流体相平衡中 Gibbs-Duhem 方程的求解问题研究

STUDY ON COMPUTATION METHOD FOR SOLVING GIBBS-DUHEM EQUATION IN FLUID PHASE EQUILIBRIUM

本文用函数逼近法求解了 N 元体系相平衡的 Gibbs-Duhem 方程。它的原理建立在变分法的基础上。其主要特点是将一个微分方程或偏微分方程组的两点边值问题转化为在一定精度要求下等价的求解最佳逼近函数或函数向量的非线性规划问题.它的优点在于它对任意维的问题都具有统一的计算结构和它只需满足本质边界条件(如 y(0)=0,y(1)=1)。本文简述了该算法的基本原理,并给出实际算例,包括二元体系和三元体系汽相组成的推算,计算结果与平行算法的结果符合良好。

In this paper,a computing method—Approximation method for solvingGibbs-Duhem equation of fluid phase equilibrium of multi-component system is pres-ented.The method is based on the calculus of variations and the main features of it is trans-forming a boundary value problem of the partial differential equations to an equivalentoptimization problem in a given precision.The advantages of this method is that it has anidentical computational form to any dimensional problem.and only needs the intrinsicboundary condition[i.e.,y_i(x_i=0)=0,y_i(x_i=1)=1]in solving the solution.Since its sim-ple computational form and less calculating time,it has evident superiority in solvingGibbs-Duhem equations of multicomponent vapor-liquid equilibrium.The principle ofthis method is stated and discussed.Some verification works,including the calculation ofvapor phase concentrations of binary and ternary systems,have been done.