Thermodynamic, Economic, and Environmental Analysis and Optimization of a Multi-Heat-Source Organic Rankine Cycle for Large Marine Diesel Engine

Abstract

The Organic Rankine Cycle (ORC)-based waste-heat recovery system represents an important technological pathway toward decarbonization in the maritime industry. This study focuses on the design and optimization of a multi-heat-source Organic Rankine Cycle (MHSORC) power generation system specifically developed for large marine diesel engines, which simultaneously utilizes exhaust gas, cylinder jacket water, and scavenging air as heat sources. Unified thermodynamic, economic, and environmental models are constructed to evaluate the coupled performance of the system.Eight low GWP working fluids are assessed, and a multi-objective optimization is performed to balance efficiency, cost, and environmental impact. The optimal design point is subsequently identified using a decision-making algorithm. The results indicate that, for the MHSORC, higher evaporating temperatures and lower condensing temperatures improve system performance, and the heat-source temperature exerts a direct and substantial influence on that performance. Among the candidate fluids, R601 exhibits the best overall performance, whereas R1234ze performs the worst. With R601 as the working fluid, the MHSORC achieves an exergy efficiency of 41.69%, a LCOE of 0.0495 $/kWh, and greenhouse gas emissions of 0.8019 kt of CO_2,eq.

1. Introduction

The world is collectively striving toward the goal of net-zero carbon emissions, and the maritime industry is no exception [1]. As a cornerstone of international trade, the shipping sector plays an indispensable role in global logistics [2]. However, ships consume substantial amounts of energy and emit significant quantities of ${\mathrm{CO}}_2$ during operation [3]. At present, most vessels rely on internal combustion engines as their primary propulsion systems. During engine operation, a considerable portion of waste heat is released into the environment, resulting in severe energy losses [4]. Consequently, waste-heat recovery (WHR) has been recognized as a feasible and effective approach to enhancing energy efficiency and reducing emissions [5]. Compared with other sources, the waste heat available on ships generally exhibits relatively low temperatures owing to the high thermal efficiency of large marine engines.

Among the available technologies, the Organic Rankine Cycle (ORC) has been identified as one of the most promising methods for converting low- and medium-grade waste heat into useful power [6]. Compared with conventional steam Rankine cycles, the ORC can efficiently recover heat from sources at relatively low temperatures, making it particularly suitable for shipboard applications where exhaust gas, cylinder jacket water, and scavenging air exhibit complementary thermal characteristics.

1.1. Review of Related Work

Vaja and Gambarotta [7] proposed a preheating-type ORC system for recovering waste heat from internal combustion engines. The system comprises a preheater and an evaporator: in the preheater, the working fluid is first heated by the cylinder jacket water, and in the evaporator, it is further heated by the exhaust gas to become superheated vapor. Their results demonstrate that integrating a preheater into a single-loop ORC system to simultaneously utilize both the jacket water and the exhaust gas yields a higher output power compared with a basic ORC system that recovers heat solely from the exhaust gas. Song et al. [8] compared a preheating-type ORC system using jacket water with ORC systems that individually employed either the jacket water or the exhaust gas for power generation. Their comparison indicated that the preheating-type ORC configuration offers certain economic advantages. Wang et al. [9] designed a dual-loop ORC system in which the high-temperature loop recovers exhaust-gas heat for power generation, while the low-temperature loop recovers residual heat from both the working fluid and the cylinder jacket water. Their analysis revealed that the dual-loop configuration increases output power by approximately 14%. Civgin and Deniz [10] developed two different dual-loop ORC systems: one employing cylinder jacket water in the low-temperature loop and the other utilizing scavenging air. Their evaluation under high-load operating conditions suggested that both dual-loop systems effectively reduce marine fuel consumption. Sabir et al. [11] conducted comprehensive thermodynamic and economic analyses of single-loop and dual-loop ORC systems. The results indicated that although the single-loop system produces a lower total output power, it achieves a shorter payback period. Overall, these studies demonstrate that coupling multiple heat sources at different temperature levels for power generation can substantially enhance the thermodynamic and economic performance of ORC systems.

To further enhance the performance of the ORC system, Akman and Ergin [12] proposed a single-loop ORC configuration that simultaneously utilizes three distinct heat sources. In this system, the working fluid is preheated by both the cylinder jacket water and the scavenging air. The analysis results revealed that when the diesel engine operates above 82% load, the ORC unit can fully satisfy the ship’s electrical demand while improving the engine’s thermal efficiency by approximately 6%. The authors also reported that although the multi-heat-source ORC (MHSORC) system entails a higher initial investment, it achieves the shortest payback period among the compared configurations. Feng et al. [13] analyzed the thermodynamic characteristics of a MHSORC and observed that elevating the preheating temperature results in increased power generation. In contrast, raising the evaporation pressure diminishes power output yet contributes to an improvement in thermal efficiency. In a related study, Li and Tang [14] examined the MHSORC system from thermodynamic, economic, and optimization perspectives. Their analysis demonstrated that although the MHSORC yields a power output comparable to that of a dual-heat-source configuration, it attains a noticeably lower LCOE, underscoring its economic superiority.

The aforementioned studies demonstrate that multi-heat-source ORC systems exhibit superior thermal efficiency and economic performance. In view of increasingly stringent carbon-emission regulations, it is also essential to integrate environmental assessment and optimization into system design. Wang et al. [15] performed a multi-objective optimization and working-fluid selection for an ORC system, in which environmental performance was incorporated as one of the objective functions. The results revealed that R600a exhibits better overall performance in both economic and environmental aspects. Chen et al. [16] conducted an environmental analysis of a liquid–air energy storage system integrated with an ORC, showing that the overall system could reduce ${\mathrm{CO}}_2$ emissions by approximately 23.4 tons. Wang et al. [17] analyzed the environmental and economic performance of a biogas-based integrated energy system containing two ORC units. Their findings demonstrated that the proposed configuration substantially reduces fossil-fuel consumption and enhances environmental sustainability. Zhou et al. [18] evaluated the environmental performance of an integrated ORC–refrigeration system and applied the NSGA-II algorithm for multi-objective optimization. Their results indicated that the proposed configuration significantly decreases ${\mathrm{CO}}_2$ emissions throughout the system’s life cycle.

