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...

The subject of this paper is a first-order system least-squares formulation for the Stokes equation which remains uniformly valid in the limit of vanishing viscosity. For this so-called Darcy-Stokes flow problem we establish continuity and coercivity of the corresponding least-squares functional in appropriate norms. Two types of finite element spaces for the approximation of the velocity field...

In this report, a partitioned time stepping algorithm which allows different time steps in the fluid region and the porous region is analyzed for the fully evolutionary Stokes-Darcy problem. This method requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a modest time step restriction of the form 4t ≤ C where C = C(physical parameters) we prove ze...

In this report, a partitioned time stepping algorithm for transient flow in a porous medium coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes-Darcy problem. This method requires only solve one, uncoupled Stokes and Darcy sub-physics and subdomain per time step. On the interface between the matrix and conduit, Beavers-Joseph int...

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which converted into fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on HAM are guaranteed to be more accurate than exact solutions, relative errors between 0.0089% and 2.64%. When λ = 0, pressure drop of Da...

This study simulates natural convection flow resulting from heat partitions in an H-shaped enclosure filled with a nanofluid using incompressible smoothed particle hydrodynamics (ISPH) method. The right area of the is saturated non-Darcy porous media. center variable walls are kept at high-temperature Th. left and positioned low temperature Tc other adiabatic. In ISPH method, source term pressu...