Analysis of pumping tests of partially penetrating wells in an unconfined aquifer using inverse numerical optimization

Inverse numerical modeling was applied to analyze pumping tests of partially penetrating wells carried out in three wells established in an unconfined aquifer in Vejen, Denmark, where extensive field investigations had previously been carried out, including tracer tests, mini-slug tests, and other hydraulic tests. Drawdown data from multiple piezometers located at various horizontal and vertical distances from the pumping well were included in the optimization. Horizontal and vertical hydraulic conductivities, specific storage, and specific yield were estimated, assuming that the aquifer was either a homogeneous system with vertical anisotropy or composed of two or three layers of different hydraulic properties. In two out of three cases, a more accurate interpretation was obtained for a multi-layer model defined on the basis of lithostratigraphic information obtained from geological descriptions of sediment samples, gamma-logs, and flow-meter tests. Analysis of the pumping tests resulted in values for horizontal hydraulic conductivities that are in good accordance with those obtained from slug tests and mini-slug tests. Besides the horizontal hydraulic conductivity, it is possible to determine the vertical hydraulic conductivity, specific yield, and specific storage based on a pumping test of a partially penetrating well. The study demonstrates that pumping tests of partially penetrating wells can be analyzed using inverse numerical models. The model used in the study was a finite-element flow model combined with a non-linear regression model. Such a model can accommodate more geological information and complex boundary conditions, and the parameter-estimation procedure can be formalized to obtain optimum estimates of hydraulic parameters and their standard deviations.