Thermo-Economic Comparison between Three Different Electrolysis Technologies Powered by a Conventional Organic Rankine Cycle for the Green Hydrogen Production Onboard Liquefied Natural Gas Carriers

Abstract

The high demand for natural gas (NG) worldwide has led to an increase in the size of the LNG carrier fleet. However, the heat losses from this type of ship’s engines are not properly managed, nor is the excess boil-off gas (BOG) effectively utilised when generation exceeds the ship’s power demand, resulting in significant energy losses dissipated into the environment. This article suggests storing the lost energy into green H₂ for subsequent use. This work compares three different electrolysis technologies: solid oxide (SOEC), proton exchange membrane (PEME), and alkaline (AE). The energy required by the electrolysis processes is supplied by both the LNG’s excess BOG and engine waste heat through an organic Rankine cycle (ORC). The results show that the SOEC consumes (743.53 kW) less energy while producing more gH₂ (21.94 kg/h) compared to PEME (796.25 kW, 13.96 kg/h) and AE (797.69 kW, 10.74 kg/h). In addition, both the overall system and SOEC stack efficiencies are greater than those of PEME and AE, respectively. Although the investment cost required for AE (with and without H₂ compression consideration) is cheaper than SOEC and PEME in both scenarios, the cost of the H₂ produced by the SOEC is cheaper by more than 2 USD/kgH₂ compared to both other technologies.

1. Introduction

Liquefied natural gas (LNG) is one of the preferred options for ships in replacing conventional marine fuels, such as marine diesel oil (MDO) and heavy fuel oil (HFO), thanks to its environmentally friendly aspects [1,2]. Moreover, LNG carriers are a significant contributor to the maritime industry, transporting natural gas (NG) over the globe [3,4,5,6,7]. The propulsion systems of LNG carriers are classified according boil-off gas (BOG), which is mainly used for mechanical or electric propulsion [8,9], with two-stroke engines being the most popular thanks to their high efficiency compared to steam turbines and four stroke engines [10]. In order to comply with the International Maritime Organization (IMO)’s regulations and restrictions concerning the decarbonisation of the maritime sector, ship owners are required to adopt different measures related to the fuel used as well as the propulsion system, reducing the ships’ emissions while improving their efficiency and flexibility [5,8,11]. The BOG generated is generally consumed by the ship’s engine; however, in cases of low power demand and in order to maintain the stable pressure of the cargo tanks, excess BOG is either sent to a reliquefication plant or burned wastefully in a gas combustion unit (GCU) [1,3,8,12]. Although reliquefication plants are still adopted onboard LNG carriers, they present disadvantages, such as their expensive cost, onboard space requirements, and the intensive energy demand [1,8,13,14].

Fernández et al. [5] suggest employing excess BOG to produce hydrogen (H₂) fuel through a steam methane reforming plant (SMR), improving the LNG carrier’s efficiency, abandoning the GCU, and reducing emissions. SMR produces around three-quarters of the available H₂ thanks to both technological maturity and H₂ production costs. However, the drawbacks of this method cannot be overlooked as it relies on fossil fuel (NG), resulting in emissions, as well as onboard space limitations [1,5,15,16]. An eco-friendly alternative is to produce H₂ via electrolysis processes as oxygen (O₂) is the only by product of the water splitting reaction. Sebbahi et al. [17] presented a comparative analysis of alkaline electrolysis (AE), proton exchange membrane electrolysis (PEME), and solid oxide electrolysis (SOEC) for H₂ production using renewable sources. They concluded that although AE is the most mature electrolysis technology, it is still less efficient than PEME and SOEC, respectively. Nejadian et al. [18] conducted a comparative analysis together with techno-economic optimisation of AE, PEME, and SOEC integrated in a multi-generation energy system for power generation, water desalination, and H₂ production. They concluded that, thanks to the cooperation of both thermal and electric energy, SOEC shows a better performance in terms of H₂ production, as well as energy and exergy efficiencies, followed by PEME and AE, in this order. According to the results of the exergy–economic optimisation using Pareto frontier, the authors concluded that SOEC registers the highest system cost rate, while PEM registers the highest H₂ cost rate. Zaccara et al. [19] compared the H₂ production achieved through different renewable energy processes: PEME, SOEC, and biomass gasification, coupled with methanol and methane synthesis included in the steel industry. The results demonstrated that the H₂ produced through biomass is less pure than that produced through both PEME and SOEC, in addition to carbon dioxide (CO₂) production. SOEC consumes less water and energy compared to PEME and is more attractive if high temperatures and waste heat sources are available. Nasser and Hassan [20] compared two different systems that included SOEC and PEME powered by waste heat obtained via steam and organic Rankine cycles. They concluded that the steam Rankine cycle (SRC) shows a better performance than the organic Rankine cycle (ORC) and the SOEC is more efficient, operates more effectively, and has a lower H₂ production cost than PEME. Ferrero et al. [21] conducted a comparative analysis between high-temperature (SOEC) and low-temperature (PEME) electrolysis for H₂ production. They concluded that, at the same H₂ production rate and pressure, SOEC is more efficient and shows a better performance than PEME. Dere et al. [22] studied H₂ production onboard ships through PEME powered by the waste heat of the engine’s excess exhaust gases. The results of this study show that the fuel consumption is reduced by 0.5% and achieved a USD 42,740 annual saving thanks to waste heat recovery. Wang et al. [23] conducted a comprehensive thermodynamic analysis of an SOEC powered by a marine engine’s waste heat through an ORC for H₂ production and power load adjustment. The results show that the proposed system recovers 44.13% of the engine’s waste heat, producing 0.431 kg/s of H₂.

According to the aforementioned literature review, there exists no article that thermo-economically compares the three electrolysis technologies for maritime transport. Hence, the novelty of this article lies in the comparison of the H₂ production onboard LNG carriers through different electrolysis processes coupled separately with an ORC system recovering the waste heat (WH) from both the ship’s engine and the BOG excess. The H₂ produced is compressed for use when required.

The article is divided as follows: first, Section 2 compares the main characteristics of the three studied electrolysis processes, then Section 3 is dedicated to the overall systems description (ORC, electrolysis processes, H₂ compression plant). The electrochemical modelling of the different electrolysers’ stacks is presented in Section 4, while Section 5 outlines the economic analysis of the overall systems. Finally, the simulations results are presented in Section 6 for a better understanding and comparison of the overall H₂ production systems.

2. Comparison between the Different Electrolysis Technologies

Table 1. Comparison between the different electrolysis technologies [24,25,26,27,28,29,30,31].

