35.75 40.81 20.96

35 38.86 73.89 57.8 53.1 25.45

25 90 95 42.11 78.03 56.43

15 66.43 116.11 68.55 74.28 95

Table 14. Comparison between WWN in Terms of Inlet and Outlet Flows of the TU IWN with IWN with IWN with IWN with primary and primary and secondary and secondary and tertiary TUs tertiary TUs tertiary TUs tertiary TUs ranking criterion inlet WW flow TU1 (t/h) inlet WW flow TU2 (t/h) inlet WW flow TU3 (t/h) outlet WW flow reused in WWN (from TU1) (t/h) outlet WW flow reused in WWN (from TU2) (t/h) outlet WW flow reused in WWN (from TU3) (t/h) total supply water (t/h)

FWC 6.67

MCL 10.27

37.80 0

44.14 0

FWC

MCL

38.74 31.67

40.05 28.60

16.17

19.57

23.06

29.40

16.93

13.86

23.06

29.40

33.1

33.43

like in the FWC case, WUs subnetwork internal water reuse is higher, causing the decrease of the treated water consumption. The network in Figure 7 needs 33.8 t/h treated water as supply (17.51 t/h from the secondary TU and 16.29 t/h from the tertiary TU). When removing the secondary TU (Figure 9), the treated water used as supply decreases to 29.40 t/h, coming only from TU 3. Again, like in the FWC case, the contaminated wastewater to be treated has been distributed between the two available TUs: the inlet wastewater is 10.27 t/h for primary TU and 33.87 t/h for tertiary TU, as compared to the optimal full IWN (Figure 7), for which the flow distribution is 20.78 t/h for primary TU, 28.47 t/h for secondary TU, and 20.07 t/h for tertiary TU. It must be emphasized that the current and subsequent analyses are based upon the previous values for the ratios

3727

between the fresh water cost and the treatment costs, so they may change as adequate figures are used, corresponding to any local particular plant. IV.4. IWN using Secondary and Tertiary TUs. Another optimization scenario takes into account only the secondary and final TUs, ranked also by the two criteria (Figures 10, FWC ranking and 11, or MCL ranking). Disregarding the primary TU seems natural, since its output is not reused at the WUs subnetwork level, feeding the final TU only. The optimized restricted IWN uses the same quantity of fresh water and also discharges the same amount in environment, like in the previous cases. Table 12 presents the actual inlet and outlet contaminant concentrations for the optimal restricted IWN ranked by FWC with secondary and final TUs only, showing where the critical concentrations were attained. Similarly, but for the optimal restricted IWN ranked by MCL, Table 13 presents the same concentrations, highlighting the critical spots. The detailed operating cost analysis of both cases at hand is presented in Table 14. Comparing the optimal restricted IWN represented in Figure 8 and Figure 10, we observe that the outlet wastewater flow of WU 1 is distributed between WUs 3, 4, and 5 given the low concentration of the makeup water coming from TU 3, which has almost the same level as the fresh water (Figure 11); in the former case, the outlet stream of WU 1 is feeds WUs 4 (which receives also water from the secondary TU) and 6 (which receives also water from the tertiary TU) only. When using secondary and tertiary TUs, the load of contaminants to be removed is better distributed between the treatment units in the case of the optimal restricted IWN ranked by FWC, for which TU2 receives 38.74 t/h and TU3 processes 31.67 t/h, (Figure 11), in comparison with the optimal restricted IWN ranked by FWC too and using primary and tertiary TUs (Figure 9) where TU1 receives 10.27 t/h and TU3 gets 33.87 t/h. Also the flow of water supply to be internally reused has increased, the network with primary and tertiary TUs reuses 23.06 t/h only, while the network with secondary and tertiary TU reuses 33.1 t/h.

Figure 11. Topology of the optimal restricted IWN ranked by MCL with secondary (TU2) and final treatment (TU3) units only.

3728


Figure 12. Topology of the optimal restricted IWN ranked by FWC with only the final treatment unit (TU3).

Figure 13. Topology of the optimal restricted IWN ranked by MCL with only the final treatment unit (TU3).

