Boundary effects on the Soil Water Characteristic Curves obtained from lattice Boltzmann simulations

Pore-scale simulations using a Lattice Boltzmann Method (LBM)-based numerical model were conducted to examine how the capillary pressure (Pc) and saturation (S) evolve within a virtual porous medium subjected to drainage and imbibition cycles. The results show the presence of a sharp front (interface separating the wetting and non-wetting fluids) across the cell during the test, which expectably moves up and down as the controlling non-wetting fluid pressure at the upper boundary varies to simulate different Pc levels over the drainage and imbibition cycle. This phenomenon, representing inhomogeneity at the simulated scale, is in conflict with the homogenization applied to the pressure cell for deriving the constitutive Pc-S relationship. Different boundary conditions, adopted to achieve more homogeneous states in the virtual soil, resulted in different Pc-S curves. No unique relationship between Pc and S, even with the interfacial area (Anw) included, could be found. This study shows dependence of the LBM-predicted Pc-S relation on the chosen boundary conditions. This effect should be taken into account in future numerical studies of multiphase flow within porous media.