Parameter Analysis of Anion Exchange Membrane Water Electrolysis System by Numerical Simulation

Abstract

Anion exchange membrane electrolysis, which combines the advantages of both alkaline electrolysis and proton-exchange membrane electrolysis, is a promising technology to reduce the cost of hydrogen production. The present work focused on the study of the electrochemical phenomena of AEM electrolysis and the investigation of the key factors of the AEM hydrogen production system. The numerical model is established according to electrochemical reactions, polarization phenomena, and the power consumption of the balance of plant components of the system. The effects of operation parameters, including the temperature and hydrogen pressure of the electrolyzer, electrolyte concentration, and hydrogen supply pressure on the energy efficiency are studied. The basic electrochemical phenomena of AEM water electrolysis cells are analyzed by simulations of reversible potential and activation, and ohmic and concentration polarizations. The results reveal that increasing the operating temperature and hydrogen production pressure of the AEM electrolyzer has positive effects on the system’s efficiency. By conducting an optimization analysis of the electrolyzer temperature—which uses the heat energy generated by the electrochemical reaction of the electrolyzer to minimize the power consumption of the electrolyte pump and heater—the AEM system with an electrolyzer operating at 328 K and 30 bar can deliver hydrogen of pressure up to 200 bar under an energy efficiency of 56.4%.

1. Introduction

Anion exchange membrane (AEM) electrolysis is a promising low-temperature electrolysis technology that has attracted much research attention in recent years. This technology combines the advantages of alkaline electrolysis (AE) and proton-exchange membrane (PEM) electrolysis, utilizing an anion exchange membrane as a separator to provide an alkaline environment for electrolysis. Additionally, the composition of the AEM water electrolyzer includes cost-effective catalysts and solid-state electrolytic components, enabling AEM water electrolysis to address the shortcomings of AE electrolysis by stably producing hydrogen at high current densities [1,2]. However, research on AEM water electrolysis technology worldwide remains focused on the development of materials and components, further efforts are needed from research teams to advance system-level and commercial technologies.

As noted earlier, the core technologies of AEM water electrolysis modules are the catalysts and the design of the membrane electrode assemblies (MEAs), which have a Technology Readiness Level (TRL) of about 2–3 [3]. This is because the electrode materials of the electrolyzer must operate in an alkaline environment and require effective conductivity testing. Numerous studies have pointed out that the technical challenges of AEM water electrolysis are primarily related to the direct transfer in the triple phase boundaries and the impact of the internal electrolyzer’s design on electrolysis activity and stability [4,5]. Consequently, recent research on AEM water electrolysis has primarily focused on the development of materials and the design of the electrode plates.

However, establishing a high-efficiency water electrolysis system is necessary for industry applications. Ju et al. [6] constructed a laboratory-scale testing system to study the performance of an AEM water electrolyzer under a high pressure of 30 bar and at 80 °C, with a reaction area of up to 19.6 cm². Furthermore, according to the study by F. Moradi Nafchi et al. [7], changes in cathode pressure impact the molar concentration of hydrogen production, influencing hydrogen diffusion within the flow channel and subsequently affecting the charge transfer process within the cell. This, in turn, impacts the performance of water electrolysis. Niyati et al. [8] showed that the Ni-based catalyst of AEM water electrolysis is affected by concentration and temperature, indicating that changes in concentration and temperature would influence the catalyst, thereby affecting the electrolyzer’s performance. Based on the results of Yang et al. [9], it can be observed that using MATLAB/Simulink 2020a enables effective system-level thermo-fluid analysis of AE systems. Nafchi et al. [7] showed that using solar energy to produce hydrogen and mixing it into natural gas pipelines is a cost-effective alternative. The AEM water electrolysis system is particularly suitable for hydrogen production systems powered by intermittent energy sources. Additionally, their research demonstrated that using a high-pressure AEM water electrolyzer and removing compressors to produce hydrogen under high pressure reduces the energy cost of high-pressure hydrogen by 29.3% [10].

Gul et al. [11] combined an AEM water electrolysis system with a solar power generation system to provide low-cost hydrogen. The study indicated that through this process, the AEM water electrolyzer could produce 15,025 MWh/year of energy at the lowest levelized cost of energy of about 0.084 EUR/kWh. Nowadays, Enapter—the electrolyzer manufacturing company—has successfully integrated AEM water electrolyzers into a more mature PEM electrolysis system, resulting in the development of a commercially available small-scale water electrolysis system [12]. The AEM water electrolysis system currently built by the company can produce 300–500 L of hydrogen per hour at an operating pressure of 3 MPa.

It is evident that research on AEM water electrolysis systems remains relatively scarce. Although some industries have begun small-scale commercial production, aspects such as material performance, system stability, and scale-up technology still require further development. Consequently, the integration performance and efficiency of water electrolysis systems have become the primary focus. According to the performance analysis of AEM water electrolysis cells by Xu et al. [13], it is known that the performance of AEM water electrolysis is influenced by the operating temperature of the cells. Based on the literature, it can be observed that recent research on AEM water electrolysis has primarily focused on experimental testing of cell materials, with relatively few studies evaluating the numerical analysis of single cells. Numerical analyses of AEM cells mainly refer to previous calculations for PEM electrolysis, and the impact of the operating environment provided by the system on cell performance and efficiency in AEM water electrolysis processes also remains to be clarified. This study addresses these issues by proposing a comprehensive computational framework from cell to system, combining thermodynamic methods with electrochemical numerical analysis to evaluate how operating conditions affect system components and AEM cell performance, thereby analyzing the impact of performance variations on overall system performance and efficiency. During system operation, maintaining the operating temperature requires heating the electrolyzer, which increases the energy consumption of the balance of plant (BoP) components in the AEM water electrolysis system, thereby affecting system electrolysis efficiency. To investigate the impact of temperature on cell performance and BoP, this study establishes a numerical model of the AEM water electrolysis system. First, it will explore the performance variations in single cells under different operating conditions, then it will compare the effects of different operating temperatures and system pressures on the cell electrolysis performance and overall system efficiency.