1.2. Research Gap and Objectives

The literature review indicates that single-loop MHSORC systems for marine diesel engine waste-heat recovery can substantially enhance both thermodynamic and economic performance. Nevertheless, comprehensive environmental evaluation and optimization remain relatively underexplored. Most existing studies have focused primarily on thermal and economic aspects, while neglecting the life-cycle environmental impact of MHSORC systems. Integrating environmental indicators into the optimization framework is therefore essential to ensure the overall sustainability of marine waste-heat recovery systems.

To address this gap, the present study performs a comprehensive thermodynamic, economic, and environmental assessment and optimization are conducted for a multi-heat-source Organic Rankine Cycle (MHSORC) system aimed at recovering waste heat from marine diesel engines. Corresponding models are developed to quantify the exergy efficiency, levelized cost of electricity (LCOE), and greenhouse gas (GHG) emissions of the system, serving as the foundation for working fluid selection. Eight environmentally benign working fluids with zero ozone depletion potential (ODP) and low global warming potential (GWP) are investigated. A multi-objective optimization procedure is implemented using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), followed by the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) to identify the best compromise solution on the Pareto front. Subsequently, Grey Relational Analysis (GRA) is applied to rank the performance of the optimized fluids and determine the most advantageous working medium.

2. Methods

2.1. Waste Heat of Large Marine Diesel Engine

During ocean navigation, the propulsion power of a ship is primarily supplied by a low-speed, two-stroke marine diesel engine [19]. During operation, the diesel engine releases a substantial amount of waste heat. The typical waste-heat distribution of a large marine diesel engine installed on an ocean-going vessel is illustrated in Figure 1.

As shown in Figure 1, a portion of the energy contained in the fuel consumed by the marine diesel engine is converted into propulsion power, while the remainder is released into the environment. Although the thermal efficiency of modern marine diesel engines can reach approximately 50%, more than half of the fuel energy is still lost as waste heat. The overall energy balance of the marine diesel engine is illustrated in Figure 2.

As shown in Figure 2, only 49.3% of the fuel’s chemical energy is transformed into effective shaft power, whereas the remainder is released as waste heat through the scavenging air, exhaust gas, cylinder cooling water, and lubricating oil. Among these, the heat loss via lubricating oil represents merely 2.9% of the total fuel energy [20]. Furthermore, since the outlet temperature of the lubricating oil is around 50 °C and its temperature plays a critical role in ensuring the stable operation of the diesel engine, this source is unsuitable for waste-heat recovery applications.

During engine operation, it is also essential to maintain the outlet temperature of the scavenging air to ensure an adequate intake-air volume. Therefore, in this study, the scavenging air is substituted with the cooling water at the outlet of the intercooler, which serves as the corresponding heat source. The waste-heat parameters of the Wärtsilä RT-flex96C marine diesel engine operating at 85% load are adopted as the basis for system design, and the detailed parameters are listed in

Table 1. The heat source parameters of the RT-flex96C large marine diesel engine under 85% load.

Heat Source	Exhaust Gas	Jacket Water	Intercooler Water	Unit
Mass flow rate	173.0	182.5	190.6	kg/s
Inlet temperature	533.15	363.15	349.15	K
Limiting outlet temperature	406.15	346.15	319.15	K

.

2.2. Description of the Multi-Heat-Source ORC System

Before establishing the configuration of the MHSORC system for marine use, the recoverable thermal characteristics of the available heat sources must be evaluated. Figure 3 illustrates the accessible temperature intervals of the three principal heat sources.

As shown in Figure 3, these temperature ranges exhibit minimal overlap, indicating that a single-loop MHSORC system is well suited for this configuration. The configuration of the MHSORC system designed for large marine diesel engines is illustrated in the following Figure 4.

As illustrated in Figure 4, the working fluid is initially pressurized by the pump and directed into heat exchanger A, where it absorbs heat from the intercooler cooling water. It then passes through heat exchanger B, gaining additional heat from the jacket water. Next, the fluid enters heat exchanger C, where it is further heated by the exhaust gas and converted into high-pressure superheated vapor. This vapor expands in the expander to generate mechanical power, resulting in low-pressure superheated vapor. Finally, the vapor is condensed in the condenser, returning to a saturated liquid state to complete the cycle.

Compared with a basic ORC system, this configuration differs primarily by the addition of multiple heat exchangers. Consequently, the existing components of the power generation system can be effectively utilized, thereby reducing the overall investment cost. Furthermore, the performance of the MHSORC system can be improved through appropriate heat-source matching, working-fluid selection, and optimization of operating parameters. The corresponding T-s diagram of the MHSORC system is illustrated in Figure 5.

2.3. Thermodynamic Model

The thermodynamic framework of the MHSORC system is developed in accordance with the first and second laws of thermodynamics. The heat exchanger energy balance can therefore be expressed as follows [21]:

$$\begin{array}{cc}\hfill {\dot{Q}}_{\mathrm{hx},i}& ={\dot{m}}_{\mathrm{r}}(h_{3,i}-h_{2,i})\hfill \\ \hfill & ={\dot{m}}_{\mathrm{hs}}{c}_{p,\mathrm{hs}}(T_{\mathrm{hs},\mathrm{in}}-T_{\mathrm{hs},\mathrm{out}})\hfill \end{array}$$

(1)

where $\dot{Q}$ denotes the heat transfer rate, $c_p$ is the specific heat capacity, $\dot{m}$ represents the mass flow rate, T is the temperature, and h refers to the specific enthalpy.

