A General Mathematical Framework for Calculating Systems-Scale Efficiency of Energy Extraction and Conversion: Energy Return on Investment (EROI) and Other Energy Return Ratios

The efficiencies of energy extraction and conversion systems are typically expressed using energy return ratios (ERRs) such as the net energy ratio (NER) or energy return on investment (EROI). A lack of a general mathematical framework prevents inter-comparison of NER/EROI estimates between authors: methods used are not standardized, nor is there a framework for succinctly reporting results in a consistent fashion. In this paper we derive normalized mathematical forms of four ERRs for energy extraction and conversion pathways. A bottom-up (process model) formulation is developed for an n-stage energy harvesting and conversion pathway with various system boundaries. Formations with the broadest system boundaries use insights from life cycle analysis to suggest a hybrid process model/economic input output based framework. These models include indirect energy consumption due to external energy inputs and embodied energy in materials. Illustrative example results are given for simple energy extraction and conversion pathways. Lastly, we discuss the limitations of this approach and the intersection of this methodology with "top-down" economic approaches.