GRAPH-THEORETIC APPROACH TO PROCESS SYNTHESIS - AXIOMS AND THEOREMS

An innovative approach, based on both graph theory and combinatorial techniques, has been proposed for facilitating the synthesis of a process system. In contrast to other general purpose mathematical programming methods, this innovative approach is designed to cope with the specificities of a process system: it represents the structure of a process system by a unique bipartite graph, termed a P-graph, and captures not only the syntactic but also the semantic contents of the process system. An axiom system underlying the approach has been constructed to define the combinatorially feasible process structures. This axiom system is based on a given set of specifications for the process synthesis problem. Such specifications include the types of operating units and the raw materials, products, by-products, and a variety of waste associated with these operating units. All feasible structures of the process system are embedded in the maximal structure, from which individual solution-structures can be extracted subject to various technical, environmental, economic, and societal constraints. Various theorems have been derived from the axiom system to ensure that this approach is mathematically rigorous, thereby rendering it possible to develop efficient process synthesis methods on the basis of a rigorous mathematical foundation. Examples are presented to highlight the significance and efficacy of the present approach.