Mass transfer with complex chemical reaction in gas—liquid ... - ITM

134 R.D. Vas Bhat et al./Chemical Engineering Science 54 (1999) 121—136Table 4Selection of enhancement factors at different Hatta numbers. Further parametric values given in Table 1 and the respective figuresFig. k k Ha E K "10 K "10 K "11(a) 1.0010 1.0010 1 1.4 1.4 1.47.8110 1.0010 128 73.4 74.5 104.59.7710 1.0010 1024 100.2 143.8 195.93.0510 5.1210 741,460 201.0 201.0 201.0K "10 K "1 K "10 2 1.0010 2.50 10!1 1 1.36 1.36 1.367.8110 2.50 10!1 128 5.10 5.18 5.189.7710 2.50 10!1 1024 5.18 6.27 7.799.7710 1.31 10 741,460 5.20 6.56 8.85K "10 K "1 K "10 4(a) 1.0010 2.50 10!1 1 1.29 1.35 1.367.8110 2.50 10!1 128 1.69 2.78 4.359.7710 2.50 10!1 1024 3.03 4.99 6.819.7710 1.31 10 74,1460 3.78 5.90 7.57Loaded solutions6(a) k k Ha K "0.01; α"0.45 1.0010 2.9810 1 1.157.8110 2.9810 128 1.289.7710 2.9810 1024 1.339.7710 1.7710 788,200 1.34K "100; α"0.91.0010 4.2110 1 1.097.8110 4.2110 128 1.149.7710 4.2110 1024 1.579.7710 2.2110 741,450 3.95qεθ " K (῟#(E !1)/q!2ε#2῟) !q A B with(16c)῟" C , B῟" D , B῟" E and q" B .B A !A The above set of equations can be solved for both loadedand unloaded solutions. The only difference being thatfor unloaded solutions the initial concentrations of all thechemical species is taken as zero.For instantaneous reversible consecutive reaction,HaPR and θ"1. With this simplification E and ε can be calculated simultaneously from Eq. (16b) and(16c). This was carried out using commercially availablesoftware (MAPLE V). The results are presented as parityplots with respect to numerical obtained values [Fig. 7(a)and (b)]. The figures show that the match between theapproximate technique and numerical values is veryclose with maximum deviation of 1.3% for unloadedsolutions and 0.3% for loaded solutions with an α of 0.1.7. ConclusionsA numerical model based on the Higbie penetrationtheory for isothermal reversible consecutive chemical reactionhas been presented in this paper. The model hasbeen successfully validated for simpler reactionstoichiometries.It has been shown that, although the Onda technique(Onda et al., 1970, 1972) for enhancement factors of irreversibleconsecutive reactions is useful in determining theintermediate asymptotic enhancement factor and thefinal infinite enhancement factor, there is some deviationfrom numerical results for the intermediate enhancementfactor (max. 6% for film theory and 4.3% for penetrationtheory).For reversible consecutive reactions, it has been shownthat the final infinite enhancement (E ) can be seen asa contribution of the infinite enhancement of the firstreaction (E ) along with the additional enhancementprovided by the second reaction (E ). This was quantitativelyshown for irreversible—reversible reactions.For the case of solute loading, enhancement factorsobtained are lower than that for the unloaded case.Unlike unloaded solutions, the value of K affects theintermediate asymptotic enhancement value for the caseof loaded solutions. Finally, an approximate technique todetermine final infinite enhancement factors based on themethod of DeCoursey (1982) has been presented forconsecutive reversible reactions with equal diffusivities.The match with numerically obtained values is very goodfor both loaded and unloaded solutions.