Evaluation and optimization of organic Rankine cycle (ORC) with algorithms NSGAII, MOPSO, and MOEA for eight coolant fluids
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Abstract
In this study, a simple organic cycle for eight subcritical coolant fluids has been studied thermodynamically and economically. For all the coolants, the present cycle was optimized for the best thermal and exergy efficiencies and the best cost of energy production. In a multipurpose procedure, using the three methods NSGAII, MOPSO, and MOEA/D, design variables in the optimization are the inlet turbine pressure and temperature, the pinch temperature difference, the proximity temperature difference in regenerator exchanger, and condenser temperature difference. The optimization results show that, in all three methods, the impact of the parameters’ inlet turbine temperature and pressure on the three objective functions is much more than other design parameters. Coolant with positive temperature gradients shows a better performance but lower produced power. In optimization methods, among all the coolants, the MOPSO method showed higher thermal and energy efficiency, and the MOEA/D showed lower production power costs. In terms of the rate of convergence, also both the MOPSO and NSGAII methods showed better performance. The fluid R_{11} with the 25.7% thermal efficiency, 57.3% exergy efficiency, and 0.054 USD cost per kWh showed the best performance among all of the coolants.
Keywords
Optimization Organic Rankine cycle Coolant fluid ExergyAbbreviations
 \(\dot{Q}\)
Heat transfer rate (kW)
 \(\dot{W}\)
Power (kW)
 \(\dot{m}\)
Mass flow rate (kg/s)
 h_{out}
Outlet enthalpy (kJ/kg)
 h_{in}
Inlet enthalpy (kJ/kg)
 \({\dot{\text{E}}\text{x}}_{i}\)
Exergy rate of each component (kW)
 s
Entropy of each component (kJ/kg K)
 T_{0}
Ambient temperature (K)
 \(\dot{I}\)
Irreversibility (kW)
 \(\dot{S}_{\text{gen}}\)
Entropy (kW/K)
 \({\dot{\text{E}}\text{x}}_{\text{out}}\)
Outlet exergy flow (kW)
 \({\dot{\text{E}}\text{x}}_{\text{in}}\)
Inlet exergy flow (kW)
 q_{j}
Transferred heat per mass (kJ/kg)
 T_{j}
Temperature of each component (K)
 ΔT_{pp}
Pinch temperature difference at regenerator (K)
 T_{H3}
Evaporator outlet temperature at the heated area of regenerator (K)
 T_{7b}
Evaporator inlet temperature at the heated area of regenerator (K)
 ΔT_{ap}
Proximity temperature difference at the regenerator (K)
 T_{7a}
Preheat outlet temperature at the cooled area of regenerator (K)
 \(\dot{m}_{\text{WF}}\)
Organic cycle fluid mass flow rate discharge (kg/s)
 \(\dot{m}_{H}\)
Heat transferring hot fluid mass flow rate discharge (kg/s)
 I_{HRVG}
Total wasted exergy at heat regenerator transducer (kW)
 η_{ST}
Turbine isentropic efficiency
 η_{mech}
Mechanic efficiency of the shaft connected to the generator
 \(\dot{W}_{\text{ST}}\)
Turbine power production (kW)
 \(\dot{W}_{\text{gen}}\)
Generator power production (kW)
 s_{1}
Inlet turbine entropy (kJ/kg K)
 P_{2}
Outlet turbine pressure (MPa)
 I_{ST}
Wasted exergy in steam turbine (kW)
 ν_{1}, ν_{2}
Specific volume of the turbine inlet and outlet fluid (m^{3}/kg)
 VER
The expansion of the fluid in steam turbines
 \(\dot{m}_{\text{Coolant}}\)
Flow discharge of cooling water in the condenser \(\left( {\frac{\text{kg}}{\text{s}}} \right)\)
 ΔT_{Cond}
Fluid temperature difference at the outlet of the condenser (K)
 I_{Cound}
Wasted exergy in condenser (kW)
 η_{P}
Pump isentropic efficiency
 h_{4}, h_{5}
Enthalpy of the pump inlet and outlet (kJ/kg)
 \(\dot{W}_{\text{P}}\)
Consumption power of pump (kW)
 \(\dot{W}_{\text{net}}\)
Net power production (kW)
 BWR
Ratio of the work needed by the pump to the work made by steam turbine
 η_{th}
Organic Rankine cycle thermal efficiency
 C_{Equ}
Steam turbine purchase cost (US$)
 C_{Gen}
Pump purchase cost (US$)
 C_{HRVG}
Heat regenerator purchase cost (US$)
 C_{cound}
Condenser purchase costs (US$)
 C_{ST}
Total cost (US$)
 C_{P}
Power generator cost (US$)
 C_{miscella}
Miscellaneous cost (US$)
 C_{T}
Total annual costs of investment (US$)
 CRF
Irreversibility factor
 C_{O&M}
Annual costs of equipment maintenance(US$/year)
 \(\left( {\dot{C}_{\text{anu}} } \right)\)
Annual investment costs of equipment, maintenance, and fuel
 β
Percentage of maintenance costs
 LHV
Low thermal value of the selected fuel per (kJ/kg)
 \(\dot{c}_{\text{fuel}}\)
Costs of each kilogram of fuel consumed (US$/kW)
 H
Annual working hours of the system per (hour/year)
 C_{kWh}
Costs of production each kilowatt of energy per hour
 OF
Desired objective function amount
Introduction
The increasing consumption of fossil fuels causes greenhouse gas emissions, global warming, and environmental degradation. Shortage of fossil fuels and the gradual rise in their cost and environmental pollution have caused a major consideration to use of energy with low or moderate temperatures. Meanwhile, the ORC (organic Rankine cycle) technology may have an important role. This cycle has a function similar to steam Rankine cycle with different that it uses organic working fluids instead of water. Due to the low critical temperature of organic fluid as compared to water, the organic Rankine cycle, unlike the steam Rankine cycle, will be able to use the lowtemperature heat sources, including industrial waste temperatures or renewable energy sources such as solar, geothermal, and biomass [12, 19].
