2017, Farzad Khadivpour Graduated

Simulation of flow in porous media using an equivalent pipe model

Abstract

The flow in porous media is a fundamental issue in geotechnical, hydrogeological, dam building and environmental engineering. The Darcy law, a linear relationship between hydraulic gradients and velocity, is assumed to be acceptable only when water flows steadily in a sand column. For coarse granular environment, the non-Darcy relations applies between the velocity and the hydraulic gradient. The flow in these coarse granular is classified into free flow and under pressure flow.

In this study, a model is presented to estimate the the flow properties in a porous granular media based on an equivalent pipe model. The diameter of the equivalent pipe is obtained in terms of the particle diameter and porosity of the porous medium. The flow velocity in the equivalent pipe was calculated based on different roughnesses and hydraulic gradients. The velocity in the porous medium is calculated from Forchheimer equation, whose coefficients are derived using previous experimental data. The relationship between the flow velocity in the porous medium and the velocity in the equivalent pipe is obtained with an appropriate correlation. An equation was proposed to estimate the friction factor of the porous medium based on the friction factor of the equivalent pipe having the modified Reynolds number in the porous medium. The correlation of this relation is 0.9 which indicates the proper relationship between friction factors in two environments. The coefficients of nonlinear relations were calculated for the Forchheimer equation with respect to the velocity and friction factor of the porous medium. The Normalized Objective Functions (NOF) of the linear coefficient of the Forchheimer equation is 0.44 and for a nonlinear coefficient is 0.37, which indicate that this method is acceptable with sufficient accuracy. With the coefficients of the Forchheimer equation in a porous medium, it is possible to obtain the velocity in a porous medium with different gradients and to calculate the amount of seepage.