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


Journal Article

© 2017 Elsevier Inc. The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, 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.

Full Text

Duke Authors

Cited Authors

  • Scovazzi, G; Wheeler, MF; Mikelić, A; Lee, S

Published Date

  • April 15, 2017

Published In

Volume / Issue

  • 335 /

Start / End Page

  • 444 - 496

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/

Citation Source

  • Scopus