Continuous distillation is feed is sent to the still all the
time and product is drawn out at the same time. The idea in
continuous distillation is that the amount going into the still
and the amount leaving the still should always equal each other
at any given point in time.
Batch distillation is when the amount going into the still and the
amount going out of the still is not supposed to be the same all
the time. The easiest example to use is like old fashioned spirit
making. The distiller fills a container at the start, then heats it,
as time goes by the vapors are condensed to make the alcoholic
drink. When the proper quantity of overhead (drink) is made, the
distiller stops the still and empties it out ready for a new batch.
This is only a simple case, in industrial usage what goes on gets
very complex.
Both continuous and batch distillation are very important to industry. Continuous distillation is most often used with big
volume products like jet fuel, benzene, plastic monomers. Batch distillation is most often used with smaller volume products and
in plants that make lots of different things and use the same still
for many products (in different batches).