Determination of groundwater flow regimes based on the spatial non-local distribution of hydraulic gradient: Model and validation

The groundwater flow in natural aquifers can change from the Darcy flow to the non-Darcian flow due to a variety of causes, such as the increase of the Reynolds number in the highly permeable media or the decrease of the hydraulic gradient below a threshold in the low-permeability media, while the representative flow regime cannot be reliably determined using the traditional criteria. To address this challenge, this paper proposes a new term called the equivalent hydraulic gradient (EHG) by generalizing the differential form of the Darcy’s law using a spatial integral of the upstream hydraulic head. The nonlocal spatial variation of the hydraulic head difference between upstream and downstream zones is assumed to be the potential cause of the transition of the groundwater flow regimes. This assumption is analogous to the common assumption used for quantifying the anomalous pollutant transport in the geological media. Applications of this idea show that the EHG concept could distinguish three main flow regimes, namely the Super-Darcy flow, the Darcy flow, and the Sub-Darcy flow, although the Super-Darcy flow regime is rarely observed in the laboratory column flow experiments. Results of this study therefore shed lights on the interpretation of the fundamental dynamics of the groundwater moving in various heterogeneous aquifers, and may lead to the rebuilding of the hydrodynamics of the surface water, the groundwater, and the soil.