Machine learning and response surface analysis of mean drop size and dispersed phase holdup in an L-shaped pulsed sieve plate column

This study explores the hydrodynamic behavior of four distinct nitric acid-TBP/kerosene systems in an L-shaped pulsed sieve-plate column (LPSPC), with a focus on predicting Sauter mean drop diameter (SMDD) and dispersed phase holdup (DPH). The complex interactions between operating parameters, pulsation intensity, flow rate, and hydrodynamic performance were modeled using response surface methodology (RSM) and artificial neural networks (ANN). This is the first side-by-side assessment of ANN versus RSM for LPSPC. The model was trained on experimental dataset, with 70% for training, 15% for validation, and 15% for testing, respectively. A compact two-hidden-layer topology with 10 and 5 neurons with trainbr was selected after a systematic search over 1–4 layers and three training algorithms. The ANN model achieved R2 values of 0.9950, 0.9970, 0.9900, and 0.9822 with MSE values of 0.000314, 0.000451, 0.000019, and 0.000001 for SMDD-horizontal, SMDD-vertical, DPH-horizontal, and DPH-vertical, respectively. At the same time, RSM was slightly better for SMDD-vertical. Complementing these data-driven models, new dimensionless semi-empirical correlations derived via Buckingham’s π-theorem agreed well with experiments, yielding AAREs of 6.95% and 8.29% for SMDD, and 6.56% and 8.68% for DPH in horizontal. Together, these tools provide accurate and usable surrogates for analyzing and optimizing extraction systems relevant to the purification of yellow cake.