8 362 Overall mass transfer coefficients Experimentally the mass transfer film coefficients k and k x are difficult to measure except for cases where the concentration difference across one phase is small and can be neglected Under these circumstanc ID: 23400 Download Pdf

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8 362 Overall mass transfer coefficients Experimentally the mass transfer film coefficients k and k x are difficult to measure except for cases where the concentration difference across one phase is small and can be neglected Under these circumstanc

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NPTEL Chemical Mass Transfer Operation 1 Joint initiative of IITs and IISc Funded by MHRD Page of MODULE 3: MASS TRANSFER COEFFICIENTS LECTURE NO. 8 3.6.2 Overall mass transfer coefficients Experimentally the mass transfer film coefficients k and k x 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 K and K 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: AG (3.76) where, K is based on the overall d riving force for the gas phase, in mole/m .s and is the value of concentration in the gas phase that would be in the equilibrium with x AL . Similarly, the entire two phase mass transfer effect can then be measured in terms of liquid p hase molar fraction driving force as: AL (3.77) where K is based on the overall driving force for the liquid phase, in mole/m .s and is the value of concentration in the liquid phase that would be in the equilibrium with y AG A relation between the overall

coefficients and the individual mass transfer film coefficients can be obtained when the equilibrium relation is linear as Ai Ai mx . The linear equilibrium condition can be obtained at the low FRQFHQWUDWLRQVZKHUH+HQU\VODZLVDSSOLFDEOH+HUHWKHSURSRUWLRQDOLW\ constant m is defined as m= H/P. Utilizing the relationship, Ai Ai mx , gas and liquid phase concentrations can be related by

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NPTEL Chemical Mass Transfer Operation 1 Joint initiative of IITs and IISc Funded by MHRD Page of AL mx (3.78)

and AG mx (3.79) Rearranging Equation (3.76), one can get AG (3.80) From geometry, AG can be written as Ai Ai AG AG (3.81) Substituting Equation (3.81) in Equation (3.80) AL Ai Ai AG Ai Ai AG AG (3.82) The substitution of Equation (3.76) into the Equation (3.82) relates overall gas phase mass transfer coefficient ( ) to the individual film coefficients by (3.83) Similarly the relation of overall liquid phase mass transfer coefficient ( ) to the individual film coefficients can be derived as follows: AL Ai Ai AG AL mN (3.84) Or mk (3.85) The following relationships between the mass transfer

resistances can be made from the Equations (3.83) and (3.85): phases both in resistance Total phase gas in Resistance (3.86) phases both in resistance Total phase liquid in Resistance (3.87)

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NPTEL Chemical Mass Transfer Operation 1 Joint initiative of IITs and IISc Funded by MHRD Page of If solute A is very soluble in the liquid, m is very small. Then the term m/k in Equation (3.83) becomes minor and consequently the major resistance is represented by 1/k . In this case, it is said that the rate of mass transfer is gas phase controlled. In the extreme it becomes: | (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 fi rst 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: | (3.89) The total resistance equals the liqu id 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, was found to be 2.75 u 10 kmol/m kPa. At one point in the column, the composition of the gas and liquid phases were 8.0 and 0.115 mole% NH , 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 ZDWHUVROXWLRQVIROORZV+HQU\VODZXSWRPROH ammonia in

the liquid, with m = 1.64 when the total pressure is 1 atm. Calculate the individual fi lm coefficients and the interfacial concentrations. Interfacial concentrations lie on the equilibrium line.

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NPTEL Chemical Mass Transfer Operation 1 Joint initiative of IITs and IISc Funded by MHRD Page of Solution 3.3: The first step in the solution is to convert the given overall coefficient from to = 2.75 u 10 u 101.3 = 2.786 u 10 kmol/m For a gas phase resistance that accounts for 85% of the total resistance, kmol/m 10 28 85 u From Equation, , by substituting the values of K , k and m =

3.05 u 10 kmol/m To estimate the ammonia flux and the interfacial concentrations at this particular point in the column use the equation, mx to calculate 10 886 10 15 64 u u u mx The flux is from equation kmol AG u u u 10 18 10 866 080 10 768 Calculate the gas phase interfacial concentration from equation, AG as 01362 10 28 10 18 080 u u AG Since the interfacial concentrations lie on the equilibrium line, 10 305 64 01362 u

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NPTEL Chemical Mass Transfer Operation 1 Joint initiative of IITs and IISc Funded by MHRD Page of Nomenclature Cross sectional area [m Fraction of surface

renewed/unit time [ Molar concentration [mol/m av Average cross sectional area for diffusion [m Diameter [m] Temperature [K] Diameter of a particle [m] Time [s] AB Diffusivity of A in B [m /s] Velocity [m/s] Eddy diffusivity [m /s] average velocity [m/s] Knudsen diffusion coefficient [m /s] D Free stream velocity [m/s] Surface diffusion coefficient [m /s] Volume [m Activation energy [J/mol] Mass fraction Molar mass velocity [mol/m .s] Mass transfer rate [mol/s] Mass velocity of gas [kg/m .s] Mole fraction for liquid [ ' Latent heat of vaporization of component A [J/mol] Mole fraction for gas [

Flux based on arbitrary reference [mol/m .s] X, Y, Z Coordinates Proportionality constant defined in Equation (1.79) [ x*,y* Equilibrium mole fraction of solute in liquid and gas phase, respectively [ Overall mass transfer coefficient [m/s] Association factor [ , k Individual mass transfer coefficient [m/s] H Porosity [

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NPTEL Chemical Mass Transfer Operation 1 Joint initiative of IITs and IISc Funded by MHRD Page of Length [m] Q Molar volume [mol/m Mass [kg] I Packing fraction [ Molecular weight V $% Characteristic length parameter of binary mixture of A and B [m] Flux [mol/m

.s] W Tortuosity [ Partial pressure [N/m : collision integral [ Total pressure [N/m U Density [kg/m Vapor pressure of A [N/m G Film thickness [m] Radius [m] P Viscosity [kg/m.s] Universal gas constant [J/mol.K] References 1. 7UH\EDO5(0DVV 7UDQVIHU2SHUDWLRQV rd Eddition, McGraw Hill, 1981 2. *HDQNRSOLV&-7UDQVSRUW3URFHVVHVDQG6HSDUDWLRQ3URFHVV 3ULQFLSOHV th Edition, Prentice Hall of India, New Delhi, 2005. 3. Dutta, B.K.,

3ULQFLSOHVRI0DVVWUDQVIHUDQG6HSDUDWLRQ3URFHVVHV Prentice Hall of India, New Delhi, 2007.

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