A coupled Lattice Boltzmann approach to simulate gas flow and transport in shale reservoirs with dynamic sorption

Abstract

Gas flow in a shale reservoir is hard to model and simulate as certain complex mechanisms should be included, for example, diffusion and sorption. As a mesoscopic approach, Lattice Boltzmann Methods can capture the flow behavior in both scales: free flow through the conventional pore channels and gas transport with sorption in the tight matrix with very small pores. In this paper, two Lattice Boltzmann (LB) schemes are presented to recover the Navier-Stokes equations and advection diffusion equation respectively, to model the flow and transport in the two scales. The Navier-Stokes type LB scheme is constructed to model the free flow in fractures and conventional pore channels in matrix, and the convection diffusion type LB scheme is constructed to model the transport in tight matrix with very small pores. Chapman-Enskog expansions are derived to show the equivalence of the two LB schemes with the two macroscopic equations. Dynamic sorption is included in the advection diffusion with the dependance of gas concentration and free flow velocities, and the absorbed amount can affect the free flow velocity as well. In our simulation of gas flow and transport in shale reservoirs, the media is generated through two methods, reading a realistic media image and generating using a pore-network model. The rock characteristics are preserved in our generated porous media, with the method we proposed to link the LB scheme with the pore network modeling method. The simulation results are reasonable to prove that our schemes are robust and efficient, and the effect of porosity and sorption parameters are presented. Furthermore, the interaction of the two-scale gas flow and transport is analyzed, and we show that the increasing adsorbed gas amount in matrix may not slow down the free flow velocity as this increase may be resulted from changes in the rock characteristics. The scheme is simple to understand and implement, because only a few modifications are needed to construct the LB schemes on the two scales.