Overall controlling factor in R1-R2-D reactions-diffusion phenomena in two-reactions-in-series systems for selectivity enhancement

The secondary internal effectiveness factor in a two-reaction-in-series system (A + B -> C + D, C + B -> E+F) can be above unity for positive-order reaction kinetics. While the controlling factor in the reaction-diffusion phenomenon for the first reaction can be determined using the Weisz criterion based on the value of the primary internal effectiveness factor, the criteria to assign the secondary effectiveness factor that is above unity do not exist yet, making difficult the development of determinable overall controlling factors in the R1-R2-D phenomena in the two-reaction-in-series system. Here, using a two-step methanol oxidation reaction as a case study, we combined an analytically derived criterion for R1-R2 phenomenon with the Weisz criterion for R1-D phenomenon to allow the development of assignment criteria for four overall controlling factors. The overall assignment criteria are found to be dependent on the internal effectiveness factors , as well as the rate of the individual reactions at the catalyst surface. When the assignments criteria are re-decomposed using assignable criteria that are based on only the two internal effectiveness factors, a child component criterion is confirmed to satisfy the overall assignment criteria. Based on the sensitivity of the overall controlling factor with respect to the reaction temperature and catalyst size, the selectivity of the formaldehyde intermediate species in methanol oxidation reaction can be enhanced at high reaction temperature when catalysts are specifically designed to enhance the rate of formaldehyde formation (rate of the first reaction). However, CO formation (the rate of the second reaction) needs to be suppressed to enhance selectivity towards formaldehyde at moderately low temperature. This reaction-diffusion theoretical framework provides guidance for the development of highly selective catalyst for two-reactions-in-series systems and can be extended for higher-number multiple reactions in series and in parallel.