		Low-Temperature Electrolysis		High-Temperature Electrolysis
		AE	PEME	SOEC
Semi-reactions	Anode	$2{\mathrm{O}\mathrm{H}}^{-}\to {\mathrm{H}}_2\mathrm{O}+{\displaystyle \frac{1}{2}}{\mathrm{O}}_2+2{\mathrm{e}}^{-}$	${\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{H}}^{+}+{\displaystyle \frac{1}{2}}{\mathrm{O}}_2+2{\mathrm{e}}^{-}$	${\mathrm{O}}^{2-}\to {\displaystyle \frac{1}{2}}{\mathrm{O}}_2+2{\mathrm{e}}^{-}$
	Cathode	$2{\mathrm{H}}_2\mathrm{O}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2+2{\mathrm{O}\mathrm{H}}^{-}$	$4{\mathrm{H}}^{+}+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2$	${\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{H}}^{+}+{\mathrm{O}}^{2-}$
Overall reaction		$2{\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{H}}_2+{\mathrm{O}}_2$	$2{\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{H}}_2+{\mathrm{O}}_2$	$2{\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{H}}_2+{\mathrm{O}}_2$
Electrolyte		Potassium hydroxide (KOH): 20–40 wt% [24,30]	Solid polymer electrolyte (Perfluoro sulfonic acid (PFSA)), usually Nafion®	Yttria stabilised zirconia (YSZ)
		Sodium hydroxide (NaOH): 20 wt% [24]
Anode electrode		Nickel coated perforated Ni-Co alloys Stainless steel Metal oxides	Platinum carbon RuO2, IrO2 Graphite-PTFE + Ti/RuO2, IrO2	Perovskites (LSCF, LSM) Ceramics (Mn, La, Cr) YSZ
Cathode electrode		Nickel coated perforated Ni-Mo alloys Ni-Co alloys Steel + Ni	Iridium oxide Pt, Pt-Pd Graphite + Pt/Pt	Ni/YSZ Zr + Ni/CeOx
Operating temperature (°C)		20–90	20–100	600–1200
Operating pressure (bar)		1–30	<70 [25,27,29]	1 [25,27,28,29]
			70 [28]	<20 [26]
			<200 [26,30]	1–5 [24]
			1–350 [24]	<25 [30]
Voltage range (V)		1.4–3	1.4–2.5	0.7–1.5
Current density (A/m2)		2000–8000	0–20,000	0–20,000
Cell area (m2)		1–3 [25]	<0.15 [25]	0.02 [25]
		<4 [26,30]	<0.13 [26]	<0.06 [26]
			<0.3 [30]	<0.01 [30]
Stack energy consumption (kWh/Nm3)		4.2–5.9	4.2–5.5	>3.2
System energy consumption (kWh/Nm3)		4.5–6.6 [26,30]	4.2–6.6 [26,30]	3.7–3.9 [26,30]
		5.55 [32]	5.4 [32]	3.8 [32]
Stack efficiency (%LHV)		50–78	50–83	80–100
System efficiency (%LHV)		51–60	46–60	76–81
Stack capital cost (USD/kW)	Minimum 1 MW	270	400	>2000
	Minimum 10 MW	500–1000	700–1400	Unknown
Maintenance cost (% of investment cost/year)		2–3 [33]	3–5 [33]	Unknown [33]
Stack lifetime (h)		60,000–120,000	20,000–100,000	8000–20,000
Maturity (Technology readiness level TRL)		Mature and commercial TRL 9	Commercial at small and medium scales TRL 8 expected to reach 9 by 2050	Development phase TRL 6 expected to reach 9 by 2050
Advantages		Cheap No need for noble metal electrocatalysts Long-term stability Reliable functioning	Space saving configuration High H2 purity Fast start-up Non-corrosive solid electrolyte High current densities High production rate	Cheap High efficiency No need for noble metal electrocatalysts High working temperature Low pressure Low energy consumption Non-corrosive solid electrolyte Low pure water requirement
Disadvantages		Low H2 purity Low current densities Slow start-up Corrosive High energy consumption	Expensive membrane and electrodes Acidic environment High pressure Ultra-pure feed water	Limited stability Small cell area Safety issues Limited application Under development

compares the main characteristics of the low- and high-temperature electrolysis technologies studied in this article, namely AE, PEME, and SOEC electrolysis. AE is a cheap technology operating at low pressures and temperatures; however, it is hindered using corrosive liquid electrolytes, has low current densities, and has a low H₂ purity requiring an additional H₂ purification stage [24,25,26]. Unlike AE, PEME is characterised by high current densities and a non-corrosive solid electrolyte. The main drawback of this technology is the need for ultra-pure feed water and expensive equipment such as the membrane and noble metal electrodes [24,25,26]. SOEC is a high-temperature electrolysis that is still under investigation; high efficiency and low energy consumption play in favour of this technology. The high temperature and thermal cycles of SOEC are limiting, respectively, its application and the materials’ lifetime [24,25,26].

3. Systems Description

This section describes the possible H₂ production chain (energy recovery, H₂ production and its compression) onboard LNG carriers. As depicted in Figure 1, an organic Rankine cycle is used to recover all the available onboard waste heat and deliver it to the electrolysis stack (AE, PEME, or SOEC) for the H₂ production. The H₂ produced is then compressed to be used as a clean fuel when needed.

3.1. Ship Model and Characteristics

The study adopts an LNG ship model propelled mechanically with two principal two-stroke engines and four auxiliary four-stroke dual fuel engines. The engines’ data are extracted from MAN-CEAS [35] and the project guide [36], respectively. The engine wastes heat through different stream sources, mainly from the jacket water (JW), scavenge air (SA), and exhaust gases (EG). For simplification and consistency in calculation, the data collected from the engines are correlated with the Engineering Equation Solver (EES), generating equations for the WH streams and the specific energy consumption as a function of the ship’s load (set to a value of 70% for the principal engines and 80% for the auxiliary engines). The main ship characteristics are summarized in

Table 2. Main characteristics of the model LNG carrier.

Ship’s Characteristic	Value
Total cargo capacity ($V_{tank}$)	1.7 × 105 m3
Propulsion system	Mechanical 2-stroke
Principal engine type	2 × MAN–5G70 ME-C10.5
Propulsion power (MCR)	2 × 12,835 kW (70.8 rpm)
Auxiliary engines type	2 × 6H35DF
	2 × 7H35DF
Auxiliary power (MCR)	2 × 2880 kW
	2 × 3360 kW
Auxiliary power demand	3448 kW
Total steam consumption	1999.2 kg/h
Boil-off rate ($BOR$)	0.10%
Freshwater generation (${\dot{m}}_{FWG}$)	20,000 kg/day

.

The heat needed ($Q_{FWG}$) to generate a given freshwater flow rate is calculated by Equation (1) with 15% of tolerance ($t_{FWG}$) [37]:

$$Q_{FWG}={\displaystyle \frac{{\dot{m}}_{FWG}}{0.03(1-t_{FWG})}}$$

(1)

The mass flow rate (${\dot{m}}_{BOG}$) of the BOG extracted from the LNG tanks is calculated by the following equations:

$${\dot{m}}_{BOG}={\dot{m}}_{{BOG}_N}-{\displaystyle \frac{{\rho }_{BOG}}{{\rho }_{LNG}}}({\dot{m}}_{LNG}+{\dot{m}}_{{BOG}_N})$$

(2)

$${\dot{m}}_{{BOG}_N}=BOR·V_{tank}·{\rho }_{LNG}$$

(3)

where ${\dot{m}}_{LNG}$ and ${\dot{m}}_{{BOG}_N}$ are the mass flow rate of the LNG extracted from the tanks and the natural BOG, respectively; ${\rho }_{BOG}$ and ${\rho }_{LNG}$ are the BOG and LNG densities; $V_{tank}$ is the total cargo capacity; and $BOR$ is the boil-off rate [38].

3.2. Waste Heat Recovery System (ORC)

Recovering the waste heat onboard ships is advantageous as it improves the ships’ energy efficiency and reduces the fuel consumption, which is turn results in lower emissions and reduced operating costs [39,40,41]. Among the different waste heat recovery (WHR) cycles, organic Rankine cycles (ORCs) are commonly studied in the literature and widely used for the WHR onboard marine vessels [39,40]. ORCs are an attractive system to recover the waste heat and convert it to a useful power [42,43,44]. They are characterised by their simplicity and the use of affordable and readily available components (similar to those in a refrigeration system), as well as their ability and flexibility to recover heat from both low- and medium-temperature sources, such as the scavenge air and jacket water [39,45,46]. Choosing the right ORC working fluid is tricky, as it involves considering several factors, including environmental impact, operating conditions (e.g., pressures and temperatures), and economic considerations [39]. This study adopts R245fa as the ORC’s working fluid (WF). Abdul Qyyum et al. [47] assessed various WFs and concluded that, among the 95 studied, R245fa is the most commonly used and optimal WF for ORC systems. In addition, despite the high global warming potential (GWP) of R245fa that reaches a value of 1030, it is a suitable WF for the WHR from marine engines [42,48,49], and it has many advantages such as the low pump power consumption, availability, nonflammability, high net power output, fire hazard reduction, and payback minimisation [42,47,50,51].

