Transient hydraulic tomography in a sandbox with deterministic heterogeneity: Validation of hydraulic conductivity and specific storage tomograms

Hydraulic tomography is a method that images the hydraulic heterogeneity of the subsurface through the inversion of multiple pumping test data. Transient hydraulic tomography differentiates itself from steady-state tomography in that it not only estimates hydraulic conductivity but also provides an estimate of specific storage. Since it adopts transient pumping test data, it utilizes more data from each pumping test than steady-state tomography. Here, we investigate the information content of transient drawdown data through the analysis of synthetic and laboratory pumping test data in a 2-dimensional sandbox. In a synthetic study, pumping tests are performed on a computer model and the data generated is then used in the inversion. For the laboratory sandbox studies, pumping tests are performed on a physical sandbox model with deterministic heterogeneity. The data generated from these "real" tests are then used for transient inversions. To validate the tomograms, we utilize other hydraulic tests conducted at multiple scales in the sandbox such as permeameter tests on extracted cores, slug tests, single-hole tests, cross-hole tests and large-scale pumping tests. Validation consists of: 1) comparing local hydraulic conductivity and specific storage values from independent hydraulic tests to local values from transient hydraulic tomography; and 2) comparing the statistical moments of hydraulic conductivity and specific storage from the inverse model to those from other measurements. After validation of the results, we examine the information content of transient drawdown data by comparing the early, intermediate and late stages of drawdown data and the corresponding tomograms resulting from these data. We also compare the transient results with the hydraulic conductivity distribution from previously conducted steady-state hydraulic tomography to examine whether transient pumping data can improve the quality of the hydraulic conductivity tomograms. Finally, we use the hydraulic conductivity and specific storage tomograms from transient hydraulic tomography to predict the drawdown curves of other pumping tests that we did not use in the inversion.