Thermal Evaluation of a Novel Integrated System Based on Solid Oxide Fuel Cells and Combined Heat and Power Production Using Ammonia as Fuel

Abstract

A novel integrated system based on solid oxide fuel cells (SOFCs), a gas turbine (GT), the steam Rankine cycle (SRC), the Kalina cycle (KC), and the organic Rankine cycle (ORC) is proposed to achieve cascade energy utilization. Mathematical models are introduced and system performance is analyzed using energy and exergy methods. The first and second laws of thermodynamics are used to analyze the system thermodynamically. In addition, exergy destruction and losses of the various integrated subsystems are calculated. The energy and exergy efficiencies of the multigeneration system are estimated to be 60.4% and 57.3%, respectively. In addition, the hot water produced during the waste heat recovery process may also be used for accommodating seafarers on ships. Sequential optimization is developed to optimize the operating conditions of the integrated system to achieve the required power output. A comprehensive parametric study is conducted to investigate the effect of varying the current densities of the fuel cell and working fluid of the ORC on the overall performance of the combined system and subsystems. The working performance of five working fluids for the ORC as candidates—R134a, R600, R601, R152a, and R124—is compared. R152a, which provides 71.23 kW of power output, and energy and exergy efficiencies of 22.49% and 42.76%, respectively, is selected as the best thermodynamic performance for the ORC.

1. Introduction

Maritime transportation is the primary means of transport and is responsible for over 80% of the world’s trade by volume [1]. Thus, it is also a major source of climate change and air pollution, which negatively impacts health and the environment [2]. In response to this issue, the International Maritime Organization (IMO) has adopted various regulations and mandatory measures to avoid further negative impacts on the environment, control airborne emissions, and decrease greenhouse gases (GHGs). The IMO 2020 lowered the limit of the sulfur content of ship fuel from 3.5% in 2015 to 0.5% [3], and the IMO GHG initial strategy also agreed to reduce carbon dioxide (CO₂) emissions per transportation by at least 40% by 2030 and total yearly GHG emissions by no less than 50% by 2050 in comparison with 2008 [4,5]. These strategies and targets have driven global maritime shipping to new technologies, renewable energy, and alternative fuel sources with low- or decarbonization. Recently, ammonia has emerged as a promising and potential marine fuel for avoiding CO₂ emissions, resulting in low climate impacts and a clean future [6].

Ammonia (NH₃) is a carbon-free compound and one of the intermediate products in various industrial applications [7,8]. NH₃ can be widely produced by well-established methods and infrastructures such as the Haber–Bosch process, the electrochemical process, and power-to-gas technologies or produced from algae through a hydrothermal gasification combined system [9]. This fuel can be easily stored, either refrigerated at −33 °C and atmospheric pressure or approximately 29.5 °C and pressurized to 800–1000 kPa [6,7,10,11]. In addition, since NH₃ contains a 45% higher volumetric hydrogen density than liquid hydrogen, it is also a potentially attractive medium for hydrogen storage. When the end-user requires hydrogen as a fuel for a specific application, ammonia can be converted to hydrogen using a very low amount of energy for the reforming process [7]. Thus, ammonia can be utilized for energy purposes in several maritime applications, such as fuel cells and internal combustion engines [7]. Aziz et al. [12] performed the comprehensive review on ammonia in terms of production, storage and applications, and proved that ammonia is a strong candidate for use as a hydrogen carrier in the future and direct ammonia fuel cells are promising in terms of total energy efficiency. Ammonia linked to fuel cells is currently being studied by researchers and manufacturers owing to its advantages over internal combustion engines, as they provide high efficiency, less noise, lower emissions of air pollutants, and higher thermal efficiencies. Depending on the working temperature of the fuel cells, ammonia can be used directly or indirectly by a reformer (that splits ammonia into H₂ and N₂ before supplying to the fuel cells). The two typical types of fuel cells that can be used with ammonia systems are solid oxide fuel cells (SOFCs) and proton-exchange membrane fuel cells (PEMFCs). Other types of fuel cells, such as alkaline and alkaline membranes, are under development, and few experimental reports are available [5]. SOFCs use ammonia directly [13,14], whereas PEMFCs require purified hydrogen (indirectly using ammonia by reforming). Focusing on the future of electric propulsion vessels, SOFCs, which consume ammonia directly for electric power and obtain reasonable energy efficiencies, possess great potential [15,16,17].

Siddiqui et al. [18] assessed the working performance of direct ammonia fuel cells and showed that an increase in electrolyte thickness decreases cell performance significantly. Thus, high-performance SOFCs can be obtained using low thickness, high temperatures, and electrolytes. Ezzat et al. [19] developed a combined system of SOFCs and gas turbines using ammonia as fuel and evaluated the proposed system using the first and second laws of thermodynamics. They recovered the waste heat of the system through Rankine cycles and produced more power by its expanders. The obtained energy and exergy efficiencies of the suggested integrated system were 58.78% and 50.66%, respectively. Grasham et al. [20] proposed a system of combined ammonia recovery and SOFCs for wastewater treatment plants and modeled it using Aspen Plus V.8.8. The results showed an increase of 45% in renewable electricity production, thereby achieving a 6% reduction in consumption and an annual reduction in GHG emissions of 3.4 kg CO₂ per person. Perna et al. [21] designed a combined heat, hydrogen, and power system using ammonia as fuel for SOFCs to generate hydrogen at 100 kg/day via two different concepts. An analysis of the trigeneration efficiencies demonstrated that the two designed concepts achieved 81% and 71%. Eveloy et al. [22] investigated a SOFC–Brayton cycle–Rankine cycle combined system to improve the efficiency and power generation of the system. The six working fluids used for the ORC were R123, R245fa, benzene, cyclohexane, toluene, and cyclopentane. The achieved energy and exergy efficiencies were 64% and 62%, respectively, and the efficiency improved by approximately 34% compared to the base gas turbine cycle. Baniasadi and Dincer [17] analyzed the energy and exergy efficiencies of an SOFC system using ammonia as fuel. The total exergy efficiency of the system, as a function of the current density, was 60–90%, while the energy efficiency varied from 60% to 40%.

A survey of the existing literature and research shows that there is a lack of comprehensive studies and analyses on the integration of the SOFC and gas turbine (GT) bottoming cycle employing ammonia as fuel for marine applications. To fill this knowledge gap in the literature, the precise objectives of this study are as follows:

-

To develop the novel integrated SOFC–GT–Rankine cycles–KC system using ammonia as a fuel.

-

To analyze the energy and exergy efficiencies of the proposed system from a thermodynamic point of view.

-

To conduct parametric studies to determine the reaction of this system to a variety of different circumstances.

-

The novel aspects of this study are as follows:

-

Usage of ammonia as ship fuel.

-

Application of an integrated SOFC-based system for shipping vessels. The influence of the current density on the efficiency of SOFC and the integrated system.

-

Usage of waste heat from an SOFC–GT hybrid system increases the thermal efficiency of the system. The estimation of energy and exergies efficiencies, the exergy destruction of main components of proposed system.

