![(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].](https://www.researchgate.net/publication/284206213/figure/fig2/AS:678818515783680@1538854354808/a-Englands-the-UKs-economy-energy-intensity-b-price-vs-EIR-p-for-coal-average_Q320.jpg)
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Article
Comparing World Economic and Net Energy Metrics,
Part 1: Single Technology and Commodity Perspective
Carey W. King 1,3,*, John P. Maxwell 2and Alyssa Donovan 3
Received: 3 March 2015 ; Accepted: 29 September 2015 ; Published: 17 November 2015
Academic Editor: Robert Lundmark
1Energy Institute, the University of Texas at Austin, 2304 Whitis Ave., C2400, Austin, TX 78712, USA
2Senate Fiscal Agency, P.O. Box 30036 Lansing, MI 48909-7536, USA; john.p.maxwell86@gmail.com
3Jackson School of Geosciences, the University of Texas at Austin, 2275 Speedway, C9000, Austin, TX 78712,
USA; alyssad13@gmail.com
*Correspondence: careyking@mail.utexas.edu; Tel.: +1-512-471-5468
Abstract: We translate between biophysical and economic metrics that characterize the role of
energy in the economy. Specifically, using data from the International Energy Agency, we estimate
the energy intensity ratio (EIR), a price-based proxy for a power return ratio (PRR ∼Pout/Pinvested).
The EIR is a useful metric, because for most countries and energy commodities, it can indicate the
biophysical trends of net energy when data are too scarce to perform an original net energy analysis.
We calculate EIR for natural gas, coal, petroleum and electricity for forty-four countries from 1978 to
2010. Global EIR values generally rise from 1978 to 1998, decline from 1998 to 2008 and then slightly
rebound. These trends indicate one interpretation of the net energy of the world economy. To add
perspective to our recent, but short, time series, we perform the same calculations for historical
England and United Kingdom energy prices to demonstrate that a given energy price translates
to different PRRs (EIR in this case) depending on the structure of the economy and technology.
We review the formulation of PRRs and energy return ratios (ERR ∼Eout/Einvested) to indicate
why PRRs translate to (the inverse of) energy prices and ERRs translate to (the inverse of) energy
costs. We show why for any given value of an ERR or PRR, there is not a single corresponding
energy cost or price, and vice versa. These principles in turn provide the basis to perform better
modeling of future energy scenarios (e.g., low-carbon transition) by considering the relationship
between economic metrics (cost and price) and biophysical metrics (energy and power return ratios)
based on energy, material and power flows.
Keywords: energy; net energy; price; cost; economics; life cycle assessment
1. Introduction
This manuscript is Part 1 of 3 papers comparing net energy and economic metrics. Each
manuscript has similar background and motivation sections. Part 1 includes a fuller background
and motivation before analyzing how net energy and power metrics translate to individual energy
commodity (and technology) costs and prices, respectively. Part 2 analyzes how net energy metrics
translate to total expenditures on energy [1]. Part 3 places the calculations of expenditures on energy
in historical, current and future contexts [2].
1.1. Background
Considerable debate exists surrounding the role of energy in society and the economy, and
much of the disagreement stems from different methodological approaches and the time span under
consideration. Conclusions range from the possible unimportance of all natural resources [3],
Energies 2015,8, 12949–12974; doi:10.3390/en81112346 www.mdpi.com/journal/energies
Energies 2015,8, 12949–12974
to energy price spikes being a chief determinant of recessions [4], to energy and prime-movers
as being equally important to labor and capital in driving economic growth [5], to energy and
prime-movers as the critical elements, more important than labor or capital, in driving economies
during industrialization [6] and possibly over the long-term, [7,8]. Countries with high per capita
gross domestic product (GDP) tend to consume more primary energy per capita [9], even more so
when considering energy embodied in imported products [10].
Access to a sufficient quantity of affordable energy and energy services is one of several
important factors (e.g., also proper governance [11]) for modern living standards in an industrial
or post-industrial economy. As we deplete fossil stocks and extract renewable flows from the
highest quality resource areas, technological improvements enable access to lower quality energy
resources, while converting those resources to services more efficiently. Yet, the end of extraction of
a particular energy resource is not marked by its full depletion, but rather by its cost of production
becoming greater than what consumers can afford to pay, are willing to pay or can pay for less
expensive alternatives (including energy efficiency). For example, due to various reasons, including
high extraction costs and less expensive imports, one regional energy resource that has undergone
an almost complete rise and fall in production is United Kingdom coal [12].
A lack of inexpensive energy options is reflected economically in higher energy prices and cost
shares. Biophysically, this higher cost is reflected in energy life cycles with lower net energy and
lower energy return ratios (ERRs), such as energy return on energy invested (EROI) [13]. Net energy
is defined as energy delivered as output (or extracted, depending on the life cycle boundary) minus
the energy invested in delivering that output. ERRs use the same data to express net energy as a ratio
of the energy delivered (or extracted) divided by the energy invested to deliver that output. From this
point forward, we use the terms energy return ratio and power return ratio (PRR) as catchall terms
for more specific net energy and power metrics defined in this paper.
Energy costs and ERRs are two ways of expressing the same concept because they are
fundamentally inversely related (as discussed in detail in this paper in Section 4.1) [14–17]. To
an economist, the costs, prices and energy cost share are important metrics; to an ecologist and
biophysical systems modeler, the ERR and PRR are important metrics for models and perspectives
not purely based on monetary flows. It is important to translate between economic and biophysical
descriptions of technologies and economies. However, exactly how can we relate economic and
biophysical perspectives? How can we measure if affordability of energy were either acting as or
indicating a constraint on economic production or growth? In this Part 1, as well as in Parts 2
and 3 [1,2], we contribute data and concepts that are important to answer these two questions at
the energy commodity and global scales.
1.2. Missing Perspective
Answering global questions requires global data, but data and perspective on global net energy
metrics are severely lacking. Thus, most macroeconomic or macrobiophysical analyses focus on
a single country, technology, commodity and/or industry that has sufficient data. This single-country
focus often limits these analyses to developed countries that have sufficient datasets: the United
States, Western Europe and Japan.
While much research effort is spent calculating ERRs of individual energy technologies and
fuels for comparative analysis [14,18–26], there is a dearth of work linking individual ERRs to
microeconomic or macroeconomic metrics. Despite four decades since the development of the
mathematical foundations in net energy analysis that relate economic accounts to country-level
energy consumption [27,28], existing research has not effectively placed technology-specific net
energy into the context of the broader macroeconomic modeling, economic projections and
energy-economic decision-making. This disconnect and missing perspective serves as a motivation
for this paper series [1,2] and other research of the corresponding author [14–16,29].
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1.3. Part 1 Goal and Content
The question answered by net energy analysis is intuitive and attractive to many: How much
energy does it take to produce and/or deliver energy? Aside from knowing that we want systems
that produce more output with fewer inputs (energy or otherwise), we do not know how much more
matters. Therefore, why do researchers calculate net energy metrics if we cannot translate them to
other indicators or apply them for decision-making? We seek to determine how we can practically
interpret net energy metrics for decision-making and to describe the (possible) structure of the
economy. Thus, the main goals of Part 1 of this manuscript series are two-fold: (1) to provide the most
comprehensive global view of the net energy (or specifically power) of world energy commodities;
and (2) to place net energy metrics into the context of the economic metrics with which people are
most familiar: cost and price.
