Cost optimization of a combined power and water desalination plant with exergetic, environment and reliability consideration

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ndS. BoxMulti stage ash desalinationReliabilityithn pl, simd aingobjilityoptimization results to improve the products' cost values. The optimization results show that the cost ofl cost impact are reduced by 13.4% and 53.4%, respectively, whereas a 14.8% in-f our litions [1teractioust, theconomDesalination 285 (2012) 123130Contents lists available at SciVerse ScienceDirectDesalinj ourna l homepage: www.e lplay a non-negligible role. A thermoeconomic analysis takes into accountboth fuel and capital costs, and allows determining the product's cost onthe basis of exergy criteria. This requires the determination of a functionalquantitative interdependence between equipment, operations costs andefciency [2,3].Large dual-purpose plants are built to reduce the cost of electricityproduction and freshwater. The dual purpose power desalination plantsmake use of thermal energy extracted or exhausted from power plantsin the form of low-pressure steam to provide heat input to thermal de-main objective of a designer is to dene the optimal plant congura-tion and operative conditions according to specied environmentalconstrains and to the user's requests. Therefore, an integrated designoptimization approach would be preferred to be able to deal with allthese aspects in real and complex energy systems. In order to incor-porate the emission assessment, Environomic is proposed to denotethe combination of Thermodynamic, Economic and Emissions. Manystudies have performed environomic consideration of energy systems[1,913].salinations, like multi-stage ash (MSF) or(MED) systems. Corresponding author. Tel.: +98 21 84063222; fax:E-mail address: amidpour@kntu.ac.ir (M. Amidpour)0011-9164/$ see front matter 2011 Elsevier B.V. Alldoi:10.1016/j.desal.2011.09.043ic and environmental as-uration is not always thel, labor, and energy costsequipment and input energy resources, operation and maintenancecosts), and the effects of undesired uxes to the ambient must beevaluated in order to answer environmental concerns. In fact, thepects of the system. The most efcient congoptimal one in terms of cost, since the capita1. IntroductionEnergy is the most important part ofound everywhere in a variety of applicaa large number and various types of intheir physical boundaries. The designermwhichdeal primarilywith the energetic,the sensitivity analysis shows the relationship between the fuel cost, pollution damage cost and the objectivefunctions. 2011 Elsevier B.V. All rights reserved.fe. The usage of energy is]. Energy systems involvens with systems outsideerefore, facemany issues,Numerous researchers, e.g. [1,48] have conducted exergy andthermoeconomic analyses and optimization for thermal systems.Using the optimization procedure with respect to thermodynamiclaws as well as thermoeconomics then becomes essential [1]. Ther-modynamic laws govern energy conversion processes, costs are in-volved in obtaining the nal products (expenses for the purchase ofmulti-effect distillation To increasesystems, it is imability on the restion of hybridcustomers. Thesystem have alwcan be dealt witSuch links can+98 21 88674748..rights reserved.water productions have not changed much. Additionally,ThermoenvironomicExergy efciencycrease happens in total exergy efciency. Therefore, improvement in all objectives has been achieved usingthe optimization process, although the power andMulti-objective optimization products and environmentaCost optimization of a combined power aenvironment and reliability considerationSeyed Reza Hosseini, Majid Amidpour , Seyed EhsanFaculty of Mechanical EngineeringEnergy Division, K.N. Toosi University of Technology, P.Oa b s t r a c ta r t i c l e i n f oArticle history:Received 26 July 2011Received in revised form 23 September 2011Accepted 29 September 2011Available online 24 October 2011Keywords:Power plantThe present study deals wmulti stage ash desalinatiopects have been consideredalgorithm (MOGA) is applietion is obtained by integratoptimization approach, thisMoreover, equipment