Fluid Dynamics

, Volume 52, Issue 4, pp 516–525 | Cite as

Investigation of time-dependent two-dimensional displacement in a porous medium in the self-similar formulation of the problem

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Abstract

Two-dimensional flow through a porous medium when a gas is injected into a permeable aquifer of infinite extension is investigated. The self-similar asymptotic solutions which describe the early stage of the time-dependent two-dimensional process of gas spreading along the caprock over the aquifer are constructed. The asymptotics are constructed on the assumption of the considerable aquifer thickness when the processes in the neighborhood of the aquifer base have no effect on flow along the caprock. Two-dimensional wave patterns describing the gas saturation distribution are investigated by means of the direct numerical simulation. The dimensions of the gas accumulation region are estimated as functions of the similarity parameters.

Keywords

flow through a porous medium gas injection self-similar solution the Buckley–Leverett problem fractional-flow theory 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

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