This chapter presents two applications of MINLP methods in the area of separations. Section 9.1 provides an overall introduction to the synthesis of separation systems. Section 9.2 focuses on sharp heat-integrated distillation sequencing. Section 9.3 presents an application of nonsharp separation synthesis. The synthesis of distillation-based separation sequences has been one of the most important subjects of investigation in the area of process synthesis. This is attributed to the significant contribution of separation processes to the total capital investment and operating expenses of a chemical plant. As a result, a lot of interest has been generated in the development of systematic approaches that select optimal sequences of distillation columns. Westerberg (1985) provided a comprehensive review of the distillation-based separation synthesis approaches, as well as presented a classification of different types of separation problems along with their associated challenges. Nishida et al. (1981) and Smith and Linnhoff (1988) reviewed the general separation synthesis problem (i.e., not only distillation-based) and presented the progress made. To illustrate the nature of the distillation-based separation system synthesis problem, let us consider its generic definition shown in Figure 9.1, which is as follows: . . . Given a number of input multicomponent streams which have specified amounts for each component, create a cost-optimal configuration of distillation columns, mixers, and splitters that produces a number of multicomponent products with specified composition of their components. . . The products feature components that exist in the input streams and can be obtained by redistributing the components existing in the input streams, while the cost-optimal configuration corresponds to the least total annual cost one. Most of distillation columns or sequences can be classified as (i) Sharp, (ii) Nonsharp, (iii) Simple, (iv) Complex, (v) Heat-integrated, and (vi) Thermally coupled. In (i), a column separates its feed into products without overlap in the components. An example is the separation of a stream consisting of four components A, B, (C, and D via a distillation column, into one product consisting of only A and another product featuring B, C, and D. If all columns are sharp, then the separation sequence is termed as sharp sequence.