IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v4y2011i8p1211-1245d13623.html
   My bibliography  Save this article

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

Author

Listed:
  • Adam R. Brandt

    (Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA)

  • Michael Dale

    (Global Climate and Energy Project (GCEP), Stanford University, Stanford, CA 94305, USA)

Abstract

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.

Suggested Citation

  • Adam R. Brandt & Michael Dale, 2011. "A General Mathematical Framework for Calculating Systems-Scale Efficiency of Energy Extraction and Conversion: Energy Return on Investment (EROI) and Other Energy Return Ratios," Energies, MDPI, vol. 4(8), pages 1-35, August.
    • Handle: RePEc:gam:jeners:v:4:y:2011:i:8:p:1211-1245:d:13623
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/4/8/1211/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/4/8/1211/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ayres, Robert U. & Warr, Benjamin, 2005. "Accounting for growth: the role of physical work," Structural Change and Economic Dynamics, Elsevier, vol. 16(2), pages 181-209, June.
    2. Philip F. Henshaw & Carey King & Jay Zarnikau, 2011. "System Energy Assessment (SEA), Defining a Standard Measure of EROI for Energy Businesses as Whole Systems," Sustainability, MDPI, vol. 3(10), pages 1-36, October.
    3. Pacca, Sergio & Sivaraman, Deepak & Keoleian, Gregory A., 2007. "Parameters affecting the life cycle performance of PV technologies and systems," Energy Policy, Elsevier, vol. 35(6), pages 3316-3326, June.
    4. Bullard, Clark W. & Penner, Peter S. & Pilati, David A., 1978. "Net energy analysis : Handbook for combining process and input-output analysis," Resources and Energy, Elsevier, vol. 1(3), pages 267-313, November.
    5. Cleveland, Cutler J., 2005. "Net energy from the extraction of oil and gas in the United States," Energy, Elsevier, vol. 30(5), pages 769-782.
    6. Richard B. Norgaard & Gwo Jiun Leu, 1986. "Petroleum Accessibility and Drilling Technology: An Analysis of U.S. Development Costs from 1959 to 1978," Land Economics, University of Wisconsin Press, vol. 62(1), pages 14-25.
    7. Herendeen, Robert A., 1978. "Input-output techniques and energy cost of commodities," Energy Policy, Elsevier, vol. 6(2), pages 162-165, June.
    8. Leach, Gerald, 1975. "Net energy analysis -- is it any use?," Energy Policy, Elsevier, vol. 3(4), pages 332-344, December.
    9. Livernois, John R & Uhler, Russell S, 1987. "Extraction Costs and the Economics of Nonrenewable Resources," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 195-203, February.
    10. Livernois, John R., 1987. "Empirical evidence on the characteristics of extractive technologies: The case of oil," Journal of Environmental Economics and Management, Elsevier, vol. 14(1), pages 72-86, March.
    11. Cleveland, Cutler J., 1992. "Energy quality and energy surplus in the extraction of fossil fuels in the U.S," Ecological Economics, Elsevier, vol. 6(2), pages 139-162, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Macías, Arturo & Matilla-García, Mariano, 2015. "Net energy analysis in a Ramsey–Hotelling growth model," Energy Policy, Elsevier, vol. 86(C), pages 562-573.
    2. Carey W. King & John P. Maxwell & Alyssa Donovan, 2015. "Comparing World Economic and Net Energy Metrics, Part 1: Single Technology and Commodity Perspective," Energies, MDPI, vol. 8(11), pages 1-26, November.
    3. King, Carey W., 2014. "Matrix method for comparing system and individual energy return ratios when considering an energy transition," Energy, Elsevier, vol. 72(C), pages 254-265.