-

Parallel integration of GT with cascaded Rankine cycles and KC to generate additional power for accommodation, lighting, auxiliary machinery and other purposes. The selection method for most suitable working fluid for optimize operation of the organic Rankine cycle.

The next structure of the current study is organized as follows. Section 2 explains the background of ammonia-fueled SOFCs and energy systems for power generation, and introduces the proposed combined heat and power (CHP) system. Section 3 evaluates each system section from a thermodynamic viewpoint and builds up the energy and exergy calculation model for each subsystem. Section 4 outlines the assumptions, methodology, and procedures used in this study. The model is verified in Section 5. The numerical modeling approach, results of this study in terms of energy and mass balances, and overall CHP performance, are presented in Section 6. The conclusions are presented in Section 7.

2. Materials and Methods: System Description

A general cargo ship with ammonia as fuel was chosen as the target of the proposed system with a total propulsion power of 3800 kW. The specifications of the modeling ship are listed in

Table 1. General specifications of the target ship.

Items	Values
Type of vessel	General cargo
Total length	120 m
Beam	13 m
DWT	3000 tonnage
Average shaft power	475 kW
Main engine power	3800 kW

. The target ship utilizes a type of electric propulsion powered by an ammonia supply system. A schematic of the overall configuration of the system is shown in Figure 1. The general idea underlying the concept integrated system is the utilization of waste heat from SOFCs to generate useful work (electricity). As shown, ammonia is supplied to the SOFC before the working temperature is obtained from the regenerative heat exchanger. The steam Rankine cycle (SRC) absorbs waste heat from the SOFC and releases it into the working fluids. These processes generate electric power through their expander devices.

The schematic in Figure 2 depicts the proposed combined system using ammonia as fuel, which comprises a fuel gas supply system, SOFC–GT, SRC, ORC and KC. The air and ammonia are supplied to the SOFC through the fuel gas supply system (FGSS). After reaction in the SOFC, the exhaust gas is led to the afterburner for completing combustion. This generates a considerable amount of heat and enlarges the temperature of the exhaust gas. Subsequently, the exhaust gas is utilized in the gas turbine (GT), heat exchangers, and bottom cycles to generate additional power. Thus, the cascade waste heat is utilized. The main components and working principles of the cycles are described below:

①

SOFC–GT: First, compressed air and ammonia are preheated in turn by the exhaust gas of the SOFC using two heat exchangers. Thus, the ammonia and compressed air can reach the required inlet temperature for the SOFCs. After preheating, the reforming and electrochemical reactions occur in the SOFC. These reactions generate electrical energy (by converting chemical energy to electrical energy) and produce a large amount of heat. Subsequently, the generated electricity (DC) is converted to an alternating current (AC) before being supplied to the ship propulsion system. There are two main exhaust streams from solid oxide fuel cells. There is exhaust of a nitrogen-rich stream from the cathode (stream 4–1) and a mixed water and nitrogen stream from the anode (stream 6–1) and main exhaust stream 6 to provide to the afterburner.

②

SRC: This operates mainly using the heat received from the exhaust gas of the heat exchanger (E-102). Water in the SRC is first pumped by a pump (P-100) to high pressure. Then, it proceeds to the heat exchanger (E-102) to become a superheated fluid. Next, the high-pressure steam (17) is depressurized in the expander (K-102) to drive the reversible heat pump and produce extra electric power. The saturated water mixture (19) is condensed in the heat exchanger (E-104) and releases heat to the fresh cooling water. This cooling water (21) after the heat exchanger (E-104) at 70.98 °C is used for the seafarers aboard ships.

③

KC: The evaporator heats the ammonia—water using the exhaust gas from the SOFC. The gas then powers the expander (K-104), which produces mechanical work. The liquid blends with the gas after the throttling valve. Subsequently, the working fluid is condensed in the condenser (E-106) before being pressurized by the pump (P-102). Finally, the working fluid is cooled to the required temperature before entering the heat exchanger (E-103) to complete the cycle.

④

ORC: The energy required by the ORC subsystem is supplied by heat exchange (E-108). 1,1-Difluoroethane (R152a) was chosen as the working fluid in this subsystem process. In addition, the working fluid is charged by heat transfer in the heat exchanger (E-108) and transferred to the ORC turbine with flow number 35. Power is produced by expanding the working fluid between flows 35 and 36. The working fluid from the ORC turbine is transferred to the heat exchanger (E-105) with a flow number of 37. In E-105, energy transfer occurs between the working fluid in the ORC and fresh cooling water, thereby providing hot water (39) for the accommodation of seafarers. The working fluid in the ORC subsystem from E-105 is transferred to the pump (P-101) with flow 37 to increase the pressure, and then to E-108 with flow 34 for energy transfer.

The subsystem coupling connection must be compatible with the exhaust gas cascade. The SRC recompression cycle works at high temperatures, but KC and ORC recover waste heat at lower temperatures, improving the thermal efficiency.

3. Materials and Methods: Thermodynamic Model and Simulation

3.1. Thermodynamic Balance Equations

The general thermodynamic balance equations, including mass and energy balance, entropy balance, and the exergy destruction rate, which are used in integrated systems, are discussed in this subsection.

-

Mass balance equation:

Under steady-state conditions, the four balance equations for each component of the system were applied. A control volume can be regarded as any component that is modeled thermodynamically. Under steady-state conditions, the rate of mass change in the control volume is zero [11]

$$\begin{gathered} {{\displaystyle \sum }}_{in}{\dot{m}}_{in}-{{\displaystyle \sum }}_{out}{\dot{m}}_{out}=\frac{d{m}_{CV}}{dt}=0 \mathrm{or} \\ {\displaystyle \sum }_{in}{\dot{m}}_{in}={\displaystyle \sum }_{out}{\dot{m}}_{out} \end{gathered}$$

(1)

where $\dot{m}$ represents the mass flow rate. The rate of change of the total mass within a control volume (CV) is equal to subtraction of the total mass flow rate entering the control volume (CV) and the total mass flow rates exiting the control volume.

-

Energy balance equation:

The first law of thermodynamics [10] was applied for energy conservation:

$$\dot{Q}-\dot{W}+{\displaystyle \sum }_{in}{\dot{m}}_{in}\left(h_{in}+\frac{V_{in}^2}{2}+g{Z}_{in}\right)-{\displaystyle \sum }_{out}{\dot{m}}_{out}\left(h_{out}\frac{V_{out}^2}{2}+g{Z}_{out}\right)=0$$

(2)

where $\dot{Q},$ $h$, and $\dot{W}$ denote the heat transfer rate, specific enthalpy of the fluid, and mechanical power, respectively.

