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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:335

Article

Scovazzi, Guglielmo¹  Wheeler, Mary F.²  Mikelic, Andro³  Lee, Sanghyun² 

[1] Duke Univ, Dept Civil & Environm Engn, Room 121 Hudson Hall,POB 90287, Durham, NC 27708 USA

[2] Univ Texas Austin, Inst Computat Engn & Sci, Ctr Subsurface Modeling, Austin, TX 78712 USA

[3] Univ Claude Bernard Lyon 1, Univ Lyon, CNRS UMR 5208, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

关键词: Miscible displacement;    Viscous fingering;    Flow instabilities;    Hele-Shaw;    Variational methods;    Numerical simulation;    Galerkin methods;   

DOI  :  10.1016/j.jcp.2017.01.021

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free