Allocation of Finite Energetic Resources Via an Exergetic Costing Method

Abstract

This paper describes a method for the assessment of an “exergetically optimal” resource allocation and distribution. Allocating a certain resource R means to make it available in a given amount at a finite or infinite number of “consumption centres”, and to find the optimal siting of the production and/or of the consumption points, so that the resource is distributed as needed, under the specified constraints, and its distribution pattern is such that it minimises the overall exergy consumption caused by the technological chain of processes the resource undergoes from its extraction to its final use (including disposal of residues). Two general formulations are possible: in the discrete problem, the number of consumption sites as well as that of the production centres is finite, and usually rather small. In the continuum problem, while the number of production sites remains small, the possible consumption points are distributed uniformly over the entire region of interest, so that in effect the resource must be made available everywhere in the domain. In both cases, the practical implementation of the method consists in the minimisation of an objective function that contains the extraction, preparation, transportation, distribution and environmental costs of the resource: the important novel feature here is the fact that these costs are expressed in exergetic units, i.e., they are represented by the amount of exergy that is expended for that particular operation. The constraints are topological (the orography and the geography of the region), technical and environmental, and are imposed in the form of exergetic penalty functions. For the continuum formulation, a similarity with a diffusion problem can be invoked to extend the mathematical analogy to the solution of a general dual dispersion equation: the reader is referred to a companion paper [10]