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Cost versus network length criteria in water network optimal design
16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering W. Marquardt, C. Pantelides (Editors) © 2006 Published by Elsevier B.V.
Cost versus Network Length Criteria in Water Network Optimal Design Petrica lancu^, V. Ple§u^, V. Lavric^'*' ^Univeristy POLITEHNICA of Bucharest, Chemical Engineering Department-CTTIP, Polizu 1-7, RO-011061, Bucharest, Romania ^Vrije Universiteit Brussel, Mechanical Engineering department, Pleinlaan 2, B-1050, Brussels, Belgium Abstract A cost-based optimization criterion is used to find the best water network topology which reduces both the investment and operating costs, when water sources with or without multiple contaminants are available. When data regarding the costs related to pipes, energy and pumps are not available, unreliable or could undergo large fluctuations, another optimization criterion could be the minimum active network length, including both the internal topology and the supply and discharge piping systems. The mathematical model of the wastewater network, assembling all the unit operations, is based upon total and contaminant species mass balances, together with the input and output constraints for each and every unit. The cost-based criterion includes the piping network cost, based upon the pipes' diameter, and the pumping cost, while the network length criterion is simply the sum of all the pipes through which contaminated water flows with a flow-rate higher than a threshold value. The optimal topologies found using these two criteria are compared against each other and also with the best topology acquired using supply water savings as criterion. In all cases, the optimization is carried out via an improved Genetic Algorithm variant, which uses one of the two aforementioned criteria and observes, in the same time, all restrictions. Keywords: wastewater network, genetic algorithms, cost based optimization, multiobjective function, threshold internal flow. 1. Introduction The problem of wastewater minimization is a challenging one at least three fold: a) lowering the fresh/supplied water consumption decreases not only its bill, knowing that low-contaminated water grows expensive, but also the operating costs; b) reusing as much water as possible not only decreases the pumping costs, but also increases the pollutant concentrations, thereby easing up the treatment operations; c) eliminating the internal loops not only saves pumping energy but also keeps the process within the bounds set by the principle of equipartition of the driving force, which ensures a lower entropy production. Ultimately, all these aforementioned factors determine a significant decrease of the water network pipes' diameter, thus lowering the investment costs. The optimization methods developed so far can be lumped into three broad categories: water pinch analysis, mathematical models of superstructure assembled systems and artificial intelligence based models and solving algorithms. Water pinch analysis embedded in wastewater minimization techniques offers simple, intuitive, geometric based methods and beneficial results, when applied to water using industries or wastewater treatment facilities (Thevendiraraj et al., 2003). Their advantage is that they provide valuable conceptual insights into the performance or
1821
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behavior of the system under consideration (Bagajewicz, 2000; Hallale, 2002; Lavric et al, 2004). These methods were appHed for single contaminant, with very Umited extension to the multicomponent mixture, although many efforts are being made to overcome these limitations (Lavric et al, 2004). The methods based upon superstructures try to capture all possible reuse, regeneration and water internal mains opportunities, leading to non-convex NLP and MINLP models, with the drawback that there is no guarantee of global optimality (Feng and Seider, 2001; Feng and Chu, 2004). Using these concepts, Suh and Lee (2002), developed a robust optimal design strategy, considering the uncertain parameter variations in both economic and technical aspects. The objective function is the net present cost, consisting of the network piping and pumps cost and the freshwater usage cost. In the last years, the concepts emerged from artificial intelligence like neural network models or genetic algorithms gained a vivid attention, the first for on-line control, due to their self-improving ability, while the later due to their capacity of well solve any non-convex problem, without being trapped into local minima (Lavric et al, 2005a&b). 