We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy-Forchheimer law while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy-Forc...

In this study, effects of microstructure on the viscous permeability and Forchheimer coefficient of monodispersed fibers are investigated. The porous material is represented by a unit cell which is assumed to be repeated throughout the medium. Based on the orientation of the fibers in the space, fibrous media are divided into three categories: one-, two-, and three-directional (1D, 2D, and 3D) ...

In this paper lattice-Boltzmann equation method is used to simulate non-Darcy flow in porous media. 2-D in-line and staggered arrangements of uniform cylinders have been considered. The results of a comprehensive computational evaluation are reported: the range of validity of Darcy-Forchheimer equation is investigated and correlations for macroscopic transport properties are presented (i. e., f...

The nonlinear Forchheimer equations are used to describe the dynamics of fluid flows in porous media when Darcy's law is not applicable. In this article, we consider the generalized Forchheimer flows for slightly compressible fluids and study the initial boundary value problem for the resulting degenerate parabolic equation for pressure with the time-dependent flux boundary condition. We estima...

We model multi-dimensional two-phase flows of incompressible fluids in porous media using generalized Forchheimer equations and the capillary pressure. Firstly, we find a family of steady state solutions whose saturation and pressure are radially symmetric and velocities are rotation-invariant. Their properties are investigated based on relations between the capillary pressure, each phase’s rel...

We study generalized Forchheimer equations for slightly compressible fluids in porous media subjected to the flux condition on the boundary. We derive estimates for the pressure, its gradient and time derivative in terms of the time-dependent boundary data. For the stability, we establish the continuous dependence of the pressure and pressure gradient on the boundary flux and coefficients of th...

We prove continuous dependence of solutions of the Brinkman–Forchheimer equations on the Brinkman and Forchheimer coefficients in H1 norm. c © 2005 Elsevier Ltd. All rights reserved.

In this paper, we study the dimension estimate of global attractor for a 3D Brinkman-Forchheimer equation. Based on differentiability semigroup with respect to initial data, show that strong solution equation has finite Hausdorff and fractal dimensions.