In the thermodynamic analysis, the specific kinetic and potential energy values associated with the entering and exiting mass flow rates were assumed to be negligible and ignored [11]:

$${\dot{Q}}_{in}+{\displaystyle \sum }_{in}{\dot{m}}_{in}\left(h_{in}\right)={\dot{W}}_{out}+{\displaystyle \sum }_{out}{\dot{m}}_{out}\left(h_{out}\right)$$

(3)

-

Entropy and exergy balance equation:

The second law of thermodynamics was applied to the entropy and exergy balance equations. Under steady-state conditions, the rate of change in entropy in a control volume is zero.

$$\begin{gathered} {{\displaystyle \sum }}_k\frac{{\dot{Q}}_k}{T_k}+{{\displaystyle \sum }}_{in}{\dot{m}}_{in}\left(s_{in}\right)+{\dot{S}}_{gen}-{{\displaystyle \sum }}_{out}{\dot{m}}_{out}\left(s_{out}\right)=\frac{d{S}_{CV}}{dt}=0 \mathrm{or} \\ {{\displaystyle \sum }}_k\frac{{\dot{Q}}_k}{T_k}+{{\displaystyle \sum }}_{in}{\dot{m}}_{in}\left(s_{in}\right)+{\dot{S}}_{gen}={{\displaystyle \sum }}_{out}{\dot{m}}_{out}\left(s_{out}\right) \end{gathered}$$

(4)

where $T$, $s$, and ${\dot{S}}_{gen},$ denote the temperature (K), specific entropy, and entropy of the thermal process, respectively.

Under steady-state conditions, the rate of change of exergy is also zero in the control volume.

$${{\displaystyle \sum }}_k(1-\frac{T_0}{T_k}){\dot{Q}}_k-{\dot{W}}_{out}+{{\displaystyle \sum }}_{in}{\dot{m}}_{in}\left(e{x}_{in}\right)-{{\displaystyle \sum }}_{out}{\dot{m}}_{out}\left(e{x}_{out}\right)-{\dot{Ex}}_{dest}=\frac{dE{x}_{CV}}{dt}=0 \mathrm{or}$$

(5)

$${\displaystyle \sum }_k(1-\frac{T_0}{T_k}){\dot{Q}}_k+{\displaystyle \sum }_{in}{\dot{m}}_{in}\left(e{x}_{in}\right)={\displaystyle \sum }_{out}{\dot{m}}_{out}\left(e{x}_{out}\right)+{\dot{W}}_{out}+{\dot{Ex}}_{dest}$$

(6)

-

Specific exergy values and the exergy destruction rate:

The entropy generation rate from the entropy balance equation can be used to compute the exergy destruction rate for any control volume or component.

$$\dot{E}{x}_{dest}=T_0{\dot{S}}_{gen}$$

(7)

Here, $T_0, ex,$ and ${\dot{Ex}}_{dest}$ represent the ambient temperature of the surrounding area (K), specific exergy of the fluid, and the exergy destruction rate, respectively. The specific exergy values are calculated using the sum of the physical, chemical, kinetic, and potential exergy as follows:

$$e{x}_j=e{x}_j^{ph}+e{x}_j^{ch}+e{x}_j^{ke}+e{x}_j^{pe}$$

(8)

In this thermodynamic analysis, the kinetic and potential exergy were assumed to be negligible and ignored. A weighted average formula applicable to ideal gas combinations was used to calculate the specific enthalpy and entropy of the SOFC exhaust gases.

$$e{x}_j=e{x}_j^{ph}+e{x}_j^{ch}$$

(9)

In this expression, the physical exergy can be calculated as:

$$e{x}_j^{ph}=\left(h_j-h_0\right)-T_0\left(s_j-s_0\right)$$

(10)

The chemical exergy can be estimated using:

$$e{x}_j^{ch}={\displaystyle \sum }_k{x}_{k }(e{x}_j^{ch}-R{T}_0{x}_k\ln \left(x_k\right))$$

(11)

where $x_k, e{x}_j^{ch},$ and $R$ denote the mass ratio of the substance within the mixture, standard chemical specific exergy, and gas constant, respectively.

3.2. Model of the SOFC

SOFC systems can be classified into two main types: oxygen-ion-conducting electrolytes (SOFC-O) and proton-conducting electrolytes (SOFC-H) [23]. The SOFC-O requires oxygen ion-conducting electrolytes, such as YSZ or SDC, and water formation at the anode side, whereas a proton-conducting ceramic electrolyte, for example barium cerate, is required for the SOFC-H, in addition to water formation at the cathode.

Since ammonia is unstable at high temperatures, it begins to decompose into H₂ and N₂ [24] from 200 °C [25], when supplied to the anode. The working temperature increases to 425 °C, and 98–99% of the ammonia will be converted. Complete conversion occurs above 600 °C (873 K) [26]. However, the conversion rate depends strongly on the catalyst and the working temperature.

$$2{\mathrm{NH}}_3\leftrightarrow { \mathrm{N}}_2+3{\mathrm{H}}_2$$

(12)

$$2{\mathrm{H}}_2\leftrightarrow 4{\mathrm{H}}^{+}+4e^{-}$$

(13)

After the first crack of NH₃ into N₂ and H₂ over the Ni-based catalyst, the generated H₂ was utilized for generating electricity electrochemically. Hydrogen is then oxidized to H₂O by oxide ions [26].

$${\mathrm{O}}_2+4e^{-}+4{\mathrm{H}}^{+}\to 2{\mathrm{H}}_2\mathrm{O}$$

(14)

The overall reaction representing ammonia completed combustion can be summarized as:

$$4{\mathrm{NH}}_3+3{\mathrm{O}}_2\to 6{\mathrm{H}}_2\mathrm{O} +2{\mathrm{N}}_2$$

(15)

During the conversion of NH₃, nitrogen oxide (NO) might be generated by the oxidation of N₂ and oxygen ions.

$${\mathrm{N}}_2+2{\mathrm{O}}^{2-}\to 2\mathrm{NO} +4e^{-}$$

(16)

Ma et al. [13] proved that the partial pressure of NO increases with the increase in NH3 conversion rate. However, the partial pressure of NO is counted as only 10⁻¹² atm with a conversion rate of ammonia of 0.99 and the operating temperature of SOFCs at 800 ℃. So, negligible amounts of NO can be produced in the case of ammonia cracks completely over the YSZ electrolyte [15].

Reaction (12) is endothermic, and influenced by factors such as the pressure and temperature. The reaction changes to the right side as the temperature rises, and to the left side as the pressure rises, producing less hydrogen. To achieve thermodynamic equilibrium of ammonia, the overall Gibbs energy of the process can be minimized [24,27,28]:

$${(\mathrm{\Delta }{G}_{system})}_{T,P}=0$$

(17)

Here, the Gibbs energy of the system is the total of the product of the moles of chemical species $i$ multiplied by the appropriate specific Gibbs energy under constant temperature and pressure:

$$G_{system}=\sum n_i{\overline{g}}_i$$

(18)

The ratio of the fugacity of a species in the system to its fugacity at standard temperature and pressure (STP) for actual gases is defined as its activity:

$${\overline{g}}_i={\overline{g}}_{fi}^0+RT ln\frac{f_i}{f_i^0}$$

(19)

The total Gibbs energy of the system can be calculated as:

$$G_{system}={(\sum n_i[{\overline{g}}_{fi}^0+RT\ln \left(y_{i}P\right)])}_{gas}+{(\sum n_i{\overline{g}}_{fi}^0)}_{condensed}$$

(20)

3.2.1. Fuel and Oxidant Utilization

The usage of ammonia can be determined in terms of the actual provide and consumption of the ammonia, or its hydrogen counterpart, such that [21,22,24,29]

$$U_{f\lambda }=\frac{{(Fuel)}_{consumed }}{{(Fuel)}_{supplied}}=\frac{{(H_2)}_{consumed}}{{(H_2)}_{supplied}}$$

(21)

The air utilization can be calculated as:

$$U_{f𝓊}=\frac{{(Air)}_{consumed }}{{(Air)}_{supplied}}=\frac{{(O_2)}_{consumed}}{{(O_2)}_{supplied}}$$

(22)

A list of operating values for the proposed system at the designated operating point is presented in

Table 2. Selected operating point.