2. Methodology of Numerical Modeling

2.1. Polarization Phenomena in AEM Water Electrolysis Cell

The aim of this study is to establish a numerical model for evaluating the efficiency of an AEM water electrolysis system. To investigate the efficiency of the AEM water electrolysis system and the power consumption in the BoP components under different operating conditions, a performance evaluation model for AEM water electrolysis cells is developed. Various approaches are integrated from the previous literature to establish the numerical model. This model evaluates the AEM system performance based on electrolyte concentration, cell pressure, and operating temperature. The overall electrochemical reactions and calculations are referred to in previous studies [14,15,16,17,18,19,20,21].

According to the electrochemical reaction process in AEM water electrolysis, hydrogen is produced through the chemical reactions of oxygen, hydrogen, and water. As the electrolyte flows through the cathode, water molecules contact the cathode surface and simultaneously receive electrical energy, which induces a reverse reaction leading to the electrochemical reaction that produces hydrogen. The electrochemical reactions are as follows [14]:

Anode:

$$2O{H}_{\left(aq\right)}^{-}\stackrel{}{\leftrightarrow }{H}_{2}O+{\displaystyle \frac{1}{2}}{O}_{2\left(g\right)}+2e^{-} E_{a0}\left(298 \mathrm{K}\right)=1.229 \mathrm{V}$$

(1)

Cathode:

$$2H_{2}O+2e^{-}\stackrel{}{\leftrightarrow }2H_{2\left(g\right)}+2O{H}_{\left(aq\right)}^{-} E_{c0}\left(298\mathrm{K}\right)=0 \mathrm{V}$$

(2)

Reaction:

$$H_2{O}_{\left(l\right)}\stackrel{}{\leftrightarrow }{H}_{2\left(g\right)}+{\displaystyle \frac{1}{2}}{O}_{2\left(g\right)} E_{rev}^0\left(298 \mathrm{K}\right)=1.229 \mathrm{V}$$

(3)

The hydrogen reaction potential in electrochemical reactions is 0 V, which is referenced in the results from Vidales, A. G. [14]. Accordingly, in the total voltage calculation, the oxidation and reduction potentials are 1.229 V and 0 V (relative potential). However, the reduction potential in alkaline electrolysis is −0.828 V and the oxidation potential is 0.4 V, which more accurately reflects the electrochemical calculations for alkaline electrolysis.

As shown in Equations (1)–(3), the AEM water electrolyzer can produce hydrogen and oxygen through electrochemical reactions that convert electrical energy. The entire electrolysis process involves the decomposition of water molecules and the phase change of hydrogen and oxygen. To implement the electrochemical reaction, a minimum voltage is required, known as the reversible potential ($E_{rev}^0$). The reversible potential for this electrolysis process can be calculated using the Nernst equation, as described below [14]:

$$E_{rev}=E_{rev}^0+{\displaystyle \frac{RT}{nF}}\ln \left({\displaystyle \frac{p_{H_2}{p}_{O_2}^{0.5}}{p_{H_{2}O}}}\right)$$

(4)

$$E_{rev}^0=1.229-0.9\times {10}^{-3}\left(T-298\right)$$

(5)

where R is the universal gas constant, T is the operating temperature, n is the number of electrons involved, and F is Faraday’s constant. The partial pressures $p_{H_2}, p_{H_{2}O}, p_{O_2}$ represent the partial pressures of hydrogen, water vapor, and oxygen.

The performance of AEM electrolysis cells is influenced by various polarization phenomena, namely activation polarization, ohmic polarization, and concentration polarization. The following section evaluates the impact of these three different polarizations on cell performance in AEM water electrolysis. Activation polarization is mainly related to the energy required for the catalytic reactions in the electrochemical process, based on the activation energy of the Hydrogen Evolution Reaction (HER) and Oxygen Evolution Reaction (OER). The reaction rate depends on the temperature, electrode properties, and electrolyte concentration. The formula for activation polarization can be defined as follows [15]:

$${\eta }_{act}={\displaystyle \frac{RT}{{\alpha }_{a}F}}arcsinh\left({\displaystyle \frac{J}{2j_{0,a}}}\right)+{\displaystyle \frac{RT}{{\alpha }_{c}F}}arcsinh\left({\displaystyle \frac{J}{2j_{0,c}}}\right)$$

(6)

where α is the charge transfer coefficient of the electrode (with a and c representing the anode and cathode); j is the operating current density; and j₀ is the exchange current density. The impact of the transfer coefficients at the anode and cathode on the temperature is investigated by the related equations proposed by Milewski et al. [16]:

$${\alpha }_a=0.0675+0.00095T$$

(7)

$${\alpha }_c=0.1175+0.00095T$$

(8)

The ohmic polarization arises from the resistance within the electrolytic cell and can be expressed by the following equation [17]:

$$V_{ohm}=\left(r_{KOH}+r_{mem}\right)i$$

(9)

where $r_{KOH}$ represents the resistance of the electrolyte; $r_{mem}$ represents the resistance of the membrane; and i is the current. The resistance of the electrolyte can be expressed by the following equation [18]:

$$r_{KOH}={\displaystyle \frac{1}{\sigma KOH}}\left({\displaystyle \frac{d_{am}}{S_a}}+{\displaystyle \frac{d_{cm}}{S_c}}\right)$$

(10)

where $d_{am}$ and $d_{cm}$ are the thicknesses of the anode and cathode; $S_a$ and $S_c$ denote the cross-sectional areas of the anode and cathode; and $\sigma KOH$ is the ionic conductivity of KOH. Based on the research of Gilliam et al. [19] and considering actual experimental data of an AEM water electrolyzer, this study proposes the following formula for calculating $\sigma KOH$:

$$\sigma KOH=-2.041 \mathrm{m}-0.0028 {\mathrm{m}}^2+0.005332 \mathrm{mT}+207.2 {\displaystyle \frac{\mathrm{m}}{\mathrm{T}}}+0.001043{\mathrm{m}}^3-0.0000003 {\mathrm{m}}^2 {\mathrm{T}}^2$$