When the ranking criterion is MCL, the topology of the optimal restricted IWN changes and so does the performances of it. The network with secondary and tertiary TUs uses more treated water (Figure 11) while more internal streams are reused by the network with primary and tertiary TUs (Figure 9). The operating cost is 6.1% higher when units are ordered by FWC, compared to the case where the network is ranked by MCL. The topology has changed, and also the distribution of internal flows. In Table 14 are summarized the data for the networks represented in Figures 10-13, i.e. the integrated wastewater network having two treatment units. It is observed that the lowest supply water is assured by the integrated WW having primary and tertiary treatment units. The highest value of supply water

is given by the integrated WW having secondary and tertiary treatment units. IV.5. IWN using Tertiary TU Only. The last optimization scenario is represented by the optimization of the complete WUs subnetwork and only the final TU. The optimal restricted IWN ranked by FWC (Figure 12; Table 15) has a 21% higher operating cost than for the optimal restricted IWN ranked by MCL (Figure 13; Table 16). The topology of the networks is different; the outlet flow of WU 1 is distributed between all the next units in sequence and the TU, when IWN is ranked by MCL. Using the other ranking criterion, the outlet stream of WU 1 is sent to WUs 4 and 6 only, and the remaining flow is sent to TU. Moreover, although the network uses more internal streams, but with lower values, the flow sent to treatment is

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 Table 15. Concentration Data for the Optimal Restricted IWN Represented in Figure 12 actual inlet concentration (ppm)


unit no.

1

2

3

1

2

3


0 14.64 0 25 20.82 5.21

0 20 0 39.75 25.74 6.06

0 24.54 0 38.10 25.76 6.37

35 23.58 73.89 86.4 62.07 20.85

25 40.87 95 60.21 100 52.98

15 39.44 116.11 99.5 83.52 95

Table 16. Concentration Data for the Optimal Restricted IWN Represented in Figure 13 actual inlet concentration (ppm)


unit no.

1

2

3

1

2

3


0 7.89 0 9.97 34.46 9.53

0 9.5 0 9.07 16.2 15.78

0 10.24 0 7.41 34.3 13.13

35 42.4 73.9 95 81.02 23.98

25 90 95 37.41 100 59.12

15 67.74 116.11 92.45 99.48 95

higher, 43.35 t/h, than in the other case when the internal flow is 34.1 t/h, although the internal streams are less in number but have higher values. More internal streams means more pipes, thus more energy consumed for pumping. At the same time, the water reused by the optimal restricted IWN ranked by FWC is 28.61 t/h, while for the other situation, the water reused is 19.35 t/h. Table 17 offers a complete overview of the inlet and outlet flows of the treatment units. The best performance in terms of supply water is given by the case with only one treatment unit, ranking by MCL; this means that the internal flows are best efficient reused. The highest supply flow is given by the case with three treatment units, thus the internal flows needed a lot of makeup water. But, when choosing just one treatment unit, the flow treated is very large in comparison with the other situations. V. Conclusions A new optimization approach, based upon ranking WUs and TUs into an oriented network and genetic algorithms as a solving strategy, was presented and applied to obtain the best topology of an IWN, which considers the water-using and the treatment units together in a single system. A mathematical model for the complete network was developed which takes into account all restrictions associated with WUs and TUs. The objective function governing the behavior of the complete network was the total fresh water consumption. This new optimization approach was used to minimize the objective function through maximization of internal wastewater reuse and treated water

