Estimation of PC-SAFT binary interaction coefficient by artificial neural network for multicomponent phase equilibrium calculations

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, ε/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.