(731a) A Rigorous Graphic Approach to Modeling Transportation Fuel Lifecycle: Axioms and Theorems

An innovative approach based on graph theory has been proposed for facilitating the lifecycle assessment of transportation fuels in general and renewable feedstock-based transportation fuels in specific. The complexity of the fuel lifecycle system is analyzed. The proposed approach is designed to tackle the specificities of a transportation fuel in its lifecycle: it represents the structure of the lifecycle by a unique graph, termed a Lifecycle graph, or an L-graph for short. This graph captures not only the syntactic but also the semantic contents of the system. A novel concept of ?material state in its lifecycle? is proposed to help describe the pathway of a transportation fuel in its lifecycle and its complexity together with the concepts of material and location. An axiom system underlying the approach has been established to define the rigorous lifecycle structure. This axiom system is based on a given set of specifications for the lifecycle assessment problem. Such specifications include the types, input and output materials, origins and destinations of processes, and a variety of parameters such as efficiencies and losses associated with these processes, natural energy sources, energy products, co-products and their geographical specificities. All pathways in the lifecycle of a specific transportation fuel are embedded in a maximal structure, from which individual pathways can be extracted. Various theorems have been derived from the axiom system to ensure that this approach is mathematically rigorous, thereby rendering it possible to develop efficient transportation fuel lifecycle pathway generation and management methods on the basis of a rigorous mathematical foundation. Examples of multiple renewable feedstock-based transportation fuels are presented to highlight the significance and efficacy of the present approach.