Energy Saving Analysis of a Marine Main Engine during the Whole Voyage Utilizing an Organic Rankine Cycle System to Recover Waste Heat

Abstract

In this study, a main marine engine with a rating power of 21,840 kW for a ship sailing in an actual voyage was obtained as the research object. The engine’s exhaust gas and jacket cooling water were adopted as the heat source of the organic Rankine cycle (ORC) system developed for the main marine engine. The engine can consume high-sulfur or low-sulfur fuel oil, respectively, according to the different emission control requirements. The impact of the use of high-sulfur or low-sulfur fuel oil, and variations in engine load, amount of recoverable waste heat, outboard seawater temperature, and the ship’s steam demand were comprehensively considered, and the validated ORC system model was used for the analysis of the system’s performance and the ship’s energy saving for the whole voyage. The results demonstrated that when the ship adopted high-sulfur or low-sulfur fuel oil, the maximum total net power output of the ORC system was 449.3 kW and 753.1 kW, respectively. During the whole voyage of 1610.7 nautical miles, when high-sulfur fuel oil was used, the ORC system reduced carbon emission by 40.3 tons and 33.8 tons, respectively, in summer and in winter, and the fuel saving rates were 2.53% and 2.12%; when low-sulfur fuel oil was used, the ship’s carbon emissions were reduced by 62.1 tons and 61.8 tons, respectively, in summer and in winter, and the fuel saving rates were 3.91% and 3.89%.

1. Introduction

Maritime transportation is the most essential mode of cargo transportation at present. By 2020, the total number of commercial ships of 100 tons and above in the world had reached 98,140, and there is still a growing trend [1]. From 2012 to 2018, the annual greenhouse gas emissions of international shipping increased from 977 million tons to 1076 million tons. It is expected that by 2050, carbon dioxide emissions will increase by 50% over 2018 and 90–130% over 2008 with the continuous growth of shipping demand [2]. The International Maritime Organization (IMO) has adopted a preliminary strategy to reduce greenhouse gas emissions from ships based on the original convention “Maritime Agreement Regarding Oil Pollution of Liability” (MARPOL 73/78) to further reduce carbon dioxide emissions from the ship. Compared with 2008, carbon dioxide emissions will be reduced by at least 40% in 2030 and 70% in 2050 [3]. At present, the thermal efficiency of a marine diesel engine is close to 50%, and the remaining large amount of waste heat is wasted in the form of liquid or gas. Making full use of waste heat to promote ship energy conservation has become a consensus in the shipping industry. Organic Rankine Cycle (ORC) waste heat recovery technology has great potential for improving the fuel saving rate and reducing carbon emissions [4].

Among many technologies used for the recovery of medium-temperature and low-temperature heat sources, ORC was considered one of the most promising technologies due to its simple structure, reliable operation, and relatively high efficiency. Currently, ORC technology has been widely used to recover the low-to-medium temperature level heat from solar radiation, geothermal reservoirs, and industrial waste heat [5]. In recent years, the technological development of ORC systems has been evolving rapidly. Song et al. [6] compared and analyzed the performance of ORC systems with different heat sources. The results suggested that the ORC system selected the engine’s jacket cooling water as the heat source and R245fa as the working fluid, the maximum net power output of the system was 10.3 kW, and the system thermal efficiency was 5.2%; when selecting the ORC system with the engine’s exhaust gas as the heat source and benzene as the working fluid, the system’s maximum net power output was 90.8 kW, and the system’s thermal efficiency was 21.3%. Mondejar et al. [7] selected a large cruise ship sailing in Stockholm and Mariehamn as a research object; they used an ORC system with a preheater and regenerator to recover the waste heat of the mixed exhaust gas from the main and auxiliary engine. The results demonstrated that the average power generation of the ORC system accounted for 16% of the ship’s electricity consumption. Using the same cruise ship, Ahlgren et al. [8] analyzed and compared ORC systems with a single preheater and with a preheater and a regenerator at the same time. The ORC system was optimized according to different speeds and loads and after that, the system with a preheater and a regenerator can generate 12% more net power output than that with only a preheater, and the average net power output of the system can account for 22% of the ship’s whole electricity consumption. Mondejar et al. [9] found that the ORC system with jacket cooling water as the preheat source and exhaust gas as the evaporation source saved 10–15% of fuel oil when ships adopted low-sulfur fuel oil. Akman et al. [10] investigated the recovery of chemicals/tanker engines by basic ORC in different loads and found that when the ORC system combined with jacket cooling water, scavenging air, and exhaust gas for the heat sources was used, the electricity generated by the system was higher than the navigating electric load when the engine load was higher than 82%. As a result, the ship’s overall thermal efficiency of the power plant was boosted by 6%. Yang and Yeh [11] reported that the thermal efficiency of the ORC system with R245fa as working fluid in recovering jacket cooling water and exhaust gas waste heat at the same time was 6% higher than that of recovering exhaust gas waste heat alone. Lion et al. [12] analyzed the thermodynamic and economic performance of large marine diesel engines using the ORC system under different emissions criteria. It was demonstrated that using the ORC system under Tier III can reduce the engine’s fuel consumption level comparable to the level under Tier II, the pollutant level was remarkably lowered, and the application of ORC saved about 5% of fuel cost per year. Grljušić et al. [13] found that the application of the ORC system can save 413–1346 tons of fuel per year compared with generator diesel engines when the main engine load of a Suezmax-size tanker was 50–100%, and the ORC system can meet all electrical and thermal demands on board when the engine load was higher than 90%. With a chemical cargo carrier sailing in Dubai and Hamburg, Burel et al. [14] analyzed the impact of using an ORC system on energy saving and emissions reduction at different speeds and loads. The results suggested that the ORC system was integrated with the propulsion system, contributing to about 5% of saving of fuel consumption. Jesper et al. [15] compared the performance of a dual-pressure SRC (Steam Rankine Cycle) system and ORC system with a 4500TEU container ship, revealing clear advantages and benefits of using the ORC system compared to the SRC system because the ORC system can utilize lower temperature jacket cooling water heat and ORC turbines can be designed with higher efficiency. Casisi et al. [16] chose to use an ORC system to recover exhaust gas heat and high temperature cooling water heat from a naval engine. It was demonstrated that when the engine operating at 100% nominal load, the simple ORC system already achieved an increase in engine power output of about 10%. Ng et al. [17] found that the multipurpose platform supply vessel of 5200DWT utilizing an ORC system to recover the waste heat of exhaust gas can save 5–9% of fuel oil annually, and the best payback time for investment was for the simple ORC configuration. Gürgen and Altın [18] selected the MAN 8G60ME-C10.5 diesel engine with 22,720 kW power and used main engine exhaust gas as the waste heat source. Ten different working fluids were evaluated and R245fa was finally selected as the working fluid, and the highest value for the thermal efficiency of ORC systems was demonstrated to be 18.7% at 35% engine load.

