Relative permeability studies of tube bundle models and unconsolidated porous media

This work is a report on fundamental research on immiscible two-phase flow in porous media; the flow of water and oil in computerized tube bundle models, and in laboratory-scale granular media packings, are considered. The displacement of oil from a porous medium due to flow of an injected water phase is examined; the boundary condition imposed on each system considered was a constant pressure drop across the porous medium. The flow is considered unsteady until no further change in the saturation of water in the medium takes place; this constitutes an oil displacement process, or a water-flood. Two types of porous media are considered in this work: (a) bundles of tubes, which constitute ideal forms of porous media, and (b) packings of granular media such as dry silica sand or glass beads. Two types of tube bundle models are developed: the bundle of parallel tubes consisting of various diameter tubes, and the bundle of serial tubes whose diameters randomly change at prescribed intervals along the direction of flow. The fluid dynamics of two-phase flow in the tube bundle models were calculated from the developed equations that account for the movement of the water/oil interfaces in the tubes over time, from a state of full oil saturation to a state of full water saturation. Local fluid pressures and flow rates were determined over time and their macroscopic quantities calculated and used to obtain relative permeabilities as functions of water saturation. The relative permeabilities were obtained by a standard technique that relies on the production data of oil and water over time; the relative permeabilities were also calculated directly using the phase-specific form of Darcy's law. Results from the two methods are compared and weaknesses in the standard theory of two-phase flow are discussed. The estimated relative permeabilities using the standard method of Johnson, Bossler and Naumann from 1959 exhibited a strong dependence on the viscosity of oil. The concept of a macroscopic capillary pressure is also presented and discussed using the results of the directly-calculated quantities and the standard semi-stable drainage capillary pressure curves.; Data are reported from an extensive set of laboratory experiments that were conducted using vertical packings of silica sand or glass beads. (Abstract shortened by UMI.)...