In the last 20 years, the use of organic Rankine cycle instead of a simple Rankine cycle has been considered The operating ORC power plants around the world, with capacities ranging from 200 kW to 130 MW, demonstrate special attention to this technology. This cycle uses heat sources with low temperatures (100–500 °C). The ORC cycle works based on the simple Rankine cycle; however, to work with organic fluids, some changes must be applied. Organic working fluid in the ORC could be selected from the hydrocarbons; however, inorganic materials such as silicon and refrigeration fluids can also be used. ORC technology is significantly used in waste heat recycling of waste heat from gas turbines and it has significant advantages compared to classical heat regenerator system using a conventional Rankine cycle [12, 19]. A great deal of research has been done in the field of organic Rankine cycle. Yamamato et al. [23] examined an organic Rankine cycle using HCFC123 as a working fluid and concluded that this system has a better performance compared to using water as the working fluid [23]. Liu et al. [10] studied the effects of different working fluid on thermal and heat regenerator efficiencies. It showed that the wet fluid is inappropriate for ORC systems [10]. Wei et al. [22] studied the analysis and optimization of organic Rankine cycle using (1,1,1,3,3 pentafluoropropane) HFCFA245 as the working fluid. The results showed that the use of the output heat is a good solution to improve the system efficiency and net output power. The condenser outlet cooling degree should be small (0.5–0.6 K). When the ambient temperature is high, system output power and efficiency was reduced about 30% from the nominal value. [22]. Saleh et al. [16] examined 31 fluids for the organic Rankine cycle operations in extremely low temperature and pressure, based on backbone relationship. Fluids include: alkanes, fluorinated alkanes, fluorinated ethers, and esters. Cycles operated between 30 and 100 °C in geothermal power plants under pressures limited to 20 Bar; however, in some cases, the supercritical pressures are considered. The thermal efficiency of operating fluids R_{125} and C_{5}F_{12}, is 2.3 and 10.5%, respectively [16]. Tchanche et al. [18] analyzed the thermodynamic characteristics and functions of 20 fluids in the solar ORCs, in low temperature, and suggested R134a as the best fluid [18].
Roy et al. [15] studied functional analysis and parameter optimization of a heat regenerator system, using fluids R12, R123, and R134A, based on ORC technology. Three different fluids were selected for this study and the productivity and Carnot efficiency were compared. The considered parameters were the output work and system efficiency. The results showed that R123 has the maximum output power and efficiency. Carnot efficiency for this fluid, in modified pressure and under the similar conditions, is close to real state. Therefore, choosing the organic Rankine cycle with the fluid R123 seems to be an ideal system for using the lowtemperature heat sources in power generation Roy et al. [15].
Rayegan and Tao [14] have developed an approach to choose the working fluid for the solar organic Rankine cycle. ORC fluid selection is critical point of performance; therefore, some of available research will focus on fluid selection. The Refprop 8 database with 117 fluids was chosen for this study. An approach for comparison of ORC working fluids was proposed based on molecular components, enthalpy versus temperature, thermal efficiency, net power production, and exergy efficiency of ORC. Fluids with best cycle performance were identified in two different categories based on two different temperature levels: coolant and noncoolant. According to the solar collectors, 11 fluids were proposed to be used in solar OCRs which used low or mediumheat solar collectors. The results showed that for the fluid selection, theoretical constraints to reduce irreversibility and exergy efficiency by improving the efficiency of the collector are 35 and 5%, respectively, when the collector’s efficiency is increased from 70 to 100%. Reconstruction impact on exergy efficiency is dependent on the fluid while improving the efficiency of the collector on exergy efficiency is independent of the type of fluid [14].
Wang et al. [20] presented the working fluid selection and parametric optimization. They used a multiobjective optimization procedure to evaluate an ORC cycle. Target functions were output power per unit input heat and thermal efficiency. Independent parameters were evaporation and condensation pressure, type of working fluid, and the speed of water cooling in the pipes. By comparing the optimization results for 13 working fluids, they showed that the economic characteristics of the system are quickly decreased with the reduction in source’s temperature. They concluded that when the heat source temperature is below 100 °C, the ORC technology is noneconomic [20].
