Abstract
It is well known that multiphase flow in porous media exhibits hysteresis. This is typically modeled by modifying the saturation dependence of the relative permeabilities. In this paper, a model for hysteretic relative permeabilities is built into the polymer flooding model and the analytical solution to the corresponding Riemann problem is constructed. This produces a nonstrictly hyperbolic system of conservation laws with a history-dependent flux function. Because the polymer model without hysteresis possesses Riemann problem solutions that are not monotonic, the introduction of hysteresis necessarily produces structurally different solutions. We show that hysteresis produces more complicated solutions with more fronts and expansions; and removes some nonuniqueness of solutions.
| Original language | English |
|---|---|
| Pages (from-to) | 205-233 |
| Number of pages | 29 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 206 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Feb 1997 |
Bibliographical note
Funding Information:I thank Professor John Trangenstein for his help and guidance in this research. His invaluable advice, direction, and encouragement are greatly appreciated. I also thank Dr. Richard Hornung for his useful comments. The author is grateful for the financial support provided by King Fahd University of Petroleum and Minerals.
ASJC Scopus subject areas
- Analysis
- Applied Mathematics