Comparing Equations for Two-Phase Fluid Flow in Porous Media
Tore I. Bjørnarå*,1 and Eyvind Aker1
1NGI, Norway
*Corresponding author: NGI, Pb. 3930 Ullevål Stadion, NO-0806 Oslo, Norway, tore.ingvald.bjornara@ngi.no
Abstract: Various types of equation system
formulations for modelling two-phase flow in
porous media using the finite element method
have been investigated. The system of equations
consists of mass balances, partial differential
equations (PDE) that describe the accumulation,
transport and injection/production of the phases
in the model. In addition, several auxiliary
equations (eg. hydraulic properties) apply to the
system, coupling the different phases in the
system together. This set of equations, PDEs and
auxiliary
equations,
allows
for
equation
manipulation such that the main differences
between the formulations are the dependent
variables that are solved for. Here we have tested
five different formulations for 2D simulations
and one for 1D; the Buckley-Leverett equation.
The various formulations are compared with
regards
to
numerical
performances
like
robustness (numerical stability) and solving time.
The purpose of the investigation is to identify a
preferred formulation that will be best suited for
more complicated modelling, by for instance
taking
into account poroelasticity, energy
balance, chemical reactions, dissolution of the
phases, etc. The tests performed strongly suggest
that the fractional flow formulation is the fastest
and most robust formulation.
Keywords: Two-phase flow, porous media,
finite element method
1. Introduction
Multi-phase flow, like two-phase flow, is
often strongly convection-dominated (as opposed
to diffusive flow). Pure convective transport is
discontinuous, convection-dominated flow exert
some diffusion, but still has a very sharp front of
the intruding phase that needs to be numerically
resolved and therefore can be very difficult,
sometimes even impossible, to solve with the
finite element method.