Multi-Objective Thermo-Economic Optimization of a Combined Organic Rankine Cycle (ORC) System Based on Waste Heat of Dual Fuel Marine Engine and LNG Cold Energy Recovery

: In this paper, a combined organic Rankine cycle (ORC) system that can e ﬀ ectively utilize the cold energy of Liqueﬁed Nature Gas (LNG) and the waste heat of dual fuel (DF) marine engine was proposed. Particularly, the engine exhaust gas and the jacket cooling water of the DF marine engine were used as heat sources. Firstly, a thorough assessment of thermo-economic performance was conducted for the combined ORC system using 11 environmentally friendly working ﬂuids (WFs). Afterwards, the e ﬀ ects of evaporation and condensation pressures on the net output work, energy e ﬃ ciency, exergy e ﬃ ciency, total investment cost and payback period were examined. Furthermore, the thermo-economic performances of the ORC system were optimized via multi-objective optimization with a genetic algorithm. Finally, exergy destructions and investment costs of each component under the optimal operating conditions were analyzed to make suggestions for further improvement. The results show that R1150-R1234yf-R600a and R170-R1270-R152a are the two most promising WF combinations. The exergy destruction of the combined ORC system mainly exists in heat exchangers. Through WF optimization, the exergy destruction in the intermediate heat exchanger was reduced by 18.99%. The proportion of expanders investment cost could be greater than 50% and the payback period of the combined ORC system varies in the range of 7.68–9.43 years. This study demonstrated that the selection of WF and the optimization of operating conditions had important potential to improve thermo-economic performances of ORC systems.


Introduction
Maritime transport enjoys low cost and accounts for 80% of global trade by volume and more than 70% of cargo value [1]. Meanwhile, burning of ship fuel brings serious environmental problems due to pollutant emissions, such as CO 2 , SOx, NOx and particle material. Moreover, the International Maritime Organization's new rules limit the sulphur content of bunker fuel to 0.5% of the weight of ocean-going ships, well below the 3.5% limit set in 2012 [2]. In this context, liquified nature gas (LNG) is considered to be the most promising marine fuel [3]. Compared with conventional heavy fuel oil, LNG could reduce emissions by 85-95% of NOx, 20% of CO 2 and 100% of SOx [4]. The number of LNG fueled ships in-service and on-order is increasing and is expected to account for 32% of shipping energy demand by 2050 [5]. results displayed that ORC system with R290 showed the best exergy efficiency (40.7%), the best net power output (116.8 kW) and the lowest annualized cost (38838 $/year).
From the above studies, the results relating to ORC systems based on LNG cold energy and waste heat recovery are summarized in Table 1. The adoption of dual-loop ORC system appears to be an efficient and viable method for waste energy cascade utilization. In addition, the benefit of intermediate heat exchanger (IHE) to the thermo-economic performance of ORC system has been demonstrated [29,49]. However, very few published studies analyze the effects of working pressure on ORC system performances with regard to the two-level heat sources. In order to fully understand the superiority of the combined ORC system, the evaporation pressure and condensation pressure in the IHE must be analyzed. Furthermore, it is not clear how to select the suitable WFs especially for a large temperature difference between cold and heat sources. Table 1. Summary of ORC system based on LNG cold energy and waste heat recovery.

Research
Heat Source (Inlet Temperature)

ORC Configuration
Working Fluid

Particle Swarm Optimization (PSO) algorithm
Han et al. [33] Seawater (20 • C) /Main engine exhaust gas (270 • C)/Jacket cooling water (90 • C) Triple ORC 15 pure fluids Self-adaptive firefly algorithm (SAFA) Sung and Kim [45] Main engine exhaust gas (230 • C)/ Jacket cooling water (91 • C) Dual-loop ORC 13 pure fluids -Habibi et al. [46] Main engine exhaust gas (300 • C)/ Jacket cooling water (90 • C) Combined ORC 6 pure fluids Non-dominated Sorting Genetic Algorithm -II (NSGA-II) Koo et al. [48] Jacket cooling water (80 • C) Six different ORCs 6 pure fluids Particle Swarm Optimization (PSO) algorithm The purpose of this paper was to explore the feasibility of ORC system based on energy cascade utilization in ship waste heat recovery and provides a method for thermo-economic performance optimization. In this paper, a combined ORC system with IHE was proposed for WHR of DF marine engine and cold energy recovery of LNG. Firstly, the applicability of 11 environmentally friendly WFs for different loops of the combined ORC system was examined and two optimal WF combinations were decided. Secondly, the effects of IHE evaporation and condensation pressure on the combined ORC system under two optimal WF combinations were investigated from the perspective of thermo-economic, including net output power, energy efficiency, exergy efficiency, initial investment and payback period. Thirdly, multi-objective optimization was performed to find the best operating condition.

Marine Engine
The type of marine engine is Wärtsilä 50DF, which is a four-stroke, non-reversible, turbocharged and inter-cooled DF marine engine with direct injection of liquid fuel and indirect injection of gas fuel. The engine can be operated in gas mode or diesel mode. In this study, the primary parameters of the Wärtsilä 50DF marine engine are summarized in Table 2. About 50% of fuel energy is converted into the propulsion energy power for the marine engine, while the other 50% is taken away by the waste heat. There are two main forms of waste heat: (1) high temperature EEG generated by fuel combustion; (2) JCW that is used to remove the excess heat of main engine and guarantee proper working temperature. In the meantime, the LNG vaporization process releases a large amount of cold energy. Table 2. Primary parameters of the Wärtsilä 50DF marine engine Reproduced from product brochure [50], the name of the publisher: Wärtsilä.