Table 3. Main characteristics of the working fluid R245fa [47,48,50,52].

Working Fluid Characteristic	Value
ASHRAE code	R245fa
Chemical name	Pentafluoro-propane
Chemical formula	CF3CH2CHF2
Type	Dry
ASHRAE safety group	B1
ODP	0
GWP	1030
Critical temperature (°C)	154
Critical pressure (bar)	36.5
Normal boiling point (°C)	15.14

summarised the key parameters of R245fa.

Figure 2 illustrates the ORC configuration adopted in this article. The organic fluid R245fa is pressurised (2) by the pump (P1), then preheated and vaporised through the different WHR streams (JW, SA, and EG) of the multi-streams heat exchanger (MSHEX). The resulting saturated vapor (3) is expanded in the turbine (T), producing mechanical power that is converted to electric energy through a generator (G). Hence, supplying the ship’s utility services with their power needs and providing the remaining energy to the electrolysis stacks. The remaining fluid (4) leaving the turbine is condensed back to a liquid state (1) and returned to the pump for a new cycle. The economiser (ECO) is used to preheat the steam required by the ship services, as well as for an additional water preheating process in the case of SOEC. Freshwater is secured onboard the ship through a freshwater generator (FWG) by using the available heat supplied by the JW.

The ORC energy efficiency (${\mathrm{ƞ}}_{ORC}$) as well as the available (${\mathrm{ƞ}}_{av, LHV}$) and recovered (${\mathrm{ƞ}}_{rec, LHV}$) system efficiencies are determined as follows:

$${\mathrm{ƞ}}_{ORC}={\displaystyle \frac{W_{Turb}-W_{Pump}}{Q_{WHR-in}}}$$

(4)

$${\mathrm{ƞ}}_{av, LHV}={\displaystyle \frac{{\dot{m}}_{H_2-prod}·{LHV}_{H_2}}{Q_{av}}}$$

(5)

$${\mathrm{ƞ}}_{rec, LHV}={\displaystyle \frac{{\dot{m}}_{H_2-prod}·{LHV}_{H_2}}{Q_{rec}}}$$

(6)

where $Q_{WHR-in}$ is the heat recovered from the engines WH streams, and $Q_{av}$ refers to all the available WH, while $Q_{rec}$ is only the WH recovered and used. $W_{Turb}$ and $W_{Pump}$ are the mechanical works of the ORC turbine and pump. ${\dot{m}}_{H_2-prod}$ is the mass flow rate of the H₂ produced, and ${LHV}_{H_2}$ is its lower heating value.

3.3. Hydrogen Production Systems

Although H₂ production through electrolysis contributes only 4% of the total worldwide production [53], it is considered the cleanest process since O₂ is the only by-product of the H₂O splitting reaction. In addition, H₂ production onboard ships through electrolysis is more advantageous than steam methane reforming (SMR) due to its ease of use and compactness. This subsection describes the different layouts of electrolysis technologies adopted in this article, namely AE, PEME, and SOEC.

3.3.1. AE Layout

The configuration of the AE adopted in this article is depicted in Figure 3. A molar fraction of 80% H₂O is mixed with 20% of an alkaline electrolyte (9), KOH in this study. The H₂O needed for the electrolysis process (10) is pumped (11) and mixed (13) with the O₂ derived from the anode electrode (12). The O₂ produced (14) and the H₂ gas leaving the cathode electrode (16) are separated from the electrolyte (22, 23) through separators (S1 and S2), respectively, at a pressure drop of 0.3 bar. The H₂ gas produced (18) is separated from the remaining H₂O (21) and undergoes further separation through (S4) to ensure its purity (19). The electrolyte residues (24) are pumped to the initial pressure (7 bar) and temperature (75 °C), then returned back to the stack (25).

3.3.2. PEME Layout

The PEME configuration, adopted from [19], is illustrated in Figure 4. H₂ and O₂ migrate the cathode (16) and anode (10) electrodes, respectively. Part of the H₂ produced gas (17) permeates through the membrane to the anode electrode (18), while part of the O₂ gas permeates to the cathode electrode (11). The permeation coefficient is calculated according to Equations (7) and (8). On one hand, the permeated O₂ is mixed (20) with the H₂ (19) derived from the cathode at 15 bar, cooled to 30 °C, then separated (22) from any H₂O residues (25). The H₂ gas is further purified (23) through S3. On the other hand, the permeated H₂ is mixed with O₂ (13) at 10% of the cathode pressure (1.5 bar), and the O₂ produced (15) is also separated from H₂O residues (27). The pressure of the remaining H₂O from O₂ (27) and H₂ (25) separation is reduced to atmospheric pressure, mixed with the recycled H₂O (29), and then returned back to the stack (31) at 15 bar and 30 °C.

$${H_2}_{perm}=\left(0.0009·e^{0.025·T}\right)·\Delta P·A_{cl}$$

(7)

$${O_2}_{perm}={\displaystyle \frac{{H_2}_{perm}}{2}}$$

(8)

3.3.3. SOEC Layout

Figure 5 illustrates the SOEC configuration used in this article. A molar fraction of 90% H₂O and 10% H₂ are mixed (14) in the SOEC stack. H₂ and O₂ ions migrate to the cathode (15) and anode (10) electrodes, respectively. In order to simplify the calculations, the O₂ sweep gas flow (9) is neglected in this study. On one hand, H₂ leaves the cathode at 800 °C and then exchanges heat gradually with H₂O through a series of heat exchangers (HE1, HE2, and HE3), decreasing its temperature to 30 °C (18). The H₂ is separated (19) and purified (20) from any residues. The remaining H₂O (23, 24) and H₂ (22) are recycled to be used in the H₂ cooling process (26, 30), along with the water makeup (25). The H₂ produced (21) is compressed for subsequent use as required. On the other hand, O₂ leaving the anode at 800 °C is separated (12) from any O₂ sweep gas (11), then cooled through (HE4) and released to the environment (13). The slightly heated H₂O (27) is reheated (28) by the steam coming from the ORC (33) and used for the O₂ cooling process in HE4. The resulting steam (29) is mixed with the recycled H₂ (22), reforming the initial composition (90% H₂O + 10% H₂), while the temperature is raised to 800 °C.

3.4. Hydrogen Compression System

Among the different possible H₂ storage methods, compressed H₂ is the most commonly used due to its simplicity and technological maturity [54,55]. Figure 6 illustrates the H₂ compression stages, the H₂ produced (37) through the different studied electrolysis processes (AE, PEME, or SOEC) is separated (38) from any possible remaining H₂O (49), then compressed through the compressors (C_i) at a constant pressure ratio, achieving a compression pressure of 150 bar. After each compression, the H₂ is cooled down to 30 °C through HE6, HE7, and HE8, then separated from H₂O residues. The compressed H₂ (47) undergoes another purification process (S9), ensuring the resulting H₂ is pure (48).

4. Electrochemical Modelling of the Electrolysis Stacks

Developing an electrochemical model of the electrolysis stacks is crucial for assessing the water splitting process. The stacks are modelled using Aspen Custom Modeler V12.1 (ACM), then exported to Aspen Hysys V12.1 for simulation with the rest of the systems’ components. An in-depth and comprehensive study of the electrochemical equations related to the different water electrolysis (AE, SOEC, and PEME) is already presented in the open literature. The following subsections will briefly state the necessary equations used in the electrochemical modelling according to each electrolysis stack type.

