Page 266 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

10.3 Packed column 267

In the above expressions, G and L are the total molar flow rates, and A t is the cross-sectional area of
the column.
Since the individual coefficients of mass transfer vary rapidly with the flow rate, the quotient of
each coefficient divided by the phase flow rate to which it
applies is more nearly constant than the coefficient itself.

Height of a transfer unit (HTU) and The quantity obtained by this division G or L is
Number of transfer units (NTU) k aA t k aA t
0
y
0
l
the height of one transfer unit (HTU), which is the bed
height required to accomplish one unit of separation. The

G
HTU based on gas phase H TOG ¼ 0 is more commonly used.
k aA t
y
Z
y 2
dyð1 yÞ iM
The corresponding driving force term N TOG ¼
y 1 ð1 yÞðy y i Þ
ð1 y i Þ ð1 yÞ
where ð1 yÞ iM ¼
ln ð1 y i Þ
ð1 yÞ
This is the number of overall gas-phase transfer units required for changing the composition of the
gas phase from y 1 to y 2 and h bed ¼ H TOG .N TOG .
It is important to note that for packed towers, the column height depends not only on the operating
and equilibrium lines but is also inversely proportional to the mass transfer coefficients that play a
relatively minor role in determining the plate efficiency.
Although the processes are similar, in the case of packed column distillation, the difficulty is
encountered in the integration to evaluate N TOG and h bed . This is
because the assumption used for gas absorption is not valid.
Although L and V (moles/hr) are constant, the corresponding
Absorption versus distillation
mass rates in kg/hr may vary appreciably due to the variation of
molecular weight with composition. Since the present mass
transfer coefficients are functions of mass flux (flow rates per unit
area), considerable variation in these coefficients may occur along the tower. In addition, the fluid
physical properties may vary significantly due to changes in both temperature and pressure.
Accordingly, the theory of distillation is not very satisfactory in packed towers.
If the x and y values for the gas and the liquid streams are below 0.1, the system is considered as a
“dilute” or “low concentration” system in the engineering sense.
The low concentration and its small change leads to only a limited
change in the volumetric flow rate of the two phases in the tower.
Design of dilute systems
Hence, it is considered that there is only a limited change in tur-
bulence along the tower, and the mass transfer coefficients are
fairly constant over the entire tower.
The design Eqs (10.11e10.14) for the dilute system thus simplifies to e
" #
G dy
Z Z
h bed y 2
iM
ð1 yÞ
h bed ¼ dz ¼ (10.15)
0 k aA t ð1 yÞ ðy y i Þ
y
0
av y 1