Page 259 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

260 Chapter 10 Absorption and stripping

the gas concentration from y Nþ1 to y 1 or more. From Fig. 10.2, this absorber requires 2.4 ideal trays. If
the overall tray efficiency of 40% is considered, the actual number of trays required is 2.4/0.4 ¼ 6
trays.
It is important to note that the enrichment per tray is lower at the dilute end, as separation is more
difficult. Therefore, the standard practice of graphical construction that produces a more accurate
estimation of the number of trays is to start from the dilute end and continue up to the final
concentration.

Minimum required liquid flow rate (L min ) in case of absorber for a given gas rate (G,G )
0
The foregoing geometrical construction to determine the number of ideal stages of contacting could be
done, only because (1) the point on the operating line corresponding to y Nþ1 is situated above the
equilibrium line, (2) the operating line and the equilibrium lines neither touch nor intersect below
y Nþ1 .

The geometric condition of the minimum liquid flow rate L min ; L 0 min for a given gas flow rate
would correspond to the operating line touching the equilibrium line. Thus, the minimum theoretical
liquid flow rate (L min ) is found from the material balance equatione L min ¼ G.(y Nþ1 y 1 )/(x N x o )

and leads to an operating line passing through (x o ,y 1 ) and x Nþ1 ; y Nþ1 , where x Nþ1 is the liquid-phase
composition in equilibrium with the vapor composition y Nþ1 . In the construction of Fig. 10.2, this
2
corresponds to x N ¼ 0.0063 and the (L min /A t ) ¼ 147.3 kg mol water/m . hr, where A t is the cross-
sectional area of the tower.
Optimum (economic) operating liquid flow rate (L, L ) is usually around 1.5 to 3 times the min-
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imum liquid flow rate.
It is important to realize that in the case of the equilibrium line touching or intersecting the
operating line at some point P, the gas composition enrichment limit is y P . This point is the “pinch
point” for the system, and if y P <y Nþ1 , enrichment up to y Nþ1 is not possible with the liquid flow rate
(L, L ) considered.
0
Approximations for low concentration system
When the concentrations are low, x o <<1 and y Nþ1 <<1, the mole ratio (X, Y) and mole fraction (x,y)
can be approximated to be equal over the entire concentration range. In this case, the partial pressure of
the inert gas remains constant throughout the column length, and the solute concentration in the liquid
and gas phase is sufficiently small.
The operating line equation reduces to the following linear expression with a slope of (L/G).

y ¼ðL = GÞ:x þ y 1 ðL = GÞ$x o (10.2)
Also, the equilibrium relationship at low concentrations is usually well approximated by Henry’s
Law that has the linear form
y ¼ Hx (10.3)
When the operating and equilibrium relationships are both linear, an analytical solution for the
number of stages (N) exists in the form of the following equation known as the Kremser equation.
In the case of absorber,
(10.4)
N ¼ log½ðy Nþ1 m:x Nþ1 Þ = ðy 1 m:x 1 ފ=logðAÞ