Exact computation of emergy based on a mathematical reinterpretation of the rules of emergy algebra

The emergy algebra is based on four rules, the use of which is sometimes confusing or reserved only to the experts of the domain. The emergy computation does not obey conservation logic (i.e. emergy computation does not obey Kirchoff-like circuit law). In this paper the authors propose to reformulate the emergy rules into three axioms which provide (i) a rigourous mathematical framework for emergy computation and (ii) an exact recursive algorithm to compute emergy within a system of interconnected processes at steady state modeled by an oriented graph named the emergy graph.Because emergy algebra follows a logic of memorization, the evaluation principles deal with paths in the emergy graph. The underlying algebraic structure is the set of non-negative real numbers operated on by three processes, the maximum (max), addition (+) and multiplication (·). The maximum is associated with the co-product problem. Addition is linked with the split problem or with the independence of two emergy flows. And multiplication is related to the logic of memorization. The axioms describe how to use the different operators max, + and · to combine flows without any confusion or ambiguity. The method is tested on five benchmark emergy examples.

► The paper proposes a reformulation of the emergy rules into axioms.
► The paper provides an algorithm solving complex graph with splits, coproducts, feedbacks and a large number of nodes.
► The paper describes how to compute the exact value of emergy flowing on an arc.
► 5 benchmark examples are detailed.
► The paper solves the problem with co-product noticed in Lazzaretto (2009, p. 2201).