# Comparing World Economic and Net Energy Metrics, Part 1: Single Technology and Commodity Perspective

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## Abstract

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## 1. Introduction

#### 1.1. Background

#### 1.2. Missing Perspective

#### 1.3. Part 1 Goal and Content

#### 1.4. Summary of Multidisciplinary Perspectives and Motivation

## 2. Methods

#### 2.1. Review of Net Energy Metrics Calculated Using Full Life Cycle Energy versus Annual Energy (or Power) Flows

- ERRs and PRRs are mathematically distinct, yet not always treated as such in the net energy literature,
- distinguishing between “gross” and “net” ratios allows one to specify the difference between extraction of primary energy (gross extraction) and delivery of energy carriers to consumers (net delivered energy) without using the same term and acronym (e.g., each term has a distinct mathematical definition [29,44]) and,
- to compare ERRs and PRRs to economic metrics (e.g., to costs and prices, respectively), it is important that we understand which metrics to use for comparison (discussed in Section 4.1).

**Figure 1.**The power flows and energy relations among various factors that are used to calculate energy and power return ratios for single energy technology life cycle (largely following [45] for nomenclature and [46] for input values). (

**a**) Pictogram depicting the assumptions and the five types of power flows for this example; (

**b**) the instantaneous power return ratios (PRRs) are defined similarly to energy return ratios (ERRs), except using only instantaneous power flow data rather than power integrated over time; (

**c**) the cumulative net energy over time is the integral of the instantaneous net power (net power = P${}_{\mathrm{out}}-$ P${}_{\mathrm{in}}$); (

**d**) the cumulative ERR for three common ERRs. EROI${}_{3}$ = EROI${}_{\mathrm{pou}}$ (EROI, energy return on energy invested) from [45] equal to the net external energy ratio (NEER) from [29,44,47]. Gross energy ratio (GER) and net energy ratio (NER) from [29]. E, energy.

**Figure 2.**The power flows and energy relations among various factors that are used to calculate energy return ratios (ERRs) for three of the same single energy technologies’ life cycle installed at different times. (

**a**) Pictogram depicting the technology being installed at three different times. The bottom image shows the power inputs and outputs for the sum of all three installations; (

**b**) The instantaneous power return ratios (PRRs) are defined the same as ERRs, except using only instantaneous power flow data rather than power integrated over time; (

**c**) The cumulative net energy over time that is the integral of the instantaneous net power (net power = P${}_{\mathrm{out}}-$ P${}_{\mathrm{in}}$); (

**d**) The cumulative energy return ratio (ERR) for three common ERRs. EROI${}_{3}$ = EROI${}_{\mathrm{pou}}$ from [45] equal to the net external energy ratio (NEER) from [29,44,47]. Gross energy ratio (GER) and net energy ratio (NER) from [29].

**Figure 3.**This figure shows that when multiple technologies are installed over time, the instantaneous power return ratios (PRRs) and the cumulative energy return ratios (ERRs) can end up greater than or less than each other (but GER > NER and GPR > NPR). (

**a**) Individual gross power ratio (GPR), net power ratio (NPR), cumulative gross energy ratio (GER) and cumulative net energy ratio (NER) for each of the three technology installations based upon the time of installation; (

**b**) The summed GPR, NPR, GER, and NER from all three technology installations.

**Figure 4.**This figure shows that when multiple technologies are installed over time, the instantaneous power return ratios (PRRs) and the cumulative energy return ratios (ERRs) can end up greater than or less than each other (but gross external energy ratio (GEER) > NEER and gross external power ratio (GEPR) > net external power ratio (NEPR)). (

**a**) Individual gross external power ratio (GEPR), net external power ratio (NEPR), cumulative gross external energy ratio (GEER) and cumulative net external energy ratio (NEER) for each of the three technology installations based on the time of installation; (

**b**) the summed GEPR, NEPR, GEER and NEER from all three technology installations.

**Table 1.**A summary of the categorization of the several energy return ratios (ERRs) and power return ratios (PRRs). For reference, EROI = energy return on (energy) invested; EROI subscripts are: ext = extraction (or Boundary 1), pou = point of use (or Boundary 3) [45].

Gross output | Net output | |||
---|---|---|---|---|

Feedstock included as input? | No | Yes | No | Yes |

Power Return Ratio | GEPR | GPR | NEPR | NPR |

Energy Return Ratio | GEER | GER | NEER | NER |

(= EROI${}_{\mathrm{ext}}=$ EROI${}_{1}$) | (= EROI${}_{\mathrm{pou}}=$ EROI${}_{3}$) |

#### 2.1.1. Power Return Ratios

#### 2.1.2. Energy Return Ratios

#### 2.2. Energy Intensity Ratios

#### 2.2.1. IEA Data

**Figure 5.**The individual price-based energy intensity ratios, EIR${}_{{p}_{n}}$, for all $n=9$ energy commodities considered in this paper show a general trend of increasing from the early 1980s through approximately 1998 followed by a decade-long decline through 2008 until the onset of the Great Recession. Thin gray lines represent individual country calculations, and the single thick red line is the GDP-weighted average of all EIR${}_{{p}_{n}}$ each year. NG = natural gas, Elec = electricity, Ind = industrial, and Res = residential, such that, for example, EIR${}_{{p}_{\mathrm{NG}},\mathrm{Res}}$ is the “EIR of the price of natural gas purchased by the residential sector.”

