Thermoeconomic analysis and multiobjective optimization of a combined gas turbine, steam, and organic Rankine cycle

Transcription

1 Received: 13 April 2018 Revised: 13 July 2018 DOI: /ese3.227 Accepted: 18 July 2018 RESEARCH ARTICLE Thermoeconomic analysis and multiobjective optimization of a combined gas turbine, steam, and organic Rankine cycle Amin Mohammadi 1 Milad Ashouri 2 Mohammad Hossein Ahmadi 3 Mokhtar Bidi 1 Milad Sadeghzadeh 4 Tingzhen Ming 5 1 Mechanical and Energy Department, Shahid Beheshti University, Tehran, Iran 2 Faculty of Engineering and Computer Sciences ENCS, Concordia University, Montreal, Quebec, Canada 3 Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran 4 Department of Renewable Energies and Environmental Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran 5 School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, China Correspondence: Mohammad Hossein Ahmadi, Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran mhosein. ahmadi@shahroodut.ac.ir, mohammadhosein.ahmadi@gmail.com and Tingzhen Ming, School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, China tzming@ whut.edu.cn. Abstract Because of the fossil fuels crisis in recent years, efficient working of power producing cycles has gained considerable importance. This study presents a detailed exergoeconomic analysis of a proposed combination of a gas turbine GT, a steam Rankine cycle SRC, and an organic Rankine cycle ORC, which are coupled together to obtain the maximum heat recovery of the GT exhaust gas. The proposed cycle was analyzed from both thermodynamic and economic viewpoints. The exergy efficiency and product cost rate of the introduced cycle were optimized simultaneously using multiobjective optimization with seven decision variables, including steam turbine inlet pressure and temperature, ORC turbine inlet pressure, ORC and steam turbine back pressures, and pinch point of heat exchangers. Sensitivity analysis revealed that the steam turbine back pressure and inlet pressure had the highest impact on product cost rate and exergy efficiency, followed by ORC turbine inlet pressure and back pressure. Also, the exergoeconomic analysis showed that the combustion chamber had the highest sum of exergy destruction costs and investment costs; more attention should thus be paid to its design procedure. Under the design conditions, the exergy efficiency of 40.75% and product cost rate of 439 million $/year could be achieved. KEYWORDS exergoeconomic, gas turbine, optimization, organic Rankine cycle, steam turbine Funding information National Natural Science Foundation of China, Grant/Award Number: ; Hubei Provincial Natural Science Foundation of China, Grant/Award Number: 2018CFA029; Key Project of ESI Discipline Development of Wuhan University of Technology, Grant/Award Number: ; Scientific Research Foundation of Wuhan University of Technology, Grant/Award Number: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited The Authors. Energy Science & Engineering published by the Society of Chemical Industry and John Wiley & Sons Ltd. 506 wileyonlinelibrary.com/journal/ese3 Energy Sci Eng. 2018;6:

2 1 INTRODUCTION With increasing fossil fuel consumption and the oil crisis, energy efficiency is becoming a major concern of the 21st century. Therefore, many attempts are being focused on maximizing the efficiency of fossil fuel- based electricity generation. One of the most common engines to convert fossil fuels to electricity is the gas turbine, which is readily available compared to other devices and can produce electricity in high amounts up to 500 MWe. However, the gas turbine usually has low fuel- to- electricity efficiency, around 30%. Combined cycles have been introduced to overcome this problem by utilizing the high temperature of the turbine exhaust gas and increasing the overall efficiency. Heat recovery steam generators HRSG are usually used to recover the exhaust gas heat and boost up the efficiency. Different schematics of HRSGs including single pressure, double pressure, and triple pressure are introduced and being investigated by several authors. Tajik Mansouri et al 1 compared the effect of HRSG configurations on the overall performance of the system using exergetic and economic analyses. Liszka et al 2 proposed to integrate a gas turbine using a low Btu cold fuel with a CHP plant. A thermoeconomic comparison between single- pressure and multipressure HRSG systems showed the latter to be a viable opportunity for increasing the efficiency. Benato et al 3 performed a comparison between two dynamic models of a single- pressure combined cycle power plants. The authors simulated the plant s operational status vs time to examine the effects of transient behavior on the system. It was demonstrated that the size of devices such as heat exchangers and pipes caused thermal inertia, which would result in a delay in system response. Gogoi et al 4 integrated a solid oxide fuel cell SOFC with a combined gas turbine and steam turbine power plant and performed a detailed exergy and energy analysis on the mentioned system. The exhaust gas provided heat for preheating the air and fuel of the SOFC system and also the subsequent single- pressure HRSG system. It was monitored that higher performance was achieved in higher pressure ratios of the compressor. Amirante et al 5 presented two micro combined cycle power plants using biomass. The low- quality biofuel was used to run a combustion chamber to provide the required heat of the gas turbine and the bottoming HRSG plant. The optimization procedure was done to find the balance point between electrical and thermal efficiencies. The system was capable of generating 50 kw electricity with 50% thermal efficiency. Soltani et al 6 performed a detailed exergy and economic analysis on a hybrid solar cogeneration cycle and optimized the plant through a genetic algorithm. This hybridization method resulted in a 48% reduction in fossil fuel consumption and also decreased the chemical exergy destruction of the plant. Carapellucci et al 7 evaluated the feasibility study of integrating a reheat gas turbine with a methane steam reformer. It was 507 demonstrated that a dual pressure reformer gives a proper performance for steam management. This method considerably augmented the efficiency of the integrated turbine 53.8% in comparison to a stand- alone gas turbine 38.3%. Exergy analysis combined with economic analysis is a powerful means to evaluate the system performance; it is also widely used for optimization purposes. Vandani et al 8 carried out an exergy analysis and an optimization on a boiler blowdown heat recovery system in a steam power plant. A flash tank was employed to recover the heat. Ashouri et al 9 modeled a Kalina cycle which used solar energy as its heat source and performed exergy and economic analysis. The daily mean sun- to- electricity exergy efficiency was 5.24%, and levelized cost of electricity was $/kwh. Also, it was shown that the variation in ammonia mass fraction had the greatest effects on exergy efficiency, solar fraction, and levelized cost of electricity. In another work, Ashouri et al 10 also conducted a thermodynamic and economic evaluation of a small- scale organic Rankine cycle coupled with a solar collector. Different working fluids were examined. It was concluded that, under the design conditions, benzene had the highest energy efficiency despite slightly increased costs, which were mainly due to its higher performance under high pressures and temperatures. Tsibulskiy et al 11 investigated the potential of low boiling fluids to be employed as a working fluid in the organic Rankine cycle ORC combined cycle gas turbine. The study was designed to find the best fluid regarding thermodynamic performance, thermophysical, and ecological properties. Among the several examined fluids, such as butane, pentane, R236ea, R123, R245ca, R245fa, R365mfc, and RC318, pentane and R365mfc provided the highest thermal net efficiency. It was reported that between thermophysical properties, the condensation temperature highly affected the net thermal efficiency. Nazari et al 12 studied the combination of an organic cycle and a gas turbine to recover the unexploited heat of the gas turbine. The proposed structure consisted of a subcritical steam Rankine cycle and a transcritical ORC. The thermodynamic performance and the exergoeconomic evaluation were assessed by considering R124, R152a, and R134a as the working fluids for the investigated system. Among them, R152a showed the best performance from the thermodynamic and economic aspects of the proposed system, which was optimized through a genetic algorithm. Khalijani et al 13 analyzed a CHP power plant from energy, exergy, and exergoeconomic viewpoints. The introduced CHP structure included a gas turbine and an ORC through a single- pressure heat recovery steam generator. It was reported that increasing the pressure ratio and the isentropic efficiency of both air compressor and gas turbine could enhance the system performance, whereas raising the mentioned parameters highly affected the total cost rate. Mohammadi and McGowan 14 studied different available possible integration