The power produced by the expander is determined by the product of the working fluid mass flow rate and the enthalpy drop across the expander, and is mathematically represented as

$${\dot{W}}_{\exp }={\dot{m}}_{\mathrm{r}}(h_{\mathrm{in},\exp }-h_{\mathrm{out},\exp }){\eta }_{\exp }$$

(2)

where $\dot{W}$ is the power output, and ${\eta }_{\exp }$ is the mechanical efficiency of the expander.

The energy balance of the condenser can be expressed as

$$\begin{array}{cc}\hfill {\dot{Q}}_{\mathrm{cond}}& ={\dot{m}}_{\mathrm{r}}(h_6-h_1)\hfill \\ \hfill & ={\dot{m}}_{\mathrm{sw}}{c}_{p,\mathrm{sw}}(T_{\mathrm{sw},\mathrm{out}}-T_{\mathrm{sw},\mathrm{in}})\hfill \end{array}$$

(3)

The net power output is

$${\dot{W}}_{\mathrm{pu}}={\displaystyle \frac{{\dot{m}}_{\mathrm{r}}(h_{\mathrm{in},\mathrm{pu}}-h_{\mathrm{out},\mathrm{pu}})}{{\eta }_{\mathrm{pu}}}}$$

(4)

The net power output of the MHSORC is determined by subtracting the power consumption of the pump from the power produced by the expander, expressed as

$${\dot{W}}_{\mathrm{net}}={\dot{W}}_{\exp }-{\dot{W}}_{\mathrm{pu}}$$

(5)

The net thermal efficiency of the MHSORC is defined as [22]

$${\eta }_{\mathrm{mhsorc}}={\displaystyle \frac{{\dot{W}}_{\mathrm{net}}}{{\displaystyle \sum _{i=1}^3}{\dot{Q}}_{\mathrm{hx},i}}}$$

(6)

Exergy represents the maximum useful work obtainable and reflects the energy quality of the system. The exergy is given by

$${\dot{E}}_i={\dot{m}}_{\mathrm{r}}[(h_i-h_0)-T_0(s_i-s_0)]$$

(7)

The exergy destruction associated with each component of the MHSORC can be expressed as

$$\begin{array}{cc}\hfill & {\dot{I}}_{\mathrm{hxa}}={\dot{E}}_8-{\dot{E}}_7+{\dot{E}}_2-{\dot{E}}_3\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill & {\dot{I}}_{\mathrm{hxb}}={\dot{E}}_{10}-{\dot{E}}_9+{\dot{E}}_3-{\dot{E}}_4\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill & {\dot{I}}_{\mathrm{hxc}}={\dot{E}}_{12}-{\dot{E}}_{11}+{\dot{E}}_4-{\dot{E}}_5\hfill \end{array}$$

(10)

$$\begin{array}{cc}\hfill & {\dot{I}}_{\mathrm{cond}}={\dot{E}}_{14}-{\dot{E}}_{13}+{\dot{E}}_6-{\dot{E}}_2\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill & {\dot{I}}_{\exp }={\dot{E}}_5-{\dot{E}}_6-{\dot{W}}_{\exp }\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill & {\dot{I}}_{\mathrm{pu}}={\dot{E}}_1-{\dot{E}}_2+{\dot{W}}_{\mathrm{pu}}\hfill \end{array}$$

(13)

Based on the aforementioned thermodynamic analysis, the total exergy losses of the MHSORC can be determined by

$${\dot{I}}_{\mathrm{tot}}={\dot{I}}_{\mathrm{hxa}}+{\dot{I}}_{\mathrm{hxb}}+{\dot{I}}_{\mathrm{hxc}}+{\dot{I}}_{\mathrm{cond}}+{\dot{I}}_{\exp }+{\dot{I}}_{\mathrm{pu}}$$

(14)

Accordingly, the exergy efficiency of the MHSORC is defined as [22]

$${\eta }_{\mathrm{exer}}={\displaystyle \frac{{\dot{W}}_{\mathrm{net}}}{{\dot{I}}_{\mathrm{tot}}+{\dot{W}}_{\mathrm{net}}}}$$

(15)

2.4. Working Fluid Selection

The power output of the MHSORC system is highly sensitive to the thermodynamic characteristics of the working fluid. Therefore, selecting an appropriate working fluid is essential. To minimize environmental impact, the candidate fluids are required to have zero ODP and low GWP [23]. An overview of the essential thermophysical parameters for the eight proposed working fluids is presented in

Table 2. The thermodynamic properties of the eight candidate working fluids.

Working Fluid	Molar Mass (kg/kmol)	Critical Temperature (K)	Boiling Temperature (K)	ODP	GWP
R1234yf	114.04	367.85	243.7	0	4
R1270	42.08	364.21	320.95	0	2
R600a	58.122	407.81	261.4	0	20
R1234ze (E)	130.5	438.75	291.47	0	7
R601	72.15	469.7	309.21	0	20
R601a	72.149	460.35	300.98	0	20
R600	58.122	425.13	272.66	0	20
R290	44.1	369.89	231.15	0	3

.

2.5. Economic Model

A detailed economic framework is formulated to facilitate the analysis and optimization of the MHSORC system from an economic perspective. The following of this section develops the economic models for each component individually, followed by the overall system-level economic model [24].

2.5.1. Heat Transfer Area

To formulate the economic model of the heat exchanger, its cost must first be quantified. As the investment cost is mainly correlated with the effective heat transfer area, this area needs to be evaluated for all heat exchangers in the system. The Logarithmic Mean Temperature Difference (LMTD) method was employed for this purpose, and the resulting expression for calculating the heat transfer area of each exchanger, including the condenser, is given by [25]

$$A={\displaystyle \frac{{\dot{Q}}_{\mathrm{hx}}}{U\Delta T_{\mathrm{LM}}F}}$$

(16)

where F is assigned a value of 0.95, U is heat overall heat transfer coefficient, $\Delta T_{\mathrm{LM}}$ is defined according to

$$\Delta T_{\mathrm{LM}}={\displaystyle \frac{\Delta T_{\max }-\Delta T_{\min }}{ln(\Delta T_{\max }/\Delta T_{\min })}}$$

(17)

The heat transfer coefficients on both the heat source side and the working fluid side of the heat exchanger are presented in

Table 3. The heat transfer coefficients of the heat exchangers.

