Analysis of steady flow in radial porous media

Abstract

Abstract The outflow depth from the radial porous media (inflow to the well) is very useful as the downstream boundary condition and the starting point for water surface profile calculations. Based on the studies, unlike the Stephenson's hypothesis (the outflow depth is equal to the critical depth), the outflow depth from the rockfill media is a coefficient (Γ) of the critical depth. In the present study, using several (large scale and almost real) experimental data in the radial non-Darcy flow condition, dimensional analysis and the particle swarm optimization (PSO) algorithm, an equation was presented to calculate the mentioned coefficient based on upstream water depth (h) and distance between the well center and the upstream (R). Then, using the calculated outflow depth and the 1D flow analysis equations, the water surface profile in the radial non-Darcy condition was calculated for the first time. The results showed that considering an outflow depth equal to the critical depth and using the proposed solution in the present study, the mean relative error (MRE) values of 83.43% and 3.53% were obtained, respectively. In addition, using the proposed solution for different experimental conditions, an average MRE of 2.58% was calculated for the water surface profile.