Figure 1 describes physical model of a methane dry reforming disk reactor with

focused solar simulator. The reformer is a disk with radius of R₃ and height of H, and catalyst is also a disk with radius of R₁. 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.

The main reaction of methane dry reforming reaction is:

CH 4 + CO 2 ↔ 2 CO + 2 H 2 ,     Δ H m = + 247.3   kJ / mol (1)

The main side reaction is:

CO 2 + H 2 ↔ CO + H 2 O ,     Δ H s = + 41.1   kJ / mol (2)

Inlet mole fraction of methane is:

y = F CH 4 , i F CH 4 , i + F CO 2 , i (3)

where F CH 4 , i and F CO 2 , i denote inlet flow rates of methane and carbon dioxide under standard condition (1 atm, 20˚C), respectively.

Methane conversion is:

X CH 4 = F CH 4 , i − F CH 4 , o F CH 4 , i (4)

where F CH 4 , o is methane outlet flow under standard condition.

Carbon dioxide conversion rate is:

X CO 2 = F CO 2 , i − F CO 2 , o F CO 2 , i (5)

where F CO 2 , o is carbon dioxide outlet flow under standard condition.

The energy flow received by reactor from solar simulator is:

E i n = ∬ S w q r d S (6)

where q r is concentrated radiant heat flux on reactor surface, S w is surface area of reactor irradiate by solar simulator.

q r = q c exp ( − 1464.3 r 2 ) (7)

where q c denotes central heat flux, and r denotes radius from focus.

Thermochemical energy storage is:

Q c h = F CH 4 ⋅ X CH 4 ⋅ Δ H m v CH 4 + F CO 2 ⋅ ( X CO 2 − X CH 4 ) ⋅ Δ H s v CO 2 (8)

where v denote mole volume under standard condition. Δ H m and Δ H s are reaction heat of main reaction and side reaction.

Sensible heat increment is [18] :

Q s e = ∑ i ∫ T s T 0 F o , i ρ o , i c p , o , i d T (9)

where ρ o , i , c p , o , i are density and specific heat of species i in product, T s and T 0 are surrounding and outlet temperatures.

Thermochemical energy storage efficiency and total energy storage efficiency are:

η c h = Q c h E i n (10)

η t o t a l = Q t o t a l E i n = Q c h + Q s e E i n (11)

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:

∂ ( ρ f u i ) ∂ x i = 0 (12)

where ρ f is density of mixed fluid, u i is superficial velocity vector based on the total cross-sectional area of fluid and porous medium.

Momentum conservation equation is expressed as:

∂ ∂ x j ( ρ f u i u j ) = ∂ ∂ x j ( μ ∂ u i ∂ x j ) − ∂ p ∂ x i + ρ f g i + S m , i (13)

where μ is dynamic viscosity, p is fluid pressure, g i is gravitational acceleration and S m , i is momentum source caused by flow in porous media. In the inlet and outlet regions, S m , i = 0 .

The momentum source for homogeneous porous media consists of viscosity loss term and inertia term as [19] :

S m , i = ( μ α u i + C 2 1 2 ρ f | u | u i ) (14)

The permeability and internal resistance factor [20] can be calculated as:

α = D p 2 150 γ 3 ( 1 − γ ) 2 (15)

C 2 = 3.5 D p 1 − γ γ 3 (16)

where D p is the diameter of catalyst particles.

During chemical reaction process, the fractions of reactants and products change, and mass transport equation is [19] :

∂ ∂ x j ( ρ f Y i u j ) + ∂ J i , j ∂ x j = r i (17)

where Y i , J i , j and r i are respectively mass fraction, diffusion flux and reaction rate for species.

Chemical reaction is assumed as volumetric reaction, and the reaction rate is calculated by standard Arrhenius equation as:

k = A e − E a / R T (18)

where A and E a 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:

∂ ∂ x i ( k w ∂ T w ∂ x i ) = 0 (19)

where T w is temperature of reactor wall, and k w is the thermal conductivity.

In fluid zone, energy conservation equation can be expressed as:

∂ ∂ x i ( ρ f c p u i T ) = ∂ ∂ x i ( k e f f ∂ T ∂ x i ) + S h (20)

where S h is energy source caused by chemical reaction, and k e f f is effective conductivity. S h 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] :

k e f f = γ k f + ( 1 − γ ) k s (21)

where k f and k s 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:

− k w ∇ T w = h n ( T w − T s ) + ε σ ( T w 4 − T s 4 ) − q r (22)

where h n is heat transfer coefficient of natural convection, σ is black body radiation constant, ε is emissivity, and T s is surrounding temperature.

The boundary condition of back surface is:

− k w ∇ T w = h n ( T w − T s ) + ε σ ( T w 4 − T s 4 ) (23)

According to the experimental results, the pre-exponential factor and activation energy of the main reaction are A 1 = 1.2 × 10 7 and E a 1 = 5.8 × 10 7 J / kmol , and those of side reaction are A 2 = 31900 and E a 2 = 1.69 × 10 7 J / kmol . The heating surface of the reactor is affected by the air-cooling system, and h h = 12.6   W / m 2 ⋅ K , while convective heat transfer coefficient on back side is h h = 4   W / m 2 ⋅ K . The emissivity ε of the outer wall surface of the reactor is 0.93, the ambient temperature was 25˚C, and the flow of the reactant inlet was uniform.

Yu et al. [22] experimentally measured tubular methane dry reforming reactor 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

mixed gas. The main reaction rate reaches the maximum value at the corner of the catalyst bed near the baffle and decreases toward the center, because reactant molar fraction as methane increase correspondingly from the center to the boundary, while product molar fraction as hydrogen decrease from the center to the boundary.

Figure 4 shows parameter change in radial direction of catalyst bed. In top boundary of catalyst bed, the temperature corresponds to the distribution of incident energy flux, which gradually decreases from center to boundary. The main reaction rate first increases and then decreases in radial direction, and reaches a maximum value at the corner of catalyst bed baffle of x = 38.7 mm for the accumulation of reactants near the corners of catalyst bed baffle.

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.

Figure 7 presents methane conversion and storage efficiency in disk reactor with different methane molar ratio. As methane molar ratio of reactants increases, methane conversion gradually decreases. The thermochemical energy storage efficiency and total energy storage efficiency increase first and then decrease as

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 H₂O produced will decrease. On the other hand, the production of H₂ gets the maximum at y = 0.5 under the ideal molar ratio.

Figure 9 describes methane conversion and energy storage efficiency in disk

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.

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.