**Abstract**

The hydrogen production by SOECs coupled with renewable energy sources is a promising route for the sustainability *hydrogen economy*. Multiphysics computing simulations appear to be the most efficient approaches to analyze the coupled mechanisms of SOEC operation. Using a relevant model, it is possible to predict the electrical behavior of solid oxide electrodes considering the current collector design. The influences of diffusion and grain diameter on cell performances can be investigated through 2D simulations, current–voltage characteristics, and current source distribution through electrodes. The simulation results emphasize that diffusion is linked to a relocation of the reaction away from the interface electrolyte/electrode, in the volume of the cathode. Furthermore, the current collector proves itself to be a great obstacle to gas access, inducing underneath it a shortage of steam. Inducing gradients of grain diameters in both anode and cathode drives the current sources to occur close to the electrode/electrolyte interface, thus decreasing ohmic losses and facilitating gas access. This approach shows the crucial importance of cathode microstructure as this electrode controls the cell response.

**Keywords:** hydrogen production, steam electrolysis (SOEC), electrochemical modeling

#### **1. Introduction**

Usual electrolyzers employ aqueous electrolytes (alkaline water electrolyzer), and the major drawback of the electrolytic hydrogen production is its high cost in comparison with the steam-methane reforming process [1]. In addition to alkalinebased electrolysis, there are mainly two technologies of electrolyzer, which are currently considered, one based on proton-exchange membrane (PEM) and the other based on solid oxide (SOECs). The electrochemical decomposition of steam into hydrogen and oxygen offers two advantages over the low-temperature process currently in use. High temperature electrolysis (HTE) is more efficient than traditional room-temperature electrolysis for many reasons. First, some of the energy is supplied as heat, which is cheaper than electricity. Secondly, at high temperature the electrolysis is less energy consuming due to the low theoretical decomposition voltage. In the 1980s, solid oxide fuel cell (SOFC) developments allowed steam electrolysis investigation [2]. Thus, several experimental studies on hightemperature electrolysis (HTEs) using practical SOFC cells [3] have been carried

out. These experiments showed encouraging results. The solid oxide electrolysis cell (SOEC) is the reverse operation of the same SOFC cell structure. Both are composed of two porous composite ceramic electrodes surrounding a gas-tight electrolyte. SOECs can rely on the interest that SOFCs have received for the past decades and thus utilize similar technology and materials. Water is reduced at the cathode Eq. (1), releasing hydrogen and oxygen ions. After crossing the electrolyte, the ions are then being oxidized to form oxygen within the anode Eq. (2). Both half reactions are balanced by general Eq. (3):

$$H\_2O + 2e^- \rightarrow H\_2 + O^{2-} \tag{1}$$

$$\text{O}^{2-} \rightarrow \vee \text{O}\_2 + 2\text{e}^- \tag{2}$$

study the delamination phenomenon at the oxygen electrode/electrolyte interface. Few micro-modeling investigations are applied to SOEC, and relevant electrochemical models are required to improve the micro-scale predictions [20–23]. Nevertheless, the results of SOFC micro-modeling can be employed to appreciate, for example, particle size, graded or homogeneously distributed porosity, or composi-

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes*

In the subsection below a multiphysics model of SOEC has been built using the commercial software Comsol Multiphysics®. Electrochemical reactions within porous electrodes are described using the Butler-Volmer equation. Modeling is based on solving conservation equations of mass, momentum, and charge balance. Simulations allow the calculation of gas concentration, current density, and potential distribution within the electrodes (i.e., interconnects and electrodes). These simulations establish how porous electrode performance is affected by current collectors and electrode microstructural parameters. The model is then applied to engineer a design of the electrode structure or current collector configurations.

In the present model, mass and charge transport phenomena coupled with chemical and electrochemical reactions have been investigated within the SOEC cell. This mathematical approach is based on classical SOFC assumptions, and thus the model should depend on operating conditions, intrinsic conductivities of materials, and geometric parameters such as porosity or grain size [21–22]. Additionally, according to the 2D model of Kenney and Karan [23], the interconnects play a critical role. Thus, a 2D approach was performed in this work. In this study, a finite element method has been used to solve mass and charge balances including transport through porous media and electrochemical reactions within the porous electrodes. The set of resulting conservation equations has been solved using the commercial software Comsol Multiphysics®. In this computational approach, steady-state conditions have been imposed. This model of SOEC is based on the

• Perfect current collectors (equipotential surface with perfect contact)

• Ionic and electronic conductivities depending solely on temperature

The electrode material is a mixed electronic and ionic conductor. For modeling purposes, this electrode is considered as a porous gas diffusion electrode wherein the electrochemical reaction occurs at the triple phase boundary, i.e., at the interface between the electronic conductor, ionic conductor, and gas phase. The current in a porous electrode can be split into two parts: one part flowing through the ionic phase and the other through the electronic phase of the porous matrix. During

Equations are detailed in this section one balance at a time.

