Regularized pilot points method for reproducing the effect of small scale variability: Application to simulations of contaminant transport

Small scale variability of hydraulic conductivity controls ground water contaminant transport and some of the subtle aspects of transport through heterogeneous media (e.g., mixing and tailing). Unfortunately, it cannot be identified. This paper addresses the question of whether the presence of high frequency fluctuations, which define small scale variability, impedes the characterization of large scale variability patterns. In parallel, we investigate whether including small scale variability allows us to reproduce tailing in breakthrough curves. To this end, we solve the inverse problem using the regularized pilot points method for simulating fields of hydraulic conductivity conditioned to available information. Heterogeneity of hydraulic conductivity is represented by two nested variograms simulating small scale (short range variogram) and large scale (long range) variability patterns. Calibrated fields are applied to the prediction of a transport problem. Application to four synthetic examples (with varying importance of the small scale variability) shows that, first, the calibrations reproduce the statistics of the “true” fields and, second, that a good characterization of the small scale variability is not critical for groundwater flow modeling. More important, small scale variability leads to increased tailing in solute breakthrough curves and needs to be acknowledged for proper transport prediction, which is rarely the case in aquifer modeling practice.