Multi-Objective Optimisation of hybrid MSF RO desalination system using Genetic Algorithm. Hassan K. Abdulrahim* and Fuad N.

Transcription

1 Int. J. Exergy, Vol. 7, No. 3, Multi-Objective Optimisation of hybrid MSF RO desalination system using Genetic Algorithm Hassan K. Abdulrahim* and Fuad N. Alasfour Mechanical Engineering Department, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait *Corresponding author Abstract: The aim of this research is to perform Multi-Objective Optimisation (MOO) study for multistage flashing with brine recirculation and hybrid MSF RO desalination systems using Genetic Algorithm (GA) technique. The hybrid MSF RO desalination system has been simulated rigorously using first and second laws of thermodynamics in addition to the plant economical aspects. Four objectives have been considered in this analysis: distillate production, product cost, Gain Ratio and exergy destruction. The desalination systems have been optimised for single, double and triple simultaneous objectives. Results showed that MOO of MSF-BR and hybrid MSF RO systems were successful and tend to enhance the performance of both systems. Keywords: MOO; multi-objective optimisation; hybrid MSF RO; GA; genetic algorithm; RO; reverse osmosis; desalination; weighted sum; aggregated objectives; exergy; second law efficiency. Reference to this paper should be made as follows: Abdulrahim, H.K. and Alasfour, F.N. (2010) Multi-Objective Optimisation of hybrid MSF RO desalination system using Genetic Algorithm, Int. J. Exergy, Vol. 7, No. 3, pp Biographical notes: Hassan K. Abdulrahim is a Senior Lecturer Assistant at Kuwait University since He received his MSc in Mechanical Engineering from Helwan University, Egypt, in 1994, and his PhD in Mechanical Engineering from Cairo University, Egypt, in His favourite fields of research include thermal systems simulation and optimisation, internal combustion engines and desalination technology. Fuad N. Alasfour is an Associate Professor at Kuwait University. He received his PhD in Mechanical Engineering from the University of Colorado at Boulder, USA, in His major fields include combustion, alternative fuels and desalination. 1 Introduction Hybrid desalination systems that combine both thermal and membrane desalination processes with power generation are currently considered as an alternative to Copyright 2010 Inderscience Enterprises Ltd.

2 388 H.K. Abdulrahim and F.N. Alasfour conventional dual-purpose plants. In desalination field, hybridisation can reduce water production cost and improves plant availability and operation flexibility. Several studies concerning the performance of hybrid MSF RO are available in literature. These studies focused on thermal analysis, exergy destruction, economics and optimisation of such systems. Nevertheless, Multi-Objective Optimisation (MOO) studies of hybrid MSF RO are very rare. Optimisation is a mathematical discipline, which been used in wide fields such as engineering, economic, operational research and systems control (Deb, 2001). It is used as a modelling and a solution tool to achieve number of objectives. Optimisation deals with decision problems that are formulated in a mathematical language. It is the art of maximising or minimising an objective function(s) while satisfying certain constraint(s). Optimisation problems consist of three basic ingredients: a objective function b variables c constraints (Eiben and Smith, 2003). a Objective function The objective function represents the quantity to be maximised or minimised, such as water cost and freshwater production in the case of desalination plant. It is worth to mention that almost all optimisation problems have single-objective function, with the following two exceptions: No objective function and multiple objective functions (Coello et al., 2002). b Variables Variables are parameters that control objective function s value. In case of desalination, variables might include streams temperature, number of stages and various flow rates. Variables are the keys that the designer can adjust to achieve the desired performance. Variables can be classified as: i design variables ii dependent variables iii state variables iv operating variables v environmental and external variables (Andersson, 2001). c Constraints Constraints are the set of boundaries that allow variables to take on certain values and exclude others. For desalination application, flow rates or temperatures cannot be negative, so constraints are placed on all flow rate and temperature variables to be non-negative. Two types of constraints can exist in an optimisation problem: a Equality constraints: x1 = a1, x2 = a2,, xn = an b Non-equality constraints: a x1 b, x2 c.