People generally want lower (energy) prices. Because most of us are more familiar with energy
prices and costs than we are with net energy metrics, it behooves us to explore how net energy
metrics relate to prices and costs. If we can understand these relations, then we can start to make
more practical use of net energy metrics for decision-making and planning, such as in the context of
a transition to a low-carbon and/or renewable economy. Instead of projecting future costs, we might
do better by projecting future net energy metrics.
Perhaps the most prominent net energy term is “energy return on energy invested”, or EROI.
However, we do not blindly adopt this term in this manuscript. Unfortunately, the term EROI is
sometimes used too broadly in that it refers to different mathematical definitions. For example, EROI
sometimes refers to ratios of energy and sometimes to ratios of power. Thus, we find it important
to distinguish among specific mathematical definitions of ratios of power (e.g., PRR) and ratios of
energy (e.g., ERR), and we use a unique name for each equation rather than a single term, such
as EROI. A single term should not refer to different mathematical definitions, and that is why this
manuscript begins with these ERR and PRR definitions.
The new calculations and results described in this paper are of energy intensity ratios (EIRs,
Section 2.2) for the major energy commodities across the world. The EIR represents how much energy
one can obtain by spending one dollar (or other monetary unit) relative to how much energy it takes
to generate an average dollar of output from the economy. As we discuss, EIRs are proxies for power
return ratios (PRRs) that derive from energy analysis and/or life cycle assessment. However, in order
to understand how to interpret the EIRs over time, we must describe the formulations of PRRs and
their integral over time, energy return ratios (ERRs). The ERRs equate quantitatively to energy output
divided by energy inputs (or energy invested), hence the popular acronym EROI.
This rest of this manuscript is organized as follows. Section 1.4 continues with additional
background to provide perspective on the different viewpoints of the role of energy in society.
Section 2describes the EIR calculations of this paper, as well as providing a background to net energy
metrics calculated in the literature. Section 2.1 provides the background for calculating energy return
ratios (ERRs) and power return ratios (PRRs). We use the terms ERR and PRR as generic descriptors
of the more specific terms described in this section. We provide significant detail on distinguishing
ERRs from PRRs, so that the reader understands that the EIRs, which use annual energy flows, are
proxies for PRRs and not ERRs. Section 2.2 explains the EIR calculation itself. Section 3.1 shows the
EIR calculations for the world (1978–2010), and Section 3.2 does the same for England and United
Kingdom (1300–2008). Section 4.1 discusses how we can relate ERRs and PRRs to costs and price,
respectively, while using the insights from the EIR calculations. Section 4.2 provides the long-term
perspective that is needed to properly consider the proposition discussed in Section 4.1. We interpret
these long-term EIRs in the context of power return ratios (PRRs) and the transition to the modern
fossil-fueled and industrial economic era. Section 5concludes the paper.
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1.4. Summary of Multidisciplinary Perspectives and Motivation
All models are wrong, but some are useful. This statement is certainly poignant for energy,
society and the economy. Researchers consider the role of energy in society from multiple
perspectives: anthropological [30–33], economic [4,6,7,34–38], ecological and biophysical [8,9,13,39],
and others. With these different perspectives come a multitude of quantitative and qualitative
methods of analysis. These analyses try to answer questions related to how energy and natural
resources influence and enable societal growth, structure and organization.
Biophysical and ecological perspectives on the economy and energy note similarities between
our natural ecology and our “industrial ecology”. Brown et al. [40] note that many global materials
have peaked in terms of global production rate per capita. Brown and colleagues also note that since
1980, the per capita energy consumption of a country scales with the 3
4power of its per capita GDP just
as a mammal’s metabolism scales with the 3
4power of its mass [9]. This comparison, while not directly
comparable (i.e., GDP per capita measures a flow of money, but animal mass measures a stock), makes
sense if one considers that both scaling relationships describe the energy cost of maintaining the
structure and/or functions of a complex adaptive system [40].
From an anthropological perspective, Tainter describes the possible economic contraction, loss of
complexity or collapse that may occur if a society consumes too much of its gross energy or resources
on acquiring, transporting and upgrading energy [30–32]. The Roman Empire is perhaps the most
classic example of collapse from diminishing returns. Its continued growth eventually became
infeasible as the resource cost to sustain the empire outpaced any resources gained from territorial
expansion [30]. Since most of the empire’s energy resources were derived from the land (e.g., food and
wood), diminished returns on expanding borders directly translated to less energy returned to Rome.
Other analyses of agrarian societies note how cycles of population growth and decline typically take
300–500 years [33]. These cycles seem to follow a common pattern across cultures and regions:
expansion of resources or food from technology and/or conquest; population increases because of
the increased bounty; eventually there are diminishing returns on productivity (e.g., food/farmer
or food/land); and finally, the governing authority loses power, and population decreases (due
to deaths or migration), because the tax base and resource can no longer support the now larger
population. According to Turchin and Nefedov [33], the United Kingdom is perhaps 200–250 years
into its latest “modern” cycle. One motivation of this paper (as well as Parts 2 and 3 [1,2]) is to
contribute to the discussion of how we can, and cannot, compare our modern industrial economy to
pre-industrial economies.
The econometric literature shows that it is valuable for econometric studies to have time series of
energy cost shares or expenditures on energy as a fraction of income, GDP or personal consumption
expenditures [6,36,37,41]. The reason is that the energy cost share serves to illuminate how
low-cost energy relates, usually positively, to economic growth. Energy cost shares for pre-industrial
economies were much higher than for industrial and post-industrial economies. Some econometric
analyses adjust the quantity of energy consumed by some quality factor to more accurately input
the concept of energy into econometric analyses. This quality factor is often one based on the
relative prices of resources (e.g., the price per MJ is higher for oil than coal) [41], thermodynamic
characterizations, such as fuel exergy, technology conversion efficiency and useful work delivered
[34,35] or emergy [42,43]. Thus, the calculations of this paper have value in that they will inform
future energy-economic analyses.
2. Methods
We undertake the calculations in this paper by utilizing the International Energy Agency (IEA)’s
rich data database of energy prices. The IEA data span dozens of countries and years. Further, we
also take this opportunity to use the rich historical data on England’s and the U.K.’s energy prices. To
our knowledge, no one has interpreted these energy and economic data in the context of net energy.
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2.1. Review of Net Energy Metrics Calculated Using Full Life Cycle Energy versus Annual Energy (or
Power) Flows
In performing energy and economic analyses, there are often limited data. Thus, it is not always
possible to directly compare a net energy metric to its most relevant monetary metric. Our purpose
for this section is to outline the power flows and energy accumulations (energy = power ×time)
associated with net energy analyses. By doing this, we highlight the difference between energy return
ratios (ERRs) calculated at the device/project level (i.e., over the entire life cycle) and power return
ratios (PRRs) that are often calculated at the industry/economy level using annual power flows. Just
as energy is the integral of power over time, ERRs are the integral of PRRs over time. Our descriptions
further allow us to focus on the power flows that most directly compare to the annual monetary flow
data that are available as prices, input-output tables or other data.
