Approximation for the enhancement factor applicable to reversible reactions of finite rate in chemically loaded solutions

Abstract

A new explicit relation is proposed for the prediction of the enhancement factor for reversible reactions of finite rate in chemically loaded solutions which also allows for unequal diffusivities. The relation for the enhancement factor is not based on an approximation of the absorption process, but is derived from a similarity which can be observed between the results of the approximation for an irreversible (1,1) order reaction given by, for example, DeCoursey (surface renewal model), and the exact numerical results. The present relation combines the solution of DeCoursey (1974 Chem. Engng Sci. 29, 1867–1872) for irreversible finite rate reactions, and the solution of Secor and Beutler (film model, 1967 A.I.Ch.E. J. 13, 365–373) for instantaneous reversible reactions. The diffusivity ratios in the solution of Secor and Beutler (1967) were replaced by the roots of these ratios in order to adapt the enhancement factors to the penetration theory. In general, this adaptation of the solution of Secor and Beutler gave reasonably good results, however, for some situations with unequal diffusivities deviations up to 20% were found. The results of the present approximation were for various reactions compared to the numerical enhancement factors obtained for the model based on the Higbie penetration theory. Generally, the agreement was reasonably good. Only 26 of 2187 preselected simulations (1.18%) had a deviation which was larger than 20%, while the average deviation of all simulations was 3.3%. The deviations increased for solutions with a substantial chemical loading in combination with unequal diffusivities of the components. For reactions with a kinetic order unequal to unity, the Ha number had to be multiplied by a factor, √ƒ, so that E a = √ƒH a A in the regime 2 < Ha A ⪡ E a,∞ . This factor agreed well with the factor given by Hikita and Asai (1964, Int. Chem. Engng 4, 332–340) in their dimensionless number.