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Growth of fingers at an unstable diffusing interface in a porous medium or hele-shaw cell

Journal Article:

Abstract

Waves at an unstable horizontal interface, between 2 fluids moving vertically through a saturated porous medium, are observed to grow rapidly to become fingers (i.e., the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approx. as (time)U2D, followed by a transition to a growth proportional to time. Correspondingly, the mean wave number decreases approx. as (time)U-1/2D. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an open set, but closure is achieved by assuming a law for the mean wave number based on similarity. (22 refs.)
Authors:
Publication Date:
Nov 27, 1969
Product Type:
Journal Article
Reference Number:
EDB-82-087687
Resource Relation:
Journal Name: J. Fluid Mech.; (United Kingdom); Journal Volume: 39
Subject:
02 PETROLEUM; POROUS MATERIALS; FLUID FLOW; DARCY LAW; DIFFUSION; EFFICIENCY; ENGINEERING; FLOW RATE; MATHEMATICS; NUMERICAL ANALYSIS; OIL WELLS; PETROLEUM; RESERVOIR ENGINEERING; WATERFLOODING; ENERGY SOURCES; FLUID INJECTION; FOSSIL FUELS; FUELS; MATERIALS; WELLS; 020300* - Petroleum- Drilling & Production
OSTI ID:
5666088
Country of Origin:
United Kingdom
Language:
English
Other Identifying Numbers:
Journal ID: CODEN: JFLSA
Submitting Site:
HEDB
Size:
Pages: 477-495
Announcement Date:

Journal Article:

Citation Formats

Wooding, R A. Growth of fingers at an unstable diffusing interface in a porous medium or hele-shaw cell. United Kingdom: N. p., 1969. Web.
Wooding, R A. Growth of fingers at an unstable diffusing interface in a porous medium or hele-shaw cell. United Kingdom.
Wooding, R A. 1969. "Growth of fingers at an unstable diffusing interface in a porous medium or hele-shaw cell." United Kingdom.
@misc{etde_5666088,
title = {Growth of fingers at an unstable diffusing interface in a porous medium or hele-shaw cell}
author = {Wooding, R A}
abstractNote = {Waves at an unstable horizontal interface, between 2 fluids moving vertically through a saturated porous medium, are observed to grow rapidly to become fingers (i.e., the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approx. as (time)U2D, followed by a transition to a growth proportional to time. Correspondingly, the mean wave number decreases approx. as (time)U-1/2D. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an open set, but closure is achieved by assuming a law for the mean wave number based on similarity. (22 refs.)}
journal = {J. Fluid Mech.; (United Kingdom)}
volume = {39}
journal type = {AC}
place = {United Kingdom}
year = {1969}
month = {Nov}
}