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Dynamic capillary effects in heterogeneous porous media. (English) Zbl 1123.76065
Summary: In standard multi-phase flow models of porous media, a capillary pressure saturation relationship developed under static conditions is assumed. Recent experiments have shown that this static relationship cannot explain dynamic effects as seen for example in outflow experiments. In this paper, we use a static capillary pressure model and a dynamic capillary pressure model based on the concept of S. Hassanizadeh and W. G. Gray [Adv. Water Res. 13, No. 4, 169–186 (1990)] and examine the behavior with respect to material interfaces. We introduce a new numerical scheme for the one-dimensional case using a Lagrange multiplier approach and develop a suitable interface condition. The behavior at the interface is discussed and verified by various numerical simulations.

76S05 Flows in porous media; filtration; seepage
76D45 Capillarity (surface tension) for incompressible viscous fluids
76M12 Finite volume methods applied to problems in fluid mechanics
Full Text: DOI
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