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 eff ectively (MR) from dye effl uent. LLEBP, a suitable

industrial process for treating dye effl uents, 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

effi ciency and distribution coeffi cient 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 signifi cantly within

the (60–100) ppm feed concentration range. Numerical optimization with desirability function criteria identifi ed 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

coeffi cient 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 effl uent, surpassing previous fi ndings 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.