The Interface Conditions for Pressures at Oil-water Flood Front in the Porous Media Considering Capillary Pressure

TL;DR

This paper investigates the interface conditions at the flood front in oil-water flow within porous media, proposing a new model (JPVCM) that accounts for pressure and velocity jumps, improving upon conventional assumptions.

Contribution

It introduces the Jump Pressures and Velocities Conditions Model (JPVCM), which accounts for discontinuities at the flood front, challenging the traditional continuous pressure and velocity assumptions.

Findings

JPVCM better explains pressure and velocity discontinuities at flood fronts.

Theoretical proof that total Darcy velocity and pressure are continuous, not individual phase velocities.

Application examples demonstrate JPVCM's improved accuracy over conventional models.

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 CPVCM). This paper has inspected it via the studying the water-oil displacement in one dimensional reservoir with considering capillary pressure but ignoring the compressibility and gravity. It is proved theoretically that the total Darcy velocity and total pressure (defined by Antoncev etc.), instead of the Darcy velocities and pressures of water and oil, are continuous at the flood front without considering the compressibility of fluid and porous media. After that, new interface conditions for the pressures and Darcy velocity of each fluid are established, which are collectively named as Jump Pressures and Velocities Conditions Model (JPVCM) because the model has shown the jump pressures and jump Darcy velocities at the flood front. Finally, three application-examples are proposed and the results show JPVCM is more reasonable than CPVCM. Keywords: Flood front; Jump Condition; Two phase; numerical flux; mathematical model