Parameters	Value
Ambient temperature	303 K
Ambient pressure	100 kPa
Utilization factor (u)	0.8
Excess air factor $\left(\lambda \right)$	1.4
SOFC efficiency	56.8%
Total power required by propulsion plant of target vessel at maximum load [29]	3800 kW

.

Through the component stack, the net power output of the SOFC system can be calculated as [30,31,32]:

$$W_{stack}=i·a·V_c{\eta }_{DA}$$

(23)

where $i, a,V_c,$ and ${\eta }_{DA}$ denote the current density (A/m²), surface area (m²), actual voltage of the stack (V), and efficiency of the inverter, respectively [19,31].

$$V_c=V_R-V_{loss}$$

(24)

where $V_R$ denotes the cell ideal reversible voltage and,

$$V_{loss}=V_{ohm}+V_{act}+V_{con}$$

(25)

In this expression, $V_{ohm}, V_{act}$, and $V_{con}$ indicate the ohmic losses (V), activation losses (V), and concentration losses (V), respectively.

$$V_{ohm}=V_{ohm,a}+V_{ohm,c}+V_{ohm,e}+V_{ohm,int}$$

(26)

$$V_{ohm,a}=\frac{i{\rho }_a (A·\pi ·D_{m)}}{8·t_a}$$

(27)

$$V_{ohm,c}=\frac{i{\rho }_c {(A·\pi ·D_m)}^2}{8· t_c} A·\left(A+2\left(1-A-B\right)\right)$$

(28)

$$V_{ohm,e}=i{\rho }_a{t}_e$$

(29)

$$V_{ohm,int}=i· {\rho }_{int}·\pi · D_m\frac{t_{int}}{w_{int}}$$

(30)

$$V_{act}=\frac{2RT}{F· n_e} Arcsinh \left(\frac{i}{2i_{0,k}}\right)$$

(31)

$$V_{con}=\frac{RT}{2F} ln\left(\frac{1-\frac{i}{i_{L,H_2}}}{1+\frac{i}{i_{L,O_2}}}\right)+\frac{RT}{2F} ln\left(\frac{1}{1-\frac{i}{i_{L,O_2}}}\right)$$

(32)

In addition, the actual voltage of the stack can also be defined based on the I-V curve [8,11,13,21,33,34]

The cell efficiency may be estimated as [17]:

$${\eta }_{cell}=\frac{V_c}{1.25}$$

(33)

Otherwise, thermodynamically, the energy efficiency of the fuel cell can be calculated as:

$${\eta }_{en, SOFC}=\frac{{\dot{W}}_{elect,SOFC}}{{\dot{m}}_{ammonia}{h}_{ammonia}+{\dot{m}}_{air}{h}_{air}-{\dot{m}}_7{h}_7}$$

(34)

Or [31,35]:

$${\eta }_{en,SOFC}=\frac{{\dot{W}}_{SOFC}}{{\dot{m}}_{N{H}_3}LH{V}_{N{H}_3}}$$

(35)

where ${\dot{m}}_{N{H}_3}$ denotes the mass flow rate of NH₃ (kg/h) and $LH{V}_{N{H}_3}$ is the low heating value of NH₃ (KJ/kg).

3.2.2. Afterburner

The afterburner was used to burn the remaining ammonia. Fresh charge injection was used to raise the temperature of the inlet turbine. The reactants were assumed to burn completely adiabatically. For this reaction, the chemical balance equation is [10]:

$$\begin{gathered} \alpha ·N{H}_3+\left(1-U\right)N{H}_{3 }+1.5U·H_{2}O+0.75 \left(\lambda -U\right)O_2+\left(2.82\lambda +0.5U\right)N_2 \\ \to 1.5\left(1+\alpha \right)H_{2}O+0.75 \left(\lambda -\left(1+\alpha \right)\right)O_2+\left(2.82\lambda +0.5\left(1+\alpha \right)\right)N_2 \end{gathered}$$

(36)

3.3. Model of the Gas Turbine System

3.3.1. Gas Turbine

The hot gaseous mixture expands when it exits the combustion chamber and enters the gas turbine, delivering useful mechanical power. The exit temperature can be calculated as follows:

$$T_{out}=T_{in }{(PR)}^{\raisebox{1ex}{$\left(k-1\right)$}\!\left/ \!\raisebox{-1ex}{$k$}\right.}$$

(37)

in which $PR=\frac{P_{in}}{P_{out}}$ and $k=\frac{{{\displaystyle \sum }}_i{y}_i {\dot{\overline{C}}}_{p,i}}{{{\displaystyle \sum }}_i{y}_i{\overline{C}}_{v,i}}$.

The isentropic efficiency can be calculated as:

$${\eta }_{s,T}=\frac{{{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{in }– {{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{out }}{{{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{in }– {{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{s, out }}$$

(38)

The exergy efficiency can be calculated as:

$$\psi { }_T=\frac{{\dot{W}}_T}{{{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{ex}}_i)}_{in }– {{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{ex}}_i)}_{ out }}$$

(39)

The energy and exergy efficiencies of the SOFC–GT subsystem can be calculated as follows:

-

Energy efficiency:

$${\eta }_{en,SOFC,GT}=\frac{{\dot{W}}_{SOFC}+{\dot{W}}_{GT}}{{\dot{m}}_{ammonia} LH{V}_{ammonia}}$$

(40)

-

Exergy efficiency:

$${\eta }_{ex,SOFC,GT}=\frac{{\dot{W}}_{SOFC}+{\dot{W}}_{GT}}{{\dot{m}}_{ammonia} e{x}_{ammonia}}$$

(41)

3.3.2. Air Compressor

Similar to the method of calculating the isentropic energy and exergy efficiencies of the gas turbine, the isentropic efficiency of the air compressor can be calculated as:

$${\eta }_{en,Compressor}=\frac{{{\displaystyle \sum }}_i({\dot{n}}_i{\overline{h}}_i)s{,}_{out }– {{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{in }}{{{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{out }– {{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{h}}_i)}_{in }}$$

(42)

and the exergy efficiency of the air compressor can be calculated as:

$${\eta }_{ex,Compressor}=\frac{{{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{ex}}_i)}_{in }– {{\displaystyle \sum }}_i{({\dot{n}}_i{\overline{ex}}_i)}_{ out }}{{\dot{W}}_{C }}$$

(43)

3.3.3. Electric Generator

The surplus power which drives the electric generator, can be estimated using:

$${\dot{W}}_G={\eta }_G \left({\dot{W}}_T-{\dot{W}}_C\right)$$

(44)

3.3.4. Heat Exchangers

The hot (exhaust gas) and cold stream (fuel or air supply) through the heat exchanger are determined as follows:

-

Hot stream:

$$\dot{Q}={\displaystyle \sum }_i{({\dot{n}}_i{\overline{c}}_{p,i})}_h \left(T_{h,in}-T_{h,out}\right)$$

(45)

-

Cold stream:

$$\dot{Q}={\displaystyle \sum }_i{({\dot{n}}_i{\overline{c}}_{p,i})}_h \left(T_{c,in}-T_{c,out}\right)$$

(46)

3.4. The Kalina Cycle System

For the control volume, the energy conservation of the Kalina cycle at the steady state is:

$$\dot{Q}+\sum {\dot{m}}_{in}{h}_{in}=\dot{W}+\sum {\dot{m}}_{out}{h}_{out}$$

(47)

The energy equation for each component of the KC was calculated as shown in

Table 3. Energy equations of main components of KC.

