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Process design for multisolute absorption

Prof. Dr. Marco Mazzotti - Institut für Verfahrenstechnik

Once temperature, pressure and initial composition of the solvent are set we can consider them as data. This is a list of known variables:

yj,1

G

L

Data and set values: j = 1,..k..,c

Specifications: k key

Unknowns: j = 1,..k..,c

yk,1

xj,o

Temperature, T

Gas final composition, yk, 1

Solvent flow rate, L

Pressure, p

Number of stages, n

Gas flow rate, G

Gas final compositions, yj, 1

Gas initial compositions, yj, n+1

Solvent final composition, xj, n

Solvent initial composition, xj,o

T

p

Equilibrium data, y = mj xj

y = mj x

n

yj, n+1

xj, n

G

L

2. From single solute to multisolute absorption

Up to this point we have been restricted to cases where there is a single solute to recover. Both the stage-by-stage McCabe-Thiele procedure (for linear and non-linear equilibrium) and the Kremser equation (for linear equilibrium) can be used for multisolute absorption if certain assumptions are valid.

The single solute analysis by the Kremser equation requires...

1. Systems that have linear equilibrium

2. Systems that are isothermal

3. Systems that are isobaric

4. Systems that have negligible heat of absorption

5. Systems that have constant flow-rates

These assumptions are still required. A new assumption must be added for the multisolute case:

6. Solutes are independent of each other

So the equilibrium for any solute does not depend on the amounts of other solutes present. This assumption requires dilute solutions.

y

y

y

y2 = m2 x2

yk = mk xk

y1 = m1 x1

yc = mc xc

x

x

x

x

3. Solving the multisolute problem

The consequence of assumption 6 is that we can solve the multisolute problem once for each solute, treating each problem as a single-solute problem. This is true for the Kremser equation (assuming linear equilibrium) and for the stage-by-stage solution method (any equilbrium relation).

Usually one outlet composition for one of the components is fixed. This component is called key component and is the specification of the problem. It is designed by the letter k.

The equilibrium information for each component is required, in order to solve the problem. Let’s consider the absorption problem of c components, all of them systems of linear equilibrium:

...

...

j = 1

j = 2

j = k

j = c

m1 > m2 > ...>mk >...> mc

Now, for the key component we can write the operating line as usual (note that the slope of the operating line does not depend on the specific solute:

The problem can be solved for k component as usual, either using Kremser or the graphical construction:

yk

j = k

Choosing A...

yk,n+1

yk,4

Calculating the slope of the operating line:

yk = mk xk

L/G

yk,3

Using Kremser equation:

yk,2

yk, 1

xk

xk,2

xk,3

xk,4

xk,o

xk,1

Once the number of stages has been found from the key solute, k, the concentrations of the other solutes can be determined by solving (c-1) fully specified simulation problems.

This means that the number of stages is known and the outlet compositions have to be calculated. This problem is similar to the one we have already discussed and called “simulation problem”. The operating lines have for every solute the same slope (L/G).

If we consider the next example, the number of stages found for the key component must be drawn for the other components. Graphically, this means...

...

j = 1

j = 2

j = c

y

y

y

yc,n+1

y2,n+1

y1,n+1

yc = mc xc

y1 = m1 x1

y2 = m2 x2

y1,1

y2,1

yc,1

x

x

x

While analytically, the following steps are followed for all the components, j, but k:

So the outlet composition in the gas can be calculated:

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