# Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI)

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## Abstract

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## 1. Introduction

## 2. A National-Level EROI: The Concept

#### 2.1. Background

#### 2.2. The Benefits of a National-Level EROI

#### 2.3. Conceptual Issues and Choices

#### 2.3.1. Boundary of Analysis

#### 2.3.2. Accounting for Embodied Energy Inputs

#### 2.3.3. Temporality

#### 2.3.4. Accounting for Energy Quality

## 3. A national-Level EROI: The Data and the Methodology

#### 3.1. Input-Output and Energy

#### 3.2. EROI_{nat(UK)}: Data

#### 3.3. EROI_{nat(UK)}: Methodology

## 4. Results and Discussion

_{iE}) in the calculation of ${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}.\text{}$ An ${\mathrm{EROI}}_{\mathrm{nat}}$ calculation, using only energy industry’s own use as the energy inputs gives higher values because there is an element missing in the denominator. By including indirect energy use (E

_{iE}), using the IO methodology described in Section 3.3, we obtain a more complete view of the energy invested into the energy producing sectors. This is the key contribution of the methodology we outline here and a step forwards in the EROI literature. Our calculations for the UK without including indirect energy (E

_{iE}) are the same order of magnitude to King et al.’s [23] calculations of EROI (or net power ratio—NPR as they call it).

_{out}) and the energy invested (denominator E

_{in}) are shown in Figure 6. Since 1999 the UK’s production of energy has been declining steadily (compensated by increased imports that are not included in ${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}$). For a national-level EROI from a production perspective, this means that we are extracting/capturing less energy by using a relatively stable stream of energy inputs. Thus the steady decline of ${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}$ from 2003 onwards.

## 5. Conclusions and Policy Implications

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

#### Appendix A.1. A Note on Notation

#### Appendix A.2. Multi-Regional Input-Output Matrix Structure, with an Energy Extension

**Z**(Figure A1). In the top left hand corner of

**Z**is the UK data, followed by 5 world regions (the Rest of Europe, the Middle East, China, the Rest of the OECD, and the Rest of the World). Each region contains 106 industry sectors.

**Z**displays sales by each industry in rows and the columns represent purchases by each industry. In other words, reading across a row reveals which other industries a single industry sells to and reading down a column reveals who a single industry buys from in order to make its product output. A single element, ${\mathrm{z}}_{\mathrm{ij}}$, within $Z$ represents the contributions from the ith supplying sector to the jth producing sector in an economy. The $Z$ matrix is in monetary units.

#### Appendix A.3. Basic Calculations: Obtaining the A, L and F Matrices

#### Appendix A.4. EROI_{nat} Specific Calculations: Obtaining Indirect Energy

## Appendix B

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**Figure 1.**Types of EROI. ${\mathrm{EROI}}_{\mathrm{stnd}}$: standard EROI. ${\mathrm{EROI}}_{\mathrm{pou}}$: EROI at the point of use. ${\mathrm{EROI}}_{\mathrm{ext}}$: extended EROI.

**Figure 2.**National level EROI—UK case. Black and dotted arrows represent what we measure, while white arrows represent flows that occur but that are not included in this approach to EROI

_{nat}given its boundary of analysis.

**Figure 5.**${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}$ (1997–2012): Comparison of results with and without indirect energy (E

_{iE}).

**Figure 7.**UK energy production: share of energy sources 1997–2012. Data taken from IEA [64].

**Figure 8.**Financial investments in the production of UK’s energy by source (1974–2012). Data taken from IEA [70].

Energy Source | Change in Production (%) | |
---|---|---|

1997–2010 | 2010–2012 | |

Coal and coal products | −0.6 | 0.0 |

Crude, NGL and feedstocks | −0.5 | −0.1 |

Natural gas | −0.3 | −0.2 |

Nuclear | −0.4 | 0.1 |

Hydro | −0.1 | 0.4 |

Solar/wind/other | 13.5 | 14.2 |

Biofuels and waste | 1.6 | 0.7 |

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## Share and Cite

**MDPI and ACS Style**

Brand-Correa, L.I.; Brockway, P.E.; Copeland, C.L.; Foxon, T.J.; Owen, A.; Taylor, P.G.
Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI). *Energies* **2017**, *10*, 534.
https://doi.org/10.3390/en10040534

**AMA Style**

Brand-Correa LI, Brockway PE, Copeland CL, Foxon TJ, Owen A, Taylor PG.
Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI). *Energies*. 2017; 10(4):534.
https://doi.org/10.3390/en10040534

**Chicago/Turabian Style**

Brand-Correa, Lina I., Paul E. Brockway, Claire L. Copeland, Timothy J. Foxon, Anne Owen, and Peter G. Taylor.
2017. "Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI)" *Energies* 10, no. 4: 534.
https://doi.org/10.3390/en10040534