Sediment size effects on non-Darcy flow: insights from Izbash equation and Forchheimer inertial coefficient analysis

Abstract

The transition from Darcy to non-Darcy flow regimes was investigated using column experiments. This revealed key relationships between sediment characteristics and critical thresholds for the onset of the non-Darcy flow regime, as well as inertial flow parameters. An exponential dependence of the critical Reynolds number (Re_c) on hydraulic conductivity (K) and a linear dependence on sediment size (d₅₀) was found. The analysis revealed a potentially universal relationship between the critical hydraulic gradient (I_c) and K, with a power-law exponent of –3/2, consistent with previous investigations. Additionally, I_c was found to be inversely proportional to the power law of the square root of d₅₀. Novel relationships are derived for estimating the Izbash equation inertial exponent (n) and the Forchheimer inertial coefficient (\(\beta\)) based on sediment characteristics. The exponent (n) was found to decrease with d₅₀ and increase with K, following power-law relationships. A new equation is proposed, capable of predicting \(\beta\) with slightly improved accuracy, outperforming numerous and previously proposed empirical equations. Additionally, these data validate the works of Ergun and Irmay as an alternative for \(\beta\) estimation using porosity and sediment size. As the attainment of statistical significance in multiparameter curve fitting can be trivial, it has led to the proliferation of empirical equations for estimating β. This study highlights the limitations of existing empirical methods in determining β and emphasizes the necessity for a universal approach to predict this critical parameter, which will facilitate broader adoption of the Forchheimer equation.