Non-Darcy Flow: Correlation between Inertial Coefficient and Particle Size Distribution of Unconsolidated Porous Media.

Characterization of non-Darcy flow in fractured gas wells is of interest for petroleum industry for evaluation of reservoir performance. Due to the high velocity of gas streams converging to wellbores, pressure drops cannot be estimated from classical Darcy equation, where the gradient is linearly related to flow velocity. Nonlinear behavior can be accounted for in the Forchheimer equation via an inertial resistance factor. Experimental values of this so-called beta factor can be used to establish theoretical and empirical relationships to porous media properties when multi-rate pressure test results are not available or too expensive to obtain. We performed high-velocity gas flow experiments with well characterized unconsolidated materials to investigate relationships between inertial resistance and medium pore structure. Furthermore, porosity and permeability, together with the Klinkenberg constant, have been determined for natural sand cores with both flat and peaked grain size distributions. Relationships between inertial resistance and particle size distribution are presented.