Dynamic accounting of emergy cycling

The emergy associated with materials can amount to a large portion of the total emergy budget required to make something or operate a system. Many materials are recycled and often retain much of their high transformity properties, but emergy accounting lacks clear rules for emergy recycling. Odum offered some guidelines on emergy recycling when he proposed that earthly biogeochemical cycles were coupled to energy flows, organized hierarchically, and could be quantified by their emergy per mass. Brown built on this early guideline to introduce the concept of “emformation,” which proposed that the emergy of materials (material–emergy) could be tracked separately from the emergy of energy (energy–emergy) and the emergy of information. Emergy accounting that adheres to emformation, distinguishes between the sources of emergy and provides a way to subtract recycled material–emergy from the emergy required to make something. The aim in this paper is to adapt Dynamic Emergy Accounting (DEA) to represent the emformation principle and to provide a means for modeling the cycling of emergy. To accomplish this, the mini-model EmCycClos was created with a closed material cycle coupled to energy throughput. Equations for tracking energy–emergy and material–emergy separately were included. Separate tracking required new emergy variables, henceforth called partial transformities and partial specific emergies. EmCycClos demonstrated that as a material is used to catalyze energy production that is stored, its emergy is added to the stored product along with the emergy from the energy that drove the process. The new storage has material–emergy and energy–emergy coupled together. The stored product then drives a second production function whereby the material is 100% recycled back to its first state, along with its material–emergy, and the second product leaves the system with only the energy–emergy. This resulted in more emergy on the internal pathway than on either the input or output. EmCycClos revealed that the emergy, transformity, specific emergy, energy and material of all flows and storages could reach steady state conditions similar to what would be expected from non-dynamic systems. The new emergy attributes behaved dynamically with the ability to increase or decrease in the face of transient perturbation, thus demonstrating that transformity and specific-emergy are dynamic variables. This expansion of DEA provides a mathematical basis for understanding the recycling of emergy on material loops, and thus offers insight on how to fine-tune emergy evaluations concerned with significant material budgets.