Interface Condition for the Darcy Velocity at the Water-oil Flood Front in the Porous Medium

TL;DR

This paper challenges the conventional continuity of Darcy velocity at water-oil flood fronts in porous media, proposing a new jump velocity condition model (JVCM) that aligns better with theoretical and numerical results.

Contribution

It introduces the Jump Velocity Condition Model (JVCM), a novel interface condition derived from fundamental equations, improving upon the traditional continuous velocity assumption.

Findings

JVCM aligns closely with exact solutions and numerical simulations.

Disproved the continuity of fluid velocities at the flood front.

CVCM leads to impractical results such as halted flood front movement.

Abstract

Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump interface is expressed as the continuous Darcy velocity and fluid pressure (named CVCM ). Our study has inspected this conclusions. First, it is revealed that the principle of mass conservation has no direct relation to the velocity conservation, and the former is not the true foundation of the later, because the former only reflects the kinetic characteristic of the fluid particles at one position(the interface), but not the neighborhood of the interface which required by the later. Then the reasonableness of CVCM is queried from the following three aspects:(1)Using Mukat's two phase seepage equation and the mathematical method of apagoge, we have disproved the continuity of each fluid velocity;(2)Since the analytical solution of the equation of Buckley-Leveret equations is acquirable, its velocity jumps at the flood front presents an appropriate example to disprove the CVCM;(3) The numerical simulation model gives impractical result that flood front would stop moving if CVCM were used to calculate the velocities at the interface between two gridcells. Subsequently, a new one, termed as Jump Velocity Condition Model (JVCM), is deduced from Muskat's two phase seepage equations and Darcy's law without taking account of the capillary force and compressibility of rocks and fluids. Finally, several cases are presented. And the comparisons of the velocity, pressure difference and the front position, which are given by JVCM, CVCM and SPU, have shown that the result of JVCM is the closest to the exact solution.