3 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 389 MOO (also called multi-criteria, multi-performance or simultaneous optimisation problem) is an important research topic because of multi-discipline nature of most real-world problems (Vince et al., 2008). The fuzziness of this kind of optimisation lies in the fact that there is no accepted definition of optimum as in single-objective optimisation problems. For MOO problems, more than one objective function can be satisfied simultaneously (Dennis et al., 2000; Tanvir and Mujtaba, 2008). In designing a desalination plant, product cost, performance and environmental impact are important characteristics that should be considered simultaneously. During plant design phase, designer must trade-off characteristics against each other. The purpose of conducting the MOO is to make these trade-offs clearly visible and quantifiable. The general multi-objective problem is expressed as follows. min/max F( X) = ( f ( X), f ( X), f ( X),, f ( X)) s.t. X S X = ( x, x, x,, x ) n T k T (1) where f1( X), f2( X), f3( X),, fk ( X) are k objective functions, (x 1, x 2, x 3,, x n ) are n decision variables, S R is a solution or parameter space, and R represents real number space. For a general optimisation problem, F is a non-linear function, and S might be defined by non-linear constraints containing both continuous and discrete variables. In the case of a desalination plant design, f 1 (X) may represent product mass flow rate (D), f 2 (X) for GR, f 3 (X) for product cost (Cst) and f 4 (X) for exergy destruction (ExD), while x 1, x 2,, x n represent the operating variables of the plant, such as TBT, Tf, m F, etc. In MOO problems, the algorithm must be capable to identify and characterise the interesting regions of solution space (trade-offs), providing the decision-maker with a number of choices, and information about those choices. With this information, decision-maker can make a qualitative choice about the proper solution from among regions that returned by optimisation algorithm, or can decide whether some unexpected interesting regions are worthy for further study, or even use results of the optimiser to debug the model. Evolutionary Algorithms (EAs) can meet all requirements (Coello et al., 2002). EAs are considered as robust optimisers that can attack most classes of problems, needing very little supplementary knowledge of the problem space, i.e., no derivatives are required for objective function or constraints. Furthermore, EAs work with a population of potential solutions so a single optimisation run can return range of possible suitable solutions, illustrating a trade-off behaviour between all objectives in a multi-objective problem (Deb, 2001). During the phase of desalination plant design, the first pass model is usually linear, and thus it is solvable by linear programming techniques. A more realistic model for the same problem may require the presence of non-linear functions, and again be solvable by a simple appropriate technique. Later, the model may prove to be highly non-linear, requiring either moving to a non-linear optimiser or converting the non-linear parts into piecewise-linear sections. In this case, two problems appear:

4 390 H.K. Abdulrahim and F.N. Alasfour a the need to continually change the optimiser used to accommodate the nature of the model b the requirement to reformulate the model to be consistent with the optimiser. The work required to make these changes is often very lengthy and complicated. EAs become attractive choice in these cases because it will find an acceptable solution to almost any problem with only minimum preparation of the problem. In cases of complex models where EAs convergence time is large, it will still be shorter than the time required to reformulate the model, or to develop new optimisation techniques (Andersson, 2001). One of the main disadvantages of EA is the difficulty of finding global optimum solution. However, this difficulty can be overcome by conducting several optimisations with different initial guess; it could only be made more probable that the global optimum is truly found. Another disadvantage with non-gradient-based methods is that they usually require more function calls than gradient methods, thus more computational expensive. However, as the capacities of the computers are increasing, this disadvantage is quickly diminishing. 2 Multi-Objective Optimisation The real engineering design problems are usually characterised by the presence of many conflicting objectives that the design has to fulfil; thus, it is a multi-objective problem. Most of the optimisation problems are multi-objective in nature, and there are many methods available to tackle these kinds of problems (Liu et al., 2003; Pohekar and Ramachandran, 2004). Generally, the MOO problem can be handled in four different ways depending on when the decision-maker introduces the preference concerning different objectives: a never b before c during d after the actual optimisation procedure. In the first two approaches, the different objectives are aggregated to one overall objective function. Optimisation is then conducted and results in one optimal design solution. The result is then strongly dependent on how the objectives were aggregated. In the literature, different methods have been developed to support the decision-maker in aggregating objectives (Andersson, 2001). The method used in this work is weighted-sum method. 2.1 Weighted-sum method The most widely used method in MOO is the weighted-sum technique. In this method, all objective functions are added together using different weighting coefficients for each one, thus the MOO problem is transformed into a single optimisation problem of the form

5 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 391 similar to the following equation (Andersson, 2001; Pohekar and Ramachandran, 2004; Tanvir and Mujtaba, 2008; Weck and Kim, 2004). AOF = min k i= 1 s.t. λ R; λ 0; λ = 1 i λ f i i k i= 1 i (2) where AOF is the normalised Aggregated Objective Function and λ i are the weighting coefficients representing the relative importance of each objective. Multiple optimisation runs can be conducted at different weight vector (λ i ) to locate multiple points on the Pareto front. However, this method has a number of minor drawbacks, depending on the scaling of different objectives, it can be hard to select the weights to ensure that points are spread evenly over the Pareto front. 3 Genetic Algorithm Genetic Algorithm (GA) approach was first used by Holland (1998); it is started as stochastic search methods that mimic the process of natural biological evolution. In GAs, each decision variable (x i ) is encoded as a gene using an appropriate representation, such as a real number or a string of binary bits (1, 0). The corresponding genes for all variables x 1, x 2, x 3,, x n form a chromosome capable to describe a single design solution. GA is a numerical search tool aiming to find global maximum or minimum of a given real objective function f(x), of one or more real decision variables x, possibly subjected to various linear or non-linear constraints, g(x) (Marseguerra et al., 2006). GA has several advantages such as it does not need an initial condition to converge, and it solves optimisation problems without the need to compute function derivatives (Mjalli et al., 2007). A set of chromosomes representing several individual design solutions comprises a population, where the fittest individuals are selected as parents for mating to reproduce new individual. Mating is performed using crossover operator to cut and combine genes from the selected parents to produce children. The children are inserted back into the population and the individuals that did not survive are removed from the population. The procedure continues and the survival of better individuals is promoted appealing to the Darwinian principle. With time, the evolution reaches a solution that meets the stopping criteria set by the modeller (Eiben and Smith, 2003). GAs have number of components and operators that must be presented to function. The most important components are (Eiben and Smith, 2003; Reeves and Rowe, 2003): 1 Representation Method 2 Initialisation Procedure 3 Evaluation or Fitness Function 4 Population Pool