reliabwater desalination plant with exergetic,hakib: 19395-1999, No. 15-19, Pardis Str., Mollasadra Ave., Vanak Sq., Tehran 1999 143344, Iranthe multi-objective optimization for designing a combined gas turbine andant. In optimization approach, the exergetic, economic and environmental as-ultaneously. In order to achieve the optimal design, Multi-objective genetics a suitable optimization technique. The thermoenvironomic objective func-the environmental impacts and thermoeconomic objective. By applying theective function is minimized, whereas system exergy efciency is maximized.using the state-space and the continuous Markov method is incorporated inationsev ie r .com/ locate /desa lcompetitiveness and market value of cogenerationportant to analyze the inuence of equipment reli-ulting cost of power and water. So reliability evalua-system is very important to both utilities andreliability and economics of a cogeneration supplyays been conicting parameters. These parametersh by establishing quantitative links between them.best be established by using probabilistic criteriaconsideration are compared and then the sensitivity of fuel cost andenvironmental damage cost on Pareto frontier of optimal solutionare presented.2. Cogeneration cycleFig. 1 illustrates the schematic of the combined GT-MSF system for si-multaneous generation of the electric power and fresh water. Powergeneration cycle includes compressor, combustion chamber and gas tur-bine that have a nominal output power of 65 MW. Also, a heat recoverysteam boiler was used to produce saturated steam of distillation unit. Allparts of systems were modeled and simulated and energy and exergyequations were developed and applied to evaluate performance of com-124 S.R. Hosseini et al. / Desalination 285 (2012) 123130NomenclatureBR Brine circulatingc Unit cost of the exergy rateCC Combustion ChamberCO Carbon monoxideCom CompressorD Distillate Exergy ratee Specic exergyGT Gas turbineHb Brine pool heightHJ Heat Rejectionwhich consider the stochastic nature of component outages, customerdemands, etc. [14]. Many studies have performed reliability modelingof systems [1520].Our previous paper considered the effect of reliability analysis onthe cost of power and water, which is obtained by thermoeconomicanalysis [15]. This paper exhibits the multi objective optimization ofa combined gas turbine and multi stage ash-brine circulating desali-nation plant. The optimization algorithm is applied for minimizingthe total product cost and maximizing overall exergy efciency ofthe dual-purpose plant. Note that the environmental equations ofpollutant gases are included in the cost of products. In addition,according to our previous paper, the equipment reliability consider-ation is incorporated in the optimization results. Finally, the resultsof base case and optimization design with and without reliabilitybined system. Technical characteristics of the proposed plant are shownin Tables 1 and 2. The exergetic, thermoeconomic and reliability analyseswere fully described in our previous paper [15]. Following is a summaryof the thermoeconomic and reliability analysis of the hybrid plant.3. Summary of thermoeconomic and reliability analysisThe cost balance equation of a component of an energy system iswritten as follows:nj1cj Ej k;in ZCIk ZOMk mj1cjEj k;out1where cj is the unit cost of exergy ($/kJ) for the jth stream to/from thecomponent, j is the exergy ow for the jth stream to/from the com-ponent (kW) and ZCIk k and ZOMk ($/s) are the related cost of capital in-HR Heat RecoveryHRSG Heat recovery steam generatorMED Multi Effect EvaporationMOGA Multi objective genetic algorithmMSF Multi Stage FlashN Number of desalination stagesOMC Operating and Maintenance CostP Probability, Pressureppm Parts per millionsPR Performance ratio (the ratio between the mass of theproduced fresh water to that of the consumed steam)TBT Top Brine TemperatureTRR Total Revenue RequirementTur TurbineTN Temperature of rejected brineTpz Adiabatic temperature in the primary zone of combus-tion chamber (K)Vv Vapor allowable velocityWnet Net powerGreek Letters Residence time in the combustion zone Exergetic