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...

Swelling media (e.g. gels, tumors) are usually described by mechanical constitutive laws (e.g. Hooke or Darcy laws). However, constitutive relations of real swelling media are not well-known. Here, we take an opposite route and consider a simple packing heuristics, i.e. the particles can’t overlap. We deduce a formula for the equilibrium density under a confining potential. We then consider its...

In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is bounded perforated 3D domain confined between two parallel plates. description of the includes small parameters: ε representing distance plates and $a_\varepsilon$ connected to microstructure such that ≪ $a_\varepsilon \ll \varepsilon$ . We consider classical setting me...

We introduce a new global pressure formulation for immiscible three-phase compressible flows in porous media which is fully equivalent to the original equations, unlike the one introduced in [5]. In this formulation, the total volumetric flow of the three fluids and the global pressure follow a classical Darcy law, which simplifies the resolution of the pressure equation. However, this global p...

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...