多组分体系单级萃取平衡的Newton-Raphson算法

NewtonRaphson Algorithm for Calculation of ExtractionEquilibrium in MultiComponent System

提出了一种多组分（λ）体系串级萃取动态仿真中的单级萃取平衡和物料平衡计算的新方法。该方法分别导出了有机相萃取量、水相洗涤量和混合萃取比等限制条件下两相组成关系的２λ元非线性方程组，构造以水相（或有机相）中某一组分的平衡含量为变量的目标函数（一元非线性方程），采用ＮｅｗｔｏｎＲａｐｈｓｏｎ迭代法求解，并以萃取平衡和物料平衡关系得到该级其它所有组分在两相的含量。与原采用的“二分法”方程求解相比，该方法具有计算速度快、收敛性好等优点，对允许误差ε＜１０－７体系的求解迭代次数一般仅为３～６次，可数倍提高运算速度，因而对微机环境下实现萃取体系的动态仿真和自动控制十分有利。

ased on the extraction equilibrium and mass balance in countercurrent extraction systems, a novel method for dealing with the extraction equilibrium and the mass distribution in the multicomponent(component) system was proposed. The 2 dimensions simultaneous equations were obtained to express the relationships of mass distribution(xi, yi; i=1, , ) between two phases. This simultaneous equations can be converted to a onedimension nonlinear equation which can be solved by NewtonRaphson algorithm within a few interactions. Compared with the normal calculation for the 2 dimensions simultaneous equations, NewtonRaphson algorithm can decrease the iteration times, increase the convergence of the equations and accelerate the speed of simulation. It was demonstrated with satisfactory results in many multicomponent systems. As an example, a fivecomponent system was shown in this paper.