Journal of Cleaner Production 13 (2005) 1405e1415

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Genetic algorithm optimisation of water consumptionand wastewater network topology

Vasile Lavric*, Petrica Iancu, Valentin PlesxuUniversity POLITEHNICA of Bucharest, Chemical Engineering Department-CTTIP, Polizu 1-7, Bucharest RO-011061, Romania

Received 25 November 2004; accepted 29 April 2005

Available online 05 July 2005

Abstract

Genetic algorithm (GA) optimisation applied to water systems with multiple contaminants and several contaminated sources ispresented. This approach generates the overall optimal water network topology with respect to the minimum supply water usage,complying, in the same time, with all restrictions. An optimal water network could be viewed as an oriented graph, starting from

unit operations which must not have contaminants at entrance (inlet contaminants-free unit operations), every next unit operation ireceiving streams from the previous operations j only (jZ 1, 2,.,i�1), and sending streams to the next operations j ( jZ iC 1,iC 2,.,N ). The mathematical model describing the unit i is based upon total and contaminant species’ mass balances, together

with the input and output constraints. Solving this optimisation problem is not trivial, since the unknowns’ number, determines thenumber of equations. The GA optimisation uses each network’s internal flow as a gene, assembling the topology intoa chromosome. The restrictions, in terms of minimum and maximum allowable flows for each gene, are dealt with naturally, during

the population generation, simply rejecting those genes outside their feasible domain. The individuals are interbred according totheir frequency of selection, using the one-point crossover method, and then mutations are applied to randomly selected individuals.The objective function is the total supply water consumption, which should be minimised.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Genetic algorithms; Water network optimisation; Fresh water reduction; Oriented graphs; Multiple contaminated sources

1. Introduction

Many industrial processes need water as either rawmaterial or utility, discharging it into the environmentafter its use. Due to the public concern, expressed inincreasingly stringent environmental regulations oneffluents, the quality of the industrial disposed water ismore and more strictly observed, severe penalties beinginflicted when violations are proven. The economicgrowth and industrialization demand increase in quan-tities of fresh water, which became a limited resource.

* Corresponding author. University POLITEHNICA of Bucharest,

Chemical Engineering Department-CTTIP, Room 056, Polizu 1-7,

Bucharest RO-011061, Romania. Tel.: C40 2121 25125.

E-mail address: vasile_lavric@webmail.pub.ro (V. Lavric).

0959-6526/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jclepro.2005.04.014

These changes have increased the need for better watermanagement, in terms of supply water savings, betteron-site water reuse and wastewater treatment, locally orat site-level [1e6]. All or parts of these actions areencapsulated in the generic term water/wastewaterminimisation. Water minimisation techniques can effec-tively reduce both overall fresh water demand, thuslowering the supply pre-treatment costs, and effluentgenerated, decreasing its treatment overheads accord-ingly [1,3]. Besides water reuse, which saves upstreamtreatment of raw water and reduces wastewater treat-ment costs, the concept of distributing the treatmentamong the various polluted streams and even decentral-izing it is increasingly used [1]. From this, the concept ofzero discharge emerged. The zero discharge means thetotal elimination of the disposal of environmentally

1406 V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

hazardous substances using a closed circuit of water,with no wastewater effluents [1]. This minimises theconsumption of fresh water to that of make-up, theassociated savings justifying the capital expenditures [6].On the other hand, there are drawbacks, like higheroperating costs due to the water treatment to the extentit is suitable for reuse, or significant capital cost inretrofit projects implying large scale re-piping and/ordisposal arrangements for the solid wastes generated.However, in some cases the solid wastes may be soldbringing in additional revenues [6]. Another way ofimproving the water reuse is employing internal watermains, which are reservoirs at uniform concentrationof contaminants. They receive water at lower level ofcontamination than theirs, and supply water to thesuitable unit operations, according to their permissivelevel of contaminant concentration. Usually, as internalwater mains are added to the network, less fresh water isconsumed, and less wastewater is discharged. However,additional internal water mains increase the complexityof the network piping [5].