ORC System Description
The cold energy and waste heat from the DF marine engine are converted into electrical energy with the combined ORC system. In order to avoid the efficiency decrease of heat transfer between large temperature difference, a combined ORC system based on energy cascade utilization principle is proposed, which is illustrated in Figure 1. LNG, used as fuel, requires gasification before entering the DF marine engine. The outlet temperature of EEG from the DF marine engine is usually higher than 300 • C. After flowing through the boiler circulation, the temperature of EEG is still higher than 150 • C. JCW of the DF marine engine is generally with the temperature in the range of 78-95 • C. Therefore, EEG and JCW from the DF marine engine work as dual heat sources for the combined ORC system. The t-s diagram of the combined ORC system is shown in Figure 2.

ORC System Description
The cold energy and waste heat from the DF marine engine are converted into electrical energy with the combined ORC system. In order to avoid the efficiency decrease of heat transfer between large temperature difference, a combined ORC system based on energy cascade utilization principle is proposed, which is illustrated in Figure 1. LNG, used as fuel, requires gasification before entering the DF marine engine. The outlet temperature of EEG from the DF marine engine is usually higher than 300 °C. After flowing through the boiler circulation, the temperature of EEG is still higher than 150 °C. JCW of the DF marine engine is generally with the temperature in the range of 78-95 °C. Therefore, EEG and JCW from the DF marine engine work as dual heat sources for the combined ORC system. The t-s diagram of the combined ORC system is shown in Figure 2. As shown in Figure 1, the combined ORC system consists of three ORC subsystems: ORC 1, ORC 2 and ORC 3. In ORC 1, LNG in the storage tank is introduced to a condenser (CON1) by a pump (P0). The released cold energy enables the working fluid 1 (WF1) condensed to subcooled liquid. Then, WF1 is pressurized by P1 and enters the evaporator (EVA1) to absorb the heat released by WF3 in ORC 3. The EVA1 in ORC 1 works as the CON3 in ORC 3. After that, WF1 becomes superheat vapor and promotes expander (EXP1) to produce electricity. In ORC 2, the partially gasified LNG served as the cold source and the EEG works as the heat source. The circulation of the WF2 in ORC 2 is similar to WF1 in ORC 1. WF2 absorbs the waste heat carried by JCW and becomes a superheated state. The superheat vapor of WF2 contributes the EXP2 to generate electricity. In ORC 3, WF3 is condensed to the subcooled fluid and then is pressurized by P3. The waste heat brought by EEG helps WF3 vaporize in EVA3. The superheat WF3 pushes EXP3 to produce electricity. Afterwards, WF3 is condensed in CON3 to the subcooled state. The electricity generated by the combined ORC system is the sum of W1, W2 and W3 and the power consumed by the system is the sum of WP0, WP1, WP2 and As shown in Figure 1, the combined ORC system consists of three ORC subsystems: ORC 1, ORC 2 and ORC 3. In ORC 1, LNG in the storage tank is introduced to a condenser (CON1) by a pump (P0). The released cold energy enables the working fluid 1 (WF1) condensed to subcooled liquid. Then, WF1 is pressurized by P1 and enters the evaporator (EVA1) to absorb the heat released by WF3 in ORC 3. The EVA1 in ORC 1 works as the CON3 in ORC 3. After that, WF1 becomes superheat vapor and promotes expander (EXP1) to produce electricity. In ORC 2, the partially gasified LNG served as the cold source and the EEG works as the heat source. The circulation of the WF2 in ORC 2 is similar to WF1 in ORC 1. WF2 absorbs the waste heat carried by JCW and becomes a superheated state. The superheat vapor of WF2 contributes the EXP2 to generate electricity. In ORC 3, WF3 is condensed to the subcooled fluid and then is pressurized by P3. The waste heat brought by EEG helps WF3 vaporize in EVA3. The superheat WF3 pushes EXP3 to produce electricity. Afterwards, WF3 is condensed in CON3 to the subcooled state. The electricity generated by the combined ORC system is the sum of W 1 , Energies 2020, 13, 1397 6 of 23 W 2 and W 3 and the power consumed by the system is the sum of W P0 , W P1 , W P2 and W P3 . Considering the characteristics of LNG-fueled ships and results in Table 1, the boundary conditions of the combined  ORC system are shown in Table 3, including environment, cold source and heat source.
Energies 2020, 13, x FOR PEER REVIEW 6 of 24 WP3. Considering the characteristics of LNG-fueled ships and results in Table 1, the boundary  conditions of the combined ORC system are shown in Table 3, including environment, cold source and heat source.

Candidate Working Fluids
To satisfy the requirements of environmentally friendly WFs, only refrigerants with zero ozone depletion potential (ODP) and global warming potential (GWP) less than 200 are considered in this study. By considering the characteristics of the heat source and cold source, 11 candidate WFs were selected for the combined ORC system. The physical parameters of the selected WFs are presented in Table 4. The classification, environmental and safety indicators are also shown in Table 4. Since the tboi relates to WF phase change and the critical temperature (tcri) limits the working region, the tboi and tcri of different WFs are illustrated in Figure 3. Considering system safety and stability, the matching relationship of WFs with different ORC subsystems was determined. R1150 and R170 are recommended for ORC 1 since they have lower tcri. R1270, R290 and R1234yf with higher tcri are used in ORC 2. R152a, R1234ze(E), R600a, R600, R601 and R601 are used in ORC 3 since their tcri are close to the temperature range of EEG. Therefore, a total of 36 cases would be produced by all possible combinations.

Candidate Working Fluids
To satisfy the requirements of environmentally friendly WFs, only refrigerants with zero ozone depletion potential (ODP) and global warming potential (GWP) less than 200 are considered in this study. By considering the characteristics of the heat source and cold source, 11 candidate WFs were selected for the combined ORC system. The physical parameters of the selected WFs are presented in Table 4. The classification, environmental and safety indicators are also shown in Table 4. Since the t boi relates to WF phase change and the critical temperature (t cri ) limits the working region, the t boi and t cri of different WFs are illustrated in Figure 3. Considering system safety and stability, the matching relationship of WFs with different ORC subsystems was determined. R1150 and R170 are recommended for ORC 1 since they have lower t cri . R1270, R290 and R1234yf with higher t cri are used in ORC 2. R152a, R1234ze(E), R600a, R600, R601 and R601 are used in ORC 3 since their t cri are close to the temperature range of EEG. Therefore, a total of 36 cases would be produced by all possible combinations.

Mathematic Model
To analyze thermal and economic performance of the ORC system with different WF combinations, a simulation model is necessary. To simplify and clarify the analysis, the following assumptions are made: (1) all components are assumed to operate under steady state conditions; (2) the heat and friction losses of the system piping and equipment are neglected; (3) the EEG is treated as ideal gas and LNG is treated as methane; (4) the kinetic and potential energy changes in the system are omitted; (5) the DF marine engine operates at full load. The thermodynamic properties of WFs at particular points in the ORC system are obtained from the REFPROP model [51]. To ensure heat transfer performance, a set of specifications and constraints are listed according to the thermodynamic principles, which are summarized in Table 5. According to Györke et al. [52] and Javanshir et al. [53], superheat does not increase the efficiency of isotropic and dry WFs, but it does increase the efficiency of wet WFs. Therefore, the superheat was set at 10 °C for wet WFs.

Mathematic Model
To analyze thermal and economic performance of the ORC system with different WF combinations, a simulation model is necessary. To simplify and clarify the analysis, the following assumptions are made: (1) all components are assumed to operate under steady state conditions; (2) the heat and friction losses of the system piping and equipment are neglected; (3) the EEG is treated as ideal gas and LNG is treated as methane; (4) the kinetic and potential energy changes in the system are omitted; (5) the DF marine engine operates at full load. The thermodynamic properties of WFs at particular points in the ORC system are obtained from the REFPROP model [51]. To ensure heat transfer performance, a set of specifications and constraints are listed according to the thermodynamic principles, which are summarized in Table 5. According to Györke et al. [52] and Javanshir et al. [53], superheat does not increase the efficiency of isotropic and dry WFs, but it does increase the efficiency of wet WFs. Therefore, the superheat was set at 10 • C for wet WFs. The subcooling of WFs at the inlet of pump is stipulated at 5 • C to prevent cavitation 4 The wet WFs are superheated with 10 • C while the isotropic and dry WFs are saturated vapor at the inlet of expander 5 The pinch point in the heat exchangers is varied in the range of 5-40 • C 6 The isentropic efficiencies of expander and pump are 80% 7 All operating pressure should be 200 kPa lower than the critical pressure to ensure stability

Thermo-Economic Analysis
Thermodynamic analysis is conducted by evaluating the energy efficiency and exergy efficiency of the overall system. Moreover, the combined ORC system with different WFs is evaluated and compared from the perspective of economy. The energy, exergy and economic analyses of the ORC system are briefly described here. In order to evaluate the efficiency of energy conversion in a thermodynamic cycle, the analysis is generally considered in terms of energy conversion quantity and quality based on the first and the second law of thermodynamics, respectively. Each component in the combined ORC system is regarded as a control volume with the mass flow (m), heat transfer (Q) and work interactions (W). The mass and energy balance equations are as Equations (1) and (2), respectively: where h is the enthalpy of the working fluid. The subscript in and out refers to the inlet and out of the volume. Exergy (Ex) is defined as the maximum output work that can be obtained when the flow reversibly changes from a given temperature and pressure to a reference state. The exergy considered in this paper is enthalpy exergy, as defined in Equation (3). Exergy is a function of enthalpy and entropy, which are functions of state. All practical processes are irreversible and thus cause the exergy degradation. Therefore, the exergy destruction (∆Ex) of a flow is defined as the difference of input exergy and output exergy, as shown in Equation (4): where t 0 is the reference temperature and h 0 and s 0 are the specific enthalpy and specific entropy evaluated under the reference state. In this paper, the values of reference temperature and pressure are 25 • C and 100 kPa, respectively. Based on the mass and energy conservation principle, energy and exergy analysis models for each component are summarized in Table 6.
The capital investment of the ORC system and its cost of electricity production are attractive to shipowner. Besides the thermodynamic performance of the combined ORC system, the economic performance is another essential indicator that should be considered. The total cost of the system (C tot ) is evaluated by Equations (5) and (6). The economic analysis model of each component is summarized in Table 7. The correlation coefficients are cited from [54], which are summarized in Table 8.   Table 7. Economic analysis model of components in ORC system.