Type	Side	Region	Coefficient Correlation
Plate heat exchanger	working fluid	single phase	${\alpha }_{\mathrm{c},\mathrm{pl}}=0.023{\displaystyle \frac{k_{\mathrm{r}}}{D_{\mathrm{e},\mathrm{pl}}}}R{e}_{\mathrm{r}}^{0.8}P{r}_{\mathrm{r}}^{0.4}{\left({\displaystyle \frac{{\mu }_{\mathrm{r}}}{{\mu }_{\mathrm{w},\mathrm{r}}}}\right)}^{0.14}$
		boiling	${\alpha }_{\mathrm{tp},\mathrm{pl}}=1.926{\displaystyle \frac{k_{\mathrm{r}}}{D_{\mathrm{e},\mathrm{pl}}}}B{o}_{\mathrm{eq}}^{-0.3}R{e}_{\mathrm{eq}}^{0.5}P{r}_{\mathrm{eq}}^{1/3}\left[(1-x)+x{\left({\displaystyle \frac{{\rho }_{\mathrm{l}}}{{\rho }_{\mathrm{g}}}}\right)}^{0.5}\right]$
		film condensation	${\alpha }_{\mathrm{con},\mathrm{pl}}=4.118{\displaystyle \frac{k_{\mathrm{r},\mathrm{l}}}{D_{\mathrm{e},\mathrm{pl}}}}R{e}_{\mathrm{eq}}^{0.4}P{r}_{\mathrm{l}}^{1/3}$
	heat source	~	${\alpha }_{\mathrm{hs},\mathrm{pl}}=0.2121{\displaystyle \frac{k_{\mathrm{hs}}}{D_{\mathrm{e},\mathrm{pl}}}}R{e}_{\mathrm{hs}}^{0.78}P{r}_{\mathrm{hs}}^{1/3}{\left({\displaystyle \frac{{\mu }_{\mathrm{hs}}}{{\mu }_{\mathrm{w},\mathrm{hs}}}}\right)}^{0.14}$
Shell and tube exchanger	working fluid	single phase	${\alpha }_{\mathrm{r},\mathrm{shell}}=0.023{\displaystyle \frac{k_{\mathrm{r}}}{D_{\mathrm{e},\mathrm{shell}}}}R{e}_{\mathrm{r}}^{0.8}P{r}_{\mathrm{r}}^{0.3}$
		boiling	${\alpha }_{\mathrm{tp},\mathrm{shell}}={\alpha }_{\mathrm{l}}\left[H_{1}H{o}^{H_2}{\left(25F{r}_{\mathrm{lo}}\right)}^{H_5}+H_{3}B{o}^{H_4}{F}_{fl}\right]$
	heat source	~	${\alpha }_{\mathrm{hs},\mathrm{shell}}=0.023{\displaystyle \frac{k_{\mathrm{hs}}}{D_{\mathrm{e},\mathrm{shell}}}}R{e}_{\mathrm{r}}^{0.8}P{r}_{\mathrm{hs}}^{0.4}$

.

Ultimately, the aggregate heat transfer area of the MHSORC system is derived by adding together the respective areas of all heat exchangers, and can be formulated as

$$A_{\mathrm{hx},\mathrm{tot}}=A_{\mathrm{hxa}}+A_{\mathrm{hxb}}+A_{\mathrm{hxc}}$$

(18)

2.5.2. Cost Model

In this work, the total capital cost of the proposed MHSORC system was evaluated using standard equipment cost estimation equations, accounting for the heat exchangers, expander, working fluid pump, and condenser. The corresponding capital cost of each MHSORC component is given by [26]

$$C_{\mathrm{BM},n}=C_{\mathrm{p},n}(B_{1,n}+B_{2,n}{F}_{\mathrm{M},\mathrm{n}}{F}_{\mathrm{P},n})$$

(19)

where subscript n represents the equipment type, and $F_{\mathrm{M}}$, $B_1$, and $B_2$ are empirical constants used in the cost correlation as presented in

Table 4. Empirical coefficients for module cost estimation equations.

Equipment Type	${\mathit{K}}_1$	${\mathit{K}}_2$	${\mathit{K}}_3$	${\mathit{C}}_1$	${\mathit{C}}_2$	${\mathit{C}}_3$	${\mathit{B}}_1$	${\mathit{B}}_2$	${\mathit{F}}_{\mathbf{M}}$
Plate heat exchanger	4.6561	−0.2947	0.2207	0	0	0	0.96	1.21	1
Shell and tube heat exchanger	4.3247	−0.3030	0.1634	0.0381	−0.11272	0.08183	1.63	1.66	1.2
Condenser	4.6561	−0.2947	0.2207	0	0	0	0.96	1.21	1
Expander	2.2476	1.4965	−0.1618	0	0	0	/	/	3.8
Working pump	3.3892	0.0536	0.1538	−0.3935	0.3957	−0.00226	1.89	1.35	1.6

.