2. The mathematical model An optimal water network, supplied with fresh water only, is an oriented graph, starting with the unit operations free from contaminants at entrance. Every other unit operation i receives streams from possibly all previous operations y only (j = 1, 2 ... i-1) and sending streams to probably all next operations A: (k = i+1, i+2 ... N). When the supply water is slightly contaminated with pollutants, the associated graph remains oriented, but the starting unit operations are lumped according to their input concentration restrictions - see Lavric et al, (2004; 2005a). In the present paper, we consider that the supply water comes from four external sources, each resource having a different level of pollutants' contamination. The complete mathematical model of the wastewater network, as resulted from total and contaminant species mass balances, together with their constraints both at input and output, is given in Lavric et al (2004; 2005a) for the general case of multiple contaminated sources at different levels of contamination. 3. The objective function The same system can have multiple optimal states, each corresponding to a different objective fiinction, which encodes the peculiar performance criteria envisaged by the problem at hand. The optimality of the wastewater network can be sought with respect to either the fresh/supply water consumption (Lavric et al, 2004; Lavric et al, 2005a), or to some profit function which encapsulates the market uncertainties. In Lavric et al, (2005b), the sum of the pumping costs and the fixed charges for the piping system was used as an economic objective function. In the present study, we employ a multi-objective function which avoids the explicit use of any economic term/criteria, knowing that these factors strongly depend upon the market conditions; sometimes, correct economic figures and/or trends are hard to estimate, thus affecting the confidence level in the results. Our objective function is the weighted sum of the normalized fresh/supply water consumption and active network pipes' length:
Y fz +z
N
Z
(
/•min
F^^ = (o^^^i^
/•min \
/;=1 -» \ , F,>(i,Wi>^
in,i
Wy z out,i)
+ (1 - (o)'-^:^^^ ^ total
/
-•
^-^ ^total
i,j
(1)
Cost Versus Network Length Criteria in Water Network Optimal
1823
Design
In equation (1), A^ stands for the number of unit operations; Ftotal is the maximum supply water the network would employ in the absence of any internal reuse; Lin,i and Lout,i are the lengths of the supplying and discharging pipes, respectively, while Ltj is the length of the pipe from unit i to unit j ; Fi>0, Wi>0 and Xij>0 are the active pipe conditions, such that its length to be considered in the summation process; Ltotai is the overall length of the wastewater network's pipe system; co is the weighting factor. Details regarding the complete development of the flow term of the objective ftinction can be found in Lavric et al (2004; 2005a). Solving the associated optimization problems is not trivial, since the unknowns' number outcomes the equations' number. We employed an improved genetic algorithm which uses each internal flow as a gene, defining a chromosome from all these flows (Lavric et al 2004). The restrictions are coped with during the population generation eliminating these individuals outside the feasible domain. The individuals are interbreeding according to their selection frequency, using one-point crossover method, and then mutation is applied to randomly selected ones. 4. Results and discussions 4.1. Cost versus Network Length Criteria - no thresholdfor inner flows In order to verify if the Network Length Criterion (NLC), as resulting from (1) putting co = 0, gives comparable results with the economic objective function (EOF) used in Lavric et al. (2005b), the same runs were carried out, the results being presented in Table 1, for both criteria. These results are compared against those obtained when only fresh/supply water (F/SW) was employed as objective function, as resulting from (1) putting o) = l. We used two ranking methods, by fresh flow needed when no internal reuse is envisaged or by maximum pollutant load, to comply with the principle of driving force equipartition, as describe in Lavric et al. (2004). Irrespective of ranking procedure, NLC gives better results than F/SW but worse than EOF, when no threshold value for the internal flows is imposed, although using maximum pollutant load as ranking criterion lowers the significantly the active pipes' length. The drawback of using NLC instead of F/SW is a slight increase in the water consumption, with a maximum of 1.786 t/h for the worst case. But, this is compensated largely since the investments are lower (48.07 km against 54.42 km and 39.7 km against 53.88 km) and so does the pumping cost, since the frictions in a smaller network will be lesser. We present in Figure 1 the best NLC topology, against the best EOF one, both corresponding to the maximum pollutant load ranking procedure. The surplus of Table 2 Results of the design of a wastewater network with 15 unit operations and 6 contaminants; all four resources, as presented in Lavric et al. (2005a), are used to supply the network Objective Function
>>
.o o> CO
a:
lo Z3 •o tn 0)
"o CD
o> CD
Supply Water
Network Length & Supplyf Water
Total Cost
Inlet Pipe's flow, t/h length, km
N
54.42
Inlet Cost, Pipe's Inlet Pipe's Inlet Pipe's k$/year flow, t/h length, km flow, t/h length, km flow, t/h length, km 207.4
27.75
48.08 457.194
LI-
CO O "O _l
Y
N
co = 0
CO = 0.5
457.194
48.07 458.88
15.21
37.44
204.6
53.88
173.5
30.18
458.044
39.79
458.62
39.7
39.6
176.0
9.72
457.194
10.28
