An experimental study on scale dependency of fractional dispersion coefficient

摘要

Six series of solute transport experiments were conducted with an objective to compare scale decency of fractional dispersion coefficient (D-f) in space fractional advection-dispersion equation (s-FADE) with that of dispersion coefficient (D) in advection-dispersion equation (ADE) at three flow rates. The experiments were performed in a 2.5 m x 0.1 m x 0.6 m (length x width x height) sandbox filled with a homogeneous or heterogeneous soil. The parameters of the s-FADE and ADE were estimated using an inverse method. The results indicated that the scale dependency of D-f was significantly less than that of D in the heterogeneous soil. The maximum variations of D-f and D for the heterogeneous soil were observed at the flow rate of 200 cm(3) min(-1), in which the ratios of the maximum D-f and D to the minimum ones were 6.009 and 39.039, respectively. However, in the homogeneous soil, the scale dependency of D-f was relatively similar to that of D. In this soil, the ratios of the maximum D-f and D to the minimum ones were 3.109 and 5.041, respectively, which were observed at the flow rate of 548 cm(3) min(-1). Contrary to D-f and D, the v values of the s-FADE and ADE for both soils varied in relatively similar ranges at the flow rates studied. Also, the fractional differentiation order (alpha) of the s-FADE described properly the heterogeneity degrees of the soils used. In a nutshell, the s-FADE is an efficient solute transport model to explain the solute transport process in natural porous media with different heterogeneity degrees.