Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk

In this paper, we used the continuous time random walk (CTRW) framework to characterize the transport process in 1250-cm long one-dimensional homogenous and heterogeneous soil columns at the experiments conducted by Huang et al. [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large, homogeneous and heterogeneous, saturated soil columns. Trans. Porous Media. 18, 283–302]. The transport process was also simulated by using the advection–dispersion equation (ADE) and the spatial fractional advection–dispersion equation (FADE) for comparison. In the homogeneous soil column, the non-Fickian behavior is found at the distances less than 1000 cm with β values larger than 1.60, but less than 2, and Fickian form transport is obtained at distances larger than 1000 cm with β values larger than 2. In the heterogeneous soil column, we found the most anomalous behavior at distances from 200 cm to 700 cm with β values ranging from 0.894 to 0.958, and non-Fickian transport process is observed at distances larger than 800 cm with β values in the range between 1 and 1.3. More significant non-Fickian behavior is found for transport in the heterogeneous soil column than that in the homogeneous soil column. The CTRW fits to the breakthrough curves (BTCs) have lower values of root mean square error (RMSE) and higher values of determination coefficient (r2), with respect to the fits of ADE and FADE. The CTRW model also is better captures the full evolution of BTCs, and especially their tails.