The reason we present a somewhat lengthy discussion of the definitions of ERRs and PRRs
is three-fold:
•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).
Our discussion follows a step-by-step process that builds information from a single life cycle to
several life cycles occurring simultaneously. Figure 1describes a single life cycle, discusses the life
cycle power flows, shows how these power flows are integrated over time and, finally, demonstrates
how the integrated power flows end up at the final ERRs at the end of the life cycle. Then, Figure 2
concatenates three of the life cycles from Figure 1, such that they overlap in time. By looking at
three life cycles, we can more easily imagine a real-world scenario with multiple energy technologies
operating simultaneously. Finally, Figures 3and 4present additional visualizations of PRRs and ERRs
of multiple life cycles concatenated upon each other, just as is the case in the real world.
In Figure 1, we use (not completely) the nomenclature of Murphy et al. [45] to demonstrate
the relations among various ERRs, as well as to indicate the PRRs for a hypothetical single energy
technology life cycle. The values of the power flows and power plant efficiency are based on the life
cycle assessment of a coal-fired power plant in Spath et al. [46] (the Lower Emission Boiler System
model). In Figure 1, P (or ˙
E) represents power, E represents energy and ηis a power conversion
efficiency of primary energy (feedstock) to an energy carrier as an output from the energy technology.
The subscripts on the power flows and energy accumulations refer to five different inputs and outputs
of the life cycle: cap = embodied energy invested over time for initial capital (e.g., manufacturing,
construction); op = power inputs invested during operation of the technology; feed = feedstock
primary power inputs for conversion (e.g., coal into a power plant); heat = heat dissipated from
burning feedstock that is converted to an energy carrier ( ˙
Eheat =˙
Efeed(1−η)); d = embodied energy
invested over time for decommissioning at the end of life; and ext = power extracted from the Earth
(e.g., primary energy).
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‐1
1
3
5
7
‐5
15
35
55
75
Cumulative
NetEnergy
EROIpou
=NEER
tEPBT =energypaybacktimeif Ed=0);
@cumulativeEROI3=NEER=1
Ecap
Eext ‐Eop
Ed
time
CumulativeEnergy
ReturnRatios(ERRs)
time NER
PowerRetur nRatios
(PRRs)
GEPR
GER
Assumptions:
Pcap =Ėcap =0.81
Pop =Ėop =0.5
Pheat =Ėheat =0.58=Ėfeed(1‐η)
Pd=Ėd=0.42
Pext =Ėext =3.6
η=0.42
(a) (b)
(c)
(d)
NEPR
GPR
NPR
time
‐1
0
1
2
3
4
5
6
7
Einvested (capital,Ecap)
Einvested (operating,Eop),and
Energyfeedstock(Efeed)dissipatedas
heat(Eheat)
Einvested (decommission,Ed)
Eextraction (extractedenergy,Eext)
time
Power
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 = Pout−Pin ); (d) the cumulative ERR for three common ERRs. EROI3= EROIpou
(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.
‐1
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
8
‐5
45
95
145
195
245
NER
Cumulative
NetEnergy
time
CumulativeERRs
time
EROIpou =NEER
PowerReturnRatios
(PRRs)
time
(a) (b)
(c)
(d)
GER
GEPR
NEPR
GPR
NPR
+
+
=
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 = Pout−Pin ); (d) The
cumulative energy return ratio (ERR) for three common ERRs. EROI3= EROIpou 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].
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(a) (b)
IndividualLifeCycles Sumofall3LifeCycles
GrossPowerRatio(GPR)
CumulativeGrossEnergyRatio(GER)
NetPowerRatio(NPR)
CumualtiveNetEnergyRatio(NER)
‐0.5
0
0.5
1
1.5
‐0.5
0
0.5
1
1.5
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.
(a) (b)
IndividualLifeCycles Sumofall3LifeCycles
GrossExternalPowerRatio(GEPR)
NetExternalPowerRatio(NEPR)
CumualtiveGEER
CumulativeNEER
‐1
0
1
2
3
4
5
6
7
8
‐1
0
1
2
3
4
5
6
7
8
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.
Here, we show summary in Table 1, to which the reader can refer during the course of reading
this paper to see the distinctions among the various energy and power return ratio acronyms.
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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
(= EROIext =EROI1) (= EROIpou =EROI3)
2.1.1. Power Return Ratios
Equations (1)–(4) show the four PRRs that we discuss in this paper. These PRRs are the
instantaneous equivalents of life cycle ERRs (Equations (5)–(8)) that life cycle researchers often
calculate. We discuss two types of PRRs (and ERRs in Section 2.1.2). The “external” ratios (e.g.,
GEPR = gross external power ratio and NEPR = net external power ratio) do not consider the portion
of feedstock fuel consumed and dissipated as heat as part of Pin during a conversion process with
efficiency, η. The other “non-external” ratios (GPR = gross power ratio and NPR = net power ratio)
do consider the heat dissipation (=˙
Efeed(1−η)) from consuming the feedstock fuel as part of Pin. If
efficiency is 100% (η=1), then the corresponding external and non-external ratios are equivalent
(e.g., NEPR = NPR, GEPR = GPR, as well as NEER = NER and GEER = GER, per the ERRs in
Section 2.1.2).
Figure 1a depicts the five power flow types that represent generic stages of the life cycle. Net
power flow (net power = Pout−Pin ) and net power ratio (NPR, Figure 1b) are negative during the
capital (E_cap) and decommission (E_d) phases and positive during the extraction (E_ext) phase.
This is because the model of Figure 1assumes the following holds during capital and decommission
phases: ˙
Eout =Pout =0, ˙
Ein =Pin >0, and thus, ˙
Eout −˙
Ein =Pout−Pin <0.
Net External Power Ratio =NEPR =˙
Eext −(˙
Ecap +˙
Eop +˙
Ed)
˙
Ecap +˙
Eop +˙
Ed
(1)
Gross External Power Ratio =GEPR =˙
Eext
˙
Ecap +˙
Eop +˙
Ed
=NEPR +1 (2)
Net Power Ratio =NPR =˙
Eext −(˙
Ecap +˙
Eop +˙
Ed+˙
Efeed(1−η))
˙
Ecap +˙
Eop +˙
Ed+˙
Efeed(1−η)(3)
Gross Power Ratio =GPR =˙
Eext
˙
Ecap +˙
Eop +˙
Ed+˙
Efeed(1−η)=NPR +1 (4)
The difference between GEPR and NEPR, as well as between GPR and NPR, is that the
denominator of the equation is subtracted from ˙
Eext in the numerator of NEPR and NPR, but not
GEPR and GPR. This distinction is why the G stands for “gross” and the N stands for “net”. Hence
“net power” (or “net energy” per Section 2.1.2) is equal to gross output minus intermediate energy
consumption and investment. Thus, for a consistently-modeled system with no assumed exogenous
information, GPR = NPR + 1 and GEPR = NEPR + 1 (see [29] for a fuller explanation).
