Particle size distribution on Forchheimer flow and transition of flow regimes in porous media

This study provides experimental evidence of Forchheimer flow and transition between flow regimes from the perspective of particle uniformity coefficient. We have designed two series of experiments to investigate the particle size control on Forchheimer flow, including two kinds of quartz sands with mixed particle sizes according to different mass ratio, and five particle sizes mixed according to different uniformity coefficients. For the experimental results of two mixed particle sizes, the critical Reynolds number (Re) corresponding to the transition of flow regimes increases with the increase of coarser particle content. Besides, deviation from Darcian flow has been observed from experimental results of mixed five particle sizes. Specifically, the pre-Darcian flow regime, or non-Darcian flow at low velocity in which the "pseudo" hydraulic conductivity increases with Re, has not been observed, where the "pseudo" hydraulic conductivity is defined as the ratio of the specific discharge over the hydraulic gradient. However, the post-Darcian flow regime, or non-Darcian flow at high velocity in which the "pseudo" hydraulic conductivity begins to decrease when Re reaches a certain value, has been identified. In contrast, above observations are absent in experiments using single-size particles even when the size of the single-size particles is the same as the mean size of the mixed-size particles. A greater discrepancy among the particle sizes in the mixed-size particles used in the flow experiments results in a lower "pseudo" hydraulic conductivity even when the mean size of the mixed-size particles remains the same. The degree of deviation from the Darcian flow has been quantified, and the relation between a newly defined Reynolds number for Forchheimer flow (Re-F) and the friction factor are constructed. Our experiments show that when Re-F is greater than 0.1, the experimental data begin to deviate from Darcian flow considerably. This study shows that the uniformity coefficient of porous media, which is a term used to describe the pore size distribution, is a critical factor for determining the flow regimes besides the mean particle sizes.