In Equation (19), $C_{\mathrm{p}}$ and $F_{\mathrm{P}}$ are expressed as [27]

$$\begin{array}{cc}\hfill lg{C}_{\mathrm{p},n}& =K_{1,n}+K_{2,n}lg{A}_n+K_{3,n}{(lg{A}_n)}^2\hfill \end{array}$$

(20)

$$\begin{array}{cc}\hfill lg{F}_{\mathrm{P},n}& =C_{1,n}+C_{2,n}lg{P}_n+C_{3,n}{(lg{P}_n)}^2\hfill \end{array}$$

(21)

Based on the CEPCI correlation, the equipment cost for 2025 is derived by applying an inflation adjustment to the 2001 baseline cost, as given by [28]

$$C_{\mathrm{BM},2025}=C_{\mathrm{BM},\mathrm{m},2001}{\displaystyle \frac{{\mathrm{CEPCI}}_{2025}}{{\mathrm{CEPCI}}_{2001}}}$$

(22)

Subsequently, the total capital expenditure (CAPEX) of the system is determined by summing the costs of all major components, expressed as

$$C_{\mathrm{tot}}=C_{\mathrm{BM},\mathrm{hxa}}+C_{\mathrm{BM},\mathrm{hxb}}+C_{\mathrm{BM},\mathrm{hxc}}+C_{\mathrm{BM},\mathrm{cond}}+C_{\mathrm{BM},\exp }+C_{\mathrm{BM},\mathrm{pu}}$$

(23)

Finally, the levelized cost of energy (LCOE)—a key techno-economic indicator that quantifies the average cost of electricity generation over the system’s lifetime—can be evaluated by [28]

$$LCOE={\displaystyle \frac{C_{\mathrm{tot}}·CRF+COM}{t_{\mathrm{op}}·{\dot{W}}_{\mathrm{net}}}}$$

(24)

where [29]

$$CRF={\displaystyle \frac{i{(1+i)}^{LT}}{{(1+i)}^{LT}-1}}$$

(25)

where $LT$ represents the life cycle duration of the MHSORC system and is assumed to be 20 years, discount rate i is set at 4.9%, $COM$ corresponds to the annual operation and maintenance expenditure.

2.6. Environmental Model

The GHG emissions of the MHSORC system are quantified through a comprehensive carbon footprint evaluation. Emissions during system construction stem from raw material processing, equipment fabrication, and transportation logistics. Since the system operates independently of external energy or additional material inputs, the operational emissions are limited to possible working-fluid leakage during maintenance activities. In the decommissioning phase, GHG contributions are associated with component recycling and waste management, along with leakage losses occurring at the end of the system’s life span. The cumulative emissions across all stages are thus calculated as [30]

$${\mathit{GHG}}_{\mathrm{tot}}={\mathit{GHG}}_{\mathrm{direct}}+{\mathit{GHG}}_{\mathrm{indirect}}$$

(26)

where

$$\begin{array}{cc}\hfill {\mathit{GHG}}_{\mathrm{direct}}& =\mathit{FC}·\left(\mathit{LT}·\mathit{ALR}+\mathit{EOL}\right)·\mathit{GWP}\hfill \end{array}$$

(27)

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill {\mathit{GHG}}_{\mathrm{indirect}}& =\mathit{LT}·\mathit{AEC}·\mathit{CE}+\mathit{m}·\mathit{CM}+\mathit{mr}·\mathit{CMR}\hfill \\ & +\left(\mathit{FC}+\mathit{LT}·\mathit{ALR}·\mathit{FC}\right)·\mathit{CFM}+\mathit{FC}·\left(1-\mathit{EOL}\right)·\mathit{CFR}\hfill \end{array}\end{array}$$

(28)

The fluid and material consumptions within the MHSORC system are evaluated according to the following equations. Specifically, for the heat exchanger, which adopts a plate heat exchanger configuration, the steel consumption is calculated as

$$m_{\mathrm{hx},\mathrm{pl}}\approx \rho V_{\mathrm{hx}}=\rho \delta A_{\mathrm{hx}}$$

(29)

For a finned-tube heat exchanger configuration, the steel consumption is estimated as

$$m_{\mathrm{hx},\mathrm{shell}}\approx \rho V_{\mathrm{tube}}=\rho ·{\displaystyle \frac{\pi \left(d_o^2-d_i^2\right)}{4}}·{\displaystyle \frac{A_{\mathrm{hx}}}{\pi d_o}}$$

(30)

In the MHSORC system, the steel requirement for the expander is determined as a function of its power output, calculated by

$$m_{\exp }=31.227{\dot{W}}_{\exp }$$

(31)

The steel consumption of the pump in the MHSORC system is estimated according to its power consumption, expressed as

$$m_{\mathrm{pu}}=14{\dot{W}}_{\mathrm{pu}}$$

(32)

The consumption of construction materials—including aluminum, copper, steel, and plastic—is determined according to a composition ratio of 12%, 19%, 46%, and 23%, respectively. The associated emission factors for recycled materials, derived from both manufacturing and recycling processes, are provided in

Table 5. Emissions of materials during manufacturing and disposal processes.

Material	Emissions of Materials During Manufacturing ${\mathbf{CO}}_{2,\mathbf{eq}}/\mathbf{kg}$	Emissions of Materials During Recycling ${\mathbf{CO}}_{2,\mathbf{eq}}/\mathbf{kg}$
Aluminum	0.54	0.07
Copper	0.63	0.07
Steel	2.46	0.07
Plastics	0.12	0.01

.

2.7. Multi-Objective Optimization

Multi-objective optimization provides an efficient framework for the simultaneous optimization of multiple conflicting objectives [31]. In this work, NSGA-II [32] is adopted owing to its strong global search ability and high computational efficiency, enabling the generation of a well-distributed Pareto-optimal frontier. In the present study, the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method demonstrated strong capability in identifying optimal trade-offs among thermodynamic, economic, and environmental objectives, significantly improving computational efficiency compared with exhaustive search methods [33]. Similar findings were reported by Gajević et al. [34], who successfully applied Taguchi–TOPSIS–Grey hybrid optimization to improve tribological performance in aluminum composites, achieving notable reductions in experimental effort and time. Afterward, GRA is applied to comprehensively evaluate and rank all Pareto-optimal candidates, assisting in the identification of the most suitable working fluid. By integrating multiple performance indicators into a single representative index [35], the GRA method allows for a systematic comparison of alternatives characterized by diverse attributes [34]. The complete workflow of the proposed multi-objective optimization and decision-making procedure is illustrated in Figure 6.

During the optimization process, Equations (15), (24) and (26) are adopted as the objective functions, representing the thermodynamic, economic, and environmental performances, respectively.

