A technical–economic framework for selection of optimal collector combinations in apatite flotation via TOPSIS multi-criteria decision-making

The sustainable beneficiation of low-grade phosphate ores, especially those containing apatite, is vital to meet the increasing global demand for phosphorus in agricultural and industrial applications. This study proposes a novel, data-driven framework for optimizing collector combinations for direct apatite flotation, through the integration of experimental evaluation and multi-criteria decision-making analysis. A series of micro- and bench-scale flotation tests were conducted on samples from the Chadormalu deposit (Iran), utilizing a wide spectrum of surfactants, including anionic, nonionic, and ethoxylated reagents. Among the tested formulations, a combined collector system consisting of Tall Oil Fatty Acid (TOFA) and oleic acid polyethylene glycol ester (OAPEGE6), designated as TO6, exhibited superior performance, achieving 91.1% recovery and 22.2% P2O5 grade in alkaline conditions (pH = 9.5). To resolve the inherent trade-offs between metallurgical performance and economic feasibility, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed as a multi-criteria decision-making tool. Performance metrics including flotation efficiency, reagent cost, and availability were normalized and objectively weighted using Shannon entropy. The integrated analysis ranked eight collector formulations, identifying the TO6–diesel system as the optimal configuration, delivering enhanced flotation performance with competitive cost efficiency. This research establishes a reproducible and quantitative framework for collector selection in apatite flotation, bridging experimental mineral processing and decision-science methodologies. The proposed approach provides a scalable strategy for improving reagent optimization in industrial phosphate beneficiation circuits.