Prediction of post-Darcy flow based on the spatial non-local distribution of hydraulic gradient: Preliminary assessment of wastewater management

Abstract

Understanding high-velocity pollutant transport dependent on the large hydraulic gradient and/or heterogeneity of the aquifer and criteria for the onset of post-Darcy flow have attracted considerable attention in water resources and environmental engineering applications. In this study, a parameterized model is established based on the equivalent hydraulic gradient (EHG) which affected by spatial nonlocality of nonlinear head distribution due to the inhomogeneity at a wide range of scales. Two parameters relevant to the spatially non-local effect were selected to predict the development of post-Darcy flow. Over 510 sets of laboratory one-dimensional (1-D) steady hydraulic experimental data were used to validate the performance of this parameterized EHG model. The results show that (1) the spatial nonlocal effect of the whole upstream is related to the mean grain size of the medium, and the anomalous variation due to the small grain size implies the existence of the particle size threshold. (2) The parameterized EHG model can effectively capture the nonlinear trend that fails to be described by the traditional local form of nonlinear models, even if the specific discharge stabilizes at the later stages. (3) The Sub-Darcy flow distinguished by the parameterized EHG model can be equated to the post-Darcy flow, and then the criteria for the post-Darcy flow will be strictly distinguished under the premise of determining the hydraulic conductivity. The results of this study facilitate the identification and prediction of high-velocity non-Darcian flow in wastewater management and provide insight into mass transport by advection at the fine-scale.

Keywords: Forchheimer number; Groundwater contamination; High velocity non-darcian flow; Particle size threshold; Spatially non-local effect.