Optimization of the Reaction Temperature During Phosphoric Acid Production Using Fibonacci Numbers and Golden Section Methods

The main objective of the present paper is to optimize the influence of temperature on the reactive crystallization phase during phosphoric acid manufacturing using Fibonacci numbers and Golden Section techniques. These sequential iterative optimization methods were performed at several temperatures ranging from 70 to 85 °C. Initially, two runs are conducted, and their results are used sequentially via a comparison-based approach to eliminate the unnecessary interval and generate the next run(s) until the desired optimum values are attained. A laboratory crystallizer was used to conduct several trials under set simulated conditions (%P₂O₅, %free sulfate, and solid content), and the final optimal chemical and industrial yields converged to the range [77–78 °C]. In addition, a number of effective computational simulations were also performed to test the validity of the experimental results and compare the efficiency of the two methods. In comparison to the Golden Section approach, which demonstrated more accuracy, the Fibonacci search method is determined to be suitable and efficient; it substantially lowers the number of tests and converges to the optimum faster, with limited time and resources.