Effects of Micro-Heterogeneities on Laboratory-Scale Pc-Kr-S Relationships

Commonly, capillary pressure-saturation-relative permeability (Pc-S-Kr) relationships are obtained by means of laboratory experiments carried out on soil samples that are up to 10-12 cm long. In obtaining these relationships, it is implicitly assumed that the soil sample is homogeneous. However, it is well known that even at such scales, some micro-heterogeneities may exist. These heterogeneous regions will have distinct multiphase flow properties and will affect the saturation and distribution of wetting and non-wetting phases within the soil sample. This, in turn, may affect the measured two-phase flow relationships. In the present work, numerical simulations have been carried out to investigate how the variations in type, quantity, and distribution of sub-sample scale heterogeneities affect Pc-S-Kr relationships for dense non-aqueous phase liquid (DNAPL) and water flow. Fourteen combinations of sand types and heterogeneous patterns have been defined. These include binary combinations of coarse sand imbedded in fine sand and vice versa. The domain size is chosen such that it represents typical laboratory samples used in the measurements of Pc-S-Kr curves. Upscaled drainage and imbibition Pc-S-Kr relationships for various heterogeneity patterns have been obtained and compared in order to determine the relative significance of the heterogeneity patterns. The results show that for micro-heterogeneities of the type used in this work, the upscaled Pc-S curve mainly follows the corresponding curve for the background sand. Irreducible water saturation (in drainage) and residual DNAPL saturation (in imbibition) are affected by the presence and intensity of heterogeneities.