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When modeling a distillation column, one can draw balances on the entire
system, the column base, the accumulator, each tray (or a group of trays).
Mass and component balances are always required. In special cases, the energy
balances can be neglected.
The overall material balance on a distillation column with NT trays is:
where F,D, and B are mass flow rates, MB is the mass in the column
base, MD the mass in the accumulator, and Mn the mass on
tray n. Often, the mass of the vapor in the column is much smaller than the
mass of the liquid in the column; in such cases, it is often a reasonable
approximation to write the mass accumulation terms for the liquid phase only.
The overall component balance is:
This can also be written with accumulation terms representing the liquid alone,
if the appropriate assumptions are made.
The balances required for the accumulator are:
where V1 is the vapor flow off the top tray to the
for a total condenser or
for a partial condenser with a vapor product.
The base and reboiler balances are
for a partial reboiler with boilup rate VB (LNT is the
liquid flow off the bottom tray of the column), and
Don't forget that xB and yB are in equilibrium with each
For each tray, we can write:
in a general form that allows one feed (Fn) and one liquid product
(Pn) on each tray. Usually, only one tray will have a feed stream,
and there will be only a few, if any sidedraw products. You can also have
vapor products, which will require replacing Pnxn in the
component balance with Pnyn.
It also may be useful to examine the steady state balances on a feed tray. The
total material balance on feed tray n is
To capture all necessary detail, one must recall that the feed can be both
vapor and liquid. As described by the feed variable q, the fraction
liquid is Fq, so the vapor rate above the feed tray and the liquid
rate below the feed tray will change. The new values will be
An equivalent analysis can be made for draw trays. It will be necessary
to specify whether the draw is made from the liquid space or vapor space
on the tray. This defines a q value for the draw. The
equations will then be essentially the same, but keep in mind that the
effect of a draw is to reduce the traffic in the column while a feed
Original: 7 February 1997
Updated: 19 February 1997, 22 Jan 1998, 14 Feb 2003
Copyright 1997, 1998, 2003 by R.M. Price -- All Rights Reserved