For continuous processes, the wastewater from oneprocess can be fed to another without sending it totreatment first, provided that the actual contaminationlevel is acceptable [1e3]. In batch processes, waterminimisation means reusing water effluents in the sameplant through storage tanks. The connections betweenthe available tanks and the water streams have beendetermined by targeting different aspects: fresh waterdemand, water cost, utility demand of water streamsand water reuse network costs [2].

Part of water/wastewater minimisation strategy,water system integration (embedding here supplies waterdiminution and optimal water network topology search)becomes an important research domain as it can givetools to maximize the water savings. It addresses theplant water-using system, considering how to allocatethe quantity and quality of water in each water-usingunit so as to maximize water reusing and to minimisewastewater discharge [4].

Despite the progress made in optimisation algo-rithms, they often require considerable computing timeif the complexity of the design problem rises due to thenumber of process units, contaminants and possiblenetwork topologies [4]. A simple but elegant solution isoffered by water pinch analysis, which recommendssimple methods and beneficial results when applied towater-using industries [3]. However, water pinch anal-yses suffer from a major drawback, since, as the numberof contaminants dealt with increases, it becomes in-creasingly difficult to be applied.

Another approach in designing water networks that isdesigned to result in wastewater minimisation in the caseof single or multiple contaminants is based on a combi-natorial search where all possible maximum reusestructures of the system are analyzed in a tree-type

fashion using a branch and bound strategy. In thisprocedure, a maximum reuse structure, possibly in-cluding the centralized or end of pipe treatment schemeis defined as a sequence in which the flow pattern ofconnections of each process is given by minimising freshwater consumption of each process [6].

At a conceptual level, the necessary conditions ofoptimality for water-using networks were given thor-ough attention. According to Bagajewicz [1], Savelskiand Bagajewicz [7e9], Savelski et al. [10] and Bagajewiczet al. [11,12], if a solution of the water allocationproblem is optimal, the following conditions hold:

� Maximum outlet concentrations: all fresh water-usingprocesses reach their maximum possible outletconcentration.

� Concentration monotonicity: at every process, theoutlet concentrations are not lower than theconcentration of the combined wastewater streamcoming from all the precursors.

Taking into account the supplemental input concen-tration restrictions, a process should comply with, thefirst necessary condition of optimality can be slightlymodified as the maximum inlet and/or outlet concen-trations, which states that, if a solution of the waterallocation problem is optimal, then either of the tworestrictions for the inlet and the outlet concentrations arefulfilled, or both, for at least one of the contaminants.

In fact, these necessary conditions of optimality arepeculiar cases of the principle of the driving forceequipartition along a process, which ensures minimumentropy generation for given operating conditions,which is a measure of the process irreversibilities.

Several techniques were derived starting from thesenecessary conditions of optimality, trying to avoid thestraight use of MINLP/NLP packages to solve thesuperstructure model together with the associated non-linear constraints that can only provide one solutionwhich is not guaranteed optimal [7e12]. Among others,the notions of Fixed Sequence (a structure where eachprocess is not a precursor of the previous members ofthe sequence [10]) or Pinch Operator [12] are used,together with combinatorial optimisation, in whicha tree searching methodology with efficient branchcutting criteria is designed to solve globally the multi-component water allocation problem [9e12].

Another technique designed to solve the wastewaterminimisation challenge combines insights from WaterPinch with mathematical programming, developingtargeted models at a conceptual stage where the processnetwork is not yet developed. The solution is foundwithout the use of MINLP solvers [13].

The Water Surplus Diagram uses the surplus conceptwhich employs the demand and source composite curvesextracted from the data; the purity of water rather than

1407V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

contaminant concentration is considered on the ordinate,while an initial value of the fresh water flow rate has beenassumed and is included in the source composite [18].

Retrofit optimisation of industrial water networks isanother methodology which has been developed in orderto merge the advantages of the global strategy of themathematical water network optimisation with thedetailed focus on the real water streams and the proofby experiments [14].

After designing or retrofitting a wastewater network,operational optimisation could be used to find theoptimal operating strategy, taking into account both theelectricity costs and the consumers’ demand which canvary greatly through a typical operating cycle [15].

All the aforementioned techniques are based upon thedeterministic algorithms, which fail to solve the MINLP/NLP optimisation problem, if it is a non-convex type,despite the efforts made to overcome this drawback.

