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

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 distinct 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 CO 2 sequestration, enhanced oil recovery, and underground waste disposal.
Authors:
ORCiD logo [1] ; ORCiD logo [2] ;  [1] ; ORCiD logo [2]
  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:
Grant/Contract Number:
FE0009563
Type:
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)
Research Org:
Princeton Univ., NJ (United States)
Sponsoring Org:
USDOE Office of Fossil Energy (FE)
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
OSTI Identifier:
1469306
Alternate Identifier(s):
OSTI ID: 1239448

Guo, Bo, Zheng, Zhong, Celia, Michael A., and Stone, Howard A.. Axisymmetric flows from fluid injection into a confined porous medium. United States: N. p., Web. doi:10.1063/1.4941400.
Guo, Bo, Zheng, Zhong, Celia, Michael A., & Stone, Howard A.. Axisymmetric flows from fluid injection into a confined porous medium. United States. doi:10.1063/1.4941400.
Guo, Bo, Zheng, Zhong, Celia, Michael A., and Stone, Howard A.. 2016. "Axisymmetric flows from fluid injection into a confined porous medium". United States. doi:10.1063/1.4941400. https://www.osti.gov/servlets/purl/1469306.
@article{osti_1469306,
title = {Axisymmetric flows from fluid injection into a confined porous medium},
author = {Guo, Bo and Zheng, Zhong and Celia, Michael A. and Stone, Howard A.},
abstractNote = {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 distinct 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.},
doi = {10.1063/1.4941400},
journal = {Physics of Fluids},
number = 2,
volume = 28,
place = {United States},
year = {2016},
month = {2}
}