Mathematical modeling of a phenomenon can be defined as the “Representation of natural phenomena using mathematical structures (equations) that allow to describe an approximation of the behavior of the same, with the smallest possible discrepancy, in a set range of operating conditions”. This definition is obviously applicable to Advanced Oxidation Processes. Mathematical modeling of AOPx is based on important steps that include: 1. An adequate understanding of the phenomena; 2. A pertinent graphic representation of the phenomenon (which implies a good understanding of it); 3. A correct delimitation of boundaries and conditions that guarantee the necessary approximations for the formulation of equations and reduction of the complexity of the system; 4. Methodological structuring of the components to be modeled in the system; 5. Formulation or implementation of equations, and 6. Numerical solution, validation and simulation of the phenomenon.

An adequate mathematical model can guarantee savings in experimental resources by allowing phenomena to be evaluated using simulation with high precision or minimal discrepancies with respect to natural behavior.

In the particular case of PAOx, the use of mathematical models and simulation has made it possible to describe, evaluate, and optimize new materials, photoreactors, contaminant degradation, radiant field, and intensified processes, and even to evaluate the performance of these processes at different scales (lab, pilot and comercial scale), at extremely low costs (computational and economic).