Components Economic Analysis Model
Condenser Table 8. Coefficients for economic analysis model.

System Performance Criteria
The system energy efficiency (η en ) is defined as the ratio of a system network (W net ) to the total heat exchange amount in the evaporators (Q EVA,i ). The W net is defined by the generated electricity W i minus the consumed power W Pi : Energies 2020, 13, 1397 10 of 23 The utilization of energy quality is more concerned than the exergy loss of each component. Therefore, the system exergy efficiency (η ex ) is defined as the ratio of system network to the sum of exergy destruction from the heat source (∆Ex hs ) and cold source (∆Ex cs ): The payback period (PBP) is the time required to recover the cost of the investment, which is defined as: where τ is the annual operating time, which is assumed to be 7200 h; c ele is the electricity price of 0.15 $/kWh; C m is the maintenance cost, which is assumed to be 2% of the system cost.

Optimization Method
Multi-objective optimization has been widely used in various subjects to minimize or maximize two or more functions simultaneously with several constraints. In this paper, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), an improved version of NSGA, is utilized for ORC system performance optimization. NSGA-II is a heuristic search algorithm inspired by natural evolutionary techniques. In the NSGA-II optimization process, all populations are modified within the constraints. At each step, the selected population is used as parents to produce offspring generations via tournament selection, cross over and mutation operators. The population that has a higher fitness function value is chosen for the next iteration. After successive generations, the population evolved to the optimal solutions. The main steps of multi-objective genetic algorithm using NSGA-II are presented in Figure 4. More details can be found in the Reference [55]. 33 10 ,, The utilization of energy quality is more concerned than the exergy loss of each component. Therefore, the system exergy efficiency (ηex) is defined as the ratio of system network to the sum of exergy destruction from the heat source (ΔExhs) and cold source (ΔExcs): The payback period (PBP) is the time required to recover the cost of the investment, which is defined as: where τ is the annual operating time, which is assumed to be 7200 hours; cele is the electricity price of 0.15 $/kWh; Cm is the maintenance cost, which is assumed to be 2% of the system cost.

Optimization Method
Multi-objective optimization has been widely used in various subjects to minimize or maximize two or more functions simultaneously with several constraints. In this paper, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), an improved version of NSGA, is utilized for ORC system performance optimization. NSGA-II is a heuristic search algorithm inspired by natural evolutionary techniques. In the NSGA-II optimization process, all populations are modified within the constraints. At each step, the selected population is used as parents to produce offspring generations via tournament selection, cross over and mutation operators. The population that has a higher fitness function value is chosen for the next iteration. After successive generations, the population evolved to the optimal solutions. The main steps of multi-objective genetic algorithm using NSGA-II are presented in Figure 4. More details can be found in the references [55].

Objective Functions and Decision Making
Two important objective functions are defined for multi-objective optimization purpose. The first objective function Π 1 is defined as the product of system energy efficiency and exergy efficiency, which should be maximized. The second objective function Π 2 is set as the system investment divided by the payback period, which should be minimized. The objective functions Π 1 and Π 2 are defined in In the multi-objective optimization, any improvement in one objective function requires at least one other objective function to be refined. Therefore, no single solution for solving the conflicts among the objective functions exists and a set of trade-off optimal solutions are generally presented, known as the Pareto front. The standard Technique for Order Preference by Similarity to Ideal Situation (TOPSIS) method attempts to choose alternatives that have the shortest distance from the ideal solution [56,57]. The TOPSIS decision making is used in the present study. In order to achieve the optimal operating parameters more reasonably, all candidate points of Π 1 and Π 2 are normalized between 0.05 and 0.95 with Equations (12) and (13), respectively.
where min and max represent the minimum and maximum values in the solution of objective functions.

