, as I promised here is a brief discussion of the different types of distillation used in the hydrocarbon processing industries that I am very familiar with ... i.e.,  oil refineries, petrochemical plants, natural gas processing plants (extracting natural gas liquids known as NGL's), and other hydrocarbon processing industries. Those industries probably have perhaps 80% or more of the industrial distillation columns in existence.

Other industries such as the pharmaceutical industry, the alcohol distilling industry and the fine chemicals industry also use quite a bit of distillation, but I am not familiar with those industries.

Major Industrial Distillation Types: The two primary types of industrial distillations are Continuous Fractionation or (Continuous Distillation) and Batch Distillation. The industrial Continuous Fractionation distillation towers are typified by the large, vertical, cylindrical columns as can be seen in the oil refinery photograph in the Fractional distillation article. Please note  that by continuous, I mean 24 hours a day for 1 to 3 years before being temporarily shut down for maintenance ... and we are talking about towers with diameters ranging from about 65 centimeters to 6 meters and heights ranging from about 6 meters to 60 meters or more.

There are many subsets of the Continuous Fractionation primary distillation type, such as: 

 Fractional distillation
 Vacuum distillation
 Azeotropic distillation 
 Extractive distillation
 Steam distillation

The above subsets would be of approximately the same size range is the primary Continuous Fractionation towers. The vacuum towers require reinforcement (provided by a number of steel beams encircling the tower exteriors) so that they can withstand the difference in pressure between the exterior atmospheric pressure and the interior vacuum. 

As for the vapor-liquid contacting trays or plates used in industrial distillation towers, it is virtually impossible to explain bubble-cap or valve trays (or sheet steel structural packing) without drawings or photographs.  We need someone who could make such drawings. We also need someone who can make a drawing of a typical kettle-type reboiler commonly used as the heat input to a  distillation tower (although there are other types of reboilers such as fired furnaces, horizontal or vertical heat exchangers, bayonet heat exchangers, etc.).

Finally, if you look at the the simple sketch that I made of a typical fractionation tower overhead system in the Fractional distillation article, that sketch needs to be made longer so that it shows the feedstream  entry (at about the center height of the tower), and the bottoms exiting the tower and entering the kettle reboiler .... with the final liquid bottoms product leaving the kettle reboiler and the reboiled vapor returning from the kettle to the tower. -