Abstract Diffusive transport in porous media is a complex process multi-scaled fractured modeling. This paper presents diffusive model for non-Dacian flow naturally reservoir with triple porosity and permeability. To address the non-Darcian behavior associated fluid media, Darcy/Forcheimer equation was used. A point-diffusive obtained from mass conservation Darcy–Forcheimer momentum equation; t...

The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of ...

Three dimensional heat transfer and water flow characteristic in a set of rectangular microchannel heat sinks for advanced electronic systems investigated in this paper. The full Navier-Stoke’s approach is employed for this kind of narrow channels for the water flow assessments. The complete form of the energy equation accompanying the dissipation terms is also linked to the momentum equations....

Hazen-Williams equation is used widely by irrigation systems’ designers due to its simplicity.However, Darcy-Weisbach equation is more accurate and reliable. The accuracy of the latter is due to its friction coefficient, which depends on both flow characteristics and pipe surface state. On the other hand, Hazen-Williams’ coefficient (C) depends only on pipe substance and age. A comparative anal...

We present a numerical analysis of an implicit time discretization method applied to Richards’ equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is base...

Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definition...

This paper discusses a novel three field formulation for the Darcy-Forchheimer flow with nonlinear viscosity depending on temperature coupled heat equation. We show unique solvability of variational problem by using; Galerkin method, Brouwer’s fixed point and some compactness properties. propose study in detail finite element approximation. A priori error estimate is then derived convergence ob...

In this article, we consider the time-dependent convection-diffusion-reaction equation coupled with Darcy equation. We propose a numerical scheme based on finite element methods for discretization in space and implicit Euler method time. establish optimal posteriori error estimates two types of computable indicators, first one linked to time second discretization. Finally, investigations are pe...