Page 309 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

11.4 Fractionator 311

Theoretical number of trays at actual reflux
The actual reflux ratio (R) and the corresponding number of trays for a particular separation
problem are related to R min and N min by the Gilliland’s correlation fairly well represented by
0:5124
S S m N N min R R min
(11.16)
¼ 0:7591 0:7532
¼
S N þ 1 R þ 1
Where N is the total number of equilibrium stages in the column including partial reboiler, but
excluding partial condenser, if any. N min is also defined in the same way. The correlation is to be used
for the RHS range from 0.02 to 0.98.
Feed tray location
Feed tray location can be estimated by the ratio of the total number of theoretical stages in the
rectification (S r ) and the stripping section (S s ) from the Fenske equation at total reflux

N r þ 1
S r log x LK;D =x HK;D z HK;F =z LK;F
(11.17)

¼ ¼
S s N s þ 1 log z LK;F =z HK;F x HK;B =x LK;B
where N r and N s are the respective number of trays in the rectification and stripping section.
This equation is solved for ðS r =S s Þ. This is not an exact answer as the feed tray composition hardly
ever matches the exact composition of the feed. Locating the feed tray utilising this ratio may be off by
two or three theoretical trays. Multiple feed tray option may be kept with three alternative feed nozzles
provided on alternate trays. Feed tray location is much more exact in case of tray to tray calculation
procedure.
Actual number of trays in the rectification section (N actual;r ) can be found as

N actual;r ¼ S r h for total condenser and N actual;r ¼ðS r 1Þ h for partial condenser.
o
o
Where h stands for overall tray efficiency and
o
S s ¼ S m =ð1 þðS r = S s ÞÞ; S r ¼ S m S s (11.18)
In case of systems with large variation in relative volatility,

log x LK;D =x HK;D

S r ¼
Top Feed
log a LK;HK
and

log x LK;F =x HK;F
(11.19)

S s ¼
Feed Bottom
log a LK;HK
1=2 1=2

Top Feed Top Feed Feed Bottom Feed Bottom
where a LK;HK ¼ a LK;HK a LK;HK and a LK;HK ¼ a LK;HK a LK;HK .
For some problems the above approach fails to generate meaningful result. The Kirkbride equation
can also be used to locate the feed tray as it expresses the ratio of S r and S s as
#
" 2 0:206
S r N r þ 1 x HK;F x LK;B B
(11.20)
¼ ¼
S s N s þ 1 x LK;F x HK;D D
In fact the Kirkbride equation is more popular. There is also another way to locate the feed tray
using ErbareMaddox empirical correlation that is not included in this text.