The simulated microreactor consists of three domains: catalyst bed, heating tubes, and insulating jacket.

Assuming that the flow regime is stable, laminar and incompressible, the gas mixture is considered as ideal gas. The mixture consists of six species: DME, CH₃OH, CO₂, CO, H₂O, and H₂. In addition, the volumetric flow is in the axial direction, while the mass transfer occurs mainly in the lateral direction of diffusion to the reactor wall. Therefore, the three-dimension model is adequate to cope with the reforming reaction.

Based on the above assumptions, the mass, momentum, energy, and species equations of the porous region can be written as follows.

The inlet and outlet boundary conditions describe a pressure drop across the bed. All other boundaries are impervious, corresponding to the condition:

− κ η ∇ p s r ⋅ n = 0 (4)

Convective heat transport at the outlet is assumed to be dominant:

n ⋅ ( k s r ∇ T s r ) = 0 (5)

For the flow of heating gas in the tubes, the boundary conditions are:

u ⋅ n = v 0 (6)

u = 0 (7)

p = p r e f (8)

Catalytic steam reforming of DME involves many reactions with different rates, the parameters in Equation (9) for DME hydrolysis into methanol were reported by Feng et al. [8] .

r DME = r DMO + = k ′ F , DMO + C R 1 + − k ′ C , DMO + C DMO + (9)

The kinetic equations [10] for methanol steam reforming and decomposition reaction are:

r R = ( 1 − ε ) ρ s k R C CH 3 OH (10)

r 3 = ( 1 − ε ) ρ s k D (11)

Here, ρ s is catalyst density, k R denotes the reforming rate constant, C CH 3 OH is the molar concentration of methanol, k D is the decomposition rate constant.

The kinetic model of WGS reactions is as following [11] :

r WGS = C WGS k WGS ( p CO p H 2 O − p CO p H 2 / K e q ) (12)

where, k WGS and K e q are the rate constant and the equilibrium constant respectively.

A reliable model is crucial to simulate the physical phenomena. In order to verify the reliability and accuracy of the simulated model, numerical results and the experimental data under the same conditions were compared. In the experimental system, the steam and DME flow was controlled by the syringe pump, the mixed gas flowed into the reactor filled with a CuO/ZnO/Al₂O₃ + ZSM5 catalyst through a mass flow controller. Reactant and product concentrations were measured by gas chromatography.

The reactant gas was preheated to 200˚C, and the steam to DME ratio was 5, the DME conversion and the hydrogen yield are defined as follows:

DME   conversion ( % ) = ( F DME , in − F DME , out ) / F DME , in × 100 % (13)

Hydrogen   yield ( % ) = F H 2 , out / F DME , in × 1 / 6 × 100 % (14)

where F_DME is the mass flow of DME, F H 2 is the mass flow of H₂.

Figure 1(a) and Figure 1(b) shows the comparison of DME and H₂ yield respectively between the simulation results and experiment data. The higher hydrogen production and DME conversion of simulation results were probably due to hydrogen spillover or hydrogen leak of the experiment.

The simulation results for DME conversion and yield agree well with the experimental data. Therefore, the numerical simulation error is small and the result is reasonable, the current model can be used to study the reactor.

Figure 2(a) and Figure 2(b) shows the DME conversion and hydrogen production as a function of temperature with different ratio of steam to DME. The inlet temperature of mixture gas was 260˚C. The ratio of steam to DME ranges from 3 to 7.

Figure 2 shows that the DME conversion and hydrogen yield increased with the increase of the steam/DME ratio. The higher steam/DME ratio accelerated the DME hydrolysis reaction and methanol reforming reaction, and the water gas shift reaction was promoted, so as to produce more H₂.

Effect of inlet temperature was shown in Figure 3. Figure 3(a) and Figure 3(b)

shows the mole fraction of DME and H₂ respectively with the change of gas inlet temperature. As seen in Figure 3, the mole fraction of DME was lowest at the temperature of 300˚C, while the mole fraction of H₂ was highest. These results indicated that higher temperature can further the DME hydrolysis, but strengthened the reverse water-gas-shift reaction. A higher temperature promoted higher conversion of DME and higher hydrogen yield.

As shown in Figure 4 was the effect of porosity on the mole fraction of DME and H₂. The range of porosity changed from 0.2 to 0.8.

Figure 4 shows that the larger the porosity, the higher mole fraction of H₂, and the lower mole fraction of DME, because the increasing porosity decreased the inlet pressure.