• Negligible convective flow through the electrodes

tion influence on electrode performance.

*DOI: http://dx.doi.org/10.5772/intechopen.90352*

**2. Model equations**

following assumptions:

• No contact resistances

• Constant pressure

**2.1 Charge balance**

**95**

$$H\_2O \to H\_2 + 1\downarrow O\_2 \tag{3}$$

Due to the high operating temperature, SOECs do not need expensive catalysts, but these must meet strict thermal, chemical, and structural requirements imposed by temperature, and hydrogen and oxygen partial pressures. However, performance still remains limited in electrolysis mode compared to fuel cell mode [4].

Comparing to PEM electrolyzers for which carbon monoxide is a poison, SOECs offer the advantage to allow the co-electrolysis of water and carbon dioxide to produce syngas [5, 6]. According to AlZahrani and Dincer [7] a SOEC system can achieve energy and exergy efficiencies of 53 and 60%, respectively. However, the high operating temperature (>1000 K) is still considered the major limiting factor of these device. Jiang [8] has shown that the hydrogen production by SOECs coupled with renewable energy sources is a promising route for the sustainability of energy in the future. The solution of a real commercially competitive SOC technologies is the materials: reliability and stability of the electrode and electrolyte materials under the reversible electrolysis and fuel cell operation modes. The reversible fuel cells have the ability to switch between electrolysis cell and fuel cell modes, and it is one of the foremost features that facilitate storing/generating energy in a costeffective manner. The optimized parameters on the designs of fell cells or of electrolyzer, solely, would not necessarily result in high performance of regenerative devices because these devices differ in electrode kinetics, gas environment, heat generation, and chemical stability. It is well known that high-temperature operation of SOECs offers inherent advantages, in terms of thermodynamics and kinetics compared with low-temperature electrolysis. In this context reversible solid oxide cells (RSOCs) are still at an early stage of development [9, 10]. Unfortunately, there is a general consensus that the performance and stability of SOECs are inferior to those of SOFCs [11], which is mainly due to the high-temperature operation.

Computing simulation appears to be one of the most efficient approaches to analyze the coupled mechanisms of SOEC operation. It can predict the SOEC behavior under various operating conditions. Mathematical modeling is an essential tool in the design of SOEC cells, as it is important to understand the limiting process of steam electrolysis. Recent literature shows a significant research and development effort focusing on the modeling of SOEC. The models developed by Udagawa et al. [12, 13] strive to describe all significant processes affecting the performance of a unit cell. These authors proposed one-dimensional or pseudo-2D simulations based on a planar geometry and taking into account mass transport. Ni et al. [14, 15] have described the mass transport within the electrode along with the electrochemical kinetics. The principal results of these investigations [16, 17] lead to a parametric control of the SOEC operation. In addition, Jin and Xue [18, 19] have developed a 2D model for a planar SOEC. The simulation results lead to a better understanding of the internal mechanisms for regenerative SOFCs. This model has been used to

#### *Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes DOI: http://dx.doi.org/10.5772/intechopen.90352*

study the delamination phenomenon at the oxygen electrode/electrolyte interface. Few micro-modeling investigations are applied to SOEC, and relevant electrochemical models are required to improve the micro-scale predictions [20–23]. Nevertheless, the results of SOFC micro-modeling can be employed to appreciate, for example, particle size, graded or homogeneously distributed porosity, or composition influence on electrode performance.

In the subsection below a multiphysics model of SOEC has been built using the commercial software Comsol Multiphysics®. Electrochemical reactions within porous electrodes are described using the Butler-Volmer equation. Modeling is based on solving conservation equations of mass, momentum, and charge balance. Simulations allow the calculation of gas concentration, current density, and potential distribution within the electrodes (i.e., interconnects and electrodes). These simulations establish how porous electrode performance is affected by current collectors and electrode microstructural parameters. The model is then applied to engineer a design of the electrode structure or current collector configurations.
