非稳态条件下壤中氡浓度数理模型探讨

Research on mathematic-physical model of radon migration in soil under unsteady conditions

壤中氡具有很强的运移能力,作为一种示踪元素被广泛应用在各个领域。分析了壤中氡的运移机理,以扩散作用和对流作用为基础,建立了非稳定条件下氡及其子体在壤中运移的定解问题。求解表明,在镭-氡平衡条件下,非稳态壤中氡浓度随深度的变化可表述为2种变化规律的合成:(1)氡浓度随深度增加呈饱和指数曲线规律增长;(2)氡浓度随时间呈余弦规律振荡,其振幅为该深度氡浓度变化极差统计平均值的1/2。通过20多天壤中氡浓度连续动态监测数据拟合表明,理论预测值与实测值基本吻合,相关系数为0.62。

Radon has very strong migration ability in soil. As a tracer element, radon is widely used in various fields, such as uranium exploration, oil gas exploration, engineering geology and earthquake prediction. This paper proposes a mathematic-physical model of radon transport in soil under the nonsteady conditions based on the diffusion and convection theory. Under the conditions of Ra-Rn radioactivity equilibrium, that the radon concentration in soils varies with depth and time can be described as the combination of two parts： 1） the radon concentration increases with depth by the rule of saturated exponent curve; 2） the radon concentration oscillates with time in the way of cosine curve and the amplitude is half of the extreme range of the radon concentration at this depth. An experiment for measuring radon concentration in soil is designed and the radon concentration in soil lasting for 20 days obtained. The results show that the radon concentration in soil calculated by the equation is basically consistent with that by the experiment and the relation coefficient between them is 0.62.