Estimating correlation lengths of aquitard hydraulic conductivity by inverse geostatistical modelling of a pumping test

Aquitards are common hydrogeological features in the subsurface and its properties are important for e.g. water resource management, subsidence, contamination transport and aquifer thermal energy storage. Typically pumping test are used to parameterize the hydraulic conductivity of aquitards. However, with analytical interpretation of pumping tests it is difficult to take spatial variability and uncertainty into account. Alternatively, core-scale measurements of hydraulic conductivity are used in geostatistical upscaling methods, for which their correlation lengths are needed. However, this information is extremely difficult to obtain. In this study we investigate whether a pumping test can be used to obtain the correlation lengths needed for geostatistical upscaling and  account for the uncertainty about heterogeneous aquitard conductivity. We generated random realizations from core scale data with varying correlation lengths and inserted these into a groundwater flow model which simulates the outcome of an actual pumping test. We selected the realizations which yielded a better fit to the pumping test data than the traditional pumping test result assuming homogeneous layers. Ranges of horizontal and vertical correlation lengths that fit the pumping test well are found. However, considerable uncertainty regarding the correlation lengths remains which should be considered when parameterizing a regional groundwater flow model.