Fluid injection into a confined porous layer

Pegler, Samuel S. and Huppert, H. E. and Neufeld, Jerome A. (2014) Fluid injection into a confined porous layer. Journal of Fluid Mechanics, 745. pp. 592-620. ISSN 0022-1120, ESSN: 1469-7645 DOI 10.1017/jfm.2014.76

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Official URL: http://dx.doi.org/10.1017/jfm.2014.76

Abstract

We present a theoretical and experimental study of viscous flows injected into a porous medium that is confined vertically by horizontal impermeable boundaries and filled with an ambient fluid of different density and viscosity. General three-dimensional equations describing such flows are developed, showing that the dynamics can be affected by two separate contributions: spreading due to gradients in hydrostatic pressure, and that due to the pressure drop introduced by the injection. In the illustrative case of a two-dimensional injection of fluid at a constant volumetric rate, the injected fluid initially forms a viscous gravity current insensitive both to the depth of the medium and to the viscosity of the ambient fluid. Beyond a characteristic time scale, the dynamics transition to being dominated by the injection pressure, and the injected fluid eventually intersects the second boundary to form a second moving contact line. Three different late-time asymptotic regimes can emerge, depending on whether the viscosity of the injected fluid is less than, equal to or greater than that of the ambient fluid. With a less viscous injection, the flow undergoes a slow decay towards a similarity solution in which the two contact lines extend linearly in time with differing prefactors. Perturbations from this long-term state are shown to decay algebraically with time. Equal viscosities result in both contact lines approaching the same leading-order asymptotic position but with a first-order correction to the distance between them that expands as t1/2t⌃{1/2} due to gravitational spreading. For a more viscous injection, the distance between the contact lines approaches a constant value, with perturbations decaying exponentially. Data from a new series of laboratory experiments confirm these theoretical predictions.

Item Type: Article
Additional Information: © 2014 Cambridge University Press
Uncontrolled Keywords: 2014AREP; IA67;
Subjects: 99 - Other
Divisions: 08 - Green Open Access
99 - Other
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 745
Page Range: pp. 592-620
Identification Number: 10.1017/jfm.2014.76
Depositing User: Sarah Humbert
Date Deposited: 01 May 2014 21:51
Last Modified: 16 May 2014 12:22
URI: http://eprints.esc.cam.ac.uk/id/eprint/3033

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