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

140 R.D. Vas Bhat et al./Chemical Engineering Science 54 (1999) 137—147Table 2Effect of diffusivity of A on the enhancement factor: K "10; K "100; K "10; k "9.7710 ms; Ha"4096Case r r r r "r (1b) (1c) E 1 0.1 1 1 1 Reversible Reversible 20.532 0.1 1 1 1 Irreversible Reversible 17.313 0.1 1 1 1 Reversible Irreversible 20.984 0.1 1 1 1 Irreversible Irreversible 17.535 0.1 1 10 1 Reversible Reversible 21.136 0.1 1 10 1 Irreversible Reversible 17.317 0.1 1 10 1 Reversible Irreversible 21.558 0.1 1 10 1 Irreversible Irreversible 17.539 0.1 0.1 0.1 1 Reversible Reversible 16.3410 0.1 0.1 0.1 1 Irreversible Reversible 19.7611 0.1 0.1 0.1 1 Reversible Irreversible 16.7512 0.1 0.1 0.1 1 Irreversible Irreversible 20.65enhancement factors (compare cases 1 and 5 and cases3 and 7). This confirms the hypothesis that higherenhancement is obtained due to the transfer of A in theform of more mobile species. Finally, in order to show that this phenomenon is onlytrue for low mobility of A, the diffusivities of C andD have also been reduced (cases 9—12). As can beexpected, the enhancement factor is higher for the casewhen both reactions are irreversible and the hypothesisis no longer valid.2.2. Diffusivity of CSince C is both a reaction product as well as a reactant,a variation in its diffusivity is expected to have a significanteffect on the mass transfer behaviour of the system.In order to distinguish between the various underlyingphenomena, enhancement factors for two extreme casesof r (0.01 and 10) have been compared (Fig. 3). Thesimulations have been carried out for K " K "100and K "10. Four distinct regions are observed(named positions I, II, III and IV). Dimensionless concentrationprofiles of all the chemical species over thepenetration depth have been presented for each position.The corresponding values of simulation parameters ateach of these positions are given along with the figures.2.2.1. Position ISince this position is before the kick-in point of reaction(1c), there is no production of E and F as can be seen inFig. 4(a) and (b). From the figure it is clear that reaction(1b) is instantaneous, indicated by the formation of a reactionzone between A and B. Thus, near the interface,the concentration of A is governed by the equilibriumconstant, K . At higher r (Fig. 4b), C produced byreaction (1b) is transferred faster into the bulk on accountof its greater mobility, thereby reducing the concentrationof C near the interface. In order to maintain K constant,the concentration of A near the interface also falls.This increases the concentration gradient of A near theinterface and, in turn, the enhancement. Conversely, forlow mobility of C [Fig. 4(a)], C formed by reactionbetween A and B remains near the interface where itincreases the concentration of A on account of the equilibriumconstraint. This results in a lower enhancementin the absorption of A.2.2.2. Position IIAt lower r , the reduced mobility of C prevents it fromdiffusing into the liquid bulk, which causes the concentrationof C near the interface to rise [Fig. 5(a)]. Thismeans that reaction (1c) will ‘kick-in’ at correspondinglylower Hatta numbers as compared to the case witha higher r . This is clearly observed in Fig. 3 where atposition II, reaction (1c) is already influencing the masstransfer for r "0.01 while its effect is much less forr "10. This is also observed from the concentrationprofiles of E (and F) in Fig. 5(a) and (b). For a lowmobility of C (r "0.01), C formed [via reaction (1b)]remains near the interface where it is available for reactionwith A [via reaction 1(c)]. Due to the high concentrationof C, the absorption rate of A is very high as well,leading to large enhancement. For a high mobility ofC(r "10), C can diffuse away from the interface so thatits interfacial concentration is low (as compared to r "0.01) and, hence, the absorption rate of A is also low.2.2.3. Position IIIOn increasing the Hatta number from position II toposition III (Fig. 3), there is an increase in enhancementdue to the reaction between C and A via reaction (1c).For a low r , C is formed by reaction (1b) away from theinterface. A fraction of this C formed diffuses towards theinterface where it reacts with A. At lower Hatta numbers(closer to position II), the diffusion rate is sufficient tosupply reaction (1c). As the Hatta number is increased