The evolutionary algorithms were developed as a reli-able tool in finding the optimal solution to non-convexproblems. Among these, genetic algorithms (GAs) occupya leading position, due to their ability to find the globaloptimum, without being trapped into local maxima orminima. The main drawback is the computation time,which can be very large in the case of a thoroughinvestigation [16,17]. Another evolutionary algorithm,the ant colony optimisation (ACO) was inspired by theaptitude of ants to find the shortest route between theirnest and a food source, even though they are almost blind.Themaindifference fromGAs is theway the trial solutionsare generated. While in GAs the system’s memory isembedded in the original trial pool, since the new solutionsare obtained through genetic manipulations of previousones, in ACO, the system’s memory is contained in theenvironment, since trial solutions are constructed in-crementally, by modifying the environment via a form ofindirect communication called stigmergy [19].

In this paper, a hybrid technique, based upon animproved GA, is used to solve the optimisation problemof finding the minimum water supply concomitantlywith the water network topology ensuring the maximumwater reuse. The hybrid character of the algorithm isgiven by the local reshape of the chromosome, at thegene level, to cope with the mass balance restrictions,while the improvement of the GA is given by theshrinking neighbourhood cloning strategy, which fa-vours the individuals surrounding the best-so-farsolution [17,20e22].

2. Modelling the wastewater network

2.1. Abstraction of the wastewater network

According to the principle of driving force equiparti-tion across the process, an optimal wastewater network,

with respect to fresh, uncontaminated water consump-tion, can be assimilated with an oriented graph startingfrom unit operations with contaminant-free constraintsat their entrance, which are supplied with fresh wateronly. Any other unit operation i, following the afore-mentioned ones, receives streams from possibly (but notnecessarily) all previous unit operations j only ( jZ 1,2,.,i�1), and sends streams to probably, but certainlynot all, subsequent operations j ( jZ iC 1, iC 2,.,N ),as presented in the Fig. 1. The oriented character of thegraph is equivalent to the absence of any internalrecirculation. If there are several water supply sourceswith different contaminant levels, the oriented characterof the graph encoding the topology is preserved usingeach contaminated source to supply its own cluster ofunit operations, according to their contaminant levelconstraints at the entrance (see Fig. 2 for details). Thefresh water feeds only the inlet contaminant-free units,grouped into the first cluster, since it is the mostexpensive. The second cluster is formed by the unitshaving moderately restrictions concerning the concen-tration of contaminants at their input, dealt with by theslightly contaminated water source. The contaminatedwater source can be, eventually, used to feed the lastcluster, with units with relaxed restrictions at their input,in terms of contaminants concentration. This distribu-tion of contaminated sources across the wastewatertopology is also in accordance with the principle ofdriving force equipartition.

The topology of the wastewater network as encodedby the oriented graph (Figs. 1 and 2) can be adequatelyrepresented by an upper triangular matrix, X. The unitslay on the diagonal positions, the uppermost positionsbeing reserved for the member of the inlet contaminant-free units’ cluster. The streams between units constitutethe elements of the matrix, their indexes corresponding

Fig. 1. The oriented graph associated with the wastewater network, for

the case when only fresh water is available. The knots are the unit

operations, the closed arches are the pipes transporting the water

reused internally. Two ranking procedures are envisaged: by load and

by fresh flow.

1408 V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

to the two linked units. In other words, Xij is the streamflowing from the unit i to the unit j [17,20e22].

2.2. Mathematical model of the wastewater network

The mathematical model of the wastewater networkis based upon the overall and species mass balancesaround each unit operation. Let us consider a genericunit operation i, as presented in Fig. 3, responsible forsending K pollutants into water, and for which we writethe mass balances.

2.2.1. Total mass balance

FiCXi�1

jZ1

Xji �Wi �XNjZiC1

Xij �LiZ0 ð1Þ

In Eq. (1),Pi�1

jZ1 Xji stands for the total flow enteringthe i unit, collected from the preceding units, whilePN

jZiC1 Xij represents the flow sent from unit i to the rest

Fig. 2. The oriented graph associated with the wastewater network, for

the case when several contaminated water sources are available (for

details, see Fig. 1 caption).