efciency Equivalent fuelair coefcientiT Gas turbine isentropic efciencyiC Compressor isentropic efciencySubscripts0 Environmental stateCC Combustion Chamberenv EnvironmentF FuelP Producttot Totalvestment and operating and maintenance for the kth componentobtained using the economic model. The economic model is basedon the Total Revenue Requirement (TRR) method (which is basedon procedures adopted by the Electric Power Research Institute) [21].An important method for reliability evaluation in continuous anddiscrete systems is Markov approach modeling. Consider the threecomponents as representing the gas turbine, the heat recoveryFig. 1. Combined gas turbine cycle and desalination. (1,2: Air; 3, 7, 14: Power; 4, 6, 8:combustion products; 5: methane; 9: water; 10: steam; 11, 15: sea water; 12: distil-late; 13: brine).steam generator and multi stage ash desalination which are compo-nents in series. To demonstrate the continuous Markov concepts, astate space diagram was applied to represent system state changes.A state is dened as a particular combination of component operationand failure. Satisfactory operation of combine system is dened asgenerating electricity and water. The failure rate and repair rate as-sumptions of the GT, HRSG, and MSF are shown in Table 3.The product costs with reliability consideration can be obtainedusing the state probabilities as weights for every possible operatingstate [14,15]:Ce iPei Cei 2Table 1Specications of the gas turbine power plant system.Parameter ValueAmbient air temp. 25 CRelative air humidity 60%Compression ratio 11Isentropic efciency of compressor 86%Isentropic efciency of turbine 87%Inlet turbine temp. 1100 CHeat loss in combustion chamber 2%Pressure loss in combustion chamber 5%Inlet HRSG water temp. 25 COutlet HRSG ue gas temp. 160 CNet power output 65 MWThermal efciency of power cycle 29.1%125S.R. Hosseini et al. / Desalination 285 (2012) 123130Cw iPwiCwi : 3Pei is the probability of the state in which the electricity is pro-duced andCei is the cost of electricity production in that state. This ex-pression is used for water production either. As was shown in [15],the effect of the inclusion of equipment reliability is to increase thewater cost due to unexpected equipment downtime resulting fromfailure and subsequent equipment repair.Table 2Specications of the MSF desalination system.Parameter ValueCapacity 42,165 m3/dayNumber of effects 32Temperature of the inlet seawater 25 CTemperature of the rejected brine 40 CTop brine temperature 106 CSalt composition of the inlet seawater 42,000 ppmSalt composition of the outlet brine 70,000 ppmOutside/inside diameters of the HR condenser tubes 34.9/31.6 mmOutside/inside diameters of the HJ condenser tubes 28.5/25.3 mmNumber of tubes in HR section 2403Number of tubes in HJ section 1653Brine velocity in the HR condenser tubes 2.37 m/sBrine velocity in the HJ condenser tubes 2.14 m/sPressure loss in the HR condenser tubes 1146 kPaPressure loss in the HJ condenser tubes 129 kPaTemperature of the inlet steam 143.6 CTotal steam consumption 50.4 kg/sTotal feed seawater 1220 kg/sTotal cooling seawater 589 kg/sTotal brine outlet 732 kg/sDesalination length 132.2 mDesalination width 18 mDesalination height 5 mPerformance ratio 9.7Specic area 333 m2/(kg/s)Total head losses outlet the MSFa 127 mPumping power consumption 4.5 kW h/m3a It is the sum of the following head losses: sea water supply to MSF, saline and cool-ing water rejected to sea, and distillate water transfer to storage tank.4. Environmental considerationThe combustion in a gas turbine is an incomplete process. The ex-haust products mainly are carbon dioxide (CO2), water vapor (H2O),excess atmospheric oxygen (O2) and nitrogen (N2). Carbon dioxideand water vapor have not always been regarded as pollutants becausethey are the natural consequence of complete combustion of a hydro-carbon fuel. However, they both contribute to global warming andcan only be reduced by burning less fuel [22].For a gas turbine engine burning a lean mixture of natural gas andair, the emissions of unburned hydrocarbons (UHC) and sulfur (SOx)are negligibly small and therefore most regulations for