Optimizing phosphoric acid concentrating using microwave technology: Theoretical and empirical model of energy efficiency and P 2 O 5 concentration

Enrichment of phosphoric acid concentration via microwave under vacuum technique has enabled us to achieve the required P 2 O 5 concentration in the concentrate. This success is influenced by factors such as irradiation time, sample volume, operating vacuum pressure, thermal insulation, and reactor shape. Through the study of these variables via experimental design, we have identified their significant impacts on the energy yield and the wt % P 2 O 5 in the concentrate. Indeed, reactor shape has a particularly significant effect on energy efficiency, which can be attributed to the sample's exterior surface area relative to its volume. Utilizing these insights and applying response surface methodology, we have developed and validated an empirical model that includes Y 1 (energy yield) and Y 2 (wt % P 2 O 5 ) as functions of irradiation time, sample volume and vacuum pressure. This enables the prediction of energy yield and wt % P 2 O 5 of the microwave enrichment phosphoric acid concentration under vacuum technique. This methodology has allowed us to predict, both theoretically and experimentally, the energy required to achieve a specified wt.% P 2 O 5 using the microwave enrichment phosphoric acid concentration under vacuum technique. In our case study, increasing P 2 O 5 concentration of phosphoric acid from 27% wt to marketable concentration of 54% wt P 2 O 5 using this technique under atmospheric pressure necessitated an energy input of 6796 kJ/kg P 2 O 5 .