(11)

In addition, the membrane resistance in the AEM water electrolyzer constitutes a significant portion of the total ohmic polarization of the cell and can be expressed as follows: [20]

$$r_{mem}={\displaystyle \frac{{\delta }_m}{A_m{\sigma }_m}}$$

(12)

where ${\delta }_m$ represents the thickness of the membrane electrode assembly (MEA); $A_m$ is the total reaction area; and ${\sigma }_m$ is the membrane’s conductivity. The membrane conductivity is further influenced by the level of humidification and the operating temperature [20]:

$${\sigma }_m=\left(0.524\lambda -0.318\right)e^{\left[1270\left(\frac{1}{303}-\frac{1}{T}\right)\right]}$$

(13)

For this study, the entire membrane is fully hydrated, and therefore, the value of λ in this equation is assumed to be 18.

The concentration polarization is primarily influenced by the diffusion capacity of the electrolyte and the catalyst layer. Therefore, the mass transport limitations occurring in AEM water electrolysis are evaluated as well as all mass flows through the porous electrode catalyst and MEA materials. During the process of AEM water electrolysis, the system requires a continuous supply of water to the cell to sustain the electrochemical reaction while simultaneously needing to remove the H₂ and O₂ products. However, at high current densities, the removal rate of H₂ and O₂ may be slower than their production rate, leading to an increase in their concentrations, which can block reaction sites and slow down the reaction rate. This phenomenon is known as mass transport limitation in electrochemical reactions, which is dependent on the concentration of substances present at the membrane/electrode interface and can be described using the Nernst equation [21].

$${\eta }_{diff}={\displaystyle \frac{RT}{4F}}ln{\displaystyle \frac{C_{O_{2.mem}}}{C_{O_{2.mem,0}}}}+{\displaystyle \frac{RT}{2F}}ln{\displaystyle \frac{C_{H_{2.mem}}}{C_{H_{2.mem,0}}}}$$

(14)

where $C_{O_{2.mem}}$ and $C_{H_{2.mem}}$ are the concentrations of oxygen and hydrogen at the membrane–electrolyte interface, respectively; $C_{O_{2.mem,0}}$ and $C_{H_{2.mem,0}}$ denote the reference concentrations under the adopted working conditions.

In the AEM electrolyzer, mass transport is controlled by the internal diffusion capacity within the cell. The gas concentrations at the electrolyte–membrane interface can be calculated by applying Fick’s law, resulting in the following relationship [21]:

$$C_{O_{2.mem}}={\displaystyle \frac{P_a\left(\frac{{\dot{n}}_{O_2}}{{\dot{n}}_{O_2}+{\dot{n}}_{H_{2}O,a}}\right)}{R{T}_a}}+{\displaystyle \frac{{\delta }_a{\dot{n}}_{O_2}}{D_{eff,a}}}$$

(15)

$$C_{H_{2.mem}}={\displaystyle \frac{P_C\left(\frac{{\dot{n}}_{H_2}}{{\dot{n}}_{H_2}+{\dot{n}}_{H_{2}O,c}}\right)}{R{T}_c}}+{\displaystyle \frac{{\delta }_c{\dot{n}}_{H2}}{D_{eff,c}}}$$

(16)

where R is the gas constant; $T_a$ and $T_c$ represent the temperatures at the anode and cathode, respectively; $P_a$ and $P_c$ are the pressures at the anode and cathode; ${\delta }_a$ and ${\delta }_c$ are the thicknesses of the anode and cathode; ${\dot{n}}_{O_2}$, ${\dot{n}}_{H_2}$, and ${\dot{n}}_{H_{2}O}$ are the molar flow rates per unit area of oxygen, hydrogen, and water in the electrode; and $D_{eff}$ is the effective binary diffusion coefficient for mass transport. The effective binary diffusion coefficients for $O_2$/$H_{2}O$ and $H_2$/$H_{2}O$ in the porous electrodes, denoted as $D_{eff,a}$ and $D_{eff,c}$, can be calculated using the following equation [21]:

$$D_{eff,A-B}=D_{A-B}\epsilon {\left({\displaystyle \frac{\epsilon -{\epsilon }_p}{1-\epsilon }}\right)}^{\alpha }$$

(17)

where α is an empirical coefficient of 0.785; ε is the porosity of the electrode; ${\epsilon }_p$ is the percolation threshold; and $D_{A-B}$ is the diffusion coefficient of the mixture. For a given mixture of substances A and B, $D_{A-B}$, can be calculated as follows [21]:

$$D_{A-B}=(a{\left({\displaystyle \frac{T}{\sqrt{T_{c,a}{T}_{c,b}}}}\right)}^b){\left(p_{c,a}{p}_{c,b}\right)}^{{\displaystyle \frac{1}{3}}}{\left(T_{c,a}{T}_{c,b}\right)}^{{\displaystyle \frac{5}{12}}}{\left({\displaystyle \frac{1}{M_{m,A}}}+{\displaystyle \frac{1}{M_{m,B}}}\right)}^{{\displaystyle \frac{1}{2}}}{\displaystyle \frac{1}{p}}$$

(18)

where p represents the electrode pressure; a and b are coefficients depending on the type of gas; and $M_m$ is the molar mass of substances A and B.

In Equations (15) and (16), the molar flow rates of ${\dot{n}}_{O_2}$ and ${\dot{n}}_{H_2}$ through the porous electrodes can be determined using Faraday’s law, which involves dividing the number of moles of gas produced at each electrode by the membrane area [21].

$${\dot{n}}_{O_2}={\displaystyle \frac{{\dot{N}}_{O_2}^{prod}}{A}}={\displaystyle \frac{i}{4FA}}$$

(19)

$${\dot{n}}_{H_2}={\displaystyle \frac{{\dot{N}}_{H_2}^{prod}}{A}}={\displaystyle \frac{i}{2FA}}$$

(20)

where ${\dot{N}}^{prod}$ represents the molar flow rate of gas produced at that location; A is the reaction area of the AEM electrode; and F is Faraday’s constant.

