Hydrodynamic behavior of standard liquid-liquid systems in Oldshue–Rushton extraction column; RSM and ANN modeling

Abstract This study aims at evaluating the dispersed phase holdup and Sauter mean drop diameter (d32) of three liquid-liquid systems in an Oldshue–Rushton pilot column. The systems include butanol–water, n-butylacetate–water, and toluene–water with a wide range of interfacial tension. Two modeling approaches of response surface methodology (RSM) and artificial neural network (ANN) are employed. Four independent factors, including rotation rate (N: 60-240 rpm), continuous phase velocity (Vc: 0.499-0.997 mm/s), dispersed phase velocity (Vd: 0.499-0.997 mm/s), and interfacial tension ( σ : 1.75-36 mN/m) are taken into account to investigate their individual and interaction impacts. Two correlations for both responses are developed according to the composite central design (CCD) method in RSM modeling. A python-based code, an open-source project NetHub, is utilized to apply a Multi-Layer Perceptron (MLP) algorithm in ANN modeling to find the best network structure with minimum mean square error (MSE) and maximum coefficient of determination (R2). The high prediction accuracy of both developed models is confirmed by the R2 values of 0.9975 and 0.9905 for RSM and ANN modeling, respectively. The optimum network structure contained four layers with 15, 20, 10, and 2 neurons at each layer, respectively, achieving the minimum MSE value of 0.0023.