The effect of permeability on Darcy-to-Forchheimer flow transition

Abstract

Flow through porous media takes place in diverse geological settings. The fluid motion through pores follows Darcy’s Law (linear rate law) in many cases, but at high flows the Forchheimer (nonlinear) flow regime emerges, where fluid flux and the hydraulic gradient are no longer linearly related. The transition to the nonlinear flow regime has many possible causes, making the prediction of its onset nearly impossible. The Reynolds number has been used for identifying the onset of nonlinear flow, but its values span across a few orders of magnitude suggesting it might be an inappropriate or inadequate metric. Through the analysis and synthesis of 2852 single-phase flow experiments in different porous media and supporting numerical pore-scale flow simulations, we observed that the critical hydraulic gradient (Ic) which determines the onset of Forchheimer flow scales with permeability (k) via a power law for high k media (k = 10−12–10−6 m2). However, when k is smaller (1 × 10−12–1 × 10−18 m2), the Forchheimer flow regime emerges at an Ic that is orders of magnitude smaller than expected, which is possibly caused by the slippery solid surfaces. Other flow processes such as flow separation and recirculation might explain the uncertainties in the power law relationship here and these merit future investigations.