DarcyLite is a Matlab toolbox for numerical simulations of flow and transport in 2-dim porous media. This paper focuses on the finite element (FE) methods and the corresponding code modules in DarcyLite for solving the Darcy equation. Specifically, four major types of finite element solvers, the continuous Galerkin (CG), the discontinuous Galerkin (DG), the weak Galerkin (WG), and the mixed fin...

Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. The coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. On the interface between the matrix and conduit, Beavers–J...

Analytical solutions are derived for a pressure transmission experiment of a saturated charged compressible porous medium. The governing equations describe infinitesimal deformations of charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoup...

Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the algebraic expression for the sum of saturations. Primary computational algorithms are implemented for such problems using the pressure equation. In this paper,...

In this work, we propose a new method called Petrov–Galerkin multiscale hybrid-mixed (PGMHM for short) as variant of the (MHM) method. Its construction starts from formulation Lagrange multiplier space, defined by enriching trial spaces with residual-based functions on partition faces. As result, jump terms are added to original MHM method, which penalizes lack conformity numerical solutions. c...

Effective numerical simulation of many EOR problems requires very accurate approximation of the Darcy velocities of the respective fluids. In this paper we describe a new method for the accurate determination of the Darcy velocity of the total fluid in the miscible displacement of one incompressible fluid by another in a porous medium. The new mixed finite-element procedure solves for both the ...

In this paper, I explore the solution of the contaminant transport problem over a random conductivity field. First, I generate a random, correlated conductivity field by convolving independent, uniformly distributed random variables with the identity function. I use finite differences to discretize the diffusion equation to solve for the steady-state pressure gradient using Backward Euler. This...

Sintered metal porous media currently plays an important role in air bearing systems. When flowing through porous media, the flow properties are generally represented by incompressible Darcy-Forchheimer regime or Ergun regime. In this study, a modified Ergun equation, which includes air compressibility effects, is developed to describe friction characteristic. Experimental and theoretical inves...