6 392 H.K. Abdulrahim and F.N. Alasfour 5 Parent Selection Mechanism 6 Variation Operators (Mutation and Crossover) 7 Survivor Selection Mechanism 8 Termination Condition. Konak et al. (2006) presented a tutorial study on MOO using GA; in their research, they presented an overview to describe GA, which has been developed specifically for problems with multi-objectives. 4 Solution method The MOO method used in this research is the weighted-sum method, where the optimisation itself was performed using GA technique. The PIKAIA code was utilised in this research (Charbonneau and Knapp, 1995; Charbonneau, 2002). The open source code was compiled into a Dynamic Linking Library (DLL) using Compaq Visual Fortran compiler (HP, 2003) and is also linked to the simulation software IPSEpro (SimTech, 2003). Figure 1 illustrates the PIKAIA-IPSEpro optimisation framework. This framework enables the GA code to utilise the simulation software, IPSEpro, to evaluate single and AOFs based on the assigned values of the decision variables, where GA code performs the optimisation calculations internally. A Java script has been written to control the process of passing variables and objective functions, and logging results from IPSEpro and PIKAIA.DLL library. Figure 1 PIKAIA IPSEpro optimisation framework

7 MOO of hybrid MSF-RO desalination system using Genetic Algorithm Literature review Industrial application of hybrid MSF RO desalination systems showed a significant performance improvements in terms of potable water production cost and operation flexibility in addition to the reduction in operation and maintenance cost (Awerbuch, 1997; Helal et al., 2003). Several studies have been performed on different hybrid desalination systems to evaluate its performance (Awerbuch, 1997; Helal et al., 2003; May, 2000). Fewer studies have been performed for optimising hybrid systems configurations. However, regarding the MOO of MSF-BR and hybrid MSF RO desalination systems, literatures were rare. Djebedjian et al. (2008) developed a methodology for optimisation of RO desalination systems performance. They used the solution-diffusion model to simulate the performance of RO membrane. The optimisation of RO system was achieved via utilising GA, using maximum permeate volumetric flow rate as a single-objective function. Their study aimed to find the optimum pressure difference across membrane to achieve maximum permeate flow under low permeate salinity constraints. Their results showed a linear relationship between the operating pressure difference across the membrane and permeate volumetric flow rate, where permeate concentration decreases with the increase in flow rate and membrane pressure difference. Murthy and Vengal (2006) performed a study to solve single-objective optimisation to optimise the performance of RO desalination system using GA. The optimisation problem aimed to maximise the observed rejection of solute by varying feed flow rate and permeate flux across membrane for constant feed concentration. They found that GA converged rapidly and efficiently to the optimum solution at 8th generation. It was noted in their research that varying computational parameters had a significant effect on the generated results. Guria et al. (2005) performed an MOO study for existing and new RO desalination plants. The simultaneous objectives considered in their study were maximum permeate flow, minimum desalination cost and minimum permeate concentration. The pressure difference across membrane, membrane effective area and module type were considered as decision variables for new plant design, whereas the pressure difference is the only variable considered in case of the existing plant. They used different adaptation of Non-dominated Sorting Genetic Algorithm (NSGA-II). They found that the membrane area was the most important variable for spiral wound RO module and operating pressure difference was the most important variable in designing the tubular RO module for brackish water desalination. Vince et al. (2008) developed a process optimisation method for the design of brackish water RO desalination system. Different system configurations were generated and evaluated economically, technically and environmentally. The process layout and operating parameters were simultaneously optimised using an MOO approach. In their research, the MOO is utilised to identify the best of technological alternatives for the set of selected objectives. The optimisation problem was formulated as Mixed Integer Non-Linear Programming (MINLP) and was solved using a conventional branch and bound algorithm. They concluded that for different optimal configurations, investment and operation and maintenance costs remained constant, whereas cost variation results rather from altering operating conditions and membrane renewal cost.

