From local measurements to an upscaled capillary pressure-saturation curve

Capillary pressure–saturation relationship plays an important role in the description of two-phase flow in porous media. Commonly, this relationship is determined in laboratory on a sample of few centimeters and it is then used in numerical modeling of two-phase in domain sizes of hundreds to thousands of meters. The correctness of such approach has been hardly ever questioned. In this study, an upscaled capillary pressure is determined from local pressure and saturation measurements employing a rigorous averaging procedure. Drainage and imbibition experiments were performed in a column of 21 cm long. The experiments were performed as a series of equilibrium steps; each time we changed the boundary pressures incrementally and then waited until an equilibrium distribution of fluids was reached. Phase pressures and saturation inside the column as well as external pressure and average saturation were recorded at each equilibrium step. Various averaging operators were considered: simple average, simple phase-average, intrinsic phase-average, and centroid-corrected average. Also, a potential-based average operator was introduced as reference curve to establish which operator gives the correct average pressure. Large differences were found for the average non-wetting phase pressure using different operators during primary drainage. However, when both phases were present throughout the domain (e.g. during main drainage) the differences between pressures obtained by various average operators were negligible. In such cases, the centroids of the two phases and the centroid of the averaging domain were close to each other. The comparison between averaged capillary pressure–saturation curves has shown that the centroid-corrected averaging operator is the most appropriate operator.