    4. Roma, Antonio & Pirino, Davide, 2009. "The extraction of natural resources: The role of thermodynamic efficiency," Ecological Economics, Elsevier, vol. 68(10), pages 2594-2606, August.
    5. Lina I. Brand-Correa & Paul E. Brockway & Claire L. Copeland & Timothy J. Foxon & Anne Owen & Peter G. Taylor, 2017. "Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI)," Energies, MDPI, vol. 10(4), pages 1-21, April.
    6. Raugei, Marco & Fullana-i-Palmer, Pere & Fthenakis, Vasilis, 2012. "The energy return on energy investment (EROI) of photovoltaics: Methodology and comparisons with fossil fuel life cycles," Energy Policy, Elsevier, vol. 45(C), pages 576-582.
    7. Alexandre Poisson & Charles A. S. Hall, 2013. "Time Series EROI for Canadian Oil and Gas," Energies, MDPI, vol. 6(11), pages 1-20, November.
    8. Kubiszewski, Ida & Cleveland, Cutler J. & Endres, Peter K., 2010. "Meta-analysis of net energy return for wind power systems," Renewable Energy, Elsevier, vol. 35(1), pages 218-225.
    9. Carey W. King & John P. Maxwell & Alyssa Donovan, 2015. "Comparing World Economic and Net Energy Metrics, Part 2: Total Economy Expenditure Perspective," Energies, MDPI, vol. 8(11), pages 1-22, November.
    10. David J. Murphy & Michael Carbajales-Dale & Devin Moeller, 2016. "Comparing Apples to Apples: Why the Net Energy Analysis Community Needs to Adopt the Life-Cycle Analysis Framework," Energies, MDPI, vol. 9(11), pages 1-15, November.
    11. Raugei, Marco & Leccisi, Enrica, 2016. "A comprehensive assessment of the energy performance of the full range of electricity generation technologies deployed in the United Kingdom," Energy Policy, Elsevier, vol. 90(C), pages 46-59.
    12. Wu, Xudong & Li, Chaohui & Shao, Ling & Meng, Jing & Zhang, Lixiao & Chen, Guoqian, 2021. "Is solar power renewable and carbon-neutral: Evidence from a pilot solar tower plant in China under a systems view," Renewable and Sustainable Energy Reviews, Elsevier, vol. 138(C).
    13. Adam R. Brandt, 2011. "Oil Depletion and the Energy Efficiency of Oil Production: The Case of California," Sustainability, MDPI, vol. 3(10), pages 1-22, October.
    14. Velasco-Fernández, Raúl & Dunlop, Tessa & Giampietro, Mario, 2020. "Fallacies of energy efficiency indicators: Recognizing the complexity of the metabolic pattern of the economy," Energy Policy, Elsevier, vol. 137(C).
    15. Enrica Leccisi & Marco Raugei & Vasilis Fthenakis, 2016. "The Energy and Environmental Performance of Ground-Mounted Photovoltaic Systems—A Timely Update," Energies, MDPI, vol. 9(8), pages 1-13, August.
    16. Lenzen, Manfred & Dey, Christopher & Foran, Barney, 2004. "Energy requirements of Sydney households," Ecological Economics, Elsevier, vol. 49(3), pages 375-399, July.
    17. Guevara, Zeus & Domingos, Tiago, 2017. "The multi-factor energy input–output model," Energy Economics, Elsevier, vol. 61(C), pages 261-269.
    18. Wu, X.D. & Ji, Xi & Li, Chaohui & Xia, X.H. & Chen, G.Q., 2019. "Water footprint of thermal power in China: Implications from the high amount of industrial water use by plant infrastructure of coal-fired generation system," Energy Policy, Elsevier, vol. 132(C), pages 452-461.
    19. A. fnMarvasti, 1996. "Reserve characteristics and mining costs An empirical study of the phosphate industry," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 7(4), pages 357-373, June.
    20. Cleveland, Cutler J. & Kaufmann, Robert K. & Stern, David I., 2000. "Aggregation and the role of energy in the economy," Ecological Economics, Elsevier, vol. 32(2), pages 301-317, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:4:y:2011:i:8:p:1211-1245:d:13623. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.