考虑弥散尺度效应与不动水体的反应性溶质运移动力学模型及半解析解

将弥散度概化为运移距离的渐进函数,并考虑土壤孔隙中存在的不动水体以及溶质的吸附和降解,建立了考虑弥散尺度效应的溶质运移两区模型(TRMS,Two-Region Model with Scale-dependent Dispersion),通过Laplace变换和de Hoog数值反演方法求得了模型的半解析解,并运用混合拉普拉斯变换有限差分法验证了半解析解的准确性。通过TRMS与弥散度为常数的两区模型(TRMC,Two-Region Model with Constant Dispersion)之间的比较,分析了弥散尺度效应对溶质运移过程的影响,并利用算术平均方法计算了TRMS的等效弥散度,最后应用TRMS和TRMC模拟了长度为1250cm的一维非均质土柱中的溶质运移过程。结果表明:TRMS的等效弥散度反映了弥散尺度效应的影响,可以近似作为区域弥散度的平均值,采用等效弥散度时,TRMC描述的穿透曲线与TRMS的模拟结果基本一致;TRMC的模拟结果与非均质长土柱的浓度实测值存在较大偏差,而TRMS的模拟精度有了较大程度的提高,能够更好地模拟非均质长土柱中溶质的不规则运移过程,说明本文建立的TRMS能够较好地模拟非均质介质中溶质在较大尺度上的运移过程。

Semi-analytical solution for reactive solute transport dynamic model with scale-dependent dispersion and immobile water

This study proposed a novel two-region model with scale-dependent dispersion (TRMS) to describe reactive solute transport in heterogeneous soils. The model was derived from the conventional TRM but assumed the dispersivity to be an asymptotic function of travel distance, considering the linear adsorption and first-order degradation of solute. The Laplace transform technique and de Hoog numerical inversion method were applied to solve the proposed model. The accuracy of semi-analytical solution was verified by a hybrid Laplace transform finite difference method. The TRMS and the two-region model with constant dispersion (TRMC) were compared to interpret the effect of scale-dependent dispersion, and the effective dispersivity for TRMS was calculated by averaging the distance-dependent dispersivity with arithmetic method. This effective dispersivity could reflect the accumulated scale-dependent dispersion effect over the entire travel domain. The TRMC with effective dispersivity could produce nearly similar breakthrough curves (BTCs) as those from TRMS. The applicability of TRMS was tested with concentration data from a 1,250-cm long and highly heterogeneous soil column. The simulation results indicated that the TRMC was unable to adequately describe the measured BTCs in the column, while the TRMS satisfactorily captured the evolution of BTCs. Therefore, this study suggests that the proposed TRMS is a simple and practical approach to describe solute transport at relatively large scale in heterogeneous porous media.