stationary gasturbines have been directed at oxides of nitrogen and carbon monox-ides. CO and NOx emissions are the pollutant emissions, and have aharmful effect on human health, as well as the environment [22].A simple model, based on semi-analytical correlations [23], is addedhere to the thermoeconomic model to determine pollutant emissions,which are essential for the setup of an environmental objective function.The adiabatic ame temperature in the primary zone of the combustionchamber is derived from the expression by Glder [24]:Tpz Aexp 2 xyz 4where is a dimensionless pressure p/pref (p being the combustion pres-sure p2, and pref=101,325 Pa); is a dimensionless temperature T/Tref(T being the inlet temperature T2, and Tref=300 K); is the H/C atomicratio (=4, the fuel being pure methane); = for b1 ( being thefuel to air equivalence ratio) and =0.7 for N1. is equivalentfuel to air ratio that is considered equal to 0.64 in this work. Parametersdenoted as x, y, z,, , and can be found in Appendix A.The adiabatic ame temperature is used in the semi-analyticalcorrelations proposed by Rizk and Mongia [23] to determine the pol-lutant emissions in grams per kilogram of fuel:NOx 0:15E160:5e 71100=Tpz p0:053 p3=p3 0:55CO 0:179E9e7800=Tpz p23 p3=p3 0:56where is the residence time in the combustion zone ( is assumedconstant and is equal to 0.002 s); Tpz is the primary zone combustiontemperature; p2 is the combustor inlet pressure; p2=p2 is the non-dimensional pressure drop in the combustor (p2=p2=0.05). Notethat the primary zone temperature is used in the NOx correlation in-stead of the stoichiometric temperature, since the maximum attain-able temperature in premixed ames is Tpz, as pointed out byLefebvre [24].Table 3Reliability assumptions of the hybrid plant.Component Failure per day Repair per dayGT 0.0033 0.03HRSG 0.002 0.19MSF 0.002 0.085. Optimization approachIn order to achieve the optimal parameters, an optimization algo-rithm tool can be used. Although gradient descent methods are themost elegant and precise numerical methods to solve optimizationproblems, however, they have the possibility of being trapped at localoptimum depending on the initial guess of solution. In order to achievea good result, these methods require very good initial guesses forbe introduced as relativeweights of each pollutantmeasure. Theweight-ing criterion may also derive from economic considerations, when theunit damage cost of each pollutant is available. In particular, links maynot exist between the environmental impact and economic objectives(e.g., taxes on pollutant emissions are not imposed in many countries,or, if they are imposed, they are often based on the installed powerand the relationship with the emission rate is not direct). Furthermore,using unit damage costs toweigh the contribution of each pollutant con-sidered in the environmental impact objective function does not affectthe exibility of taking into account pollution costs in the economic ob-jective. In other words, the minimization of the environmental impactremains a distinct objective from the minimization of system total costeven if pollution costs themselves are already included in the economicobjective, as suggested in environomics. As a nal remark, note thatwhen the only pollutant considered is CO2 production, which is directlyproportional to fuel consumption, and in turn depends on the exergeticefciency, the environmental objective does not compete with the ener-126 S.R. Hosseini et al. / Desalination 285 (2012) 123130parameters. Stochastic optimization method such as genetic algorithm(GA) that has been applied for this study seems to be a promising alter-native for solving this problem. The genetic algorithm (GA) is a popula-tion based optimization technique that searches the best solution of agiven problem based on the concepts of natural selection, geneticsand evolution [25]. The search is made starting from an initial popula-tion of individuals, often randomly generated. An individual is consid-ered a possible candidate solution for the optimization problem inhand. At each evolutionary step, individuals are evaluated using an ob-jective function [26]. Three