(188b) Automatic Generation of Optimal Structure for Distillation Processes Using Stepwise VLE Description

A systematic synthesis procedure of ternary distillation processes is proposed. The proposed procedure automatically generates the optimal process structure without any assumption on partial process structures. In most of the superstructure-based synthesis methods, some partial process structures have been prepared as the building blocks in advance, which are conventional distillation columns, thermally coupled columns, and/or sections of those columns. There is little possibility of creating a completely new process structure as far as those well-known structures are used as the building blocks of separation processes. In order to create unknown innovative process structures systematically, we developed a process synthesis procedure based on the superstructure whose building block is a tray, the minimum element of distillation columns.

In the proposed design procedure, first, the entire liquid composition space is divided into many small regions, and each region is assigned to a separation module that corresponds to a tray of a distillation column. Then, for each region of liquid composition, the unique vapor composition is assigned. As the vapor composition is a constant in a region, the vapor-liquid equilibrium (VLE) is expressed by a stepwise function. However, by determining the size of each region appropriately, the stepwise VLE successfully emulate the real VLE. Then, a superstructure is generated by connecting vapor and liquid flow paths between arbitrary separation modules. A large number of variables which refers to flow rates of those flow paths is used to express the material and enthalpy balances at each module. Thus, it is very important to reduce the non-linearity in the mathematical model. In the previous paper ^[1], the liquid and vapor compositions in a module were treated as constants so as to express the material and enthalpy balances by linear equations.

In the new formulation, the material and enthalpy balances are expressed by linear equations even though the liquid composition of a module is treated as variables having lower and upper bounds. By this expansion of the model, it becomes possible to reduce the number of tiny flows that arises for adjusting the material balance at each module.

In the proposed synthesis procedure, the energy consumption is minimized at the first step optimization. Various structures of processes achieve the minimum energy consumption, and the obtained process structure has many modules and many secondary flows with small flow rates. Thus, at the second optimization step, the number of modules used in the structure is minimized under the constraint on the energy consumption. This optimization problem is formulated as a mixed integer linear programming problem. Finally, at the third step, the process structure is simplified by reducing the number of flows among modules under the constraints on the number of modules and the energy consumption.

In the case studies, the proposed method was applied to several separation problems of ternary mixtures. The result showed that the optimal process structure for each design requirement was systematically synthesized without any structural assumption.

Reference;

[1] H. Takase, S. Hasebe, â??Optimal Structure Synthesis of Internally Heat Integrated Distillation Columnâ?, Journal of Chemical Engineering of Japan, 48, pp. 222-229, 2015