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Ph.D.
(Science)
ASYMPTOTIC BEHAVIOUR OF NONLINEAR FLUID
FLOW PROBLEMS IN POROUS MEDIA

Ph.D. Scholar : Patel Dhara Tejas
Research Supervisor : Prof. (Dr.) Amit K. Parikh

Regi. No.: 17146061001
Abstract :
Recent research has placed a lot of emphasis on the flow of fluid via porous media. Fluid
flow through porous media occurs in a wide range of application, including geophysical
flow, recovery of crude, natural gas and minerals from nature, chemical processes, and
hydrology of ground water. Over the past three to four decades, there has been a lot of
interest in research on fluid flow via porous media. This is a result of the importance of
this study field in several engineering and scientific fields, including petrochemical
engineering, reservoir engineering, construction engineering, ecological engineering,
underground hydrology, material sciences, biomedical science etc. Fluid moving via
porous media significance growing as demand of crude oil is increasing day by day and
freshwater supplies become less accessible due to increased demand of water. There are
numerous applications for multiphase flow studies in heterogeneous and naturally
fractured reservoirs in crude oil retrieval. Natural cracks have a significant influence on oil
and gas recovery. In these reservoirs, fractures provide for enhanced fluid flow paths,
while porous rock allows for storage capacity.
When oil and water moving simultaneously in porous medium, some physical
phenomena occurs. To understand the behaviour of physical phenomenon in the fluid
flow through porous media, various mathematical models have been established. The
mathematical formulation of these physical phenomena leads to the non-linear partial
differential equations. The present study focuses on the three main phenomenon such as
instability phenomenon,imbibition phenomenon and fingero-imbibition in homogeneous,
heterogeneous and fractured porous media during secondary oil retrieval procedure. In
this work, we have discussed Homotopy Analysis Laplace Transform Method (HALTM)
and Homotopy Perturbation Laplace Transform Method (HPLTM) to obtain the
approximate solution of nonlinear partial differential equations which arise in fluid flow
through porous media. The thesis discusses approximate solutions of instability
phenomenon in inclined homogeneous porous media with magnetic effect and without
magnetic effect. Also solution of instability phenomenon in inclined heterogeneous
porous media is discussed. Solution of imbibition phenomenon in heterogeneous and
fractured heterogeneous porous media in horizontal direction and vertical downward
direction is discussed. Fingero-imbibition phenomenon in heterogeneous porous media in
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