Component	Energy Equation		References
Turbine K-104	${\eta }_{is, T}=\frac{W_{is}}{W_a}$$, {\dot{W}}_T={\dot{m}}_{25} \left(h_{25}-h_{26}\right)$	(48)	[36,37]
Evaporator E-103	${\dot{m}}_{13}\left(h_{13}-h_{14}\right)={\dot{m}}_{23}\left(h_{23}-h_{22}\right)$	(49)	[38]
Separator V-100	${\dot{m}}_{23}{x}_{23}={\dot{m}}_{24}{x}_{24}+{\dot{m}}_{25}{x}_{25}$	(50)	[32]
Pump P102	$w_{p,102}={\dot{m}}_{30}\left(h_{30}-h_{31}\right)$	(51)	[32]
Heat exchanger E-106	${\dot{m}}_{30}\left(h_{30}-h_{29}\right)={\dot{m}}_{32}\left(h_{32}-h_{33}\right)$	(52)	[32]
Heat exchanger E107	${\dot{m}}_{31}\left(h_{31}-h_{22}\right)={\dot{m}}_{27}\left(h_{27}-h_{24}\right)$	(53)	[32]

.

-

Kalina input energy:

$$\dot{Q}{ }_{in, KC}={\dot{m}}_{13}\left(h_{13}-h_{14}\right)$$

(54)

-

Net electric power of the Kalina cycle (KC):

$${\dot{W}}_{net, KC}={\dot{W}}_{ KC, Turbine}-{\dot{W}}_{ KC, Pump}$$

(55)

-

Energy efficiency of the KC:

$${\eta }_{en,KC}=\frac{{\dot{W}}_{net, KC}}{\dot{Q}{ }_{in, KC}}\times 100$$

(56)

-

Kalina input exergy:

$${\dot{Ex}}_{in, KC}={\dot{m}}_{13}\left[\left(h_{13}-h_{14}\right)-T_{14}\left(s_{13}-s_{14}\right)\right]$$

(57)

-

KC exergy efficiency:

$${\eta }_{ex,KC}=\frac{{\dot{W}}_{net, KC}}{ {\dot{Ex}}_{in, KC}}\times 100$$

(58)

3.5. The Steam Rankine Cycle and ORC Power Plant

3.5.1. The Steam Rankine Cycle (SRC)

The energetic balance equation applied for the turbines in the SRC is:

$${\dot{m}}_{wf,SRC}{h}_{17}={\dot{W}}_{SRC,T}+{\dot{m}}_{wf,SRC}{h}_{18}$$

(59)

The net power output of the SRC can be calculated as:

$${\dot{W}}_{net,SRC}={\dot{W}}_{SRC,Turbine}{\dot{-W}}_{P_{100}}$$

(60)

Its energy and exergy efficiencies are:

$${\eta }_{en,SRC}=\frac{{\dot{W}}_{elec,RT}}{{\dot{m}}_{12} \left(h_{12}-h_{13}\right)}$$

(61)

$${\eta }_{ex,SRC}=\frac{{\dot{W}}_{elec,RT}}{{\dot{m}}_{12} \left(e{x}_{12}-e{x}_{13}\right)}$$

(62)

3.5.2. The Organic Rankine Cycle (ORC)

The energy and exergy efficiencies of the ORC are given by:

$${\eta }_{en,ORC}=\frac{{\dot{W}}_{elec,ORC,Turbine}}{{\dot{m}}_{14} \left(h_{14}-h_{15}\right)}$$

(63)

$${\eta }_{ex,ORC}=\frac{{\dot{W}}_{elec,ORC,Turbine}}{{\dot{m}}_{14} \left(e{x}_{14}-e{x}_{15}\right)}$$

(64)

The exergy destruction rates of the main components are calculated as shown in

Table 4. Exergy destruction equations of the main components.

Components	Exergy Destruction Rate
SOFC	${\dot{Ex}}_{air}+{\dot{Ex}}_{ammonia}+{\dot{Ex}}_8-{\dot{Ex}}_6 – {\dot{W}}_s={\dot{Ex}}_{des}$	(65)
Afterburner	${\dot{Ex}}_7-{\dot{Ex}}_9={\dot{Ex}}_{des}$	(66)
Gas turbine	${\dot{Ex}}_9-{\dot{Ex}}_{10} – {\dot{W}}_{Gas turbine}={\dot{Ex}}_{des}$	(67)
Air heat exchange (Air Hex)	${\dot{Ex}}_1+{\dot{Ex}}_{10}-{\dot{Ex}}_2 – {\dot{E}}_{11}={\dot{Ex}}_{des}$	(68)
Fuel heat exchange (Fuel Hex)	${\dot{Ex}}_{ammonia from tank}+{\dot{Ex}}_{11}-{\dot{Ex}}_{12} – {\dot{E}}_3={\dot{Ex}}_{des}$	(69)
SRC regenerator (SRC Hex)	${\dot{Ex}}_{12}+{\dot{Ex}}_{16}-{\dot{Ex}}_{17} – {\dot{E}}_{13}={\dot{Ex}}_{des}$	(70)
SRC turbine	${\dot{Ex}}_{17}-{\dot{Ex}}_{18} – {\dot{W}}_{S\_Turbine}={\dot{Ex}}_{des}$	(71)
KC regenerator (KC Hex)	${\dot{Ex}}_{13}+{\dot{Ex}}_{22}-{\dot{Ex}}_{14} – {\dot{E}}_{23}={\dot{Ex}}_{des}$	(72)
KC turbine	${\dot{Ex}}_{25}-{\dot{Ex}}_{26} – {\dot{W}}_{K\_turbine}={\dot{Ex}}_{des}$	(73)
ORC regenerator (ORC Hex)	${\dot{Ex}}_{14}+{\dot{Ex}}_{34}-{\dot{Ex}}_{15} – {\dot{E}}_{35}={\dot{Ex}}_{des}$	(74)
ORC turbine	${\dot{Ex}}_{35}-{\dot{Ex}}_{36} – {\dot{W}}_{O\_Turbine}={\dot{Ex}}_{des}$	(75)

.

