Packed Towers notes

MASS TRANSFER APPROACH (HTU, NTU)

Packing Height (Z) = height of transfer unit (HTU) x number of transfer units (NTU)

Evaluating height based on HTU-NTU model

NOG is evaluated graphically by numerical integration using the equilibrium and operating lines. • Draw 1/(yA* -yA) (on y-axis) vs. yA (on x-axis). Area under the curve is the value of integration. Alternative Mass Transfer Grouping Phase LOCAL coefficient Gas Phase Z = HG x NG Mass Transfer Coeff.: kya Driving force: (y –yI) Liquid Z = HL x NL Mass Transfer Coeff.: Phase kxa Driving force: (x –xi)

OVERALL coefficient Z = HOG x NOG Mass Transfer Coeff.: Kya Driving force: (y –y*) Z = HOL x NOL Mass Transfer Coeff.: Kxa Driving force: (x –x*)

OPERATING LINES Absorber Solute mole balance: xinLin + yVl = xLl + youtVout For dilute solutions, V and L are approximately constant: Packed absorber operating line mole fractions y and x bulk compositions of gas and liquid in contact at any vertical location Stripper Solute mole balance: xLl + yinVin = xoutLout + yVl For dilute solutions, V and L are approximately constant: Packed stripper operating line

Material balance over dl: Change in gas phase: V (y + dy) - Vy Transfer to liquid phase: Kya (y y*) S dl What leaves the gas, goes to the liquid: -V dy = Kya(y-y*)Sdl

The smaller the HTU, the more efficient the contacting The larger the NTU the greater the time or area of contact required.

Integral in the equation represents the change in vapour concentration divided by the average driving force and is called the number of transfer units (NTU). The subscripts show that NOG is based on the overall driving force for the gas phase. The other part of the equation has the units of length and is called the height of a transfer unit (HTU) HOG. The design method is to determine NOG from the y-x diagram and multiply it by HOG obtained from the literature or calculated from mass-transfer correlations: The operating line lies above the equilibrium line for absorption For a stripping (removal of gas from liquid stream) the operating line must lie below the equilibrium line in order for the drving force to act from the liquid phase toward the gas phase

For concentrated solutions Operating line using solute-free basis Absorber: XinL’ + YV’ = XL’ + YoutV’ Stripper: XL’ + YinV’ = XoutL’ + YV’

One hundred kmol/h of air containing 20 mol% Cl2 enters a packed bed, where 95% of the Cl2 is absorbed by water at 20oC and 1 atm. Using the given x–y equilibrium data below, obtain: (a) minimum water rate in kg/h, and (b) NOG for twice the minimum water rate. Equilibrium data at 20oC in Cl2 mole fractions is: x 0.0001 0.00015 0.0002 0.00025 0.0003 0.000450 0.000576 0.000695 y 0.006 0.012 0.024 0.04 0.06 0.132 0.197 0.263

Straight Operating And Equlibrium Lines

Can integrate assuming a linear equilibrium, y*=Kx, to eliminate y and a linear solute material-balance operating line, (dilute solutions), to eliminate x, giving:

Letting L/KV= A, and integrating

Given Ky (overall gas-phase MTC), flow rates (L/V), and K, we can get lT. An easier method

1) Use Arithmetic Average Driving Force 2) Use Logarithmic Mean Driving Force

Consider the case when both the equilibrium and operating lines are straight and parallel The driving force is then constant throughout the process and can be moved outside the integral, leading to

4 basic types of mass transfer coefficient: Gas Film:

Liquid Film

Overall Liquid

Overall Gas

We wish to strip SO2 from water using air at 20oC. The inlet air is pure. The outlet water contains 0.0001 mole fraction SO2, while the inlet water contains 0.0011 mole fraction SO2. Operation is at 855 mmHg and L/V = 0.9×(L/V)max. Assume HOL= 2.76 m and that the Henry’s law constant is 22,500 mmHg/mole frac SO2. Calculate the packing height required