Ahmadi and Rosen [1] examined a triple comprehensive generation model consisting of a triple system for cooling, heating, and power generation which includes a cycle gas turbines, organic Rankine cycle, a singleeffect absorption cooler, and a conventional water heater. The results are as follows: greater exergy efficiency and less carbon dioxide emission from the trigeneration system compared to combined heating and power systems or gas turbine cycles. The greatest exergy destruction was happened in combustion chamber due to chemical reactions and hightemperature difference between the working fluid and medium. Parametric studies showed that the compressor pressure ratio, gas turbine inlet temperature, and isentropic efficiency of gas turbines greatly affected on the exergy efficiency and environmental impact of the trigeneration systems. In addition, with the increase in turbine inlet temperature, the environmental impact costs are primarily reduced by the decrease in combustion chamber volume flow rate [1].
Pierobon et al. [11] found the MWsize optimal organic Rankine cycles using the multiobjective optimization with genetic algorithms. They had three objective functions: the thermal efficiency, the total volume of the system, and the net present value. The variables of the working fluid optimization were the turbine inlet temperature, pressure, and the temperature of flow rate at the compact heat exchangers. They used this approach to retrieve the waste heat from gas turbines SGI500 installed on draugen oil and gas platform in the North Sea. Optimization results showed that the thermal efficiency and net present value for cyclopentane are higher than acetone [11]. Wang et al. [21] used a genetic algorithm as the optimization method for a comparative study of ORC and working fluid R134A, for lowgrade waste heat regenerator. Exergy efficiency and total investment costs were considered as the objective function to optimize the waste heat under certain conditions. The obtained Pareto efficiency indicated that the increase in exergy efficiency can increase the total investment costs for the ORC system [21].
Quoilin et al. [12] explained the current state of ORC technology with emphasis on heating values and the properties of each fluid. The working fluids and expansion equipment’s are the two characteristics of ORC technology. This research has investigated numerous studies on working fluids in the literature and also noted the limitations. In their research, the review on different applications of ORC has been provided. A proposed market review includes forms of the costs for several ORC business units and producers. A precise analysis of the technical challenges related to this technology has been reported, such as the working fluid and the expansion device issues. Technological constraints and optimization methods are widely described and discussed [12].
Ataei et al. [3] conducted thermodynamic assessments based on the first and second laws of thermodynamics to simulate the different organic fluids and different ORC states in different ambient temperatures by the use of engineering equation solver (EES) and assess the environmental functions using the sustainability method. Energy analysis showed that ORC renovated with IHE (intermediate heat exchanger) had the best thermodynamics performance. In this study, it was revealed that Nhexane, which has the highest boiling point and critical temperature, is the most efficient working fluid for the cycle. The results showed that a decrease in ambient temperature caused an increase in first and second law efficiencies and made the system more stable [3].
Darvish et al. [7] simulated the thermodynamic performance of a regenerative organic Rankine cycle that uses lowtemperature heat sources. They made use of thermodynamic models to evaluate the thermodynamic parameters such as power output and energy efficiency of ORC. In addition, in this study, the cost of electricity was estimated by the exergyeconomic analysis. The working fluid was considered as a part of evaluation to identify the highest power output and energy efficiency in the specific system conditions. [7].
Ashouri et al. [2] studied an ORC in terms of thermodynamics and economic for power generation with a smallscale up to 100 kW. This parametric study indicated the impact of key parameters such as temperature and turbine inlet pressure on the parameters of the system such as network, thermal efficiency, oil and total heat transfer coefficient, the heat transfer area of the thermal exchangers of the shell and tube, as well as the system costs. The results showed that the dependency of system efficiency and its cost on operating pressure of heat exchangers. They proved that the existence of regenerator is relatively effective on the increase in cycle efficiency, and in some cases, it reduces the overall costs due to reduction in condenser load. The comparison between different working fluids such as benzene, butane, pentane, isopentane, R_{123,} and R_{245}FA was conducted to detect a wide range of operational pressures and temperatures. The results showed that benzene has the best thermodynamic performance among the other fluids, and after it, isopentane, R_{123}, R_{245}FA, and butane showed the best performance. Benzene also has the highest cost of all the other fluids and after it come pentane, isopentane, butane, R_{123,} and R_{245}FA [2].

