A mathematical model for the middle vessel batch distillation column ({MVC}) is developed using the concept of warped time analysis and used to study the qualitative dynamics of the {MVC} when it is used to separate multicomponent azeotropic mixtures. A limiting analysis is then developed for a {MVC} with an infinite number of trays, operated under infinite reflux/reboil ratios, under the assumption of linear separation boundaries. It is determined that, under limiting conditions, the distillate product drawn from the {MVC} is given by the alpha limit set of the {MVC} still pot composition, while the bottoms product drawn from the {MVC} is given by the omega limit set of the {MVC} still pot composition. The net product composition is determined by taking a convex combination of the two products. The notions of steering the still pot composition, the vector cone of possible motion for the still pot composition, and the equivalency of the {MVC} to the combined operation of a batch rectifier and a stripper are also explored. The definition of batch distillation regions for the {MVC} operated at a given value of the middle vessel parameter lambda, and the bifurcation of these regions with the variation of lambda, are investigated. Lastly, a mathematical model incorporating the concept of warped time is developed for a multivessel column. The {MVC} can be viewed as a specific case of the multivessel column.