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 α limit set of the MVC still pot composition, while the bottoms product drawn from the MVC is given by the ω 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 λ, and the bifurcation of these regions with the variation of λ, 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.

On the basis of the analytical tools developed for the middle vessel column (MVC) operated under limiting conditions, analysis of the qualitative dynamics of the MVC in separating an azeotropic mixture is extended to the more realistic case in which the separation boundaries are nonlinear. The differences between batch stripper pot composition boundaries and batch rectifier pot composition boundaries in the presence of curved separatrices results in the MVC still pot composition being able to cross these pot composition boundaries. On the basis of these insights, operating procedures are developed in which ternary azeotropic mixtures of acetone, benzene, and chloroform can be separated into their constituent pure components, a separation not achievable with either the batch stripper or the batch rectifier. The operating procedures suggested for separating the ternary azeotropic mixture of acetone, benzene, and chloroform in the MVC are then shown to be the time analogues of sequences of continuous distillation columns that achieve the same separation. On the basis of this space-time analogy, further analogies are developed between the MVC and a continuous column, and it is postulated that many complex separations currently achieved with sequences of continuous columns can also be achieved with a single MVC. Thus, the MVC represents the ultimate multipurpose solvent recovery technology, as it can handle, in a batch multipurpose mode, separations that will otherwise require a dedicated continuous distillation sequence. Finally, the characteristics of perfect MVC batch entrainers, which allow the complete separation of any azeotrope into its constituent pure components in a single MVC, are discussed.

A dimensional time model of the middle vessel batch distillation column (MVC) is developed in the ABACUSS process modeling environment, and simulations are conducted to validate the theoretical insights developed for the operation of the MVC based on a warped time model of the MVC. The qualitative dynamics of the MVC operated in the presence of linear separation boundaries are validated via simulations conducted on the ternary azeotropic mixture of acetone, chloroform, and methanol. It is also shown via simulation that the separation results obtained from a column with significant but reasonable amounts of holdup on the trays are not significantly different from a column in which holdup in the trays is assumed to be negligible. Theoretical operating policies for separating the azeotrope of acetone and chloroform using benzene as a batch entrainer are also validated using the ABACUSS model. Finally, we explore the advantages and disadvantages of different feasible operating policies for separating a mixture of acetone, benzene, and chloroform completely into its constituent pure components.

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