using new equations to calculate the cost of the equipment installed in an organic Rankine cycle;

triobjective optimization (cost, exergy efficiency, and thermal efficiency) by changing the five design variables;

using three optimization methods NSGAII, MOPSO, and MOEA/D to compare the results of these three methods.
Analysis of exergy and energy
In general, the organic Rankine cycle includes heat regenerator, turbines, condenser, and pump. This cycle is divided into hypercritical and subcritical categories according to turbine inlet pressure. The current research has been done on subcritical cycle.
Subscript 0 the basic state which equals the environmental conditions at 15 °C and pressure of 1 atm.
The heat regenerator in the organic cycle is divided into three parts as preheater, evaporators, and superheater. Organic fluid, at the two locations of the preheater and superheater, is single phase and it are two phases at evaporator. Usually, the heat exchanger in an organic cycle is in the form of a single cross flow.
In the above equations, \(\dot{m}_{\text{WF}}\) and \(\dot{m}_{\text{H}}\) are the cycle organic fluid’s mass flow rate and heat transfer fluid’s mass flow rate in the regenerator \(\left( {\frac{\text{kg}}{\text{s}}} \right)\), and \(\dot{Q}\) is the rate of transferred heat at any location (kW).
\({\dot{\text{E}}\text{x}}\) is any exergy rate which is calculated from Eq. (2).
In the above equation, s _{1} is the inlet entropy to the turbine \(\left( {\frac{\text{kJ}}{{{\text{kg}}\;{\text{K}}}}} \right)\) and P _{2} is the outlet pressure from the turbine (kPa).
In the above equations, ν _{1} and ν _{2} are the specific volume of the input and output fluid of turbine \(\left( {\frac{{{\text{m}}^{ 3} }}{\text{kg}}} \right)\), and VER is the rate of fluid expansion ratio of the steam turbine.
Economic analysis
In the above equations, C _{st}, C _{p}, C _{Cond}, C _{HRVG}, C _{Gen}, and C _{Equ} are the purchase costs of steam turbine, pump, condenser, heat regenerator exchanger, power generator, and sum of all of these costs, respectively, given in USD. The amounts of \(\dot{W}\) and \(\dot{Q}\) are per (kW).
Optimization method selection
Optimization variables alongside with their changes range
Highest design level  Lowest design level  Design parameter 