The decision variables include the evaporation temperature $T_{\mathrm{ev}}$, condensation temperature $T_{\mathrm{cond}}$, superheat degree $T_{\sup }$, condenser pinch-point temperature difference $T_{\mathrm{pp},\mathrm{cond}}$, and the outlet temperatures of each heat source $T_{\mathrm{ex},\mathrm{out}}$, $T_{\mathrm{jw},\mathrm{out}}$, and $T_{\mathrm{iw},\mathrm{out}}$. The decision variables are presented as

$$X={\left[T_{\mathrm{ev}},T_{\mathrm{cond}},T_{\sup },T_{\mathrm{pp},\mathrm{cond}},T_{\mathrm{ex},\mathrm{out}},T_{\mathrm{jw},\mathrm{out}},T_{\mathrm{iw},\mathrm{out}}\right]}^T$$

(33)

The constraint conditions are defined by the pinch-point temperature differences and the minimum allowable temperatures required for the heat sources, which are presented in Table 1.

3. Results and Discussion

3.1. Model Validation

The thermodynamic model of the MHSORC system was developed in MATLAB 2021a using the CoolProp 7.1.0 library [37]. CoolProp was employed to evaluate the thermophysical properties of both the working fluids and the exhaust gas. The model established in MATLAB was validated by comparison with the results reported in Ref. [23]. The information about the model and software used in this study is shown in

Table 6. Information of the software used in this study.

Software	Version	Manufacturer	License Type	Primary Application in This Study
MATLAB	9.10	MathWorks Inc. Natick, MA, USA	Academic License	Development of thermodynamic and economic models; implementation of NSGA-II optimization; numerical simulation
CoolProp	7.1.0	Open-source	MIT Open License	Calculation of thermophysical properties of working fluids

.

The comparative data between this study and the reference are presented in

Table 7. Comparison of the MHSORC model with previous research Ref. [23].

Working Fluid	W (kW)	${\mathit{\eta }}_{\mathbf{exer}}$ (%)	LOCE ($/kWh)	GHG (ton ${\mathbf{CO}}_{2,\mathbf{eq}}$)
R290 [23]	87.83	53.02	0.0938	15.43
R290 (Present)	87.28	52.88	0.0931	15.43
R1234yf [23]	79.34	50.94	0.0951	27.76
R1234yf (Present)	79.01	50.68	0.0949	27.66

. The minor deviations observed between the two sets of results can be attributed to differences in the thermophysical property databases employed. Specifically, Ref. [23] utilized the REFPROP 9.1 software for calculating fluid properties, whereas the present study adopted the CoolProp library.

3.2. Effect of Evaporating Temperature

The performance behavior of the MHSORC system is highly sensitive to changes in evaporation temperature. To elucidate this relationship, this subsection explores the influence of evaporation temperature on power output, exergy efficiency, economic indicators, and environmental impact. The trend of power output variation with evaporation temperature is shown in Figure 7.

Figure 7 illustrates the variation in the MHSORC system’s output power with respect to the evaporation temperature. As shown in the figure, the output power increases with rising evaporation temperature for all working fluids. This trend can be attributed to the fact that the selected evaporation temperature range does not reach the optimal evaporation temperature for each fluid, resulting in a continuous increase in power output. Moreover, under identical evaporation temperatures and other operating conditions, R290 exhibits the highest output power, whereas R1234yf and R600 yield the lowest. At lower evaporation temperatures, R600 demonstrates relatively low power output; however, once the evaporation temperature exceeds a certain threshold, its output surpasses that of R1234yf. This observation suggests that R600 may be a more suitable working fluid for application in the MHSORC system.

Figure 8 presents the variation in the MHSORC system’s exergy efficiency with respect to the evaporation temperature. As shown in the figure, the exergy efficiency increases as the evaporation temperature rises. This trend can be attributed to the increase in system output power, while the available energy of the heat source remains constant, given that the outlet temperature of the heat source is unchanged. Consequently, the higher power output leads to an improvement in exergy efficiency. It is also observed that R1234yf exhibits the lowest exergy efficiency, whereas R601a achieves the highest. The exergy efficiency of R1234yf differs markedly from that of the other working fluids, indicating that R1234yf may not be suitable for applications involving relatively high heat-source temperatures. Moreover, at lower evaporation temperatures, the differences in exergy efficiency among the working fluids are relatively small; however, these differences gradually increase as the evaporation temperature rises.

Figure 9 illustrates the variation in the LCOE of the MHSORC system with respect to the evaporation temperature. As shown in the figure, the LCOE decreases with increasing evaporation temperature. Moreover, the rate of decline in LCOE gradually slows as the evaporation temperature continues to rise. This trend can be attributed, on one hand, to the increase in power output, which reduces the LCOE, and on the other hand to the reduction in the pinch-point temperature difference within the heat exchanger at higher evaporation temperatures, which leads to a larger required heat-transfer area. It is also observed that R1234yf exhibits the highest LCOE, indicating the poorest economic performance, whereas R601a has the lowest LCOE, suggesting superior economic performance among the evaluated working fluids.

Figure 10 depicts the variation in the GHG emissions of the MHSORC system with respect to the evaporation temperature. As shown in the figure, GHG emissions exhibit an increasing trend as the evaporation temperature rises. This behavior can be attributed to the fact that higher evaporation temperatures lead to larger heat-exchanger areas and higher power outputs, both of which contribute to an increase in total GHG emissions. Among the investigated working fluids, R1234ze exhibits the highest GHG emissions, whereas R601 shows the lowest. This can be explained by the fact that R1234ze has the highest ${\mathrm{CO}}_{2,\mathrm{eq}}$ emissions during its manufacturing process, while R601 not only achieves higher exergy efficiency but also produces lower ${\mathrm{CO}}_{2,\mathrm{eq}}$ emissions during production.

3.3. Effect of Condensing Temperature

The condensing temperature, representing the heat-rejection level of the MHSORC, critically influences both the thermodynamic efficiency and the integrated performance of the system. Figure 11 presents how the system’s output power varies with changes in condensing temperature.

