Title: Axisymmetric flows from fluid injection into a confined porous medium

Abstract

In this work, we study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and Γ, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R²/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ $$\ll$$ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ$$\ll$$ 1 and M = 1), where we find a self-similar solution that predicts a distinctmore » parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ $$\ll$$ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ $$\gg$$ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. “Axisymmetric gravity currents in a porous medium,” J. Fluid Mech. 543, 293–302 (2005)]. The various axisymmetric flows are summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime. The implications of the regime diagram are discussed using practical engineering projects of geological CO₂ sequestration, enhanced oil recovery, and underground waste disposal.« less

Authors:

Guo, Bo  ^[1];

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Zheng, Zhong  ^[2];

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Celia, Michael A. ^[1]; Stone, Howard A.  ^[2]

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+ Show Author Affiliations

1. Princeton Univ., NJ (United States). Dept. of Civil and Environmental Engineering
2. Princeton Univ., NJ (United States). Dept. of Mechanical and Aerospace Engineering

Publication Date:

Thu Feb 25 00:00:00 EST 2016

Research Org.:

Princeton Univ., NJ (United States)

Sponsoring Org.:

USDOE Office of Fossil Energy (FE)

OSTI Identifier:

1469306

Alternate Identifier(s):

OSTI ID: 1239448

Grant/Contract Number:  

FE0009563

Resource Type:

Journal Article: Accepted Manuscript

Journal Name:

Physics of Fluids

Additional Journal Information:

Journal Volume: 28; Journal Issue: 2; Journal ID: ISSN 1070-6631

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

42 ENGINEERING; equations of fluid dynamics; fluid mixing; porous media; gravity currents; wave mechanics; flow instabilities; lubrication flows; energy storage; energy production, transmission and distribution; thermodynamic states and processes