4.1. Standard Electrochemical Equations

Both heat and electricity sources are mandatory inputs to drive the splitting reactions in the different stacks [23,56]. The electric power input ($W_{el}$) is calculated as follows [18,57]:

$$W_{el}=V_{st}·I_{st}$$

(9)

$$V_{st}=V_{cl}·N_{cl}$$

(10)

$$I_{st}=J·A_{cl}$$

(11)

where $V_{st}$ and $V_{cl}$ are, respectively, the stack and cell voltages, $I_{st}$ is the stack current, J the current density, $A_{cl}$ the cell area, and $N_{cl}$ the stack number of cells.

The heat required/generated ($Q_{st}$) by the electrolysis stack is determined by Equation (12) [24,58], deciding if the electrolysis process operates in an endothermic ($Q_{st}<0$), exothermic ($Q_{st}>0$), or thermoneutral $(Q_{st}=0)$mode:

$$Q_{st}=I_{st}·N_{cl}·\left(V_{cl}-V_{th}\right)$$

(12)

$$V_{th}={\displaystyle \frac{\Delta H}{2F}}$$

(13)

where $V_{th}$ is the thermoneutral voltage, $\Delta H$ is the total energy consumption, and $F$ the Faraday constant.

The heat losses ($Q_{losses}$) are calculated in this study as 10% of the electrolysis thermal heat (Equation (14)), while the heat excess ($Q_{excess}$), if any, is determined by applying the global energy balance (Equation (15)):

$$Q_{losses}=10\%·\left|Q_{st}\right|$$

(14)

$$Q_{excess}=Q_{st}-Q_{losses}$$

(15)

The energy (${\mathrm{ƞ}}_{en-LHV})$ and exergy (${\eta }_{ex}$) efficiencies of the electrolysis stacks are assessed by Equations (16) and (17) as follows:

$${\mathrm{ƞ}}_{en-LHV}=100·{\displaystyle \frac{{\dot{m}}_{H_2-prod}·{\mathrm{L}\mathrm{H}\mathrm{V}}_{H_2}}{W_{el}+Q_{in-heat}}}$$

(16)

$${\eta }_{ex}={\displaystyle \frac{{\dot{n}}_{H_2-prod}·E_{H_2}}{E_{el}+E_{heat}}}$$

(17)

$$E_{el}=W_{el}$$

(18)

$$E_{heat}=Q_{in-heat}\left(1-{\displaystyle \frac{T_0}{T}}\right)$$

(19)

where $Q_{in-heat}$ is the sum of all heat inputs required by the electrolysis stack, ${\mathrm{L}\mathrm{H}\mathrm{V}}_{H_2}$ is the H₂ lower heating value, ${\dot{m}}_{H_2-prod}$ and ${\dot{n}}_{H_2-prod}$ are the mass and molar flow rates of the H₂ produced, respectively, $E_{H_2}$ is the H₂ standard chemical exergy, $E_{el}$ and $E_{heat}$ are the rate of the electric and thermal exergy inputs, $T$ is the stack temperature, and $T_0$ the reference environment temperature.

4.2. AE Stack Modelling

The electrochemical modelling of the AE stack is based on the equation used by [24,59,60]. In general, the cell voltage required for an electrolysis is the sum of the reversible voltage and the voltages generated by irreversible losses. Sánchez et al. [59] have developed comprehensive equations (Equations (20) and (22)) to calculate the cell ($V_{cl}$) and reversible ($V_{rev}$) voltages using empirical correlations as functions of the stack temperature ($T$) and pressure ($P$) as follows [60]:

$$V_{cl}=V_{rev}+\left(\left(r_1+d_1\right)+r_{2}T+d_{2}P\right)·J+s·log\left[\left(t_1+{\displaystyle \frac{t_2}{T}}+{\displaystyle \frac{t_3}{T^2}}\right)·J+1\right]$$

(20)

$$V_{rev}=V_{rev}^0+{\displaystyle \frac{RT}{zF}}ln{\displaystyle \frac{\left[H_2\right]{\left[O_2\right]}^{0.5}}{\left[H_{2}O\right]}}$$

(21)

$$V_{rev}=a_1-a_{2}T+a_{3}Tln(T)+a_4{T}^2+a_{5}Tln(P)+a_{6}P-a_7{\displaystyle \frac{P}{T}}-a_8{\displaystyle \frac{P^2}{T}}+a_9{\displaystyle \frac{P^2}{T^{3/2}}}+a_{10}{\displaystyle \frac{P^2}{T^2}}-a_{11}{\displaystyle \frac{P^2}{T^3}}$$

(22)

where r_i, d_i, t_i, a_i, and s are constant parameters obtained by [24] through experiment (

Table 4. Experimental parameters used for the calculation of the AE cell voltage [24,57,59].

Parameter	Value	Unit
Cell voltage
r1	4.45153 × 10−5	Ω m2
r2	6.88874 × 10−9	Ω m2/°C
t1	−0.01539	m2/A
t2	2.00181	m² °C/A
t3	15.24178	m² °C2/A
d1	−3.12996 × 10−6	Ω m2
d2	4.47137 × 10−7	Ω m2/bar
s	0.33824	V
Reversible voltage
a1	1.5184	V
a2	0.0015421	V/K
a3	0.00009523	V
a4	0.0000000984	V/K2
a5	0.000064629	V/K bar
a6	0.000021946	V/bar
a7	0.0055433	V·K/bar
a8	0.0000095196	V·K/bar2
a9	0.00013914	V·K3/2/bar2
a10	0.0026144	V·K2/bar2
a11	0.4953	V·K3/bar2

), and $J$ is the current density traversing the AE stack.

Faraday efficiency (${\eta }_{faraday}$) is calculated to measure the AE process effectiveness [57]. In general, ${\eta }_{faraday}$ is the ratio (Equation (23)) between the actual ${(\dot{m}}_{H_2-prod})$ and theoretical ${\dot{(m}}_{H_2-theor})$ H₂ production rate based on the consumed intensity. ${\eta }_{faraday}$ is also known as the “current efficiency” due the effect of the parasitic current losses throughout the gas conduits [61], these later are affected by the temperature while the pressure has a slight influence [57]; hence, for a given temperature, ${\eta }_{faraday}$ can be expressed by an empirical equation based on the four related parameters f_ij presented in

Table 5. Faraday and HTO diffusion experimental parameters used for AE stack modelling [24,57,59].

Parameter	Value	Unit
Faraday efficiency
f11	478,645.74	A2/m4
f12	−2953.15	A2/m4 °C
f21	1.03960	--
f22	−0.00104	°C−1
Hydrogen to oxygen diffusion
C1	0.09901	--
C2	−0.00207	°C−1
C3	1.31064 × 10−5	°C−2
C4	−0.08483	--
C5	0.00179	°C−1
C6	−1.13390 × 10−5	°C−2
C7	1481.45	A/m2
C8	−23.60345	A/m2 °C1
C9	−0.25774	A/m2 °C2
E1	3.71417	--
E2	−0.93063	Bar−1
E3	0.05817	Bar−2
E4	−3.72068	--
E5	0.93219	Bar−1
E6	−0.05826	Bar−2
E7	−18.38215	A/m2
E8	5.87316	A/m2 Bar
E9	−0.46425	A/m2 Bar2

(Equation (24)) [57,59,61]:

$${\eta }_{faraday}={\displaystyle \frac{{\dot{m}}_{H_2-prod}}{{\dot{m}}_{H_2-theor}}}$$

(23)

$${\eta }_{faraday}=100·\left({\displaystyle \frac{J^2}{f_{11}+f_{12}T+J^2}}\right)·\left(f_{21}+f_{22}T\right)$$