8 394 H.K. Abdulrahim and F.N. Alasfour Yuen et al. (2000) developed a mathematical model to study a simple MOO using a Non-dominated Sorting Genetic Algorithm (NSGA). Two objectives were considered in hollow fibre membrane separation module. Their results showed that the inner radius of the hollow fibres is the most important decision variable. Hybrid (thermal/membrane/power) plants are characterised by flexibility in operation, less specific energy consumption, low construction cost, better power and water matching (Hamed, 2005). Marcovecchio et al. (2005) presented a rigorous NLP MOO for hybrid MSF RO desalination system. Once through Multi-Stage Flashing (MSF-OT) has been considered in their research. The objectives of their research were to determine the optimal process design and operating conditions for a given water production. The mathematical model contains inherently non-linear and non-convex constraints. Their results provide the basic design for both MSF and RO systems. For MSF case, the results evaluated the optimum geometric design of each stage, heat transfer surface area and brine velocity, whereas for RO system, operating pressure, flow rate and permeate concentration have been evaluated. Tanvir and Mujtaba (2008) developed MINLP technique in their optimal design and operation of MSF. Three objectives have been considered: freshwater demand, seawater temperature and water production cost. Their results revealed the possibility of designing stand-alone flash stage, which would offer flexible scheduling in terms of various units and efficient maintenance. In addition, operation at low temperature throughout the year can reduce design and operating cost. The sensitivity analysis of the cost parameters showed that optimal design and operation are sensitive to some of parameters. Helal et al. (2003) presented a feasibility study of hybrid MSF RO desalination system. The study performed a single-objective optimisation to predict minimum water production cost. Seven different process layouts of hybrid MSF RO desalination systems have been investigated. Simple thermodynamic models for both MSF and RO desalination systems have been utilised. In addition to that, economical model for evaluating water production cost has also been adopted. The models have been implemented and solved using SOLVER tool of Microsoft Excel. The SOLVER was able to converge to an optimum solution in each case. Vince et al. (2006) presented a computer-aided method for design and optimisation of hybrid MSF RO desalination system using MINLP optimisation strategy. The optimisation carried out on technical, economical and environmental performance in an MOO framework. They used MINLP solvers for network design problem. In their research, results have been illustrated with an industrial case study (30,000 m 3 /day production of potable water with 100 ppm maximum salinity). Their results showed that MINLP has flexibility with an outstanding advantage. Their optimisation strategy can be globalised to dual-purpose water and power production schemes but may also be applied to simpler configurations such as single membrane or distillation plant. The aim of this research is to perform an MOO study of hybrid MSF RO desalination system under four objectives namely maximum distillate production, minimum cost, maximum GR and minimum exergy destruction. PIKAIA GA will be used for optimisation.

9 MOO of hybrid MSF-RO desalination system using Genetic Algorithm Hybrid MSF RO desalination system In the proposed hybrid MSF RO desalination system, the cooling water from the MSF plant is used as feed for the RO plant. In this case, RO plant benefits from the high-temperature feed water, which improves the RO performance. Figures 2(a) and (b) presents a schematic diagram and flow sheet simulation for the proposed hybrid MSF RO desalination system. The benefits of hybridising MSF with RO can be summarised as follows (Awerbuch, 1997; Helal et al., 2003; May, 2000): 1 Use a common seawater intake for both plants, which results in a capital cost saving. 2 Distillate products from MSF plant section can be blended with RO permeate to obtain suitable water quality, which extend membrane life, and allow the use of single-stage RO process. 3 Using a common post-treatment plant can handle the combined product of two plants to reduce the capital cost. 4 Short start-up and shutdown time requirements of RO plant can be utilised to minimise the total power consumption of the hybrid plant by shutting down RO plant daily during peak hours, which improve operation flexibility. 5 Reduce the cost of seawater desalination and electrical power production via the integration of current and future thermal desalination, membrane desalination and power generation technologies in one facility. 6 Full integration of RO and MSF plants provides better control of feed water temperature to RO plant by using warm-rejected coolant water from MSF heat rejection section. Experimental data revealed that water production increased by 42 48% by preheating feed water to RO plant section up to 33 C, compared with a sole RO plant operated with feed temperature of 15 C. The mathematical model of MSF is presented by the authors elsewhere (Abdulrahim, 2006; Alasfour and Abdulrahim, 2009) and for RO is presented in Appendix A. Figure 2(a) Schematic diagram for hybrid MSF RO system

10 396 H.K. Abdulrahim and F.N. Alasfour Figure 2(b) Flow sheet simulation for hybrid MSF RO system (see online version for colours) 7 Optimisation methodology In this work, the proposed hybrid MSF RO desalination system was investigated and the operating conditions were optimised according to the following procedures: 1 MSF-BR desalination system was first optimised for single, double and triple simultaneous objectives, where the individual objectives are: a Minimum product cost (Cst). b Maximum production rate (D). c Maximum GR. d Minimum exergy destruction (ExD). 2 Each two objectives were aggregated together to form double-objective optimisation problem, where the following objectives were considered: a Minimum product cost and exergy destruction. b Maximum production rate and GR. c Minimum product cost and maximum GR.

