Dynamic Effects in Two-Phase Flow in Porous Media: Inclusion of 3D and Microscale Heterogeneity Effects

To quantify nonaqueous phase liquids (NAPLs) transport in the subsurface, one requires a correct description of multiphase flow behaviour. This involves the determination of various fluid and porous media parameters and, the constitutive relationships among capillary pressure (Pc), fluid phase saturation (S) and relative permeability (Kr). The determination of Pc-S-Kr relationships is particularly difficult because of two effects: (i) presence of heterogeneities in the flow domain and (ii) dynamic effects in Pc-S-Kr relationships (see below for definition). While the significance of individual factor has been studied at various scales using different approaches, the combination of the two effects on Pc- S-Kr relationships are not well characterised at any scale of observation. Micro-scale heterogeneities in porous media occur at length scales below those of typical laboratory measurement devices (core scale). These micro-heterogeneities play a significant role in laboratory determination of Pc-S-Kr relationships. The dependence of the Pc-S-Kr relationships on the rate of change of saturation is known as the dynamic effect. Obviously, the dynamic effect stems from the fact that the time duration necessary for obtaining equilibrium flow conditions may be long (e.g., many days to weeks at laboratory conditions) depending on soil and fluid properties, scale of observation, degree of saturation, boundary conditions, types of media heterogeneity, if any, etc. One may also argue that since fluids do not necessarily flow under static conditions at shorter time periods, the empirical multiphase models, which assume that Pc is a unique function of fluid saturation, are not sufficient to account for the physics of the flow. Hence, there is an increasing interest in characterising the significance of dynamic effects for multi- phase flow in porous media. Most previous work on this area has assumed simple scenarios ranging from pore scale and bundle of capillary tube model to 2D domain, which may or may not include media heterogeneities. It seems that there is little information on dynamic effects for two-phase flow in 3D domains which include both heterogeneity and gravity effects. In this study, we carry out a systematic analysis of the effects of various flow and media properties on dynamic two-phase flow in 3D core scale domain, which include micro-heterogeneities. A number of factors are considered, e.g., boundary conditions; pore size distribution; permeability anisotropy, variations in nature, amount and distribution of the micro-scale heterogeneity, etc. Their effects on dynamic two-phase flow behaviour are quantified in terms of a capillary damping coefficient, which establishes the speed at which flow equilibrium is reached. Binary combinations of fine sand imbedded in coarse sand are used. Drainage dynamic and static curves for various 3D homogeneous and heterogeneous models have been obtained and compared to determine the relative significance of the heterogeneity patterns and intensity. Values of dynamic coefficient obtained in this work are higher than most previously reported values, but this is plausible considering the fact that we consider both 3D and micro-heterogeneity effects. Simulations have also been conducted to compare dynamic effects in domains of various shapes but of equal volume, namely, cylindrical, 3D rectangle (brick shape) and 2D rectangle. Our results suggest that similar curves may be obtained; however, the dynamic coefficient may be very different from one domain to another. This implies that the dynamics of the flow depend on the shape of domain and Pc-S-Kr relationships obtained for one domain shape may not be used directly for domain of another shape at dynamic conditions. All in all, the results obtained in our study give further evidence that the non- uniqueness in curves are caused by different factors: dynamic effects, applied boundary condition, micro-heterogeneities, pore size distribution, media anisotropy, domain shape and size, to mention just a few. For micro-heterogeneities of the type used in our study, we find that, in general, with the increase in the degree of heterogeneity, dynamic coefficient increases. However, this dependence is not a linear function and depends on a complex interplay of various factors, as mentioned above.