Page 303 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

11.4 Fractionator 305

In case of subcooled reflux, the reflux stream on reaching the tray heats up to its bubble point,
consuming latent heat of vaporisation from the vapour approaching the tray and causing it to condense.
This causes the internal reflux ratio (R int ) within the rectifying section of the column to be higher than
the reflux ratio (R) from the reflux drum. The number of equilibrium stages is slightly overestimated if
this is ignored.
The R int value for the McCabeeThiele construction in such a case can be estimated from R by an
approximate energy balance around the top tray as

c pL DT subcooling
(11.9)
R int ¼ R 1 þ
l
where c pL is the molar specific heat of reflux liquid, l is the molar latent heat of vaporisation and
DT subcooling is the degree of subcooling in the external reflux, i.e., the difference between the actual
reflux temperature and the bubble point of same at the column top pressure.
Accordingly, R int should be used instead of R in Eq. 11.1 and the rectifying section operating line
equation becomes

R int x D
y ¼ x þ
R int þ 1 R int þ 1

Effect of increasing the ratio ðR=R min Þ
Capital cost: A tower theoretically requires infinite number of trays at minimum reflux ðR=R min ¼ 1Þ
and hence the corresponding capital investment for the system comprising of the column, condenser,
reflux drum, reflux pump and reboiler is infinite. Higher ðR=R min Þ ratio reduces the number of trays and
consequently the column height but increases the column diameter due to increased vapour and liquid
traffic in the column. The corresponding reboiler and condenser heat duties also increase. Thus, increase
in (R/R min ) from its minimum value of 1 decreases the capital cost for the system from a very large value
due to the effect of lowering of tower height overriding the opposite effect of diameter increase. This
reduction goes on up to a limit, beyond which the capital cost increases again due to the effect of increase
in tower diameter and also due to increased heat duty and corresponding bigger sizes of the condenser
and the reboiler.
Operating cost: Operating cost includes costs for manpower, maintenance, depreciation and taxes
and the cost of coolant in the condenser and heat energy added to the reboiler. If the coolant is cooling
water and the heat supplied to the reboiler is by condensing steam, then the cost of these utilities
constitute the corresponding component of operating cost expressed in Rs/year. Except manpower, the
remaining components of operating cost increase with increase in the ratio (R/R min ).
Optimum (economic) design
Optimum design is arrived at by minimising the annualised total cost. Fixed investment cost and
the annual operating cost are added to give the annualised total cost in Rs/year. If borrowed capital is
used for the investment, the interest per annum to be paid thereon is the annualised fixed investment
cost. Information on the market borrowing (interest) rate is required in this case. In case of investment
of own capital, the interest revenue loss from the alternative of keeping the same (investment) amount
as deposit in bank is considered.