458.14
9.76
457.194
12.09
15.33
1824
P. lancu et al
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Figure 1 Optimal network topology using as objective function the total costs or the active pipes' length (bold-italic figures) - all flows are taken into consideration; Resources A, B, C and D are the same as in Lavric et al. (2005a) 9.52 km of pipes serves to a more uniform internal flow distribution, at the expense of operating and investments costs. But, in the same time, the NLC topology is quite independent to the market fluctuations. Combining both F/SW and NLC criteria into a single multi-objective function, putting CO = 0.5 in equation (1), made no improvement into the topology of the optimal network, irrespective of the ranking procedure we used. Still the cost based optimized network is at least 30% smaller. The network changed, in terms of active pipes and internal flows, but its total length did not. However, it is worth mentioning that the fresh/supply water consumption decreased either to its minimum value, whenfi*eshflow needed when no internal reuse was used for ranking, or close to this value, when maximum pollutant load was used instead. 4.2. Cost versus Network Length Criteria -threshold of 1 t/hfor inner flows A completely different behavior of the optimization results was observed when we imposed a threshold value of 1 t/h to the internal flows (the lines corresponding to Y in the second column of Table 1), even when only the F/SW criterion was used, although in this case, after reaching the minimum of 457.194 t/h fresh/supply water consumption, the algorithm ceases to search for a better topology. The lengths of 37.44 t/h and
Cost Versus Network Length Criteria in Water Network Optimal Design
1825
39.6 t/h, respectively, were obtained after several runs with the genetic algorithm optimization starting from random internal flows. It must be stated that the final active lengths were all in the vicinity of these values. Quite remarkably, putting a threshold value for the internal flows improved dramatically the topology of the EOF optimized wastewater network (see Figures 1 and 2 for details). In both these Figures, the EOF optimized topology corresponds to the normal written numbers. What is really surprising is the way the internal water reuse simplifies when there is this threshold value - see the conNLCtions between unit operations below 11 in Figure 2 in comparison with Figure 1. Although only two links have actually their flows below 1 t/h (0.964 t/h from 1^12 and 0.205 t/h from 9^12), their disappearance completely changed the topology. The internal flows grow bigger and its distribution between the first half units of the network changed such that the input pollutant concentrations approach to a greater extent the imposed limits, decreasing the need for internal reuse among the terminal units. This has as result a reduction of the active network length to 32.2% of the previously optimum value, at the expense of an increase with 1.44% of the costs. This increase is due to the raise of pipe diameters and fluid velocities, but the simplified network will imply lower maintenance costs, not included in the EOF.
•(8)375,008
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Figure 2 Optimal network topology using as objective fiinction the total costs or the total pipes' length {bold-italic figures) - the flows under 1 t/h are disregarded; Resources A, B, C and D are the same as in Lavric et al. (2005a)
1826
P. lancu et al
When NLC objective function is used (with co = 0) to find the optimum wastewater network topology, disregarding the flows under 1 t/h, the changes are even more dramatic, the result obtained being very close to the one owed to EOF (see Figure 2 for details). Not only had the supplemental fresh water added to the network through unit 13 dropped with 33.71%, but also the internal network architecture simplified almost as much as when EOF was used, under the same circumstances. There are only one supplemental flow introduced (10.071 t/h from 4^'14) and one discharge instead of internal reuse (6.552 t/h from 11-^12 is directly sent to treatment from unit 11). The main differences come from neglecting several internal water reuses and modifying the internal flows, accordingly. But the important benefice is that we obtained the same simplification of the internal network for the last half units. Using a multi-objective optimization fimction does not improve the resulting topology. On the contrary, the beneficial effect of NLC is hindered partially by the use of F/SW, the system increasing slightly the active pipes' length, although the fresh/supply water consumption reaches the aforementioned lowest value. 