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Optimization of Water-Allocation Networks with Multiple Contaminants using Genetic Algorithm *Md.

Alauddin Department of Petroleum Studies, F/o Engineering & Technology, AMU, Aligarh, UP, India. Email: alauddinchem@gmail.com

ABSTRACT: This is to show that Genetic Algorithm can be used effectively to solve water allocation network problems. In this paper a multi-contaminant problem discussed by Li & Chang [1] has been taken and Genetic Algorithm is used to optimize the model for minimization of freshwater consumption. The freshwater consumption was found to be 104.91 (t/h) which is comparative to Li & Chang that reported as 105.67 (t/h). The model has been written in a different way to reduce the number of effective variables. In Li & Chang paper, there were 40 continuous variable in NLP and 40 continuous and 15 binary variables in MINLP while this paper requires only 12 continuous variable in NLP and 12 continuous and 12 binary variables in MINLP. In addition to this Chang used GAMS environment where it is necessary to initialize and the choice of this initialization has a wide role on the convergence of the solution, where as in this paper GA is used, where no initialization of the variable s is needed, its automatically set by the algorithm, we have to select some parameters like cross over fraction, mutation etc. Keywords: Evolutionary Technique, GA, GAMS, MINLP, Multi Objective Optimization, Water Allocation Network 1. INTRODUCTION Water is one of the most important natural resource. It is widely used in most of the industrial operations particularly in chemical, petrochemical and paper & pulp industries. Water is used in two types of operations. One is mass transfer based operation in which contaminants are transferred from process stream to water streams e.g, in pulp washing in paper mills. The second is non-mass transfer operation in which water is generated or consumed e.g, steam generation. The huge volume of water usage can be figure out with following data1. 

To produce one kg of paper, approximately 300 lit of water is required



To manufacture one complete car, including tires, 147,972 lit of water is used.



It takes 215,000 lit of water to produce one ton of steel

Figure 1.1 shows a typical water network with m sources WW1, WW2,........WWm, n processing units P1,P2....Pn, k treatment units TTP1,TTP2,.......TTPk discharge units and their interconnections.1

Fig. 1.1: Typical water network Optimization can be defined as the search for the best possible solution(s) to a given

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problem while satisfying all the constraints [1]. Practical optimization problems, especially the engineering design optimization problems, seem to have a multi objective nature much more frequently than a single objective one. Typically, some structural performance criteria are to be maximized, while some others like weight of the structure and the implementation costs should be minimized simultaneously. For example, consider designing a car, the comfort for the passenger should be maximized, while simultaneously cost is to be minimized. But these two objectives are conflicting to each other. If we want to minimize the cost then comfort level should be compromised and vice-versa. Hence there is a trade-off between cost and comfort level, as shown in fig 1.2 [2].

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Solution A dominates solution C because Solution A results in an improvement in Objective 1 with no change in Objective 2 when compared with Solution C. Solution B dominates solution C because Solution B results in an improvement in Objective 2 with no change in Objective 1 when compared with Solution C. As a result, Solution C is dominated and thus, is not part of the Pareto-optimal front.

Fig. 1.3 Decision and objective space

Fig. 1.2: Trade-off between cost and comfort level In MOP we have to deal with two types of spaces: decision space as well as objective space, as shown in fig. 1.3. These types of problems result in a set of optimal solution called Pareto Optimal Front, which is locus of non-dominated points. That is, none of the points from the set is the best with respect to all objectives, there is no single optimal, rather, and there exist a number of solutions which are all optimal. Fig 1.4 shows a Pareto front of two objectives – objective 1 and objective2, both are to be minimized. Solutions A and B are nondominated solutions and therefore, they reside on the nondominated Pareto-optimal front.

Fig. 1.4 Pareto front 2. Literature survey Researchers in the field of water network, since one and half a decade, a nice review is presented in this regard by Bagajewicz [4], Foo [5] and Jacek Jez’owski [6]. It is to minimize the fresh water consumption that will result not only the processing cost but also capital cost. Saveleski and Bagajewics [7] reported, higher the flow rate through the process, larger the equipment size. Das et al.[8], shows simple structure with fewest possible inter connection

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will result in high level of controllability, operability and safety. There are broadly two conventional methods for design of water network as shown in figure (2.1). One is graphical method associated with pinch design and the other is mathematical programming (Optimization based).

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model. GA is used prior to optimize over all water network by some workers. Lavric[19] that deals with the multi contaminant in which every unit operation was recieving streams from previous operations only. Motension [20] used modified GA in water distribution network. Wan [21] used advanced GA to reduce the cost of water supply under the constraint with hydraulic condition in annular pipe. 3 Mathematical modelling Fig (3.3) shows general water using unit network where W represents Water source, M as mixing unit, S splitting unit and D as demand. And fig (3.4) depicts a water using unit ‘i’ of the network. Here a modified version of equations is written for the Le and Chang Model which is given in appendix A.