The overall energy and exergy efficiencies for the entire integrated system are expressed as follows [11,36]:

Energy efficiency:

$${\eta }_{en,overall}=\frac{{\dot{W}}_{elec,total} }{{\dot{m}}_{ammonia} LH{V}_{ammonia}}$$

(76)

In these expressions, ${\dot{W}}_{elec,total}$ denotes the net power production and consumption of the system:

$$\begin{gathered} {\dot{W}}_{elec,total}={\dot{W}}_{elec,SOFC}+{\dot{W}}_{Gasturbine}+{\dot{W}}_{SRC, turbine}+{\dot{W}}_{KC, turbine}+{\dot{W}}_{ORC,turbine} \\ -{\dot{W}}_{Air comp}-{\dot{W}}_{SRC, pump}-{\dot{W}}_{KC, pump}-{\dot{W}}_{ORC, pump} \end{gathered}$$

(77)

$LH{V}_{ammonia}$ represents the lower heating value of ammonia (kJ/kg).

Exergy efficiency:

$${\eta }_{ex,overall}=\frac{{\dot{W}}_{elec,total}}{{\dot{m}}_{ammonia} e{x}_{ammonia}}$$

(78)

4. Materials and Methods: Simulation and Assumptions

The proposed direct ammonia system for the SOFC–GT–SRC–KC-ORC integrated system was simulated using ASPEN-HYSYS, which offers a large database and powerful methods for calculating physical parameters [39,40]. The simulation used REFPROP of the Aspen Physical Property System [39]. The Peng–Robinson (PR) equation of states was selected for estimating the thermodynamic properties of the compositions of the stream and operating conditions of all components of the SOFC–GT–SRC–KC-ORC integrated system. The spreadsheet tool is employed to calculate cell voltage, fuel and air utilization factors and electrical aspects of the SOFC under the given current density value [41]. This is also used to run of process variables and post-processing calculated. The trial and error method is selected to evaluated and determined the average stack operating temperature of the SOFC. The internal reforming module is used to model the temperature profile of the fuel cells and the change of composition in the internal reforming process. These steps are repeated until the assumed average cell temperature and the calculated average cell temperature agree.

The following general assumptions were made to simplify the thermodynamic analysis of the system:

①

The ammonia entering the fuel gas supply system was at 29.85 °C and 400 kPa.

②

The pressure drop in all the pipe components was ignored.

③

The pressure drops on the tube side and shell side of the heat exchange were 34.47 and 6.895 kPa, respectively.

④

The system was in a steady state, and its heat loss was ignored.

⑤

The air is mainly composed of 79% N₂ and 21% O₂ at 29.85 °C and 100 kPa

⑥

The minimum temperature approach of the heat exchangers was 7 °C.

⑦

The reference state temperature and pressure of the system were 29.85 °C and 1.013 bar, respectively.

The simulation boundary conditions are presented in

Table 5. The design and operating parameters of system.

Component	Parameter	Value
SOFC	Ambient temperature (°C)	29.85
	Ambient pressure (bar)	1.013 bar
	Operating pressure (bar)	4
	Operating temperature (°C)	878.1
	Number of single cells	17,360
	Fuel cell current density (A/m2)	1430
	Active surface area (m2)	0.22
	Anode thickness (cm)	0.0020
	Cathode thickness (cm)	0.0020
	Electrolyte thickness (cm)	0.0040
	Stoichiometric rate of hydrogen	1.2
	Stoichiometric rate of oxygen	2
	Fuel utilization factor in SOFCs	85%
	Gas turbine cycle compression ratio	13
Compressor	Isentropic efficiency (%)	82
Pumps	Isentropic efficiency (%)	82
Expanders	Isentropic efficiency (%)	80
Heat exchangers	Minimum temperature approach (°C)	7
Converter	DC-AC converter efficiency (%)	98

[11,19].

5. Materials and Methods: Modeling Verification

The values calculated using the integrated model employing ammonia as fuel, which was proposed in this study, and the corresponding values listed in the literature are presented in

Table 6. Comparison of the simulation results of the proposed integrating model with the corresponding values obtained from the literature.

Parameter	Modelling	Reported [31]	Different (%)
SOFC temperature (°C)	857.8	870	1.06
Gas turbine inlet temperature (°C)	1192	1201	0.61
Cell voltage (V)	0.71	0.747	4.9
Current density (A/m2)	1430	1429	0.06
SOFC efficiency	56.8	50.96	5.84

. The estimated values are consistent with the data in the literature, and the discrepancy between the current data and the literature data is maintained within a tolerable range.

The proposed system has the potential to simultaneously supply power for the propulsion plant and other electric equipment, and provide hot water for the seafarers on board ships.

Since the subsystem is responsible for 26.59% of the total power production of the integrated system, its verification is critical. Unfortunately, there are no experimental installations of the SOFC–GT subsystem with direct ammonia injection accessible [9]; however, there are experimentally validated models in the literature. Chitgar et al. [32] reported a multigeneration system, SOFC–GT, that generated a total power of 4910.4 kW (0.07% difference) with energy and exergy efficiencies of 56.9% and 54.7%, respectively. The present model has relative errors of 3.5% and 2.6% for the SOFC–GT energy and exergy efficiencies, respectively. These error values demonstrate that the proposed model yields reasonable results.

6. Results and Discussion

6.1. Sequential Optimization

Sequential optimization involves optimizing the operating conditions of the SOFC–GT system first and then achieving SRC–KC–ORC power generation. The methods adopted for the SOFC system, SRC, KC, and ORC are REFPROP and the Peng–Robinson equation [30]. In the SOFC–GT system, streams 1–2, ammonia from tank 3, 16–17, 22–23 and 34–35 in E-100, E-101, E-102, E-103, E-104, E-105, and E-106 were selected to perform heat integration. The enthalpy values of the inlet and outlet streams were used to compute the heat load of the component. However, for the component stack of the SOFC system, the difference between the inlet and outlet enthalpies of the component is calculated as the sum of the electric power and heat released. Because the heat load of the component stack is small, the component stack is assumed to be ideal for simplifying the calculation, which only produces electricity without heat loss. The power calculations are shown in Equations (21)–(35), respectively: For an SOFC system that does not require thermal utilities, the process parameters of the SOFC system are optimized to maximize the stack power, as shown in

Table 7. Detailed operating conditions of the SOFC system under the conditions of maximum power.

Parameter	Value
E-100 inlet temperature (°C)	203.4
E-100 outlet temperature (°C)	492.6
E-101 inlet temperature (°C)	29.85
E-101 outlet temperature (°C)	492.6
Stack temperature (°C)	878.1
Afterburner temperature (°C)	1193

.

The SRC–KC–ORC was optimized under the optimal operating conditions of the SOFC system. During optimization, the hot/cold identity of streams 1–2 and ammonia from tank 3 in E-100 and E-101 were identified based on the heat load. In this sense, the corresponding constraints were calculated using ASPEN HYSYS V12.1. The temperature difference of the pinch points was assumed to be 5 °C. Meanwhile, the optimal solution can be obtained in a few loop iterations using a genetic algorithm. At this point, the SRC, KC, and ORC power generation reaches a stable level, and the optimal parameters are listed in

Table 8. Simulation results for SRC, RC and ORC.

