土壤一维稳态溶质迁移研究的边界层方法比较

A Comparative Analysis of Boundary Layer Methods in Solving Convectiondispersion Equation of Solute Transport

边界层方法为土壤溶质迁移研究中描述一维稳态流条件下,仅考虑吸附作用的对流-弥散方程(Convection-dispersion equation,CDE)的求解和参数估算提供了简单可靠的新手段,利用该方法可以有效避免参数反演的不唯一性。对不同边界层解(多项式解、指数解、复合解、对数解和微小通量解)在预测溶质浓度分布和估算溶质迁移参数方面的精度进行了对比研究,归纳了边界层解的适用范围和选取方法。结果表明:边界层解的精度受平均孔隙水流速、弥散系数和延迟因子共同影响,当溶质浓度随剖面深度的变化率呈不断减小趋势时边界层解与精确解最接近;边界层解预测溶质分布误差随时间推移先减小后增加,溶质迁移过程初期三次多项式解精度最高,后期指数解表现最好;边界层方法对延迟因子的估算结果优于弥散系数,且不同边界层解对延迟因子的估算值近似,三次多项式解和对数解估算弥散系数最为准确。

【Objective】Understanding the behaviours of solute transport in soils is of great importance to agricultural management,resource utilization and environmental protection.Introducing boundary-layer theory to solve solute transport problems provides a simple and accurate alternative method to predict solute profile distribution and estimate transport parameters.Appropriate selection of boundary layer solutions requires an overall understanding of the characteristics of boundary layer solution accuracy under different conditions.【Method】This study compared the accuracy of the polynomial solution,exponential solution,combined solution,logarithmic solution and small flux solution based on multiple parameter combinations.Solute front movement with time in soil column experiments was further used to evaluate the performance of boundary layer solutions for parameter estimation.【Result】The accuracy of boundary layer solutions for predicting solute concentration profile increased first and then decreased with time.Comparison of different boundary layer solutions indicated that the cubic polynomial solution was optimal at the beginning while the exponential solution turned to be better afterwards for most cases.Importantly,the boundary layer methods performed better in estimating retardation factor than dispersion coefficient.The retardation factor obtained from boundary layer solutions was almost the same but with an exception of the small flux solution.The dispersion coefficient was greater than the breakthrough curve fitting method and varied between boundary layer solutions.The cubic polynomial and logarithmic solutions had a minimum error in the determination of the dispersion coefficient.【Conclusion】Boundary layer solutions can be used to accurately predict solute profile distribution for the early stage of solute transport processes.Cubic and exponential solutions had better performance than other solutions.Neverthless,cubic and logarithmic solutions can be the first choice for estimating parameters.