Few of the published studies about the use of ORC technology to recover the waste heat of ships report a full account of the variation in the ship’s operating conditions during a whole voyage. Moreover, in most of previous published studies, scholars directly obtained the exhaust gas after passing through the turbocharger of a main engine instead of that passing through the exhaust gas boiler to work as the heat source of the ORC system. In real application, merchant ships usually adopt the exhaust gas boiler to generate steam to heat fuel oil and lubricating oil and meet daily life needs onboard. Therefore, the waste heat utilization of the exhaust gas should first meet the demand of the exhaust gas boiler for producing steam. The rest of the available waste heat from exhaust gas exiting the boiler can then be recovered by ORC. Additionally, influenced by the emission control areas, ships may be required to alternatively use high-sulfur or low-sulfur fuel oil during navigation. The different sulfur content of fuel oil adopted by ships will affect the amount of the available waste heat, which consequently affects the performance of ORC system. Therefore, in order to obtain more reliable and convincible data on the energy saving benefits of large commercial ships using ORC technology to recover waste heat, in this paper, the energy saving analysis of ORC system is carried out based on the actual navigation data of a ship during a whole voyage, taking into account the influence caused by the use of high-sulfur or low-sulfur fuel oil, and the variations in main engine load, amount of recoverable waste heat, outboard seawater temperature, and the ship’s steam demand at the same time.

In this study, the actual navigation data of a ship during a specific whole voyage is given first; the state parameters of the ship’s waste heat source including exhaust gas and jacket cooling water are then calculated and listed. Second, according to the temperature range of the ship’s available waste heat source, the structure of the ORC system and its appropriate working fluid are proposed, and its operating parameters are described. Third, the thermodynamic simulation model of the ORC system is established and validated, and the calculation methodology of fuel saving and carbon emission reduction for the ORC system is introduced. Finally, using the validated simulation model of the ORC system, the system’s performance, especially the relationship between the thermal efficiency or net power output and the temperature of seawater outboard, is studied in detail; and thereby the calculated saving of fuel oil and carbon emission reduction for the ship during the whole voyage is shown and demonstrated to evaluate the impact of ORC technology.

2. Voyage Route and Waste Heat Sources

2.1. Route Overview

In this study, the departure port of the voyage route is Dalian (CHINA) and the destination port is Qinzhou (CHINA). The voyage totals 1610.7 nautical miles and took 184.63 h. The specific route was illustrated in Figure 1, and the navigation data are presented in

Table 1. Route data.

Route	Events	Speed (kn)	Time (h)	Voyage (n mile)	Main Engine Load (%)	Seawater Temperature in Summer (°C)	Seawater Temperature in Winter (°C)
China coastal route	Unberthing	0–7.4	1.38	0.6	0–90	25	10
	High speed	9.18	12.83	123	90	25	11
	High speed	10	45.4	455.5	90	26	15
	High speed	10	37.16	389.6	90	28	20
	High speed	10	60.3	622.4	90	29	24
	Low speed	4.8	0.3	1.2	50	29	24
	Anchor	0	24	0	0	29	24
	Low speed	4.72	0.3	1.1	50	29	24
	High speed	9	2.16	16.2	90	30	25
	Low speed	4.3	0.3	0.8	50	30	25
	berthing	3.4–0	0.5	0.3	50–0	30	25

, which were obtained from the ELANE Inc. data product [19].

Except for the speed of unberthing and berthing in the table above, the other speeds were the average speed of their respective voyage stages or events. The seawater temperature was obtained from the meteorological data along the route in summer and winter. The seawater temperature given in the table was the average temperature in the sea area corresponding to the navigation under each stage or event.

2.2. Waste Heat Sources

The waste heat sources available on board mainly include the exhaust gas, jacket cooling water, charge air, scavenging air, and lubricating oil cooling water of the main engine. Exhaust gas is the highest quality waste heat source. The exhaust gas temperature still reaches 170–180 °C, even after leaving exhaust gas boiler. The outlet temperature of the jacket cooling water is generally set at 80–90 °C, and its mass flow rate is relatively large although the temperature is not as high as the exhaust gas. Both these sources involve a large amount of waste heat. Therefore, the mixed exhaust gas after passing through the exhaust gas boiler and jacket cooling water were separately used as the heat source of the ORC system in this study.

2.2.1. Main Engine Operating Parameters

The MAN 8S65ME-C8.6 two-stroke main marine engine equipped on the ship, with a rating power of 21,840 kW at 100% SMCR, was obtained as the research object, and high-sulfur or low-sulfur fuel oil was burned according to different emission control requirements. According to the CEAS database provided by MAN company, which is the giant of the marine engine industry, the related parameters of the exhaust gas and jacket cooling water were obtained when the main engine burned fuel with different sulfur content [20]. Considering the actual operation of the ship and the high-related working conditions of the ship were relatively stable during navigation, this paper focused on the conditions at 90% load and 50% load of the main engine. The relevant parameters of the main engine are listed in

Table 2. Main engine operating parameters.

Fuel oil Sulfur Content	Engine Load (%)	Power (kW)	Speed (r/min)	SFOC (g/kWh)	Exhaust Gas Amount (kg/s)	Exhaust Gas Temperature (°C)	Jacket Cooling Water Heat Release(kW)	Steam Produced (kg/h)
Low	90	19,656	91.7	163.3	45.9	222	2420	2732
	50	10,920	75.4	164.4	28.9	229	1640	2176
High	90	19,656	91.7	163.6	45	231	2420	3332
	50	10,920	75.4	164.4	28.3	237	1650	2530

. The composition of exhaust gas was provided in

Table 3. Exhaust gas composition.

Composition	CO2	H2O	O2	CO	SO2	NOx (NO2)	HC (CH4)	N2
Mass fraction (%)	6.5	2.31	16	-	-	-	-	75.19

. The specific calculations for the content of the exhaust gas components were conducted according to the different main engine types [21].

In order to prevent the low-temperature acid corrosion on the engine’s exhaust duct which may be caused by the sulfide content of exhaust gas, the temperature of exhaust gas passing through the evaporator of the ORC system was set at 175 °C and 110 °C when the main engine was burning high-sulfur or low-sulfur fuel oil, respectively.

2.2.2. Jacket Cooling Water Parameters

According to the actual outlet temperature of the jacket cooling water of most diesel engines, the outlet temperature of the jacket cooling water of the main engine using high-sulfur or low-sulfur fuel oil was set at 90 °C and 85 °C, respectively, in order to prevent low-temperature corrosion of the cylinder liner. Then, the other jacket cooling water operating parameters including mass flow rate under different main engine loads were calculated according to the relevant operating parameters given in Table 2 [22]. The calculation results for the 90% and 50% engine loads were shown in

Table 4. Jacket cooling water parameters.

Fuel oil Sulfur Content	Engine Load (%)	Jacket Cooling Water Heat Release (kW)	Jacket Cooling Water Mass Flow Rate (kg/s)	Outlet Temperature of Jacket Cooling Water (°C)	Inlet Temperature of Jacket Cooling Water (°C)
Low	90	2420	41.2	90	75
	50	1640	27.9	90	75
High	90	2420	41.2	85	70
	50	1640	27.9	85	70

.

