Special Module - Mass Transfer | Mass Transfer - Chemical Engineering PDF Download

Special Module 
Multi-component absorption 
S1. Introduction 
In multi-component absorption, a gas mixture is contacted with a liquid solvent to selectively dissolve more components by mass transfer from the gas to the liquid solvent. The components transferred to the liquid are referred to as solute or absorbate. The absorption is used to separate gas mixtures, remove impurities from a gas or recover valuable chemicals. A typical absorption operation is shown in Figure S1.

 
Figure S1: Typical absorption process

The gas containing air (oxygen, nitrogen and argon of 21, 78 and 1% respectively), water vapor and acetone vapor is fed in a counter-current multistage absorber to remove acetone vapor by contacting the gas mixture with suitable solvent like water. From the material balance analysis as per system shown in Figure, 99.5% of the acetone is absorbed. The gas leaving the absorber contains some other components. Though the major component acetone vapor is absorbed, the small amounts of other components nitrogen and oxygen are also absorbed by the water solvent. The fraction of component absorbed in the absorber depends on the number of equilibrium stages and the absorption factor (A = L/KV) for that component. The equilibrium relationship between composition in the gas and the liquid phase in the absorber is expressed as:
                              (S1)
where
y = mole fraction of specified component in the gas phase,
x = mole fraction of specified component in the liquid phase,
K = vaporization equilibrium constant for specified component on plate or stage n,
n = arbitrary theoretical plate in the absorber.
In terms of total molar flow rates of the gas and liquid, and the flow rates for the specified component Equation (S1) can be written as
                             (S2)
Or
                           (S3)

where l_n = mole of specified component in the liquid stream leaving plate n,
v_n = mole of specified component in the vapor stream leaving plate n,
L_n = total mole of liquid stream leaving plate n,
V_n = total mole vapor stream leaving plate n
In Equation (S3), the term L_n /K_nV_n is referred to as the absorption factor which is expressed as
                                  (S4)
where A_n is the absorption factor.

Kremser and Brown equation for multicomponent absorption 
The general equations involving the theoretical plate concept and the assumption of equilibrium between a gas and a liquid on each theoretical plate can be derived by writing material balances around any plate and in the column. The material balance equation is then combined with the equilibrium expressions to give a generalized equation for the absorption.
The material balance for any component around plate n of the absorber shown in the can be written as 
                     (S5)
The equations suitable for predicting component distributions in multicomponent absorption is more easily handled if compositions are placed as defined by X’ and Y’, where X’= moles of one component in the liquid stream per mole of solvent entering the absorber, Y’= moles one component in the gas stream leaving any plate
For plate n these concentration are defined as
                                             (S6)
and
                                        (S7)
Then the Equation (S5) can be written as;
                  (S8)
The material balance equation can be written for overall column as
                     (S9)
Equation (S9) can be plotted as straight lines and can be used for any absorption process. The equilibrium relationship between the gas and liquid on the tray in terms of the new composition parameters can be written as:
                    (S10)
By substituting the Equation (S10), the Equation (S8) becomes
                               (S11)
where  For a one-plate absorber Equation (S11) is
                   (S12)
For the second plate the material balance would be
                              (S13)
By combining Equations (S12) and (S13) the material balance for a two tray absorber can then be written as
                   (S14)
The same procedure is followed for an absorber with three plates and finally, for absorber with N trays

To obtain the equation in terms of the absorber terminal conditions, Y^/_N can be determined by combining Equation (S15) with an overall component material balance around the column. The overall component material balance is
                             (S16)
An expression obtained from Equation (S10) for X^/_N is
                              (S17)
If the X^/_N is replaced in Equation (S16) by Equation (S17), one can write
                       (S18)
By introducing the Equation (S18), Equation (S15) can then be written in terms of the terminal absorber conditions as:

The Equation (S19) can be used to determine terminal stream flow rates in a multicomponent absorber. The left side of Equation (S19) is the fractional absorption for any component if the liquid and gas flow rates for each tray in the column in addition to the tray is known. If an average value of the absorption factor is assumed to be valid for each tray as A=A₁=A₂=…..=A_N, the absorption factors in Equation (S19) can be written as
              (S20)
and
         (S21)
By substituting the identities above into Equation (S19), the following expression can be obtained
                   (S22)
where A is the average absorption factor. The Equation (S22) is known as the Kremser (1930) and Brown (1932) equation. If the value of the average absorption factor for that component is known, the composition of the off-gas from the absorber and the amount of material absorbed into the solvent may be readily calculated. The average absorption factor can be defined as:
                                                       (S23)
where K_avg is the value of the average equilibrium constant for each component at the average temperature and pressure in the absorber. Equation (S22) can be solved either analytically or graphically. Any variable may be determined if the other two are known.