Parameter	Value
SRC evaporating temperature (°C)	360.9
SRC evaporating pressure (kPa)	19,000
SRC power (kW)	175.8
KC evaporating temperature (°C)	175
KC evaporating pressure (kPa)	6493
KC power output (kW)	24.37
ORC evaporating temperature (°C)	223
ORC evaporating pressure (kPa)	12,500
ORC power output (kW)	71.23
Stack power (kW)	3800
Gas turbine power (kW)	1114
Total power output (kW)	5185.46

. The detail operational specification of each node is presented on

Table 9. Operational specification of each node of proposed system.

Node	Temperature	Pressure	Molar Flow	Mass Flow	Liquid Volume Flow
Unit	C	kPa	kgmole/h	kg/h	m3/h
Air in	29.85	101.30	213.38	6156.00	7.12
Ammonia from tank	29.85	400.00	90.90	1548.00	2.51
1	203.36	400.00	213.38	6156.00	7.12
2	492.60	396.55	213.38	6156.00	7.12
3	492.60	396.55	90.90	1548.00	2.51
4	152.64	396.55	119.41	1548.01	3.45
5	386.22	393.11	351.74	8109.49	11.16
6	857.78	393.11	379.09	8109.48	11.78
7	857.78	393.11	360.14	7704.01	11.19
8	857.78	393.11	18.95	405.47	0.59
9	1191.64	393.11	363.52	7703.99	11.13
10	880.03	95.00	363.52	7703.99	11.13
11	725.70	88.11	363.52	7703.99	11.13
12	576.81	81.21	363.52	7703.99	11.13
13	375.78	74.32	363.52	7703.99	11.13
14	311.07	67.42	363.52	7703.99	11.13
15	211.10	60.53	363.52	7703.99	11.13
16	72.12	19,000.00	56.62	1020.00	1.02
17	360.90	18,996.55	56.62	1020.00	1.02
18	74.69	38.00	56.62	1020.00	1.02
19	70.00	31.11	56.62	1020.00	1.02
20	20.00	100.00	444.07	8000.00	8.02
21	70.98	96.55	444.07	8000.00	8.02
22	71.00	6496.55	34.95	602.00	0.90
23	175.00	6493.11	34.95	602.00	0.90
24	175.00	6493.11	7.10	124.85	0.16
25	175.00	6493.11	27.84	477.15	0.74
26	108.66	1450.00	27.84	477.15	0.74
27	69.66	6486.21	7.10	124.85	0.16
28	70.59	1450.00	7.10	124.85	0.16
29	101.40	1450.00	34.95	602.00	0.90
30	47.31	1446.55	34.95	602.00	0.90
31	48.76	6500.00	34.95	602.00	0.90
32	20.00	201.33	288.65	5200.00	5.21
33	49.51	194.43	288.65	5200.00	5.21
34	39.59	12,500.00	42.39	2800.00	3.04
35	223.00	12,496.55	42.39	2800.00	3.04
36	76.48	700.00	42.39	2800.00	3.04
37	30.26	693.11	42.39	2800.00	3.04
38	18.00	201.33	832.63	15,000.00	15.03
39	32.28	197.88	832.63	15,000.00	15.03

.

Figure 3 shows that there is only one pinch point in the integrated system, which is approximately 5 °C. The exergy efficiency of the sequential optimization was calculated as follows:

$${\eta }_{system}=\frac{{\dot{W}}_{SOFC}+{\dot{W}}_{bottoming cycle}}{E{x}_{fuel}+E{x}_{air}}=60.04\%$$

(79)

According to the optimized component and stream parameters, the matching situations of the cold and hot streams in the SOFC–SRC–KC-ORC system can be obtained to minimize the number of heat exchangers. A process stream can be split into several branches while searching for heat exchange, and the number of branches corresponds to the number of process streams. The derived heat exchanger network is illustrated in Figure 4.

6.2. Energy and Exergy Efficiencies of the System

The vessels require 3800 kW of electric power and hot water for seafarers’ purposes. The utilization factor and energy efficiency of the SOFC were 0.85 and 56.8%, respectively. After applying the thermodynamic model introduced above to analyze the proposed integrated system, the output power of the integrated system was estimated as 5185.46 kW, which is sufficient to drive a vessel and provide additional power for other purposes. This comes from six different power components, including the SOFC fuel cells, gas turbine, and three turbines of the bottoming cycles. Out of this, 73.3% of the total power is produced by the SOFC while 26.7% is generated by the subsystems, which indicates that subsystems control the operation of the proposed system as anticipated. Considering the entire system in

Table 10. Energy and exergy efficiencies of the systems.

Subsystem	Energy Efficiency	Exergy Efficiency
SOFC–GT	61.4	58.2
SRC	25.6	40.4
KC	11.86	18.58
ORC	22.49	42.76
Total System	60.4	57.3

, the overall energy and exergy efficiencies were 60.4% and 57.3%, respectively.

It is interesting to note that the SRC subsystem is energetically more efficient than both the ORC and KC. Its energy and exergy efficiencies are 25.6% and 40.4%, respectively, which lies between those of ORC and KC, whose exergy efficiencies are 42.76% and 18.58%, respectively.

In Figure 5, the key components of the proposed system are examined in terms of exergy destruction rates associated with the thermal processes occurring within them. The two uppermost exergy destruction rates of 2102.79 and 938.18 kW correspond to the SOFC and afterburner, respectively. This high exergy destruction rate implies that the afterburner, rather than other equipment, has significant potential for improvement. The third one is three heat exchangers (heat exchanger E-100, E-101, and E-102) and gas turbine with values of 151.82, 132.83, 127.94 and 101.52 kW, respectively. The lowest exergy destruction corresponds to the turbine of the KC owing to higher entropy generation at lower temperatures with a constant heat transmission rate.

6.3. Parametric Study

The capital, installation and maintenance cost of the SOFC and other auxiliary equipment such as afterburner, gas turbine, heat exchangers, air compressors, equipment of SRC, ORC, KC are included in the economic analysis feasibility. In this case the net present value is calculated by:

$$NPV={{\displaystyle \sum }}_{k=0}^n\frac{R_k}{{(1+i)}^k}$$

(80)

where NPV denotes net present value and k is the investment period. For more comprehensive analysis, data for investment and payback cost are required.

A parametric investigation was conducted using the first and second laws of thermodynamics to evaluate the overall performance of the combined system. The parametric study examined the effect of modifying the current density cell stack of an SOFC on the overall energy and exergy efficiency of the system. In addition, the impact of working fluids on ORC performance was examined.