(24)

The molar flow rates of the H₂O consumed (${\dot{n}}_{H_{2}O-cons}$) during the AE process as well as the H₂ (${\dot{n}}_{H_2-prod}$) and O₂ (${\dot{n}}_{O_2-prod}$) produced are calculated by the following equations:

$${\dot{n}}_{H_2-prod}={\eta }_{faraday}·{\displaystyle \frac{J·A_{cl}·N_{cl}}{2F}}$$

(25)

$${\dot{n}}_{H_{2}O-cons}={\dot{n}}_{H_2-prod}$$

(26)

$${\dot{n}}_{O_2-prod}={\displaystyle \frac{{\dot{n}}_{H_2-prod}}{2}}$$

(27)

According to [24,57], during the AE process, part of the H₂ flow (${\dot{n}}_{HTO}$) is diffused into the O₂ channel (from cathode to anode) through AE diaphragms. The amount of ${\dot{n}}_{HTO}$ is expressed by Equation (28) using the hydrogen to oxygen (HTO) diffusion coefficient Equation (29). The counter-diffusion (oxygen to hydrogen (OTH)) is neglected due to the small amount (0.1 to 0.5%) of the O₂ is diffused to the H₂ channel [57]:

$${\dot{n}}_{HTO}={\displaystyle \frac{HTO·{\dot{n}}_{O_2-prod}}{1-HTO}}$$

(28)

$$\begin{gathered} HTO=\left(C_1+C_{2}T+C_3{T}^2\right)+\left(C_4+C_{5}T+C_6{T}^2\right) exp\left({\displaystyle \frac{C_7+C_{8}T+C_9{T}^2}{J}}\right)+\left(E_1+E_{2}P+E_3{P}^2\right) \\ +\left(E_4+E_{5}P+E_6{P}^2\right) exp\left({\displaystyle \frac{E_7+E_{8}P+E_9{P}^2}{J}}\right) \end{gathered}$$

(29)

where C_i and E_i are the gas purity parameters related to the temperature (T) and pressure (P), respectively, their values are summarised in Table 5.

The AE electrodes are submerged in a KOH electrolyte. Hence, the molar flow rates of H₂, O₂, H₂O, and KOH at the anode and cathode are calculated as follows:

Anode:

$${\dot{n}}_{H_2-an}={\dot{n}}_{HTO}$$

(30)

$${\dot{n}}_{O_2-an}={\dot{n}}_{O_2-prod}$$

(31)

$${\dot{n}}_{H_{2}O-an}={\displaystyle \frac{{\dot{n}}_{H_{2}O-in}-{\dot{n}}_{H_{2}O-cons}}{2}}$$

(32)

$${\dot{n}}_{KOH-an}={\displaystyle \frac{{\dot{n}}_{KOH-in}}{2}}$$

(33)

Cathode:

$${\dot{n}}_{H_2-cat}={\dot{n}}_{H_2-prod}$$

(34)

$${\dot{n}}_{O_2-cat}=0$$

(35)

$${\dot{n}}_{H_{2}O-cat}={\dot{n}}_{H_{2}O-an}$$

(36)

$${\dot{n}}_{KOH-cat}={\dot{n}}_{KOH-an}$$

(37)

${\dot{n}}_{KOH-in}$ and ${\dot{n}}_{H_{2}O-in}$ are known molar inlet flows of KOH and H₂O.

AE Stack Validation

In order to validate the AE stack modelling, the cell voltage–current density curve is compared with the curve obtained by Sánchez et al. [57] and the Aspentech modified modelling version [60] under the conditions presented in

Table 6. Input data for the AE simulation and validation [57,60].

Variable	Value	Unit
T	75	°C
P	7	Bar
Wel	10	kW
Ncl	12	--
Acl	0.1	m2
ṁin	900	Kg/h
Inlet composition (H2O–KOH)	35–65	% Mass fraction basis

. According to Figure 7, the curve displays a significant concordance with the existing findings.

4.3. PEME Stack Modelling

The PEME stack is modelled according to the equations used in research studies such as [62,63,64]. The cell voltage ($V_{cl}$) is the sum of the reversible voltage ($V_{rev}$) calculated by the Nernst equation, activation overpotentials (V_act) at both anode and cathode electrodes, and the ohmic overpotential of the electrolyte ($V_{ohm}$). The concentration overpotentials (V_conc) are negligible for high current densities not exceeding 10,000 A/m² [64].

$$V_{cl}=V_{rev}+V_{act}+V_{ohm}$$

(38)

$$V_{rev}=1.229-8.5\times {10}^{-4}\left(T-298\right)$$

(39)

$$V_{act}=V_{act,a}+V_{act,c}$$

(40)

$$V_{act,i}={\displaystyle \frac{RT}{F}}ln\left[{\displaystyle \frac{J}{2J_{0,i}}}+\sqrt{{\left({\displaystyle \frac{J}{2J_{0,i}}}\right)}^2+1}\right], (i=a,c)$$

(41)

$$J_{0,i}=J_{exp,i}exp\left({\displaystyle \frac{-E_{act,i}}{RT}}\right)$$

(42)

$$V_{ohm}=J{R}_{el}$$

(43)

$$R_{el}={\int }_0^L{\displaystyle \frac{dx}{\sigma \left[\lambda \left(x\right)\right]}}$$

(44)

$$\sigma \left[\lambda \left(x\right)\right]=\left[0.5139\lambda \left(x\right)-0.326\right]·exp\left[1268\left({\displaystyle \frac{1}{303}}-{\displaystyle \frac{1}{T}}\right)\right]$$

(45)

$$\lambda \left(x\right)={\displaystyle \frac{{\lambda }_a-{\lambda }_c}{L}}x+{\lambda }_c$$

(46)

where T(K) is the stack temperature, J_0,i is the exchange current density of anode (a) and cathode (c), J_exp,i is the pre-exponential factor, E_act,i is the activation energy, R_el is the overall ohmic resistance, L is the membrane thickness, σ[λ(x)] refers to the local ionic conductivity of the PEME, λ(x) is the water content at a location x in the membrane, and λ_a and λ_c are the water contents at anode and cathode membrane interfaces, while x is the distance calculated from the cathode–membrane interface. The parameters used in this study are summarised in

Table 7. Parameters adopted for the PEME stack electrochemical modelling [63].

Parameter	Value	Unit
J0,a	1 × 10−5	A/m2
J0,c	10	A/m2
Eact,a	76 × 103	J/mol
Eact,c	18 × 103	J/mol
L	50 × 10−6	m
λa	14	--
λc	10	--

.

The molar flow rates of the H₂O reacted in the electrolysis process (${\dot{n}}_{H_{2}O-react}$), the H₂ produced (${\dot{n}}_{H_2-prod}$), and the remaining H₂O (${\dot{n}}_{H_{2}O-out}$) are calculated by the following equations:

$${\dot{n}}_{H_{2}O-react}={\displaystyle \frac{I·N_{cl}}{2F}}$$

(47)

$${\dot{n}}_{H_2-prod}={\dot{n}}_{H_{2}O-react}$$

(48)

$${\dot{n}}_{H_{2}O-out}={\dot{n}}_{H_{2}O-in}-{\dot{n}}_{H_{2}O-react}$$

(49)

The molar flow rates of H₂, O₂ and H₂O at cathode and anode are calculated as stated below:

Anode:

$${\dot{n}}_{H_2-an}=0$$

(50)

$${\dot{n}}_{O_2-an}={\displaystyle \frac{{\dot{n}}_{H_2-prod}}{2}}$$

(51)

$${\dot{n}}_{H_{2}O-an}={\dot{n}}_{H_{2}O-in}-{\dot{n}}_{H_{2}O-react}$$

(52)

Cathode:

$${\dot{n}}_{H_2-cat}={\dot{n}}_{H_2-prod}$$

(53)

$${\dot{n}}_{O_2-cat}=0$$

(54)

$${\dot{n}}_{H_{2}O-an}=0$$

(55)

PEME Stack Validation

The cell voltage–current density curve of the PEME stack modelling is validated with the finding reported by Mohtaram et al. [65] using the data of Zaccara et al. [19] as outlined in

Table 8. Input data for the PEME simulation [19].

