Quantitative evaluation of forchheimer equation for non-darcy flow in porous media

Abstract

The Forchheimer equation is one of the basic equations widely used in non-Darcy seepage. The determination of coefficients A and B in the equation has always been a hotspot and difficulty in the field of porous media seepage. Different studies have proposed various empirical formulas for the coefficients A and B from seepage experiments. However, there are few studies evaluating the applicability of each empirical formula under homogeneous condition and heterogeneous with mixed particle size. In this study, to provide basic information for selecting the empirical formula of the Forchheimer equation under different porous media conditions, the normalized objective function (NOF) and linear regression method are used to evaluate the applicability of the empirical formula of the Forchheimer equation, on the basis of the seepage resistance experiment. The results show that: for homogeneous porous media, Sidiropoulou’s formula has a good prediction effect on hydraulic gradient. For the porous media mixed two kinds of particle size, the mass ratio and size factors of the mixed particle size should be considered based on the average particle size. The prediction effect of the Macdonald formula is slightly affected by the mass ratio and the mixed particle size; while the predicted hydraulic gradient from the Kadlecan and Knight formula is relatively stable. As to the porous media mixed five kinds of particle size, the predictive effect of using d60 as the characteristic particle size is fine.The Kadlecan and Knight formula is suitable to predict coefficient A, and the Ergun formula is effective to predict coefficient B. This study can provide a basis for selecting the Forchheimer equation for seepage of homogeneous and heterogeneous loose sand and gravel porous media in engineering.

Keywords

• porous media
• forchheimer equation
• non-darcy flow
• quantitative evaluation
• empirical equation