5. Conclusions In this paper, we presented a multi-objective optimization criterion which can be successfully used to find the best network topology. The parameter of the function permits its use for composite demands, starting from the plain S/FW minimization and ending with optimal NLC. As expected from our previous researches largely presented in Lavric et al (2004; 2005a&b), ranking the network by the maximum pollutant load gives better topologies, no matter the parameter's value. Another important finding is that the resulting complexity of the network is heavily lowered when a given threshold value is imposed upon the internal flows, situation in which both EOF and NLC gave almost the same results. So, a straightforward continuation should be a thorough investigation of this threshold value upon the optimal topology. References M. Bagajewicz, 2000, A review of recent design procedures for water networks in refineries and process plants. Computers and Chemical Engineering, 24, 2093-113 X. Feng and W.D. Seider, 2001, A new structure and design methodology for water networks, Ind. Eng. Chem. Res., 40(26), 6140-6 X. Feng and K.H. Chu, 2004, Cost optimization of industrial wastewater reuse systems, Trans IChemE, Part B, Process Safety and Environmental Protection, 82(B3), 249-55 N. Hallale, 2002, A new graphical targeting method for water minimisation, Advances in Environmental Research, 6, 377-90 V. Lavric, P. lancu and V. Ple§u, 2004, Optimal Water System Topology through Genetic Algorithm under Multiple Contaminated-Water Sources Constraint. In Computer-Aided Chemical Engineering (Barbosa-Povoa A, Matos H, Editors), 18, Elsevier, 433-8 V. Lavric, P. lancu and V. Ple§u, 2005a, Genetic Algorithm Optimization of Water Consumption and Wastewater Network Topology, Journal of Cleaner Production, 13(15), 1405-15 V. Lavric, P. lancu, V. Ple§u, I. Ivanescu and M. Hie, 2005b, Cost-Based Water Network Optimization by Genetic Algorithm, Chem. Engng. Transactions 7, 755-60 M.-H.Suh and T.-Y. Lee, 2002, Robust Optimal Design of Wastewater Reuse Network of Plating Process, Journal of Chemical Engineering of Japan, 9, 863-73 S. Thevendiraraj, J. Klemes, D. Paz, G. Aso and G.J. Cardenas, 2003, Water and wastewater minimization study of a citrus plant. Resources, Conservation and Recycling 37,227-50 Y.H. Yang, H.H. Lou and Y.L. Huang, 2000, Synthesis of an optimal wastewater reuse network. Waste Management 20: 311-9
Cost versus Network Length Criteria in Water Network Optimal Design Petrica lancu^, V. Ple§u^, V. Lavric^'*' ^Univeristy POLITEHNICA of Bucharest, Chemical Engineering Department-CTTIP, Polizu 1-7, RO-011061, Bucharest, Romania ^Vrije Universiteit Brussel, Mechanical Engineering department, Pleinlaan 2, B-1050, Brussels, Belgium Abstract A cost-based optimization criterion is used to find the best water network topology which reduces both the investment and operating costs, when water sources with or without multiple contaminants are available. When data regarding the costs related to pipes, energy and pumps are not available, unreliable or could undergo large fluctuations, another optimization criterion could be the minimum active network length, including both the internal topology and the supply and discharge piping systems. The mathematical model of the wastewater network, assembling all the unit operations, is based upon total and contaminant species mass balances, together with the input and output constraints for each and every unit. The cost-based criterion includes the piping network cost, based upon the pipes' diameter, and the pumping cost, while the network length criterion is simply the sum of all the pipes through which contaminated water flows with a flow-rate higher than a threshold value. The optimal topologies found using these two criteria are compared against each other and also with the best topology acquired using supply water savings as criterion. In all cases, the optimization is carried out via an improved Genetic Algorithm variant, which uses one of the two aforementioned criteria and observes, in the same time, all restrictions. Keywords: wastewater network, genetic algorithms, cost based optimization, multiobjective function, threshold internal flow. 1. Introduction The problem of wastewater minimization is a challenging one at least three fold: a) lowering the fresh/supplied water consumption decreases not only its bill, knowing that low-contaminated water grows expensive, but also the operating costs; b) reusing as much water as possible not only decreases the pumping costs, but also increases the pollutant concentrations, thereby easing up the treatment operations; c) eliminating the internal loops not only saves pumping energy but also keeps the process within the bounds set by the principle of equipartition of the driving force, which ensures a lower entropy production. Ultimately, all these aforementioned factors determine a significant decrease of the water network pipes' diameter, thus lowering the investment costs. The optimization methods developed so far can be lumped into three broad categories: water pinch analysis, mathematical models of superstructure assembled systems and artificial intelligence based models and solving algorithms. Water pinch analysis embedded in wastewater minimization techniques offers simple, intuitive, geometric based methods and beneficial results, when applied to water using industries or wastewater treatment facilities (Thevendiraraj et al., 2003). Their advantage is that they provide valuable conceptual insights into the performance or
1821
1822
P. lancu et al
