Dynamic effects in capillary pressure-saturations relationships for two-phase flow in 3D porous media: implications of micro-heterogeneities

The capillary pressure–saturation (Pc–S) relationships are essential in characterising two-phase flow behaviour in porous media. However, these relationships are not unique and depend on the flow dynamics, i.e., steady state or dynamic, among other factors. It has been shown that empirical models describing two-phase flow processes in porous media may be inadequate to account fully for the physics of flow in dynamic conditions. New capillary pressure relationships have been proposed which include an additional term to account for the dependence of capillary pressure on saturation and time derivative of saturation (∂S/∂t)(∂S/∂t). This parameter is a capillary damping coefficient, also known as dynamic coefficient (τ)(τ), which establishes the speed at which flow equilibrium is reached. The dependence of Pc–SPc–S relationships on ∂S/∂t∂S/∂t is called dynamic effects. In most laboratory experiments for measuring two-phase flow properties, it is implicitly assumed that the sample is homogeneous. However, this is not the case and micro-heterogeneities with their distinct multiphase flow properties may exist within the domain. They affect the dynamics of the multiple fluid phases and saturation distributions in the domain. These issues have been studied individually but the combination of dynamic effects and micro-scale heterogeneities on the Pc–SPc–S relationships has not been quantified accurately, particularly in 3D domains. Consequently, there are significant uncertainties on the reported values of ττ in the literature. In this work, we have carried out a numerical study to investigate how the presence of micro-scale heterogeneities affects the dynamics of dense non-aqueous phase liquid (DNAPL) and water flow in porous domain. The relative significance of the variations in nature, intensity and distribution of micro-scale heterogeneities on dynamic flow conditions are manifested on Pc–SPc–S curves which are quantified in terms of the dynamic coefficient, ττ. There is a complex interplay of various factors (e.g., dynamic flow conditions, distribution and intensity of micro-heterogeneity, pore size distribution, domain size and geometry and media anisotropy) which affects Pc–SPc–S curves. However, our results show that as the intensity of heterogeneity increases the dynamic coefficient at a given saturation increases, provided all other factors remain the same. The effects of domain shapes (cylindrical vs. rectangle), aspect ratios, dimensionality (2D vs. 3D), permeability anisotropy on ττ are also analysed in order to generalise their effects as far as possible. We envisage that our simulations will minimise some of the inconsistencies on the reported data on ττ in the literature