The deformation of fluid elements governs many processes in porous media, including the transport, dispersion and mixing solutes, chemical reactions colloidal particles. Recently, it has been shown that even strongly heterogeneous steady three-dimensional (3-D) Darcy flow with isotropic hydraulic conductivity admits only constrained kinematics. This is due to its inherently helicity-free nature...

Unconventional hydrocarbon resources from low-permeability formation, i.e., tight sands and shales, are currently received great attention because of their potential to supply the entire world with sufficient energy for the decades to come. In the past few years, as a result of industry-wide R&D effort, progresses are being made towards commercial development of gas and oil from such unconventi...

The acid treatment of carbonate reservoirs is a widely practiced oil and gas well stimulation technique. The injected acid dissolves the material near the wellbore and creates flow channels that establish a good connectivity between the reservoir and the well. Such flow channels are called wormholes. Different from the traditional simulation technology relying on Darcy framework, the new Darcy-...

Least stable mode of convective flow, induced by external pressure gradient and buoyancy force in the vertical pipe filled with porous medium, is investigated. Non-Darcy Brinkman-extended model has been considered. To study least stable mode of the fully developed flow linear theory of stability analysis has been used for an wide range [0.01, 100] of Prandtl number (Pr). To this end, coupled or...

A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady-state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model-...

This paper presents a finite volume discretization of two-phase Darcy flows in discrete fracture networks taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain, leading to the so called hybrid dimensional Darcy flow model. The pressures at ...

The flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector, is an important parameter in applications such as particle capture, filtration, and sedimentation. In this work, flow permeation through a porous circular cylinder located symmetrically between two impermeable parallel plates is investigated numerically under different fl...

A local interpolation operator, preserving the divergence, is constructed explicitly, which is the first ever one for the divergence-free elements. A divergence-free finite element method is applied to the Darcy-Stokes-Brinkman flow in a mixed region of both free and porous medium. The method is of optimal order in contrast to the traditional H and H mixed finite elements, which work for either...

Darcy’s Law is the fundamental equation describing the flow of fluid through porous media including groundwater. It forms the quantitative basis of many science and engineering disciplines including hydrology, hydrogeology, soil science, civil engineering, petroleum engineering and chemical engineering. The year 2006 marked the 150th anniversary of the publication of Henry Darcy’s most famous t...

Vibrational mixed convection inside an open-ended cavity filled with a porous medium is investigated in this work. Vertical vibration on the left wall and buoyancy induced flow are considered. The effect of variations in governing parameters, such as vibrational Reynolds number, modified Rayleigh number, and the Darcy number on streamlines, isotherms, and the average Nusselt number is discussed...