types of operators do the evolution (i.e., thegeneration of a new population): breeding, mutation and selectionwhile selection includes killing a given proportion of the populationbased on probabilistic survival of the ttest. Killed individuals are su-perseded by children, which are created by breeding the remaining in-dividuals in the population. For each child produced, breeding rstrequires probabilistic selection of two parent individuals, getting morechance to choosetter individuals.Mutation allows new areas of the re-sponse surface to be explored by random alterations of optimizationvariables. GA iteratively improved the set of tentative solutions by ap-plying the aforementioned stages to nd a good solution.5.1. Description of the multi-objective optimization algorithmA multi-objective optimization problem requires the simultaneoussatisfaction of a number of different and often conicting objectives.When it is tried to optimize several objectives simultaneously, the searchspace also becomes partially ordered. To gain the optimal solution, therewill be a set of optimal trade-offs between the objectives. Hence, the op-timum solution for multi objective optimization is not necessarilyunique. In a typicalmulti objective optimization problem, the interactionof multiple objectives yields a set of efcient or non-dominated solu-tions, known as Pareto-optimal solutions, which give a decision makermore exibility in the selection of a suitable alternative [27].There are several ways to approach a multi objective optimizationproblem, that all of them focus on the approximation of the Pareto-optimal solutions. For multi objective optimization, evolutionary al-gorithms have been widely used because of their natural propertiessuited for these types of problems. So, in this paper multi objectivegenetic algorithm (MOGA) was applied for nding optimal solution.The ow chart of the GA is shown in Fig. 2. A detailed introductionto evolutionary computation is presented in [2832].5.2. Objective functionsThe three objective functions of the multi-criteria optimizationproblem are the total exergetic efciency (to be maximized), the totalcost rate of products (to beminimized) and the environmental impact(to be minimized). In this research the cost of pollution damage is as-sumed to be added directly to the expenditures that must be paid forproduction of system products. Therefore, the environmental objectivefunction is addedwith thermoeconomic one to form a unique objectiveknown as thermoenvironomic objective in this work. Themathematicalformulation of objective functions is as the following.Exergetic overall EPEF E12 E13 E15E11 W netW pumpsE fuel E17Economic C Ptot C F kZ k C env 8Environmental C env CCOmCO CNOx mNOx 9A single pollutant can be considered in such an environmental im-pact objective according to its degree of harmfulness. If more than onepollution source is taken into account, their degrees of harmfulness cangetic one (exergetic efciency). In this case, the surface of the Paretofront degenerates to the curve of the optimal solutions of the two-objective (energetic and economic) optimization problem [9].In Eq. (9) the associated cost of the environmental impact is con-sidered to be a part of expenditures that should be paid for produc-tion of the system products. Values for the external environmentalcosts (damage cost) are taken from [33]. (CNOx and CCO are equal to4.98 $/kgNOx and 1.68 $/kgCO, respectively).5.3. Decision variablesIn thermal system design and optimization, it is convenient toidentify two types of independent variables. These variables are deci-sion variables and parameters. The decision variables may be variedin optimization process. However, the parameters remain xed in agiven application. All other variables are dependent variables. Theirvalues are calculated from independent variables using thermody-namic relations.The selected decision variables in this work are:The compressor pressure ratio 8P2=P115 10The turbine inlet temperature 900T41300 -C 11Isentropic efficiency of the turbine 0:75iT0:9 12Isentropic efficiency of the compressor 0:75iC0:9 13Number of desalination stages 24N37 14Temperature of