Fig. 3. Schematic model of unit operation i; Xji is the water flow from j

to i unit operations, likewise Xij is the water flow from i to j ones. Ckjis

the k pollutant concentration coming from j unit operation

(Cpmax

kj means that, for at least one contaminant, p, the inlet

concentration can be at the maximum level) and Cqmax

ki is the k pollutant

concentration going to i unit operation (q means that, for at least one

contaminant, the outlet concentration can be at the maximum level);

Wi is the exit of unit operation i, Li is the possible flow loss and mki is

the k pollutant released in water in unit operation i.

of the units. The oriented nature of the graph prohibitsthe recirculation of any stream from unit i backwards, tounits with lower rank j, jZ1,2,.,i�1.

2.2.2. Partial mass balance, for the contaminant k

FiCskCXi�1

jZ1

�XjiCkj

�CmkiZ

WiCLiC

XNjZiC1

Xij

!Cki ð2Þ

Eq. (2) was written for the most general case,corresponding to the contaminated supply water, withCs

kas the inlet concentration for the k pollutant. Hereand in subsequent equations, k takes all the values from1 to K. When dealing with fresh water only, the firstterm of the left hand side of Eq. (2) drops, one obtainingthe classical partial mass balance for the pollutant k.

2.2.3. Outlet set of constraintsThe outlet set of constraints for unit operation i

concerns the observation of the maximum admissiblelevels of concentration for the contaminants in theoutput water, as resulted from technological, corrosion,erosion or any other imperatives. Again, we should takeinto account that the supply water could have a certainlevel of contaminants in it (see Fig. 3):

CkiZ

FiCskC

Pi�1

jZ1

�XjiCkj

�Cmki

WiCLiCPN

jZiC1

Xij

!

Z

FiCskC

Pi�1

jZ1

�XjiCkj

�Cmki

FiCPi�1

jZ1

Xji

! %Cout;maxki ð3Þ

For the fresh water supply case, the partial massbalance takes the typical expression:

CkiZ

Pi�1

jZ1

�XjiCkj

�Cmki

WiCLiCPN

jZiC1

Xij

!ZPi�1

jZ1

�XjiCkj

�Cmki

FiCPi�1

jZ1

Xji

! %Cout;maxki

ð4Þ

In Eqs. (3) and (4), the total mass balance (Eq. (1))was used to express the output pollutant concentrationsof unit operation i in function of feeding supply waterand the preceding units.

2.2.4. Inlet set of constraintsThe inlet set of constraints concerns the observation

of the maximum admissible input concentrations for the

1409V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

contaminants, this time, and is intrinsically related tothe technological restrictions as well. Considering thegeneral case, when the supply water contains anacceptable level of pollutants, the mass balance for thepollutant species k at the inlet of the unit operation ireads (see Fig. 3):

FiCskCXi�1

jZ1

XjiCkjZ

FiC

Xi�1

jZ1

Xji

!Cin

ki ð5Þ

Eq. (5) permits to explicitly define the set ofrestrictions in term of the relationship between Cin

kiandthe maximum inlet concentrations of the pollutants:

CinkiZ

FiCskC

Pi�1

jZ1

XjiCkj

FiCPi�1

jZ1

Xji

%Cin;maxki ð6Þ

When the supply is with fresh water only, the set ofrestrictions simplifies to the usual expression:

CinkiZ

Pi�1

jZ1

XjiCkj

FiCPi�1

jZ1

Xji

%Cin;maxki ð7Þ

This concludes the mathematical model’s develop-ment for the generic unit operation i. The completemathematical model of the wastewater network is givenby Eqs. (1)e(3) and (6), applied for each and everybelonging unit operation.

2.3. Optimisation of the wastewater network

The optimisation of the wastewater network is fullydependent upon the objective envisaged. Generallyspeaking, this can be reduced to either a complexallocation problem, when there are several ‘‘dirty’’sources available, with different degrees of contamina-tion, or an investment and/or operating costs problem,when piping and pumping costs are of primaryimportance. Although it may seem that the bestapproach would be to jointly use these criteria,optimizing the wastewater network in terms of alloca-tion of available resources may damage the topology (aswe show later in this paper), when there is more thanone water supply.

