Synthesis of peroxypropionic and peroxyacetic acids from hydrogen peroxide and their carboxylic acids was carried out in a continuous fixed-bed reactor, demonstrating the concept of green process technology: biodegradable chemicals are made with the aid of heterogeneous catalysts. This reactor was constructed with several sampling locations along its length, allowing a better kinetic investigation. A profound study of the mean residence time distribution (RTD) was performed to analyze the behavior of the flow pattern at different liquid flow rates and catalyst loadings by using step and impulse methods with different tracer molecules. It was found that impulse experiments with HCl as a tracer is the most reliable method to study the RTD, because of this tracer does not interact with the catalyst. Based on the RTD study, it was demonstrated that the temperature (in the range 30–60 °C) and the catalyst distribution inside the reactor do not affect the flow pattern, but the ratio of the catalyst mass-to-liquid ratio affects the mean residence time and the liquid dispersion. Furthermore, it was shown that the presence of an axial dispersion is negligible when the average particle diameter is <1.38 mm, e.g., Péclet number exceeds 100. The kinetic study was carried out at different mean residence times (from 10 to 55 min), at different wet catalyst loadings (from 25 to 49 g) and reactor temperatures (from 30 to 60 °C). Mathematical models comprising kinetic and dispersion parameters were developed to compare the estimated parameters obtained from the continuous fixed-bed reactor with the ones obtained from a batch reactor.