Abstract Perturbed-Chain Statistical Associating Fluid Theory Equation of State (PC-SAFT EoS) requires cross interaction parameter for each binary pair in the mixture. For real mixtures, these parameters should be corrected by binary interaction coefficients (kij's). The values of kij's are tuned by an optimization method in order to minimize the deviation from equilibrium data. The Particle Swarm Optimization (PSO) algorithm is employed for optimization of kij's due to the continuous nature of kij and highly nonlinear nature of PC-SAFT EoS. Although kij can be adjusted using the mentioned algorithm, it is cumbersome and highly time-consuming because the optimization should be performed for each pair that exists in the multicomponent mixture. It has been shown that these optimal values can be obtained based on the basic characteristic properties of the participating molecules in each pair, this is particularly useful to avoid solving any optimization problem. Furthermore, Artificial Neural Networks (ANNs) as powerful function approximators have been used to predict binary interaction coefficients based on basic characteristic properties of molecules that exist in each pair. Two types of characteristic properties have been examined as inputs of the ANN's utilized to predict the optimum kij's. The first one contains PC-SAFT parameters (m, e / k , σ) and molecular weight of each component; while the second category contains specific gravity, normal boiling point and molecular weight of each component. The best structure of ANN has been obtained by two approaches: 1) Genetic Algorithm (GA) and 2) a constructive approach. GA can find the structure with any possible connections between neurons whereas the constructive approach can only find the best structure for fully connected networks. The results show that the genetically designed ANN that uses the second set of inputs outperforms the others. This ANN is used to estimate kij's of PC−SAFT for a wide range of non-associating materials where the predicted kij's are in close agreement with those obtained by PSO with coefficient of determination R2 = (0.9921, 0.9631) for training and validation data, respectively. In addition to the evaluation of the ANN by validation data, its performance has been examined by using its estimated kij's in flash calculation of a synthesized multi-component mixture and bubble point calculation of a reservoir fluid. Comparing the results of equilibrium calculations with their experimental counterparts shows that they closely follow the measured data. Furthermore, its performance has been compared with other approaches of estimation of kij such as London theory and QSPR method and the results show that the proposed ANN outperforms the others.

中文翻译：

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用于多组分相平衡计算的人工神经网络估计PC-SAFT二元相互作用系数

摘要 扰动链统计关联流体理论状态方程 (PC-SAFT EoS) 需要混合物中每个二元对的交叉相互作用参数。对于实际混合物，这些参数应通过二元相互作用系数 (kij's) 进行校正。kij 的值通过优化方法进行调整，以最小化与平衡数据的偏差。由于kij 的连续性和PC-SAFT EoS 的高度非线性特性，粒子群优化(PSO) 算法被用于优化kij。尽管可以使用上述算法调整 kij ，但它很麻烦且非常耗时，因为应对多组分混合物中存在的每一对进行优化。已经表明，可以基于每对中参与分子的基本特性来获得这些最佳值，这对于避免解决任何优化问题特别有用。此外，人工神经网络 (ANN) 作为强大的函数逼近器已被用于根据每对分子中存在的分子的基本特征来预测二元相互作用系数。已经检查了两种类型的特征属性作为用于预测最佳 kij 的 ANN 的输入。第一个包含 PC-SAFT 参数 (m, e / k , σ) 和每个组分的分子量；而第二类则包含各组分的比重、正常沸点和分子量。ANN的最佳结构通过两种方法获得：1) 遗传算法 (GA) 和 2) 一种建设性的方法。GA 可以找到神经元之间具有任何可能连接的结构，而构造方法只能找到完全连接网络的最佳结构。结果表明，使用第二组输入的基因设计人工神经网络优于其他人工神经网络。该 ANN 用于估计各种非关联材料的 PC-SAFT 的 kij，其中预测的 kij 与 PSO 获得的那些非常一致，确定系数 R2 = (0.9921, 0.9631) 用于训练和验证数据，分别。除了通过验证数据对 ANN 进行评估之外，还通过在合成多组分混合物的闪蒸计算和储层流体的泡点计算中使用其估计的 kij 来检查其性能。将平衡计算的结果与他们的实验对应物进行比较，表明它们与测量数据密切相关。此外，其性能已与其他估计 kij 的方法（如伦敦理论和 QSPR 方法）进行了比较，结果表明所提出的 ANN 优于其他方法。