For the present paper, by optimisation of thewastewater network, we seek to find the associatedtopology that ensures the minimum supply waterconsumption,

PNiZ1 F

si ; s˛f1; 2;.;Sg, subject to Con-

straints (3) and (6), observed for all unit operations. Thesuperior index s designates the water resource with thehighest level of contamination still complying with Inlet

restrictions (6) for the unit operation i. Optimumtopology is, thus, given by the values of the uppertriangular matrix X, whose elements represent thestreams flowing in cascade throughout the network.

2.3.1. Deriving the objective functionThe optimisation problem at hand, finding the

optimum water resource allocation and the wastewaternetwork which minimises the supply water consump-tion, has no trivial solution, since the unknowns’number outcomes the equations’ number and a properobjective function has to be derived [17,20e22]. Theconstraint values, Cout;max

ij and Cin;maxki , together with the

loads of each unit operation, mki, are the imposedparameters for the design or retrofit of the network. Thetotal number of unknowns is NðNC3Þ=2, since theupper triangular matrix X, encoding the network, hasNðN� 1Þ=2 elements, while F and W have, each, Nelements. Considering the overall mass balance (1), theeffluents to the treatment section can be expressed withrespect to the influents and internal streams, while usingthe partial mass balance (2), the influents can be ex-pressed with respect to the internal flows only, thuslowering the total number of unknowns to NðN� 1Þ=2,equal to the number of elements of matrix X. So, thesolution should be iterative in nature; one starts witha guessed topology, in terms of internal flows, thenverifies if the mathematical model, including theconstraints, holds; if not, it modifies the topology ina suitable manner to obtain a better approach, under theimperative of minimum supply water consumption, asexpressed by the corresponding objective function [17].

The derivation of the objective function for severalwater sources with different levels of contamination ispresented, following the procedure outlined in [17].

For a given contaminant k, the Inequality (6) holds ifthe supply water has at least the value obtained solvingthe corresponding equality:

Fs;minik

��inZ

Pi�1

jZ1

Xji

�Ckj �Cin;max

ki

�Cin;max

ki �Csk

ð8Þ

In Eq. (8), Csk is the concentration of the contaminant

k in the supply water, coming from source s, which wasallocated to the unit i because it has the maximumpollutant concentrations observing yet the input re-strictions. Due to the cascaded nature of the topology,all the information associated with the preceding unitsare already computed, i.e. Xji and Ckj, while Cs

k andCin;max

ki are fixed. So, there are K possible flows for thewater supply, as resulted from the repeated applicationof Eq. (8). From these, the maximum value should bekept, since it guarantees the strict observation of Eq. (6)by the rest of the contaminants’ concentration.

1410 V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

F s;mini;in Zmaxk

�Fs;minik

��in

�ð9Þ

Applying the same reasoning for the output con-straints [17], we get the minimum supply water neededto contain the contaminant k under its imposed limit.

F s;minik

��outZ

Pi�1

jZ1

Xji

�Ckj �Cout;max

ki

�Cmki

Cout;maxki �Cs

k

ð10Þ

In order for Constraint (3) to hold for all pollutants,the maximum value from the K inlets predicted by Eq.(10) should be observed.

F s;mini;out Zmaxk

�F s;minik

��out

�ð11Þ

A final observation which permits us to conclude thederivation of the objective function is that bothConstraints (3) and (6) hold for the largest value ofthe two previously calculated from Eqs. (9) and (11).With this remark, the objective function which guaran-tees the optimal solution, i.e. the minimum total amountof the supply water, is:

FZXNiZ1

max�F s;mini;in ;Fs;min

i;out

�ð12Þ

2.4. Optimisation algorithm

The optimisation algorithm is based upon a hybridvariant of a classical GA, and is fully presentedelsewhere, together with some comparisons made withmathematical programming results, for some difficultproblems already published [17,20e22]. The algorithmwas coded into original software, whose main window ispresented in Fig. 4, showing its salient features.

