From Thermodynamics to Economics and Ecology - Thanatia: The Destiny of the Earth's Mineral Resources - page 77

that can be disaggregated. Exergy can also be disaggregated into its mechanical,
thermal or chemical components which all have their own history of formation. Each
sub-process has consumed resources to produce a particular change in pressure,
temperature or chemical potential. The flow history and exergy cost, i.e. the
amount of given resources to produce that flow, can always be reconstructed. By
undertaking a systematic account of these consumed resources, a physical cost can
be associated with each identified flow, representing the sum of the resources needed
to produce it under the given circumstances.
Costs can also be allocated to co-products, byproducts and wastes when flow bi-
furcations appear. Any bifurcated flow belongs to one of three categories: resource,
F, product, P, or waste, R. Lozano and Valero (1993) suggested the following
F P R rules, which can be summarised as follows:
F: The output flow of a subsystem identified as a non-spent resource keeps the
same cost per unit of exergy as the input.
P: The cost of co-products that are obtained simultaneously in a single subsys-
tem are allocated in proportion to their exergy. Byproducts are an intermediate
case between final products and wastes. They save resources and decrease the
cost of production, being allocated as their “avoided” exergy costs.
R: The costs of wastes are allocated by accounting the additional resources
needed to dispose of or treat them.
In order to allocate the above costs, three conditions need to be met. First,
system boundaries must be set. Second, a system's structure must be defined in a
way in which all the components or processes can be described in terms of black
boxes interacting with each other through energy flows. And third, the definition
of the purpose of production for each and every component must be agreed upon.
Accordingly, a systematic exergy analysis of any process requires a classification
of flows according to their purpose with all flows entering or exiting representing
either a resource or fuel, product, co-product, byproduct or waste 8 (which is really
an undesirable byproduct). Therefore, in each individual process as in the overall
one, the Second Law applies: any exergy expended is used in the creation of products
and wastes and in the generation of irreversibility. Since exergy is a measure of the
driving power of each operation, exergy e ciency 9 can be defined as the exergy of
products divided by that of the expended resources. Moreover, the exergy e ciency
of a waste disposal system is equal to the exergy decrease of wastes divided by that
of expended resources.
In the product cost formation process, an analytical search for the locations and
physical mechanisms that make up a specific productive flow is essential. In an in-
tertwined way there is also a waste cost formation process that locates and quantifies
8 Note that not every entering flow is an input nor every exiting one an output. Unexpended fuels
may also be outputs whilst pre-fabricated products, still requiring processing, may be an input.
9 Note that e ciency and purpose do not depend on Physics but on the designer.