HOW SEDIMENT TEXTURE CONTROLS INERTIAL FLOW PHENOMENA OF POROUS MEDIA: A PORE-SCALE PERSPECTIVE

In the sciences and engineering, there are numerous applications for studying how high velocity fluids pass through porous media. Darcy's law governs the linear relationship between velocity and hydraulic gradient, but when inertia becomes dominant, the relationship between velocity and hydraulic gradients follows the non-linear Forchheimer equation. Previous theoretical and empirical studies have tried to predict the Forchheimer inertial coefficient ß, which can be distinguished into two common approaches; 1) based on porosity and sediment size (e.g., d₅₀) and 2) based on the combined effect of porosity and permeability. The goal of this research is to predict ß as a function of sediment and hydraulic characteristics, e.g., d₅₀ and permeability (k) since it enables the usage of Forchheimer equation based on groundwater equations for engineering projects such as energy storage of hydrogen fuel, nutrient cycling, groundwater storage and recovery, and movement of human waste prediction. We create 2D microstructures with variable porosity ranging from 25% to 40% in this computational modeling study. As non-linearity thresholds, we calculate critical head gradient and critical Reynolds number. We investigate mechanisms such as energy dissipation and velocity distribution that control ß. We find, 1) the relationship between ß and permeability follows a power law relationship and 2) critical head gradient follows a power law relationship with porosity and permeability, and 3) normalized energy dissipation depends linearly on hydraulic gradient from viscous to inertial flow regimes.

Keywords: Forchiemer equation; Forchheimer inertial coefficient ; Permeability; Mechanisms of Non-linear flow; Darcy law