Solution Algorithm and Model Validation
The calculations of thermophysical properties of WFs and energy balance are implemented in Aspen Hysys (V9.0, Aspen Tech, Bedford, MA, USA). The PR (Peng-Robinson) equation is used in the simulation process. However, the optimization capacity of Aspen Hysys V9 is very limited. Considering the convenience of optimization toolbox, the optimization of the ORC system was realized by MATLAB (2017b, MathWorks, Natick, MA, USA). By adjusting the interactions between thermophysical properties and operating parameters of the combined ORC system, the calculation procedure of the optimization parameters is shown in Figure 5. Firstly, specific parameters and basic assumptions were given. The corresponding component and the energy, exergy and economic model were established. Secondly, ORC performance simulation was carried out under the initial conditions to determine the optimal WFs combinations for further study. Thirdly, the boundaries and constraints for the specified WF combination were set. The evaporation pressure and condensation pressure increased gradually within the specified scope. For each loop, the performance criteria and the objective functions were calculated. Finally, the optimization was carried out and the Pareto solution was obtained. Values of important parameters in GA are presented in Table 9. To ensure reliability and validity of the proposed model, comparisons between the previously published results and this paper were conducted. Sun et al. [58] proposed a cascade two-stage ORC system, which consists of two ORC subsystems sharing the same evaporative condenser. The structure Energies 2020, 13, 1397 12 of 23 is similar to part of the proposed combined ORC system. However, economic analysis was not carried out in their work. Yang [59] investigated the payback period of ORC system with waste heat recovery from exhaust gas of a large marine diesel engine, which could provide reference for the economic analysis of this paper. Therefore, comparisons with previous studies [58,59] were conducted. The initial conditions and all calculation results are listed in Table 10. The mean relative errors of thermal and economic indexes are within 28%. Comparing the exergy efficiency, this paper obtained lower results than for that in [58], especially for the waste heat at high temperature. The reason for this can be attributed to the evaporation pressure limited by heat source. Therefore, the developed model could be employed for further performance analysis of the combined ORC system. To ensure reliability and validity of the proposed model, comparisons between the previously published results and this paper were conducted. Sun et al. [58] proposed a cascade two-stage ORC system, which consists of two ORC subsystems sharing the same evaporative condenser. The structure is similar to part of the proposed combined ORC system. However, economic analysis was not carried out in their work. Yang [59] investigated the payback period of ORC system with waste heat recovery from exhaust gas of a large marine diesel engine, which could provide reference for the economic analysis of this paper. Therefore, comparisons with previous studies [58,59] were conducted. The initial conditions and all calculation results are listed in Table 10. The mean relative errors of thermal and economic indexes are within 28%. Comparing the exergy efficiency, this paper obtained lower results than for that in [58], especially for the waste heat at high temperature. The reason for this can be attributed to the evaporation pressure limited by heat source. Therefore, the developed model could be employed for further performance analysis of the combined ORC system.

WF Combination Selection
The thermal criteria (energy efficiency and exergy efficiency) and economic criteria (system cost and payback period) for 36 WF combinations are demonstrated in Figure 6a,b, respectively. In order to evaluate the comprehensive performance of WF, Π 1 and Π 2 of the ORC system with the predetermined 36 WF combinations are summarized in Table 11. From Table 11, it can be seen that case 15 demonstrates the best thermal performance with Π 1 equals 6.68% and case 19 shows the best economic performance with Π 2 equals 2.66 × 10 5 $/year. Instead of optimizing the WF combination, this paper would focus on working pressure optimization. Therefore, case 15 and case 19 are selected as two optimal WF combinations and would be further studied.
system with the predetermined 36 WF combinations are summarized in Table 11. From Table 11, it can be seen that case 15 demonstrates the best thermal performance with Π1 equals 6.68% and case 19 shows the best economic performance with Π2 equals 2.66 × 10 5 $/year. Instead of optimizing the WF combination, this paper would focus on working pressure optimization. Therefore, case 15 and case 19 are selected as two optimal WF combinations and would be further studied.     Figure 7 illustrates the system net output work (W net ) and system total cost (C tot ) with the variation of p CON and p EVA for case 15 and case 19. As observed from Figure 7a,b, the W net of case 15 and case 19 varies in the range of 99-294 kW and 55-247 kW, respectively. As the p CON increases, the W net of case 15 and case 19 increases, even though the increase gradually slows down. At the same time, the W net for case 15 and case 19 decreases with the increase of p EVA . The results of the C tot are shown in Figure 7c,d demonstrating that the C tot case 15 is higher than that of case 19. The C tot of case 15 and case 19 vary in the range of 1.5 × 10 6 -2.3 × 10 6 $ and 1.3 × 10 6 -2.0 × 10 6 $, respectively. Similar to the variation trend of W net , the C tot case 15 and case 16 increases with the p CON increase, while it decreases with the p EVA increase. This is clearly indicating that larger output work requires larger system investment. From a practical point of view, a contradiction exists in the two parameters and it makes sense to carry out multi-objective optimization.

36
R170-R1234yf-R601 5.03 2.73  Figure 7 illustrates the system net output work (Wnet) and system total cost (Ctot) with the variation of pCON and pEVA for case 15 and case 19. As observed from Figure 7a and Figure 7b, the Wnet of case 15 and case 19 varies in the range of 99-294 kW and 55-247 kW, respectively. As the pCON increases, the Wnet of case 15 and case 19 increases, even though the increase gradually slows down. At the same time, the Wnet for case 15 and case 19 decreases with the increase of pEVA. The results of the Ctot are shown in Figure 7c and Figure 7d demonstrating that the Ctot case 15 is higher than that of case 19. The Ctot of case 15 and case 19 vary in the range of 1.5 × 10 6 -2.3 × 10 6 $ and 1.3 × 10 6 -2.0 × 10 6 $, respectively. Similar to the variation trend of Wnet, the Ctot case 15 and case 16 increases with the pCON increase, while it decreases with the pEVA increase. This is clearly indicating that larger output work requires larger system investment. From a practical point of view, a contradiction exists in the two parameters and it makes sense to carry out multi-objective optimization. The variation of energy efficiency (ηen) and exergy efficiency (ηex) with pCON and pEVA are shown in Figure 8. As shown in Figure 8a and Figure 8b, the ηen for case 15 is higher than that for case 19 on the whole. ηen increases with the increase of pCON while decreases with the increase of pEVA. ηen for case 15 and case 19 varies in the range of 7.9%-18.9% and 4.5-16.7%, respectively. In the area with high pCON, ηen increases dramatically. This is because the power output increases faster than the heat absorbed from heat source. The effect of pEVA on ηen gradually decreases with pEVA increasing. As shown in Figure 8c and Figure 8d, the ηex for case 15 and case 19 varies in 12.7%-35.4% and 7.1%-30.2%, respectively. ηen and ηex have the same variation trend with the pressures.

