# Assessing Global Long-Term EROI of Gas: A Net-Energy Perspective on the Energy Transition

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## Abstract

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## 1. Introduction

#### 1.1. Gross and Net Energy

#### 1.2. Eroi of Gas at Global Scale

#### 1.3. Eroi of Gas at Local, Regional or National Scale

## 2. Materials and Methods

#### 2.1. Gas Production Model

#### 2.2. EROIs Yearly Values

#### 2.2.1. EROIs Estimates

#### 2.2.2. EROIs Dynamic Functions

## 3. Results

#### 3.1. Net vs. Gross Energy from Gas

#### 3.2. Scenario-Based Sensitivity Analysis

#### 3.2.1. EROI Estimates

#### 3.2.2. Dynamic Functions

#### 3.3. Robustness of the Results

## 4. Discussion

#### 4.1. Implications for the Low-Carbon Energy Transition

#### 4.2. On the Need of Net-Energy Studies

#### 4.3. Limitations and Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CBM | Coal Bed Methanes |

DNV | Det Norske Veritas |

EIA | Energy Information Administration |

EROI | Energy Return On Investment |

GEFC | Gas Exporting Countries Forum |

IEA | International Energy Agency |

INRIA | French National Institute for Research in Digital Science and Technology |

NEA | Net Energy Analysis |

OPEC | Organization of the Petroleum Exporting Countries |

PROI | Power Return On Investment |

STGs | Shale/Tight Gases |

URR | Ultimately Recoverable Resources |

WEC | World Energy Council |

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**Table 1.**Two-dimensional EROI nomenclature: boundaries for energy inputs and outputs. Source: Murphy et al. [26].

Energy Inputs | Extraction | Processing | End-Use |
---|---|---|---|

Direct energy and material | EROI${}_{1,d}$ | EROI${}_{2,d}$ | EROI${}_{3,d}$ |

Indirect energy and material | EROI${}_{stnd}$ | EROI${}_{2,i}$ | EROI${}_{3,i}$ |

Indirect labor consumption | EROI${}_{1,lab}$ | EROI${}_{2,lab}$ | EROI${}_{3,lab}$ |

Auxiliary services consumption | EROI${}_{1,aux}$ | EROI${}_{2,aux}$ | EROI${}_{3,aux}$ |

Environment | EROI${}_{1,env}$ | EROI${}_{2,env}$ | EROI${}_{3,env}$ |

**Table 2.**Identified models forecasting global gas supply, sorted by descending score (total number of criteria met).

Authors | Ref. | Time | Subdivision | Access | Reliability | Score |
---|---|---|---|---|---|---|

GlobalShift | [62] | 1950–2050 | 🗸 | 🗸 | 🗸 | 3 |

Maggio & Cacciola | [63] | 1940–2060 | 🗸 | 🗸 | × | 2 |

Mohr et al. | [64] | 1900–2300 | 🗸 | 🗸 | × | 2 |

DNV | [65] | 1980–2050 | × | 🗸 | × | 1 |

GEFC | [66] | 2000–2050 | 🗸 | × | × | 1 |

IEA | [67,68] | 1995–2040 | 🗸 | × | × | 1 |

Kontorovich et al. | [69] | 1900–2040 | × | 🗸 | × | 1 |

Laherrère | [70] | 1900–2150 | × | 🗸 | × | 1 |

Valero & Valero | [71] | 1900–2150 | × | 🗸 | × | 1 |

Wang & Bentley | [72] | 1990–2050 | × | 🗸 | × | 1 |

WEC | [73] | 1970–2060 | 🗸 | × | × | 1 |

Zou et al. | [74] | 1800–2200 | × | 🗸 | × | 1 |

BP | [1] | 1900–2050 | × | × | × | 0 |

EIA | [75,76] | 1980–2054 | × | × | × | 0 |

OPEC | [77] | 2019–2045 | × | × | × | 0 |

**Table 3.**Indicative Gross Heating Value of natural gas of the ten major producing countries. Source: IEA (2021) [78].

Country | Conversion Factor (PJ/bcm) | Production in 2018 (Mtoe) |
---|---|---|

United States | 38.53 | 719.0 |

Russia | 38.23 | 606.6 |

Iran | 39.36 | 190.6 |

Canada | 39.07 | 154.7 |

Qatar | 41.40 | 147.4 |

China | 38.93 | 135.3 |

Norway | 39.47 | 106.4 |

Australia | 39.76 | 101.2 |

Algeria | 39.57 | 82.6 |

Saudi Arabia | 38.00 | 79.1 |

Gas Type | Low | Medium | High | Source | EROI |
---|---|---|---|---|---|

Field gas | EROI${}_{\tilde{CF},1}$ | EROI${}_{\tilde{CF},2}$ | EROI${}_{\tilde{CF},3}$ | [30,72,79] | EROI${}_{1,lab}$ |

Shale-Tight gas | 32 | 51.9 | 82 | [44,54,56,61] | EROI${}_{stnd}$ |

Coal Bed Methane | 10 | 12.5 | 15 | [57] | EROI${}_{stnd}$ |

Offshore 0–500 m | EROI${}_{\tilde{CF},1}$ | EROI${}_{\tilde{CF},2}$ | EROI${}_{\tilde{CF},3}$ | [30,72,79] | EROI${}_{1,lab}$ |

Offshore 500–1000 m | 34.2 | 42.8 | 51.3 | [80] | EROI${}_{stnd}$ |

Offshore 1000–2000 m | 23.05 | 29.6 | 39.2 | [38,40] | EROI${}_{stnd}$ |

Offshore +2000 m | 11.9 | 16.4 | 27.1 | [40] | EROI${}_{stnd}$ |

**Table 5.**Summary of EROI dynamic functions (DF), with EROI${\left(y\right)}_{0}$ being the initial EROI value at the year 1950. They apply as long as EROI$\left(y\right)$ is greater or equal to 1, which is the minimum value EROI can hypothetically reach.

