(71k) A Generalized Mathematical Model for Sustainability

At the 2005 Spring Meeting of the AIChE, we discussed sustainability in a broad context and proposed that the limitations imposed by the second law of thermodynamics and process rates be considered as well as merely the conservation of energy, matter, species, and ecosystems; and furthermore that more care be taken in identifying the system being considered, that is, the location of the physical or conceptual envelope surrounding the system of interest. Our analysis suggested that the choice of different envelopes is the primary source of the contradictory conclusions concerning sustainability that pervade the current literature relative to particular fuels and processes.

Here, we propose a mathematical model for the quantitative description and comparison of various fuels, processes, infrastructures, and schemes in order to determine their relative degrees of sustainability, thereby providing an improved basis for technological and public choices. This model is intended to be dynamic and scale-independent, and, by taking into account spatial and temporal factors of processing, to be applicable, for example, to individual items of equipment, chemical processes as a whole, entire chemical plants, communities, cities, countries, and the earth itself. The model includes both stationary and dynamic behavior and extends beyond the conservation of species and energy, In so-doing it places long-term sustainability alongside short-term efficiency in the cost-benefit calculus of choosing engineering processes and technologies. Even so, the new mathematical model is limited to some extent by the difficulty of describing factors such as the quality of life in quantitative terms. The formulations are first given in general and then reduced and specialized for illustrative processes.