Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Guglielmo Scovazzi (1) , Mary Wheeler (2) , Andro Mikelic (3) , Sanghyun Lee (2)

1 Department of Civil and Environmental Engineering, Duke University
2 ICES - Institute for Computational Engineering and Sciences [Austin]
3 MMCS - Modélisation mathématique, calcul scientifique

The miscible displacement of one fluid by another in a porous medium has received considerable attention in sub-surface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns-referred to as viscous fingering-may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods.

Mots clés: flow instabilities; Hele-Shaw; viscous fingering; Galerkin methods; variational methods; numerical simulation; Miscible displacement

Domaines: Equations aux dérivées partielles [math.AP]

Guglielmo Scovazzi, Mary Wheeler, Andro Mikelic, Sanghyun Lee. Analytical and variational numerical methods for unstable miscible displacement flows in porous media. Journal of Computational Physics, 2017, 335, pp.444--496. ⟨10.1016/j.jcp.2017.01.021⟩. ⟨hal-01380352⟩