Effect of Condensation and Evaporation Pressures
The trend of payback period (PBP) for case 15 and case 19 is displayed in Figure 9. The PBP of The variation of energy efficiency (η en ) and exergy efficiency (η ex ) with p CON and p EVA are shown in Figure 8. As shown in Figure 8a,b, the η en for case 15 is higher than that for case 19 on the whole. η en increases with the increase of p CON while decreases with the increase of p EVA . η en for case 15 and case 19 varies in the range of 7.9-18.9% and 4.5-16.7%, respectively. In the area with high p CON , η en increases dramatically. This is because the power output increases faster than the heat absorbed from heat source. The effect of p EVA on η en gradually decreases with p EVA increasing. As shown in Figure 8c,d, the η ex for case 15 and case 19 varies in 12.7-35.4% and 7.1-30.2%, respectively. η en and η ex have the same variation trend with the pressures.  The trend of payback period (PBP) for case 15 and case 19 is displayed in Figure 9. The PBP of case 15 and case 19 varies between 7.0-14.2 years and 7.3-21.6 years, respectively. Even though the system total cost of case 19 is less than case 15, the PBP of case 19 is much longer than case 15. The reason can be attributed to the lower output power and lower energy utilization efficiency, which are illustrated in Figures 7 and 8, respectively. The higher the p CON is, the shorter the PBP is. The higher the p EVA is, the longer the PBP is. These results can prove that the variation trends of output power and system cost are correct. Figure 10 depicts the variations of the Logarithmic Mean Temperature Difference (LMTD) and the cost of EVA1 (C EVA1 ) for case 15 and case 19. As shown in Figure 10a,b, the LMTDs for the two cases have the same behavior of a decreasing trend with the increase of p CON when the p EVA remains at 100 kPa. In addition, the LMTD variation of case 15 is more dramatic than that of case 19. The LMTD Energies 2020, 13, 1397 16 of 23 of case 15 and case 19 varies in the range of 10.1-82.7 • C and 17.1-60.3 • C, respectively. The decrease of LMTD would lead to an increase of EVA1 heat transfer area, and thus result in C EVA1 increase. As shown in Figure 10c,d, the LMTD increases with the increase of p EVA when the p CON maintains at their highest pressure. The LMTD of case 15 increases from 10.1 • C to 90.6 • C when the p EVA increasing from 100 kPa to 850 kPa. The LMTD variation of case 19 is larger than that of case 15, which changes from 17.1 • C to 145.9 • C when the p EVA varies in the range of 100 kPa to 3500 kPa. The C EVA1 decreases with the increase of p EVA and the results are in accordance with the results shown in Figure 7c,d.

Overall Thermo-Economic Performances
The variation of Π1 and Π2 with the three optimal WF combinations with pCON and pEVA is

Overall Thermo-Economic Performances
The variation of Π1 and Π2 with the three optimal WF combinations with pCON and pEVA is displayed in Figure 11. Compare Figure 11a-Figure 11d, it could draw a conclusion that case 15 has

Overall Thermo-Economic Performances
The variation of Π 1 and Π 2 with the three optimal WF combinations with p CON and p EVA is displayed in Figure 11. Compare Figure 11a-d, it could draw a conclusion that case 15 has the highest thermal efficiency with Π 1 equals 6.7% and the lowest system cost with Π 2 equals to 0.6 × 10 5 $/year that obtained from case 19. As observed from Figure 11a,b, Π 1 decreases with the increase of p EVA even though the extent of the reduction gradually diminishes. With the increase of p EVA , the LMTD of the EVA3 decreases, which contributes to worse energy and exergy utilization from the exhaust gas. Π 1 increases with the increase of p CON and the increase tends to be flat. This is primarily caused by the increase of output power in EXP1. As shown in Figure 11c,d, the economic index Π 2 shows the same variation tendency with Π 1 , that is, Π 2 decreases with p EVA increase, while it increases with p CON increase.
Energies 2020, 13, x FOR PEER REVIEW 18 of 24 10 5 $/year that obtained from case 19. As observed from Figure 11a and Figure 11b, Π1 decreases with the increase of pEVA even though the extent of the reduction gradually diminishes. With the increase of pEVA, the LMTD of the EVA3 decreases, which contributes to worse energy and exergy utilization from the exhaust gas. Π1 increases with the increase of pCON and the increase tends to be flat. This is primarily caused by the increase of output power in EXP1. As shown in Figure 11c and Figure 11d, the economic index Π2 shows the same variation tendency with Π1, that is, Π2 decreases with pEVA increase, while it increases with pCON increase.

