Abstract
Based on thermodynamic considerations, we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.
Highlights
The simultaneous flow of immiscible fluids through porous media has been studied for a long time (Bear 1988)
Alex.Hansen@ntnu.no Santanu Sinha santanu@csrc.ac.cn Dick Bedeaux Dick.Bedeaux@ntnu.no Signe Kjelstrup Signe.Kjelstrup@ntnu.no 1 PoreLab and Department of Physics, Norwegian University of Science and Technology, 7491 Trondheim, Norway 2 Computational Science Research Center (CSRC), 10 East Xibeiwang Road, Haidian District, Beijing 100193, China 3 PoreLab and Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway scales, the porous medium is treated as a continuum governed by effective equations that encode the physics at the pore scale
In 1940, Leverett combined capillary pressure with the concept of relative permeability, and the framework which dominates all later practical analyses of immiscible multiphase flow in porous media was in place (Leverett 1940)
Summary
The simultaneous flow of immiscible fluids through porous media has been studied for a long time (Bear 1988). It is a problem that lies at the heart of many important geophysical and industrial processes. The length scales in the problem span numerous decades, from the pores measured in micrometers to reservoir scales measured in kilometers.
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