An Analytical Solution for Non-Darcian Flow on a Constant Head Packer Test in the Interlayer Staggered Zone

Abstract

Groundwater flow in an aquifer has frequently been found to be non-Darcian by performing in situ tests. A novel analytic model is proposed in this study for describing the unsteady non-Darcian flow in a confined aquifer by taking advantage of the observed flow rate and injection pressure during the constant head packer test. A linearization approximation of the Izbash equation is used to approximate the nonlinear term in the governing equation. This analytic model is applied to describe the non-Darcian flow in the interlayer staggered zone at the Baihetan hydropower station, China. The test results inversed by the genetic algorithm show that non-Darcian flow happened during the test under the injection pressure 0.3 MPa with the power index $n$ is 1.278, non-Darcian hydraulic conductivity $k_1$ is $1.613\times {10}^{-5}$  cm/s and the specific storage $S_{\text{s}}$ is $9.757\times {10}^{-5}$  m-1, respectively. The sensitivity analysis indicated that when the power index $n$ or the specific storage $S_{\text{s}}$ is larger, and the hydraulic head will increase more slowly and needs longer to stabilize, but the non-Darcian hydraulic conductivity $k_1$ shows the opposite trend. Moreover, the hydraulic head is more sensitive to the power index $n$ compared to other parameters at late times. The findings of this study reveal the non-Darcian flow during the constant head packer test and provide a simple and fast way to estimate parameters for more accurate seepage field simulation.