3 508 methods for cogeneration of power and fresh water or power and cooling, and trigeneration of power, cooling, and fresh water. The studied system composed of a steam regenerative Rankine cycle with condensation and steam extractions, driven by a concentrated solar tower. It was concluded that steam extraction with a lower temperature and pressure could improve the system efficiency, whereas the best trigeneration structure could be the combination of a multieffect desalination and a single- effect absorption cooling unit with a Rankine cycle. In recent years, more efficient technologies have been introduced to increase the use of low- grade heat. Among these, some thermodynamic cycles, such as ORC, Kalina cycle, and transcritical CO 2 power cycles, have drawn much attention. Numerous studies investigated these thermodynamic cycles for power generation, 15 showing that combined cycles have the best energetic performance. Rayegan et al 16 developed a procedure to select the working fluids used in solar ORCs and found that eleven working fluids are recommended for low- or medium- temperature systems. Wang et al 17 conducted a comparative study of pure and zeotropic mixtures in low- temperature solar ORC and expressed that the zeotropic mixtures had the potential to improve the overall system performance. Torres et al 18 carried out a theoretical analysis of a low- temperature solar ORC. The overall efficiency of the solar ORC and its optimization with different collector types and working fluids were explored, and the influences of the regeneration process and cycle configuration on its performance were examined. Wang et al 19 performed an analysis and optimization of an ORC using steam at 150 C and optimized the cycle considering total capital cost and exergy efficiency using a genetic algorithm. Song et al 20 conducted a detailed thermodynamic analysis of a transcritical CO 2 power cycle using a low- grade heat source of flat plate solar collector, and the liquefied natural gas as the heat sink. The results showed a good capability of the CO 2 cycle to use the low- temperature water to produce electricity. The system operated at the turbine inlet temperature of 65 C and obtained an efficiency of 6%. Al- Sulaiman 21 performed a detailed exergy analysis of a solar thermal power plant based on the conventional Rankine cycle and a bottoming binary ORC cycle, which showed that the binary cycle outperformed the conventional steam Rankine cycle. Yari et al 22 performed an exergoeconomic comparison between the Kalina cycle, ORC, and Trilateral Rankine cycle TLC at 120 C with water as the heat source. It was shown that optimum design parameters for maximum power generation differed from that for minimum product costs. Also, the turbine inlet temperature increased the net generated power and decreased the product cost for the TLC system, but not for the ORC system. Boyaghchi and Heidarnejad 23 proposed a micro CCHP system composed of solar collectors and ORC and performed an exergoeconomic optimization on the mentioned system. All these studies show that there is a good opportunity to use bottoming cycles to boost the efficiency and increase the use of low- grade heat to reduce the thermal losses. Certain combined gas turbine plants use only a singlepressure HRSG, which has lower efficiency compared to double- or triple- pressure ones; also, their exhaust gases are of high value and can be used more with bottoming cycles. However, substituting these plants with double- or triplepressure HRSG systems may impose high costs on the owners. One way to boost the efficiency of these plants without imposing high costs is to couple a bottoming cycle to a single- pressure HRSG system. This way, the system will be more efficient by using the total possible energy content of flue gases. As it appears from the literature, it is also advantageous to combine a single- pressure HRSG system with an organic Rankine system. Thus, the system efficiency is raised up dramatically due to further utilization of the available heat, whereas the simplicity of the system is still maintained compared to a multipressure HRSG system. In this study, a combined single- pressure HRSG was coupled with an ORC to increase the total efficiency of the system by employing the highest possible heat recovery from the exhausted flue gases. The feasibility of the proposed system was assessed from both economic and thermodynamic aspects. The ORC was utilized instead of a multipressure HRSG system to increase the thermal efficiency of the plant. Exergy analysis has been performed to find the main sources of destruction and to possibly further improve the system s efficiency. Also, using exergoeconomic criterion, the system status was evaluated in detail regarding exergetic and economic criteria. A detailed parametric study was done to uncover the effects of key parameters on the system performance. The investigated parameters were the turbine inlet pressure and temperature, pinch point temperature difference, and turbine back pressure. Also, the system has been optimized regarding exergy efficiency and product cost rate by applying a genetic algorithm. This paper gives the reader an insight into the positive effects of adding an ORC bottoming cycle to an existing single- pressure HRSG system. 2 SYSTEM DESCRIPTION In many cases, a single- pressure HRSG is used to produce the steam. This equipment uses the hot outlet flue gas of the gas turbine to produce steam. Since the HRSG operates at just one pressure level, it is not capable of using the whole available energy. Therefore, some of the energy is wasted undesirably. Usually, the temperature of the outlet flue gas of single- pressure HRSG is lower than 300 C. Thus, it is better to use a low- temperature ORC cycle to recover the wasted energy; the new configuration that can achieve this is proposed in Figure 1. The proposed structure is a combination of