90% critical pressure  10% critical pressure  (P _{1}) 
180 °C  70 °C  (T _{1}) 
20 °C  8 °C  (ΔT _{pp}) 
12 °C  5 °C  (ΔT _{app}) 
25 °C  12 °C  (ΔT _{Cond}) 
Conditions of cycle designing and optimizing
\({\text{Cons}}_{1} = \left\{ \begin{aligned} T_{\text{H1}} > T_{1} \hfill \\ T_{\text{H2}} > T_{8} \hfill \\ T_{\text{H3}} > T_{{ 7 {\text{b}}}} \hfill \\ T_{\text{H4}} > T_{6} \hfill \\ \end{aligned} \right\}\) 
Cons_{2} = X _{2} > 0.99 
Cons_{3} = T _{1} ≥ T _{sat} (P _{8}) 
\({\text{Cons}}_{1} = \left\{ \begin{aligned} T_{\text{H1}} > T_{1} \hfill \\ T_{\text{H2}} > T_{8} \hfill \\ T_{\text{H3}} > T_{{ 7 {\text{b}}}} \hfill \\ T_{\text{H4}} > T_{6} \hfill \\ \end{aligned} \right\}\) 
Cons_{2} = X _{2} > 0.99 
Cons_{3} = T _{1} ≥ T _{sat} (P _{8}) 

NSGAII method
The nondominated sorting genetic algorithm is one of the bestknown and mostapplicable multiobjective optimization algorithms which was first introduced by Debb in 2002. This method is based on genetic algorithm. The main difference between NSGAII and the simple genetic algorithm is in population layout. In this algorithm, the population is selected first based on quality and then based on distribution [5, 13].

MOPSO method
Multiobjective particle swarm optimizers is a metaheuristic stemmed from PSO method of optimization. The difference between the two methods is in detection of the best position of the particle and particle local memory [6].

MOEA/D method
This method is a modern multiobjective algorithm which solves a set of decompressed objectives in an interactional manner. The main difference between this method and the classical methods of multivariate optimization (weighted sum, goal programming, and goal attainment) is the reaction in finding the answers to different objectives [24]. In fact, this algorithm solves a multiobjective problem through several interactional singleobjective problem. This algorithm was first introduced by Zhang and Li [24].
Results and discussion
Characteristics of gas input to the heat regenerator
Variable  Unit  Value 

Inlet gas temperature  ^{o}C  200 
Inlet gas pressure  MPa  0.12 
Inlet gas mass flow rate  kg/s  15 
Mass ratio of gas  
CO_{2}  %  51.2 
N_{2}  %  48.8 
Fluid characteristics [9]
Physical specification  Chemical formula  Fluid  

P _{cr} (MPa)  T _{cr} (°C)  M (kg/kmol)  
2.045  147.41  288.03  CF_{3}(CF_{2})CF_{3}  C_{5}F_{12} 
3.8  152  58.12  CH_{3}–CH_{2}–CH_{2}–CH_{3}  Butane 
3.64  134.7  58.12  CH(CH_{3})_{2}–CH_{3}  Isobutane 
4.41  198  137.37  CC_{13}F  R_{11} 
3.6  183.68  152.93  CHC_{12}CF_{3}  R_{123} 
4.25  204.2  16.95  CH_{3}CC_{12}F  R_{141}B 
3.64  154.05  134.05  CF_{3}CH_{2}CHF_{2}  R_{245}FA 
Fixed coefficients of modeling
Value  Unit  Parameter 