#### 2.2.2. Aggregation of EIR${}_{{p}_{n}}$

#### 2.2.3. England and United Kingdom Data

## 3. Results

- All world average EIR${}_{{p}_{n}}$ follow a similar trend over the studied time periods, as they increase from 1978 to the late 1990s and early 2000s, before they decline through 2008 with a slight rebound to 2010 after the Great Recession in 2008.
- The time series for England and the U.K. indicates that high EIR${}_{{p}_{n}}$ are not unprecedented before World War II, but that EIR${}_{{p}_{n}}$ of coal generally declined from 1300 to 1850.

#### 3.1. Energy Intensity Ratios: World

#### 3.2. Energy Intensity Ratios: Historical England and U.K.

**Figure 6.**Energy intensity ratios for England and the United Kingdom for the following commodities: (

**a**) wood and coal; (

**b**) oil and natural gas; and (

**c**) electricity. Calculations use three data sources for comparison: all nine energy commodity prices from the International Energy Agency (IEA) data (1978–2010), historical oil price from the BPStatistical Review (1861–2010) and historic firewood, coal, gas and electricity prices from Fouquet [54] (1300–2008). NG = natural gas, Elec = electricity, Ind = industrial and Res = residential. EIR${}_{{p}_{\mathrm{NG},\mathrm{Res}}}$ is the “EIR of the price of natural gas purchased by the residential sector”.

## 4. Discussion

#### 4.1. Energy and Power Return Ratios in Relation to Cost and Prices (for Future Energy Scenarios)

**Figure 7.**U.S. oil first purchase price versus both EIR${}_{\mathrm{oil}}$ and EROI${}_{1}=$ EROI${}_{\mathrm{ext}}=\mathrm{GEPR}$ as calculated by [21,51] for the U.S. oil and gas sector. Both figures show the same data: (

**a**) uses linearly-scaled axes; and (

**b**) uses logarithmically-scaled axes. See King and Hall [15] for a full explanation. Oil prices are annual U.S. crude oil first purchase prices from the Energy Information Administration’s Annual Energy Review and Monthly Energy Review. MROI = monetary return on investment relating to annual profit (MROI = 1 is breakeven).

EIR${}_{\mathrm{oil}}$ | EROI${}_{\mathrm{oil}}$ | EROI${}_{\mathrm{petroleum}}$ | EIR${}_{\mathrm{oil}}$ | EIR${}_{\mathrm{NG},\mathrm{Industry}}$ | EROI${}_{\mathrm{O}\&\mathrm{G}}$ | |
---|---|---|---|---|---|---|

Year | Norway | Norway | Norway | World | World | World |

This Paper | [63] | [63] | This Paper | This Paper | [64] | |

1991 | 50 | 35 | 44 | 34 | 31 | – |

1992 | 54 | 35 | 44 | 37 | 32 | 26 |

1996 | 59 | 46 | 59 | 36 | 34 | 34 |

1999 | 73 | 40 | 56 | 46 | 40 | 35 |

2006 | 29 | 26 | 47 | 16 | 23 | 18 |

2008 | 21 | 20 | 40 | 11 | 22 | – |

**Figure 8.**Price vs. EIR${}_{{p}_{n}}$ for the 44-country “world” aggregate prices, weighting each country price by the country GDP, for: (

**a**) oil; (

**b**) natural gas; and (

**c**) electricity, along with the price of coal and NG purchased by electric generators; (

**d**) the subfigure shows that depending on the characteristics of the required inputs (money and/or energy) for the energy supply chain or life cycle, a calculated ERR or PRR can relate to a range of prices, or vice versa.

#### 4.2. Historical England and U.K. EIR${}_{p}$

**Figure 9.**(

**a**) England’s/the U.K.’s economy energy intensity; (

**b**) price vs. EIR${}_{p}$ for coal (average) and firewood for England and the United Kingdom from 1300 to 2008. Three example inverse curves show the constant energy intensity of England’s/the U.K.’s economy at 390,1000 and 150 Mtoe/£2000 in the years 1560, 1870 and 2008, respectively. Data from Fouquet [54].

## 5. Conclusions

## Supplementary Files

Supplementary File 1Supplementary File 2## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

King, C.W.; Maxwell, J.P.; Donovan, A.
Comparing World Economic and Net Energy Metrics, Part 1: Single Technology and Commodity Perspective. *Energies* **2015**, *8*, 12949-12974.
https://doi.org/10.3390/en81112346

**AMA Style**

King CW, Maxwell JP, Donovan A.
Comparing World Economic and Net Energy Metrics, Part 1: Single Technology and Commodity Perspective. *Energies*. 2015; 8(11):12949-12974.
https://doi.org/10.3390/en81112346

**Chicago/Turabian Style**

King, Carey W., John P. Maxwell, and Alyssa Donovan.
2015. "Comparing World Economic and Net Energy Metrics, Part 1: Single Technology and Commodity Perspective" *Energies* 8, no. 11: 12949-12974.
https://doi.org/10.3390/en81112346