Simple relationships for estimating intraparticle transport effects for catalytically promoted endothermic reactions

Relationships for estimating effectiveness factors for porous-solid-catalyzed fluid reactions can result from assuming approximations to temperature and concentration profiles. Approximations designed to simplify the outcome result in simple, explicit, analytic relationships for both isothermal and nonisothermal nth-order reaction systems. For isothermal systems, formulas developed predict effectiveness within 25% of the true isothermal effectiveness factors ({eta}`s) over the range 0.1 > {eta} > 0.99. For isothermal or endothermic reaction systems with {eta} > 0.65, errors are less than 10%. Even in the maximum-error region, estimates for endothermic systems are within a factor of two of those obtained by solution of the rigorous heat and mass transfer equations. For isothermal or endothermic systems with {eta} > 0.95, errors are less than 1%. Thus the formulas can also serve diagnostic uses that confirm presence or absence of significant internal heat or mass transport effects in porous reacting systems. Extension of the approach to non-nth-order reactions is possible; formulas are derived for simple isothermal and nonisothermal Langmuir-Hinshelwood reaction systems. Application of the work to exothermic reactions was not tested, but steeper gradients in such systems would tend to degrade accuracy of the relationships. The equations derived in this work are simpler and easier of application than any others proposed thus far.