Developing RSM-CCD model as the essential steps in the description of mass transfer efficiency of Scheibel exctractor

•Examination of the mass transfer efficiency in the pilot plant Scheibel extraction column.•Assessment the impact of operational conditions, such as mixing rate, continuous and dispersed phase velocities on the continuous phase overall mass transfer coefficient.•Developed a novel correlation as function of Sherwood and Reynolds number and also hold-up of dispersed phase to predict Koc.•Proposed a quadratic model by RSM-CCD modeling in terms of independent variables. Extraction columns are crucial equipment utilized in the liquid–liquid extraction (LLE) separation process. Examining mass transfer efficiency of the extraction columns is essential for their design and scale-up. In the current research, the mass transfer efficiency of two standard systems is examined in the Scheibel extraction column. A total of 42 experimental data points were collected to assess the impacts of different operating conditions such as Vd, Vc, and N on the quantities of interfacial area and Koc for d to c and c to d mass transfer directions. Based on the results, Koc increases with an enhancement in the mixing rate and Vd, but the impact of Vc is marginal. To predict Koc, a novel empirical correlation was developed as function of Shoc, Re, and φ for both mass transfer directions. This correlation is more precise and reliable than previous models and correlations, with an AARE% of less than 15. Furthermore, a quadratic model was proposed using RSM-CCD modeling as a function of independent variables such as Vd, Vc, N, and σ. The experimental data exhibited a satisfactory agreement with the outputs of the quadratic model when estimating Shoc and Koc.