behavior of the system under consideration (Bagajewicz, 2000; Hallale, 2002; Lavric et al, 2004). These methods were appHed for single contaminant, with very Umited extension to the multicomponent mixture, although many efforts are being made to overcome these limitations (Lavric et al, 2004). The methods based upon superstructures try to capture all possible reuse, regeneration and water internal mains opportunities, leading to non-convex NLP and MINLP models, with the drawback that there is no guarantee of global optimality (Feng and Seider, 2001; Feng and Chu, 2004). Using these concepts, Suh and Lee (2002), developed a robust optimal design strategy, considering the uncertain parameter variations in both economic and technical aspects. The objective function is the net present cost, consisting of the network piping and pumps cost and the freshwater usage cost. In the last years, the concepts emerged from artificial intelligence like neural network models or genetic algorithms gained a vivid attention, the first for on-line control, due to their self-improving ability, while the later due to their capacity of well solve any non-convex problem, without being trapped into local minima (Lavric et al, 2005a&b). 2. The mathematical model An optimal water network, supplied with fresh water only, is an oriented graph, starting with the unit operations free from contaminants at entrance. Every other unit operation i receives streams from possibly all previous operations y only (j = 1, 2 ... i-1) and sending streams to probably all next operations A: (k = i+1, i+2 ... N). When the supply water is slightly contaminated with pollutants, the associated graph remains oriented, but the starting unit operations are lumped according to their input concentration restrictions - see Lavric et al, (2004; 2005a). In the present paper, we consider that the supply water comes from four external sources, each resource having a different level of pollutants' contamination. The complete mathematical model of the wastewater network, as resulted from total and contaminant species mass balances, together with their constraints both at input and output, is given in Lavric et al (2004; 2005a) for the general case of multiple contaminated sources at different levels of contamination. 3. The objective function The same system can have multiple optimal states, each corresponding to a different objective fiinction, which encodes the peculiar performance criteria envisaged by the problem at hand. The optimality of the wastewater network can be sought with respect to either the fresh/supply water consumption (Lavric et al, 2004; Lavric et al, 2005a), or to some profit function which encapsulates the market uncertainties. In Lavric et al, (2005b), the sum of the pumping costs and the fixed charges for the piping system was used as an economic objective function. In the present study, we employ a multi-objective function which avoids the explicit use of any economic term/criteria, knowing that these factors strongly depend upon the market conditions; sometimes, correct economic figures and/or trends are hard to estimate, thus affecting the confidence level in the results. Our objective function is the weighted sum of the normalized fresh/supply water consumption and active network pipes' length:
Y fz +z
N
Z
(
/•min
F^^ = (o^^^i^
/•min \
/;=1 -» \ , F,>(i,Wi>^
in,i
Wy z out,i)
+ (1 - (o)'-^:^^^ ^ total
/
-•
^-^ ^total
i,j
(1)
Cost Versus Network Length Criteria in Water Network Optimal
1823
Design
In equation (1), A^ stands for the number of unit operations; Ftotal is the maximum supply water the network would employ in the absence of any internal reuse; Lin,i and Lout,i are the lengths of the supplying and discharging pipes, respectively, while Ltj is the length of the pipe from unit i to unit j ; Fi>0, Wi>0 and Xij>0 are the active pipe conditions, such that its length to be considered in the summation process; Ltotai is the overall length of the wastewater network's pipe system; co is the weighting factor. Details regarding the complete development of the flow term of the objective ftinction can be found in Lavric et al (2004; 2005a). Solving the associated optimization problems is not trivial, since the unknowns' number outcomes the equations' number. We employed an improved genetic algorithm which uses each internal flow as a gene, defining a chromosome from all these flows (Lavric et al 2004). The restrictions are coped with during the population generation eliminating these individuals outside the feasible domain. The individuals are interbreeding according to their selection frequency, using one-point crossover method, and then mutation is applied to randomly selected ones. 4. Results and discussions 4.1. Cost versus Network Length Criteria - no thresholdfor inner flows In order to verify if the Network Length Criterion (NLC), as resulting from (1) putting co = 0, gives comparable results with the economic objective function (EOF) used in Lavric et al. (2005b), the same runs were carried out, the results being presented in Table 1, for both criteria. These results are compared against those obtained when only