4 three different cycles. In the first part, the air flows through the compressor and expands in the turbine to generate power after the combustion process. The hot outlet flue gas is used in an HRSG to produce the steam for a steam turbine. Then, the flue gas again flows through a series of heat exchangers and its heat is utilized in an ORC cycle. For better performance, a regenerative ORC is selected, in which the outlet stream of the turbine is used to preheat the organic fluid benzene in this case before entering into the heat exchangers. 3 MATHEMATICAL MODEL The plant was modeled in Matlab software to analyze the system s performance, and thermodynamic and economic relations were applied to each component. The Reference Fluid Thermodynamic and Transport Properties Database REFPROP was used to calculate the physical properties of working fluids. 24 After calculating the thermodynamic parameters including temperature, pressure, enthalpy, entropy, and mass flow rate, exergy of each stream was calculated. Then, by using the economic relations, the exergoeconomic analysis was performed, and the product and fuel cost of each component was computed. Some assumptions were made to simplify the analysis, as follows: The system is working under a steady-state condition. Air and flue gases are assumed to be ideal gas mixtures. Air is assumed to consist of 79% N 2 and 21% O 2. Natural gas is used in the combustion chamber as fuel. All components are assumed to be adiabatic. The allowable temperature rise of cooling water in the condenser is assumed to be 10 C. Ambient temperature is 20 C and pressure is bar. 3.1 Energy analysis As mentioned before, the whole plant consisted of three sections, including Brayton, Rankine, and ORC cycles. Thermodynamic relations for each section were as follows: Brayton cycle The air enters the compressor at ambient condition. The outlet temperature of the compressor is calculated as follows: T 2 = T η comp where η comp, r p, and γ a are the efficiency of the used compressor, the compressor pressure ratio, and the specific heat ratio of air, respectively. r γ a 1 γa p The following equation was used to compute the power needed by the compressor: Ẇ comp = ṁ a C pa T2 T 1 2 Here, Ẇ comp is the required work for compression stage, ṁ a is the mass flow rate of the flowing air, and C pa indicates the thermal- specific heat of the air. Since the air is regarded as an ideal gas, its specific heat is only a function of temperature and obtained as follows 25 : C pa T = T 5.49T T T The cycle is working under steady state and full load condition; therefore, the turbine inlet temperature TIT is constant. The specific heat of the turbine inlet could be calculated using the following equation 25 : 6.997T 2.712T T 3 C pg T = The mass flow rate of the fuel is computed through the energy balance equation for the combustion chamber: ṁ a C pa T 2 +ṁ f LHV = ṁ g C pg T η CC ṁf LHV In Equation 5, ṁ f is the mass flow rate of the used fuel in the combustion chamber and LHV is the associated lower heating value. The efficiency of the combustion chamber is expressed as η CC. ṁ g and C pg represent the mass flow rates of the flue gas and its thermal- specific heat, respectively. Also, a pressure drop is considered in the combustion chamber ΔP CC and the pressure of the outlet stream is obtained as follows: P 3 = P 2 1 ΔPCC 6 Using the inlet temperature of the turbine T 3, its isentropic efficiency η GT, specific heat ratio γ g, and pressure ratio P 3 P 4, the outlet temperature of the turbine, T 4, is obtained as: T 4 = T 3 1 η GT 1 P3 The generated power of the turbine is calculated as follows: Ẇ GT = ṁ g C pg T3 T 4 8 P 4 1 γ g γ g

