河流BOD一级和二级衰减反应下氧垂公式的讨论

Discussion on DO Sag Equations for First-order and Second-order BOD Decay in River

BOD一级反应的氧垂公式呈现指数形式 ,通过求导 ,可准确求得其到达最小溶解氧浓度的时间 .推导出二级反应的氧垂公式呈现指数积分形式 ,通过求导 ,利用牛顿法可近似求得其到达最小溶解氧浓度的时间 .由实验原始数据分析出 BOD一级反应和二级反应下的氧垂曲线基本相同 ,但它们的最小溶解氧浓度、最小溶解氧浓度出现的时间及趋向饱和的快慢不同 .模型中的参数估计采用非线性最小二乘法 .

The DO sag equation for first order BOD decay incorporates exponential function. By derivation, the time at which the minimum DO concentration occurs is calculated with great accuracy. It is derived that the DO sag equation for second order BOD decay incorporates exponential integral function. By derivation, the time at which the minimum DO concentration occurs is calculated approximately with Newton's method. Based on the original test data, it is derived that although the curves of first order and second order are similar, there are differences in the minimum DO concentrations, the time at which the minimum DO concentration occurs and the speed of approaching saturation. The parameters are estimated with non linear least square method.