Abstract In this study, the PC-SAFT equation of state is used for vapour-liquid equilibrium calculations using as independent variables the mixture composition, density and temperature. The method is based on unconstrained minimisation of the Helmholtz Free energy via a combination of the successive substitution iteration and Newton-Raphson minimisation methods with line-search; the positive definiteness of the Hessian is guaranteed by a modified Cholesky decomposition. The algorithm consists of two stages; initially, the mixture is assumed to be a single-phase and its stability is assessed; in case of being found unstable, a second stage of phase splitting (flash) takes place, in which the pressure of the fluid and compositions of both the liquid and vapor phases are calculated. The reliability of two different methods presented in the existing literature, (i) using mole numbers and (ii) using the logarithm of the equilibrium constants as iterative variables, is evaluated in terms of both iterations and computational time needed to reach convergence, for seven test cases. These include both single and multicomponent Diesel fuel surrogates, known to give incomplete density information when using pressure and temperature as independent variables. Results show that iterating with the logarithm of the equilibrium constants also reproduces this issue, while it requires a smaller number of iterations than using with mole numbers as independent variables. However, the total computational time needed for the latter case is vastly inferior. Pressure and vapor volume fraction fields are discussed for a range of temperatures and densities, apart from the number of iterations needed during the flash calculation stage. A performance comparison is obtained against the Peng-Robinson equation of state, showing similar number of iterations required but a computational time increasing with the number of components. While for a single component PC-SAFT needs around 3 times more CPU time, for 4 components it is 6 times and for a mixture of 8 components it increases up to 14 times. Finally, the method is demonstrated to converge unconditionally for all conditions tested.

中文翻译：

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使用扰动链统计相关流体理论 (PC-SAFT) 状态方程在指定成分、密度和温度下计算气液平衡

摘要 在本研究中，PC-SAFT 状态方程用于以混合物成分、密度和温度为自变量的汽液平衡计算。该方法基于 Helmholtz 自由能的无约束最小化，通过将连续替换迭代和 Newton-Raphson 最小化方法与线搜索相结合；Hessian 的正定性由修正的 Cholesky 分解保证。该算法由两个阶段组成；最初，假设混合物为单相并评估其稳定性；如果发现不稳定，则进行第二阶段的分相（闪蒸），在此阶段计算流体的压力以及液相和气相的组成。现有文献中提出的两种不同方法的可靠性，(i) 使用摩尔数和 (ii) 使用平衡常数的对数作为迭代变量，根据迭代和达到收敛所需的计算时间来评估，对于七个测试用例。这些包括单组分和多组分柴油替代品，已知在使用压力和温度作为自变量时会提供不完整的密度信息。结果表明，使用平衡常数的对数进行迭代也重现了这个问题，但与使用摩尔数作为自变量相比，它需要的迭代次数更少。然而，后一种情况所需的总计算时间要差得多。除了闪蒸计算阶段所需的迭代次数外，还针对一系列温度和密度讨论了压力和蒸汽体积分数场。对 Peng-Robinson 状态方程进行了性能比较，显示所需的迭代次数相似，但计算时间随着组件数量的增加而增加。对于单个组件 PC-SAFT 需要大约 3 倍的 CPU 时间，对于 4 个组件是 6 倍，对于 8 个组件的混合，它增加到 14 倍。最后，证明该方法对于所有测试条件无条件收敛。显示所需的迭代次数相似，但计算时间随着组件数量的增加而增加。对于单个组件 PC-SAFT 需要大约 3 倍的 CPU 时间，对于 4 个组件是 6 倍，对于 8 个组件的混合，它增加到 14 倍。最后，证明该方法对于所有测试条件无条件收敛。显示所需的迭代次数相似，但计算时间随着组件数量的增加而增加。对于单个组件 PC-SAFT 需要大约 3 倍的 CPU 时间，对于 4 个组件是 6 倍，对于 8 个组件的混合，它增加到 14 倍。最后，证明该方法对于所有测试条件无条件收敛。