Premium
Fronts in two‐phase porous media flow problems: The effects of hysteresis and dynamic capillarity
Author(s) -
Mitra K.,
Köppl T.,
Pop I. S.,
van Duijn C. J.,
Helmig R.
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12304
Subject(s) - hysteresis , porous medium , saturation (graph theory) , context (archaeology) , capillary action , mechanics , homogeneous , flow (mathematics) , capillary pressure , porosity , mathematics , statistical physics , physics , thermodynamics , geotechnical engineering , geology , condensed matter physics , paleontology , combinatorics
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.