Hysteresis models and gravity fingering in porous media

Rätz, Andreas; Schweizer, Ben

doi:10.1002/zamm.201200052

Cited by 27 publications

(32 citation statements)

References 19 publications

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“…Such regularisation has been used in [39,42] for proving the existence of weak solutions to such models, and for developing appropriate numerical schemes. It is an intriguing question whether this approach is motivated physically, and in particular how the parameter ε can be interpreted from physical point of view.…”

Section: Scaling and Assumptionsmentioning

confidence: 99%

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

Duijn

Mitra

Pop

2018

Nonlinear Analysis: Real World Applications

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The Richards equation is a mathematical model for the unsaturated flow through porous media. This paper considers an extension of the Richards equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the saturation. The focus is on travelling wave solutions, for which the existence is investigated first for the model including hysteresis and subsequently for model including dynamic capillarity effect. In particular, such solutions may have non monotonic profiles, which are ruled out when considering standard, equilibrium type models, but have been observed experimentally. The paper ends with numerical experiments confirming the theoretical results. In this sense the original system of partial differential equations is solved by means of an implicit scheme. This relies on an equivalent, mixed formulation of the system. For solving the resulting nonlinear, time-discrete problems, a linear iterative scheme is proposed.

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Section: Scaling and Assumptionsmentioning

confidence: 99%

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

Duijn

Mitra

Pop

2018

Nonlinear Analysis: Real World Applications

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“…[] analyzed flows where the displaced fluid has viscosity; and determined how the overshoot saturation S K is related to

S_{J}, S_{I}

, and the dynamic parameter. Since relaxation models predict oscillations, hysteresis was included in these model calculations by Rätz and Schweizer [].…”

Section: Saturation Overshoot Paradigmmentioning

confidence: 99%

“…[], Chapwanya and Stockie [], Kissling et al . [], and Rätz and Schweizer [] have also produced physical looking fingering displacements using the dynamic extensions with the latter including hysteresis.…”

Section: Saturation Overshoot Paradigmmentioning

confidence: 99%

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

DiCarlo

2013

Water Resources Research

112

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Gravity‐driven multiphase flow in porous media is ubiquitous in the geophysical world; the classic case in hydrology is vertical infiltration of precipitation into a soil. For homogenous porous media, infiltrations are sometimes observed to be stable and laterally uniform, but other times are observed to be unstable and produce preferential flow paths. Since Saffman and Taylor (1958), researchers have attempted to define criteria that determine instability. Saffman and Taylor's analysis consisted of two regions of single phase flow, while Parlange and Hill (1976) integrated this analysis with the multiphase flow equations to provide testable predictions. In the subsequent 40 years, great advances have been made determining the complex interactions between multiphase flow and instability. Theoretically, the stability of the standard multiphase flow equations has been verified, showing the necessity of extensions to the multiphase flow equations to describe the observed unstable flow. Experimentally, it has been shown that the instability is related to a phenomena in 1‐D infiltrations called saturation or pressure overshoot. In this review, the connection between overshoot and instability is detailed, and it is described how models of overshoot can simplify the analysis of current and future models of instability and multiphase flow.

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“…Well‐posedness results for play‐type hysteresis model are found in Refs. 8, 9, 11, 12, 27. It has a physical basis 4,28 and it can be extended to depict the realistic cases accurately 24 .…”

Section: Introductionmentioning

confidence: 99%

“…39. Since then the dynamic capillary term has been measured experimentally 40,41 and it was used successfully to explain overshoots 9,11,12,42‐45 . Also the well‐posedness of the dynamic capillarity model has been proved 46‐49 and numerical methods have been investigated 50‐54 …”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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In this work, we study the behavior of saturation fronts for two-phase flow through a long homogeneous porous column . In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the permeabilities. The analysis uses traveling wave approximation. Entropy solutions are derived for Riemann problems that are arising in this context. These solutions belong to a much broader class compared to the standard Oleinik solutions, where hysteresis and dynamic effects are neglected. The relevant cases are examined and the corresponding solutions are categorized. They include nonmonotone profiles, multiple shocks, and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we discuss the implication of our findings in the context of available experimental results.

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Hysteresis models and gravity fingering in porous media

Cited by 27 publications

References 19 publications

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

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

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