fresh/supply water (F/SW) was employed as objective function, as resulting from (1) putting o) = l. We used two ranking methods, by fresh flow needed when no internal reuse is envisaged or by maximum pollutant load, to comply with the principle of driving force equipartition, as describe in Lavric et al. (2004). Irrespective of ranking procedure, NLC gives better results than F/SW but worse than EOF, when no threshold value for the internal flows is imposed, although using maximum pollutant load as ranking criterion lowers the significantly the active pipes' length. The drawback of using NLC instead of F/SW is a slight increase in the water consumption, with a maximum of 1.786 t/h for the worst case. But, this is compensated largely since the investments are lower (48.07 km against 54.42 km and 39.7 km against 53.88 km) and so does the pumping cost, since the frictions in a smaller network will be lesser. We present in Figure 1 the best NLC topology, against the best EOF one, both corresponding to the maximum pollutant load ranking procedure. The surplus of Table 2 Results of the design of a wastewater network with 15 unit operations and 6 contaminants; all four resources, as presented in Lavric et al. (2005a), are used to supply the network Objective Function
>>
.o o> CO
a:
lo Z3 •o tn 0)
"o CD
o> CD
Supply Water
Network Length & Supplyf Water
Total Cost
Inlet Pipe's flow, t/h length, km
N
54.42
Inlet Cost, Pipe's Inlet Pipe's Inlet Pipe's k$/year flow, t/h length, km flow, t/h length, km flow, t/h length, km 207.4
27.75
48.08 457.194
LI-
CO O "O _l
Y
N
co = 0
CO = 0.5
457.194
48.07 458.88
15.21
37.44
204.6
53.88
173.5
30.18
458.044
39.79
458.62
39.7
39.6
176.0
9.72
457.194
10.28
458.14
9.76
457.194
12.09
15.33
1824
P. lancu et al
Nia3ioj
kl49.S5fi
-{8)375,008 14.434 3.9S9
^••2.872^
-(A| 3 2 . 4 3 6 — • ! U-3 2C14
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, .07-i
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,
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-.^^
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' i f 5 j-iss.s&y
Figure 1 Optimal network topology using as objective function the total costs or the active pipes' length (bold-italic figures) - all flows are taken into consideration; Resources A, B, C and D are the same as in Lavric et al. (2005a) 9.52 km of pipes serves to a more uniform internal flow distribution, at the expense of operating and investments costs. But, in the same time, the NLC topology is quite independent to the market fluctuations. Combining both F/SW and NLC criteria into a single multi-objective function, putting CO = 0.5 in equation (1), made no improvement into the topology of the optimal network, irrespective of the ranking procedure we used. Still the cost based optimized network is at least 30% smaller. The network changed, in terms of active pipes and internal flows, but its total length did not. However, it is worth mentioning that the fresh/supply water consumption decreased either to its minimum value, whenfi*eshflow needed when no internal reuse was used for ranking, or close to this value, when maximum pollutant load was used instead. 4.2. Cost versus Network Length Criteria -threshold of 1 t/hfor inner flows A completely different behavior of the optimization results was observed when we imposed a threshold value of 1 t/h to the internal flows (the lines corresponding to Y in the second column of Table 1), even when only the F/SW criterion was used, although in this case, after reaching the minimum of 457.194 t/h fresh/supply water consumption, the algorithm ceases to search for a better topology. The lengths of 37.44 t/h and
Cost Versus Network Length Criteria in Water Network Optimal Design
1825
39.6 t/h, respectively, were obtained after several runs with the genetic algorithm optimization starting from random internal flows. It must be stated that the final active lengths were all in the vicinity of these values. Quite remarkably, putting a threshold value for the internal flows improved dramatically the topology of the EOF optimized wastewater network (see Figures 1 and 2 for details). In both these Figures, the EOF optimized topology corresponds to the normal written numbers. What is really surprising is the way the internal water reuse simplifies when there is this threshold value - see the conNLCtions between unit operations below 11 in Figure 2 in comparison with Figure 1. Although only two links have actually their flows below 1 t/h (0.964 t/h from 1^12 and 0.205 t/h from 9^12), their disappearance completely changed the topology. The internal flows grow bigger and its distribution between the first half units of the network changed such that the input pollutant concentrations approach to a greater extent the imposed limits, decreasing the need for internal reuse among the terminal units. This has as result a reduction of the active network length to 32.2% of the previously optimum value, at the expense of an increase with 1.44% of the costs. This increase is due to the raise of pipe diameters and fluid velocities, but the simplified network will imply lower maintenance costs, not included in the EOF.
