Absorption Resistance Notes | Study Mass Transfer - Chemical Engineering

4.9.5. Absorption resistance 
During absorption, when transport from the bulk of the gas phase to that of the liquid phase, the possibility of the transport resistance arising on the gas side. This is relatively infrequent occurrence in absorption process. But it can be found under certain circumstances where fast and instantaneous reactions are involved, especially when combined with low gas phase of the reactant.
The absorption rate for fast pseudo-fast-order reaction is
                                                                 (4.76)
The relation for instantaneous reaction is
                                      (4.77)
Using Henry’s law (p_Ai=Hc_Ai), the interface concentration can be removed from Equation (4.77) to give
                                                            (4.78)
when the reaction is at the interface:
                                                                (4.79)
If
                                                               (4.80)
then transport resistance is mainly on the gas side and the absorption rate is
                                                                                     (4.81)

Example Problem 4.4: 
In a reactor Carbon dioxide is absorbed in NaOH. The CO₂ partial pressure ranges from 2.5 bar at the reaction inlet and (0.025) at the outlet. The liquid phase has a roughly constant composition of 0.96 M NaOH. Find out the absorption rate at reactor inlet.
Data: k_L = 0.025 cm/s, k_G = 2.5×10^-5 mol.cm^-2s^-1bar^-1 , H = 56.2 bar l mol^-1 , D_CO2 = 1.6×10^-5 cm²s^-1 , D_OH/D_CO2 = 1.7, k₂C⁰_OH = 7000S^-1 , C⁰_OH = 0.40

Solution 4.4: 
Parameter M is calculated as an initial step
  
The enhancement factor E_i is
      
As  = p/H, it follows that

Hence, Ei = 16.28 at the reactor inlet and Ei = 1528.64 at the outlet. E is determined iteratively from the Wellek’s equation In the present problem its value is 3.492. Hence, absorption rate at the reactor inlet is 


Nomenclature 
ā  Specific interfacial contact area between gas and liquid, m² /m³
Ls  Liquid flow rate per unit area basis, (solute free basis) mol/h.m²
Ā, An  Absorption factor M Parameter defined in Equation (4.77)
G^/  Gas flow rate per unit area basis, mol/h.m² 
N_tG   Number of gas phase transfer units
G_s   Gas flow rate per unit area basis,(solute free basis) mol/h.m²
  Stripping factor
h_T Packing height, m
U Overall gas phase conversion
H_tG Height if transfer units, m
  Moles of Nth component in the liquid stream per mole of solvent entering the absorber
K_Y Overall gas phase mass transfer coefficient, kmol/m²h (ΔX)
x, y Mole fraction of solute in liquid and gas
kx, ky Individual gas phase mass transfer coefficients, kmol/m2 h (ΔX)
X, Y Mole ratio of solute in liquid and gas
K_G Overall gas phase mass transfer coefficient, kmol/m² h (Δp)
  Moles of Nth component in the gas stream leaving any plate
L^/ Liquid flow rate per unit area basis, mol/h.m²