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Exact Solutions for Gravity-Segregated Flows in Porous Media

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  • Pavel Bedrikovetsky

    (Australian School of Petroleum and Energy Resources, The University of Adelaide, Adelaide, SA 5000, Australia)

  • Sara Borazjani

    (Australian School of Petroleum and Energy Resources, The University of Adelaide, Adelaide, SA 5000, Australia)

Abstract

The review is devoted to exact analytical solutions for quasi-2D gravity segregated flows or gravity currents in subterranean porous formations. The problems under consideration are quasi-linear. The driving forces are two components of the buoyancy—one exerting the bulk of the light fluid and one due to the curvilinearity of the interface between the fluids. In the case of homogeneous formation or where the seal slope is negligible, the transport equation is parabolic and allows for a wide set of self-similar solutions. In a large-scale approximation of the buoyancy domination, the governing equation is hyperbolic; the method of characteristics allows for a detailed analytical description of gravity current propagation with final accumulation in the geological trap. Analytical models for leakage via the caprock seal are also discussed. The work was completed by formulating some unsolved problems in segregated flows in porous media.

Suggested Citation

  • Pavel Bedrikovetsky & Sara Borazjani, 2022. "Exact Solutions for Gravity-Segregated Flows in Porous Media," Mathematics, MDPI, vol. 10(14), pages 1-32, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2455-:d:862614
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    References listed on IDEAS

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    1. James E. Anderson, 2011. "The Gravity Model," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 133-160, September.
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    Cited by:

    1. Alexander V. Aksenov & Andrei D. Polyanin, 2025. "Symmetries, Reductions and Exact Solutions of Nonstationary Monge–Ampère Type Equations," Mathematics, MDPI, vol. 13(3), pages 1-24, February.
    2. Andrei D. Polyanin & Alexander V. Aksenov, 2024. "Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions," Mathematics, MDPI, vol. 12(13), pages 1-29, July.

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