Comparison of Quadratic and Power Law for Nonlinear Flow through Porous Media

The quadratic and power laws are two typical formulations that can be used to extend the Darcy law to non-Darcy flows through porous media. Both laws are reformulated in the dimensionless form in this study. They are then evaluated by fitting to experimental data with specified variations in seepage velocity, which were specifically collected for a simplified ordered porous model. The results show that the quadratic law is applicable to both linear and nonlinear flow regimes but the two coefficients vary at different regimes. In comparison, the power law appears not workable if the seepage velocity varies over a wide range. This study also demonstrates that the two parameters included in the power law are generally interrelated, and the relationship derived based on the quadratic law compares well with the experimental results. To help understand the non-linear behavior associated with the simplified porous model, CFD simulations were also performed to visualize and elucidate localized 3D flow phenomena.