rejected brine 30TN50 -C 15Fig. 2. Basic concept of an evolutionary algorithm [1].Top brine temperature 100TBT120 -C 16Inlet steam pressure 300P10800 kPa: 175.4. ConstraintsThe following process limitations are considered in the cogenera-tion plant:6. ResultsAs it was mentioned, multi-objective optimization was performedfor nding minimum total cost rate and maximum overall exergeticefciency of the cogeneration system. The tuning parameters of theoptimization program are presented in Table 4.Fig. 3 is the Pareto optimum frontier in multi-objective optimiza-tion. Selection of the nal solution among optimum points that existon Pareto front needs a process of decision-making. This process ismostly carried out based on engineering experiences and importanceof each objective for decision makers. In fact, in multi-objective opti-mization, all point located on the Pareto front are potentially an opti-mum solution. The selection of the nal optimum point amongavailable solutions depends on importance of each objective for de-signers. The selected optimum in this paper is according the authors'preferences and it might be different in another cases and conditions.Moreover, for each optimum solution on Pareto frontier, it is possibleto dene a weighting coefcient for each objective.According to Fig. 3, it could be observed that, by applying the reli-ability analysis the Pareto front moves to different cost points. Inother words, the total product cost is increased for constant exergyTable 4Tuning parameters in MOGA optimization program.Tuning parameters ValuePopulation size 400Maximum no. of generations 700Minimum function tolerance 1e-5Probability of crossover (%) 80Probability of mutation (%) 1Number of crossover point 2Selection process TournamentTournament size 2127S.R. Hosseini et al. / Desalination 285 (2012) 123130Outlet HRSG flue gas temp: T7N160 -C 18Brine mass flow rate per stage width 200bVbb350 kg=ms 19Brine velocity in condenser tubes Vtubeb3ms20Brine pool height Hbb0:5 21The vapor allowable velocity Vvmax 8ms22Temperature difference perstages Tstage2 -C: 23In addition, it was decided to have the specied production ofpower and water in the optimization approach:Net power production 64:5Wnet65:5 MW 24Desalination capacity 40;000D43;000m3=day: 25Since the amount of power and water production does not changemuch, so it is assumed that the failure and repair rates of componentsremain constant.51005150520052505300ost rate ($/hr)Non reliabilityWith reliability4850490049505000505030.4 30.6 30.8 31Total products cTotal exergyFig. 3. Pareto frontier: best trade off vefciency (As noted, the effect of the inclusion of equipment reliabil-ity is to increase the production costs due to unexpected equipmentdowntime resulting from failure and subsequent equipment repair).In this paper, it is supposed that the total exergy efciency is notless than 31% that this limitation is the designer's criterion for select-ing the optimal point. Thus according to Fig. 3 the selected optimumpoint is chosen for the system with reliability consideration.The amount of objective functions is shown in Fig. 4. As it can beseen, by applying the optimization approach, the cost of productsand environmental cost impact are reduced by 13.4% and 53.4%, re-spectively, despite a 14.8% increase that happened in total exergy ef-ciency. Therefore, improvement in all objectives has been achieved,although the power and water productions have not changed much.Moreover, it should be noted that according to our model, the envi-ronmental cost impact is directly considered in expenditure that mustbe allocated to the production of the system products. Therefore,the total cost rate of system product (thermoenvironomic objective=thermoeconomic objective+environomic objective) after optimizationwill be 5174 $/h.Fig. 5 illustrates the amount of exergy destruction of the systemcomponents for the base case design and optimization approach. Ascan be seen, by using Genetic algorithm the value of exergy destruc-tion of each part is decreased. Note that the maximum and minimumSelected Optimal Point31.2 31.4 31.6 31.8 efficiency (%)alues for the objective functions.27315771499538417901000200030004000500060007000252627282930313233Base case OptimizationTotal products cost rate ($/hr)Total exergy efficiency (%)Total exergy efficiency Environomic objectiveThermoeconomic objectiveFig. 