3729

use. The procedure was tested on a synthetic example, consisting of a network with six water-using and three treatment units dealing with three contaminants. Two ranking criteria of the water-using units were envisaged. The results were compared to the base case (i.e., a network with only the water-using units) in terms of fresh water consumption, network’s length and operating cost. It was observed that in an IWN, treated water could replace 55% from the fresh water needed, which is important due to the scarcity of fresh water. An IWN uses a smaller number of pipes than a WN which has a major impact upon investment costs and, also, on operating costs, since fewer pipes means less energy consumed for pumping (see Figures 4-13 for details). Another design strategy for the optimal IWN considered active only two of the treatment units: the tertiary treatment together with the primary or the secondary stages. Irrespective of the scenario the optimized networks consume and discharge into environment the same amount of fresh water, 45% less than WN consumption. The same is true for the optimum IWN with only the third TU active, but here there is a rather large discrepancy between the water treated and reused in the network, according to the ranking criterion (see Table 17 for details). Contrary to our expectations, the network performing best, in terms of costs, was the WN (for which the treatment costs were computed as well, considering that its exit should be discharged into environment, eventually) followed by the full IWN, then the one with the secondary and tertiary TUs active, and last the IWN with primary and tertiary TUs active. This order is valid irrespective of the ranking criterion. A special case is illustrated by the IWN with the tertiary TU active, for which the ranking of the WUs discriminates between a very cost effectively topology (MCL ensures the second place after the WN) and a very expensive architecture (FWC guarantees one of the last places in series). This is not surprising, after all, taking into account that WN reuses only internal wastewater, with no cost associated to it, except for pumping, but this was not included in our analysis. On the contrary, an IWN uses both internal (from one WU to the next ones) and external supplies, the latter being the wastewater treated in one of the TUs, which bears a supplemental cost. But, instead of being a drawback, this in fact is the main advantage of an IWNsit brings down the fresh water consumption with 55% and even more, making the solution attractive for the regions where water is rather scarce, despite its supplemental cost. Moreover, a thorough economic analysis could reveal new insights on how and where to act to decrease more the costs associated with IWN. A future development of the study should focus on a more detailed investment and operating costs evaluation of an integrated water and wastewater treatment network starting from the benchmarks emphasized in the economical analysis pre-

Table 17. Comparison between IWNs in Terms of Inlet and Outlet Flows of the TU IWN with primary and tertiary TUs

no. crt. 1 2 3 4 5 6 7 8

ranking criterion inlet WW flow TU1 (t/h) inlet WW flow TU2 (t/h) inlet WW flow TU3 (t/h) outlet WW flow reused in WWN (from TU1) (t/h) outlet WW flow reused in WWN (from TU2) (t/h) outlet WW flow reused in WWN (from TU3) (t/h) total WW flow (t/h) total WW reused in WWN (t/h) total treatment costs (× P-1) (mu)

FWC 6.67

MCL 10.27

37.81 0

44.15 0

23.06 44.48 23.06 2549.15

29.40 54.42 29.40 2667.01

IWN with secondary and tertiary TUs

IWN with tertiary TUs

FWC

MCL

FWC

MCL

38.74 31.67

40.05 28.60

43.35

34.1

16.17 16.93 70.41 33.10 2424.27

19.57 13.86 68.65 33.43 2341.76

28.61 43.35 28.60 2545.65

19.36 34.10 19.36 2136.43

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sented in this paper. This should be done in conjunction with considering regeneration as a possibility of delocalizing partially the treatment and how this could affect both the costs and the topology of an IWN. Acknowledgment Prof. Vasile Lavric gratefully acknowledges the financial support of UEFISCSU Project no. 663/19.01.2009 Abbreviations WW ) wastewater WU ) water-using units TU ) treatment units WN ) water network WSI ) water system integration PA ) pinch analysis IWN ) integrated water network WTN ) water treatment network GA ) genetic algorithm FWC ) fresh water consumption MCL ) maximum contaminant load MINLP ) mixed integer nonlinear programming MU ) monetary units Nomenclature Fi ) fresh water flow entering water-using unit Ui [kg/h] CkiU,in ) contaminant k concentration entering water-using unit Ui [ppm] CkiU,in,max ) maximum contaminant k inlet concentration admitted by water-using unit Ui CkiU,out ) contaminant k concentration leaving water-using unit Ui [ppm] CkiU,out,max ) 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] Li ) flow of water that is lost within the water-using unit Ui [kg/h] Wi ) flow of wastewater leaving water-using unit Ui [kg/h] CT,in kt ) contaminant k concentration entering treatment unit Tt [ppm] CT,in,min ) minimum contaminant k concentration entering treatment kt unit Tt [ppm] CT,out ) contaminant k concentration leaving treatment unit Tt [ppm] kt ∆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]

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ReceiVed for reView October 28, 2009 ReVised manuscript receiVed February 4, 2010 Accepted March 5, 2010 IE901687Z

Optimization of Total Networks of Water-Using and ... - ACS Publications

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