The molar flow rates of water through the anode and cathode, ${\dot{n}}_{H_{2}O,a}$ and ${\dot{n}}_{H_{2}O,c}$, concern the water consumed or produced at the electrodes as well as the net water flow through the membrane. Therefore, the water through the anode is the sum of the water transported to the other side of the membrane ${\dot{N}}_{H_{2}O}^{mem}$ and the water produced by the OER at the anode ${\dot{N}}_{H_{2}O}^{prod}$. For the cathode, it is the net water transported through the membrane ${\dot{N}}_{H_{2}O}^{mem}$ minus the water consumed by the HER at the cathode ${\dot{N}}_{H_{2}O}^{cons}$ [21].

$${\dot{n}}_{H_{2}O,a}={\displaystyle \frac{{\dot{N}}_{H_{2}O}^{mem}+{\dot{N}}_{H_{2}O}^{prod}}{A}}$$

(21)

$${\dot{n}}_{H_{2}O,c}={\displaystyle \frac{{\dot{N}}_{H_{2}O}^{mem}-{\dot{N}}_{H_{2}O}^{cons}}{A}}$$

(22)

The molar flow rate of water produced at the anode by the OER and the molar flow rate of water consumed at the cathode by the HER are related to the electrochemical reactions in the cell through Faraday’s law [21].

$${\dot{N}}_{H_{2}O}^{prod}={\displaystyle \frac{i}{2F}}$$

(23)

$${\dot{N}}_{H_{2}O}^{cons}={\displaystyle \frac{i}{F}}$$

(24)

As in Equations (22)–(24), this study calculates the water flow rate in the AEM water electrolyzer. The total water transport across the AEM water electrolysis electrolyte, ${\dot{N}}_{H_{2}O}^{mem}$, is calculated as the sum of the water flow due to diffusion ${\dot{N}}_{H_{2}O}^{diff}$, electro-osmotic drag ${\dot{N}}_{H_{2}O}^{eod}$, and the pressure effect ${\dot{N}}_{H_{2}O}^{pe}$. The corresponding formula is as follows:

$${\dot{N}}_{H_{2}O}^{mem}={\dot{N}}_{H_{2}O}^{diff}-{\dot{N}}_{H_{2}O}^{eod}-{\dot{N}}_{H_{2}O}^{pe}$$

(25)

As $O{H}^{-}$ ions counterbalance with anions, water transport occurs due to ${\dot{N}}_{H_{2}O}^{eod}$, where water molecules are carried across the AEM. The molar flow rate is related to the electro-osmotic drag parameter $n_d$, which represents the number of water molecules carried per hydroxide ion and the flow of hydroxide ions through the membrane [22].

$${\dot{N}}_{H_{2}O}^{eod}={\displaystyle \frac{n_{d}i}{F}}$$

(26)

The amount of water transported across the membrane due to the pressure gradient ${\dot{N}}_{H_{2}O}^{pe}$ depends on the permeability of the membrane and can be calculated using Darcy’s law [21].

$${\dot{N}}_{H_{2}O}^{pe}={\displaystyle \frac{K_{darcy}A}{{\mu }_{H_{2}O}}}\nabla p{\displaystyle \frac{{\rho }_{H_{2}O}}{M_{m,H_{2}O}}}{\displaystyle \frac{1}{{\delta }_{mem}}}$$

(27)

where $K_{darcy}$ is the membrane’s permeability; ${\mu }_{H_{2}O}$ is the viscosity of water; A is the electrochemical reaction area; ${\rho }_{H_{2}O}$ is the density of water; $M_{m,H_{2}O}$ is the molar mass of water; p is the pressure gradient; and ${\delta }_{mem}$ is the membrane thickness. The performance of the AEM water electrolysis cell can be evaluated based on these calculations, and the performance comparison of the cell would be conducted with respect to cell pressure, electrolyte concentration, and operating temperature. The results are applied to the performance and efficiency calculations of the AEM water electrolysis system loop. Subsequent sections provide detailed calculations and explanations regarding the performance of the necessary components within the system loop.

In addition to the calculation processes described for the AEM water electrolysis cell, the internal numerical calculations of the AEM water electrolysis would be based on the design parameters of the AEM prototype system, as referenced in [14,15]. The detailed numerical parameters are presented in

Table 1. AEM water electrolysis simulation parameters [14,15].

Parameters	Value	Unit
Universal gas constant R	8.3145	J mol−1 K−1
Faraday’s constant F	96,485	A s mol−1
Operating temperature T	333.15	K
Operating pressure P	1	atm
LGDL thickness	0.2	m
Water molar mass $M_{m,H_{2}O}$	18 × 10−3	kg mol1
Oxygen molar mass $M_{m,O_2}$	32 × 10−3	kg mol1
Water viscosity $\mu H_{2}O$	1.1 × 10−3	Pa s
Membrane water permeability $K_{darcy}$	1.58 × 10−18	m2
Membrane humidification degree λ	18
Ni nanoparticle (HER) exchange current density jo	1.91	A m−2
Ni oxide (OER) exchange current density jo	0.056	A m−2
Critical pressure of $H_2$	12.8	atm
Critical temperature of $H_2$	33.3	K
Critical pressure of $O_2$	49.7	atm
Critical temperature of $O_2$	154.4	K
Critical pressure of $H_{2}O$	218.3	atm
Critical temperature of $H_{2}O$	647.3	K
Empirical a	3.640 × 10−4
Empirical b	2.334
Empirical α	0.785
Diffusion coefficient of water $D_w$	1.28 × 10−1	m2 s−1
Electro-osmotic drag coefficient $n_d$	3
Hydrogen gas partial pressure $P_{H_2}$	0.5	Pa
Oxygen gas partial pressure $P_{O_2}$	0.2	Pa
Water vapor partial pressure $P_{H_{2}O}$	1	Pa
Anode and cathode cross-sectional surface areas $S_a,S_c$	0.1	m2
Thickness of the anode and cathode ${\delta }_a,{\delta }_c$	0.0002	m
Pressure at anode $P_a$	1	atm
Pressure at cathode $P_c$	13.6	atm
Active area of the membrane $A_m$	0.0005	m2
Porosity of the electrode $\epsilon$	0.3
Percolation threshold of the electrode ${\epsilon }_p$	0.11
Distance between the anode or cathode and the membrane $d_{am},d_{cm}$	10−5	m
Number of electrons n	2
AEM thickness	100 × 10−6	m

below.