4. Objective functions values for the base case design and optimization.5,95225,628 32,3240,616 28,43280,000Base case Optimization128 S.R. Hosseini et al. / Desalination 285 (2012) 123130761,20930,00040,00050,00060,00070,000gy destruction (kw)values of exergy destruction rate are related to combustion chamberand compressor, respectively.The amount of decision variables, thermoeconomic parametersand specication of gas turbine and desalination plant for base caseand optimal designs are shown in Tables 5 and 6.As can be seen, the total capital investment of desalination plantreduces by 17% although a slight increase happens in the stage4,8575,5694,4504,1572010,00020,000Com CC Tur HRSG MSFExerFig. 5. Exergy destruction of the system for the base case design and optimization.Table 5Decision variables and economic parameters values at the base case and nal selectedoptimum solution of the cogeneration system.Parameters Unit Base case OptimizationDecision variablesP2/P1 11 14.9Tinlet tur. C 100 1255iT % 87 89iC % 86 84N 32 37TN C 40 41TBT C 106 118P10 kPa 400 525Economic parametersCost of electricity with reliability $/kWh 0.0378 0.0344Cost of water with reliability $/m3 1.886 1.655Cost of electricity without reliability $/kWh 0.0363 0.0333Cost of water without reliability $/m3 1.772 1.555Total capital investment of power plant $ 61,573,000 52,985,000Total capital investment of desalination $ 54,123,000 44,878,000Fuel cost of power plant in rst year $ 20,402,000 17,784,000Fuel cost of desalination plant in rst year $ 89,914,000 71,818,000O and M cost of power plant in rst year $ 4,607,600 3,965,000O and M cost of desalination in rst year $ 80,337 66,614Table 6Specication of the gas turbine andMSF-BR desalination plant at the base case and nalselected optimum solution.Parameters Unit Base case OptimizationPower plantNet power Mw 65 64.6Thermal efciency of power cycle % 29.1 33.2Outlet HRSG ue gas temp. C 160 C 160 CAir rate m3/s 213.2 160.8Ambient air temp. C 25 25Relative air humidity % 60 60NOx emission kg/h 1.9 3.9CO emission kg/h 223 95.3DesalinationDesalination capacity m3/day 42,165 40,179Number of tubes in HR section 2403 1947Number of tubes in HJ section 1653 1298Brine velocity in the HR condenser tubes m/s 2.37 2.42Brine velocity in the HJ condenser tubes m/s 2.14 2.08Pressure loss in the HR condenser tubes kPa 1146 1324Pressure loss in the HJ condenser tubes kPa 129 119Temperature of the inlet Steam C 143.6 153.7Total steam consumption kg/s 50.4 42.2Total feed seawater kg/s 1220 1163Total cooling seawater kg/s 589 216Total brine outlet kg/s 732 697Desalination length m 132.2 129.6Desalination height m 5 4.7Performance ratio 9.7 11Specic area m2/(kg/s) 333 328Pumping power consumption kW h/m3 4.5 4.3numbers. Decreasing the capital investment of desalination is becauseof reducing the number of condenser tubes and the specic heattransfer area. On the other hand, by using the optimization approachthe performance ratio and specic electricity consumption of the MSFplant are improved although a slight decrease happens in the desali-nation capacity. Table 6 also indicates that the process of optimizationleads to 14% increases in the thermal power efciency and 8.2% re-duction in the cost of electricity. Note that, by the optimization ap-proach, the CO generation is decreased inasmuch as the NOxemission is increased (fold double), because it is more harmful ascan be seen from the cost for its emission.7. Sensitivity analysisThe purpose of a sensitivity analysis is to study the impacts of im-portant parameters on hybrid plant performance. This analysis whichis performed based on changes in a related parameter as well as someIt was mentioned that multi criteria optimization approach, whichis a general form of single objective optimization, enables us to con-sider various and ever competitive objectives. The optimization re-sults showed that by applying the reliability analysis, the Paretofront approaches to different