Absorption With Chemical Reaction | Mass Transfer - Chemical Engineering PDF Download

4.9. Absorption with chemical reaction 
Operations in which one or more components of a gas phase are absorbed into a liquid phase are common throughout the chemical process industries and frequently serve to achieve desired reactions among components in the two phases (Lee & Tsui, 1999). Such operations are often called reactive absorption because of the combination of reaction and absorptive mass transport. There are a number of cases in which a gas, on absorption, reacts chemically with a component of the liquid phase. In such processes, the conditions in gas phase are similar to those of an entirely physical absorption process, but in the liquid phase, there is a liquid film followed by a reaction zone. As an example, in the absorption of carbon dioxide by caustic soda, the carbon dioxide reacts directly with the caustic soda. An advantage of absorption plus reaction is the increase in the mass-transfer coefficient. This may be due to a greater effective interfacial area. The process hydrodynamics can also be directly involved via correlations for the hold-up, pressure drop, and mass transfer coefficients, etc.

4.9.1. Absorption-Reaction Model 
The fundamental relations governing simultaneous diffusion and chemical reaction of a dissolved species have been reviewed by Danckwerts (1970). For one-dimensional diffusion of a single species (A) with diffusivity independent of concentration
                         (4.47)
The reaction rate term r, is generally a function of solute concentration and of one or more liquid reactant concentrations. If these reactant concentrations vary appreciably, continuity equations for each reactant must be solved simultaneously with Equation (4.47) to obtain the solute concentration profile. An increase in the rate of absorption caused by reaction is a result of a concentration drop in the bulk liquid phase.
                    (4.48)
As per film model, the concentration gradient at the interface becomes steeper while the mass transfer coefficient kL remains unchanged.

4.9.2 Absorption accompanied by irreversible first-order reaction 
The bulk concentration becomes zero when the absorption process is accompanied by a fast irreversible first-order reaction. Then as per film theory the following balance can be written:
                                       (4.49)
The reaction rate term r = k₁C_A for an irreversible reaction. k1 is the rate constant. The Equation (4.49) can be solved by incorporating boundary conditions:
                         (4.50)
                            (4.51)
The absorption rate RA can be estimated from the concentration profile
                           (4.52)
By introducing the solution of Equations (4.49-4.51) one can get
                             (4.53)
Where
                      (4.54)
This can be interpreted as ratio of diffusion time  to reaction time (1/k₁). When  , then tanh   and Equation (4.7) can be written as
                                                                          (4.55)

The Equation (4.55) indicates that the absorption rate is independent of the mass transfer coefficient and therefore the hydrodynamic conditions prevailing at the interface. The Equation (4.55) can be used to estimate the interfacial area (Si) in gas-liquid reactor as
                                                                                                        (4.56)
where  is the initial molar flow and U is the overall gas phase conversion. Therefore the specific interfacial area (the interfacial area per unit volume of liquid (V_L) in the reactor) can be expressed as
                                                                                            (4.57)

As per Danckwert’s surface renewal theory, the absorption rate can be derived as
                                                             (4.58)
The ratio of specific absorption rate (R_A) to the    k is called enhancement factor of absorption from the diffusion regime. The Equation (4.58) also forms the basis for the calculation of absorption rate referred to as the liquid volume (V_L):
                                                                                (4.59)

Example Problem 4.3. 
In a batch catalytic reactor, chlorination with toluene is carried out. It is found from the reaction that the film mass transfer coefficient (k_L) is 5 X 10^-4 cm/s, the specific interfacial area is 3.6 cm^-1 . The liquid holdup (ε_L) of the reactor was 0.74. The reaction is first order and the equilibrium constant (k₁) of the reaction is 3.5X10^-4 s ^-1 . The overall gas phase conversion is 80%. The initial molar concentration of the gas phase was 1.2 X 10^-7 mol/cm³ . Find out the enhancement factor of the absorption and the rate of absorption for this reaction. The diffusivity of the chlorine is 3.74 X 10^-5 cm²/s.

Solution4.3:
The parameter M from Equation (4.54) is equal to

Therefore the enhancement factor can be found from the Equation (4.58) as

The chlorine concentration as a function of physical solubility can be calculated from the relation:
 
Therefore the absorption rate (R_Aa) can be calculated from the Equation (4.59) as

=2.64 X 10^-10 mol/cm³s