5 CC Comp GT Tur Sup Eva Eco HX HRSG Tur ORC ST SRC Cond Rec Pump 24 Cond 25 Pump Water out Water in Water out Water in FIGURE 1 Proposed combined gas turbine, steam, and organic Rankine cycle In which ṁ g is the mass flow rate of the flue gas which is the sum of the air mass flow and fuel mass flow, C pg is its associated thermal- specific heat, and Ẇ GT denotes the resulted power from the gas turbine. Total generated power of the Brayton cycle can be expressed as: Ẇ Brayton = Ẇ GT Ẇ comp Steam Rankine cycle To calculate the mass flow rate of the steam produced by the HRSG, a set of equations should be applied. The temperature changes in both flue gas and steam in different sections of the HRSG are shown in Figure 2. Thermodynamic parameters of the inlet flue gas to the HRSG are known from the previous section. By applying the 9 following equations, the total mass flow rate of the produced steam could be calculated: ṁ g C pg T4 T 5 = ṁs h11 h 10 ṁ g C pg T5 T 6 = ṁs h10 h 9 ṁ g C pg T6 T 7 = ṁs h9 h h 8 - h 11 express the amount of enthalpy through stages 8 to 11. Total power generated by the Rankine cycle is computed as: Ẇ Rankine = Ẇ ST Ẇ pump 13

6 where Ẇ ST and Ẇ pump are the output power rate of the steam turbine and the demanded work at pumps ORC cycle Like the HRSG in the steam Rankine cycle, a set of equations should be solved to calculate the produced mass flow rate of the heat exchanger in the ORC cycle. It should be noted that the temperatures of inlet flue gas and outlet organic fluid are related using the following equation see Figure 1: Power produced by the ORC cycle is obtained as: And the net generated power by the plant is calculated as: The constant parameters used in the simulation of the plant are represented in Table Exergy analysis T 20 = T 17 pinch ORC Ẇ ORC = Ẇ Tur Ẇ pump Ẇ net = Ẇ Bryton +Ẇ Rankine +Ẇ ORC Exergy balance for a control volume is represented as 26 : Ė Q + ṁ i e i = Ė W + ṁ o e o +Ė D 17 where subscripts i and o are the representative of inlet and outlet streams of the control volume, respectively, and Ė D is the exergy destruction rate. Other parameters are defined as follows: Ė Q = 1 T 0 Q T r 18 Ė W = Ẇ Ė Q, Ė W, T 0 and T r are defined as the exergy amounts associated to the heat rate of Q, the exergy of the consumed or produced work, Ẇ, the ambient temperature, and the temperature of the heat source of Q, respectively. In this case, the terms of kinetic and potential exergies can be neglected. So, the specific exergy, e, is calculated as follows: e = e ph +e ch The physical exergy, e ph, is obtained as follows: e ph = h h 0 T0 s s0 h h0 and s s0 state the variation of enthalpy and entropy from the referenced state, respectively Pinch HRSG 10 L 10 g Pinch HX 21 L g 19 FIGURE 2 HX Temperature profile in steam HRSG Economizer Evaporator Superheater

7 512 And the chemical exergy, e ch, is computed as: TABLE 1 Input parameters for the combined plant e ch = y i e ch i +RT 0 yi ln y i where y i is the molar fraction, and R is the universal constant of gases. To simplify the calculation of chemical exergy of fuels e fuel, the following relation is used 27 : e fuel = ξ LHV where ξ is a constant- specific parameter for different fuels and is close to unity and LHV is the lower heating value of the fuel. For example, ξ CH4 = After calculating all the parameters in the equation 17, the exergy destruction of each component could be computed. Table 2 shows the exergy destruction and exergy efficiency equations of all components in the proposed plant. 3.3 Exergoeconomic analysis Exergoeconomics is the branch of engineering that appropriately combines, at the level of system components, thermodynamic evaluations based on an exergy analysis and economic principles. It provides useful information in design and operation of a cost- effective system when the desired answer is not achievable by conventional energy and exergy analyses and economic analysis. 28 Defining the concepts of fuel and product is essential to perform the exergoeconomic analysis. Both of these concepts are expressed regarding exergy. The fuel is defined as the source that is consumed to generate the products and is different from actual fuel such as natural gas and diesel that is used in the plant. The product is the desired result generated by using the fuel. In exergoeconomics, a parameter called flow cost rate is attributed to each stream, Ċ. Cost balance for a control volume is defined as follows: Ċ Q + Ċ i +Ż = Ċ W + Ċ o Ċ = cė In equation 24, parameter Ż is the investment cost rate which is computed as 29 : Ż = Z.CRF.φ H 26 CRF is the Capital Recovery Factor, which is defined as follows: CRF = i1+in 1+i N 1 27 In the above equations, Z is the purchased cost, and CRF stands for capital recovery factor. φ is the maintenance factor Parameter and is equal to H denotes the total annual working hours of the plant and is assumed to be 7446 hours. i denotes the annual interest rate and N specifies the lifetime of the plant. The investment cost of each component is obtained based on thermodynamic parameters by using the equations in Table 3. 23,29 It should be noted that the components of HRSG in the Rankine cycle are considered separately. The logarithmic mean temperature difference LMTD approach is utilized to calculate the required area of each component A in the HRSG: A = 28 where Q is the transferred heat, and U states the overall heat transfer coefficient. As shown in Table 4, 30 the total heat transfer coefficients of the economizer, evaporator, and superheater are assumed to be constant. The equations used to estimate the capital cost of different components are published in different years. Therefore, they should bring to a reference year to perform the economic analysis more accurately. This procedure is performed using the Chemical Engineering Plant Cost Index CEPCI 31 to convert all costs to the year The cost balance and auxiliary equations of each component are described in Table 5. Q UΔT LMTD Value Brayton cycle Compressor mass flow [kg/s] 500 η comp 0.85 r P 12 PD CC [%] 4 η CC 0.95 η GT 0.88 TIT [ C] 900 LHV [kj/kg] Rankine cycle Pinch [ C] 10 Steam Turbine inlet temperature[ C] 430 Steam Turbine inlet pressure [bar] 80 η ST 0.85 Condenser pressure [bar] 0.1 η pump 0.8 ORC cycle Turbine inlet pressure [bar] Turbine outlet pressure [bar] Pinch [ C] 5 Pinch of Recuperator [ C] 5