Figure 11 illustrates the effect of condensing temperature on the output power of the MHSORC system. As shown in the figure, the output power decreases with increasing condensing temperature. This phenomenon occurs because the condensing temperature directly affects the theoretical cycle efficiency, leading to a reduction in power output. In addition, as the condensing temperature increases, the corresponding condensing pressure also rises, which elevates the expander outlet pressure and consequently decreases the expander’s power output. Furthermore, the higher condensing pressure results in increased power consumption by the working-fluid pump. Under identical operating conditions, R1234ze exhibits the highest output power, whereas R1234yf yields the lowest. Moreover, for all working fluids except R1234ze, the differences in output power gradually diminish as the condensing temperature increases.

Figure 12 presents the variation in the MHSORC system’s exergy efficiency with respect to the condensing temperature. As shown in the figure, the exergy efficiency decreases consistently as the condensing temperature increases. This decline can be attributed to two primary factors: the reduction in theoretical cycle efficiency and the corresponding decrease in output power. Among the investigated working fluids, R1234ze exhibits the highest exergy efficiency, whereas R1234yf shows the lowest—consistent with the power output trend observed in Figure 11. R1270 and R601 display similar exergy-efficiency characteristics: R1270 performs better at lower condensing temperatures, while R601 achieves higher efficiency at elevated temperatures. The remaining four working fluids exhibit comparable exergy-efficiency trends, with R600 showing slightly higher values than R290, R601a, and R600a.

Figure 13 illustrates the variation in the LCOE with increasing condensing temperature. As shown in the figure, the LCOE rises as the condensing temperature increases, and the rate of increase becomes more pronounced at higher condensing temperatures. This behavior can be attributed, on one hand, to the rapid decline in MHSORC output power, and on the other hand, to the fact that although the required heat-transfer area decreases with decreasing power output, the reduction in the heat-exchanger area is not proportional to the loss in power, thereby resulting in a higher LCOE. Among the investigated working fluids, R1234yf exhibits the highest LCOE, indicating the poorest economic performance, whereas R601a shows the lowest, demonstrating superior economic performance.

Figure 14 shows the effect of condensing temperature on the GHG emissions of the MHSORC system. As illustrated in the figure, GHG emissions gradually decrease with increasing condensing temperature. This trend can be attributed to the reduction in power output, which leads to lower GHG emissions during both the manufacturing and operational stages. Moreover, the rate of decrease in GHG emissions slows as the condensing temperature continues to rise, primarily because the decline in manufacturing-related GHG emissions becomes less significant at higher condensing temperatures. Among the examined working fluids, R601 exhibits the lowest GHG emissions, whereas R1234ze shows the highest, consistent with the results presented in Figure 10.

3.4. Effect of Superheat Temperature

The superheat temperature is a critical operating parameter for the MHSORC system, as it directly influences both system safety and overall performance. The following figure illustrates the effect of superheat degree on the output power of the MHSORC system.

Figure 15 illustrates the variation in the MHSORC system’s output power with respect to the degree of superheat. As shown in the figure, for R290 and R1270, the output power increases with rising superheat, indicating that higher superheat levels can enhance power output for these two working fluids. In contrast, for R600, R600a, R601, and R601a, the output power decreases as the superheat increases, suggesting that a lower degree of superheat is more favorable for achieving higher power output. For R1234yf and R1234ze, the output power first increases and then decreases with increasing superheat, implying the existence of an optimal degree of superheat for these two working fluids.

Figure 16 presents the variation in exergy efficiency with increasing degree of superheat. The trend of exergy efficiency is consistent with the variation in power output shown in Figure 15. It is noteworthy that, for R290 and R1270, the rate of increase in exergy efficiency gradually slows as the superheat degree rises. Moreover, it can be observed that, compared with other operating parameters, the degree of superheat exerts a relatively minor influence on the overall system performance.

Figure 17 presents the influence of the superheat degree on the LCOE. For working fluids such as R290, R1270, R1234yf, and R1234ze, an increase in superheat results in a decline in LCOE. This behavior can be explained by the reduction in power output at higher superheat levels, which leads to lower electricity costs. Specifically, for R1234yf and R1234ze, elevated superheat enlarges the temperature difference across the heat exchangers, thereby decreasing the required heat-transfer area. In contrast, for R600, R600a, R601, and R601a, the LCOE exhibits an increasing trend with rising superheat, suggesting that the higher cost is mainly associated with the corresponding drop in power generation.

Figure 18 shows the variation in GHG emissions with respect to the degree of superheat. As illustrated in the figure, GHG emissions decrease as the superheat increases. This reduction can be attributed to the overall decline in GHG emissions during both the manufacturing and operational stages of the system as the degree of superheat rises.

3.5. Effect of Heat Souce Outlet Temperature

The outlet temperature of the heat source serves as a key indicator of the recoverable thermal potential within the MHSORC system. The relationship between the exhaust gas outlet temperature of the final heat source and the corresponding power output is depicted in Figure 19.

Figure 19 presents the variation in the MHSORC system’s output power with changes in the exhaust-gas outlet temperature. As shown in the figure, an increase in the exhaust-gas outlet temperature results in a noticeable decline in system output power, indicating that the available thermal energy exerts a significant influence on the system’s performance. Moreover, it can be observed that R1234ze exhibits the lowest output power, whereas R600a achieves the highest when the outlet temperature of the heat source is relatively low.

Figure 20 illustrates the variation in the system’s exergy efficiency with increasing exhaust-gas outlet temperature. As shown in the figure, the exergy efficiency of the system increases as the exhaust-gas outlet temperature rises. This behavior occurs because a higher exhaust-gas outlet temperature indicates that the MHSORC system can utilize waste heat of higher energy quality, thereby enhancing its exergy efficiency. In addition, the rate of increase in exergy efficiency becomes more pronounced as the exhaust-gas outlet temperature continues to rise. Among the investigated working fluids, R1234ze exhibits the lowest exergy efficiency, whereas R600 achieves the highest. However, the overall differences in exergy efficiency among the working fluids remain relatively small.

