A Novel Semi‐Analytical Model of Pumping Test With Depth‐Decaying Hydraulic Conductivity

Depth‐decaying hydraulic conductivity () broadly exist in aquifers due to the increasing vertical geostatic stress, while it was generally estimated by the Uniform‐ model. In this study, a novel semi‐analytical model of pumping tests with depth‐decaying was developed using the Laplace transform method, Goldstein‐Weber transform method, and the Green's function method. The decay of along the depth profile was described using an exponential function. The new model was named the Decay‐ model, and it was tested by the finite‐difference solution and field data. Results indicated that the attenuation coefficient () had a significant impact on drawdown, and greater values resulted in greater drawdown rates. Although the Uniform‐ model performed well when fitting to the observation data at any one of the spatial locations in the heterogeneous aquifer, the estimated parameters cannot represent the real aquifer with decaying . The determination of aquifer heterogeneity required two or more sets of time‐serials drawdown at different aquifer locations with the distance between them as far as possible. The drawdown was more sensitive to the parameters of and the hydraulic conductivity at aquifer top than the other parameters. The Decay‐ model was an extension of the Uniform‐ model, and it outperformed in the interpretation of field pumping tests. The Decay‐ model is recommended, regardless of homogeneous or heterogeneous aquifers.