The denominator of Equations (3) and (4) is not equal power invested, because it includes the
continuous flow of feedstock into the technology. We defer further discussion of the inclusion of
feedstock until the next section on ERRs, such that we can relate to existing literature that calculates
the net energy ratio (NER) and the gross energy ratio (GER). We show equations for NPR and GPR
for completeness, yet do not propose how to compare them with economic metrics.
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2.1.2. Energy Return Ratios
We now review four energy return ratios (ERRs) definitions in Equations (5)–(8). These four
equations refer to energy output and energy invested over the full life cycle of a technology or system.
Thus, they are the integral of the PRRs over the entire life cycle from initial time to=0 to final
lifetime tf. The units represented by E in the equations are those of energy (e.g., J), not power (e.g.,
J/s = W). Note that compared to Murphy et al. [45] (for example), we choose not to give the same
name (e.g., EROI) to two equations that have different definitions. In Murphy et al. [45], their Equation
(1) defines EROI (energy return on energy invested) as a function of a quantity of energy divided
by another quantity of energy, and their Equation (2) again uses the acronym EROI, but defined as
an instantaneous power flow divided by another instantaneous power flow. Here, we treat ratios of
energy as mathematically and conceptually distinct from ratios of power.
Net external energy ratio (NEER, as in King [29] and Brandt et al. [44]) is a calculation at
the same boundary condition as energy return on energy invested (EROI) at Boundary 3, EROI3,
of Murphy et al. [45]. Here, we make a distinction from Murphy et al. [45] in that to discuss
energy delivered (as an energy carrier, such as gasoline) to the “point of use”, we must subtract
the denominator (invested energy) from the numerator. The calculation of Equation (5) has also
been phrased as EROI at the point of use (EROIpou), the energy payback ratio [48] and the external
energy ratio [46]. By omitting the invested life cycle energy from the numerator, we are left with the
gross primary energy extracted only. Equation (6) shows that this change provides the gross external
energy ratio (GEER) as in King [29] and Brandt et al. [44], also equal to EROI1, or EROI at the point of
extraction, of: Murphy et al. [45].
NEER =EROIpou =EROI3=Ztf
0NEPRdt =Rtf
0(˙
Eext −(˙
Ecap +˙
Eop +˙
Ed))dt
Rtf
0(˙
Ecap +˙
Eop +˙
Ed)dt
=Eext −(Ecap +Eop +Ed)
Ecap +Eop +Ed
(5)
GEER =EROIext =EROI1=Ztf
0GEPRdt =Rtf
0˙
Eextdt
Rtf
0(˙
Ecap +˙
Eop +˙
Ed)dt
=Eext
Ecap +Eop +Ed
=NEER +1 (6)
Equations (7) and (8) are the same as Equations (5) and (6), respectively, except that they
include as part of energy input the energy that is dissipated as waste heat (Eheat =Efeed(1−η))
when consuming the feedstock fuel. This quantity is not the same as “cumulative energy demand”
as calculated in many life cycle assessments that include the full energy content of feedstocks (as
discussed in [49]). As discussed in King [29], Equations (7) and (8) count feedstock energy input
only as that energy that is dissipated as heat by the technology being modeled (e.g., energy leaving
a power plant originated in the feedstock, but was not dissipated within the plant boundary) [29].
NER =Ztf
0NPRdt =Rtf
0(˙
Eext −(˙
Ecap +˙
Eop +˙
Ed+˙
Efeed(1−η)))dt
Rtf
0(˙
Ecap +˙
Eop +˙
Ed+˙
Efeed(1−η))dt
=Eext −(Ecap +Eop +Ed+Efeed(1−η))
Ecap +Eop +Ed+Efeed(1−η)(7)
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GER =Ztf
0GPRdt =Rtf
0˙
Eextdt
Rtf
0(˙
Ecap +˙
Eop +˙
Ed+˙
Efeed(1−η))dt
=Eext
Ecap +Eop +Ed+Efeed(1−η)=NER +1 (8)
One goal of this manuscript is to show which ERRs can be compared to monetary flows to gain
insight into relations between energy and the economy. Thus, it is important to consider the NEER
vs. NER and GEER vs. GER distinction if we want to compare energy flows to monetary, or cash,
flows. We describe in Section 4that NEER and GEER are metrics to be compared to costs (inversely
related [16]) and not NER nor GER. However, the inverse relationship is difficult to precisely describe
in practice (see Section 4.1).
Now that we have reviewed ERRs, we can refer to the ERR calculations in the example of
Figure 1. Figure 1c shows the integral of the net power, or the cumulative net energy, at each point
in time in the life cycle. The cumulative net energy first decreases at the beginning during the capital
phase before increasing once energy extraction begins. Once the Eext−Eop = Ecap+Ed, this time is
called the energy payback time (tEPBT). The energy payback time is the instant when cumulative net
energy output is equal to all embodied energy invested over the life cycle. For visualization purposes,
in Figure 1c, we label tEPBT assuming that Ed=0. The tEPBT is longer than labeled if Ed>0.
Figure 1d shows that the final cumulative ERR values are the same as the ERRs calculated
in Equations (5)–(8). The cumulative ERRs are defined as the integral of the PRRs up until some
intermediate time, t. Equation (9) shows cumulative NEER, and the other ERRs follow the same
formulation using their respective numerators and denominators. It takes the full lifetime of the
technology or system to reach the final ERR. Note that if there is an investment of energy for
decommissioning, then just before the decommissioning phase, the cumulative ERR is greater than
the final ERR. The differences between cumulative ERRs and full life cycle ERRs are important as
we consider comparing ratios of power and energy (power integrated over time) to monetary flows.
Those differences are also relevant in the context of the practical reality of modeling impacts from
retiring energy infrastructure.
cumulative NEERt=Rt
0(˙
Eext −(˙
Ecap +˙
Eop +˙
Ed))dt
Rt
0(˙
Ecap +˙
Eop +˙
Ed)dt (9)
Figure 1considers modeling a single technology life cycle, but in the real world, there are many
energy technologies and systems being installed (practically) simultaneously. Figure 2takes the
information from the single technology in Figure 1and assumes that technology is installed at three
different times with the life cycles overlapping in time (see Figure 2a). Because each life cycle is the
same, the PRRs of the three combined life cycles never exceed their respective maximum values of
the PRRs of the individual life cycle (see Figure 2b). The PRRs of the combined system do, however,
fluctuate depending on when each individual life cycle begins and ends.
In Figure 2c, we show that the cumulative net energy at the final time is three times the
cumulative net energy at the end of a single life cycle. Furthermore, the ERRs at the final time of
the three life cycle scenario (see Figure 2d) are equivalent to the ERRs at the final time of the single
life cycle. The cumulative NEER in Figure 2d most clearly shows how the cumulative ERRs can
fluctuate over time depending on when energy technologies are installed and decommissioned.
Figure 3compares “non-external” PRRs and ERRs on the same figure, and Figure 4compares
the “external” PRRs and ERRs. The interpretation of the power and energy return ratios, however, is
the same in both cases. We focus our discussion on Figure 3, and we notice some important features.
