Hysteresis and Horizontal Redistribution in Porous Media

Abstract

It is well known that multiphase flow in porous media exhibits hysteretic behaviour. This is caused by different fluid-fluid behaviour if the flux reverses. For example, for flow of water in unsaturated soils the process of imbibition and drainage behaves differently. In this paper we study a new model for hysteresis that extends the current playtype hysteresis model in which the scanning curves between drainage and imbibition are vertical. In our approach the scanning curves are non-vertical and can be constructed to approximate experimentally observed scanning curves. Furthermore our approach does not require any book-keeping when the flux reverses at some point in space. Specifically, we consider the problem of horizontal redistribution to illustrate the strength of the new model. We show that all cases of redistribution can be handled, including the unconventional flow cases. For an infinite column, our analysis involves a self-similar transformation of the equations. We also present a numerical approach (L-scheme) for the partial differential equations in a finite domain to recover all redistribution cases of the infinite column provided time is not too large.

Fronts in two‐phase porous media flow problems: The effects of hysteresis and dynamic capillarity

“…8, 9, 11, 12, 27. It has a physical basis 4,28 and it can be extended to depict the realistic cases accurately 24 . A similar hysteretic behavior is observed for the relative permeabilities too, although to a lesser extent.…”

“…An extension describing nonvertical scanning curves is discussed in Ref. 24 and chapters 3,11 of Ref. 27.…”

“…A comprehensive study of these models can be found in Ref. 24. Using thermodynamically constrained averaging theory (TCAT), 25,26 one can eliminate hysteresis in capillary pressure altogether by introducing interfacial area and Euler characteristics as additional unknowns.…”

“…Thus, their analysis is beyond the scope of the present work. In this paper, we will use the play‐type hysteresis model 4,24 that approximates scanning curves as constant saturation lines. Such models are generally implemented in classical porous media simulators.…”

Wetting fronts in unsaturated porous media: The combined case of hysteresis and dynamic capillary pressure

“…In this paper we consider, in addition to (1.4), an extension of play-type hysteresis by introducing non-vertical scanning curves. It is achieved by adapting (1.4) in the following way (for small ε > 0) Such an extension was proposed in [6] and similar models were studied in [1,17]. In [6] it is shown that the model is consistent if ε satisfies certain upper bounds.…”