Coning during withdrawal from two fluids of different density in a porous medium

Thermosolutal Convection of Micropolar Rotating Fluids Saturating a Porous Medium

Double-diffusive convection in a micropolar fluid layer heated and soluted from below in the presence of uniform rotation saturating a porous medium is theoretically investigated. An exact solution is obtained for a flat fluid layer contained between two free boundaries. To study the onset of convection, a linear stability analysis theory and normal mode analysis method have been used. For the ...

A two-dimensional sink in a density-stratified porous medium

Contour dynamics of incompressible 3-D fluids in a porous medium with different densities

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele-Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness wh...

A note on withdrawal from a two-layer fluid through a line sink in a porous medium

The steady response of the free surface of a fluid in a porous medium is considered during extraction of the fluid through a line sink. A conformal mapping approach is used to derive exact solutions to a family of problems in which the line sink is place at the apex of a wedge-shaped impermeable boundary, including the limiting cases of an ubounded aquifer and a flat-bottomed aquifer of finite ...

Numerical Evaluation of Hydraulic Fracturing Pressure in a Two-Phase Porous Medium

Hydraulic fracturing is a phenomenon in which cracks propagate through the porous medium due to high pore fluid pressure. Hydraulic fracturing appears in different engineering disciplines either as a destructive phenomenon or as a useful technique. Modeling of this phenomenon in isothermal condition requires analysis of soil deformation, crack and pore fluid pressure interactions. In this paper...