Comparing Equations for Two-Phase Fluid Flow in Porous Media

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.

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