Lattice Boltzmann simulations of wetting and its application to disproportionate permeability reducing gel

The binary fluid lattice Boltzmann method is a promising numerical scheme to simulate the flow of two immiscible fluids at the pore level. In particular, the method minimizes an appropriate free energy functional thus ensuring a thermodynamically consistent behaviour in equilibrium. We present an extension of this method, such that walls with different wettability can be included. This is done by adding a “background chemical potential” to the fluid chemical potential. A calibration of the wettability is given, showing how the equilibrium contact angle depends on the background chemical potential. Next, the method is used in a qualitative study of gel-placement in a fractional-wet porous medium model. The presence of gel shows to reduce the water permeability more than the oil permeability. Thus, the wanted disproportionate permeability reduction (DPR) effect applies.