Fig. 2.1: Classification of design method of water networks The basis of pinch analysis for water network was put forward by Wang & Smith [9]. This focuses on to maximize water reuse and recycle strategy. In this the limitation is that as the number of contaminants increases, it becomes more and more difficult. Mathematical modeling, on the other hand handle multi component problems and produce global or near optimal solution. Takama et. al [10] established a super structure of all possible reuse and regeneration opportunities which was then optimized by series of workers. Polley [11], Yang et.al [12] and Poplewski et.al [13] optimized the networks for fixed flow operation and single component. These models were linear in nature .The model were minimized using LP for fresh water and MILP for minimum interconnection. Smith ([14],[15]), Chang( [16], [17],[18]) come up with multi-component problems and NLP & MINLP as solution strategies.

Fig. 3.3: A water using network

Fig. 3.4 A water using Unit Writing Material Balances we getTotal mass balance can be given as in (3.1) ∑

In this paper a multi contaminant problem discussed by Chang[17] has been presented and Genetic Algorithm is used to optimize the

∑

Partial mass balance, for k pollutant species is written as in (3.2)

IJCBS RESEARCH PAPER VOL. 1 [ISSUE 1] April, 2014

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∑ ∑

(

) Parameters

The first set of constraints can be given as in (3.3) ∑ ∑ ∑ ∑ And the second set of constraints can be written as in (3.4) ∑ ∑ Binary Variable

Objective Functions: There are two objective functions one is minimization of fresh water consumption ( ) and another is minimization of number of inter connections (

Positive Variables

Minimization of fresh water consumption-

Pollutant concentration k going to operation i

∑

Pollutant concentration of k coming from operation j

Minimization of number of interconnections=min[∑ ∑

∑

∑ ∑

∑

∑ ]

Exit flow from unit operation i

(3.6)

Water flow from j to i operation (likewise Indices

Xij) 3.4 Result & Discussion

Sets

The model was tested on a well-known petroleum refining problem (given in table 3.1), studied by many workers and currently by Li Chang (2007 & 2011). The example was modelled and executed on MATLAB 7.15a (2008) using optimtool, GA- Genetic Algorithm as solver. The parameters used were population size as 120, number of generation as 100, Cross over fraction as 0.8 and all the others are listed in the table 4.2. The freshwater consumption was found to be 104.91 t/h and there were 9 inter connections. The result is shown in

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matching matrix in table 3.2. We can see the comparative results of this with that of the Li Chang (in Table 3.3). Fig (3.5) and fig (3.6) show

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the solver result respectively.

for

NLP

and

MINLP

Table 2 (a): Current result using GA (MATLAB)

Fig. 3.5: Solver output for NLP

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Fig. 3.6: Solver output for MINLP

Table 3.1: Process limiting data

Table 3.2: GA Parameters settings

IJCBS RESEARCH PAPER VOL. 1 [ISSUE 1] April, 2014

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Chichester, UK, 2001.

5 Conclusions 



The freshwater consumption was found to be 104.91 t/h almost same as 105.67 as reported in Li & Chang [32] and Number of interconnection was same as in Li Chang. In Li & Chang paper, there were 40 continuous variable in NLP and 40 continuous and 15 binary variables in MINLP while this paper requires only 12 continuous variable in NLP and 12 continuous & 12 binary variables in MINLP In addition to this Chang used GAMS environment where it is necessary to initialize and the choice of this initialization has a wide role on the convergence of the solution, where as in this paper GA is used, where no initialization of the variable s is needed, its automatically set by the algorithm, we have to select some parameters like cross over fraction, mutation etc. The convergence is highly susceptible on the choice of the parameter to be selected particularly on Population size, Ellite Counts, cross over fractions. We cannot access the same random number voluntarily if we want i,e., we do not have control on the random number The constraints is not 100 % meet though very small degree of violation 9.99*e-7. We are not getting Pareto fronts- What we are doing is that First minimization of Fresh water and assuming the obtained value as an additional constraint we are minimizing the Number of interconnections.

References

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Foo, D. C. Y., “State-of-the-art review of pinch analysis techniques for water network synsthesis.” Ind. Eng. Chem. Res., 48, pp.5125–5159, 2009.

Jezowski, J., “ Review of water network design methods with literature annotations” Ind. Eng. Chem. Res. 49, pp. 4475–4516, 2010.

Bagajewicz, M., Savelski, M., “On use of linear models for the design of water utilization systems in process plants with a single contaminant” Trans IchemE Part A 79, pp. 600– 610, Jul. 2001.

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12. Liu, Z. Y., Yang, Y., Wan, L. Z., Wang, X., Hou, K. H., “A heuristic design procedure for water-using networks with multiple contaminants” AIChE J., 55 (2), pp. 374–382, 2009.

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