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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, M_{B} is the mass in the column
base, M_{D} the mass in the accumulator, and M_{n} 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 V_{1} is the vapor flow off the top tray to the
condenser, and

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 V_{B} (L_{NT} is the
liquid flow off the bottom tray of the column), and

Don't forget that x_{B} and y_{B} are in equilibrium with each
other.

For each tray, we can write:

in a general form that allows one feed (F_{n}) and one liquid product
(P_{n}) 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 P_{n}x_{n} in the
component balance with P_{n}y_{n}.