Numerical Study of Methane Dry Reforming Reaction in a Disk Reactor with Focused Solar Simulator

Heat transfer and thermochemical energy storage process of methane dry reforming in a disk reactor with focused solar simulator was modeled and analyzed. The results showed that thermochemical energy storage efficiency of disk reactor can reach 28.4%, and that is higher than that of tubular reactor. The maximum reaction rate occurs at catalyst bed corner near the baffle, because the corner has high temperature and high reactant molar fraction. As reactant flow increases, methane conversion and thermochemical energy storage efficiency decrease as catalyst bed temperature and heat loss decrease. The thermochemical energy storage efficiency increased first and then decreased with methane molar ratio increasing, while methane conversion and the thermochemical energy storage efficiency increased with reactant temperature increasing. As catalyst bed porosity rises, methane conversion and thermochemical energy storage efficiency increased first and then decreased, and optimum porosity is 0.31.


Introduction
Solar energy is a kind of abundant clean energy, but the cost of energy development and utilization is high and the efficiency is low due to its dispersion and instability. Thermochemical energy storage technology is the most promising high-temperature energy storage method. Research in the past two decades has shown that solar thermal energy can effectively drive chemical conversion reactions [1] [2]. Methane dry reforming thermochemical energy storage is a form of efficient energy utilization that can convert solar energy into stable chemical combustion energy [1]. Its main advantages [2] include large storage capacity per unit of methane, high temperature reaction condition (>600˚C), and full use of greenhouse gases CH 4 and CO 2 .
In recent years, solar reforming reactors are mainly developed into three types: indirectly heated reformer, tubular reformer-receiver and the windowed or volumetric reformer-receiver [3]. ASTERIX [4] [5] carried out solar steam reforming experiment of methane in the early 1990s, and studied details and related problems of process heat demand of industrial chemical process with solar energy and high temperature using indirect heating converter. The catalytically enhanced solar absorption receiver (CAESAR) [6] [7] test was used to determine the thermal, chemical, and mechanical properties of a commercial scale dish-shaped direct catalytic absorption receiver reactor under a series of steady-state and transient operating conditions. In order to perform an efficient carbon dioxide and water vapor reforming reaction, Weizmann Institute of Science designed a solar receiver with storage and transportation for high-temperature technology development, and tested it in a 480 kW reformer [8]. Jin et al. [9] proposed a methane reforming reactor with a compound paraboloid concentrator and a mesh porous ceramic. The simulation results show that compared with the traditional reactor design, the reactor design proposed in this study can improve the photochemical efficiency of solar methane conversion.
In addition to experimental research, the researchers conducted a large number of numerical simulation studies. Rubin et al. [10] proposed a numerical model based on Arrhenius equation for simulating methane steam reforming, and simulation results were in agreement with experimental results. Akpan et al. [11] established a reaction kinetics model for carbon dioxide methane reforming under Ni/CeO 2 -ZrO 2 catalyst through experiments and simulations. Akbanri et al. [12] established a three-dimensional microreactor model for simulating methane autothermal reforming in fuel cells, and studied the effects of airspeed, air/fuel ratio, water-fuel ratio and inlet temperature on the reaction. Wang et al. [13] [14] [15] used combined method with Monte Carlo Ray Tracing method and Finite Volume Method to establish heat and mass transfer model coupled with thermochemical reaction kinetics for porous medium solar thermochemical reactor. The numerical results showed that concentrated solar irradiation affects reactor thermal performance, methane steam reforming chemical reaction rate and hydrogen production. Gu et al. [16] analyzed heat transfer and storage performance of steam methane reforming in tubular reactor with focused solar simulator by measurement and simulation. Fernando et al. [17] found that methane steam reforming in a fixed-bed reactor can efficiently store thermal energy in high temperature. Benguerba et al. [18] analyzed the effect of using different temperatures on the methane dry reforming performance in a fixed-bed catalytic reactor by a one-dimensional heterogeneous model. At present, the research on methane dry reforming thermochemical energy storage process in enhanced reactor still need to be further investigated. In this paper, the thermochemical storage performance of methane dry reforming disk reactor was studied with focused solar simulator. The reactant flow, reactant methane molar ratio, reactant temperature and catalyst bed porosity were analyzed for mechanism of methane dry reforming process in the disk reactor, to find a new method to improve the methane conversion and energy storage efficiency of the system.  focused solar simulator. The reformer is a disk with radius of R 3 and height of H, and catalyst is also a disk with radius of R 1 . The inlet region and outlet region are separated by catalyst bed and two baffles. The outer surface with quartz glass at y = 0 is heated by concentrated heat flow from solar simulator.

Model Introduction
The main reaction of methane dry reforming reaction is: The main side reaction is: Inlet mole fraction of methane is: Methane conversion is: is methane outlet flow under standard condition. Carbon dioxide conversion rate is: where c q denotes central heat flux, and r denotes radius from focus.
Thermochemical energy storage is: where v denote mole volume under standard condition.

