Page 261 - Introduction to chemical reaction engineering and kinetics

242 Chapter 9: Multiphase Reacting Systems
9.2.3 Kinetics Regimes for Two-Film Model

9.2.3.1 Classijication in Terms of Location of Chemical Reaction
The rate expressions developed in this section for gas-liquid systems, represented by
reaction 9.2-1, are all based on the two-film model. Since liquid-phase reactant B is
assumed to be nonvolatile, for reaction to occur, the gas-phase reactant A must enter
the liquid phase by mass transfer (see Figure 9.4). Reaction between A and B then
takes place at some “location” within the liquid phase. At a given point, as represented
in Figure 9.4, there are two possible locations: the liquid film and the bulk liquid. If the
rate of mass transfer of A is relatively fast compared with the rate of reaction, then A
reaches the bulk liquid before reacting with B. Conversely, for a relatively fast rate of
reaction (“instantaneous” in the extreme), A reacts with B in the liquid film before it
reaches the bulk liquid. Since the intermediate situation is also possible, we may initially
classify the kinetics into three regimes:

(1) Reaction in bulk liquid only;
(2) Reaction in liquid film only;
(3) Reaction in both liquid film and bulk liquid.

We treat each of these three cases in turn to obtain, as far as possible, analytical or
approximate analytical rate expressions, taking both mass transfer and reaction into
account. Each of these cases gives rise to important subcases, some of which are de-
veloped further, and some of which are left to problems at the end of the chapter. In
treating the cases in the order above, we are proceeding from special, relatively simple,
situations to more general ones, the reverse of the approach taken in Section 9.1 for
gas-solid systems.
It is necessary to distinguish among three rate quantities. We use the symbol NA to
represent the flux of A, in mol m-2 s-l, through gas and/or liquid film; if reaction takes
place in the liquid film, NA includes the effect of reaction (loss of A). We use the symbol
(-rA), in mol mP2 s-r, to represent the intensive rate of reaction per unit interfacial
area. Dimensionally, (-r*) corresponds to NA, but (- Y,J and NA are equal only in the
two special cases (1) and (2) above. In case (3), they are not equal, because reaction
occurs in the bulk liquid (in which there is no flux) as well as in the liquid film. In this
case, furthermore, we need to distinguish between the flux of A into the liquid film at
the gas-liquid interface, NA(z = 0), and the flux from the liquid film to the bulk liquid,
NA(z = l), where z is the relative distance into the film from the interface; these two
fluxes differ because of the loss of A by reaction in the liquid film. The third rate quantity
is ( -rJinr in mol m-3 s-l, the intrinsic rate of reaction per unit volume of liquid in the
bulk liquid. (-T*) and (- rA)inr are related as shown in equation 9.2-17 below.

9.2.3.2 Reaction in Bulk Liquid Only; Relatively Slow Reaction
If chemical reaction occurs only in the bulk liquid, but resistance to mass transfer of
A through gas and liquid films is not negligible, the concentration profiles could be as
shown in Figure 9.5. This is essentially the same as Figure 9.4, except that a horizontal
line is added for cn.
We assume that the reaction is intrinsically second-order (first-order with respect to
each reactant), so that

NA = (-rA) = (-rA)intlui = (kAlui)cAcB = k;c,c, (9.2-17)

where, for consistency with the units of (-r,J used above, the interfacial area ai (e.g.,
m2 (interfacial area) mT3 (liquid)) is introduced to relate (-T*) to ( -Y*)~~~ (in mol mP3
(liquid) s-i.