It is not intuitive or easy to envision the power flows of several life cycles added together. Figures 3b
and 4b show that the instantaneous summed PRRs are sometimes less and sometimes more than the
respective instantaneous cumulative and final ERRs. That is to say, GPR is greater than cumulative
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and final GER most of the time, but when the life cycles begin and end (e.g., in the middle of the time
series), GPR <GER during the capital construction and decommission phases (i.e., during times of
high investment). Similarly, NEPR is greater than cumulative and final NEER most of the time, but
when the life cycles begin and end (e.g., in the middle of the time series), NEPR <NEER during the
capital construction and decommission phases.
2.2. Energy Intensity Ratios
Previously, the corresponding author introduced a proxy metric for a power return ratio (PRR)
called the energy intensity ratio (EIR) [14,50] in which he calculated the EIR of coal, oil, natural gas
and electricity for the United States. EIR is a ratio of two energy intensities: the energy intensity
of an energy commodity (the energy content purchased by a dollar, e.g., MJ/$ of oil) divided by
the energy intensity per unit of GDP of the country in which that commodity price exists (see
Equation (10)).
EIR is a PRR “proxy” because, unlike most PRRs that strive to convert input and output
information into units of power (often energy/year), including embodied energy translated from
mass or monetary data, EIR is price based. Our EIR uses annual data (e.g., energy/year, GDP/year)
and annual average prices, which are affected by short-term supply and demand. Thus, EIR is
an analog to PRRs, and not ERRs.
Equation (10) defines the price-based EIRpnof energy commodity nin a country for a given time
period. In this paper, we use annual data, where pis the price in units of money per energy content, e
is the energy intensity of the country, TPES is total primary energy supply (energy/year; see Section 4
of the Supplemental Information for the IEA definition) and GDP is the gross domestic product based
on market exchange rates. We believe it is important to use GDP at market exchange rates, because
oil is priced in U.S. dollars, and expenditures for oil are larger than for each other energy commodity.
EI R pn=
1
pn
e=
1
pn
TPES
GDP
[MJ/unit
$/unit ]
[MJ/yr
$/yr ](10)
Effectively, EIRpnscales prices (p) for an energy commodity (n) into a dimensionless ratio.
King [14] showed that the time series of EIR correlates well to those of PRRs based on running
average investments and energy production data of the United States. The major reason for this high
correlation is as follows. The EIR represents how much power one can obtain by spending one dollar
relative to how much power it takes to generate an average dollar of output from the economy. The
numerator represents the price of an energy commodity output from an industry or sector; thus, it is
akin to a system energy or power output. The EIR denominator represents the power input needed
to produce GDP (money/year); thus, it is akin to a system energy or power input (see Equation (11)).
EI R pn=
1
pn
TPES
GDP
[MJ/unit
$/unit ]
[MJ/yr
$/yr ]
∝
˙
Eout
$/yr
˙
Einput
$/yr
∝˙
Eout from energy life cycle
˙
Einvest into energy life cycle =PRR (11)
There is another reason that EIR correlates well with existing PRR calculations, such as in
Guilford et al. [21] and Cleveland [51], and it has to do with the inclusion of indirect energy or
power inputs. These two references calculate the invested power (or energy/year) as both direct
and indirect. The direct power is from energy carriers, such as diesel and electricity. The indirect
power is that power embodied in monetary investments. For example, Guilford et al. [21] assume
a nominal energy intensity of the U.S. oil and gas industry as 14 MJ/$2005. That is to say, for every
dollar produced by oil and gas extraction, 14 MJ of primary energy were assumed to be extracted
to support all subsequent activities. The indirect investments can be a substantial fraction of the
total. Figure 2 of King and Hall [15] indicates that since 1980 for the U.S. oil and gas industry, annual
indirect energy investments are roughly equal to annual direct energy investments.
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Therefore, a full PRR (or ERR) calculation cannot neglect indirect power (or energy) investments.
These indirect estimates can be estimated as monetary investment multiplied by the energy intensity
(MJ/$) of the sector from which the purchase is made. The weighted average of the energy intensities
of all economic sectors is the energy intensity of the overall economy, e= TPES/GDP. Thus, one
could make a broad simplification that all investments, in energy or non-energy sectors, occur at
the average energy intensity of the overall economy, e, and Henshaw et al. [16] demonstrated this
simplified approach. In effect, the EIR calculation makes this same simplifying assumption that all
monetary investments to produce energy occur at the overall economy energy intensity rather than
at some industry-specific energy intensity.
The EIR represents how much energy one can obtain by spending one dollar (or other monetary
unit) relative to how much energy it takes to generate an average dollar of output from the economy.
One benefit of using EIRpnas a PRR proxy is that energy commodity price data are more readily
available for individual countries than data for energy production inputs (e.g., diesel, steel, etc.).
Thus, one can gain insight into the net energy of commodities in countries with few data or low
domestic energy production. In some sense, the EIR might be the only option for a calculation to
estimate the net energy of commodities in countries with few data.
2.2.1. IEA Data
We obtain the energy intensity of each country, the ratio e=TPES/GDP, directly from the
IEA data in tonnes of oil equivalent (toe) per thousand $2005 USD and convert to MJ assuming the
conversion factor 41,868 MJ = 1 toe. For each of nine commodity prices, we calculate country-specific
and a “worldwide” average energy intensity ratio (EIRpn). We calculate the world average EIRpn
by weighting each of 44 country-specific EIRpnby the fraction of GDP that country contributes to
the summed GDP of the countries (see Figure 5) (the 44 countries with data in the IEA database
are: the United States, the United Kingdom, Spain, Russia, the Netherlands, Japan, Italy, Germany,
Canada, France, Austria, Denmark, Finland, Norway, Sweden, Argentina, Australia, Belgium, Brazil,
China, Chinese Taipei, Colombia, Czech Republic, Greece, Hungary, India, Indonesia, Iran, Iraq,
South Korea, Kuwait, Libya, Malaysia, Mexico, New Zealand, Nigeria, Poland, Portugal, Qatar, Saudi
Arabia, South Africa, Switzerland, Turkey and Venezuela) [52]. If the IEA data do not list a price for
a given commodity in a given country, no value is plotted in Figure 5.
We use annual average prices that represent the energy commodity sales at a particular point in
the supply chain. It is important to compare only EIRs and PRRs at similar boundary conditions, or
points in the supply chain. Gasoline and ethanol prices, EIR and PRRs can be compared, as they are
both energy carriers refined for final consumption, but neither should be compared to oil, because it
is a primary energy feedstock for various refined products. As such, EIRp,oil >EIRp,gasoline , just as
the price of oil is less than the price of gasoline.
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0
25
50
75
100
125
150
175
EIRp,Coal−Elec
EIRp,Coal−Ind
EIRp,Coal−Res
0
25
50
75
100
125
150
175
EIRp,Oil
EIRp,NG−Elec
EIRp,NG−Ind
1980 1990 2000 2010
0
5
10
15
20
25
30
35
40
EIRp,NG−Res
1980 1990 2000 2010
EIRp,Elec−Ind
1980 1990 2000 2010
EIRp,Elec−Res
Figure 5. The individual price-based energy intensity ratios, EIR pn, 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 EIRpneach year. NG = natural gas, Elec = electricity, Ind = industrial, and
Res = residential, such that, for example, EIRpNG, Res is the “EIR of the price of natural gas purchased
by the residential sector.”
