The estimation of the spatial variability of the flow parameters using hydraulic tomography

Abstract

Natural geologic systems are heterogeneous with complex patterns of spatial variability and this heterogeneity strongly influences groundwater flow and contaminant transport. Therefore, the estimation of the spatial variability of subsurface flow parameters is essential for the modeling and prediction of groundwater flow and contaminant transport. Pumping tests are often used for the estimation of flow parameters. However, the interpretation of these tests is routinely performed using conventional methods that assume the parameters are uniform which is in contradiction with most real systems. The main objective of this thesis is to combine a recently developed pumping test interpretation technique, referred to as the Continuous Derivation method, with data obtained from hydraulic tomography. Hydraulic tomography is a novel field data acquisition technique that involves the sequential pumping from a number of wells and observing the groundwater drawdown in adjacent wells as a function of time. Particularly, the goal was to extend the method to the estimation of the statistical spatial structure of the transmissivity using hydraulic tomography data. In geostatistics, the statistical spatial structure of a parameter refers to the pattern of how this parameter varies in space. The emphasis was on estimating how the transmissivity varies with distance from the pumping well and then use that information to estimate the statistical parameters, namely the integral scale and variance. Synthetic pumping tests were used to evaluate the performance of the pumping test interpretation procedure. Heterogeneous transmissivity fields were first generated and then used to simulate transient drawdown data. The drawdown data and their time derivatives were subsequently used to estimate the flow parameters by applying the Continuous Derivation method. Single-well pumping test data as well as hydraulic tomography data derived from multiple wells were used in the interpretation method. After that, two approaches, a weighted least-squares approach and a Bayesian approach were considered for the estimation of the statistical parameters of the heterogeneous transmissivity field (integral scale and variance). The results of this study indicate that some information about the spatial structure of the transmissivity can be inferred from pumping tests. The estimation of the variance and the integral scale is however challenging in part due to the lack of ergodicity when the number of pumping test is low. The Bayesian approach was found to be somewhat superior because of its ability to account for parametric uncertainty by formulating the parameter estimation problem in a probabilistic framework.