The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (\(d_{50 }>0.39\) mm) to gravel (\(d_{50}=6.3\) mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size \((d_{50})\) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased \(C_{u}\) values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size \((d_{50})\) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal \(d_{50}\), resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of \(d_{m}-\sigma \) as characteristic pore length predicted the coefficients a and b accurately.