2.2.2. Aggregation of EIRpn
There are several energy commodities, and thus, there are several EIRpn. Equations (12) and
(13) show that by aggregating all EIRpnby the proportion of expenditures on that commodity n, one
arrives at a value that equates to the inverse of total expenditures on energy for that country, f−1
e,GDP
(see Part 2 of this series for a full discussion and calculation of fe,GDP [1]).
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weighted EI R pn=∑9
n=1(EI R pnpncn)
∑9
n=1pncn
=∑9
n=1(1
pn
GDP
TPES pncn)
∑9
n=1pncn
=GDP∑9
n=1cn
TPES
∑9
n=1pncn
(12)
Because the sum of all energy consumption is the definition of TPES (i.e.,∑9
n=1cn=TPES),
weighted EI R pn=GDP ∑9
n=1cn
TPES
∑9
n=1pncn
=GDP(TPES
TP ES )
∑9
n=1pncn
=GDP
∑9
n=1pncn
=GDP
expenditures on energy =f−1
e,GDP
(13)
The utility of the framework of Equations (12) and (13) is not so much that one could use
system-wide EIRpnprojections to project future expenditures on energy for energy scenarios. EIRpn
is a retrospective metric based on historical price and macroeconomic data. The real utility would be
to substitute for EIRpna time series of an appropriate ratio of biophysical energy output and input
flows. The power flows in turn come from the life cycle processes modeled to calculate PRRs and
ERRs of individual technologies. Thus, a sequence of historical, or future (e.g., scenario), investments
in multiple energy systems can translate to a time series of power input and output flows for the
entire system or economy.
That is to say, as we contemplate scenarios of increasing use of energy production technologies
that do not have individually-listed commodity prices (e.g., no commodity electricity price for wind
and photovoltaic power), PRRs and ERRs calculated from net energy analyses can inform estimates
of future total expenditures on energy and, thus, the economic implications of a time series of energy
investments. For future scenarios, instead of projecting future prices without a biophysical basis, net
energy analysts could project future PRRs, ERRs, materials and labor needs and then back out cost
shares and cost supply curves (not necessarily prices).
2.2.3. England and United Kingdom Data
We use Roger Fouquet’s collection of historical data on England’s and the United Kingdom’s
energy prices, gross domestic product and total primary energy supply [53–55]. As noted in
Fouquet [54], average heating fuel prices are weighted by consumer expenditures (i.e., price
multiplied by consumption) on the fuels. Fouquet’s data are largely estimates of annual
average prices.
3. Results
The major results from calculating country-specific and worldwide aggregate energy intensity
ratios (EIR) are as follows, with more detail in the rest of this section:
•All world average EIRpnfollow 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.
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•The time series for England and the U.K. indicates that high EIRpnare not unprecedented before
World War II, but that EIRpnof coal generally declined from 1300 to 1850.
3.1. Energy Intensity Ratios: World
In a previous paper that introduced the EIR, King [14] showed that there was a high correlation
of U.S. EIRs with existing calculations of EROI (using input data on annual flows, as energy/year and
money/year, not power integrated over time) for two of the U.S. energy sectors: coal, as well as oil
and gas. We interpret the trends of EIR in this paper in the same manner. There are very few ERR
or PRR calculations of energy commodities or sectors by country or the world. Table 2in Section 4.1
compares our EIR calculations to a couple of relevant calculations in the literature.
The following EIRpnpatterns generally hold: EIRpcoal, Elec >EIRpcoal, Ind >EIRpcoal, Res and
EIRpNG, Elec >EIRpNG, Ind >EIRpNG, Res ; Elec = for electric sector, Ind = for industrial sector and
Res = for residential sector. This pattern is due to the fact that higher costs and prices, hence
lower EIR, are associated with the increased distribution infrastructure and investment (e.g.,
pcoal, Elec <pcoal, Ind <pcoal, Res , where pn,i is the price of commodity nfor purchase by consumer
i). More infrastructure and investment is required to deliver energy to many residential consumers
than fewer industrial consumers and to even fewer electricity generating plants. In other words,
EIRpn, or energy return ratios (ERRs) and power return ratios (PRRs) more generally, are higher (e.g.,
costs and prices are lower) when analyzing smaller boundaries or shorter subsets of supply chains.
For the same reasons, EIRpNG, Ind >EIRpElec, Ind and EIRpNG, Res >EIRpElec, Res .
The anomalously high average values for EIR of residential NG (EIRpNG, Res ) in 1993 and 1994 are
due to significantly lower reported prices for Russia during those two years. The only other years
with Russia residential NG prices are 2000–2004. The single anomalous high value for EIR of coal for
electricity (EIRpCoal, Elec ) in 1980 is for Poland. The high outlier time series for EIR of coal for residential
consumption (EIRpCoal, Res ) is for South Africa.
Our calculations show that the overall global EIR trend for each energy commodity increases
from 1978 to the late 1990s and early 2000s before it declines through 2008 with a slight rebound to
2010 after the Great Recession in 2008. The trend for the two decades leading up to 2000 implies
that power return ratios of energy commodities were increasing following the Western governments’
supply and efficiency responses to the practically simultaneous 1973 Arab oil embargo and OPEC
rise in posted oil price [56]. For the decade leading up to 2008, the global EIRpndecline indicates
that energy commodities were becoming more expensive to the economy, which implies a broad
decreasing trend in net energy output relative to energy inputs to produce the energy. This decline
in EIRpnfrom 1998 to 2008, or steady increase in prices, has also been attributed to increased
globalization and demand for resources. For example, Kilian describes the global oil price rise
from 2003 to 2008 primarily as a function of unexpected increasing demand (relative to supply) in
emerging Asian economies (e.g., China) [57]. One future research goal is to explain when changes in
EIR are simply driven by supply and demand versus when they indicate a change in the underlying
biophysical cost of production (i.e., net energy, ERR, PRR).
3.2. Energy Intensity Ratios: Historical England and U.K.
We present the long-term EIRpnof various energy commodities for England and the United
Kingdom (U.K.) in Figure 6. The plot on the right of each (a)–(c) subset of Figure 6is to enable
easier comparison of the calculations using Fouquet and IEA data for the last 30 years. These EIRpn
are perhaps the only biophysical-like metrics over such a long time period. Because EIRpnare highly
correlated for U.S. time series, as investigated by King [14], we hypothesize that the same holds for
other countries that produce the particular energy commodities under study. For most of the history
of England and the U.K., we can assume they produced the vast majority of their energy from wood,
coal (perhaps up to 1950, as U.K. coal production peaked in 1913 [12]) and gas. U.K. oil production
(e.g., in the North Sea) occurs after 1970, and thus, the pre-1970 EIRpOil is simply a measure of the
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relative economic effectiveness of U.K. consumption of oil imports. The U.K. produced practically
all of its natural gas (and town gas per Fouquet data) until approximately 2005. To make compatible
comparisons of the two data sources used for Figure 6, we have used the data collected by Fouquet to
calculate energy intensity to then scale both his and the IEA energy prices into EIRpn[53–55]. Here,
we calculate the England/U.K. energy intensity as the total energy consumption from Fouquet [53]
(energy consumed for domestic heat, industrial heat, power (industry), passenger transport, freight
transport and light) divided by GDP estimates. The historical (1270–1870) GDP estimates are those
from Broadberry et al. [58].