Definition | Mathematical Formulation | |
---|---|---|

DF1 | Constant | $\mathrm{EROI}\left(y\right)=\mathrm{EROI}\left({y}_{0}\right)$ |

DF2 | Linear decrease | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{\delta}_{I}\times (y-{y}_{D}),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{D}\hfill \end{array}$ |

DF3 | Linear decrease | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{\delta}_{II}\times (y-{y}_{D}),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{D}\hfill \end{array}$ |

DF4 | Geometric decrease | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ {\gamma}_{I}\times \mathrm{EROI}(y-1),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{D}\hfill \end{array}$ |

DF4 | Geometric decrease | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ {\gamma}_{II}\times \mathrm{EROI}(y-1),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{D}\hfill \end{array}$ |

DF6 | Exponential decrease | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{e}^{\frac{y-{y}_{D}}{{\tau}_{I}}},\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{D}\hfill \end{array}$ |

DF7 | Exponential decrease | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{e}^{\frac{y-{y}_{D}}{{\tau}_{II}}},\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{D}\hfill \end{array}$ |

DF8 | Linear bump | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)+{\delta}_{I}\times (y-{y}_{D}),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{y}_{D}\u2a7dy{y}_{B}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{\delta}_{I}\times (y-{y}_{D}),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{B}\hfill \end{array}$ |

DF9 | Linear bump | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)+{\delta}_{II}\times (y-{y}_{D}),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{y}_{D}\u2a7dy{y}_{B}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{\delta}_{II}\times (y-{y}_{D}),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{B}\hfill \end{array}$ |

DF10 | Geometric bump | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ (1-{\gamma}_{I})\times \mathrm{EROI}(y-1),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{y}_{D}\u2a7dy{y}_{B}\hfill \\ {\gamma}_{I}\times \mathrm{EROI}(y-1),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{B}\hfill \end{array}$ |

DF11 | Geometric bump | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ (1-{\gamma}_{II})\times \mathrm{EROI}(y-1),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{y}_{D}\u2a7dy{y}_{B}\hfill \\ {\gamma}_{II}\times \mathrm{EROI}(y-1),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{B}\hfill \end{array}$ |

DF12 | Exponential bump | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)+{e}^{\frac{y-{y}_{D}}{{\tau}_{I}}},\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{y}_{D}\u2a7dy{y}_{B}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{e}^{\frac{y-{y}_{D}}{{\tau}_{I}}},\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{B}\hfill \end{array}$ |

DF13 | Exponential bump | $\mathrm{EROI}\left(y\right)=\left(\right)open="\{"\; close="\}">\begin{array}{cc}\mathrm{EROI}\left({y}_{0}\right),\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y{y}_{D}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)+{e}^{\frac{y-{y}_{D}}{{\tau}_{II}}},\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{y}_{D}\u2a7dy{y}_{B}\hfill \\ \mathrm{EROI}\left({y}_{0}\right)-{e}^{\frac{y-{y}_{D}}{{\tau}_{II}}},\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}y\u2a7e{y}_{B}\hfill \end{array}$ |

Output Assessed | High | Medium | Low |
---|---|---|---|

Peak year | 2038 | 2037 | 2036 |

Peak magnitude | 226.4 | 214.7 | 189.5 |

Decrease/increase ratio | 0.8 | 0.9 | 1.2 |

Output Assessed | Constant | Constant, Decrease | Constant, Bump |
---|---|---|---|

Peak year | 2037 | 2037 | 2037 |

Peak magnitude | 211.8 | 210.0 | 211.5 |

Decrease/increase ratio | 0.9 | 1.0 | 0.9 |

Output Assessed | Gross Energy | Net-Energy | $\left(\right)open="|"\; close="|">\frac{{\mathbf{x}}_{\mathbf{gross}}-{\mathbf{x}}_{\mathbf{net},\mathbf{avg}}}{{\mathit{\sigma}}_{\mathbf{net}}}$ | Scale |
---|---|---|---|---|

Peak year | 2040 | 2037 | 3.6 | ++ |

Peak magnitude | 249 | 211 | 2.5 | ++ |

Pre-peak increase | 4.3 | 3.4 | 1.8 | + |

Post-peak decrease | 2.6 | 3.1 | 2.5 | ++ |

Decrease/increase ratio | 0.6 | 0.9 | 1.8 | + |

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## Share and Cite

**MDPI and ACS Style**

Delannoy, L.; Longaretti, P.-Y.; Murphy, D.J.; Prados, E.
Assessing Global Long-Term EROI of Gas: A Net-Energy Perspective on the Energy Transition. *Energies* **2021**, *14*, 5112.
https://doi.org/10.3390/en14165112

**AMA Style**

Delannoy L, Longaretti P-Y, Murphy DJ, Prados E.
Assessing Global Long-Term EROI of Gas: A Net-Energy Perspective on the Energy Transition. *Energies*. 2021; 14(16):5112.
https://doi.org/10.3390/en14165112

**Chicago/Turabian Style**

Delannoy, Louis, Pierre-Yves Longaretti, David. J. Murphy, and Emmanuel Prados.
2021. "Assessing Global Long-Term EROI of Gas: A Net-Energy Perspective on the Energy Transition" *Energies* 14, no. 16: 5112.
https://doi.org/10.3390/en14165112