Variable	Value	Unit
T	90	°C
P	Cathode 15-Anode 1.5 (10%)	Bar
${\dot{\mathrm{n}}}_{{\mathrm{H}}_2\mathrm{O}-\mathrm{i}\mathrm{n}}$	352,080	kg/h
Acl	1 (*)	m2
Ncl	12 (*)	--
Wel	1,988,900	kW

^(*) Values estimated for modelling purpose.

. The curve results shown in Figure 8 are in good agreement with the findings of [65].

4.4. SOEC Stack Modelling

The required equations for the SOEC electrochemical modelling are extracted from research studies such as [18,23,56,66,67,68,69,70,71,72]. The cell voltage (V_cl) of the SOEC stack is calculated as the sum of the reversible voltage (V_rev), ohmic overpotential (V_ohm), activation overpotentials (V_act), and concentration overpotentials (V_conc) presented below:

$$V_{cl}=V_{rev}+V_{ohm}+V_{act}+V_{conc}$$

(56)

$$V_{rev}=V_0+{\displaystyle \frac{RT}{2F}}·\mathrm{l}\mathrm{n}\left({\displaystyle \frac{P_{H2}^0{·\left(P_{O2}^0\right)}^{1/2}}{P_{H2O}^0}}\right)$$

(57)

$$V_0=1.253-2.4516·{10}^{-4}T$$

(58)

$$P_{H_2}^0=y_{H_2}·P$$

(59)

$$P_{O_2}^0=y_{O_2}·P$$

(60)

$$P_{H_{2}O}^0=y_{H_{2}O}·P$$

(61)

$$V_{ohm}=2.99·{10}^{-5}·exp\left({\displaystyle \frac{10300}{T}}\right)·J·L$$

(62)

where $P_{H_{2}O}^0$, $P_{H_2}^0$, and $P_{O_2}^0$ are the partial pressures of H₂O, H₂, and O₂, respectively, while $y_{H_{2}O}$, $y_{H_2}$, and $y_{O_2}$ are the corresponding input molar fractions, V₀ the standard potential, L the electrolyte layer thickness (

Table 9. Parameters adopted for the SOEC stack electrochemical modelling [23,73].

Parameter	Value	Unit
L	12.5 × 10−6	m
da	17.5 × 10−6	m
dc	12.5 × 10−6	m
ε	0.48	--
ξ	5.4	--
rad	1.385 × 10−6	m
εH2O/k	809.1	K
εH2/k	59.7	K
σH2O	2.641	m
σH2	2.827	m
Jexp,a	2.051 × 109	A/m2
Jexp,c	1.344 × 1010	A/m2
Eact,a	1.2 × 105	J/mol
Eact,c	1 × 105	J/mol

), J the current density, and T(K) the stack temperature.

V_act is calculated in the same way as in the case of PEME with the parameters summarised in Table 9. (Check Equations (40)–(42))

$$V_{conc}=V_{conc,a}+V_{conc,c}$$

(63)

$$V_{conc,a}={\displaystyle \frac{RT}{4F}}·ln\left({\displaystyle \frac{\sqrt{{\left(P_{O_2}^0\right)}^2+\frac{R·T·J·\mu ·d_a}{2F{·B}_g}}}{P_{O2}^0}}\right)$$

(64)

$$V_{conc,c}={\displaystyle \frac{RT}{2F}}·ln\left({\displaystyle \frac{1+\frac{J·R·T·d_c}{2F·D_{H_{2}O}^{eff}·P_{H_2}^0}}{1-\frac{J·R·T{·d}_c}{2F·D_{H_{2}O}^{eff}{·P}_{H_{2}O}^0}}}\right)$$

(65)

where d_a and d_c are the anode and cathode thickness, respectively, µ is the dynamic viscosity (Equation (66)), B_g is the flow permeability (Equation (67)), and $D_{H_{2}O}^{eff}$ is the effective diffusion coefficient (Equation (68)). Note that $P_{H_{2}O}^0$, $P_{H_2}^0$, and $P_{O_2}^0$ are in Pascal.

$$\mu =-1.692+889.75\left({\displaystyle \frac{T}{1000}}\right)-892.79{\left({\displaystyle \frac{T}{1000}}\right)}^2+905.98{\left({\displaystyle \frac{T}{1000}}\right)}^3-598.36{\left({\displaystyle \frac{T}{1000}}\right)}^4+221.64{\left({\displaystyle \frac{T}{1000}}\right)}^5-34.75{\left({\displaystyle \frac{T}{1000}}\right)}^6$$

(66)

$$B_g={\displaystyle \frac{{\epsilon }^3}{72\xi {\left(1-\epsilon \right)}^2}}{\left(2rad\right)}^2$$

(67)

$${\displaystyle \frac{1}{D_{H_{2}O}^{eff}}}={\displaystyle \frac{\xi }{\epsilon }}·\left({\displaystyle \frac{1}{D_{H_2-H_{2}O}}}+{\displaystyle \frac{1}{D_{H_{2}O-K}}}\right)$$

(68)

where rad is the average pore radius, while ε and ξ are the electrode porosity and tortuosity, respectively, and their values are presented in Table 9. The Knudsen ($D_{H_{2}O-K}$) and the molecular ($D_{H_2-H_{2}O}$) diffusions are calculated as follows:

$$D_{H_{2}O-K}={\displaystyle \frac{2}{3}}rad\sqrt{{\displaystyle \frac{8R·T}{\pi {·M}_{H_{2}O}}}}$$

(69)

$$D_{H_2-H_{2}O}=0.00133{\left({\displaystyle \frac{1}{M_{H_2}}}+{\displaystyle \frac{1}{M_{H_{2}O}}}\right)}^{{\displaystyle \frac{1}{2}}}{\displaystyle \frac{T^{\frac{3}{2}}}{P·{{(\sigma }_{H_2-H_{2}O})}^2{·\Omega }_D}}$$

(70)

$${\Omega }_D={\displaystyle \frac{1.06036}{{T^{\ast }}^{0.1561}}}+{\displaystyle \frac{0.193}{\mathrm{e}\mathrm{x}\mathrm{p}\left(0.47635T^{\ast }\right)}}+{\displaystyle \frac{1.03587}{{\mathrm{e}\mathrm{x}\mathrm{p}(1.52996T}^{\ast })}}+{\displaystyle \frac{1.76474}{{\mathrm{e}\mathrm{x}\mathrm{p}(3.89411T}^{\ast })}}$$

(71)

$$T^{\ast }={\displaystyle \frac{T}{\frac{{\epsilon }_{H_2-H_{2}O}}{k}}}$$

(72)

$${\displaystyle \frac{{\epsilon }_{H_2-H_{2}O}}{k}}=\sqrt{{\displaystyle \frac{{\epsilon }_{H_2}}{k}}{\displaystyle \frac{{\epsilon }_{H_{2}O}}{k}}}$$

(73)

$${\sigma }_{H_2-H_{2}O}={\displaystyle \frac{{\sigma }_{H_2}+{\sigma }_{H_{2}O}}{2}}$$

(74)

M_j is the molecular mass of species j (j = H₂, O₂, H₂O), Ω_D is the dimensionless diffusion collision integral, and σ_H2O and σ_H2 the collision diameters of steam and H₂, while ε_H2O/k and ε_H2/k are the Lennard-Jones potentials. T* is the dimensionless temperature.

