李-凯斯勒方程的牛顿-二分求解法

李-凯斯勒方程能够准确描述烃类多组分混合流体的P-V-T性质,在稠油化学复合冷采过程中,李-凯斯勒方程常常被用于计算稠油的物性。通过对牛顿法和二分法进行优势互补,本文提出了基于最小自由能原理的李-凯斯勒方程牛顿-二分混合求解算法。该算法先是参照二分法的思路迅速从李-凯斯勒方程的定义域内搜寻出目标区间,随后利用牛顿迭代公式求解出区间内的实根及对应的吉布斯自由能,最后迭代这一过程直至自由能不再下降。牛顿-二分混合算法的优点包括：①对初值不敏感,无需配合复杂的初值生成规则使用；②收敛速度快,相较于二分法而言可以加速1-2倍；③适用范围广,可同时适用于气相与液相流体。相较于牛顿法和二分法而言,牛顿-二分混合算法更适合嵌入各类模拟软件中进行混合流体的P-V-T性质计算。

Hybrid Newton-Bisection algorithm based on the minimum free energy principle for solving Lee-Kesler equation

The Lee-Kesler equation can accurately describe the P-V-T properties of multi-component hydrocarbon mixtures, which is usually used to calculate the state of equation of the heavy oil during simulating the chemical compound flooding process. By incorporating the advantages of Newton and bisection methods, a hybrid Newton-Bisection algorithm based on the minimum free energy principle is proposed for solving the Lee-Kesler equation. This algorithm follows the idea of bisection method at the beginning to quickly find the target interval from the definition domain of Lee-Kesler equation. After that, the Newton iterative formula is used to calculate the real root in the interval and the corresponding Gibbs free energy. Finally, the process is iterated until the free energy no longer decreases. There are three advantages of the hybrid Newton-Bisection algorithm. First of all, it is robust and insensitive to the initial value. Secondly, the calculation can be converged quickly, which is 1-2 times faster than the bisection method. Moreover, it has a wide range of applications and can be applied to calculate the P-V-T properties of both gas and liquid mixtures. Compared with the Newton and bisection methods, the hybrid Newton-Bisection algorithm is more suitable to be embedded in simulation software to calculate the P-V-T properties of the hydrocarbon mixtures.