0
20
40
60
80
100
120
140
1300 1400 1500 1600 1700 1800 1900 2000
EIRp
EIRp,pitheadCoal(Fouquet) EIRp,avg.Coal(Fouquet)
EIRp,avg.Wood(Fouquet) CoalEIRp_Elec
CoalEIRp_Ind CoalEIRp_Res
EIRCoal(avg) EIRCoal(NE,pithead)
EIRpCoal (avg.,Fouquet)
EIRpCoal,Elec (IEA)
EIRpCoal,Res (IEA)
EIRpCoal (pithead,Fouquet)
EIRpWood (avg.,Fouquet)
EIRpCoal,Ind (IEA)
0
20
40
60
80
100
120
140
1975 1985 1995 2005
(a)
0
20
40
60
80
100
120
140
1840 1860 1880 1900 1920 1940 1960 1980 2000
EIRp
EIRGas(Fouquet) NGEIRp_Elec
NGEIRp_Ind NGEIRp_Res
CrudeOilEIRp_1st_Import_EIRp EIRp,Oil(BPoilprice)
0
20
40
60
80
100
120
140
1975 1985 1995 2005
EIRpNG,Elec (IEA)
EIRpNG,Res (IEA)
EIRpOil (BP)
EIRp,Gas (Fouquet)
EIRpNG,Ind (IEA)
EIRpOil (IEA)
(b)
Figure 6. Cont.
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0
5
10
15
20
1880 1900 1920 1940 1960 1980 2000
EIRp
EIRElectricity(Fouquet) ElecEIRp_Ind ElecEIRp_Res
0
5
10
15
20
1975 1985 1995 2005
EIRpElec,Res (IEA)EIRp,Elec (Fouquet) EIRpElec,Ind (IEA)
(c)
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. EIRpNG, Res is the “EIR of the price of natural gas purchased by
the residential sector”.
4. Discussion
Individual energy technology life cycles are characterized by the series of processes, or
investments, that are required to build the technology. Each investment in turn requires a certain
amount of primary energy as an input (e.g., part of TPES) and produces a certain amount of net
economic output (e.g., part of GDP) (see [27,28,59] for the methods that calculate the energy intensity
of each economic sector). The former divided by the latter is an energy intensity (primary energy
inputs divided by net economic output) that describes the structure of the technology life cycle. Some
energy technology life cycles have investments with low overall energy intensity (e.g., those with
a high ratio of services as investment) and some with high overall energy intensity (e.g., those with
a high ratio of energy carriers as investment).
Like individual life cycles, economies can also have different structures that are partially
characterized by the energy intensity of the economy. When we mention the energy intensity
of an economy (e.g., e=TPES/GDP), this single number is really an average of all of the
energy intensities of all individual industries and products in the economy: energy industries and
non-energy industries. Thus, it is impossible to discuss the energy intensity of an overall economy
without understanding the energy intensities of the underlying industries and processes that reside
within the economy.
Hence, in net energy analysis, it is important to understand the linkages between the energy
intensity of individual energy technology life cycles and the energy intensity, and hence structure,
of the overall economy. Our discussion focuses on how we can use this understanding to translate
between economic and biophysical descriptions of the economy.
4.1. Energy and Power Return Ratios in Relation to Cost and Prices (for Future Energy Scenarios)
The purpose of this section is to present the case that energy return ratios (ERRs) can provide
insights into monetary costs of energy, as well as power return ratios (PRRs) can infer energy prices
and/or operational costs. We believe one goal of using ERRs and PRRs is to relate to costs and prices,
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respectively, and thus help project the economic ramifications of future energy scenarios. Let us be
clear, we are not the first to propose to use net energy as an indicator for technology assessment or
projections. The Federal Nonnuclear Energy Research and Development Act of 1974 specified the
calculation of net energy to evaluate energy technologies for research, development and deployment:
“Section 5904 (a)(5): The potential for production of net energy by the proposed technology at the
stage of commercial application shall be analyzed and considered in evaluating proposals”. [60].
The energy intensity ratio (EIR) is by definition inversely related to the price, pn, of an energy
commodity. EIR also follows the same trend as PRRs in that the numerator represents an energy flow
output (the commodity) and the denominator represents the average primary energy input per dollar
of output, or energy intensity (e=TPES/GDP), of the economy that purchased the energy output (see
Equation (11)). Proper interpretation of data is needed to understand how much the domestic price
actually relates to domestic production. The net energy analyses of the 1970s, such as [27,61], used
economic I-O tables to break the assumption that every dollar invested from different industries and
sectors was associated with the same amount of primary energy. Thus, some sectors are more energy
intensive than other. Costanza [28] and Costanza and Herendeen [59] demonstrate that the differences
in the calculated energy intensities among industries depends on two modeling assumptions: how
one assumes energy “enters” the economy and the boundary between intermediate consumption
(e.g., the input-output transactions of the producing part of the economy) and output. For modeling
energy inputs, those authors demonstrate energy entering the economy at the point of physical entry
into sectors (e.g., oil and gas energy enters into the oil and gas extraction sector) and energy entering
as the relevant quantities at the points of consumption by each economic sector (not only energy
sectors). In addition, Costanza and Herendeen [59] discuss implications of including labor costs and
personal consumption within the input-output transactions matrix instead of considering them, as
usual, as external to the input-output transactions matrix.
Most net energy analyses of energy industries (e.g., oil and gas) over time are actually
formulations of PRRs, rather than ERRs, since they use data in units of power, or energy flows per
year. Hall’s and Cleveland’s analyses of the U.S. oil and gas sector are good examples [21,51]. They
term their calculation EROI, what we term GEPR in this present paper. King and Hall [15] plotted
U.S. oil prices versus the EROI results of Guilford et al. [21] and hypothesized inverse curves governing
the underlying trend between the two. Heun and de Wit [17] also explored the inverse relationship
between GEPR (using the term EROI) and oil price. Here, we make Figure 7, similar to that in King
and Hall [15], that also includes EIRoil. We use Figure 7only to enhance the interpretation of Figure 8,
which uses the calculations of the present paper.
In interpreting Figure 7, it is important to note that today, oil prices are dictated by global supply
and demand pressures. However, this was not always the case. Before 1970, the U.S. was the marginal
oil producer, and during the few decades leading up to 1970, the Texas Railroad Commission (RRC)
was able to maintain price stability by throttling Texas oil production to prevent a price collapse due
to overproduction [62]. Until the late 1970s, EIRoil and GEPR = EROIO&G were quite similar, and
King [14] (Figure 3) shows that U.S. EIRoil was less than GEPR = EROIO&G when considering only the
direct energy inputs, but greater than GEPR = EROIO&G when considering both indirect and direct
energy inputs. In effect, it seems the Texas RRC was effective at incentivizing some, but not too
much, annual investment for oil production in order to minimize price volatility. The RRC set the oil
price higher than needed to cover operational costs, but not too much higher, to induce new capital
investment and allow profits.
