Impact of fractional probability distributions on statistics of hydraulic conductivity, dynamics of groundwater flow and solute transport at a low‐permeability site

Abstract

AbstractThe fractional Brownian motion (fBm) and fractional Lévy motion (fLm) can easily describe the geometry and the statistical structure of hydraulic conductivity (K) for real‐world. However, the fBm and fLm models have not been systematically evaluated when building the K field for a low‐permeability site. In this study, both the fBm and fLm are used to simulate the low‐K field at NingCheGu (NCG), Tianjin, China. Groundwater flow and solute transport are then computed using MODFLOW and MT3DMS, respectively, and the influence of the fBm/fLm models for K on groundwater flow and solute transport is discussed. Results show that the fLm fits better the statistics of the low‐K medium than fBm, and the random logarithmic K (LnK) field generated by fLm is more stable because the resultant LnK field captures more of the measured properties at the field site than that generated by fBm. In contrast, the LnK generated by fBm is more likely to form both high‐K channels and low‐K barriers. The fBm therefore predicts more extreme behaviours in flow and transport, including the preferential flow, low‐concentration blocks and solute retention. The overall groundwater renewal period and solute travel time for the fLm simulation are slightly shorter than those for fBm. The impacts of the fLm and fBm models on the statistics of the resultant LnK fields and the dynamics of groundwater flow and solute transport revealed by this study shed light on the selection and evaluation of the fractional probability distribution models in capturing the K fields for low‐K media.