2.2.3. Exhaust Gas Parameters

Ships are generally equipped with exhaust gas boilers to consume part of the high-quality exhaust gas. The amount of steam produced by the exhaust gas boiler may not be enough to offset the consumption of the whole ship when the main engine load is low. However, the amount of steam produced by the exhaust gas boiler generally exceeds the consumption of the whole ship when the main engine load is high, resulting in part of the exhaust gas waste heat not being recovered.

Degiuli et al. [23] studied the container ship with a main engine power of 21,840 kW and noted that the steam consumption of the whole ship was about 2455–2732 kg/h under high load operation. MAN conducted a low-speed sailing survey on a total of 149 ships including container ships, bulk carriers, and oil tankers, and it was demonstrated that when 56.2% of container ships and 82.2% of bulk carriers set the main engine load at 30–50%, the steam demand of the whole ship can be satisfied [24]. Hence, in this paper, combined with the actual operation of the ship, a 1367 kg/h steam flow rate corresponding to the 30% engine load condition and a 2384 kg/h steam flow rate corresponding to the 35% engine load condition were selected as the maximum steam consumption for the ship’s navigation in summer and winter, respectively.

The thermal efficiency of the exhaust gas boiler is generally 0.8–0.96; its steam working pressure is typically 0.7 MPa; its feed water temperature is 60 °C and steam working temperature is 170 °C. The heat exchanging process of the boiler is shown in Figure 2. Where T is the temperature and Q is the heat exchange quantity between exhaust gas and water; ${\mathrm{T}}_{\mathrm{eg},\mathrm{in}}$ and ${\mathrm{T}}_{\mathrm{eg},\mathrm{out}}$ are the inlet and outlet temperature of exhaust gas in the boiler; ${\mathrm{T}}_{\mathrm{w},\mathrm{in}}$ and ${\mathrm{T}}_{\mathrm{w},\mathrm{out}}$ are the inlet and outlet temperature of water or steam in the boiler; $\Delta {\mathrm{T}}_{\mathrm{p}}$ is the pinch point temperature. The thermal efficiency of the exhaust gas boiler was set as 0.9. According to the different steam demands of the ship in summer and winter, the exhaust gas temperature at the outlet of the exhaust gas boiler was then calculated using the parameters given in Table 2.

With the main engine operating at high load, the excess exhaust gas was bypassed through the boiler, and the bypassed exhaust gas was then mixed with that leaving the outlet of the boiler for recovery. Since it was difficult to calculate the temperature of the mixed exhaust gas directly, an equivalent substitution method was employed. The amount of heat of exhaust gas consumed by the boiler was deducted from the total of the waste heat to obtain the mixed exhaust gas parameters. The specific calculation process is as follows:

$${\dot{\mathrm{Q}}}_{\mathrm{v},\mathrm{tot}}=\frac{{\mathrm{m}}_{\mathrm{s}}\times \left({\mathrm{h}}_{\mathrm{w},\mathrm{out}}-{\mathrm{h}}_{\mathrm{w},\mathrm{in}}\right)}{0.9}$$

(1)

where ${\dot{\mathrm{Q}}}_{\mathrm{v},\mathrm{tot}}$ is the heat release required to meet the steam consumption of the ship, ${\mathrm{m}}_{\mathrm{s}}$ denotes the maximum amount of steam needed for the ship in summer and winter, and ${\mathrm{h}}_{\mathrm{w},\mathrm{in}}{ \mathrm{and} \mathrm{h}}_{\mathrm{w},\mathrm{out}}$ are defined as the inlet and outlet enthalpy of water or steam in the boiler, respectively.

$${\dot{\mathrm{Q}}}_{\mathrm{v},\mathrm{tot}}={\dot{\mathrm{Q}}}_{\mathrm{v},\mathrm{b}}$$

(2)

$${\dot{\mathrm{Q}}}_{\mathrm{v},\mathrm{b}}={\mathrm{m}}_{\mathrm{eg}}\times \left({\mathrm{h}}_{\mathrm{eg},\mathrm{in}}-{\mathrm{h}}_{\mathrm{eg},\mathrm{out}}\right)$$

(3)

where ${\dot{\mathrm{Q}}}_{\mathrm{v},\mathrm{b}}$ represents heat exchange quantity between exhaust gas and boiler, ${\mathrm{m}}_{\mathrm{eg}}$ indicates exhaust gas mass flow rate, and ${\mathrm{h}}_{\mathrm{eg},\mathrm{in}} \mathrm{and} {\mathrm{h}}_{\mathrm{eg},\mathrm{out}}$ are the inlet and outlet enthalpy of exhaust gas in the boiler, respectively.

When the main engine load is low, the exhaust gas is completely used to generate steam by boiler, and the ORC system will no longer work.

The outlet temperature of the mixed exhaust gas after the boiler can be obtained by the above method. The specific calculation results are presented in

Table 5. Exhaust gas parameters at the outlet of the boiler in summer.

Fuel Oil Sulfur Content	Engine Load (%)	Exhaust Gas Mass Flow Rate (kg/s)	Boiler Steam Production (kg/h)	Ship Steam Consumption (kg/h)	Inlet Temperature of Boiler (°C)	Outlet Temperature of Boiler (°C)
Low	90	45.9	2732	1367	222	200
	50	28.9	2176	1367	229	194
High	90	45	3332	1367	231	209
	50	28.3	2530	1367	237	202

and

Table 6. Exhaust gas parameters at the outlet of the boiler in winter.

Fuel Oil Sulfur Content	Engine Load (%)	Exhaust Gas Mass Flow Rate (kg/s)	Boiler Steam Production (kg/h)	Ship Steam Consumption (kg/h)	Inlet Temperature of Boiler (°C)	Outlet Temperature of Boiler (°C)
Low	90	45.9	2732	2384	222	183
	50	28.9	2176	2384	229	175
High	90	45	3332	2384	231	192
	50	28.3	2530	2384	237	175

.

3. Methodology

3.1. Structure and Design Parameters of ORC System

3.1.1. Working Fluid Selection

Owing to the very strict safety requirements particularly for ships’ equipment, the safety of the working fluid should be given the first priority when selecting the onboard ORC system. Lion et al. [25] pointed out that R245fa was the most suitable working fluid for the ORC system recovering waste heat from the main engine’s jacket cooling water. Beyene et al. [26] analyzed the application and development of an ORC system for ships in the last decade, and found that R245fa was presently the most suitable for the ship’s waste heat source with a temperature of 80 °C to 150 °C. Until now, most of the real applications of ORC systems on ships all used R245fa as the working fluid. For example, the R245fa ORC system developed together by the Calnetix Technologies and Mitsubishi Heavy Industries (MHI) has been certified by the marine classification society and installed on some ships for demonstration [27]. Enertime and Kobe Steel also used R245fa as the working fluid for their own ORC products for ships [9]. Therefore, considering the feasibility of the practical application of ORC systems on ships and the temperature range of ships’ recoverable waste heat source, R245fa was selected as the working fluid in this study. The property of R245fa is as shown in

Table 7. Property of working fluid.