11 MOO of hybrid MSF-RO desalination system using Genetic Algorithm Three objectives have been aggregated to form triple-objective optimisation problem, where the following objectives were simultaneously considered: a Minimum product cost and exergy destruction with maximum production rate. b Maximum production rate and GR with minimum product cost. As this work had been applied on an existing desalination plant, all design parameters were kept constant during the optimisation and considered as constraints. The design parameters include: a the maximum flow rates, which is controlled by the installed pumps capacities b the heat transfer surface area, which is controlled by the stage size and number of tubes c the maximum TBT, which is controlled by MSF acid treatment d the maximum flow rate of steam, which is available from power plant. An arbitrary RO desalination plant was designed and integrated with the existing MSF-BR system to form hybrid MSF RO desalination system. The operating parameters of the MSF RO hybrid desalination system were then optimised according to the following objectives: 1 Single-objective optimisation a Minimum product cost (Cst) b Maximum production rate (D) c Minimum exergy destruction (ExD). 2 Double-objectives optimisation a Minimum product cost and maximum production rate b Maximum production rate and minimum exergy destruction c Minimum product cost and exergy destruction. 3 Triple-objective optimisation a Maximum production rate with minimum production cost and exergy destruction. Optimisation of the hybrid MSF RO desalination system subjected to the same constraints stated earlier in addition to the maximum operating pressure and temperature of the membrane; total dissolved salts (TDSs) of resultant mixed product was also considered as constraint. All applicable operating or environmental variables were considered as decision variables in the optimisation process. These variables include:

12 398 H.K. Abdulrahim and F.N. Alasfour a b Top brine, feed seawater and discharged brine temperatures Feed seawater, recirculation brine and discharge brine salinity c Mass flow rate of feed, recirculation, brine and make-up streams d RO feed, ratio of RO product to the total product of hybrid plant. As mentioned earlier, the MOO was not aiming to get a single solution for the problem; rather, it provides a set of optimal solutions according to the weights of each objective among others. These solutions provide trade-offs between the objectives. The decision maker then can choose the optimum solution based on his or her preferences. It is also interesting to mention that the optimisation problems involve many variables changing at the same time, so the results are presented in tables and bar charts showing the optimum value of the objective function for different optimisation cases. 8 Results 8.1 MSF-BR optimisation Before attempting to optimise MSF system, the GA code behaviour has been investigated first. The optimiser behaviour during MSF optimisation is shown in Figures 3 6. Figure 3 shows the change of the optimum value of the GR after each generation. In this figure, the number of generations and total number of individuals per generation were 100 generation and 150 individuals, respectively. However, as it can be seen, the code converged to the optimum value at the 20th generation, with number of fit individuals increased to 140 out of 150 in the 30th generation. For these reasons, the total number of generations was reduced to 50 generations only on the subsequent runs to reduce the calculation time, since there was no influential improvement in the value of GR after the 20th generation. Also, the number of individuals was increased to 200 to increase the number of fit individuals especially in the first few generations. In this study, the number of generations has been used as the stopping criteria for the GA code. Figure 3 Gain ratio optimisation of MSF-BR

13 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 399 Figure 4 Product cost optimisation of MSF-BR Figure 5 Distillate production optimisation of MSF-BR Figure 6 Total exergy destruction optimisation of MSF-BR

14 400 H.K. Abdulrahim and F.N. Alasfour Single-objective optimisation for MSF-BR The selected decision variables for this optimisation study were feed flow rate, feed temperature and brine salinity. The values of the decision variables for each individual objective are shown in Table 1, where the numbers in parentheses in the first row indicate the bound values of each decision variable. Table 1 Values of the decision variables for each individual objective Optimised objective function Optimum value F ( ) (kg/s) T f (25 35)( o C) x b ( ) Cst $/m D kg/s GR ExD kw Results in Table 1 show that for minimum product cost, the feed flow rate and the brine salinity were minimal; in fact, it was the lower bound of the variable. In case of minimising the exergy destruction, the feed flow and the brine salinity were the highest among other cases. Figure 4 shows the GA code behaviour during optimising MSF-BR system for minimum product cost. As mentioned before, the number of generations was reduced to 50, whereas the number of individuals was increased to 200. The optimiser showed a consistent behaviour and converged to the optimum minimum value in the 20th generation. The number of fit individuals also increased to the maximum value in the 25th generation. These results indicated that the optimisation code can operate satisfactorily in these conditions, which have been used in the remaining optimisation cases. Figures 5 and 6 show the optimisation of distillate production and exergy destruction, respectively. The optimum value of the objective function and maximum number of fit individuals were reached in the 15th generation in both cases, which indicated that the selection of the number of generation and population size were successful in this case. Table 2 presents the optimum value of each objective function along with its non-optimal values obtained during optimising other functions. Optimum value of each objective function formatted in bold face is given in Table 2, whereas other numbers present the non-optimal values of that function. Table 2 Values of optimised individual objective function for MSF-BR system Cst D GR ExD OF $/m 3 % Norm kg/s % Norm % Norm MW % Norm Cst D GR ExD