The molar flow rates of the H₂O reacted during the electrolysis process and the H₂ and O₂ produced are calculated by the following equations:

$${\dot{n}}_{H_{2}O-react}={\displaystyle \frac{I·N_{cl}}{2F}}$$

(75)

$${\dot{n}}_{H_2-prod}={\dot{n}}_{H_{2}O-react}$$

(76)

$${\dot{n}}_{O_2-prod}={\displaystyle \frac{{\dot{n}}_{H_2-prod}}{2}}$$

(77)

On the other hand, the molar flow rates of H₂, O₂, and H₂O at the anode and cathode electrodes are determined as follows:

Anode:

$${\dot{n}}_{H_2-an}=0$$

(78)

$${\dot{n}}_{O_2-an}={\dot{n}}_{O_2-prod}$$

(79)

$${\dot{n}}_{H_{2}O-an}=0$$

(80)

Cathode:

$${\dot{n}}_{H_2-cat}={\dot{n}}_{H_2-prod}$$

(81)

$${\dot{n}}_{O_2-cat}=0$$

(82)

$${\dot{n}}_{H_{2}O-an}={\dot{n}}_{H_{2}O-in}-{\dot{n}}_{H_{2}O-react}$$

(83)

SOEC Stack Validation

The cell voltage–current density curve of the SOEC stack modelling is validated with the findings of [66] using the input data of [23] (

Table 10. Input data for the SOEC simulation [23].

Variable	Value	Unit
T	850	°C
P	1.01325	bar
ṁin	36,000	kg/h
J	8000	A/m2
Acl	0.04	m2
Ncl	130,000	--
Inlet composition (H2O–H2)	80–20	% Molar fraction basis

). The cell voltage–current density curve depicted in Figure 9 shows a good agreement with the findings of [66].

5. Economic Analysis

The equipment cost of the three H₂ production overall systems is determined by the Aspen Process Economic Analyzer V12.1 (APEA). However, the electrolysers’ cost functions are calculated separately by using the following equations [18,74]:

$$Z_{SOEC}=2285 (\mathrm{U}\mathrm{S}\mathrm{D}/\mathrm{k}\mathrm{W})·W_{el.SOEC}$$

(84)

$$Z_{PEME}=2068 (\mathrm{U}\mathrm{S}\mathrm{D}/\mathrm{k}\mathrm{W})·W_{el.PEME}$$

(85)

$$Z_{AE}=1268 (\mathrm{U}\mathrm{S}\mathrm{D}/\mathrm{k}\mathrm{W})·W_{el.AE}$$

(86)

Note that the electrolysers’ cost functions are calculated for the year 2020, while the equipment cost is given for the year 2019. For accurate and significant results, the total equipment costs as well as the electrolysers’ cost are updated to the same year (2022 in this study), using the chemical plant cost index (CEPCI) as shown in the following equation:

$$Z_{2022}={\displaystyle \frac{{CEPCI}_{2022}}{{CEPCI}_{equipment year}}}·Z_{equipment year}$$

(87)

The cost of the H₂ produced by each overall system is determined through the calculation of the levelised cost of H₂ (LCOH) as follows [66]:

$$LCOH={\displaystyle \frac{{\dot{Z}}_{capital cost}+{\dot{Z}}_{O\&M}+{\dot{Z}}_{electricity}+{\dot{Z}}_{fuel}}{{{\dot{m}}_{H_2}}_{pr}}}$$

(88)

$${\dot{Z}}_{capital cost}={\displaystyle \frac{Z_{total}·CRF}{T_{W.hr}}}$$

(89)

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

(90)

$${\dot{Z}}_{O\&M}=\alpha ·Z_{total}$$

(91)

where ${\dot{Z}}_{capital cost}$ is the investment cost rate, ${\dot{Z}}_{O\&M}$ is the operating and maintenance annual cost, and ${\dot{Z}}_{electricity}$ and ${\dot{Z}}_{fuel}$ are the electricity and fuel costs which are excluded from consideration in this study since all the energy used is that recovered from the WH without any additional energy. $Z_{total}$ is the total equipment cost, CRF refers to the capital recovery factor, and $T_{W.hr}$ is the uptime per year, while i, N, and α are the interest rate, the plant lifetime, and the operating and maintenance factor, respectively. The parameters adopted in this study are summarised in the following

Table 11. Parameters adopted for the economic analysis [75,76,77].

Parameter	Value
${\mathrm{T}}_{\mathrm{W}.\mathrm{h}\mathrm{r}}$	8000 h
i	10%
N	20 years
α	3%
CEPCI2019	607.5
CEPCI2020	596.2
CEPCI2022	816

:

6. Results and Discussion

This section is dedicated to compare the three studied electrolysis in this article (AE, PEME, and SOEC). First, the electrolysis stacks are compared, separately, between each other in Section 6.1, then an overall comparison of the onboard H₂ production system is discussed in Section 6.2. Finally, Section 6.3 presents an economic analysis of the overall systems.

6.1. Electrolysis Stacks’ Comparison

The AE, PEME, and SOEC stacks are compared in this subsection using the same possible input data. The results summarised in

Table 12. Results comparison between the AE, PEME, and SOEC stacks.

Variable	Unit	AE	PEME	SOEC
T	°C	80	80	800
P	bar	1.01325	1.01325	1.01325
ṁin	kg/h	36,000	36,000	36,000
Inlet composition (molar fraction basis)	%	90% H2O + 10% KOH	100% H2O	90% H2O + 10% H2
J	A/m2	5000	5000	5000
Acl	m2	0.04	0.04	0.04
Ncl	--	500	500	500
ṁH2-prod	kg/h	3.562	3.760	3.761
ṁO2-prod	kg/h	28.273	29.844	29.848
Wel	kW	199.97	200.46	98.93
Vcl	V	2.000	2.005	0.989
ηEN-LHV	%	59.38	62.52	97.44
ηEX	%	58.54	61.64	96.76

as well as in Figure 10 and Figure 11 demonstrate the following:

• SOEC (3.761 kg/h) and PEME (3.760 kg/h) stacks produce more H₂ than the AE (3.652 kg/h) stack for the same current density J;
• There is a slight difference between PEME and SOEC H₂ production; however, PEME as well as AE consume more than double the energy (Wel) of SOEC;
• The cell voltage required for the SOEC process is lower than for PEME and AE,
• SOEC stack is more efficient than PEME and AE, respectively.

6.2. Overall Systems’ Comparison

After comparing the different electrolysis stacks separately, this section compares the overall H₂ production systems from energy harvesting to the H₂ compression stage. The thermodynamic properties of the different systems are presented in the Supplementary Materials, while

Table 13. WHR parameters at 70% of the engine’s load.

Variable	Unit	JW	SA	EG
Temperature	°C	90.0	153.3	196.1
Pressure	bar	1.01325	1.01325	1.01325
Mass flow	kg/h	144,842	140,422	142,579
Heat flow	kW	1856	4780	3237

outlines the input parameters of the WHR sources as a function of the engine’s load which is set at a fixed value of 70%.

The input data together with the simulation results of the different H₂ production chain systems are summarised in

Table 14. Comparison results of the overall H₂ production system.