8 TABLE 2 Exergy destruction and exergy efficiency equations of all components Component Exergy destruction Exergy efficiency Compressor Combustion chamber Ė D comp = Ex in Ex out +Ẇ AC Ė D CC = Ex in + Ex fuel Ex out ψ CC = ψ comp = Ex out Ex in Ẇ comp Ex out Ex in + Ex fuel 513 Gas turbine HRSG Steam turbine Condenser Pump Ė D GT = Ex in Ex out Ẇ GT ψ GT = Ė D HRSG = Ex in Ex out Ė D ST = Ex in Ex out Ẇ ST ψ ST = Ė D cond = Ex in Ex out Ė D pump = Ex in Ex out +Ẇ Pump Ẇ GT Ex in Ex out Ex ψhrsg = s,e Ex s,i Ex g,e Ex g,i Ẇ ST Ex in Ex out Ex ψcond = 1 D,Cond Ex in ψ Pump = Ex out Ex in Ẇ Pump For comparison of the exergoeconomic performance of the system s components, several parameters such as average cost per unit exergy of fuel c F,k and product c P,k are defined as follows: c F,k = c P,k = Ċ F,k Ė F,k Ċ P,k Ė P,k In line with the equations 29 and 30, the relative cost difference of a component is defined as: r k = c P,k c F,k c F,k This parameter r k the relative cost difference of component k shows the difference between the average cost of products c P,k and fuels c F,k, which is due to the destruction and the investment cost. Also, cost flow rates associated with the exergy destruction and the exergoeconomic factor are expressed as follows: Ċ D,k = c F,k Ė D k f k = 33 Ż k +Ċ D,k Ċ D,k is defined as the cost associated to the exergy destruction of Ė D k. Ż k is the capital investment cost flow rate of the component k. f k denotes the exergoeconomic factor. The exergoeconomic factor states the relative importance of a component cost to the cost of exergy destruction and the loss associated with that component OPTIMIZATION Genetic Algorithm GA is an evolutionary algorithm developed by Holland 32 in The basic idea of GA is Darwin s Ż k theory, which states that the chance of surviving of the fittest ones is the highest. Genetic Algorithm can handle the nonlinear problems and therefore is a good choice to perform on the engineering optimization problems. To perform the optimization, GA produces random binary numbers for each decision variable, called chromosomes. The goal is to minimize the objective function by selecting the best value for each decision variable; thus, to maximize the objective function, the negative form of the objective function should be used. The generated chromosomes constitute the first generation. The next generation is produced by applying the crossover and mutation operators on the selected chromosomes. Chromosome selection is based on the fitness values, which are somehow related to the objective function. Crossover operator combines the selected chromosomes called parents to produce the next chromosomes called children. Also, the mutation operator changes one or more genes of a chromosome to maintain the diversity. In this way, completely different chromosomes are produced to help the GA avoid the local minima. Generation production is continued until a chromosome dominates the other individuals in the population, which means that the algorithm reached convergence and the dominated chromosome is the optimum solution. More details about Genetic Algorithm are explained in Ref RESULTS AND DISCUSSION The results of energy and exergy analyses of the proposed system are shown in Figure 1, and the state points for the base case are shown in Table 6. It should be highlighted that states 14 and 27 are assumed in ambient temperature and pressure, and thus the specific exergy of these states equals zero. The system exergy efficiency was 41.23%, and the product cost rate for the base case was million $/year. The detailed exergoeconomic parameters are described in Table 7. According to the exergoeconomic criteria, more attention should be paid to the components with higher Ż +Ċ D