Name	Chemical Formula	Molecule Weight (kg/kmol)	Critical Temperature (°C)	Critical Pressure (MPa)	Normal Boiling Point (°C)	Characteristic	Safety	ODP	GWP
R245fa	CF3CH2CHF2	134.5	154	3.65	15.14	Dry	B1	0	820

.

3.1.2. Structure of ORC System

Although the advanced architectures such as dual-loop cycle [28] and cascade cycle [29] were often adopted by some researchers for ORC systems recovering the waste heat of main marine engines, the ORC systems with advanced architecture were complex and are now difficult to put into real application onboard. The ORC system with basic architecture is simple but reliable, and therefore is proposed here and exhibited in Figure 3.

The ORC system proposed consists of an exhaust gas side subsystem and a jacket cooling water side subsystem. The two subsystems are independent. Each subsystem was equipped with an evaporator, an expander, a condenser, and a feed pump. The working process of the ORC subsystems is as shown in Figure 4. In each subsystem, the low-pressure working fluid in the condenser was pressurized by the feed pump (1→2) and entered the evaporator to absorb the heat of the waste heat source (2→3→4). The generated vapor of the working fluid entered the expander to perform work (4→5). Afterward, the working fluid flew into the condenser to release heat to the cooling water (5→6→1), and turned into low-pressure liquid which was then boosted by the feed pump for the next cycle. The ORC subsystem on the exhaust gas side adopted the exhaust gas of the main engine as the waste heat source. The exhaust gas from the main engine was first used by the boiler to generate steam, and then mixed with the part of exhaust gas bypassed at the outlet of boiler. The mixed exhaust gas was sent to the evaporator of the ORC subsystem to heat the working fluid in the evaporator. The ORC subsystem on the jacket cooling water side adopted the main engine jacket cooling water as the waste heat source. It utilized the hot jacket cooling water to heat the working fluid in the evaporator.

3.1.3. Operating Parameters of ORC System

During navigation, the performance of the ORC system was affected by the use of high-sulfur or low-sulfur fuel oil, variations in engine load, amount of recoverable waste heat, outboard seawater temperature, and the ship’s steam demand. The operation parameters of the ORC system are different under different working conditions. The system’s operating parameters at the main engine load of 90% and of 50% are shown in

Table 8. ORC system operating parameters.

Parameters	90% Main Engine Load (Summer)		50% Main Engine Load (Summer)		90% Main Engine Load (Winter)		50% Main Engine Load (Winter)
Fuel oil sulfur content	High	Low	High	Low	High	Low	Low
Exhaust gas inlet temperature (°C)	209	200	202	194	192	183	175
Exhaust gas outlet temperature (°C)	175	110	175	110	175	110	110
Exhaust gas mass flow rate (kg/s)	45	45.9	28.3	28.9	45	45.9	28.9
Evaporating temperature of exhaust gas side ORC (°C)	150	100	143	94	150	100	92
Evaporation pressure of exhaust gas side ORC (MPa)	3.39	1.26	2.98	1.1	3.39	1.26	1.05
Jacket cooling water inlet temperature (°C)	90	85	90	85	90	85	85
Jacket cooling water outlet temperature (°C)	75	70	75	70	75	70	70
Jacket cooling water mass flow rate (kg/s)	41.2	41.2	27.9	27.9	41.2	41.2	27.9
Evaporating temperature of jacket cooling water side ORC (°C)	70	65	70	65	70	65	65
Evaporation pressure of jacket cooling water side ORC (MPa)	0.6	0.53	0.6	0.53	0.6	0.53	0.53

. When the high-sulfur fuel oil was used and the main engine was running at 50% load in winter, the system operating parameters were not given in the above Table 8, because after passing through the boiler, the exhaust gas was not suitable for the ORC system to recover owing to the high acid dew point temperature of the exhaust gas.

3.2. System Modeling and Fuel Saving Calculation

3.2.1. Thermodynamic Model of ORC System

The ORC system was modeled using the software MATLAB Simulink. When modeling, the following assumptions were made about the operating conditions of the ORC system:

(1) The pressure loss and heat loss inside each component of the system were neglected, which would have little influence on the steady-state system-level energy saving analysis.

(2) The isentropic efficiency of the expander was set as 0.8.

(3) The isentropic efficiency of the feed pump was set as 0.8.

(4) The outboard seawater was used as a cold source of the condenser; the isentropic efficiency of the cooling seawater pump was 0.8.

Although the isentropic efficiency of the expander and pumps can be changed with the operating condition of the ORC system, the varying range was limited within 10% under normal operating conditions. Moreover, the fixed value of 0.8 was common and suitable for the expander and pumps, especially for carrying out the system energy saving analysis [6].

The circulation process of the working fluid of ORC system in each component meets the following basic equations.

The circulation process of the ORC system is as shown in Figure 4. Process 1 to 2 is the pressurization process of the working fluid by the feed pump. Its power consumption by the pump can be calculated as follows:

$${\dot{\mathrm{W}}}_{\mathrm{f},\mathrm{p}}={ \mathrm{m}}_{\mathrm{r}}\left({\mathrm{h}}_2-{\mathrm{h}}_1\right)=\frac{{\mathrm{m}}_{\mathrm{r}}\left({\mathrm{h}}_{2\mathrm{s}}-{\mathrm{h}}_1\right)}{{\mathsf{\eta }}_{\mathrm{f},\mathrm{p}}}$$

(4)

where ${\dot{\mathrm{W}}}_{\mathrm{f},\mathrm{p}}$ indicates the power consumption by the feed pump, ${\mathrm{h}}_{2\mathrm{s}}$ denotes the working fluid at the feed pump outlet for an isentropic compression process, ${\mathsf{\eta }}_{\mathrm{f},\mathrm{p}}$ represents isentropic efficiency of the feed pump, ${\mathrm{h}}_1{ \mathrm{and} \mathrm{h}}_2$ are defined as the inlet and outlet absolute enthalpy of the working fluid in the feed pump, respectively, ${\mathrm{m}}_{\mathrm{r}}$ refers to the working fluid mass flow rate, calculated as follows:

$${\mathrm{m}}_{\mathrm{r}}=\frac{{\dot{\mathrm{Q}}}_{\mathrm{v}}}{{\mathrm{h}}_4-{\mathrm{h}}_2}$$

(5)

where ${\dot{\mathrm{Q}}}_{\mathrm{v}}$ denotes the heat quantity contained in the heat source, ${\mathrm{h}}_2{ \mathrm{and} \mathrm{h}}_4$ are defined as the inlet and outlet enthalpy of the working fluid in the evaporator, respectively. The calculation of ${\dot{\mathrm{Q}}}_{\mathrm{v}}$ is:

$${\dot{\mathrm{Q}}}_{\mathrm{v}}={\mathrm{C}}_{\mathrm{P}}\times {\mathrm{m}}_{\mathrm{hs}}\times \left({\mathrm{T}}_2-{\mathrm{T}}_4\right)$$

(6)

where ${\mathrm{C}}_{\mathrm{P}}$ represents the specific heat capacity of the heat source, and its temperature is the average temperature of the heat source inlet and outlet, ${\mathrm{m}}_{\mathrm{hs}}$ denotes heat source mass flow rate, ${\mathrm{T}}_2{ \mathrm{and} \mathrm{T}}_4$ indicate the inlet and outlet temperature of the heat source in the evaporator, respectively.