Figure 21 presents the variation in the LCOE with changes in the exhaust-gas outlet temperature. As shown in the figure, the system’s LCOE increases as the exhaust-gas outlet temperature rises. This behavior indicates that the system’s output power exerts a dominant influence on the LCOE. Moreover, it can be observed that the working fluid R601a exhibits the lowest LCOE, whereas R1234ze shows the highest.

Figure 22 illustrates the effect of the exhaust-gas outlet temperature on the GHG emissions of the MHSORC system. As shown in the figure, an increase in the heat-source outlet temperature leads to a reduction in the system’s GHG emissions. This behavior primarily occurs because the decrease in system output power results in lower GHG emissions during both the manufacturing and operational stages.

3.6. Multi-OBJECTIVE Optimization of MHSORC

In this study, a multi-objective optimization of the MHSORC system was performed from thermodynamic, economic, and environmental perspectives. Because it is impossible to achieve simultaneous optimality for all objectives, the Pareto frontier was generated using NSGA-II.

Figure 23 presents the Pareto front obtained for the MHSORC system using different working fluids. As shown in the figure, the MHSORC system exhibits relatively higher exergy efficiency when employing R601 or R601a as the working fluid. However, when R1234ze is used, the system tends to display a higher LCOE. The differences in GHG emissions among the MHSORC systems with these working fluids are relatively small.

For each working fluid, the optimal solutions on the Pareto front are determined using the TOPSIS, and the corresponding performance scores are evaluated through the GRA method. The results are summarized in

Table 8. GRA -based ranking of the MHSORC with various working fluids.

Working Fluid	GRA
R601	0.4394
R601a	0.4164
R600a	0.3965
R600	0.3686
R290	0.2966
R1270	0.2937
R1234yf	0.2893
R1234ze	0.2414

.

As shown in Table 8, the MHSORC system attains the highest gra score when using R601 as the working fluid, whereas R1234ze exhibits the lowest score. This outcome is generally consistent with the preceding analysis results. The relatively low score of R1234ze can be attributed to its comparatively higher GHG emissions under certain operating conditions.

The detailed parameters corresponding to the optimal operating results of the MHSORC system using R601 as the working fluid are listed in

Table 9. GRA-based ranking of the MHSORC with various working fluids.

Parameter	Value	Unit
$T_{\mathrm{ev}}$	466.7	K
$T_{\mathrm{cond}}$	305.15	K
$T_{\sup }$	28.41	K
$T_{\mathrm{pp},\mathrm{cond}}$	10.93	K
$T_{\mathrm{ex},\mathrm{out}}$	476.37	K
$T_{\mathrm{jw},\mathrm{out}}$	362.52	K
$T_{\mathrm{iw},\mathrm{out}}$	348.94	K
${\eta }_{\mathrm{exer}}$	41.69	%
$LCOE$	0.0495	$/kWh
$GH{G}_{\mathrm{tot}}$	0.8019	kilotons ${\mathrm{CO}}_{2,\mathrm{eq}}$

.

As shown in Table 9, the detailed system parameters of the MHSORC operating under optimal conditions with R601 as the working fluid are presented. In this case, the evaporating temperature approaches the critical temperature of R601. It can also be observed that the MHSORC extracts less heat from the cylinder jacket water while recovering more heat from the intercooler cooling water. Under these conditions, the exergy efficiency of the MHSORC reaches 41.69%, the LCOE is 0.0495 $/kWh, and the greenhouse gas (GHG) emissions amount to 0.8019 kilotons ${\mathrm{CO}}_{2,\mathrm{eq}}$.

4. Conclusions

This study conducted a comprehensive thermodynamic, economic, and environmental analysis, followed by a multi-objective optimization of the MHSORC system. Eight GWP working fluids were selected as candidates, and the performance of the MHSORC system was evaluated under varying evaporating temperatures, condensing temperatures, degrees of superheat, and heat-source outlet temperatures. The Pareto frontier was generated using NSGA-II, and the optimal solution was determined through the TOPSIS and GRA methods. The main findings are summarized as follows:

• For all working fluids, higher evaporating temperatures increase output power and exergy efficiency, and reduce the LCOE but lead to slightly higher GHG emissions.
• An increase in condensing temperature results in deterioration of all system performance indicators.
• Under varying degrees of superheat, some working fluids exhibit improved performance with higher superheat, whereas others possess an optimal superheat degree.
• The outlet temperature of the heat source has a substantial impact on overall system performance, directly determining recoverable energy and system feasibility.
• Among the eight working fluids, R601 demonstrates the best comprehensive performance, achieving an exergy efficiency of 41.69%, an LCOE of 0.0495 $/kWh, and GHG emissions of 0.8019 kilotons ${\mathrm{CO}}_{2,\mathrm{eq}}$.

Overall, this study provides a systematic thermodynamic, economic, and environmental assessment and optimization framework for MHSORC systems, offering theoretical guidance for their practical application in marine environments. The results confirm that the MHSORC configuration can significantly enhance waste-heat utilization efficiency and contribute to the decarbonization of marine propulsion systems. Future studies should extend this work by developing dynamic MHSORC models capable of capturing transient ship-engine behavior and enabling real-time predictive control. The integration of artificial intelligence and machine learning techniques—such as surrogate modeling and hybrid Grey–TOPSIS-based optimization—can further enhance computational efficiency and decision accuracy. Experimental validation on large two-stroke marine engines (e.g., Wärtsilä RT-flex96C) is recommended to verify performance under realistic conditions. In addition, comprehensive life-cycle cost and environmental assessments should be conducted to evaluate long-term sustainability in accordance with IMO decarbonization targets. Finally, coupling the MHSORC with renewable or hybrid onboard energy systems (e.g., fuel-cell or LNG waste-heat recovery) represents a promising pathway toward integrated, low-emission ship-energy architectures.