Theoretical Assumption and Model
Based on existing experimental data, a three-dimensional model of disk reactor with solar simulator is established. The entire process is assumed to be steady, and fluid is assumed to be ideal gas. The model contains solid domain of reactor wall, fluid domain with porous media inside reactor. Catalyst bed is assumed as porous media. The fluid zone includes inlet and outlet regions, and porous zone of catalyst bed. Continuity equation can be expressed as: where f ρ is density of mixed fluid, i u is superficial velocity vector based on the total cross-sectional area of fluid and porous medium.
Momentum conservation equation is expressed as: where µ is dynamic viscosity, p is fluid pressure, i g is gravitational acceleration and The momentum source for homogeneous porous media consists of viscosity loss term and inertia term as [19]: The permeability and internal resistance factor [20] can be calculated as: where p D is the diameter of catalyst particles.
During chemical reaction process, the fractions of reactants and products change, and mass transport equation is [19]: where A and a E mean pre-reaction factor and activation energy.
In solid zone of reactor wall, heat transfer is controlled by heat conduction, and its governing equation is: where w T is temperature of reactor wall, and w k is the thermal conductivity.
In fluid zone, energy conservation equation can be expressed as: where h S is energy source caused by chemical reaction, and eff k is effective conductivity. h S is directly calculated by enthalpy difference of reactants and products.
The effective thermal conductivity is calculated as volume average of thermal conductivities of fluid and solid as [21]: where f k and s k are conductivity of fluid and porous medium, respectively.
The heat loss from the reactor wall is primarily determined by natural convection and radiation. The boundary condition for heating surface is: where n h is heat transfer coefficient of natural convection, σ is black body radiation constant, ε is emissivity, and s T is surrounding temperature.
The boundary condition of back surface is:

Calculation Condition and Model Validation
According to the experimental results, the pre-exponential factor and activation energy of the main reaction are Yu et al. [22] experimentally measured tubular methane dry reforming reactor Y. R. Wang et al. based on solar radiation, which is similar to present model. Table 1 shows comparison of experimental and simulation results of methane conversion and thermochemical storage efficiency at different conditions. The results show that present numerical model is effective, and methane dry reforming energy storage system can be further analyzed. Figure 2 shows temperature and main reaction rate distribution of disk reactor. The heat flux distribution of solar simulator conforms to Gaussian distribution, resulting in high energy near the focus which causes high temperature, so the temperature of catalyst bed is a corresponding circular distribution from the center to boundary. Figure 3 shows molar fraction distribution of     Figure 5 describes the changes of methane conversion and thermochemical storage efficiency with reactant flow in disk reactor system. As the reactant flow increases, catalyst bed temperature and mixed gas outlet temperature decrease, and conversion of methane and carbon dioxide both are reduced, while the thermochemical energy storage efficiency increases. Figure 6 describes the energy ratio of disk reactor as a function of reactant flow. As reactant flow increases, although the mixture gas outlet temperature decreases slightly, the sensible heat storage efficiency increases due to the increase in the total gas volume. The heat loss is reduced for wall temperature decreasing, so the total energy storage efficiency increases.   methane molar ratio increases, reaching a maximum value at y = 0.5, which is due to the best chemical reaction rate under the ideal molar ratio. Figure 8 presents molar fraction in disk reactor. Increasing the proportion of carbon dioxide can promote the reverse reaction of water vapor shift reaction. As methane molar ratio of reactants increases, the amount of carbon dioxide gradually decreases, which reduces the likelihood of the reverse reaction of the   water vapor shift reaction going forward, thus the amount of by-product H 2 O produced will decrease. On the other hand, the production of H 2 gets the maximum at y = 0.5 under the ideal molar ratio.  reactor with different reactant temperature. As reactant temperature rises, methane conversion increases, because inside catalyst bed temperature increases, and then the reaction rate and methane conversion increase accordingly. Since the catalyst bed temperature in reactor does not increase significantly with the increase of reactant temperature, the sensible energy storage decreases significantly. Therefore, the thermochemical energy storage efficiency increases, and the total energy storage efficiency increases slightly and then gradually decreases, as shown in Figure 10.

Effect of Catalyst Bed Porosity
The porosity of catalyst bed has important effect on heat and mass transfer process inside the reactor. Figure 11 describes methane conversion and thermochemical energy storage efficiency in disk reactor with different catalyst bed porosity. The methane conversion and thermochemical energy storage efficiency both increase first and then decrease with the increase of catalyst bed porosity, and the optimal porosity is 0.31.

Conclusions
In this paper, heat transfer and energy storage performance of methane carbon dioxide disk reactor with concentrated heat flux were numerically studied, and conclusions are as follows: 1) The thermochemical energy storage efficiency of disk reactor can reach 28.4%, and that is remarkably higher than that of traditional tube reactor.
2) The maximum reaction rate occurs at catalyst bed corner near the baffle, because catalyst bed corner has high temperature and high reactant molar fraction.
3) The trends of methane conversion and thermochemical energy storage efficiency are similar. As the reactant flow increases, methane conversion and thermochemical energy storage efficiency decrease as catalyst bed temperature DOI: 10.4236/epe.2020.122005 70 Energy and Power Engineering  and heat loss decrease. 4) Increasing reactant temperature is conducive to improving methane conversion and thermochemical energy storage efficiency. 5) As catalyst bed porosity increases, methane conversion and thermochemical storage efficiency increase first and then decrease, and optimum porosity is 0.31.