Asymptotic regimes in unstable miscible displacements in random porous media

We study two asymptotic regimes of unstable miscible displacements in porous media, in the two limits, where a permeability-modified aspect ratio, R L = L/ H( k v/ k h) 1/2, becomes large or small, respectively. The first limit is known as transverse (or vertical) equilibrium, the second leads to th...

Full description

Saved in:
Bibliographic Details
Published in:Advances in water resources 2002-08, Vol.25 (8), p.885-898
Main Authors: Yang, Z.M., Yortsos, Y.C., Salin, Dominique
Format: Article
Language:English
Subjects:
Earth sciences
Earth, ocean, space
Exact sciences and technology
Hydrogeology
Hydrology. Hydrogeology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study two asymptotic regimes of unstable miscible displacements in porous media, in the two limits, where a permeability-modified aspect ratio, R L = L/ H( k v/ k h) 1/2, becomes large or small, respectively. The first limit is known as transverse (or vertical) equilibrium, the second leads to the problem of non-communicating layers (the Dykstra–Parsons problem). In either case, the problem reduces to the solution of a single integro-differential equation. Although at opposite limits of the parameter R L , the two regimes coincide in the case of equal viscosities, M=1. By comparison with high-resolution simulation we investigate the validity of these two approximations. The evolution of transverse averages, particularly under viscous fingering conditions, depends on R L . We investigate the development of a model to describe viscous fingering in weakly heterogeneous porous media under transverse equilibrium conditions, and compare with the various existing empirical models (such as the Koval, Todd–Longstaff and Fayers models).
ISSN:0309-1708
1872-9657
DOI:10.1016/S0309-1708(02)00043-X