2.2. Balance of Plant in AEM Water Electrolysis System Heat Transfer

During the operation of the AEM water electrolysis system, a heater is used to provide an operating environment with different temperatures, facilitating heat exchange between the exhaust gases from the electrolyzer outlet and a low-temperature fluid. In the heat exchange calculation process, the electrochemical heat and ohmic resistance heat from the AEM water electrolysis calculation in Section 2.1 would be considered. The electrolyte in the AEM water electrolysis system loop would serve as the medium for heat exchange calculations, facilitating the processes of system heat recovery and mass–energy calculations. This section introduces the calculation procedures for heat exchange within the system, which is primarily based on equilibrium thermodynamics—considering the heat capacity of the gases flowing through the heating components and the system’s heat exchange efficiency—to determine the thermal energy and gas temperature changes within each component [23].

$$\left\{\begin{array}{c}{C}_C=\sum q_C{C}_{P,C}\\ C_C=\sum q_C{C}_{P,h}\end{array}\right. \left[{\displaystyle \frac{mole}{s}}\times {\displaystyle \frac{J}{mole\times K}}={\displaystyle \frac{W}{K}}\right]$$

(28)

To calculate the amount of heat transfer during the heat exchange process, the heat exchange efficiency of the components is used as the standard in the calculation. The formula for calculating the heat exchange efficiency is as follows [23]:

$$\epsilon {=q/q}_{\max }$$

(29)

As shown in Equation (30), the relationship between the thermal energy and the temperature changes in the high- and low-temperature heat reservoirs during the heat exchange process in the system is given by Equation (30) [23].

$$q_{\max }{=\mathrm{C}}_{\min }\left(T_{\mathrm{h},1}-{\mathrm{T}}_{\mathrm{c},1}\right)$$

(30)

where T_h,1 and T_c,1 represent the inlet temperatures of the high-temperature gas and low-temperature gas, respectively. Additionally, to calculate the outlet temperatures of the high- and low-temperature fluids, the heat exchange efficiency introduced in Equation (30) and the thermal energy calculation formula in Equation (30) would be used, as shown below in Equation (31) [23].

$$\epsilon ={\displaystyle \frac{C_h\cdot \left(T_{\mathrm{h},1}-{\mathrm{T}}_{\mathrm{h},2}\right)}{C_{\min }\left(T_{\mathrm{h},1}-{\mathrm{T}}_{\mathrm{C},1}\right)}}={\displaystyle \frac{C_h\cdot \left(T_{\mathrm{C},2}-{\mathrm{T}}_{\mathrm{C},1}\right)}{C_{\min }\left(T_{\mathrm{h},1}-{\mathrm{T}}_{\mathrm{C},1}\right)}}$$

(31)

With relation to thermal energy and heat exchange efficiency, the temperatures of the thermal components can be determined using the formulas in Equations (32) and (33). Once the calculations in Equations (30) and (31) are completed, the heat exchange calculation process for a thermal component is finalized [23].

$$T_{\mathrm{h},2}{=\mathrm{T}}_{\mathrm{h},1}-{\displaystyle \frac{q}{C_h}}$$

(32)

$$T_{\mathrm{C},2}{=\mathrm{T}}_{\mathrm{C},1}+{\displaystyle \frac{q}{C_C}}$$

(33)

2.2.1. Electrical Heater

To simulate the external heat source required for electrolysis, electrical heating is used to maintain the operating temperature of the water electrolysis system. The electric heater, which primarily generates heat through the thermal effect of electric current, relies on heating resistor elements as the main heating components. The power calculation for a pure resistive circuit is given by Equation (34).

$${\mathrm{Power}}_{\mathrm{Heater}}=\mathrm{V}\times \mathrm{I}=\mathrm{W}/\mathrm{t}$$

(34)

where V is the voltage; and I is the current.

2.2.2. Compressor

The compressor is primarily used for secondary pressurization at the hydrogen outlet of the AEM water electrolysis. In the calculation process, thermodynamic methods are used to model an ideal compressor, requiring the application of a polytropic relation (pvⁿ = constant) between the input and output states to determine the thermodynamic state of the output and the required mechanical power [24].

$${\mathrm{Power}}_{\mathrm{compressor}}={\displaystyle \frac{n\left(p2v2-p1v1\right)}{1-n}}$$

(35)

$${\displaystyle \frac{T2}{T1}}={\left({\displaystyle \frac{p2}{p1}}\right)}^{{\displaystyle \frac{\left(n-1\right)}{n}}}$$

(36)

where p is pressure; v is the specific volume; n is the polytropic coefficient. Index 1 indicates the input to the compressor, index 2 indicates the output. Based on the literature [25], the polytropic coefficient for hydrogen is 1.4. Therefore, this coefficient would be used in the compressor’s design.

2.2.3. Electrolyte Pump

The electrolyte pump is used to provide the required water flow for the AEM water electrolyzer and to increase pressure according to system operating requirements. It determines the thermodynamic state of the outgoing flow, along with the required mechanical power consumption of the electrolyte pump. The electrolyte pump is modeled based on isentropic efficiency and the general relations are provided below [24].

