用正交配置法求解搅拌槽液相吸附动力学模型──以权函数数ω(x)=1和球形吸附剂为基础

SOLUTION OF ADSORPTION MODELIN A BATCH ADSORBER USING ORTHOGONALCOLLOCATION METHOD BASEDON w(x) = 1 AND SPHERICAL ADSORBENTS

用正交配置法求解了球形吸附剂在搅拌槽中的液相吸附动力学模型，并构造出权函数ω（x）＝1时配置点数从1至20且适用于球体对称性问题的正交配置系数表，同时还讨论了权函数对收敛速度和粒内吸附量分布的影响．结果表明，对于文中所讨论的搅拌槽液相吸附，若用低次正交多项式求解，则对大部分吸附过程，权函数为ω（x）＝1－x2时的收敛速度比权函数为ω（x）＝1时的更快；而仅在吸附初始阶段，后者的收敛速度才比前者的更快．与权函数ω（x）＝1-x2时一样，矩阵A和B具有各行元素之和等于零的特性，而矩阵W具有各个元素之和等于形状因子之倒数的特性．

This paper is concerned with the numerical solution of the equations ofliquid-phase adsorption in a batch adsorber by the orthogonal collocation method. It is discussed that the effect of weighting functions on both convergency and intraparticle adsorbateconcentration. The orthogonal collocation coefficients for symmetric sphere are constructedfor the collocation points N which are ranged from 1 to 20, based on the weighting functionw(x) = 1. The matrixes A and B are characterized by that the summation of all elements ineach row of A or B is equal to zero, and the matrix W is characterized by that the summationo f all elements in W equals the reciprocal of the shape factor (a), as that as in w(x) =1-x2.FOr the discussed adsorption model, low-order approximations using the weighting functionw(x) = 1-x2 are better than that using the weighting function w(x) = 1 except for thestarting part of the process.