85  %  Turbine efficiency 
85  %  Pump efficiency 
20  °C  Coolant fluid temperature 
20  kg/s  Coolant fluid mass flow rate 
20  °C  Medium temperature 
1  Atm  Medium pressure 
10  %  Annual interest rate 
20  Year  Year performance 
8322  Hours  Hours of operation during a year 
4  %  Operation and maintenance percent 
Fluid simulation results in three different states
State 1  State 2  State 3  

η _{I} (%)  η _{II} (%)  \(C_{\text{kWh}} \left( {\tfrac{\text{USD}}{\text{kWh}}} \right)\)  η _{I} (%)  η _{II} (%)  \(C_{\text{kWh}} \left( {\tfrac{\text{USD}}{\text{kWh}}} \right)\)  η _{I} (%)  η _{II} (%)  \(C_{\text{kWh}} \left( {\tfrac{\text{USD}}{\text{kWh}}} \right)\)  
Ammonia  4.5  17.5  0.135  5.2  20.4  0.117  8  29.8  0.081 
Butane  15.5  51.6  0.050  15.9  53  0.048  17.7  57  0.047 
C_{5}F_{12}  14.8  51.6  0.053  15.1  52.8  0.052  16.4  61.7  0.050 
Isobutane  13  45.2  0.058  13.4  46.8  0.056  15.4  51.9  0.053 
R_{11}  21.7  63.8  0.038  22.1  64.9  0.037  23.4  65.7  0.038 
R_{123}  20.6  62.1  0.039  21  63.3  0.039  22.3  64.3  0.039 
R_{141}B  22.4  64.3  0.037  22.7  65.4  0.036  23.9  65.6  0.038 
R_{245}FA  16.7  55.1  0.046  17.1  56.5  0.045  18.6  59.4  0.044 
Different optimization algorithms settings
NSGAII  MOPSO  MOEA/D  

Maximum iteration  500  Maximum iteration  500  Maximum iteration  500 
Population size  50  Number of particle  50  Population size  50 
Crossover probability  0.7  Repository Size  100  Archive size  100 
Mutation probability  0.02  Inertia Weight  1  Number of neighbors  10 
Selection process  Tournament  Inertia weight damping rate  0.95 
Range of the changes in exergy efficiency in optimization of different fluids in three methods of optimization
Fluid  MOEA/D  MOPSO  NSGAII  

η _{II}  MIN (%)  MAX (%)  MIN (%)  MAX (%)  MIN (%)  MAX (%) 
Butane  5.7  66.5  4.8  57.4  4.3  42.4 
Isobutane  5.0  63.7  4.7  57.7  8.6  54.1 
C_{5}F_{12}  4.9  55.9  3.6  51.6  3.6  49.8 
R_{245}FA  9.6  67.0  6.3  59.1  6.9  66.3 
R_{11}  54.4  59.8  55.6  58.3  55.5  59.7 
R_{123}  49.6  59.5  49.7  57.1  52.4  59.3 
R_{141}B  53.2  57.9  55.4  57.9  51.1  59.3 
Ammonia  10.1  54.0  6.8  52.7  7.4  55.8 
Range of the changes in thermal efficiency in optimization of different fluids in three methods of optimization
NSGAII  MOPSO  MOEA/D  Fluids  

MIN (%)  MAX (%)  MIN (%)  MAX (%)  MIN (%)  MAX (%)  η _{I} 
1.6  21.6  1.3  19.8  1.7  18.2  Butane 
1.3  19.5  1.3  17.8  2.3  19.2  Isobutane 
1.3  16.2  1.0  15.3  1.0  15.5  C_{5}F_{12} 
2.7  21.5  1.7  19.9  1.9  21.4  R_{245}FA 
24.3  25.7  22.4  24.4  23.3  25.1  R_{11} 
22.0  24.8  20.9  23.4  21.2  24.8  R_{123} 
23.7  25.3  21.9  24.1  18.5  25.7  R_{141}B 
2.9  19.7  1.9  19.1  2.0  20.9  Ammonia 
Range of the changes in costs in optimization of different fluids in three methods of optimization
NSGAII  MOPSO  MOEA/D  Fluids  

