Dynamic Capillary Pressure Curve for Water/Oil Displacement in Porous Media: Theory vs. Experiment

Abstract The dependence of the capillary pressure on the flow rate, for two-phase flow in porous media, has been theoretically and experimentally investigated. A theoretical dynamic expression for the capillary pressure has been derived which involves a dynamic term which is proportional to the time derivative of the saturation. A series of waterfloods have been performed at different flow rates. While flowing the cores, capillary pressure and saturations have been locally measured. Capillary pressure has been found to depend on the flow rate as theoretically predicted: it increases with the flow rate and its derivative with respect to saturation mostly decreases when the flow rate is increased. The dynamic term is interpreted as the contribution of the viscous forces to the pressure drops. A strong impact of this dynamic expression on two-phase flow modelling and calculation of relative permeabilities has been found. Introduction The standard framework used to model two-phase flow in porous media relies on the notion of relative permeabilities and capillary pressure. Relative permeabilities reflect the viscous effects, while capillary pressure incorporates the capillary effects. These flow parameters are assumed to depend only on saturation. Relative permeabilities have been introduced to generalize the Darcy law. These flow parameters express the fact that one phase reduces the flow paths accessible to the other phase. The apparent permeability to this second phase is thus lowered due to the presence of the first phase. Therefore, relative permeabilities are known to be less than unity and dependent on saturation. The notion of capillary pressure originates from the generalization of the Laplace law. When an oil/water meniscus separates two phases, oil and water, and is positionned in a capillary tube of radius R, the difference in pressures, Pc, across the meniscus, i.e. the capillary pressure, will be proportional to the meniscus curvature C: Pc = C. This curvature is known to be equal to 2cos /R, where is the contact angle between the meniscus and the solid surface. The coefficient of proportionality is the interfacial tension. Assuming that a non-wetting phase displaces a wetting phase and that a porous medium can be seen as a set of capillary tubes, for a given capillary pressure level, the menisci will be located at the entry of capillary tubes with a radius equal to 2y cos / Pc. The set of accessible tubes is related thus to a given saturation. This is why the capillary pressure Pc is assumed to be a function of saturation. This function is then used to interpret two-phase flow in porous media though the Laplace law is valid only under static conditions. P. 491^