Title: Flow regimes for fluid injection into a confined porous medium

Abstract

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governing equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutionsmore » are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Authors:

Zheng, Zhong  ^[1];

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Guo, Bo ^[1]; Christov, Ivan C. ^[2]; Celia, Michael A. ^[1]; Stone, Howard A. ^[1]

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+ Show Author Affiliations

1. Princeton Univ., NJ (United States)
2. Princeton Univ., NJ (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Tue Feb 24 00:00:00 EST 2015

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1215503

Report Number(s):

LA-UR-14-23552
Journal ID: ISSN 0022-1120; applab; PII: S0022112015000683

Grant/Contract Number:  

AC52-06NA25396

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Fluid Mechanics

Additional Journal Information:

Journal Volume: 767; Journal ID: ISSN 0022-1120

Publisher:

Cambridge University Press

Country of Publication:

United States

Language:

English

Subject:

58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; geophysical and geological flows; gravity currents; porous media