Fig. 9. Example of mathematical modeling of reaction rate and effectiveness factor for the case with diffusion for various values of k₁ and k₂ with a fixed diffusion distance (L=104.5) and O₂ boundary concentration of 7.85 µmol l^–1. The experimentally measured rate of AP recovery of 0.379 mmol l^–1 min^–1 is indicated by the unbroken line, which shows the range of values of k₁ and k₂ that satisfy this rate (left panel), and the corresponding effectiveness factor (right panel). Values of k₁ and k₂ that satisfied the observed rate and maximized the effectiveness factor were then determined using a root-finding method (see text).