Multiple-relaxation-time lattice Boltzmann simulation for flow, mass transfer, and adsorption in porous media

In this paper, to predict the dynamics behaviors of flow and mass transfer with adsorption phenomena in porous media at the representative elementary volume (REV) scale, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for the convection-diffusion equation is developed to solve the transfer problem with an unsteady source term in porous media. Utilizing the Chapman-Enskog analysis, the modified MRT-LB model can recover the macroscopic governing equations at the REV scale. The coupled MRT-LB model for momentum and mass transfer is validated by comparing with the finite-difference method and the analytical solution. Moreover, using the MRT-LB method coupled with the linear driving force model, the fluid transfer and adsorption behaviors of the carbon dioxide in a porous fixed bed are explored. The breakthrough curve of adsorption from MRT-LB simulation is compared with the experimental data and the finite-element solution, and the transient concentration distributions of the carbon dioxide along the porous fixed bed are elaborated upon in detail. In addition, the MRT-LB simulation results show that the appearance time of the breakthrough point in the breakthrough curve is advanced as the mass transfer resistance in the linear driving force model increases; however, the saturation point is prolonged inversely.

Figure 1

Schematic of relationship between the pore scale and the REV scale.

Figure 2

Schematic of the Poiseuille flow in a 2D porous channel.

Figure 3

Velocity profiles of the Poiseuille flow for different Reynolds and Darcy numbers. (a) $\mathrm{Da}={10}^{-5}$; (b) $\mathrm{Re}=0.1$.

Figure 4

Comparisons between MRT-LB results and analytical solutions of the thermal Poiseuille flow. (a) Temperature; (b) flux $J_x^{*}$; (c) flux $J_y^{*}$.

Figure 5

Comparisons between MRT-LB results and FDM solutions of the thermal Poiseuille flow in 2D porous channel. (a) Temperature; (b) flux $J_x^{*}$.

Figure 6

Comparisons between MRT-LB results and analytical solutions of the mass diffusion with an unsteady state source term. (a) $k_m^{*}=0.72$; (b) $k_m^{*}=7.2$; (c) $k_m^{*}=36$.

Figure 7

Schematic of the transfer and adsorption of carbon dioxide in a porous fixed bed.

Figure 8

Breakthrough curves of adsorption process.

Figure 9

Numerical results of the mole flux distribution and transient concentration along length direction. (a) Mole flux; (b) transient concentration.

Figure 10

Effect of LDF mass transfer coefficient on breakthrough curves.