During the process from 2 to 4, the working fluid enters the evaporator to absorb heat and becomes saturated vapor, which is expressed as:

$${\dot{\mathrm{Q}}}_{\mathrm{e}}={\mathrm{m}}_{\mathrm{r}}\left({\mathrm{h}}_4-{\mathrm{h}}_2\right)$$

(7)

where ${\dot{\mathrm{Q}}}_{\mathrm{e}}$ indicates the thermal power interchange in the evaporator.

During the process from 4 to 5, the saturated vapor enters the expander to perform work, which is expressed by:

$${\dot{\mathrm{W}}}_{\exp }={\mathrm{m}}_{\mathrm{r}}\left({\mathrm{h}}_4-{\mathrm{h}}_5\right)={\mathrm{m}}_{\mathrm{r}}\left({\mathrm{h}}_4-{\mathrm{h}}_{5\mathrm{s}}\right){\mathsf{\eta }}_{\exp }$$

(8)

where ${\dot{\mathrm{W}}}_{\exp }$ indicates the power generated by the expander, ${\mathrm{h}}_{5\mathrm{s}}$ denotes the working fluid at the expander outlet for an isentropic expansion process, ${\mathsf{\eta }}_{\exp }$ represents isentropic efficiency of the expander, and ${\mathrm{h}}_4{ \mathrm{and} \mathrm{h}}_5$ are defined as the inlet and outlet enthalpy of the working fluid in the expander, respectively.

During the process from 5 to 1, the vapor of the working fluid enters the condenser to exchange heat with the cooling seawater and becomes a saturated liquid. The calculation of the heat exchange quantity in the condenser is as follows:

$${\dot{\mathrm{Q}}}_{\mathrm{con}}={\mathrm{m}}_{\mathrm{r}}\left({\mathrm{h}}_5-{\mathrm{h}}_1\right)$$

(9)

where ${\dot{\mathrm{Q}}}_{\mathrm{con}}$ denotes the heat exchange quantity in the condenser, ${\mathrm{h}}_5{ \mathrm{and} \mathrm{h}}_1$ indicate the inlet and outlet enthalpy of the working fluid in the condenser, respectively.

The calculation of the mass flow rate of the cooling water required for this process is:

$${\mathrm{m}}_{\mathrm{c},\mathrm{w}}=\frac{{\dot{\mathrm{Q}}}_{\mathrm{con}}}{{\mathrm{C}}_{\mathrm{p},\mathrm{c},\mathrm{w}}\left({\mathrm{T}}_{\mathrm{c},\mathrm{w},\mathrm{out}}-{\mathrm{T}}_{\mathrm{c},\mathrm{w},\mathrm{in}}\right)}$$

(10)

where ${\mathrm{m}}_{\mathrm{w}}$ refers to the mass flow rate of cooling water, ${\mathrm{C}}_{\mathrm{p},\mathrm{c},\mathrm{w}}$ denotes the specific heat capacity of cooling water, and its temperature is the average temperature of the condenser inlet and outlet, ${\mathrm{T}}_{\mathrm{c},\mathrm{w},\mathrm{in}}{ \mathrm{and} \mathrm{T}}_{\mathrm{c},\mathrm{w},\mathrm{out}}$ are defined as the inlet and outlet temperature of cooling water in the condenser, respectively.

The power consumption of cooling seawater pump is ${\dot{\mathrm{W}}}_{\mathrm{c},\mathrm{p}}$, calculated as:

$${\dot{\mathrm{W}}}_{\mathrm{c},\mathrm{p}}=\frac{{\mathrm{m}}_{\mathrm{c},\mathrm{w}}\left({\mathrm{h}}_{\mathrm{c}, \mathrm{p},\mathrm{out}}-{\mathrm{h}}_{\mathrm{c},\mathrm{p},\mathrm{in}}\right)}{{\mathsf{\eta }}_{\mathrm{c},\mathrm{p}}}$$

(11)

where ${\mathrm{h}}_{\mathrm{c},\mathrm{p},\mathrm{in}}{ \mathrm{and} \mathrm{h}}_{\mathrm{c},\mathrm{p},\mathrm{out}}$ designate the inlet and outlet enthalpy of cooling water of the pump, respectively, ${\mathsf{\eta }}_{\mathrm{c},\mathrm{p}}$ denotes the isentropic efficiency of the cooling water pump.

The net power output generated by the ORC system is ${\dot{\mathrm{W}}}_{\mathrm{net}}$, calculated as:

$${\dot{\mathrm{W}}}_{\mathrm{net}}={\dot{\mathrm{W}}}_{\exp }-{\dot{\mathrm{W}}}_{\mathrm{f},\mathrm{p}}-{\dot{\mathrm{W}}}_{\mathrm{c},\mathrm{p}}$$

(12)

The ORC system thermal efficiency is then defined as:

$${\mathsf{\eta }}_{\mathrm{orc}}=\frac{{\dot{\mathrm{W}}}_{\mathrm{net}}}{{\dot{\mathrm{Q}}}_{\mathrm{v}}}=\frac{{\dot{\mathrm{W}}}_{\exp }-{\dot{\mathrm{W}}}_{\mathrm{f},\mathrm{p}}-{\dot{\mathrm{W}}}_{\mathrm{c},\mathrm{p}}}{{\dot{\mathrm{W}}}_{\mathrm{v}}}$$

(13)

3.2.2. Thermodynamic Model Validation

The ORC system thermodynamic model established in this paper was validated using the published experimental data given in the article by Song et al. [6]. The ORC system thermodynamic model to be validated adopts the exhaust gas of diesel engine as the heat source. Specifically, the exhaust gas mass flow rate was 1.98 kg/s, the inlet and outlet exhaust gas temperatures were 300 °C and 105 °C, respectively, and the condensation temperature of the system was 38 °C. The comparison between the simulation results and the experimental data is illustrated in

Table 9. Comparison between experimental data and simulation result.

Working Fluid	Cyclohexane			Benzene			Toluene
	Experimental Data	Simulation Data	Error	Experimental Data	Simulation Data	Error	Experimental Data	Simulation Data	Error
Evaporation temperature (K)	518.3	518.5	-	479.8	480	-	477.2	477.2	-
Working fluid mass flow rate (kg/s)	0.62	0.61	1.6%	0.68	0.68	-	0.67	0.67	-
Net power output (kW)	90.1	89.33	0.9%	90.8	90.22	0.6%	89.2	88.92	0.3%
Thermal efficiency (%)	21.2	21.19	-	21.3	21.4	0.5%	21	21.9	0.4%

. The performance of the system with three different working fluids was all compared. It can be found that the maximum relative error was 1.6%, which was within the allowable range, and thus the rationality of the system model can be effectively validated.

