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**4.9.3. Absorption accompanied by irreversible m ^{th} order reactions: **

According to film model when a gas component is subject to an mth or pseudomth order reaction, the absorption rate is expressed by

(4.60)

By introducing M for the mth-order reaction, the absorption rate can be expressed as:

(4.61)

where

(4.62)

As an example, the oxygen takes part in a second-order reaction in the sulphite oxidation system which is often used for comparing gas-liquid interfacial area in various reactors. A more detailed information of mth order reactions can be found from article published by Hikita and Asai (1964).

The gas-liquid reactions are found in many chemical industries where a gas component A reacts with a liquid component B as:

(4.63)

The rate of absorption depends on the reaction range of absorption. In Table 4.1, the various formulas for absorption rate at different reaction range are given (Deckwer, 1992).

Case (a): The liquid component B is not significantly broken at the interface if the concentration of B is large in comparison with c

Case (b): When components A and B react so quickly that they cannot coexist at the same location to any significant extent (â€˜instantaneous reactionâ€™). The film model gives for this case

(4.64)

where Î´' is the reaction plane at the condition v

(4.65)

Substituting the Equation (4.65) in Equation (4.64), the absorption rate can be written as:

(4.66)

which follows since k

(4.67)

The expression in brackets called the enhancement factor E

(4.68)

From Equation (4.67), if then

(4.69)

The absorption rate is entirely controlled by the diffusion of B and is independent of C*

Case (c): If the concentration of B drops distinctly in comparison with the bulk concentration, yet does not reach zero, the film model produces two coupled differential equations which can be solved numerically. Van Krevelen and Hoftijzer (1948) have provided an approximated solution as:

(4.70)

where

(4.71)

E_{i} is given by Equation (4.68). From the Equation (4.70) it is observed that for various E_{i}, E increases for a given E_{i} with increasing as long as E =E_{i.} Hence the expression for E_{i} can be used for E, if >10E_{i} and

(4.72)

On the other hand E is near the diagonal E = and subsequent products are based on a pseudo-first-order reaction if

(4.73)

The van Krevelen and Hoftijzer Equation (4.70) does not give an explicit value for E (Deckwer, 1992). Wellek et al. (1978) provided further details and recommended the following explicit equation for the calculation of E:

(4.74)

where

(4.75)

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