Variable	Unit	AE	PEME	SOEC
Temperature	°C	80	80	800
Pressure	bar	7	15	1.01325
Inlet composition (molar fraction basis)	%	90% H2O + 10% KOH	100% H2O	90% H2O + 10% H2
$A_{cl}$	m2	0.04	0.04	0.04
$N_{cl}$	--	500	500	500
PORC	kW	921.4	921.4	940
$Q_{av}$	kW	9873	9873	9873
$Q_{rec}$	kW	6882	6882	6910
$W_{el}$	kW	796.25	797.69	743.53
J	A/m2	14,942	18,557.7	29,174.9
$V_{cl}$	V	2.664	2.149	1.274
ṁin	kg/h	143.5	138.6	248.2
${\dot{n}}_{H_2-prod}$	kg/h	10.74	13.96	21.94
${\dot{n}}_{O_2-prod}$	kg/h	85.22	110.78	174.161
${\mathrm{ƞ}}_{en-LHV}$	%	44.95	58.33	64.34
ηORC-av	%	8.80	8.80	8.96
ηORC-rec	%	12.62	12.62	12.80
${\mathrm{ƞ}}_{av, LHV}$	%	3.63	4.71	7.41
${\mathrm{ƞ}}_{rec, LHV}$	%	5.20	6.76	10.59

. The results demonstrate that SOEC consumes less energy (743.53 kW) than both PEME (797.69 kW) and AE (796.25 kW) while producing more H₂ (21.94 kg/h) compared to 13.96 kg/h by PEME and 10.74 kg/h by AE. The difference in the power output between the ORC coupled with SOEC and the ORC coupled with PEME or AE is attributed to the slightly elevated temperature of the EG. This increase in temperature results from the additional heating process of the water needed by SOEC to reach the high operating temperature (800 °C).

Considering only the recovered WH, the overall system efficiency employing SOEC electrolysis is 10.59% with a stack efficiency of 64.34%_LHV and an ORC efficiency of 12.80%, exceeding those of PEME and AE. The PEME and AE overall system efficiencies are 6.76% and 5.20%, respectively, while the stacks’ efficiencies register 58.33%_LHV and 44.95%_LHV. The ORC efficiency is 12.62% for both PEME and AE. Whether considering all the available onboard WH or solely the recovered one, the SOEC system outperforms both PEME and AE in terms of energy efficiencies, particularly the overall system efficiency, which is almost double, as well as H₂ production thanks to the high operating temperatures.

6.3. Economic Analysis of the Overall H₂ Production Systems

This subsection economically compares the overall systems using SOEC, PEME, or AE as the H₂ production process in order to decide the most viable technology to be adopted onboard maritime vessels.

Table 15. Equipment costs of SOEC with and without compression plant (2022).

Equipment		SC-1	SC-2
Compressors	C1	1,329,000
	C2	1,375,100
	C3	1,434,500
Condenser	COND	538,100	538,100
SOEC heat exchangers	HE1	51,900	51,900
	HE2	7800	7800
	HE3	15,400	15,400
	HE4	18,900	18,900
	HE5	11,000	11,000
	HE6	17,300	17,300
H2 compression coolers	HE7	20,700
	HE8	17,200
	HE9	18,300
Multi-streams heat exchanger	MSHEX	381,900	381,900
ORC pump	P1	33,800	33,800
ORC turbine	T	487,700	487,700
Ztotal (USD)		5,758,600	1,563,800

,

Table 16. Equipment costs of PEME with and without a compression plant (2022).

Equipment		SC-1	SC-2
Compressors	C1	1,232,100
	C2	1,266,300
	C3	1,289,700
Condenser	COND	546,900	546,900
PEME heat exchanger	HE1	14,300	14,300
H2 compression coolers	HE7	14,300
	HE8	15,000
	HE9	16,100
Multi-streams heat exchanger	MSHEX	548,600	548,600
ORC pump	P1	33,800	33,800
PEME pump	P2	17,000	17,000
Turbine	T	479,900	479,900
Ztotal (USD)		5,474,000	1,640,500

and

Table 17. Equipment costs of AE with and without a compression plant (2022).

Equipment		SC-1	SC-2
Compressors	C1	1,232,300
	C2	1,258,700
	C3	1,289,700
Condenser	COND	546,900	546,900
AE heat exchanger	HE1	13,300	13,300
H2 compression coolers	HE7	15,000
	HE8	14,700
	HE9	15,200
Multi-streams heat exchanger	MSHEX	548,600	548,600
ORC pump	P1	33,800	33,800
AE pump	P3	4400	4400
	P4	4900	4900
Turbine	T	479,900	479,900
Ztotal (USD)		5,457,400	1,631,800

summarise the equipment’ cost functions of the three studied systems: SOEC, PEME, and AE, respectively, considering two different scenarios: (with (SC-1) or without (SC-2) a H₂ compression plant. As mentioned before, the cost function of the electrolysers is calculated separately, the results are shown in

Table 18. Electrolysers’ cost (2020).

Electrolyser Type	Power (kW)	Cost (USD)
SOEC	743.53	1,698,975
PEME	797.69	1,649,620
AE	796.25	100,964

.

Both the total equipment cost and the electrolysers’ costs are updated to the same year (2022 in this study) by using the aforementioned Equation (87) for an accurate and precise comparison. As illustrated in Figure 12, excluding the H₂ compression plant (SC-2) reduces the total investment cost by more than half for all of the three overall systems studied. Including the H₂ compression system (SC-1) makes SOEC increase the plant investment cost by half a million compared to the PEME system, while excluding the compression plant plays in favour of SOEC by reducing its cost by almost USD 36,000. This is mainly due to the compressors’ costs affected by the H₂ produced and the slight difference between the SOEC and PEME electrolyser’s costs. AE is the cheapest system.

According to the results illustrated in Figure 13, the H₂ production cost including an AE electrolysis system is higher than PEME and SOEC, in this order, in both scenarios. In addition, in the case of SC-1, the H₂ production cost by the SOEC system is cheaper than AE and PEME systems by more than 6 USD/kg_H2 and 4 USD/kg_H2, respectively. In the case of SC-2, there is a small difference between the LCOH registered by AE and PEME systems (0.24 USD/kg_H2), while SOEC is cheaper by more than 2 USD/kg_H2 compared to both systems. This is due to the higher H₂ production by SOEC.

7. Conclusions

The article investigates the H₂ production on board LNG carriers through three different electrolysis processes: AE, PEME, and SOEC. A comparison between the three electrolysers helps in ascertaining the most suitable and efficient technology for the onboard H₂ production. The required energy by the electrolysis stacks to drive the water splitting reactions is secured by the total WH energy of the LNG carrier’s propulsion system through an ORC.

The electrolysis stacks are modelled through ACM V12.1 then exported to Aspen Hysys V12.1 for simulation with the rest of the plant component system. Aspen EDR V12.1 is used for the heat exchangers’ design, while APEA is used for the economic analysis. According to the results, the main conclusions are as follows:

• SOEC consumes less energy (743.53 kW) than PEME (796.25 kW) and AE (797.69 kW), respectively, while producing more H₂, 21.94 kg/h compared to 13.96 kg/h by the PEME and 10.74 kg/h by the AE;
• The SOEC system electrolyser’s efficiency (64.34%_LHV), ORC efficiency (12.8%), and overall system efficiency (10.59%) are all higher than those of PEME registering 58.33% for the electrolyser, 12.62% for the ORC, and 6.76% for the overall system; while AE registers 44.95% for the electrolyser, 12.62% for the ORC same as the PEME, and 5.2% for the overall system;
• Although the total investment cost of the plant including the SOEC system is higher than both PEME and AE, the LCOH of the overall SOEC system is lower by almost double in cost compared to PEME and AE.

To conclude, H₂ fuel is a promising alternative to fossil fuels in reducing emissions and aiming towards the decarbonisation of maritime transport. Among the three studied electrolysis systems, SOEC proves to be more advantageous than both PEME and AE for the onboard H₂ production as it consumes less energy while producing almost double the mass flow of H₂ per hr at a lower cost and being more efficient.