Incompressible, axisymmetric laminar flow downstream of a porous expansion is simulated. Effect of the Darcy number and inertia coefficient on flow and heat transfer characteristics downstream of the expansion is investigated. The simulation revealed circulation downstream of the expansion. Decreasing the Darcy number is shown to decrease the circulation region. The Nusselt number, friction coe...

Shale and tight hydrocarbons are vital to global energy dynamics. The fluid flow in sub-micron pores of oil reservoirs varies from bulk flow. Darcy law is widely accepted model creeping petroleum reservoirs. However, traditional reservoir modeling approaches fail account for the mechanisms that govern accuracy simulators has been improved by incorporating influence effects. there still factors ...

We study the asymptotic behavior of the infinite Darcy-Prandtl number DarcyBrinkman-Boussinesq system for convection in porous media at small Brinkman-Darcy number. The existence of a boundary layer with thickness proportional to the square root of the BrinkmanDarcy number for the velocity field is established in both the L∞(H1) norm (2 and 3 d) and the L∞(L∞) norm (2d only). This improves an e...

A mathematical and numerical model describing chemical transport in a Stokes– Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with couplin...

[1] This paper presents an approximate analytical solution for non-Darcy flow of a slightly compressible fluid through a fractured reservoir. The analytical solution is obtained using the traditional Warren-Root solution superposed on a dimensionless non-Darcy flow coefficient. The model formulation incorporates the Forchheimer equation into the Warren-Root model for describing non-Darcy flow t...

The flow past an impermeable sphere embedded in a fluid saturated porous medium was studied numerically considering valid the Brinkman−Forchheimer−Darcy (or Brinkman−Hazen−Dupuit−Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function vorticity equations were solved numerically in spherical c...

When one thinks about porous media, the immediate concepts that come to mind are porosity, permeability and Darcy’s law. The latter is probably one of the most important tools in hydrodynamics and engineering presenting numerous applications in oil recovery, chemical engineering, nuclear safety and many other engineering field. It has been first formulated by the French engineer Henri Darcy in ...

Water movement in an unsaturated porous medium (soil) can be expressed by Richards equation with the mass conservation law and Darcy-Buckingham's law. This three different forms as pressure head-based, moisture content based mixed from. In this study, we solve one dimensional Equation form numerically using finite difference method various time-stepping schemes: Forward Euler, Backward Crank-Ni...

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...

There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem, as well as methods for uncoupling the problem into subdomain, subphysics solves. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The numerical analysis and algorithm development for the evolutionary transport...