**1. Introduction**

As a clean, highly efficient and sustainable energy carrier, hydrogen is considered one of the most promising forms of alternative energy to conventional fossil fuels [1,2]. Under the increasingly severe situation of energy and environmental issues, the development of affordable, clean, and efficient hydrogen production technology is particularly important for hydrogen utilization [3]. Currently, hydrogen production methods can be broadly classified into three major categories based on the nature of their chemical processes and/or energy inputs: thermochemical, electrochemical, and biological methods [4]. Among these, thermochemical water splitting has attracted considerable attention because water is considered an ideal source due to its clean, abundant, and renewable characteristics [1,5]. However, the water splitting reaction for hydrogen generation is a thermodynamically limited reaction. The efficient hydrogen production from water (2H2O H2+O2 ) remains difficult due to the low equilibrium constant, e.g., Kp ≈ 2 × 10−<sup>8</sup> at 900 ◦C, and only low equilibrium concentrations of PO2 = 4.6 × 10−<sup>6</sup> bar and PH2 = 9.2 × 10−<sup>6</sup> bar are achieved [6]. Even at high temperatures, only a small amount of hydrogen can be obtained, e.g., the generated hydrogen concentration is only 0.1% at 1600 ◦C.

Recently, a technique of the oxygen transport membrane (OTM) reactor was developed for hydrogen production via water splitting. The OTMs are made of mixed ionic and

**Citation:** Zhao, T.; Chen, C.; Ye, H. CFD Simulation of Hydrogen Generation and Methane Combustion Inside a Water Splitting Membrane Reactor. *Energies* **2021**, *14*, 7175. https://doi.org/10.3390/en14217175

Academic Editors: Mahesh Suryawanshi and Bahman Shabani

Received: 20 September 2021 Accepted: 27 October 2021 Published: 1 November 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

electronic conducting materials that can simultaneously conduct electrons and oxygen ions. Thus, the membrane has a 100% selectivity to oxygen while it is impermeable to other gases; only oxygen can permeate through the membrane [7]. In a water splitting membrane reactor, one side of the membrane (defined as the feed side) is exposed to the water vapor, where water splits into oxygen and hydrogen at an elevated temperature. Inert gases (such as N2, He or Ar) or reactive gases (such as reducing gases: CO, syngas, or CH4) are introduced into the other side (defined as the sweep side) to take away or react with the permeated oxygen to form a low oxygen partial pressure on this side. Driven by the oxygen partial pressure difference between the two sides, oxygen can continuously transport from the feed side to the sweep side. Through the instantaneous removal of water decomposition products O2, the equilibrium of the water splitting reaction will be broken and shifted toward the decomposition into oxygen and hydrogen. Then, the continuous production of a substantial quantity of hydrogen can be achieved [2]. It is feasible to use the OTM reactor for water splitting to produce hydrogen. Park et al. [8] reported an experiment of using an OTM reactor based on the La0.7Sr0.3Cu0.2Fe0.8O3-<sup>δ</sup> (LSCuF−7328) membrane for hydrogen generation with water vapor fed into the feed side and coal gas (CO/CO2) fed into the sweep side. The coal gas consumed the permeated oxygen, thus improving the oxygen permeation rate and hydrogen generation (e.g., a hydrogen yield of 4.7 cm3/min·cm2 at 900 ◦C could be achieved). Zhu et al. [1] systematically investigated the behavior of water splitting in a La0.9Ca0.1FeO3-<sup>δ</sup> (LCF−91) OTM reactor under different reducing atmospheres (i.e., CO, H2/CO, and CH4). The results show that the LCF-91 membrane exhibits a favorable oxygen permeability and hydrogen production rates under reducing atmospheres (i.e., 6.17 × 10<sup>−</sup>8, 5.23 × 10−<sup>8</sup> and 3.90 × 10−<sup>8</sup> mol/cm2·s under CO, H2/CO and CH4, respectively). If the water splitting reaction is fast enough, then the oxygen permeation process will be the controlling step of the hydrogen production. The studies of Park et al. [8] on the La0.7Sr0.3Cu0.2Fe0.8O3-<sup>δ</sup> (LSCuF−7328) membrane reactor, Hong et al. [9] and Habib et al. [10] on the La0.1Sr0.9Co0.9Fe0.1O3-<sup>δ</sup> (LSCoF−1991) membrane reactor, Ben-Mansour et al. [11] on the Ba0.5Sr0.5Co0.8Fe0.2Ox (BSCoF−5582) membrane reactor, Jiang et al. [12] on the BaCoxFeyZr1-x-yO3-<sup>δ</sup> (BCoFZ) membrane reactor, Lee et al. [13] on La0.6Sr0.4Ti0.2Fe0.8O3-<sup>δ</sup> (LSTF−6428) membrane reactor, and Zhu et al. [1] on La0.9Ca0.1FeO3-<sup>δ</sup> (LCF−91) membrane reactor all show that, compared with inert gas, the use of reducing/reacting gas as a sweep gas can improve the oxygen permeability of the membrane reactor, thus leading to a higher hydrogen yield.