3.2.3. Calculation of Fuel Saving and Carbon Emission Reduction

The total fuel oil consumption of the main engine during the whole voyage is calculated by:

$${\mathrm{N}}_{\mathrm{oil}}={\displaystyle \sum }\frac{{\dot{\mathrm{W}}}_{\mathrm{M}/\mathrm{E}}\times {\mathrm{b}}_{\mathrm{M}/\mathrm{E}}\times {\mathrm{t}}_1}{{10}^6}$$

(14)

where ${\mathrm{N}}_{\mathrm{oil}}$ denotes the total fuel oil consumption, ${\dot{\mathrm{W}}}_{\mathrm{M}/\mathrm{E}}$ indicates the main engine operating power, ${\mathrm{b}}_{\mathrm{M}/\mathrm{E}}$ represents the corresponding Specific Fuel Oil Consumption (SFOC), ${\mathrm{t}}_1$ is the corresponding running time.

The ORC system uses its recovered power output for electricity generation, saving fuel oil during the whole voyage. The calculation of the fuel saving by the ORC system $,{ \mathrm{M}}_{\mathrm{oil}}$, is as follows:

$${\mathrm{M}}_{\mathrm{oil}}=\frac{{\dot{\mathrm{W}}}_{\mathrm{net}}\times {\mathrm{b}}_{\mathrm{A}/\mathrm{E}}\times \mathrm{t}}{{10}^6}$$

(15)

where ${\mathrm{b}}_{\mathrm{A}/\mathrm{E}}$ indicates SFOC of the generator diesel engine or auxiliary engine, and 189 g/kWh was used in this paper [30], and t denotes the running hours of the ORC system during the whole voyage.

The fuel saving rate F refers to the percentage of fuel oil saved by the ORC in the total fuel oil consumption of the main engine is expressed as:

$$\mathrm{F}=\frac{{\mathrm{M}}_{\mathrm{oil}}}{{\mathrm{N}}_{\mathrm{oil}}}\times 100\%$$

(16)

The carbon emissions reduction indicates the reduction of the emissions of greenhouse gas, carbon dioxide, generated during the voyage, and is calculated by:

$${\overline{\mathrm{m}}}_{{\mathrm{co}}_2}={\mathrm{M}}_{\mathrm{oil}}\times {\mathrm{C}}_{\mathrm{F}}$$

(17)

where ${\mathrm{C}}_{\mathrm{F}}$ denotes the ${\mathrm{CO}}_2$ emission factors, and 3.1 t-${\mathrm{CO}}_2$/t-fuel is used for the heavy fuel oil here [31].

4. Results and Discussions

Using the thermodynamic model of the ORC system developed and validated above, the simulation study on the thermodynamic performance of the exhaust gas side ORC subsystem and jacket cooling water side ORC subsystem was carried out. The variations in thermal efficiency and the net power output of the ORC subsystems following with the changes in outboard seawater temperature, the sulfur content of fuel oil, and main engine load which in turn can affect the average temperature of the waste heat sources and amount of recoverable waste heat together were comprehensively investigated. Based on the actual navigation data of the ship and the meteorological data along the route in summer and winter, the saving of fuel oil and carbon emission reduction during the whole voyage were calculated and analyzed.

4.1. Analysis of Exhaust Gas Side ORC Subsystem

The evaporation temperature and evaporation pressure of the exhaust gas side ORC subsystem will be adjusted with the changes of exhaust gas temperature. The temperature of the main engine exhaust gas after passing through the exhaust gas boiler will vary when the main engine operates at different loads during navigation. Considering that the operating time of the ship at 90% and 50% main engine load accounted for about 98% of the total operating time, the relationship between the net power output and thermal efficiency of the subsystem and the change in outboard cooling seawater temperature during the whole voyage were analyzed at two main engine loads of 90% and 50%, respectively. The change in seawater temperature was negatively related to the thermal efficiency of the system, and the changes in thermal efficiency will cause the changes in the net power output of the subsystem. Therefore, with the increase in the seawater temperature, the thermal efficiency of the subsystem will decrease to certain degrees under different main engine loads, and the net power output of the subsystem will also decrease. The analysis results are presented in Figure 5. When burning high-sulfur fuel oil, the thermal efficiency of the system was higher than that of low-sulfur fuel oil. This was because the average temperature of the exhaust gas passing through the system’s evaporator was higher than that when burning high-sulfur fuel oil due to the influence of the acid dew point temperature of the exhaust gas. However, when burning low-sulfur fuel oil, the net power output of the ORC system was higher than that of the high-sulfur fuel oil. This was because the temperature of the exhaust gas leaving the system’s evaporator was as low as 110 °C when burning low-sulfur fuel oil, which significantly enlarged the amount of waste heat recovered.

When the ship adopted low-sulfur fuel oil in summer and the seawater temperature increased from 25 °C to 30 °C along the route, the thermal efficiency of the subsystem decreased correspondingly from 11.75% to 10.97% at the main engine load of 90%, and the net power output of the subsystem was reduced from 510 kW to 476.3 kW. At the main engine load of 50%, the thermal efficiency of the subsystem decreased from 11.11% to 10.3%, and its net power output was reduced from 283.1 kW to 262.7 kW. When in winter, the seawater temperature increased from 10 °C to 25 °C along route, the thermal efficiency of the subsystem decreased from 14.07% to 11.75% at the main engine load of 90%, and its net power output was reduced from 494.6 kW to 413 kW. At 50% main engine load, the thermal efficiency of the subsystem decreased from 13.29% to 10.88%, and its net power output was reduced from 261.7 kW to 214.2 kW.

When the ship adopted high-sulfur fuel oil in summer and the seawater temperature increased from 25 °C to 30 °C along the route, the thermal efficiency of the subsystem decreased from 15.02% to 14.38% at the main engine load of 90%, and its net power output was reduced from 243.3 kW to 232.3 kW. At the main engine load of 50%, the thermal efficiency of the subsystem decreased from 14.89% to 14.23%, and its net power output was reduced from 120.3 kW to 115 kW. When in winter, the seawater temperature increased from 10 °C to 25 °C along the route, the thermal efficiency of the subsystem decreased from 17% to 15.02% at the main engine load of 90%, and its net power output was reduced from 137.4 kW to 121.4 kW. At the main engine load of 50%, the exhaust gas temperature of the main engine was close to the acid dew point temperature, and therefore the exhaust gas was not suitable for the ORC system to recover.

