A numerical study of two-phase miscible flow through porous media with a Lagrangian model

TL;DR

This paper develops a Lagrangian numerical model to simulate two-phase miscible flow in porous media, highlighting the effects of pressure drag and skin friction on solvent dispersion, with implications for enhanced oil recovery.

Contribution

It extends a streamline-based Lagrangian approach to accurately model dispersion and diffusion in miscible flows, accounting for nonlinear effects of pressure drag and skin friction.

Findings

Numerical results agree with asymptotic analysis.

Darcy's method fails to capture nonlinear effects when skin friction dominates.

Mass conservation is validated and useful for oil recovery optimization.

Abstract

The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To simulate such flows, volume averaging spatial operators are considered to incorporate pressure drag and skin friction experienced by a porous medium. In this work, a streamline-based Lagrangian methodology is extended for an efficient numerical approach to handle dispersion and diffusion of solvent saturation during a miscible flow. Overall pressure drag on the diffusion and dispersion of solvent saturation is investigated. Numerical results show excellent agreement with the results obtained from asymptotic analysis. The present numerical simulations indicate that the nonlinear effects due to skin friction and pressure drag cannot be accurately captured by Darcy's method if the contribution of the skin friction dominates over that of the pressure drag. Moreover, mass conservation law is investigated, which is an important feature for enhanced oil recovery, and the results help to guide a good agreement with theory. This investigation examines how the flow regime may be optimized for enhanced oil recovery methods.