From the first law of thermodynamics for electrolyte pumps, the following can be obtained:

$$\dot{m}\left(h_{in}+{\displaystyle \frac{1}{2}}{v}_{in}^2\right)=\dot{m}\left(h_{out}+{\displaystyle \frac{1}{2}}{v}_{out}^2\right)+\dot{W}$$

(37)

Simplifying to

$$\dot{m}\left(h_{out}-h_{in}\right)={\displaystyle \frac{\dot{m}\left(p_{out}-p_{in}\right)}{\rho }}$$

(38)

where $p_{out}$ and $p_{in}$ are the pressure of the outlet and inlet of the electrolyte pump. The work is calculated by the following:

$$\dot{{\displaystyle \frac{\dot{W}}{\dot{m}}}={\displaystyle \frac{h_{out}-h_{in}}{\eta }}}={\displaystyle \frac{p_{out}-p_{in}}{\eta \rho }}$$

(39)

where $\eta$ is the electrolyte pump efficiency. The required electric power Pel is calculated as outlined below:

$${\mathrm{Power}}_{\mathrm{pump}}={\displaystyle \frac{\dot{m\mathsf{\Delta }p}}{\rho \eta }}$$

(40)

where $\rho$ denotes the density. Based on previous work, the efficiency of a typical electrolyte pump is approximately 0.8. Therefore, this coefficient would be used in the design of the electrolyte pump.

2.2.4. AEM Water Electrolysis System Configuration

The overall system configuration is illustrated in Figure 1. The present study optimizes the heat exchange and heat recovery of the electrolyte within the electrolyzer of AEM water electrolysis to enhance the system’s heat recovery capability and reduce the electrical power required by the system’s electric heater. Additionally, during system operation, the energy consumption calculations of the cells and components would be referenced, along with thermodynamic methods, to evaluate the system’s performance and efficiency. The relevant assumptions and system operating conditions are detailed in Table 2 and the following descriptions:

• All system components are operated in a steady state;
• All gases used in the system are assumed to be ideal;
• Radiant heat transfer is not considered in this study;
• In the AEM water electrolysis system, heat exchange calculations between the cell stack and the heat exchanger are conducted based on ref. [22], considering the electrochemical heat generated during water electrolysis in the cell stack and the heat exchange processes in both the heater and heat exchanger;
• The hydrogen production pressure in AEM water electrolysis would be managed in two stages: primary pressurization through cell stack operating pressure and secondary pressurization via a downstream hydrogen compressor;
• To standardize the application of the system’s electric heater, it is assumed that the electrolyzer and the inlet temperature of the electrolyzer must be ≤10 °C, with the outlet temperature equal to the electrolyzer temperature.

Table 2. Basic operating parameters of the AEM system module [11,12].

Parameter	Value
Number of electrolyzers in the AEM water electrolysis system	1
Number of single cells in an electrolyzer	120
The efficiency of the heat exchanger (%)	70
The efficiency of the electrolyte pump (%)	80
Polytropic coefficient of the hydrogen compressor	1.4
The efficiency of the heater (%)	100

Table 2. Basic operating parameters of the AEM system module [11,12].

Parameter	Value
Number of electrolyzers in the AEM water electrolysis system	1
Number of single cells in an electrolyzer	120
The efficiency of the heat exchanger (%)	70
The efficiency of the electrolyte pump (%)	80
Polytropic coefficient of the hydrogen compressor	1.4
The efficiency of the heater (%)	100

Figure 1. Schematic diagram of the AEM water electrolysis system.

Figure 1. Schematic diagram of the AEM water electrolysis system.

3. Results and Discussion

3.1. Effects of Operating Parameters on AEM Water Electrolysis Cell

Before analyzing the impact of parameters on the AEM water electrolysis cell, it is necessary to validate the numerical model established in this study. To ensure that the model developed here can be applied to actual AEM electrolysis system analysis, performance validation would be conducted by comparison with the primary reference used in this study, as shown in

Table 3. Performance calculation results validation between this study and reference [14].

Current Density (A/cm2)	1	1.1	1.2	1.3	1.4	1.5	1.6	1.7	1.8	1.9	2
Voltage of this study	2.06	2.09	2.12	2.14	2.16	2.19	2.21	2.23	2.25	2.27	2.30
Voltage of ref. [15]	2.01	2.05	2.08	2.12	2.14	2.17	2.19	2.20	2.21	2.22	2.23
Error rate (%)	2.73	1.97	1.69	0.91	1.07	0.74	0.86	1.41	1.95	2.47	2.98

. From Table 3, the cell performance calculation results obtained from this numerical model differ by less than 3% from those in reference [14], demonstrating the model’s feasibility. Additionally, according to the findings of reference [16], the established numerical model aligns with experimental measurements of actual AEM water electrolysis cells, indicating that the results of the AEM water electrolysis model developed in this study can effectively assess the performance of practical AEM water electrolysis cells.

The present study analyzes the electrochemical and mechanical phenomena of the AEM water electrolysis system by modeling key components such as the electrolyzer, heater, electrolyte pump, and hydrogen compressor. Figure 2 shows the reversible potential of an AEM water electrolysis cell and the effects of activation, ohmic, and concentration polarizations on the current density of the AEM cell. It shows that in a low current density zone, less than 100 mA/cm², the activation and concentration polarizations dominate and construct a barrier to hydrogen production. In the high current density zone, the gradients of activation and concentration polarizations gradually reduce.

The ohmic polarization is an effect that occurs with the increase or decrease in current and shows a linear relationship with the current density variations. As shown in Figure 2, the effect of ohmic polarization on the low current density zone is less than activation and concentration effects; however as the current density increases above 600 mA/cm², the ohmic polarization effect is significant and can be greater than the activation term at a high current density operation.

