Numerical modelling of multiphase flow in porous media

Abstract

The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation often offers the only viable approach to the mathematical modeling of multiphase flows. This paper provides an overview of the types of models that are used in this field and highlights -some of the numerical techniques that have appeared recently. The exposition includes discussions of multiphase, multispecies flows in which chemical transport and interphase mass transfers play important roles. The paper also examines some of the outstanding physical and mathematical problems in multiphase flow simulation. The scope of the paper is limited to isothermal flows in natural porous media; however, many of the special techniques and difficulties discussed also arise in artificial porous media and multiphase flows with thermal effects.

Sessile droplet spread into porous substrates—Determination of capillary pressure using a continuum approach

“…Therefore, the governing equations need to account for the presence of all phases [17][18][19]. In these equations, two additional transport parameters are present-relative permeability and a capillary pressure function that includes the interaction parameters between phases [20].…”

Application of Smoothed Particle Hydrodynamics (SPH) to Flow Simulations in Oil Reservoir Rocks

“…[18][19][20] For chemically reacting fluid phases, terms accounting for the interfacial transfer rate of mass I α and momentum α M must be added as sources on the right-side of Equations (1) and (2), respectively. 7 On the other hand, if heat transfer effects are important, Equations (1) and (2) must be complemented with a transport equation for the internal energy or enthalpy. However, a simplification of the above model can be obtained in the framework of continuum mixture theory.…”

“…[2][3][4][5][6] Numerical models aimed at solving oil extraction problems involve mainly the solution of the nonlinear fluid equations for multiphase and multicomponent flows through a heterogeneous medium (porous rock). 3,[7][8][9] When describing the flow at a microscopic level (or pore scale), the Navier-Stokes equations coupled to the mass conservation law for multiphase flow must be solved, while at a macroscopic level Darcy´s law is employed in place of the Navier-Stokes equations to describe the flow behavior. At the microscopic scale, the fluid motion is mainly controlled by the effects of interfacial tension, viscosity, and capillary pressures.…”

Compositional simulation of groundwater contamination by organic compounds: 1. Model development and verification

“…In order to ensure convergence of a finite d•erence solution to the co•ect saturation or concentration distribution, sufficient dissipation, either physical or numefic•, must be present to satisfy the entropy (E) condition [Allen, 1985]. …”