15 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 401 In first row of Table 2, first objective function considered is the product cost. The optimum minimum value of product cost was $/m 3. In this case of optimisation, the non-optimal value of the distillate production was 0.56% less than the optimum maximum value obtained for the distillate production rate, which is 393 kg/s. Also, the value of GR was less than the optimum maximum value by 0.012%, and the exergy destruction was higher than the optimum minimum value by 1.049%. Table 2 also shows the optimum maximum value of distillate production along with the non-optimal values of the other objective functions in second row. During the distillate production optimisation, the product cost increased compared with its optimum minimum value by 1.81%, whereas the GR was reduced by 0.368% and exergy destruction increased by 0.61% compared with their optimum values. In case of the exergy destruction optimisation minimisation, the product cost increased by 2.45%. Figure 7 summarises the results of Table 2. Figure 7 Single-objective optimisation of MSF-BR It is worth noting that during the optimisation of product cost function, the exergy destruction was off-optimal value by 1.05%, which represents the maximum deterioration in the optimum value of exergy destruction among other optimisation cases. Again, during the optimisation of exergy destruction, the product cost was off-optimal value by 2.45%, which is also the highest change in product cost value among other optimisation cases, Table 2. These two findings implied that the product cost and exergy destruction are the most highly competitive objectives among others, the conditions that lead to optimum value for one substantially move the other function off its optimal value. These results indicate the importance of the MOO of MSF-BR desalination system Double-objective optimisation for MSF-BR The MSF-BR system is optimised for two simultaneous objectives, where two individual objectives were aggregated together using normalised weighted-sum method. The weight of each objective was varied in steps to obtain different values of the Pareto optimal front. The aggregated objectives were selected as follows:

16 402 H.K. Abdulrahim and F.N. Alasfour a minimum product cost and exergy destruction (ExD Cst) b maximum production rate and GR (D GR) c minimum product cost and maximum GR (Cst GR). These functions were selected for two reasons: 1 they are highly competing 2 they represent different variants of the aggregation. In the first case, both objectives are to be minimised simultaneously whereas in the second case they have to be maximised and in the last case, one need to be minimised whereas the other one need to be maximised. The AOF was normalised using the optimum value of each individual objective function obtained from single-objective optimisation procedure. The AOF for each case is presented as follows: a ExD Cst ExD Cst AOF = min λ + (1 λ) where λ = 0.25, 0.50, 0.75 (3) b D GR D GR AOF = max λ + (1 λ) where λ = 0.25, 0.50, 0.75 (4) c Cst GR Cst GR AOF = min λ (1 λ) where λ = 0.25, 0.50, (5) The GA code behaviour for double-objective problem is shown in Figure 8, the objective function in that figure refers to equation (3). In this set of double-objective optimisation, the total number of generations used was 30, and maximum population size was 150. GA code converged to the optimum solution in less than 20 generations. Also, the number of fit individuals reached the population size (150 individuals) in generation 20. This behaviour confirms the capability of GA code to solve double-objective problem. Table 3 represents the optimum value of each objective function along with its non-optimum values, which has been obtained during optimising of other AOFs. The change in the optimum values of the individual objective function for different values of weight (λ) has no physical interpretation in this problem; it only reflects

17 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 403 the optimisation preferences. First row of Table 3 shows the optimum value of product cost at different values of weights (λ) during the optimisation of the three AOFs, equations (3) (5). Figure 8 Double-objective optimisation (ExD Cst) of MSF-BR Table 3 Double-objectives optimisation for MSF-BR system Objectives Aggregated function (ExD Cst) (D GR) (Cst GR) λ Cst D GR ExD Figure 9 represents the normalised value of the individual objectives at different values of λ. Results showed that increasing λ increases the value of product cost, since it reduces the weight of the product cost, (1 λ), in the AOF, equation (3). It is worth to note that the optimum value of product cost obtained during this optimisation at λ = 0.25 was $/m 3, which is very close to the optimum value in Table 2, and the corresponding value of exergy destruction was MW, which is only 0.5% higher than the optimum value in Table 2. Comparing the deterioration of the optimum value of the exergy destruction in case of single- and double-objective optimisation for the product cost, it is clear that in case of double-objective optimisation of the ExD and Cst, the deterioration in exergy destruction was only 50% of that in single-objective optimisation case. These findings demonstrate the benefits of MOO of the MSF desalination system.

