Abstract Previously, hydrogeologists and petroleum engineers use seepage experiments to measure permeability. This paper develops a novel method calculate matrix permeability from velocity attenuation of an ultrasonic S-wave. At first, is derived as function frequency when S-wave scans fluid-saturated rock. Substituting the into previous model gives theoretical attenuation, in which nexus param...

An H(div) conforming mixed finite element method has been proposed for the coupled Darcy-Stokes flow in [30], which imposes normal continuity on the velocity field strongly across the Darcy-Stokes interface. Here, we develop an a posteriori error estimator for this H(div) conforming mixed method, and prove its global reliability and efficiency. Due to the strong coupling on the interface, speci...

A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov-Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions ...

Darcy flow is a steady-state model for laminar flow of a fluid through a porous medium. The present work proposes an extended model of laminar Darcy flow by introducing dynamic pressure and velocity to the classical formulation. The solution of the proposed time-space model is attained by discretizing the problem with a stabilized mixed Galerkin method in space and a forward Euler method in tim...

A . This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes-Darcy problem. The four methods uncouple each time step into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based...

Numerical simulation of uid ow in a hydrocarbon reservoir has to ac count for the presence of wells The pressure of a grid cell containing a well is di erent from the average pressure in that cell and di erent from the bottomhole pressure for the well Peaceman This paper presents a study of grid pressures obtained from the simulation of single phase ow through an isotropic porous medium using d...

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...

Motivated by casting of fresh concrete in reinforced concrete structures, we introduce a numerical model of a steady-state non-Newtonian fluid flow through a porous domain. Our approach combines homogenization techniques to represent the reinforced domain by the Darcy law with an interfacial coupling of the Stokes and Darcy flows through the Beavers-Joseph-Saffman conditions. The ensuing two-sc...

In this article, we analyze the flow of a fluid through a coupled Stokes-Darcy domain. The fluid in each domain is non-Newtonian, modeled by the generalized nonlinear Stokes equation in the free flow region and the generalized nonlinear Darcy equation in the porous medium. A flow rate is specified along the inflow portion of the free flow boundary. We show existence and uniqueness of a variatio...

Abstract—This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers r...