The temperature effects on the polarization phenomena are shown in Figure 3 and Figure 4. In this study, the phenomena at operating temperatures of 313 K, 333 K, and 353 K are studied with a hydrogen production pressure of 1 bar and electrolyte concentration of 8 M. Considering the stability of the anion exchange membrane, higher operating temperatures are not adopted. The results show that high temperatures would increase the energy barriers that must be overcome in activation polarization and concentration diffusion, but at the same time, significantly reduce the electrolytic resistance. As shown in Figure 3, temperature effects on the polarization overpotential within the cell demonstrate that temperature primarily influences activation polarization by affecting the limiting current density, thereby altering the overpotential, as described in Equation (6). Observing Equation (6) reveals that the impact of temperature on activation overpotential remains minimal, which is reflected in Figure 3a, where activation polarization shows no significant overpotential changes with temperature variation. In contrast, Figure 3b illustrates that ohmic polarization varies considerably with temperature; higher temperatures result in a reduction in overpotential caused by ohmic polarization. Equations (9)–(13) indicate that temperature effects enhance the conductivity of the KOH electrolyte and the membrane material. Increasing temperature promotes conductivity, enhancing internal conductivity within the cell, and improving performance. This analysis suggests that temperature effects in AEM water electrolysis primarily reduce ohmic overpotential by enhancing the conductivity of both the membrane material and electrolyte.

As a result, increasing the operating temperature of the AEM electrolyzer has positive effects on the water electrolysis phenomena, as shown in Figure 4. Since the operating temperature is related to the thermal equilibrium of the whole electrolysis system, which is dominated by the electrolyzer and heater, the maximum energy efficiency of the AEM system is implemented by an optimum synergy of the BoP components.

Figure 5 and Figure 6 show the pressure effects on the polarization phenomena with a hydrogen production pressure of 1, 3, 5, 10, and 30 bar. The electrolyzer temperature is 333 K and electrolyte concentration adopts 8 M. Since the activation and ohmic polarization are material-behavior-dependent, the variation in hydrogen production pressure with relation to transport phenomena mainly affects the concentration polarization. As the results in Figure 5c display, the increment from 1 bar to 30 bar is about 0.07~0.08 V/cell as the current density exceeds 100 mA/cm². It is noted that the effects of hydrogen production pressure on the polarization phenomena are consistent at high-current operation, while the effects of temperature are current-density-dependent, as shown in Figure 4.

The concentration of the electrolyte is an important factor affecting the polarization phenomena of the AEM cell as well as temperature and hydrogen pressure. Gilliam et al. [19] reported that the specific conductivity increases with electrolyte concentration and achieves a maximum value under different operating environments. Figure 7 and Figure 8 show the simulation results of the AEM electrolyzer operating as 333 K and 1 bar of hydrogen pressure with different electrolytes of 2 M, 4 M, 8 M, and 12 M concentrations. Obvious overpotential differences are found in the ohm polarization curves, in which the case of 8 M has the best performance. The results are consistent with Gilliam et al.’s work [19].

3.2. Effects of Operating Parameters on AEM Water Electrolysis System

As shown in Figure 1, in addition to the performance of the electrolyzer, the overall energy efficiency of the system is also dominated by the power consumption of the key components of the system—the electrolyte pump, heater, and hydrogen compressor. The output of the electrolyte pump and heater are adjusted based on the thermal management requirements of the electrolyzer, while the hydrogen compressor has a different power consumption according to the application’s demand.

For example, for on site applications for boilers or industrial processes, the hydrogen pressure requirement is within 30 bar. Figure 9 shows the impact of a hydrogen production pressure of 1~30 bar on the energy efficiency under three operating temperatures of the electrolyzer. In the case of 313 K, increasing the hydrogen production pressure of the electrolyzer can reduce the power consumption of the compressor. However, raising the electrolyte pump pressure simultaneously increases the power consumption. Otherwise, as mentioned above, high hydrogen production pressure would also reduce the performance of the electrolyzer, i.e., increase the energy consumption of hydrogen production. As a result, for the electrolyzer operating at 313 K, the energy efficiency of the hydrogen production system decreases as the hydrogen pressure of the electrolyzer increases.

When the electrolyzer is operated at 333 K, the performance of the electrolyzer is improved; however, due to the increase in heater power being significant, the energy efficiency is reduced. As the hydrogen production pressure is increased, the high pressure of the electrolyte pump increases the overall heat transfer efficiency, and less power for the heater is needed to increase the temperature of the electrolyzer. The heater can be used to increase the temperature of the electrolyzer. Therefore, increasing the pressure of hydrogen production is conducive to improving overall energy efficiency. For a higher operating temperature, as in the case of 353 K in Figure 9, since the self-generated source caused by the electrochemical reaction is insufficient to maintain the electrolyzer operating temperature, more heater energy is required, and hence, the energy efficiency is lower than 333 K. The results reveal there is an optimum operating temperature of the electrolyzer with relation to the thermal equilibrium of the AEM water electrolysis system.

In addition to on site hydrogen production and application, hydrogen can be stored at a pressure of up to 200 bar and transported to users. The simulation results in Figure 10 show that the phenomenon is consistent with pressurizing it to 30 bar but the overall efficiency decreases slightly because of the increase in compressor power consumption. It is noted that increasing the hydrogen production pressure of the electrolyzer has a positive impact on the energy efficiency of the overall hydrogen supply. The greater the demand for hydrogen pressure, the more significant this effect will be. Taking the electrolyzer operating temperature of 333 K as an example, Figure 10 shows that when the demand hydrogen delivery pressure is 30 bar, the system efficiency of a hydrogen production pressure at 30 bar is 1.1% larger than at 1 bar. However, for the case of 200 bar hydrogen delivery pressure demand, increasing the hydrogen production pressure of the electrolyzer to 30 bar can increase the efficiency by 2.4%. The simulation results show that a high hydrogen production pressure of the electrolyzer can effectively reduce the power consumption of the hydrogen booster device. In the present study, the energy efficiency of the AEM systems for 30–200 bar hydrogen supply at a hydrogen production pressure of 1–30 bar are simulated, as seen in Figure 11.

From the perspective of the energy consumption incurred by hydrogen pressurization, increasing the hydrogen production pressure of the electrolyzer can effectively reduce the compression power consumption, thereby achieving higher overall energy efficiency. For the cases in Figure 12, in which hydrogen production by the electrolyzer at 1 bar pressure is delivered to 30 bar on site application and 200 bar high-pressure storage, the energy efficiency is 56.5% and 54%, respectively. That is, increasing the pressure to 200 bar reduces the energy efficiency by 2.5%. However, as the hydrogen production pressure of the electrolyzer increases to 30 bar, the energy efficiency difference between on site hydrogen production and high-pressure storage applications is only 1.1%. This reveals that the high hydrogen production pressure of the electrolyzer can contribute to the low power consumption required to boost the hydrogen pressure.

The results in Section 3.1 represent that 30 bar is the optimal hydrogen production pressure of the electrolyzer. In addition, the operating temperature of the electrolyzer is also an important factor concerning to the system efficiency and with relation to the electrolyte pump and heater for the thermal equilibrium of the AEM electrolysis system. The present study conducts an optimization analysis of the temperature of the electrolyzer, using the heat energy generated by the operation of the electrolyzer to maintain the temperature of the electrolyzer and minimize the power consumption of the electrolyte pump and heater. As shown in Figure 13, the simulated optimal operating temperature of the AEM electrolyzer is 328 K, which presents higher efficiency than at 333 K. As shown in Figure 13, the BoP components significantly influence the energy consumption performance of the AEM water electrolysis system, primarily due to contributions from the pump, hydrogen compressor, and heater. This component energy consumption arises from the system’s need to provide optimal operating conditions for the AEM electrolyzer stack. As demonstrated in previous cell performance, temperature effects enhance electrolysis capacity but increase the energy required by the heater. While the operating pressure of the electrolyzer stack raises the pump energy consumption and reduces stack performance, it significantly decreases the energy consumption of the hydrogen compressor. Based on the analysis of operating conditions, system optimization in this study involves reducing heater energy consumption by maintaining the system’s operating temperature through internal heat recovery using ohmic heat from the stack and a heat exchanger. Additionally, increasing the stack operating pressure lowers the hydrogen compressor energy consumption, achieving optimal operational efficiency.

4. Conclusions

The present work studied the electrochemical phenomena of anion exchange membrane electrolysis and investigated the key factors concerning hydrogen production by the AEM water electrolysis system. A numerical model is constructed according to electrochemical reactions, polarization phenomena, and power consumption of BOP components, such as the electrolyte pump, heater, hydrogen compressor, and heat exchanger in the system. The effects of operation parameters on the energy efficiency of hydrogen production are discussed, including the electrolyzer temperature from 313 K to 353 K, 1~30 bar hydrogen pressure of the electrolyzer, an electrolyte concentration of 2 M~12 M, and a 30~200 bar hydrogen supply pressure for on site application or storage for delivery.

For the electrochemical phenomena of the AEM water electrolysis cell, the reversible potential and activation, ohmic, and concentration polarizations are analyzed. This reveals that in a low current density zone of less than 100 mA/cm², the activation and concentration polarizations dominate and construct a barrier to hydrogen production, while in the higher current density zone, the gradients of activation and concentration polarizations gradually reduce and the ohmic polarization dominates. The study of temperature effects reveals that high temperatures would increase the energy barriers that must be overcome in activation polarization and concentration diffusion, but at the same time, significantly reduce the electrolytic resistance; therefore, increasing the operating temperature of the AEM electrolyzer has positive effects on the water electrolysis phenomena. The simulations of different hydrogen production pressures of the AEM electrolyzer show only concentration polarization increases at high-pressure operation, which affects the diffusion phenomena. The concentration of the electrolyte affects only the ohmic polarization. In this work, the electrolyte concentration of 8 M shows the best performance with comparison to other concentrations.

Since the hydrogen delivery cost is directly related to the overall energy efficiency of a hydrogen production system, the power consumption of the key components of a system—the electrolyte pump, heater, and hydrogen compressor—are significant as well and studied in this work. The results show that increasing the hydrogen production pressure of the electrolyzer can reduce the power consumption of the compressor but simultaneously increases the electrolyte pump power and concentration polarization of the electrolyzer. It reveals that as the hydrogen pressure of the electrolyzer increases, the energy efficiency of the hydrogen production system with an electrolyzer operating at 313 K decreases but increases at 333 K and 353 K.

For the scenario of hydrogen compressed to 200 bar for transportation, increasing the hydrogen production pressure of the electrolyzer is found to have a positive impact on the energy efficiency of the overall hydrogen supply. By comparison, between the cases of 1 bar and 30 bar of hydrogen pressure of the electrolyzer, the difference in the system efficiency is 1.1% for the hydrogen delivery pressure of 30 bar but enlarged to 2.4% in the case of 200 bar. This means that the high hydrogen production pressure of the electrolyzer can effectively reduce the power consumption of the hydrogen booster device. Finally, an optimization analysis of the electrolyzer operating temperature is conducted using the heat energy generated by the electrochemical reaction of the electrolyzer to minimize the power consumption of the electrolyte pump and heater. The simulated optimal operating temperature of the AEM electrolyzer is 328 K with an energy efficiency of 56.4% to deliver hydrogen at a pressure of up to 200 bar. The results of this work represent a numerical scheme to model the physical and chemical properties of AEM water electrolysis and create the criteria to achieve maximum energy efficiency by optimal operation parameters.

In conclusion, the computational framework and results of this study reveal a significant contribution to establishing a comprehensive numerical evaluation model for efficiency analysis from single cells to the system level. This model enables comparisons of operating conditions for the AEM water electrolyzer stack and their impact on system performance and efficiency, including the effects of stack operating pressure and hydrogen storage pressure on system efficiency. The findings from this study provide a valuable reference for future AEM water electrolysis system designs. However, the cell operating pressure considered in this study primarily focuses on the overall cell pressure, and the effects of differing operating pressures between the cathode and anode remain to be evaluated. Additionally, for system-level considerations, future energy management strategies should assess heat losses between components to reduce discrepancies between experimental and numerical simulation results. These insights from component assessments can serve as further references for system designs.