Plate or stage columns can be used as absorbers. In such cases (Figure 5-27) the liquid (absorbing) stream and the gas streams move countercurrently.

Figure 5-27: Schematic of plate absorption column (3, 38).

In essence the absorber works like a stripping column.

In absorption, we convert the mole fractions and flow rates to a solute-free basis if the system is not dilute. This process makes the mass balance lines linear. The primed quantities are created by the conversion Y' = [ Y/(1- Y)] and X' = [ X/1- X)]. For dilute cases, Y = Y' and X = X'.

Then,

(5-32)

where L _M' and G _M' are the molal mass velocities in kg-moles per hour-square foot for solute-free liquid and gas streams.

If we do a mass balance on an overall basis, then

(5-33)

for a dilute gas

(5-34)

solution for the number of ideal stages involves the McCabe-Thiele method. Figure 5-28 illustrates such a solution.

Figure 5-28: McCabe-Thiele solution for plate absorber (3, 38).

The equilibrium line in Figure 5-28 is linear (i.e., Y=HX; Henry's law). See that the slope of the mass balance line is L _M/ G _M and that X ₀, Y ₁ is the column top while X _N, Y _N+1 is the column bottom.

A case corresponding to minimum reflux exists for absorption. In this instance we have...