Revolutionizing Dye Removal: Unleashing the Power of Liquid–Liquid Extraction Batch Process

This study focuses on numerically optimizing key process parameters related to the liquid–liquid extraction batch process (LLEBP) technique for carrying out batch runs to remove methyl red effectively (MR) from dye effluent. LLEBP, a suitable industrial process for treating dye effluents, depends on the number of reaction parameters such as feed concentration, extraction time, and dye ratio (solution/solvent). The current research utilized a central composite design (CCD) of experiments along with numerical optimization techniques to optimize process parameters over a range of dye concentrations: (20–100) ppm, extraction time range 10–30 min, and dye ratio 1–3 mL/mL (solution/solvent). The batch runs performed at room temperature and a constant pH of 3, according to the experimental design criteria, suggest that maximum dye removal efficiency and distribution coefficient value could be achieved within the feed concentration range of (20–30) ppm, 20–30 min of extraction time, and 1–3 mL/mL of dye ratio (solution/solvent). Solvent capacity increases significantly within the (60–100) ppm feed concentration range. Numerical optimization with desirability function criteria identified optimal conditions: 20 ppm dye concentration, 30 min extraction time, and 3 mL/mL dye ratio ensuring maximum LLEBP yield. The current investigation achieved a 4% higher dye removal (%) of 85.682 compared to the previous study. The distribution coefficient and solvent capacity attained were 5.287 and 4.504 mg/L, respectively. The research enhances understanding of the optimization process for LLEBP in MR dye removal from textile effluent, surpassing previous findings within the same input range. The manuscript aims to maximize process optimization using CCD, promoting sustainable industry progress in line with UN sustainable development goals.