cost points. It means that the total costof product increases for specied exergy efciency. So, introductionof reliability leads to the higher product costs due to reduced plantuptime. In addition, the process of optimization leads to 53.4% and13.4% reduction in the environmental cost impact and the cost rateof system product, respectively. Moreover, the total exergy efciencywas increased by 14.8%, whereas the power and water productionswould not change much (electricity production being less than0.76% and for water production being less than 5.1%). Eventually, sen-sitivity analysis was shown that in comparison with the fuel cost, theenvironment damage cost has a little inuence on the total productcost rate.Appendix A. (Adiabatic ame temperature constants)Following are the constants of the adiabatic ame temperatureequation:x, y and z are quadratic functions of in accordance withthe following equations [24]:x a1 b1 c12 A:1y a2 b2 c22 A:2z a3 b3 c32: A:3The constants in equations (A.1)(A.3) are given in Table A.1.rgyuel=ox=O=Table A.1Constants for equations (A.1)(A.3) [22].129S.R. Hosseini et al. / Desalination 285 (2012) 123130other modeling parameters help us to predict the results while somemodications are necessary in modeling.Fig. 6 shows the sensitivity of the Pareto optimal Frontier to the spe-cic fuel cost (which increases by 50%) and specic environment dam-age cost (which increases by 50%) of the system. This gure shows thatthe Pareto Frontier shifts upward since the specic fuel cost increases.Further, at the constant exergy efciency by increasing the fuel cost,the total cost rate of product increases since the fuel price plays a sig-nicant role in this objective function. As can be seen, by increasingthe specic environment cost, the Pareto Frontier shifts a little upward.It means that in comparison with the fuel cost, the pollution damagecost has a slight inuence on the total product cost rate.8. ConclusionIn this paper, multi-objective optimization for designing a combinedgas turbine andmulti stageash desalination plantwas investigated. Theproposedmethod covered exergetic, economical, environmental and re-liability aspects of the system design and the component selection. Forthe optimization procedure, evolutionary algorithm (i.e. genetic algo-rithm) was utilized for multi-objective optimization of the cogenerationplant. Moreover, the needs to quantify the environmental impacts leadto the introduction of pollution-related costs in our economic objectivefunction. The thermoeconomic model was developed based on theexergy and economics analysis. The new environmental costing functionwas merged in thermoeconomic objective and a new thermoenviro-nomic function was obtained. By applying genetic algorithm, this objec-tive function was minimized, whereas system exergy efciency wasmaximized. Furthermore, equipment reliability using the state-spaceand the continuous Markov method was incorporated in optimizationresults to improve the product cost values.5000550060006500700030.6 30.8 31Total cost rate of products ($/hr)Total exec-Fuel=3.7 $/Gjc_Nox=4.98 $/kgc_CO=1.68 $/kg c-Fc_Nc_CFig. 6. Sensitivity of Pareto optimum solution to th31.2 31.4 31.6 efficiency (%)5.55 $/Gj4.98 $/kg1.68 $/kg c-Fuel=3.7 $/Gjc_Nox=7.47 $/kgc_CO=2.52 $/kg Constants 0.31.0 1.01.60.922.0 2.03.2 0.922.0 2.03.2A 2361.7644 2315.7520 916.8261 1246.1778 0.1157 0.0493 0.2885 0.3819 0.9489 1.1141 0.1456 0.3479 1.0976 1.1807 3.2771 2.0365a1 0.0143 0.0106 0.0311 0.0361b1 0.0553 0.0450 0.0780 0.0850c1 0.0526 0.0482 0.0497 0.0517a2 0.3955 0.5688 0.0254 0.0097b2 0.4417 0.5500 0.2602 0.5020c2 0.1410 0.1319 0.1318 0.2471a3 0.0052 0.0108 0.0042 0.0170b3 0.1289 0.1291 0.1781 0.1894c3 0.0827 0.0848 0.0980 0.1037e specic fuel cost and pollution damage cost.References[1] P. Ahmadi, A. Almasi, M. Shahriyari, I. Dincer, Multi-objective optimization of acombined heat and power (CHP) system for heating purpose in a paper millusing evolutionary algorithm, Energy Research 12 (35) (2011).[2] Y. Sanjay, O. Singh, B.N. Prasad, Energy and exergy analysis of steam cooled reheatgassteam combined cycle, Appl. Therm. 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