4.2. Analysis of Jacket Cooling Water Side ORC Subsystem

The jacket cooling water side ORC subsystem was utilized to recover the waste heat of the jacket cooling water for the main engine. The mass flow rate of the jacket cooling water changed correspondingly when the main engine was at different loads during navigation. However, the variation in engine load did not affect the temperature of the jacket cooling water, which made the evaporating temperature and evaporating pressure of the ORC subsystem unchanged, and hence did not change the thermal efficiency of the subsystem. When the ship adopted high-sulfur or low-sulfur fuel oil, it resulted in different inlet and outlet temperatures in the jacket cooling water of the engine, which should be matched with different evaporation temperatures for the ORC subsystem. The jacket cooling water mass flow rate was 41.2 kg/s and 27.9 kg/s at 90% main engine load and 50% main engine load, respectively. The simulation results are illustrated in Figure 6.

When the ship adopted low-sulfur fuel oil in summer and the seawater temperature increased from 25 °C to 30 °C along the route, the thermal efficiency of the ORC subsystem decreased correspondingly from 7.14% to 6.17%. At main engine loads of 90% and 50%, the net power output of subsystem was reduced from 185.5 kW to 160 kW and 125.4 kW to 108.4 kW, respectively. When in winter and the seawater temperature increased from 10 °C to 25 °C along the route, the thermal efficiency of the subsystem decreased from 9.97% to 7.14%, and its net power output decreased from 258.5 kW to 185.2 kW. Moreover, its net power output was reduced from 175.1 kW to 125.4 kW when the main engine load was 50%.

When the ship adopted high-sulfur fuel oil in summer, and the seawater temperature increased from 25 °C to 30 °C along the route, the thermal efficiency of the subsystem decreased from 7.94% to 7%. Its net power output decreased from 206 kW to 181.7 kW and 139.5 kW to 123.1 kW at the main engine load of 90% and 50%, respectively. When in winter and the seawater temperature increased from 10 °C to 25 °C along the route, the thermal efficiency of the subsystem was reduced from 10.68% to 7.94%, and its net power output was reduced from 277 kW to 206 kW and 187.6 kW to 139.5 kW at the main engine load of 90% and 50%, respectively.

4.3. Energy Saving Analysis of the Whole Voyage

In this section, the energy saving of the whole voyage of the ship after using the ORC system for waste heat recovery in different seasons was mainly analyzed when the ship burned fuels with different sulfur content. The whole voyage lasted a total of 184.63 h and sailed 1610.7 nautical miles. According to the actual operation of the ship, the respective energy recovered in different events or voyage stages can be obtained by multiplying their corresponding operation time and the net power output of the ORC system at different main engine loads. During the unberthing and berthing operation, the main engine load was divided equally according to the running time, and then the net power output at different main engine loads was calculated. The total work produced by the ORC system and the total energy recovered or saved for the ship during the whole voyage was then calculated through accumulating the respective work or energy in different events or voyage stages.

The energy saving data of the ORC system at different voyage stages or events of the whole voyage for when the ship adopted high-sulfur fuel oil are illustrated in

Table 10. Total work or amount of energy saving produced by ORC system when adopting high-sulfur fuel oil.

Events	Time (h)	Voyage (nmile)	Exhaust Gas Side ORC Subsystem in Summer (kWh)	Jacket Cooling Water Side ORC Subsystem in Summer (kWh)	Exhaust Gas Side ORC Subsystem in Winter (kWh)	Jacket Cooling Water Side ORC Subsystem in Winter (kWh)
Unberthing	1.38	0.6	169.7	213.3	35.9	286.8
High speed	12.83	123	3121.5	2643.0	1748.7	3493.6
High speed	45.4	455.5	10,950.5	9134.5	5992.8	11,513.4
High speed	37.16	389.6	8806.9	7116.1	4786.2	8896.1
High speed	60.3	622.4	14,164.5	11,252.0	7386.8	12,711.2
Low speed	0.3	1.2	34.8	37.9	0.0	42.8
Anchor	24	0	0.0	0.0	0.0	0.0
Low speed	0.3	1.1	34.8	37.9	0.0	42.8
High speed	2.16	16.2	502.8	392.5	262.2	445.0
Low speed	0.3	0.8	34.5	36.9	0.0	41.9
berthing	0.5	0.3	38.8	54.0	0.0	61.3
Total	184.63	1610.7	37,858.8	30,918.1	20,212.6	37,534.9

and

Table 11. Energy saving and fuel saving rate of the ship when adopting high-sulfur fuel oil.

Type		Total Energy Recovery (kWh)	Fuel Saving (t)	Carbon Emissions Reduction (t)	Fuel Saving Rate (%)
Summer	Exhaust gas side ORC	37,858.8	7.16	22.2	1.39
	Jacket cooling water side ORC	30,918.1	5.84	18.1	1.14
	Total	68,776.9	13	40.3	2.53
Winter	Exhaust gas side ORC	20,212.6	3.82	11.8	0.74
	Jacket cooling water side ORC	37,534.9	7.09	22	1.38
	Total	57,747.5	10.91	33.8	2.12

and Figure 7. When the ship sailed in summer, the total work or amount of energy saving produced by the ORC subsystem on the exhaust gas side and that on the jacket cooling water side during the whole voyage was 37,858.8 kWh and 30,918.1 kWh, respectively. In winter, the total work of the subsystem on the exhaust gas side and that on the jacket cooling water side was 20,212.6 kWh and 37,534.9 kWh, respectively. It can be seen that in different seasons, the net power output of the ORC subsystem on the exhaust gas side varied dramatically. The main reason was that the ship’s steam demand was less in summer and more waste heat can be recovered by the subsystem, and there was a relatively huge steam demand for ships in winter and the waste heat was not suitable for the ORC system to recover when the main engine was at low main engine load. Although the net power output and total work produced by the ORC subsystem on the jacket cooling water side in different seasons was not affected by the steam demand of the ship, the changes in seawater temperature can induce the changes in the thermal efficiency of the system, which in turn can influence the total net power output. Therefore, the total work of the ORC subsystem on the jacket cooling water side operating in winter was higher than that in summer.

The total work or amount of energy saving produced by the ship’s ORC system during the whole voyage was 68,776.9 kWh and 57,747.5 kWh in summer and winter, respectively. It can be seen from Figure 7 that the main engine consumed 513.6 tons of high-sulfur fuel oil for the whole voyage, and the energy saving of ships in summer was better than that in winter. When the ORC subsystems on the exhaust gas side and jacket cooling water side were operated simultaneously, the fuel was saved by up to 13 tons, and carbon emissions were reduced by 40.3 tons of CO₂; the fuel saving rate reached 2.53% for the whole voyage.

The energy saving data of the ORC system at different stages or events of the whole voyage when the ship adopted low-sulfur fuel oil are exhibited in

Table 12. Total work or amount of energy saving produced by the ORC system when adopting low-sulfur fuel oil.

