Studying a doubly nonlinear model of slightly compressible Forchheimer flows in rotating porous media

PROPERTIES OF GENERALIZED FORCHHEIMER FLOWS IN POROUS MEDIA By

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...

A two-pressure model for slightly compressible single phase flow in bi-structured porous media

Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of pore-scale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the pore-scale are generally approximated by Darcy's law at a larger scale. In this work, we develop an alternative model to Da...

Structural Stability of Generalized Forchheimer Equations for Compressible Fluids in Porous Media

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...

Secondary flows and particle centrifugation in slightly tilted rotating pipes

A theoretical analysis is presented of viscous incompressible laminar flow in a pipe which rotates around an axis held at small angle with respect to its symmetry-axis. Analogous to the results of Barua and Benton [1, 2], solutions in closed-form are given for circulatory flows in the crosssectional plane of the pipe due to Coriolis forces in combination with Hagen-Poiseuille flow through the p...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows