An important process-design problem in multicomponent separations is separation sequencing, which is concerned with the selection of the best method and sequence for a separation system. Essentially all of the published work on this subject has been limited to high-recovery or sharp separations, in which each component to be separated appears in one and only one product stream. In industrial practice, however, it is often useful to permit components that are being separated to appear in two or more product streams. This type of separation results in products that have overlapping components and is called nonsharp or sloppy separations. The present work proposes and demonstrates a simple and practical approach to the systematic synthesis of sloppy multicomponent separation sequences. The task of synthesizing sloppy multicomponent separation sequences is inherently more complicated than that of synthesizing sharp separation sequences as identification of infeasible splits and stream splitting, and transformation of infeasible product sets into equivalent feasible product sets are examples of some difficult tasks involved. A successful synthesis strategy calls for the development of an effective and flexible framework for representing the synthesis problem and for analyzing the feasibility of component splits. In this thesis, we propose a "component assignment diagram (CAD)" for problem representation. It is shown that the use of a CAD allows the design engineer to consider many alternative solutions (or sequences) and eliminate all infeasible component splits. Further, a "separation specification table (SST)" is proposed for feasibility analysis. In particular, the use of an SST provides a means to : (i) properly define and specify key and nonkey components; (ii) quickly identify feasible and infeasible splits; (iii) effectively deal with fuel products with unmatched compo- nent specifications; and (iv) systematically consider sloppy separations with multiple split points. One difficult problem arising from the design of multicomponent distillation columns for sloppy separations is to appropriately specify the distributions of non-key components in both overhead and bottoms products. Despite the importance of these specifications, there is very little information available on this subject in the literature. This thesis reports the results from a comparative study of rigorous simulation and shortcut modeling of multicomponent distillation columns for sloppy separations. One objective was to obtain improved quantitative understanding and practical design insights into the characteristics of nonkey distributions through a shortcut modeling based upon the Fenske equation. One method proposed in this work for synthesizing sloppy multicomponent products is a heuristic method that involves a two-phase approach. The first phase is concerned with the feasibility analysis of splits pertinent to a CAD with the aid of an SST. The second phase is to specify systematically a subsequent split by applying heuristics, an activity that involves the sequential application of several "rank-ordered" heuristics. A unifying approach is proposed and demonstrated for the synthesis of sloppy multicomponent product sets. Its objective is to generate equally good initial separation schemes, featuring as many as three characteristically different sequences, including all-sharp, all-sloppy, and both sharp and sloppy (i.e., mixed separation). The proposed methods have been applied to a number of industrial separation problems. The results show that the new methods offer an extremely useful means for design engineers to generate a number of good initial sequences for obtaining sloppy multicomponent product sets prior to the ultimate separator optimization and heat integration. / Ph. D.