•(8)375,008
^A) 32.436™-*4
• CD| 7232
-(CH2.457--"-*!
- f ^ 0 J4g.
Figure 2 Optimal network topology using as objective fiinction the total costs or the total pipes' length {bold-italic figures) - the flows under 1 t/h are disregarded; Resources A, B, C and D are the same as in Lavric et al. (2005a)
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When NLC objective function is used (with co = 0) to find the optimum wastewater network topology, disregarding the flows under 1 t/h, the changes are even more dramatic, the result obtained being very close to the one owed to EOF (see Figure 2 for details). Not only had the supplemental fresh water added to the network through unit 13 dropped with 33.71%, but also the internal network architecture simplified almost as much as when EOF was used, under the same circumstances. There are only one supplemental flow introduced (10.071 t/h from 4^'14) and one discharge instead of internal reuse (6.552 t/h from 11-^12 is directly sent to treatment from unit 11). The main differences come from neglecting several internal water reuses and modifying the internal flows, accordingly. But the important benefice is that we obtained the same simplification of the internal network for the last half units. Using a multi-objective optimization fimction does not improve the resulting topology. On the contrary, the beneficial effect of NLC is hindered partially by the use of F/SW, the system increasing slightly the active pipes' length, although the fresh/supply water consumption reaches the aforementioned lowest value. 5. Conclusions In this paper, we presented a multi-objective optimization criterion which can be successfully used to find the best network topology. The parameter of the function permits its use for composite demands, starting from the plain S/FW minimization and ending with optimal NLC. As expected from our previous researches largely presented in Lavric et al (2004; 2005a&b), ranking the network by the maximum pollutant load gives better topologies, no matter the parameter's value. Another important finding is that the resulting complexity of the network is heavily lowered when a given threshold value is imposed upon the internal flows, situation in which both EOF and NLC gave almost the same results. So, a straightforward continuation should be a thorough investigation of this threshold value upon the optimal topology. References M. Bagajewicz, 2000, A review of recent design procedures for water networks in refineries and process plants. Computers and Chemical Engineering, 24, 2093-113 X. Feng and W.D. Seider, 2001, A new structure and design methodology for water networks, Ind. Eng. Chem. Res., 40(26), 6140-6 X. Feng and K.H. Chu, 2004, Cost optimization of industrial wastewater reuse systems, Trans IChemE, Part B, Process Safety and Environmental Protection, 82(B3), 249-55 N. Hallale, 2002, A new graphical targeting method for water minimisation, Advances in Environmental Research, 6, 377-90 V. Lavric, P. lancu and V. Ple§u, 2004, Optimal Water System Topology through Genetic Algorithm under Multiple Contaminated-Water Sources Constraint. In Computer-Aided Chemical Engineering (Barbosa-Povoa A, Matos H, Editors), 18, Elsevier, 433-8 V. Lavric, P. lancu and V. Ple§u, 2005a, Genetic Algorithm Optimization of Water Consumption and Wastewater Network Topology, Journal of Cleaner Production, 13(15), 1405-15 V. Lavric, P. lancu, V. Ple§u, I. Ivanescu and M. Hie, 2005b, Cost-Based Water Network Optimization by Genetic Algorithm, Chem. Engng. Transactions 7, 755-60 M.-H.Suh and T.-Y. Lee, 2002, Robust Optimal Design of Wastewater Reuse Network of Plating Process, Journal of Chemical Engineering of Japan, 9, 863-73 S. Thevendiraraj, J. Klemes, D. Paz, G. Aso and G.J. Cardenas, 2003, Water and wastewater minimization study of a citrus plant. Resources, Conservation and Recycling 37,227-50 Y.H. Yang, H.H. Lou and Y.L. Huang, 2000, Synthesis of an optimal wastewater reuse network. Waste Management 20: 311-9