Multi-objective Optimization Results
Based on the two selected WF combinations of different evaporation pressures and condensation pressures, the combined ORC system is optimized under the fixed heat source and cold source. The objective function Π1 regarding energy and exergy utilization should be maximized while the objective function Π2 regarding cost and payback period should be minimized. The Pareto front and the optimal results of the two normalized objective functions calculated by NSGA-II iteration are demonstrated in Figure 12. The Pareto optimization results illustrate the conflict between the two objective functions. After Π1 reaches a certain value, Π2 increases sharply. In this paper, the most favorable point in the Pareto front was defined as the minimum normalized distance to the ideal point, i.e., the end of the x-axis. Thus, optimized working conditions and results for three cases were respectively decided, which are listed in Table 12

Multi-Objective Optimization Results
Based on the two selected WF combinations of different evaporation pressures and condensation pressures, the combined ORC system is optimized under the fixed heat source and cold source. The objective function Π 1 regarding energy and exergy utilization should be maximized while the objective function Π 2 regarding cost and payback period should be minimized. The Pareto front and the optimal results of the two normalized objective functions calculated by NSGA-II iteration are demonstrated in Figure 12. The Pareto optimization results illustrate the conflict between the two objective functions. After Π 1 reaches a certain value, Π 2 increases sharply. In this paper, the most favorable point in the Pareto front was defined as the minimum normalized distance to the ideal point, i.e., the end of the x-axis. Thus, optimized working conditions and results for three cases were respectively decided,   In order to have a further understanding of the combined ORC system, the exergy destruction and cost of each component are analyzed under the optimized working conditions. The chart of the exergy destruction of each component in the combined ORC system is illustrated in Figure 13. In all cases, the exergy destruction mainly occurs in the heat exchangers. The exergy destruction in CON1 accounts for the largest part (up to 40%) of system exergy destruction. The reason is given to the large temperature difference between LNG evaporation temperature and WF1 condensation temperature. Limited by the required pressure of DF marine engine, the corresponding temperature of LNG is −134.6 °C. The optimized condensation temperature of the selected WF1 for case 15 and case 19 is −103.8 °C and −88.6 °C, respectively. Therefore, future work could be carried out in the optimization of CON1. The second place of exergy destruction goes to EVA1. Therefore, it proves true that the study of pressure variation in EVA1. The exergy destruction in EVA1 for case 19 is larger than that for case 15, which is mainly caused by the larger LMTD as shown in Table 10. Comparing Figure 13a and Figure 13b, we can draw the conclusion that the matching degree in EVA1 for case 15 (R1150 and R600a) is more reasonable than that for case 19 (R170 and R152a). Compared to case 19, the exergy destruction in EVA1 for case 15 could be reduced up to 18.99%. In addition, the exergy destructions in pumps are relatively small.  In order to have a further understanding of the combined ORC system, the exergy destruction and cost of each component are analyzed under the optimized working conditions. The chart of the exergy destruction of each component in the combined ORC system is illustrated in Figure 13. In all cases, the exergy destruction mainly occurs in the heat exchangers. The exergy destruction in CON1 accounts for the largest part (up to 40%) of system exergy destruction. The reason is given to the large temperature difference between LNG evaporation temperature and WF1 condensation temperature. Limited by the required pressure of DF marine engine, the corresponding temperature of LNG is −134.6 • C. The optimized condensation temperature of the selected WF1 for case 15 and case 19 is −103.8 • C and −88.6 • C, respectively. Therefore, future work could be carried out in the optimization of CON1. The second place of exergy destruction goes to EVA1. Therefore, it proves true that the study of pressure variation in EVA1. The exergy destruction in EVA1 for case 19 is larger than that for case 15, which is mainly caused by the larger LMTD as shown in Table 10. Comparing Figure 13a,b, we can draw the conclusion that the matching degree in EVA1 for case 15 (R1150 and R600a) is more reasonable than that for case 19 (R170 and R152a). Compared to case 19, the exergy destruction in EVA1 for case 15 could be reduced up to 18.99%. In addition, the exergy destructions in pumps are relatively small.
The cost of each component cost and its ratio to the system total cost are demonstrated in Figure 14. Under different cases, the proportion of component cost is different. The costive components are generally expanders. For example, the cost of expanders in case 15 account for more than 50% of the system total cost. Meanwhile, the cost of expanders reflects the contribution of different ORC stages to the system net output work. The output work is sorted as ORC 3, ORC 1 and ORC 2 for both cases. The cost of heat exchangers basically depends on the area of heat exchanger. EVA3 and EVA2 is the most costive heat exchanger for case 15 and case 19, respectively. The reason could be attributed to its large heat transfer area caused by small LMTD between working fluid and heat source. Similarly, the proportion of CON2 cost could be explained as well. Based on the optimized working conditions, the proportion of EVA1 cost is small, which is 3.9% and 4.08% for case 15 and case 19, respectively. The cost of all pumps accounts for 4.90% and 6.06% for case 15 and case 19, respectively. cases, the exergy destruction mainly occurs in the heat exchangers. The exergy destruction in CON1 accounts for the largest part (up to 40%) of system exergy destruction. The reason is given to the large temperature difference between LNG evaporation temperature and WF1 condensation temperature. Limited by the required pressure of DF marine engine, the corresponding temperature of LNG is −134.6 °C. The optimized condensation temperature of the selected WF1 for case 15 and case 19 is −103.8 °C and −88.6 °C, respectively. Therefore, future work could be carried out in the optimization of CON1. The second place of exergy destruction goes to EVA1. Therefore, it proves true that the study of pressure variation in EVA1. The exergy destruction in EVA1 for case 19 is larger than that for case 15, which is mainly caused by the larger LMTD as shown in Table 10. Comparing Figure 13a and Figure 13b, we can draw the conclusion that the matching degree in EVA1 for case 15 (R1150 and R600a) is more reasonable than that for case 19 (R170 and R152a). Compared to case 19, the exergy destruction in EVA1 for case 15 could be reduced up to 18.99%. In addition, the exergy destructions in pumps are relatively small. The cost of each component cost and its ratio to the system total cost are demonstrated in Figure  14. Under different cases, the proportion of component cost is different. The costive components are generally expanders. For example, the cost of expanders in case 15 account for more than 50% of the system total cost. Meanwhile, the cost of expanders reflects the contribution of different ORC stages to the system net output work. The output work is sorted as ORC 3, ORC 1 and ORC 2 for both cases. The cost of heat exchangers basically depends on the area of heat exchanger. EVA3 and EVA2 is the most costive heat exchanger for case 15 and case 19, respectively. The reason could be attributed to its large heat transfer area caused by small LMTD between working fluid and heat source. Similarly, the proportion of CON2 cost could be explained as well. Based on the optimized working conditions, the proportion of EVA1 cost is small, which is 3.9% and 4.08% for case 15 and case 19, respectively. The cost of all pumps accounts for 4.90% and 6.06% for case 15 and case 19, respectively.  The cost of each component cost and its ratio to the system total cost are demonstrated in Figure  14. Under different cases, the proportion of component cost is different. The costive components are generally expanders. For example, the cost of expanders in case 15 account for more than 50% of the system total cost. Meanwhile, the cost of expanders reflects the contribution of different ORC stages to the system net output work. The output work is sorted as ORC 3, ORC 1 and ORC 2 for both cases. The cost of heat exchangers basically depends on the area of heat exchanger. EVA3 and EVA2 is the most costive heat exchanger for case 15 and case 19, respectively. The reason could be attributed to its large heat transfer area caused by small LMTD between working fluid and heat source. Similarly, the proportion of CON2 cost could be explained as well. Based on the optimized working conditions, the proportion of EVA1 cost is small, which is 3.9% and 4.08% for case 15 and case 19, respectively. The cost of all pumps accounts for 4.90% and 6.06% for case 15 and case 19, respectively.

