Study of pore level displacement mechanisms through arbitrary triangular tubes

Modeling three-phase flows through porous media is of great importance in the improved oil recovery processes. In order to predict the three-phase relative permeabilities and capillary pressure functions in regions of the reservoir where water, oil, and gas flow simultaneously, a proper understanding of the basic three-phase displacement mechanisms and multiphase flow physics is required. There are numerous models dealing with multiphase flow in porous media, but not many of them include all necessary fundamental phenomena and physics, which may lead a less reflective result.;This thesis systematically investigates the pore level displacement mechanisms occurring in multiphase flow through arbitrary triangular tubes. These mechanisms can be incorporated into pore-scale modeling of multiphase flow. The thesis shows the advantages in using an arbitrary triangular tube for modeling a porous medium. Slow viscous flow through arbitrary triangular tubes is studied theoretically and numerically. The average velocity of viscous flow through an arbitrary triangular tube can be readily calculated. A wide range of variation in porosity and permeability with a fixed pore size distribution is possible by using various combinations of three types of triangular tubes. Analytical expressions for the normalized threshold curvatures and the wetting phase saturations in two-phase displacement in arbitrary triangular tubes are derived. Comparison of the results for triangular tubes with different triangular shapes of the same shape factor shows, for the first time, that geometrically different triangles have the same capillary behaviour even though they may have different numbers of corners occupied by the wetting phase. In order to elucidate how the oil in the three-phase system is mobilized, oil spreading in a three-phase system in both a capillary corner and an arbitrary triangular tube is studied. The calculations are based on the method proposed by Dong et al. (1995). The critical minimal oil saturation and the critical maximal water saturation controlling the oil spreading process in a three-phase system in an arbitrary triangle are derived analytically. It is first found that geometrically different triangles having with the same shape factor have the same minimal oil saturation and maximal water saturation for all contact angles (gas/water, gas/oil, oil/water) for the three-phase system. To apply the pore level mechanisms developed, a triangular bundle model made by connecting triangular tubes in series is proposed. The critical size ratio of neighbouring tubes controlling the phenomena of snap off is derived, and the critical size ratio of the neighbouring segments is 1.59 for perfect wetting conditions if only the equilateral triangular shape is utilized. Snap off will only take place if the ratio is larger than or equal to the critical value. The critical size ratio will be smaller for the irregular shape and the snap off will take place more easily when irregular triangular tubes are utilized. The snap off and oil break up phenomena can be simulated, and the mechanisms of these phenomena are given.