Design Of Packed Tower Based On Overall Mass Transfer Coefficient | Mass Transfer - Chemical Engineering PDF Download

4.4. Design of packed tower based on overall mass transfer coefficient 
From overall mass transfer equation, N_A = Ky (y_AG -y*_A) one can write for packed tower as N_A=K_y(y-y*)
Then,
                                               (4.10)
where, y* is solute concentration in gas phase that is capable of remaining in equilibrium with a liquid having a bulk concentration of x.
Therefore,
 

                                    (4.11) 
Graphical integration of right hand side of Equation (4.11):
Operating line AB is drawn in xy plane. Any point (x,y) is taken in operating line. A vertical line is drawn upto equilibrium line to get y*.
                      (4.12)

5.5. Design based on height of a transfer unit (HTU) 
Equation 4.7 can be written as
                          (4.13)
where,  

                                                                                (4.14)
As,  remains constant at the packing section though G/ varies. This quantity is called ‘height if transfer units’ (HTU) and designated as H_tG. It is important to measure the separation effectiveness of the particular packings for a particular separation process. It also describes the mass transfer coefficient. Larger mass transfer coefficient leads to the smaller value of HTU.
Hence,
                                                                                        (4.15)
The integral part of Equation (4.14) is called number of gas phase transfer units as N_tG.
h_T= H_tG ×N_tG
When overall gas phase mass transfer coefficients are used, the height of the packing is as follows:
                (4.16)

where, 

4.6. Design Equations based concentration in mole ratio unit 
If kx, ky are individual gas phase mass transfer coefficients and KY is overall gas phase mass transfer coefficient, height of packed tower is expressed as:                    (4.17)


Slope of operating line =
Overall gas-phase mass transfer coefficient, K_Y is correlated with individual mass transfer coefficients as follows:

 Example Problem 4.1. 
Solute A is to be absorbed from a binary mixture containing 7.5% of A with solvent B in a packed tower. Based on flooding calculation, a tower diameter of 1.2 m is selected. Total gas flow rate is 60 kmol/h. The exit gas must not contain 0.2% of solute A. Solute free liquid B enters from the top of the tower at 40 kmol/h. The gas phase and liquid phase mass transfer coefficients based on mole ratio unit are: k_X =2.05 kmol/m²h (ΔX) and k_Y =1.75 kmol/m²h (ΔY). The equilibrium line Equation is Y=0.63X. Specific interfacial area of gas-liquid contact (ā) is 71 m²/m³ . (a) Calculate packing height required for the desired separation. (b) For 99.5% solute A removal, what % increase in packed height is needed? (c) Determine slopes of operating line in each case.

Solution 4.1: 
Gas flow rate, G₁ =60 kmol/h; y₁=0.075
Area of tower cross-section (1.2)² = 1.131 
 = 53.05 kmol/m².h
 =53.05(1-0.075) kmol/m².h = 49.07 kmol/m².h

Solute concentration in exit gas is 0.2%.
Therefore,
Liquid flow rate, L_s=40 kmol/h

X₂=0
Overall mass balance Equation for the solute concentration in exit liquid as follows:

49.07(0.011-0.00204) = 35.37(X₁-0)
X₁ = 0.1097
Overall gas-phase mass transfer coefficient, KY:


K_Y=1.138 kmol/m²h (ΔY)


Y* can be expressed in terms of Y.
The operating line Equation can be expressed as:

49.07(Y-0.00204) = 35.37(X-0)
X=1.387(Y-0.00204)
We have
Y* = αX = 0.63×1.387(Y-0.00204) = 0.874Y-0.00178
Therefore,

(a) Packed height, h_T=H_toG×N_toG=0.0607×13.9 m=8.46 m.
(b) For 99.5% solute removal, Y₂=0.0811×0.0005=4.05×10^-4 .

49.07(Y-4.05×10^-4) = 35.37(X-0)
X = (1.387Y – 5.62×10^-4 )
Hence, Y* = αX = 0.63×(1.387Y – 5.62×10^-4 ) = 0.874Y-0.000354
Therefore,

Required packed height, h_T=H_toG×N_toG=0.0607×22 m=13.35 m.

(c) For both the cases slope of the operating will remain same