18 404 H.K. Abdulrahim and F.N. Alasfour Figure 9 Double-objective optimisation (ExD Cst) of MSF-BR Triple-objectives optimisation for MSF-BR The MSF-BR system was optimised using triple objectives aggregated functions. The aggregated objectives were selected as follows: a maximum production rate, minimum product cost and maximum GR (D Cst GR) b maximum production rate, minimum product cost and minimum exergy destruction (D Cst ExD). In case of (D Cst GR), the AOF will be in the following form: D 1 λ Cst 1 λ GR AOF = max λ where λ = 0.2, 0.4, 0.6, 0.8 (6) for case (D Cst ExD), the AOF is D 1 λ Cst 1 λ ExD AOF = max λ where λ = 0.2, 0.4, 0.6, 0.8. (7) One should note that the weights of the second and third terms of the AOF were assumed to be equal for simplification. However, different arbitrary weights can be used. Table 4 shows the results of the individual objectives when performing triple-objective optimisation for MSF-BR system. Two triple objectives aggregated functions were examined, a D Cst GR b D Cst ExD. Each aggregated function was optimised at different weights for each individual objective function.

19 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 405 Table 4 Triple-objective functions optimisation for MSF-BR system AOF D Cst GR D Cst ExD λ Individual objectives Cst D GR ExD The optimisation code showed consistent results at different values of the objective weights. The higher the objective weight the more the objective has been optimised. In case of (D Cst GR), λ represents the weight of the distillate (D), which needs to be maximised. Results showed that as λ increased the optimum value of D increased. Also, as λ increased, the weight of the other objectives is decreased, so they become less optimised, for instance, the value of Cst increased and GR decreased, i.e., less optimum behaviour. As shown in Figure 10, for λ = 0.2 and 0.4, the values of the optimised objectives (D, Cst and GR) are very close to 1.0. This means that they are close to the optimum value, which has been reported in Table 2, at the same time the value of exergy destruction is far from optimal. Increasing λ to 0.8 tends to deteriorate the value of Cst and GR while improving the value of D, since GA code pays more attention to distillate production rather than other objectives. Figure 10 Triple objectives optimisation (D Cst GR) of MSF-BR Optimisation of the second aggregated function, equation (7), is presented in Figure 11. The GA code showed consistent behaviour, as the weight of the objective increased, more optimisation is gained.

20 406 H.K. Abdulrahim and F.N. Alasfour Figure 11 Triple-objectives optimisation (D Cst ExD) of MSF-BR 8.2 Hybrid MSF RO optimisation Single-objective optimisation for hybrid MSF RO The hybrid MSF RO desalination system is optimised for the following objectives: minimum cost, maximum product rate and minimum exergy destruction. The results are shown in Table 5. The decision variables were RO permeate, membrane area, recovery ratio and hybrid plant feed flow rate. Table 5 Optimised objective function Single-objective optimisation for hybrid MSF RO desalination system Cst D ExD $/m 3 % kg/s % kw % Cst D ExD The GA code performance in case of hybrid MSF RO optimisation is shown in Figure 12. The numbers of generation and population size were varied during the optimisation of production rate. It is evident that increasing population size and generation number has great effect on the optimum value. The maximum value of the objective function has been obtained for number of generations between 40 and 50. The number of generations chosen in this case is 50 and population size is 100 individuals. The large number of population is important especially for the very first generations. However, the numbers of fit individuals in the first generations are greater than that of MSF-BR, which implies good performance of the optimisation code.

21 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 407 Figure 12 GA code performance for MSF RO optimisation (see online version for colours) Figure 13 represents the optimisation of single-objective function of hybrid MSF RO desalination system. Results showed that the minimum cost is lower compared with MSF-BR. The hybrid MSF RO plant can produce about double the amount of freshwater, which could be produced from MSF-BR plant, but at a very high cost (more than 175% of the minimum cost) because of the substantial increase in the required membrane area in this case. The highest exergy destruction was adjoining the high product rate owing to the increase in RO exergy destruction. The hybrid MSF RO plant can operate according to different objectives depending on the decision-maker preferences, which could be assisted by optimisation study. Figure 13 Single-objective optimisation of hybrid MSF RO system

22 408 H.K. Abdulrahim and F.N. Alasfour Double-objective optimisation for hybrid MSF RO The main objectives of the proposed hybrid MSF RO system were increasing the production rate and reducing the product cost of existing MSF systems. For this reason, the hybrid MSF RO system was optimised according to the following aggregated function, which combines the product rate with the product cost, equation (8). The optimisation results at different objective weights are shown in Table 6 and Figure 14. D Cst AOF = max λ (1 λ) where λ = 0.25, 0.50, (8) Figure 14 Double-objectives optimisation (D Cst) of hybrid MSF RO system Table 6 Objectives Double-objectives functions optimisation for hybrid MSF RO system AOF D Cst λ D Cst ExD Results show consistent performance of the optimiser, as the weight of each individual function increases its value is more optimised. As shown in Table 6, the product of the plant was increased from kg/s to kg/s when the weight of the product increased from 0.25 to At the same time, the value of the product cost was increased from $/m 3 to $/m 3 since its weight is reduced from 0.75 to The exergy destruction was increased as the product rate increased similar to the case of single-objective optimisation. Comparing the values between Tables 5 and 6, results show that, in case of single-objective optimisation and at the optimum value of the product, D = kg/s, the cost is Cst = $/m 3, while in case of double-objective optimisation for both production rate and product cost, at D = kg/s (at λ = 0.75),

