Handbook of Chemical Reactor Design, Optimization, and Scaleup

Molecules must come into contact for a reaction to occur, and the mechanism for the contact is molecular motion. This is also the mechanism for diffusion. Diffusion is inherently important whenever reactions occur, but there are some reactor design problems where diffusion need not be explicitly considered, e.g., tubular reactors that satisfy the Merrill and Hamrin criterion, Equation (8.3). For other reactors, a detailed accounting for molecular diffusion may be critical to the design.
Diffusion is important in reactors with unmixed feed streams since the initial mixing of reactants must occur inside the reactor under reacting conditions. Diffusion can be a slow process, and the reaction rate will often be limited by diffusion rather than by the intrinsic reaction rate that would prevail if the reactants were premixed. Thus, diffusion can be expected to be important in tubular reactors with unmixed feed streams. Its effects are difficult to calculate, and normal design practice is to use premixed feeds whenever possible.
With premixed reactants, molecular diffusion has already brought the reacting molecules into close proximity. In an initially mixed batch reactor, various portions of the reacting mass will start at the same composition, will react at the same rate, and will thus have the same composition at any time. No concentration gradients develop, and molecular diffusion is unimportant during the reaction step of the process even though it was important during the premixing step. Similarly, mechanical mixing is unnecessary for an initially mixed batch reactor, although...