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 advectiondiffusion equation that describes the time evolution of the sharp fluidfluid 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 R^{2}/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) injectiondriven flow with the injected fluid being more viscous than the displaced fluid ( Γ $$\ll$$ 1 and M < 1) where we identify a selfsimilar solution that indicates a parabolic interface shape; (ii) injectiondriven flow with injected and displaced fluids of equal viscosity ( Γ$$\ll$$ 1 and M = 1), where we find a selfsimilar solution that predicts a distinct parabolic interface shape; (iii) injectiondriven flow with a less viscous injected fluid ( Γ $$\ll$$ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the SaffmanTaylor instability does not occur at the reservoir scale; and (iv) buoyancydriven flow ( Γ $$\gg$$ 1) for which there is a wellknown selfsimilar 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:

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 Princeton Univ., NJ (United States). Dept. of Civil and Environmental Engineering
 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 10706631
 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 advectiondiffusion equation that describes the time evolution of the sharp fluidfluid 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) injectiondriven flow with the injected fluid being more viscous than the displaced fluid (Γ $\ll$ 1 and M < 1) where we identify a selfsimilar solution that indicates a parabolic interface shape; (ii) injectiondriven flow with injected and displaced fluids of equal viscosity (Γ$\ll$ 1 and M = 1), where we find a selfsimilar solution that predicts a distinct parabolic interface shape; (iii) injectiondriven flow with a less viscous injected fluid (Γ $\ll$ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the SaffmanTaylor instability does not occur at the reservoir scale; and (iv) buoyancydriven flow (Γ $\gg$ 1) for which there is a wellknown selfsimilar 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 ΓM 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}
}