Two are the criteria used to rank the units inascending order, thus orienting the associated graph,in accordance with the equipartition of the driving forceprinciple: ‘‘by load’’, which means that the maximumload of the units should progressively increase frominput to output, or ‘‘by fresh water’’, meaning that theunits are ranked according to their need of fresh water,in absence of any water reuse; it should be mentionedthat the inlet contaminant-free units are always placedfirst. Both criteria give the same result if the number ofunits and contaminants is low, but different topologiesand supply water consumptions for networks with manyunits and contaminants. Taking into account thestochastic nature of the GA, several replicates shouldbe made for each case, in order to be certain that theglobal optimum was achieved.

3. Results and discussions

In order to study the influence of the available supplysources upon the topology of a complex wastewaternetwork with many contaminants, a synthetic examplewas made, with 10 unit operations and six contami-nants, which is a simplified version of an industrialnetwork presented elsewhere [22]. Table 1 displays thecharacteristics of the unit operations, and Table 2 showsthe contamination level of the four available watersupplies to choose from.

Analysing Table 1, in terms of input restrictions, it isreadily observed that Source 4 cannot be used alone tofeed all the unit operations, since its contamination levelis higher than the inlet maximum technologicallyimposed values for some of the units. So, it has to beused jointly with one of the other three.

A thorough analysis was done to emphasize if there isa link between the resulting topology and supply waterconsumption and its level of contamination. Thesoftware was used to search for the optimum networksupplied, separately, with water from Sources 1e3. As

Fig. 4. The main window of the software encoding the present

algorithm.

1411V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

Table 1

The loads and concentration restrictions for the unit operations of the wastewater network, due to confidentiality clause, no information is given

regarding the nature or the real value of the contaminants

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10

Contaminant load per unit, g/h 31.2 16.4 1.2 4.8 2.64 132.6 8.2 12.1 10.35 8.62

7.8 4.1 1.325 5.3 2.79 124.8 42.0 14.55 12.0 1.95

7.8 4.1 4.25 4.1 3.25 50.7 3.56 7.73 2.12 3.4

5.46 2.87 3.35 1.4 2.12 1.95 11.2 5.5 3.2 2.5

5.46 2.87 5.35 2.4 5.12 6.78 10.64 6.17 3.04 7.7

109.6 57.61 8.98 35.9 10.77 62.4 103.6 1.35 29.6 9.9

Maximum inlet concentration, ppm 40 40 16 16 16 16 40 40 40 40

20 20 3.5 3.5 3.5 3 15 15 15 15

40 40 20 2 2 1.5 15 15 15 15

3 3 3 3 3 1 1 1 1 1

3 3 3 3 3 1 1.2 1.2 1.2 1.2

63 63 24 24 24 24 63 63 63 63

Maximum outlet concentration, ppm 80 80 40 40 60 50 45 45 45 45

30 30 30 30 50 35 30 30 30 30

50 50 25 20 20 28 35 25 35 5

10 10 10 10 50 15 5 10 5 10

10 10 10 10 50 12 5 12 5 12

223.5 233.5 213.5 253.5 273.5 40 100 83 100 73

the level of contamination of the supply water increases,the driving force of the mass transfer for each unitoperation decreases together with its degrees of freedomat inlet. An uncontaminated supply water can be used todiminish the pollution level of the unit operation i inletwater, permitting the reuse of some streams comingfrom previous unit operations, even if their exit concen-trations are higher e see Inequality (7). As the contamin-ation level of the supply water increases, up to the inletrestrictions, less and less reused water can be used tomake-up the inlet stream of the unit operation i. So, thetopology tends to stiffen up to the point that there will beno internal reuse, when the contamination level of thesupply water equals the inlet restrictions for each andeveryunit.The internalwater reuse increases fromSource1(Fig. 5) to Source 3 (Fig. 6) but is completely absent (thenetwork stiffed e Fig. 7) for Source 2. As the contami-nation level increases for the water supply, its mass flowincreases too, to compensate the mass driving forcedecrease for themass transfer in each unit operatione seetotal mass flows inlet/outlet in Figs. 5e7. In the case ofSource 3, whose contamination level is intermediate,between Sources 1 and 2 (see Table 2 for details), thedecrease in the driving force is balanced by an increase ofthe internal complexity of the water reuse and flow.