Conclusions
In this paper, a combined ORC system was proposed for cascade utilization of waste heat from dual fuel marine engine and cold energy from LNG. The waste heat from engine exhaust gas and

Conclusions
In this paper, a combined ORC system was proposed for cascade utilization of waste heat from dual fuel marine engine and cold energy from LNG. The waste heat from engine exhaust gas and jacket cooling water worked as dual heat sources. First, the applicability of 11 working fluids for the combined ORC system was studied. Afterwards, the performances of the ORC system with two selected working fluid combinations were analyzed from the perspective of thermo-economic. In particular, the effects of condensation pressure and evaporation pressure on the ORC system performance were investigated. Finally, a multi-objective optimization was conducted to decide the best working condition. Exergy destructions and costs of each component were presented with the optimized working conditions. The main conclusions drawn from this study can be summarized as following: (1) A mathematical model for ORC system simulation was established. The results of the literature and the present paper were compared and analyzed, which verified the feasibility of the proposed model. The top 2 working fluid combinations for the ORC system were selected as R1150-R1234yf-R600a (with Π 1 equals 6.68%) and R170-R1270-R152a (with Π 2 equals 2.66 × 10 5 $/year) based on the basic working conditions.
(2) The effects of the condensation pressure (p CON ) and evaporation pressure (p EVA ) in the intermediate heat exchanger on the ORC performances were investigated. The increase in p EVA resulted in a decrease of energy utilization objective function Π 1 , while the increase in p CON contributed to a higher Π 1 . Meanwhile, the variation trend of economic objective function Π 2 with p EVA and p CON demonstrated the same trend as that of Π 1 .
(3) A multi-objective optimization model was taken into account to decide the most suitable p CON and p EVA for two selected working fluid combinations. The optimized operating pressures for the two cases were 796.87/112.21 kPa and 204.79/214 kPa, respectively. With the optimized working conditions, the energy efficiency was in the range of 11.59-16.32% and the exergy efficiency was in the range of 19.47-29.06%. The total cost of the ORC system with different working fluid combinations varied in the range of 1.58 × 10 6~1 .96 × 10 6 $ and the payback period varies in the range of 7.68-9.43 years.
(4) Exergy destruction mainly occurred in heat exchangers. Searching for working fluid combination could reduce the exergy destruction in the intermediate heat exchanger (EVA1). The results indicated that the fluids matching degree in case 15 (R1150-R600a) were more reasonable, which generated 18.99% reduction in exergy destruction compared to case 19 (R170-R152a). In addition, the EVA1 investment cost in case 15 and case 19 accounted for 3.89% and 4.08% of the system cost, respectively. However, the cost of expanders could exceed 50% of the system cost. Therefore, the total investment cost could be reduced by optimizing expanders.