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Pegler, Samuel S.; Huppert, H. E.; Neufeld, Jerome A.
Publisher: CUP
Languages: English
Types: Article
Subjects: sub-99

Classified by OpenAIRE into

arxiv: Physics::Fluid Dynamics
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.
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    • ABRAMOWITZ, M. & STEGUN, I. A. 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover.
    • ACTON, J. M., HUPPERT, H. E. & WORSTER, M. G. 2001 Two-dimensional viscous gravity currents flowing over a deep porous medium. J. Fluid Mech. 440, 359-380.
    • BARENBLATT, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.
    • BEAR, J. 1988 Dynamics of Fluids in Porous Media. Dover.
    • BICKLE, M. J., CHADWICK, R. A., HUPPERT, H. E., HALLWORTH, M. A. & LYLE, S. 2007 Modelling carbon dioxide accumulation at Sleipner: implications for underground carbon storage. Earth Planet. Sci. Lett. 255, 164-176.
    • BOAIT, F. C., WHITE, N. J., BICKLE, M. J., CHADWICK, R. A., NEUFELD, J. A. & HUPPERT, H. E. 2012 Spatial and temporal evolution of injected CO2 at the Sleipner field, North Sea. J. Geophys. Res. 117, B03309.
    • CHADWICK, R. A., ZWEIGEL, P., GREGERSEN, U., KIRBY, G. A., HOLLOWAY, S. & JOHANNESSEN, P. N. 2004 Geological reservoir characterization of a CO2 storage site: the Utsira Sand, Sleipner, northern North Sea. Energy 29, 1371-1381.
    • DAKE, L. P. 2010 Fundamentals of Reservoir Engineering. (Developments in Petroleum Science), vol. 8. Elsevier.
    • GOLDING, M. J. & HUPPERT, H. E. 2010 The effect of confining impermeable boundaries on gravity currents in a porous medium. J. Fluid Mech. 649, 1-17.
    • GRUNDY, R. E. & MCLAUGHLIN, R. 1982 Eigenvalues of the Barenblatt-Pattle similarity solution in nonlinear diffusion. Proc. R. Soc. Lond. A 649, 89-100.
    • GUNN, I. & WOODS, A. W. 2011 On the flow of buoyant fluid injected into a confined, inclined aquifer. J. Fluid Mech. 672, 109-129.
    • GUNN, I. & WOODS, A. W. 2012 On the flow of buoyant fluid injected into an aquifer with a background flow. J. Fluid Mech. 706, 274-294.
    • HESSE, M. A., ORR JR, F. M. & TCHELEPI, H. A. 2008 Gravity currents with residual trapping. J. Fluid Mech. 611, 35-60.
    • HESSE, M. A., TCHELEPI, H. A., CANTWELL, B. J. & ORR JR., F. M. 2007 Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363-383.
    • HUPPERT, H. E. 1986 The intrusion of fluid mechanics into geology. J. Fluid Mech. 173, 557-594.
    • HUPPERT, H. E. & WOODS, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55-69.
    • LYLE, S., HUPPERT, H. E., HALLWORTH, M., BICKLE, M. & CHADWICK, A. 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293-302.
    • MACMINN, C. W. & JUANES, R. 2009 Post-injection spreading and trapping of CO2 in saline aquifers: impact of the plume shape at the end of injection. Comput. Geosci. 13, 480-491.
    • MACMINN, C. W., SZULCZEWSKI, M. L. & JUANES, R. 2010 CO2 migration in saline aquifers. Part 1: Capillary trapping under slope and groundwater flow. J. Fluid Mech. 662, 329-351.
    • MACMINN, C. W., SZULCZEWSKI, M. L. & JUANES, R. 2011 CO2 migration in saline aquifers. Part 2: Combined capillary and solubility trapping. J. Fluid Mech. 688, 321-351.
    • MATHUNJWA, J. S. & HOGG, A. J. 2006 Self-similar gravity currents in porous media: linear stability of the Barenblatt-Pattle solution revisited. Eur. J. Mech. (B/Fluids) 25, 360-378.
    • NORDBOTTEN, J. M. & CELIA, M. A. 2006 Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307-327.
    • ORR JR., F. M. 2009 Onshore geological storage of CO2. Science 325, 1656-1658.
    • PEGLER, S. S., HUPPERT, H. E. & NEUFELD, J. A. 2013a Topographic controls on gravity currents in porous media. J. Fluid Mech. 734, 317-337.
    • PEGLER, S. S., KOWAL, K. N., HASENCLEVER, L. Q. & WORSTER, M. G. 2013b Lateral controls on grounding-line dynamics. J. Fluid Mech. 722, R1.
    • PEGLER, S. S., LISTER, J. R. & WORSTER, M. G. 2012 Release of a viscous power-law fluid over an inviscid ocean. J. Fluid Mech. 700, 261-281.
    • SAFFMAN, P. G. & TAYLOR, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312-329.
    • TAYLOR, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186-203.
    • VASCO, D. W., RUCCI, A., FERRETTI, A., NOVALI, F., BISSELL, R. C., RINGROSE, P. S., MATHIESON, A. S. & WRIGHT, I. W. 2010 Satellite-based measurements of surface deformation reveal fluid flow associated with the geological storage of carbon dioxide. Geophys. Res. Lett. 37, L03303.
    • VELLA, D. & HUPPERT, H. E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353-362.
    • WOODS, A. W. & MASON, R. 2000 The dynamics of two-layer gravity-driven flows in permeable rock. J. Fluid Mech. 421, 83-114.
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