Table 2

The contamination levels for the available supply water sources; as the

source is dirtier, it costs less, so its use should be encouraged

Source 1 Source 2 Source 3 Source 4

Contaminant level, ppm 0 16 2 40

0 3 2 15

0 1.5 1.5 15

0 1 0.8 3

0 1 0.65 3

0 24 14 63

Another important observation is that the way theranking of the unit operations is made to have anoriented graph plays a significant role in getting the finaloptimal topology and water consumption (see Fig. 5(a)and (b) for the two types of ranking already presented).Although the difference is not impressive in terms offresh water (0.676 t/h less, when ranking is made byload), it should be noted the change in topology e thegain in fresh water is compensated through a higherdegree of internal water reuse.

Under the imperative of diminishing the operatingcosts while reducing fresh water utilization, the beststrategy is to jointly use two or more water supplysources, allocated corresponding to their contaminationlevel (see Fig. 2 and the previous discussions). Whenusing multiple supply sources, the software computesthe minimum distance between the contaminant supplylevel and the inlet imposed concentration level for a unitoperation; then, the source with the minimum distance isallocated for the given unit operation. This way, themost contaminated sources are used first, and the lesscontaminated are used only when really needed, therebydecreasing the supply water costs.

Based upon this strategy, we searched for the optimaltopology when all the supply sources were considered.As expected, the preferred sources, since they are theclosest to the technological inlet restrictions for the unitoperations were Sources 2 and 4, the cheapest, since theyare the most polluted ones (see Fig. 8). The drawback isthat, again, the network was made less flexible; no waterreuse is possible, since the supply water matches the inletrestrictions. For the cases when the match is notcomplete, the distance, in terms of concentrations, issufficiently small to avoid the possibility of any waterreuse, due to the large contaminant concentrations with

1412 V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

0.64

2.24

3

2

1

5

6

10

9

8

7

4

8.322

0.095

0.18

0.119

3.194

0.583

0.496

0.24

0.535

8.322

0.33

0.297

1.404

0.604

0.108

0.728

3.474

0.18

0.776

0.4190.115 0.033

0.139 0.073

0.332 0.183

0.497 0.029

0.264 0.141

a)

5

6

7

8

9

10

3

1

2

4

0.163

0.49

0.64

0.68

0.535

0.546

0.287

0.24

3.196

2.221

0.163

0.123

0.361

0.59

0.414

0.002

0.581

0.602

2.292

3.872

8.9988.998

0.044

0.029 0.07

0.1210.555

b)

Fig. 5. The optimal topology and supply water consumption, when Source 1 alone is used: (a) ranking ‘‘by load’’; (b) ranking ‘‘by fresh flow’’ (the

flows are in t/h e when the value is absent from the arch, the flow can be readily computed through mass balance: (a) X34, X78 and X9,10 (b) X42 and

X98).

which it exits from the previous units. Although it mightseem strange, the networks depicted in Figs. 7 and 8have the same topology, because the water from themost polluted source is used only for units 1 and 2. Thiswater has enough mass transfer potential to completelyremove the contaminants within the same flows such aswater from Source 2.

4. Conclusions

A hybrid optimisation technique, based upon animproved version of GA, was presented. Encoded in easyto use software, this algorithm guarantees both the

optimal topology of the unit operations’ network andthe minimum supply water consumption, observing theimposed inlet and outlet constraints. If several watersupply sources are available (fresh or contaminated), thesoftware enables their allocation according to closenessbetween their contamination level and the inlet restric-tions for each unit. The optimal topology depends uponthe way the unit ranking is done (by load or by fresh flow)to make the oriented graph associated with the network,so both cases should be investigated. Since it is stochasticin nature, due to the GA foundations, the algorithmshould be repeatedly applied, starting from differentpoints, to guarantee that the overall optimum wasattained. After proving its capacity of better-solving, of