9 514 Component Compressor Z comp = 71.1ṁ a r p lnr p 0.9 η comp TABLE 3 component Investment cost of each Combustion chamber Gas turbine Economizer Evaporator Superheater Steam turbine Z CC = 46.08ṁ a1+exp0.018t P 3 P 2 Z GT = ṁ g ln P3 1+exp0.036T3 P η GT Z eco = 45.7 A eco Z eva = 34.9 A eva Z sup = 96.2 A sup Z ST = Ẇ 0.7 ST exp 1 η ST T Condenser Z cond = 1773ṁ CW Pump Z pump = Ẇ pump η pump ORC Heat recovery 0.78 AHX Z HX = ORC Turbine log Z tur = log Ẇ tur log Ẇtur 2 and Ė D in designing a new system. As it is shown in Table 7, gas turbine components combustion chamber, compressor, and gas turbine have the highest exergy destruction and the sum of Ż +Ċ D. This is due to the chemical reactions and high temperature difference in the combustion process; a more complete reaction is required to reduce these effects. In addition, a high isentropic efficiency of the gas turbine plays an important role in reducing the exergy destruction. Therefore, the gas turbine components compressor, combustion chamber, and gas turbine should be designed carefully. For example, the exergy destruction in the combustion chamber could be avoided by preheating the inlet air and fuel and reducing the heat loss and also introducing excess air to the combustion chamber. The highest value of exergy destruction in bottoming cycles, including SRC and ORC, belongs to the steam turbine, superheater, and steam cycle condenser. It is worth mentioning that the same sequence regarding Ż +Ċ D occurs in all components except for the condenser, which has a higher value than the superheater. This is mainly due to the higher capital cost of the condenser. The large value of factor f for the ORC condenser suggests that its capital investment and operation and maintenance O&M costs is dominant. Moreover, the amount of cost difference, r, is relatively high for the ORC condenser. Thus, decreasing the amount of Ż for the ORC condenser would result in improving the cost effectiveness of the entire system. This can be achieved by lowering the mass flow rate of water which is applicable when water at a lower temperature is available. The evaporator has the lowest r value in comparison to other components. As the f value indicates, almost 80% of the relative cost difference is caused by exergy destruction. Thus, a decrease in exergy destruction of the evaporator could be cost- effective for the entire system, although this would increase the investment costs associated with this component TABLE 4 Component Total heat transfer coefficient for HRSG component Economizer 42.6 Evaporator 43.7 Superheater 50 Total heat transfer coefficient U [W/mK] Ż. On the other hand, the maximum value of r occurs in the ORC heat exchanger. This parameter indicates that exergy destruction and cost of the ORC heat exchanger are high and can be improved. Also, a relatively low value for f states that the exergy destruction of the ORC heat exchanger contributes more to the increase in r. This can be achieved through using more efficient heat exchangers with lower minimum pinch temperature for instance, flat plate heat exchangers. Although this leads to a higher capital cost of the plant, it reduces the amount of exergy destruction based on the low value of f, which is highly beneficial and effective for the overall performance. Other detailed parameters for each component of the entire system are shown in Table 7. The effect of key parameters on the system performance is demonstrated in Figures Effect of turbine inlet temperature The effect of variation in steam turbine inlet temperature is illustrated in Figure 3. As it is known, increasing the turbine inlet temperature causes the enthalpy difference across the turbine to rise. With increasing enthalpy difference, the energy balance of the system requires a reduction in the mass flow rate of the produced steam. The net effect is decreasing

10 TABLE 5 Cost balance and auxiliary equations of each component Component Cost rate balance Auxiliary equation Compressor Ċ 1 +Ċ W,comp +Ż comp = Ċ 2 Ċ 1 = Combustion chamber Ċ 2 +Ċ fuel +Ż CC = Ċ 3 Gas turbine Ċ 3 +Ż GT = Ċ 4 +Ċ Ċ W,GT 3 = Ċ4 Ė 3 Ė 4 Ċ W,comp = ĊW,GT Ẇ comp Ẇ GT Superheater Ċ 4 +Ċ 10 +Ż sup = Ċ 5 +Ċ Ċ 11 4 = Ċ5 Ė 4 Ė 5 Evaporator Ċ 5 +Ċ 9 +Ż eva = Ċ 6 +Ċ Ċ 10 5 = Ċ6 Ė 5 Ė 6 Economizer Ċ 6 +Ċ 8 +Ż eco = Ċ 7 +Ċ Ċ 9 6 = Ċ7 Ė 6 Ė 7 Steam turbine Ċ 11 +Ż ST = Ċ 12 +Ċ Ċ W,ST 11 = Ċ12 Ė 11 Ė 12 Steam cycle Condenser Ċ 12 +Ċ 14 +Ż cond = Ċ 13 +Ċ Ċ = Ċ13 Ė 12 Ė 13 Ċ 14 = 0 Steam cycle Feed pump Ċ 13 +Ċ W,pump +Ż pump = Ċ Ċ 8 W,pump = ĊW,ST Ẇ pump Ẇ ST ORC Heat exchanger Ċ 7 +Ċ 19 +Ż HX = Ċ 18 +Ċ Ċ 22 7 = Ċ18 Ė 7 Ė 18 ORC Turbine Ċ 22 +Ż ORC tur = Ċ 23 +Ċ Ċ W,ORC tur 22 = Ċ23 Ė 22 Ė 23 ORC Recuperator Ċ 23 +Ċ 26 +Ż ORC Rec = Ċ 19 +Ċ Ċ = Ċ24 Ė 23 Ė 24 ORC Condenser Ċ 24 +Ċ 27 +Ż ORC Cond = Ċ 25 +Ċ Ċ = Ċ25 Ė 24 Ė 25 Ċ 27 = 0 ORC Pump Ċ 25 +Ċ W,ORC pump +Ż ORC pump = Ċ Ċ 26 W,ORC pump = ĊW,ORC tur Ẇ ORC pump Ẇ ORC tur steam turbine power output as shown in Figure 3B due to the dominant effect of the mass flow rate. On the other hand, decreasing the mass flow rate of the steam turbine leads to a rise in output temperature of HRSG. Therefore, a higher amount of energy is available for the ORC subsection and consequently the mass flow rate and power generation of the ORC are increased, as shown in Figure 3A,B. It is worth mentioning that the reduction in steam turbine output 331 kw is lower than the increase in ORC output 1183 kw. Therefore, the net generated power is higher Figure 3B. Also, the exergy efficiency is increased as a result of increasing the net output power with constant fuel input to the whole plant. On the other hand, the product cost of the system increases with increasing steam turbine inlet temperature TIT, as shown in Figure 3C, which is mainly due to larger equipment. 5.2 Effect of steam turbine inlet pressure A similar trend can be seen with increasing the steam turbine inlet pressure as shown in Figure 4A- C. An important point to mention is that the effect of steam turbine TIP on the net power output is higher than TIT; TIP increases the net output power by 1141 kw, whereas an 852 kw increase is observed in the case of TIT. However, the increase in product cost rate for TIP is almost twice as much as for TIT. Therefore, it is better to use TIT increment to increase the net output power compared to TIP because the product cost rate is increased by a lesser amount. 5.3 Effect of steam turbine back pressure Figure 5A,B represent the effect of steam turbine back pressure on the net output power, exergy efficiency, and product cost rate of the system. It is concluded from Figure 5A that increasing the turbine back pressure will result in decreasing the steam turbine output power. The results are understandable because the reduction in pressure ratio leads to lower enthalpy difference across the turbine. On the other hand, increasing the steam turbine back pressure results in a higher turbine steam outlet temperature. Therefore, a lower amount of energy is needed in HRSG to produce the steam. As a consequence, the temperature of the HRSG outlet stream is increased, which leads to the higher output power of the ORC cycle, as shown in Figure 5A. Overall, a reduction is monitored in the net output power, which is shown in the Figure 5. The decrease in net power causes the exergy efficiency to reduce at a fixed fuel input to the system. Also, increasing the steam turbine back pressure leads to increased product cost rate, mainly due to higher exergy destruction in the components and higher heat transfer area in the ORC

