Development of adaptive neuro-fuzzy inference system and stochastic simulation for mean droplet size modeling in rotatory agitated columns under different mass transfer scenarios

Artikel i vetenskaplig tidskrift, 2024

The liquid–liquid extraction types of equipment are of substantial significance in industrial fields due to their effectiveness in facilitating the separation and purification of substances. Different types of rotatory agitated columns, such as RDC, ARDC, PRDC, Oldshue-Rushton, Kühni, and Scheibel, are evaluated for their performance. The nonlinearity and complexity of the mechanisms in these columns present challenges for accurately predicting the droplet behavior using available empirical models. Hence, this paper developed machine learning (ML) models, adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), support vector regression (SVR), and gradient boosting algorithm (GBA) utilizing a dataset of 1135 experimental points to predict mean droplet size (d32) under different mass transfer conditions. The ANFIS model surpasses ANN, SVR, and GBA models, demonstrating enhanced precision and resilience. The mean squared error (MSE) values for the ANFIS were recorded at 0.004 and 0.009, while the root mean squared error (RMSE) values stood at 0.065 and 0.094 during both the training and validation stages, respectively. Subsequently, the Monte Carlo simulation (MCS) was utilized, employing the PERT distribution function to model uncertain variables within the ANFIS model, considering their asymmetric distributions. The simulations revealed a mean d32 of 2.0482 mm with a 90% confidence interval of [2.0398 mm, 2.0567 mm], a standard deviation of 0.5154 mm, skewness of −0.5882, and kurtosis of 3.6297. The sensitivity analysis based on permutation importance highlighted agitation speed as the most influential parameter, followed by fractional free area and interfacial tension, indicating their significant impact on d32. The optimized model's capacity to efficiently manage the intricacies and non-linearities present in dispersed phase droplets represents the first comprehensive progression from conventional empirical approaches, opening up possibilities for enhanced efficiency and dependability in industrial applications.