Heat integrated distillation apparatus

A distillation apparatus includes a rectifying column, a stripping column, a first pipe that communicates a column top of the stripping column with a column bottom of the rectifying column, and a compressor configured to compress vapor from the stripping column and then to feed the compressed vapor to the rectifying column. The distillation apparatus further includes a heat exchanger located at a predetermined stage of the rectifying column, a liquid withdrawal unit located at a predetermined stage of the stripping column and configured to withdraw a part of liquid from the predetermined stage to an outside of the column, a second pipe that introduces the liquid from the liquid withdrawal unit to the heat exchanger, and a third pipe that introduces fluids introduced through the second pipe to the heat exchanger and then discharged out of the heat exchanger to a stage directly below the liquid withdrawal unit.