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

Koondanibha Mitra (Corresponding author), Tobias Köppl, Hans van Duijn, Iuliu Sorin Pop, Rainer Helmig

Research output: Contribution to journalArticleAcademic

11 Citations (Scopus)
148 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)449-492
Number of pages44
JournalStudies in Applied Mathematics
Issue number4
Publication statusPublished - May 2020


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


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