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 ( d 50 ) 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 d 50 . Novel relationships are derived for estimating the Izbash equation inertial exponent ( n ) and the Forchheimer inertial coefficient ( $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> ) based on sediment characteristics. The exponent ( n ) was found to decrease with d 50 and increase with K , following power-law relationships. A new equation is proposed, capable of predicting $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> 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 $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> 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.