基于微分方程和非线性动力学的水源污染机理分析

Analysis of Water Source Pollution Mechanism Based on Differential Equations and Nonlinear Dynamics

摘要: 河水流经地表时会渗入地下，补给地下水。一旦河流被污染往往在较短时间内导致下游河流或傍河水源受到污染。因此分析河流–地下水系统中有机污染物的对流、弥散和吸附机理具有重要理论意义和社会机制。本文用对流、弥散和吸附的综合微分方程，分析了有机污染物的行为过程。用Linear和Langmuir等温吸附模型结合的双模式函数建立等温非平衡吸附试验模型，用非线性动力学吸附方程描述吸附过程。其次针对一般等温线性吸附模型进行适当优化，对数据进行Matlab最小二乘法数值拟合，借助有限差分法和Matlab软件得出了模型在有机污染物对流、弥散时的解，即污染物浓度与距离和时间之间的关系的三维视图以及污染物扩散逐渐缓慢的结论。

Abstract: When river water flows through the surface, it seeps into the ground and recharges groundwater. Once a river is polluted, it often leads to the contamination of downstream rivers or adjacent water sources within a short period of time. Therefore, it is important to analyze the convection, dis-persion and adsorption mechanisms of organic pollutants in the river-groundwater system with theoretical significance and social mechanism. In this paper, the behavioral processes of organic pollutants are analyzed using the integrated differential equations of convection, dispersion and adsorption. The isothermal non-equilibrium adsorption test model is established with a dual-mode function combining Linear and Langmuir isothermal adsorption models, and the adsorption process is described by a nonlinear kinetic adsorption equation. Secondly, appropriate optimization was carried out for the general isothermal linear adsorption model, and the data were fitted numeri-cally by Matlab least squares method, and the solution of the model at convection and dispersion of organic pollutants was derived with the help of finite difference method and Matlab software, i.e., the three-dimensional view of the relationship between pollutant concentration and distance and time, as well as the conclusion that the pollutants diffuse gradually and slowly.