1413V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

6

2

1

5

10

9

8

7

3

4

3.782

0.155

0.972

0.555

0.523

1.987

0.551

0.249

0.121

0.229

2.022

0.259

0.565

2.765

0.612

0.748

0.785

0.18

0.777

0.411

9.1249.124

0.209

0.026 0.78 0.77

0.414

0.012

0.002

0.014

0.135

0.121

0.244

0.066

Fig. 6. The optimal topology and supply water consumption, when Source 3 alone is used (ranking ‘‘by fresh flow’’ e X12 and X78 can be readily

computed through mass balance; ranking ‘‘by load’’ gave a slightly increased value for water consumption).

some literature test cases [17,20e22] the algorithm wasused for the more difficult problem of finding an optimaltopology of the wastewater network when multiplecontaminated water sources are available. The allocationof thewater sources closely follows the inlet restrictions ofall units, with the drawback of stiffing the network to suchan extent that nowater reuse is possible.Onone hand, thisreduces the investment costs, since the piping correspondsto the degenerate solution, but, on the other hand, it

increases the operating costs, since, due to the diminishedmass transfer driving force, the water flows should begreater, in order to remove the same quantity of contamin-ant from each and every unit operation. So, a furtherdevelopment of the algorithm should include the optimaldiameter computation for the piping system and thepossibility to economically discriminate between candi-date solutions, taking into account both the investmentand operating costs.

3

1

2

10

9

8

7

6

5

4

0.176

0.594

0.267

0.176

3.9

2.8

0.8

0.611

0.971

0.41

0.78

11.309

0.78

0.41

0.971

0.8

2.8

0.611

3.9

0.267

0.594

11.309

Fig. 7. The topology and supply water consumption, when Source 2 alone is used e the optimal network is degenerated, since no internal reuse is

possible, due to the high level of supply water contamination.

1414 V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

1

10

9

8

7

6

5

4

3

2

0.78

0.611

2.8

3.9

0.176

0.267

0.594

0.41

0.971

0.8

0.78

0.41

0.594

0.267

0.176

2.8

3.9

0.611

0.8

0.971

11.309

1.19

10.119

Source 4

Source 2

Fig. 8. The topology and supply water consumption, when the Sources 2 and 4 are used e the optimal network is degenerated, since no internal reuse

is possible, due to the match between the inlet restrictions and the contamination level of the supply water.

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1415V. Lavric et al. / Journal of Cleaner Production 13 (2005) 1405e1415

Vasile Lavric is Professor at Department of Chemical Engineering and

Group Leader of Application of IT&C in process industries in the

Centre for Technology Transfer in Process Industries at University

POLITEHNICA of Bucharest. His research covers biological, bio-

chemical and chemical reactors, System optimisation and optimal

control, Artificial Neural Networks and Genetic Algorithms, Flow

Modelling in Complex Structures, Chemical Reactors Energy In-

tegration and Pinch Analysis. In 1998 he received the Romanian

Academy’s Chemical Division Award ‘‘Nicolae Teclu’’ for the

applications of Artificial Neural Networks in Chemical Engineering.

He is member of the Romanian Society of Bioengineering and

Biotechnology, Romanian Society of Chemical Engineering and

European Federation of Biotechnology, Section of Biochemical

Engineering Science.

Petrica Iancu is Lecturer at Department of Chemical Engineering of

the Centre of Technology Transfer in the Process Industries (CTTPI)

at University POLITEHNICA of Bucharest. She is involved in

designing and managing projects run in CTTPI. She is member of

the Management Committee of the Romanian Society of Chemical

Engineering. Her academic activity includes Computer Applications in

Chemical Engineering for undergraduate students.

Valentin Plesxu is Professor at Department of Chemical Engineering

and General Director of Centre for Technology Transfer in Process

Industries at University POLITEHNICA of Bucharest. His academic

activity concerns Modelling and Simulation of Chemical Processes,

Mathematical Methods in Chemical Engineering and his research

interests include mathematics applied in chemical engineering, mass

transfer, computers applied in chemical engineering, sustainable

development of process plants. He gained expertise in European

R&D projects. He developed projects in engineering education, e-

learning and computer aided process design. He is member of the

Editorial Board of the international journal INTEGRIROVANNYE

TEHNOLOGII I ENERGOSBEREGENIE (Integrated Technologies

and Energy Saving), Ukraine.