Fronts in two‐phase porous media flow problems: The effects of hysteresis and dynamic capillarity. Issue 4 (2nd March 2020)

• Record Type: Journal Article
• Authors: Mitra, K.; Köppl, T.; Pop, I. S.; van Duijn, C. J.; Helmig, R.
• Is Part Of: Studies in applied mathematics. Volume 144:Issue 4(2020)
• Page Start: 449
• Page End: 492
• Publication Date: 2020-03-02
• Subjects: dynamic capillarity -- hysteresis -- Riemann problem -- traveling waves -- two‐phase flow; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12304
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: 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.