Novel Mathematical Approaches for Multiscale Modelling of Three-Phase Porous Media Flow

Our research explores the feasibility of novel mathematical approaches for multiscale modelling of three-phase (i.e. oil, gas, water) porous media flow, thereby crossing traditional boundaries between petroleum engineering, physics, and applied mathematics. A key aim is to investigate if a suitable alternative to three-phase Darcy's law can be developed in such a way that it can be solved in the mathematically robust and efficient manner that is required for successful use in daily engineering applications. An alternative is required because Darcy's law for three-phase flow is intrinsically not valid in certain flow regimes, that is when one or more phases move as discontinuous blobs and ganglia. Yet it is exactly this situation that is of most interest to engineering, for example when predicting the migration of residual oil in a depleted hydrocarbon reservoir.

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