23 MOO of hybrid MSF-RO desalination system using Genetic Algorithm 409 the cost is only $/m 3, which is 33% less. This result shows the benefits of the MOO compared with the single-objective one Triple-objective optimisation for hybrid MSF RO The hybrid MSF RO system was optimised according to triple simultaneous objectives. The individual objectives were the production rate, product cost and exergy destruction. The AOF is presented by equation (9) and the results are shown in Table 7 and Figure 15. The optimised objectives showed a consistent behaviour with the objective weights similar to the previous results. As the weight of the production rate increased, its value is more optimised, i.e., increased. D 1 λ Cst 1 λ ExD AOF = max λ where λ = 0.2, 0.4, 0.6, 0.8. (9) Table 7 Individual objectives Triple-objective functions optimisation for MSF RO system Aggregated function D Cst ExD λ D Cst ExD Figure 15 Triple-objectives optimisation (D Cst ExD) of hybrid MSF RO system Comparing results between Tables 6 and 7, it is worth noting that, at λ = 0.8, the production rate is kg/s, which is higher than the value at λ = 0.75 in Table 6, with exergy destruction is only 26,608 kw, less than the value in Table 6. These results are due to the simultaneous optimisation of production rate, product cost and exergy destruction in Table 7 while in Table 6 the production rate and cost were the objectives.

24 410 H.K. Abdulrahim and F.N. Alasfour 9 Conclusions An MOO study for MSF-BR and hybrid MSF RO desalination systems were performed using GA technique. Four simultaneous objectives have been considered in this research: maximum distillate production, minimum product cost, maximum GR and minimum exergy destruction. Results demonstrated the importance and benefits of using MOO technique for optimising the desalination plants. Single-objective optimisation for MSF-BR improved each objective while deteriorating other ones. Product cost and exergy destruction were the highest competing objectives. MOO, on the other hand, can improve one objective while keeping other ones near to their optimum values depending on the weight of each objective. It is important to mention that the results are highly depending on the process synthesis and the required objectives, so, generalisation of optimised results is not possible. Each system should be treated individually depending on the desired objectives and decision-maker preferences. The GA is an efficient tool to be used in these kinds of studies. The weighted-sum method for MOO showed logical and consistent results. However, other methods for MOO should be used and results should be compared. The following general conclusions can be drawn: 1 GA is a powerful tool for optimising hybrid desalination systems 2 Utilising single-objective function to optimise desalination systems is not a successful method, where number of competing objectives needs to be satisfied simultaneously 3 Weighted-sum is a successful yet simple method to achieve number of simultaneous objectives in desalination systems. References Abdulrahim, H.K. (2006) Multi-Objective Optimization of MSF-RO and MSF-MVC Hybrid Desalination Systems using Genetic Algorithm, PhD Thesis, Cairo University, Egypt. Alasfour, F.N. and Abdulrahim, H.K. (2009) Rigorous steady state modeling of MSF-BR desalination system, J. Desalination and Water Treatment, Vol. 1, pp Alasfour, F.N. and Bin Amer, A.O. (2006) The feasibility of integrating ME-TVC + MEE with azzour south power plant: economic evaluation, J. Desalination, Vol. 197, pp Al-Bastaki, N.M. and Abbas, A. (1999) Modeling an industrial reverse osmosis unit, J. Desalination, Vol. 126, pp Al-Mutaz, I.S. and Al-Ghunaimi, M.A. (2002) Performance of reverse osmosis units at high temperatures, Presented at the IDA World Congress on Desalination and Water Reuse, Bahrain, October, Andersson, J. (2001) Multiobjective Optimization in Engineering Design: Applications to Fluid Power Systems, Linkoping Studies in Science and Technology, Dissertations No. 675, Department of Mechanical Engineering, Linköping University, Sweden. Awerbuch, L. (1997) Power-desalination and the importance of hybrid idea s, IDA World Congress Proceedings, Madrid, pp Charbonneau, P. and Knapp, B. (1995) A User s Guide to PIKAIA 1.0, National Center for Atmospheric Research (NCAR), Technical Note, NCAR/TN-418+IA. Charbonneau, P. (2002) Release Notes for PIKAIA 1.2, National Center for Atmospheric Research (NCAR) Technical Note, NCAR/TN-451+IA.

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