We study the generalized Forchheimer equations for slightly compressible fluids in porous media. The structural stability is established with respect to either the boundary data or the coefficients of the Forchheimer polynomials. An inhomogeneous Poincare-Sobolev inequality related to the non-linearity of the equation is used to study the asymptotic behavior of the solutions. Moreover, we prove...

SONG, H. and TAO, L., 2007. Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media. Journal of Coastal Research, SI 50 (Proceedings of the 9th International Coastal Symposium), pg – pg. Gold Coast, Australia, ISBN 1-891276-54-9 In this paper, the 1D unsteady, nonlinear groundwater flow through porous media, corresponding to flood in an aquifer between two reservoirs, ...

We prove the existence of regular dissipative solutions and global attractors for the 3D Brinkmann-Forchheimer equations with the nonlinearity of an arbitrary polynomial growth rate. In order to obtain this result, we prove the maximal regularity estimate for the corresponding semi-linear stationary Stokes problem using some modification of the nonlinear localization technique. The applications...

The numerical prediction of channel segregations during two-dimensional columnar solidification of Sn-Pb alloy is analyzed when inertia is considered in the dendritic mushy zone. This contribution is included in the momentum transport equation through the quadratic Forchheimer correction term. A significant influence of the Forchheimer term in the vicinity of the liquidus region is found. The n...

[1] Step‐drawdown tests (SDTs) typically involve pumping a well at a constant rate until a quasi‐steady state (QSS) is observed in the drawdown response. The well is then pumped at a higher constant rate until a new QSS is achieved. The process is repeated for additional flow rates. Analysis involves plotting the QSS drawdowns against their corresponding abstraction rates and fitting a nonlinea...

In this paper, we obtain the continuous dependence and convergence results for the Brinkman and Forchheimer coefficients of a differential equation that models the flow of fluid in a saturated porous medium.

distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we derive some estimates for the 3D non-autonomous linearization Brinkman-Forchheimer equation with singularly oscillating forces together with the averaged equation.

Based on the production data and statistical information of a practical oilfield, it is proved that the flow rule in wormhole or extra wormhole can be regarded as a high speed Non-Darcy flow, and used the Forchheimer equation to represent. The Forchheimer model is superior to the exponent model and Mazaheri model. Then, the productivity equation of poorly consolidated reservoir with wormhole is...

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence constraint. The nonlinear equation can be solved element-wise with a closed formulae. The linear saddle point system for the constraint is reduced into a sy...

In this study, effects of porosity and fiber orientation on the viscous permeability and Forchheimer coefficient of mono-dispersed 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: 1D, 2D, and 3D structures. Paralle...