MIN  MAX  MIN  MAX  MIN  MAX  \(C_{\text{kWh}} \left( {\frac{\text{USD}}{\text{kWh}}} \right)\) 
0.03  0.012  0.03  0.1  0.03  0.11  Butane 
0.03  0.14  0.03  0.11  0.04  0.09  Isobutane 
0.03  0.09  0.03  0.09  0.03  0.08  C_{5}F_{12} 
0.03  0.11  0.03  0.09  0.03  0.11  R_{245}FA 
0.01  0.05  0.03  0.05  0.01  0.05  R_{11} 
0.02  0.06  0.04  0.06  0.02  0.06  R_{123} 
0.02  0.04  0.03  0.05  0.01  0.05  R_{141}B 
0.04  0.08  0.03  0.08  0.03  0.08  Ammonia 
In Table 8, the highest and lowest exergy efficiency in the Pareto chart of the three optimization methods for all the fluids is provided. As it is seen, for the fluids R_{11}, R_{123}, and R_{141}B which are dry or isentropic fluids, the obtained range in Pareto chart for their exergy is much lower than other fluids. It means that the optimization results for these three fluids in all the three methods show similar or close exergy efficiency, while for other fluids, it is not the same and the obtained range is significantly great. The results of the Pareto chart of the fluid C_{5}F_{12} contain the points with lowest exergy efficiency. In Table 9 that shows the highest and lowest thermal efficiency of Pareto chart for different fluids. Again, it is seen that the fluids R_{11}, R_{123}, and R_{141}B have the lowest efficiency. This also indicates closeness of the thermal efficiency of these fluids according to the Pareto chart results. Again, C_{5}F_{12} has the lowest thermal efficiency. In Table 10, the lowest and highest obtained costs in the Pareto chart of the fluids optimization are shown. Again, the fluids R_{11}, R_{123}, and R_{141}B cover a smaller range that indicates the closeness of the Pareto chart results for the three fluids.
Conclusion
In the current study, first, after reviewing the modelling and using the organic Rankine cycle at low temperature, conservation equations of mass and energy for the cycle equipment were provided. Then, the model of the economic modelling of the equipment was elaborated and afterwards, the parametric evaluation of this cycle for the variables inlet turbine temperature and pressure, the pinch and proximity temperature difference at the regenerator exchanger, and the condenser’s temperature difference were analyzed. Finally, the triobjective optimization results (exergy efficiency, thermal efficiency, and cost of each kWh) in the three methods NSGAII, MOPSO, and MOEA/D were provided and analyzed.
 1.
The inlet turbine temperature and pressure have the greatest effect on the thermal and exergy efficiency as well as the costs. However, the effects of the other three parameters (pinch and proximity temperature difference at the regenerator exchanger and condenser temperature difference) is lower than those two. These five variables have different effects on the efficiency and costs. The increase in the system performance will lead to the increase in costs.
 2.
Choosing the working fluid is very important and vital for the ORC. The dry fluids R_{11}, R_{123}, and R_{141}B has the best performance in terms of exergy and thermal efficiency as well as the costs. The fluid R_{11} with the exergy efficiency of 57.3% and thermal efficiency of 25.7% and cost of 0.0542 USD per kWh of energy production had the best performance among all the fluids. It indicates that using the dry fluids instead of wet fluids in the organic cycles has a better performance in terms of efficiency and costs. However, in terms of useful power production, these fluids act quite contrariwise. In power generation, the fluid generates the highest power with 376.6 kWh and the fluid R_{11} generates the lowest power with 27.5 kWh. This phenomenon indicates the importance of the desired objective in cycle design. In cases there is no limits in terms of need to power, the fluid R_{11} is the best choice; however, when a specific power is desired, it is not the best choice.
 3.
The selection of the optimization method depends on the desired objective of optimizing and the selected fluid. For optimization, the MOPSO method shows the best performance in terms of exergy and thermal efficiency; however, in terms of the costs, the three methods show different performance in different fluids. In butane, The MOPSO method with a 47.75 exergy efficiency improvement compared to MOEA/D, and 68.3 thermal efficiency improvement compared to MOEA/D, shows the best performance; however, there are different trends in reduction of the costs in the fluid and we cannot definitely choose a method.
Notes
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