Matrix method for comparing system and individual energy return ratios when considering an energy transition

ERRs (Energy return ratios) are valuable metrics for understanding and comparing the contributions of individual energy technologies. It is also important to calculate ERRs in the context of a system, or economy, using a mix of energy technologies. In this paper I demonstrate a framework to simultaneously consider individual energy technology and system-wide ERRs using a process-based input-output model approach. I demonstrate the approach via an example calculating grid electricity ERRs assuming constant technology with only a shift in dominance from fossil to renewable technology. The framework also enables interpretation of changes in individual ERRs due to a shift from one technology to another, with implications for energy scenario analyses. Another finding of this paper is that the ERR GER (gross energy ratio, often assumed equal to EROImm (energy return on energy invested at the 'mine mouth')), is only well-defined for primary energy extraction and not energy carriers such as gasoline and electricity. NER (Net energy ratio) and NEER (net external energy ratio), also known as EPR (energy payback ratio), are the most appropriate metrics for describing energy carriers sold to consumers.