APPROXIMATION FOR THE ENHANCEMENT FACTOR APPLICABLE TO REVERSIBLE-REACTIONS OF FINITE RATE IN CHEMICALLY LOADED SOLUTIONS

A new explicit relation is proposed for the prediction of the enhancem ent factor for reversible reactions of finite rate in chemically loade d solutions which also allows for unequal diffusivities. The relation for the enhancement factor is not based on an approximation of the abs orption process, but is derived from a similarity which can be observe d between the results of the approximation for an irreversible (1,1) o rder reaction given by, for example, DeCoursey (surface renewal model) , and the exact numerical results. The present relation combines the s olution of DeCoursey (1974 Chem. Engng Sci. 29, 1867-1872) for irrever sible finite rate reactions, and the solution of Secor and Beutler (fi lm 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 t he enhancement factors to the penetration theory. In general, this ada ptation of the solution of Secor and Beutler gave reasonably good resu lts, however, for some situations with unequal diffusivities deviation s up to 20% were found. The results of the present approximation were for various reactions compared to the numerical enhancement factors ob tained for the model based on the Higbie penetration theory. Generally , the agreement was reasonably good. Only 26 of 2187 preselected simul ations (1.18%) had a deviation which was larger than 20%, while the av erage 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 , root f so that E-a = root f Ha(A) in the regime 2 < Ha(A) << E-a,E-i nfinity. This factor agreed well with the factor given by Hikita and A sai (1964, Int. Chem. Engng 4, 332-340) in their dimensionless number. (C) 1997 Elsevier Science Ltd.