6.3.1. Effect of the Current Density

The current density is a key metric for the performance of the fuel cell and the entire system. The influence of the current density on the energy efficiency of the essential components of the system is depicted in Figure 6. Current densities ranging from 930 to 1830 A/m² are shown in this graph. The efficiency of the SOFC decreases as the current density increases because the SOFC cell voltage drops as the current density increases. In addition, the net power output of the SOFC increased with the current density. At 930 A/m², the maximum net electrical cycle efficiency was 66.4%, while the lowest was 46.4% at 1830 A/m². The energy efficiency of the SOFC–GT system also diminished from 71.55% to 50% with increasing current density. It is mainly because of an increase in the mass flow rate from 0.37 to 0.53 kg s⁻¹, and an increase in current density from 930 to 1830 A/m², to maintain the power output of the system at predetermined levels. Conversely, at a current density of 930 A/m², the highest heating cogeneration (integration of the SOFC with heating load) efficiency was 70.72%, and at a current density of 1830 A/m², the minimum was 47.52%. The lowest gain in efficiency of the trigeneration cycle when compared to the net electrical efficiency is likewise significant at 47.52%. It is also noteworthy that the energy efficiency of the subsystem appears to be unaffected by changes in the current density.

Figure 7 shows the influence of the current density on the exergy efficiency. The net electrical exergy efficiency was observed to decline with increasing current density owing to a decrease in cell voltage, decreasing the power produced by the SOFC. For the range of current densities investigated, the net electrical exergy efficiency decreased from 52.3% to 36.4%. The cooling cogeneration exergy efficiency is approximately 0.5% greater than the net electrical exergy efficiency, owing to the small cooling energy flows in the system relative to the electrical energy flows.

6.3.2. Effect of the Working Fluids in ORC

The quality of the working fluid affects the power output and cycle efficiency significantly. The candidate of working fluid is selected in consideration with aspects from environmental friendliness, safety, availability and suitable for working condition of marine vessels and working performance. According to the recommendation from the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) and related technical documents, the five working fluids, R134a, R600, R601, R152a, and R124, were chosen to improve the ORC cycle performance. The properties of proposed candidates working fluids are presented on

Table 11. Properties of working fluids [42,43,44,45,46].

Working Fluid	ODP	GWP	Molecular Mmass (g/mol)	Safety Class (ASHRAE 34)	Boiling Temperature [℃]	Critical	Critical
						Temperature [℃]	Pressure [kPa]
R134a	0	1320	102.03	A1	−26.1	101.1	4059
R124	0.02	609	136.48	A1	−11	122.4	3624
R152a	0	124	66.05	A2	−14	113	4517
R600	0	20	58.13	A3	−0.55	151.98	3796
R601	0	20	72.15	A3	36	187.55	3390

.

The impacts of the specified expander inlet temperature on the ORC performance were investigated to determine the net power, thermal efficiency, scroll expander rotational speed, and condenser load of the ORC system, as shown in Figure 8. After the heat exchange on E-103, the temperature of stream 18 is approximately 311.1 °C. Therefore, the maximum evaporation temperature of the working fluids in the ORC was set at 305 °C to recover the waste heat energy completely. The specified evaporating temperature of the ORC equals the expander inlet temperature when the expander inlet temperature lies between 150 and 305 °C, and the expander inlet condition is positioned at the saturated vaporization line of the working fluid.

As shown in Figure 8, the net power generation of the ORC increased from 11.72 kW to approximately 110.9 kW as the specified turbine inlet temperature increased from 110 to 290 °C, according to the results. The performance of the ORC systems using R600 and R601 changes slightly when superheated from 100 to 166 °C. Subsequently, they increase significantly with the temperature of the turbine inlet. When R152a is utilized as the ORC working fluid, the best performance of the system is 110.9 kW at 290 °C under the intended superheated inlet temperature. However, the LMTD of the heat exchanger E108 increases with the evaporator temperature and consequently, the contact areas of the heat exchanger become insufficient.

Figure 9 shows that for various working fluids, the average energy efficiency of the ORC system ranged from 11.85% to 25.29% when the superheated temperature of the working fluid increased. R152a and R601 exhibit the maximum and minimum energy efficiencies, respectively, across the entire spectrum of superheated temperatures because different working fluids have varying boiling points. Owing to the enthalpy change, it makes different exchangers duty after heat exchange E-108. Consequently, different operating fluids exhibit different exergy efficiencies.

As shown in Figure 10, the exergy efficiency tends to increase with the superheated temperature. R152a exhibited the highest energy efficiency among the five working fluids tested. Therefore, considering the effects of each working fluid on the performance of the system, R152a was selected for the ORC cycle.

Using R152a as the working fluid, a case study was performed by changing the turbine inlet pressure and superheated temperature to determine the optimal working parameters of the system.

Figure 11 shows the influence of turbine inlet pressure on the power generation of the turbine, energy efficiency, and exergy efficiency of the system. The pressure was changed from 4500 to 15,700 kPa, and the energy and exergy efficiencies first increased and stabilized at 13,500 kPa. The power output of the turbine first increased and then decreased when the pressure exceeded 10,900 kPa. This may be the effect of decreasing the enthalpy of the inlet stream turbine when the pressure increased.

Figure 12 shows the influence of the superheated temperature on the ORC system. The superheated temperature was changed from 110 to 305 °C as the inlet temperature of the turbine. The energy and exergy efficiencies increased from 15.9% to 22.72% when the temperature increased from 110 to 223 °C. After this temperature, the increase in the LMTD will result in smaller areas of the heat exchanger and inefficient heat exchange.

7. Conclusions

Ammonia is a promising candidate as a hydrogen carrier, especially in the maritime sector. An integrated SOFC–SRC–ORC–KC system that uses ammonia as fuel to produce electric power to the main propulsion plant and recover waste heat from SOFCs to generate more electricity for auxiliary machinery and accommodation purposes was proposed and investigated. The proposed multigeneration energy system aims to provide alternative environmentally clean options by utilizing sustainable and carbon-free fuels in power plants. Energy and exergy analyses were performed, and a comprehensive parametric study was conducted to assess the working performance and energy harvesting of the proposed system. R152a is selected as the most suitable working fluid for ORC through parametric study with the performance of five candidates. The following significant conclusions can be drawn from this study:

①

This study presented a novel SOFC–GT system integrated with SRC–KC–ORC. The overall energy and exergy of the integrated system can reach high values of 60.4% and 57.5%, respectively, which are comparatively higher than those of simple ammonia SOFC–GT powering systems. The SRC–KC–ORC generated and provided 1376.46 kW to the system, equivalent to 26.6% of the total power supply of the system. Hot water was also produced for the seafarers aboard ships.

②

The parametric studies demonstrated that increasing the current density from 930 to 1830 A/m² reduced the energy and exergy efficiencies of the SOFC–GT subsystem from 71.55% to 50% and 67.8% to 47.38%, respectively. This is mainly because of the effective decrease in cell voltage, and thus the efficiency of the fuel cell was reduced as well.

③

For the ORC system, a parametric study was conducted with five working fluids as candidates—R152a, R600, R601, R134a, and R124—and the efficiency of the system for each working fluid was estimated. R152a showed the highest energy and exergy efficiencies of 22.49% and 42.76%, respectively.

Those results suggest that direct ammonia fuel cells are promising in the further development of high-efficiency combined SOFC–GT–SRC–KC-ORC marine propulsion plants. Future studies on the assessment of the economic and stainability aspects of the system are to be performed to fully determine the applicability of the combined system. Since this integrated system is proposed for marine vessel applications, the dynamic behavior of the system should also be implemented in future studies.