Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev

Mass Transfer

Chemical Engineering : Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev

The document Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev is a part of the Chemical Engineering Course Mass Transfer.
All you need of Chemical Engineering at this link: Chemical Engineering

3.6.2 Overall mass transfer coefficients 
Experimentally the mass transfer film coefficients ky and kx are difficult to measure except for cases where the concentration difference across one phase is small and can be neglected. Under these circumstances, the overall mass transfer coefficients Ky and Kx are measured on the basis of the gas phase or the liquid phase. The entire two-phase mass transfer effect can then be measured in terms of gas phase molar fraction driving force as:
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                                      (3.76)
where, Ky is based on the overall driving force for the gas phase, in mole/m2.s and y*A  is the value of concentration in the gas phase that would be in the equilibrium with xAL. Similarly, the entire two-phase mass transfer effect can then be measured in terms of liquid phase molar fraction driving force as:
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                         (3.77)
where Kx is based on the overall driving force for the liquid phase, in mole/m2.s and x*A  is the value of concentration in the liquid phase that would be in the equilibrium with yAG. A relation between the overall coefficients and the individual mass transfer film coefficients can be obtained when the equilibrium relation is linear as yAi = mxAi . The linear equilibrium condition can be obtained at the low concentrations, where Henry’s law is applicable. Here the proportionality constant m is defined as m= H/P. Utilizing the relationship, yAi =mxAi   , gas and liquid phase concentrations can be related by 
y*A = mxAL                                                          (3.78)
and
yAG = mx*A                                                  (3.79)

Rearranging Equation (3.76), one can get
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                                             (3.80)
From geometry, yAG - y*A  can be written as
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                       (3.81)

Substituting Equation (3.81) in Equation (3.80)
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                      (3.82)
The substitution of Equation (3.76) into the Equation (3.82) relates overall gas phase mass transfer coefficient (Ky) to the individual film coefficients by
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                                              (3.83)
Similarly the relation of overall liquid phase mass transfer coefficient (Kx) to the individual film coefficients can be derived as follows:
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                              (3.84)

Or

Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                                        (3.85)
The following relationships between the mass transfer resistances can be made from the Equations (3.83) and (3.85):
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                            (3.86)
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                           (3.87) 
If solute A is very soluble in the liquid, m is very small. Then the term m/kx in Equation (3.83) becomes minor and consequently the major resistance is represented by 1/ky. In this case, it is said that the rate of mass transfer is gas phase controlled. In the extreme it becomes:
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                     (3.88)
The total resistance equals the gas film resistance. The absorption of a very soluble gas, such as ammonia in water is an example of this kind. Conversely when solute A is relatively insoluble in the liquid, m is very large. Consequently the first term of Equation (3.85) becomes minor and the major resistance to the mass transfer resides within the liquid. The system becomes liquid film controlling. Finally this becomes:
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev                      (3.89)
The total resistance equals the liquid film resistance. The absorption of a gas of low solubility, such as carbon dioxide or oxygen in water is of this type of system.

Example problem 3.3: 
In an experimental study of the absorption of ammonia by water in a wetted-wall column, the value of overall mass transfer coefficient, KG was found to be 2.75 x 10-6 kmol/m-s-kPa. At one point in the column, the composition of the gas and liquid phases were 8.0 and 0.115 mole% NH3, respectively. The temperature was 300K and the total pressure was 1 atm. Eighty five % of the total resistance to mass transfer was found to be in the gas phase. At 300 K, Ammonia –water solutions follows Henry’s law upto 5 mole% ammonia in the liquid, with m = 1.64 when the total pressure is 1 atm. Calculate the individual film coefficients and the interfacial concentrations. Interfacial concentrations lie on the equilibrium line. 

Solution 3.3: 
The first step in the solution is to convert the given overall coefficient from KG to Ky.
Ky = KG P = 2.75 x 10-6 x 101.3 = 2.786 x 10-4 kmol/m2-s

For a gas-phase resistance that accounts for 85% of the total resistance,
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev  
From Equation, Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev  by substituting the values of Ky , ky and m
kx = 3.05 x 10-3 kmol/m2-s

To estimate the ammonia flux and the interfacial concentrations at this particular point in the column use the equation, y*A = mxA,L to calculate
y*A = mxA,L = 1.64 x 1.15 x 10-3 = 1.886 x 10-3  
The flux is from equation
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev
Calculate the gas-phase interfacial concentration from equation,
Na = ky( yAG - yA,i) as
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev
Since the interfacial concentrations lie on the equilibrium line,
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev
 

Nomenclature

a  Cross-sectional area [m2 ]                             
s  Fraction of surface renewed/unit time [-]
C  Molar concentration [mol/m3 ]                       
Sav Average cross-sectional area for diffusion [m2 ]
d  Diameter [m]                                                   
T  Temperature [K]
dp  Diameter of a particle [m]                               
t  Time [s]
DAB    Diffusivity of A in B [m2/s]                               
u  Velocity [m/s]
DE  Eddy diffusivity [m2/s]                                     
U  average velocity [m/s]
DK  Knudsen diffusion coefficient [m2/s]               
Ua  Free stream velocity [m/s]
DS  Surface diffusion coefficient [m2/s]               
V   Volume [m3 ]
ED  Activation energy [J/mol]                               
w  Mass fraction [-]
Gm  Molar mass velocity [mol/m2.s]                   
W  Mass transfer rate [mol/s]
Gy  Mass velocity of gas [kg/m2.s]                       
x  Mole fraction for liquid [-]
ΔHVA  Latent heat of vaporization of component A [J/mol]   
y  Mole fraction for gas [-]                                                       
J  Flux based on arbitrary                                     
X,Y, Z  Coordinates
K  Proportionality constant defined in Equation (1.79) [-]                                
x*,y* Equilibrium mole fraction of solute in liquid and gas phase,respectively [-]
K  Overall mass transfer coefficient [m/s]             
φ  Association factor [-]
k/,k Individual mass transfer coefficient [m/s]
ε     Porosity [-] l  Length [m]                                                       
v  Molar volume [mol/m3 ]                   
m  Mass [kg]                                                           
Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev Packing fraction [-]
M  Molecular weight                                               
σAB   Characteristic length parameter of binary mixture of A and B [m]
N  Flux [mol/m2.s]                                                     
τ  Tortuosity [-]
p   Partial pressure [N/m2 ]                                     
Ω  collision integral [-]
P  Total pressure [N/m2 ]                                       
ρ  Density [kg/m]
PVVapor pressure of A [N/m2 ]                           
δ  Film thickness [m]
r  Radius [m]                                                         
μ Viscosity [kg/m.s]
R   Universal gas constant [J/mol.K]

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!
29 videos|46 docs|44 tests

< Previous

Dynamic Test

Content Category

Related Searches

ppt

,

Exam

,

Semester Notes

,

MCQs

,

mock tests for examination

,

Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev

,

study material

,

past year papers

,

Summary

,

Objective type Questions

,

Extra Questions

,

video lectures

,

practice quizzes

,

Viva Questions

,

Free

,

Sample Paper

,

Important questions

,

Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev

,

Previous Year Questions with Solutions

,

Overall Mass Transfer Coefficients Chemical Engineering Notes | EduRev

,

pdf

,

shortcuts and tricks

;