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

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. Ent...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2019-06
Main Authors: Mitra, Koondanibha, Köppl, Tobias, van Duijn, Cornelis Johannes, Iuliu Sorin Pop, Helmig, Rainer
Format: Article
Language:English
Subjects:
Capillarity
Capillary pressure
Capillary waves
Economic models
Hysteresis models
Pressure effects
Saturation
Traveling waves
Two phase flow
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422