11 516 TABLE 6 Base case state points for the combined cycle State point Fluid type T [ C] P [bar] h [kj/kg] s [kj/kg] ṁ [kg/s] ex [kj/kg] 1 Air Air Flue gas Flue gas Flue gas Flue gas Flue gas Water Water Water Water Water Water Water Water Flue gas Flue gas Flue gas Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Water Water cycle. Therefore, increasing the steam turbine back pressure has a negative effect on both exergy efficiency and product cost rate, as depicted in Figure 5B. 5.4 Effect of HRSG pinch temperature difference It is concluded from Figure 6 that both the exergy efficiency and the product cost rate increase by increasing the minimum pinch point temperature difference in HRSG. Decreasing the available heat for steam generation results in a decrease in the output power of the steam turbine. On the other hand, the heat input to the ORC subsystem is increased, and thus the ORC turbine produces more power. The net effect is the increase of accumulated power which leads to slightly higher exergy efficiency. These effects are illustrated in Figure 7. It is concluded from Figures 6 and 7 that the ORC cycle has the dominant effect on the exergy efficiency of the plant in case of pinch point variation. 5.5 Effect of ORC minimum pinch temperature The effect of ORC Heat exchanger minimum pinch point temperature on the exergy efficiency and product cost rate is shown in Figure 8. Raising the minimum pinch temperature causes a reduction in ORC turbine output power because of a reduction in the mass flow rate of the ORC cycle. However, the input temperature to ORC heat exchangers T 7 is constant, but the outlet temperature T 17 is increased by increasing the minimum pinch temperature, thus lower amount of heat is available. It must be noted that the steam cycle remains unchanged and the variation in exergy efficiency is low 0.25%. Hence, ORC heat exchangers can be constructed

12 517 TABLE 7 Exergoeconomic parameters of the combined cycle Component c F $.Gj 1 c P $.Gj 1 Ė D kw Ċ D $.year 1 Ż $.year 1 Ż +Ċ D $.year 1 f % r % Compressor Combustion chamber Gas turbine Economizer Evaporator Superheater Steam turbine Condenser Pump Heat exchanger ORC turbine Recuperator ORC Condenser ORC pump FIGURE 3 Effect of Steam turbine inlet temperature on: A, mass flow rate of Rankine and ORC cycles; B, output power of Rankine and ORC cycles; C, product cost rate and exergy efficiency with higher pinch temperature with a low reduction in exergy efficiency to lower the costs. 5.6 Effect of ORC turbine inlet pressure Despite increasing the enthalpy difference across the ORC turbine, with increasing the ORC turbine inlet pressure, the mass flow rate of the ORC cycle can be decreased. The net effect is the loss of the ORC output power which has a direct impact on exergy efficiency according to Figure 9. Also, the increase in turbine inlet pressure leads to ORC heat exchangers to have less heat transfer area and less cost, along with the lower cost for ORC turbine. All these effects result in a decrease in product cost rate. Comparison

13 518 FIGURE 4 Effect of Steam turbine inlet pressure on: A, mass flow rate of Rankine and ORC cycles; B, output power of Rankine and ORC cycles; C, product cost rate and exergy efficiency FIGURE 5 Effect of Steam turbine back pressure on: A, output power of Rankine and ORC cycles; B, product cost rate and exergy efficiency between Figures 4C and 9 illustrates that the turbine inlet pressure has an opposite effect on the steam cycle and the ORC cycle. It is worth mentioning that the ORC turbine inlet pressure does not affect the steam cycle, which is apparent in a slight decrease in the exergy efficiency of the total system. 5.7 Effect of ORC turbine back pressure The effect of ORC turbine back pressure on exergy efficiency and product cost rate is depicted in Figure 10. Increasing the back pressure causes a reduction in enthalpy difference with unchanged mass flow rate. Therefore, the exergy efficiency of the system is exposed to be decreased as a result of a reduction in output power. Similarly, the product cost rate of the system could be lowered by increasing the turbine back pressure. 5.8 Optimization results The overall cycle has been optimized regarding exergy efficiency and product cost rate with seven decision variables including the steam turbine inlet pressure and temperature, the ORC turbine inlet pressure, the ORC and steam turbine

