Fronts in two-phase porous media flow problems: the effects of hysteresis and dynamic capillarity

Koondanibha Mitra, Tobias Köppl, Hans van Duijn, Iuliu Sorin Pop, Rainer Helmig

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Abstract

In this work, we study the behaviour 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 travelling 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 non-monotone profiles, multiple shocks and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we compare experimental results with our theoretical findings.
Original languageEnglish
JournalStudies in Applied Mathematics
Publication statusAccepted/In press - 30 Jul 2019

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Porous Media Flow
Capillarity
Two-phase Flow
Hysteresis
Porous materials
Saturation
Entropy Solution
Mathematical Analysis
Traveling Wave
Permeability
Shock
Cauchy Problem
Two phase flow
Numerical Results
Entropy
Experimental Results
Approximation
Model

Keywords

  • two-phase flow
  • hysteresis and dynamic capillarity
  • Riemann problem
  • Travelling waves

Cite this

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title = "Fronts in two-phase porous media flow problems: the effects of hysteresis and dynamic capillarity",
abstract = "In this work, we study the behaviour 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 travelling 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 non-monotone profiles, multiple shocks and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we compare experimental results with our theoretical findings.",
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author = "Koondanibha Mitra and Tobias K{\"o}ppl and {van Duijn}, Hans and Pop, {Iuliu Sorin} and Rainer Helmig",
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journal = "Studies in Applied Mathematics",
issn = "0022-2526",
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T1 - Fronts in two-phase porous media flow problems: the effects of hysteresis and dynamic capillarity

AU - Mitra, Koondanibha

AU - Köppl, Tobias

AU - van Duijn, Hans

AU - Pop, Iuliu Sorin

AU - Helmig, Rainer

PY - 2019/7/30

Y1 - 2019/7/30

N2 - In this work, we study the behaviour 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 travelling 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 non-monotone profiles, multiple shocks and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we compare experimental results with our theoretical findings.

AB - In this work, we study the behaviour 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 travelling 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 non-monotone profiles, multiple shocks and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we compare experimental results with our theoretical findings.

KW - two-phase flow

KW - hysteresis and dynamic capillarity

KW - Riemann problem

KW - Travelling waves

M3 - Article

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

ER -