In recent years, researchers have proposed the concept of coupling water splitting with the partial oxidation of methane (POM) reaction, allowing the two reactions to proceed simultaneously in one apparatus [1,14–18]. The feed side is fed with water vapor while the sweep side is fed with methane. At 800–900 ◦C, the water splitting first occurs on the feed side; the product O2 permeates from the water splitting side to the sweep side through the OTM to provide the oxygen required for the POM reaction. A valuable advantage of this membrane reactor is that it can produce hydrogen and syngas simultaneously. In addition, POM is a slightly exothermic reaction, the heat released by the POM reaction can partially compensate for the heat required for water splitting. However, at a high temperature such as 800 ◦C, the enthalpy change for the water splitting is approximately +248 kJ/mol, and is only −23 kJ/mol for the POM reaction. Therefore, a large amount of heat needs to be provided to the reactor from the outside to facilitate the proceeding of water splitting. For this reason, if the methane combustion reaction is coupled with water splitting in an OTM reactor, more heat can be provided for the water splitting by the complete combustion of methane to further improve the hydrogen yield.

In this work, the La0.7Sr0.3Cu0.2Fe0.8O3-<sup>δ</sup> (LSCuF−7328), with a high oxygen permeability and appreciable stability, was selected as the membrane material, a CFD model for water splitting coupled with methane combustion in the LSCuF−7328 membrane reactor was developed and validated. The endothermic effect of the water splitting reaction was taken into account by adding an energy source term on the feed side. The contribution of this work is that the effect of the coupling of methane combustion on the water splitting reactor performance is analyzed and compared with the reactor without combustion. Furthermore, the effects of the sweep gas flow rate, the methane content and the inlet temperature on the reactor performance, such as the membrane temperature distribution, the oxygen permeation rate, the methane conversion and the hydrogen production rate were investigated.

#### **2. Model**

#### *2.1. Descriptions of the Membrane Reactor*

Figure 1 shows the schematic diagram of the 2D axisymmetric representation of the water splitting membrane reactor coupled with methane combustion, with *x* representing the axial direction and *r* representing the radial direction. The geometry consists of two concentric horizontal tubes with the outer tube made of quartz and the inner tube made of the LSCuF−7328 oxygen transport membrane. The reactor is divided into two zones by the membrane: a feed side and a sweep side. High-temperature water vapor in the mixture with N2 is fed into the feed side, while CH4 in mixture with CO2 as the sweep gas is introduced into the sweep side (i.e., the sweep gas is a mixture of CH4 and CO2). Both N2 and CO2 are used as the carrier gases. At an elevated temperature, oxygen and hydrogen are produced by a water splitting reaction on the feed side. Driven by the oxygen partial pressure differences across the membrane, oxygen permeates through the membrane from the feed side to the sweep side and then reacts with CH4. The permeated oxygen is consumed rapidly, the equilibrium of the water splitting reaction continues to move in the direction of generating hydrogen and oxygen, and then hydrogen is generated continuously.

**Figure 1.** Schematic diagram of 2D axisymmetric representation of the coupled membrane reactor.