14 519 C p $ 10 6 /y Productcost rate eta-exe HRSG minimum pinch C η ex % C p $ 10 6 /y Product cost rate eta_exe ORCTIP bar 41 η ex % FIGURE 6 Effect of HRSG minimum pinch on product cost rate and exergy efficiency FIGURE 9 efficiency Effect of ORC TIP on product cost rate and exergy W ORC kw HRSG minimum pinch C FIGURE 7 output power ORCturbine Steamturbine Sum of SRC and ORC Effect of HRSG pinch temperature difference on W ST kw W ST +W ORC kw C p $ 10 6 /y Productcost rate eta-exe ORC turbine backpressure bar FIGURE 10 Effect of ORC turbine back pressure on product cost rate and exergy efficiency η ex % C p $ 10 6 /y Productcost rate eta-exe ORC HX minimum pinch C FIGURE 8 Effect of ORC HX minimum pinch on product cost rate and exergy efficiency back pressure, and the minimum pinch point temperature difference of steam HRSG and ORC heat exchangers. The optimal values, called Pareto frontier, are demonstrated in Figure 11. It can be seen that when the exergy efficiency of the plant varies from 40.68% to 41.64%, there is approximately a linear increase in the corresponding product cost rate from to million $/year. Although the exergy efficiency can be raised slightly higher, up to 41.73%, the product cost rate increases nonlinearly to a considerable value which is not economically favorable. η ex % It is worth mentioning that the optimal points in a multiobjective optimization are a set of values, and experts are needed to choose from these values according to their needs. However, a satisfactory optimal point, in which the values of both defined objectives are optimal, is depicted in Figure 11 as Equilibrium Point EP. Equilibrium Point is an independent hypothetical point where objectives do not affect each other. It is obvious that it is impossible for both objectives to be at their optimum points simultaneously. Thus, the minimum distance method was applied to choose the Optimal Point OP, which is shown in the Figure 11. The related values of the decision variables and the two objective functions, including the total product cost rate and the total exergy efficiency, are listed in Table 8. It seems that the optimized case has a slightly lower efficiency less than 1 percent, but leads to a lower product cost rate, which is desirable. 6 CONCLUSION In this investigation, a detailed exergoeconomic study of a combined GT, SRC, and ORC cycle was performed to evaluate the system from the viewpoints of exergy analysis and

15 520 TABLE 8 Base case and optimal case values of the decision variables and objective functions C p $ 10 6 /y Parameter Unit Range Optimal Population size 20 Crossover probability Mutation probability Steam TIP Bar Steam TIT C Steam turbine back pressure Steam HRSG pinch temperature Bar C ORC TIP Bar ORC turbine back pressure ORC minimum pinch point Bar C Product cost rate 10 6 $/year Exergy efficiency % OP EP Exergy efficiency % FIGURE 11 Pareto frontier, showing the best trade- off values for the objective functions product cost rate. Introducing the ORC system can improve the cycle performance by recovering the maximum available heat. The cost balance equations were presented for each component. The average costs per exergy unit at different state points were calculated by solving these equations simultaneously. Exergy efficiency and product cost rate were estimated at 41.23% and million $/year for the total system for the base case condition. The values of exergoeconomic variables for each component of the plant indicate that combustion chamber, compressor, and gas turbine are the components with higher values of Ż +Ċ D. Parametric analysis was done by assessing the effect of key thermodynamic parameters on system exergy efficiency and product cost rate. The results show that lower product cost rate can be achieved in lower steam TIT, lower steam TIP, and HRSG minimum pinch, higher steam turbine back pressure, ORC heat exchanger minimum pinch, ORC TIP, and ORC turbine back pressure. Multiobjective optimization was applied to carry out an optimization which satisfies the exergy efficiency and product cost rate at the same time. Finally, optimum points of 40.75% and million $/year for exergy efficiency and product cost rate simultaneously under design conditions were determined. ACKNOWLEDGMENTS This research was supported by the National Natural Science Foundation of China Grant No , Hubei Provincial Natural Science Foundation of China Grant No. 2018CFA029, Key Project of ESI Discipline Development of Wuhan University of Technology Grant No , the Scientific Research Foundation of Wuhan University of Technology Grant No NOMENCLATURE A Area [m 2 ] c Cost per unit exergy [$/GJ] Ċ Flow cost rate [$/year] Cp Specific Heat [kj/kg K] Ė Exergy [kw] e Specific exergy [kj/kg] e ch Standard chemical exergy [kj/kg] f Exergoeconomic factor [%] GT Gas Turbine h Specific Enthalpy [kj/kg] LHV Lower Heating Value ṁ Mass flow rate [kg/s] n Plant life time [year] P Pressure [bar] Q Heat [kw] R Universal gas constant [kj/kkmol] r Relative cost difference [%] r p Compressor pressure ratio [-] s Specific entropy [kj/kg K] T Temperature [K] TIP Turbine Inlet Pressure [bar] TIT Turbine Inlet Temperature [ C] U Total heat transfer coefficient [W/m 2 C] Ẇ Power [kw] y Molar fraction Ż Capital cost rate [$/year] Z Component purchase cost [$] Greek symbol γ Specific heat ratio η Isentropic efficiency