Accounting for viscous instability in reservoir simulation of heavy oil displacement

The subject of the study is viscous instability (viscous fingering) of the displacement front that arises under an unfavorable mobility ratio during waterflooding of heavy oil reservoirs, and the ways to account for it in reservoir simulation. The aim of the work is a quantitative assessment of the reproduction of viscous instability on computational grids of different resolution, identification of the limitations of numerical formulations, and substantiation of the concept of coarse-grid accounting through calibrated pseudo-displacement parameters. The open-source simulator porousMultiphaseFoam (PMF), built on the OpenFOAM platform, was used as the reference tool; an industrial (commercial) reservoir simulator was used for comparison. Two series of numerical experiments were performed: a direct comparison of the two simulators on an identical heavy-oil displacement problem, and a study of the influence of the grid block size in PMF under an unchanged physical formulation. The comparison was carried out by water-saturation fields and integral production indicators – oil and water production dynamics, water cut, and the oil recovery factor. It was found that a continuum two-phase formulation in a homogeneous medium without an explicit source of perturbations does not initiate fingering, while the inherent numerical diffusion of finite-volume schemes suppresses viscous fingers; with sufficient grid refinement the instability appears and substantially reduces the predicted oil recovery factor. The results justify the need to construct pseudo-displacement parameters for full-field models. The results are applicable in the design of waterflooding systems and enhanced oil recovery methods at heavy-oil fields.

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