Events	Time (h)	Voyage (nmile)	Exhaust Gas Side ORC Subsystem in Summer (kWh)	Jacket Cooling Water Side ORC Subsystem in Summer (kWh)	Exhaust Gas Side ORC Subsystem in Winter (kWh)	Jacket Cooling Water Side ORC Subsystem in Winter (kWh)
Unberthing	1.38	0.6	424.7	191.8	425.1	267.2
High speed	12.83	123	6543.3	2380.0	6276.4	3255.0
High speed	45.4	455.5	22,849.8	8181.1	21,220.0	10,641.8
High speed	37.16	389.6	18,201.0	6320.9	16,762.9	8167.8
High speed	60.3	622.4	29,124.9	9955.5	25,235.6	11,469.1
Low speed	0.3	1.2	80.0	33.5	65.2	38.6
Anchor	24	0	0.0	0.0	0.0	0.0
Low speed	0.3	1.1	80.0	33.5	65.2	38.6
High speed	2.16	16.2	1028.8	345.6	892.1	400.0
Low speed	0.3	0.8	78.8	32.5	64.3	37.6
berthing	0.5	0.3	104.0	47.6	89.5	55.1
Total	184.63	1610.7	78,515.4	27,522	71,096.2	34,370.7

and

Table 13. Energy saving and fuel saving of the ship when adopting low-sulfur fuel oil.

Type		Total Energy Recovery (kWh)	Fuel Saving (t)	Carbon Emissions Reduction (t)	Fuel Saving Rate (%)
Summer	Exhaust gas side ORC	78,515.4	14.84	46	2.89
	Jacket cooling water side ORC	27,522	5.2	16.1	1.01
	Total	106,037.4	20.04	62.1	3.91
Winter	Exhaust gas side ORC	71,096.2	13.44	41.7	2.62
	Jacket cooling water side ORC	34,370.7	6.5	20.1	1.27
	Total	105,466.9	19.94	61.8	3.89

and Figure 8. When the ship sailed in summer, the total work or amount of energy saving produced by the ORC subsystem on the exhaust gas side and that on jacket cooling water side during the whole voyage was 78,515.4 kWh and 27,522 kWh, respectively. In winter, the total work produced or amount of energy saving by the subsystem on exhaust gas side and that on jacket cooling water side was 71,096.2 kWh and 34,370.7 kWh, respectively.

The total work or amount of energy saving by the ship’s ORC system during the whole voyage was 106,037.4 kWh and 105,466.9 kWh in summer and winter, respectively. It can be found that the total work of the ORC system operating in summer was just slightly higher than that in winter, while the difference between them was not significant. The main reason was that although the thermal efficiency of the jacket cooling water side ORC subsystem decreased due to the increased temperature of seawater in summer, the ship’s steam demand in summer was less than that in winter and thus the available temperature range of the exhaust gas for the ORC subsystem was expanded, and consequently, the energy recovered by the exhaust gas side ORC subsystem increased. In winter, the ship’s steam demand increased and thus the available temperature range of the exhaust gas for the ORC subsystem decreased, while the thermal efficiency of the jacket cooling water side ORC subsystem increased due to the decreased temperature of seawater in winter.

It can be seen from Figure 8 that the main engine consumed 512.7 tons of low-sulfur fuel oil for the whole voyage. When the ORC subsystems on the exhaust gas side and jacket cooling water side were operated simultaneously, the fuel saved up to 20.04 tons, and carbon emissions were reduced by 62.1 tons of CO₂. The fuel saving rate reached 3.91% for the whole voyage.

When the ship adopted low-sulfur fuel oil, because the sulfur content of exhaust gas was less and hence its acid dew point was as low as about 110 °C, the temperature difference between exhaust gas at the inlet and outlet of the evaporator of the ORC system was significantly enlarged. Consequently, the ORC system can recover more waste heat due to the wider range of temperature of exhaust gas available for the exhaust gas side ORC subsystem. When operated in summer, the maximum net power output of the exhaust gas side ORC subsystem can reach 510 kW under the condition of engine load of 90% and seawater temperature of 25 °C. Therefore, the ships that burn low-sulfur fuel oil are generally better than ships that burn high-sulfur fuel oil in terms of amount of energy saving by the ORC system, carbon emissions reduction, and fuel saving rate from the whole voyage.

5. Conclusions and Future Work

In this paper, the thermal efficiency and net power output of the ORC system used to recover ship waste heat were analyzed when main engine burned fuel oils with different sulfur content, taking into account the variations in engine load, outboard seawater temperature, ship’s steam demand and amount of recoverable waste heat. Then, combined with the specific sailing data of the ship during the whole voyage, including the sailing time corresponding to different voyage stages or events, the total work or amount of energy saving produced by the ORC system during the whole voyage was calculated, and the impact on the energy saving, fuel saving rate, and carbon emission reduction of the ship during the whole voyage was analyzed. The main conclusions are as follows:

(1) When the ship adopted high-sulfur fuel oil, the ORC subsystem on the exhaust gas side and that on the jacket cooling water side could reach the maximum thermal efficiency of 17% and 10.68%, respectively, when the seawater temperature was 10 °C in winter. The maximum net power output of the exhaust gas side ORC subsystem was 243.3 kW when the seawater temperature was 25 °C in summer, while the jacket cooling water side ORC subsystem could achieve a maximum net output power of 277 kW when the seawater temperature was 10 °C in winter.

When the ship adopted low-sulfur fuel oil, the ORC subsystem on the exhaust gas side and that on the jacket cooling water side could reach the maximum thermal efficiency of 14.07% and 9.97%, respectively, when the seawater temperature was 10 °C in winter. The maximum net power output of the exhaust gas side ORC subsystem was 510 kW when the temperature was 25 °C in summer, while the jacket cooling water side ORC subsystem could achieve the maximum net power output of 258.5 kW when the seawater temperature was 10 °C in winter.

(2) When the ship adopted high-sulfur or low-sulfur fuel oil, the net power output generated by the ORC system to recover waste heat was higher than that of the ship using high-sulfur fuel oil under the same conditions, and the difference could reach a maximum of 338.7 kW in winter, which is 45% higher. Therefore, it is more favorable for the application of ORC technology to recover ship waste heat when ships burn low-sulfur fuel oil.

(3) After the whole voyage of 184.63 h and 1610.7 nautical miles, when high-sulfur fuel oil was adopted by the ship, the ORC system could save 13 tons and 10.91 tons of fuel oil in summer and winter, reduce carbon emissions by 40.3 tons and 33.8 tons of CO₂, respectively; and the fuel saving rate was 2.53% and 2.12%, respectively. When low-sulfur fuel oil was adopted by the ship, the ORC system could save 20.04 tons and 19.93 tons of fuel in summer and winter, reduce carbon emissions by 62.1 tons and 61.8 tons of CO₂, respectively. The fuel saving rate was 3.91% and 3.89%, respectively.

In this study, the ORC system recovering a ship’s waste heat was composed of two independent subsystems and its configuration was relatively simple. In the future, the optimization for the system’s architecture, working fluid, and designing parameters shall be carried out according to the characteristics of recoverable waste heat onboard to further enhance the system’s thermal efficiency. Using the optimized ORC system, the analysis of energy saving during a whole voyage can provide more comprehensive and valued investigation and suggestion to the ship field. Moreover, the economic evaluation including the calculation of the capital cost and feedback period for the ORC system shall be conducted in the future to help achieve a more objective and reliable assessment of the application of ORC system on ships.