Absorption design with nonlinear equilibrium

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Absorption design with nonlinear equilibrium
Prof. Dr. Marco Mazzotti - Institut für
Verfahrenstechnik
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1. Introduction to nonlinear equilibrium
Up to now, we always treated the case of linear
equilibrium. In the linear case, the equilibrium
can be described with the simple equation y mx.
However, we dont always have such an easy
relation between the gas and the liquid phase.
The equilibrium relation can only be described by
the general formula
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When y mx does not apply, then Kremsers
equation is useless. However, the graphical
stage-by-stage construction (and the
corresponding calculation) can still be applied.
Considering the initial compositions of the gas
yn1 and of the solvent x0 and the specification
made for the gas outlet composition y1, we can
draw in the diagram
y1
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The operating line is not influenced by a
nonlinear equilibrium. Therefore, the same
operating line equation is still valid.
The slope of the operating line depends on the
solvent flow-rate L. When one of the lines is
chosen as operating line, then the slope is set
and thus, the required solvent flow-rate can be
calculated.
y
yn1
L1 /G
L2 /G
y f(x)
L3 /G
y1
x0
x
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2. Choosing an operating line
There is a special operating line among the
infinite number we can choose. This is the one
that touches the equilibrium line at the point
(xn, yn1). Therefore, the following equation is
valid at that point
y
yn1
Lmin /G
The slope corresponding to this line is the
smallest possible slope, because the process
cannot go beyond the equilibrium line.
y f(x)
y1
x0
x
The slope of this operating line can be
calculated
In practice, the slope for the operating line is
taken as 1 to 2 times the minimum slope
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3. Graphical construction
Once the operating line is set, we can proceed
with the construction seen in the linear case.
The usual stage-by-stage construction is adopted,
switching between equilibrium line and operating
line. This gives us the number of stages, n.
y
yn1
y3
3
L /G
y f(x)
y2
2
y1
1
x0
x
x1
x2
x3
In the beginning, we had the following unknowns
L, n and xn. The liquid flowrate L can be
calculated with the slope of the operating line
L/G, knowing the gas flow rate G. The number of
stages n and the mole fraction xn can be read out
of the graph. In our example the stage number is
at least n 3.