It is not a surprise that this U.S. example shows that EIRoil is similar to EROIO&G = GEPRO&G
from Guilford et al. [21] and Cleveland [51]. Both metrics utilize information about how the economy
uses energy to produce GDP (e.g., U.S. energy intensity informs both of the calculations, but in
different ways). Thus, this feedback exists, perhaps driving them to similar results. We do not have
many calculations of the GEPR (= EROI) of production in various countries or the world overall to
which to compare our present EIR calculations. Hence, the EIR calculations have value in that they
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use prices to provide some feel for the underlying GEPRs (= EROIs) of global production. They are
not a PRR or an ERR calculation, but they are more than nothing. Table 2shows our EIR calculations
compared to two calculations of oil and gas EROI (Norway and a global estimate). The EIRs follow
generally the same pattern over time and are close in estimation, particularly after 2000, when global
commodity prices were generally increasing until 2008.
$0
$10
$20
$30
$40
$50
$60
$70
$80
$90
$100
0 5 10 15 20 25 30 35 40
Crude OilFirstPurchsePrice,
($2005/BBL)
GEPRO&G ~EROI1,O&G=EROIext,O&G
(a)
2014
1972
1981
1999
1994
$10
$100
440
Crude OilFirstPurchsePrice,
($2005/BBL)
GEPRO&G ~EROI1,O&G=EROIext,O&G
MROI=1.1;MJ/$2005=33 MROI=1.5;MJ/$2005=33
MROI=1.1;MJ/$2005=19 MROI=1.5;MJ/$2005=19
MROI=2.1;MJ/$2005=19ORMROI=1.5;MJ/$2005=13.5
EIR:OilFirstPurchasePrice(1949‐2014) EROIO&G‐Guilford(2011)(1919‐1977)
EROIO&G‐Guilford(2011)(1982‐2002) EROIO&G‐Guilford(2011)(2007)
EROIO&GCleveland(2005)(1954‐1997)
(b)
2014
1972
1981
1999
1994
Figure 7. U.S. oil first purchase price versus both EIRoil and EROI1=EROIext =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).
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Energies 2015,8, 12949–12974
Table 2. Comparisons of EIR to EROI (= GEPR) calculations in the literature (selected years cited in
references): Grandell et al. [63] for Norway oil and petroleum and Gagnon et al. [64] for the world oil
and gas.
EIRoil EROIoil EROIpetroleum EIRoil EIRNG, Industry EROIO&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 8plots average prices ($2005/MJ) for the 44-country aggregate (weighted by GDP of each
country) versus the EIRpnusing that price and the 44-country energy intensity (= TPES/GDP). As
mentioned earlier in the paper, we expect an ERR or a PRR analysis of a commodity or a technology
to calculate smaller metrics for larger life cycle boundaries or longer supply chains. Figure 8b shows
that residential NG has a higher price, and lower EIRp, than NG for industrial purchase. Further,
Figure 8c shows that electricity has a higher price, and lower EIRp, than the NG and coal that fuel
thermal power plants. We do not need EIR (nor ERRs, nor PRRs) to understand these points, but
plots as in Figure 8help us imagine how we can use ERR and PRR calculations to inform future
energy scenarios (e.g., prices or other metrics). For example, net energy calculations can inform if
distributed generation and storage technologies that can employ different supply chains and business
models and infrastructure can supply residential electricity at higher ERR and PRR than the existing
or future electric grid.
The two inverse curves in Figure 8a–c represent the 44-country world energy intensity in 1978
(13.9 MJ/$2005) and 2010 (10.5 MJ/$2005). We show these curves to help envision that as the
economy becomes more efficient, the curves move up and to the right of the figure. Similarly, a single
technology life cycle, or its annual embodied power inputs, can have a range from a low to a high
overall energy intensity for the investment. This concept is shown in Figure 7. The postulated solid
curve (lower-leftmost) relates GEPR and oil price via relatively high energy-intensive (33 MJ/$2005)
investments for oil and gas development. The postulated dotted curve (upper-rightmost) represents
investments at higher profit and lower energy intensity (13.5 MJ/$2005). Increased wages and
use of services are one reason for a time period of lower energy intensity for investing in oil and
gas development.
We use Figure 8d to think more conceptually about how the energy intensity of the investment
for energy production can relate economic and net energy metrics. The y-axis can represent
a marginal price that might relate well to a PRR. Furthermore, the y-axis might represent a levelized
cost of energy, that would better relate to an ERR of a full life cycle. For example, previously, the lead
author simultaneously calculated (using a wind farm installation cash flow model) the energy return
ratio of NEER (= EROIpou) and (inversely related) levelized cost of energy (LCOE) [16].
Assume that we have calculated the ERR1of an energy technology, as in Figure 8d. If the
technology investments leading to ERR1were mostly for up-front capital (e.g., manufacturing,
construction) and services (e.g., engineering consulting), then the overall lifetime investments would
be of low energy intensity because capital and services have relatively low energy intensity. That
technology might have cost c1,high. However, if an energy technology with ERR1had high operating
costs and direct energy inputs, then its overall investment would be of relatively higher energy
intensity, and it might have cost c1,low. This insight follows from the fact that energy carriers (e.g.,
direct energy inputs) are characterized by higher MJ/$ than the average product from the overall
economy. The same rationale holds if we estimate a price (or a cost), p2, for an energy technology
instead of an ERR or PRR. This single price or cost might correspond to a range of low to high PRRs or
ERRs, respectively. Thus, just as one could project monetary metrics to back calculate ERRs and PRRs,
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Energies 2015,8, 12949–12974
one could project ERRs and PRRs to project monetary metrics. Perhaps some hybrid combination is
also possible.
0 102030405060708090100
EIRp
0
5
10
15
20
25
30
Price ($2005/GJ)
Coal for Electricity
EI = 13.9 MJ/$2005
EI = 10.5 MJ/$2005
NG for Electricity
Industrial Electricity
Residential Electricity
EI = 13.9 MJ/$2005
EI = 10.5 MJ/$2005
0 102030405060
EIRp
0
1
2
3
4
5
6
7
8
9
10
Price ($2005/GJ)
Oil
(a)
(c) (d)
ERR(NEER,EROI)orPRR(GEPR,NEPR)
CostorPrice($/MJ)
LowMJ/$investment
HighMJ/$investment
EI = 13.9 MJ/$2005
EI = 10.5 MJ/$2005
0 102030405060
EIRp
0
1
2
3
4
5
6
7
8
9
10
Price ($2005/GJ)
NG for Industry
NG for Residential
c1,high
c1,low
p2
ERR1PRR2,low PRR2,high
(b)
Figure 8. Price vs. EIRpnfor 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. EIRp
In considering the historical EIRpntime series of England and the U.K. (Figure 6), one of the
main trends that stands out is that EIR of coal (at the pit and average) has a secular decline from
1300 to 1860. Fouquet [54] notes that over this time, his average coal price becomes dominated by the
price in London, which includes taxes as nearly one-third of the price. Further, Fouquet’s (domestic)
firewood price reflects considerable transport costs to non-local areas. Thus, our EIRp,wood translates
best to a net external power ratio, or energy return on investment at the point of use. Coal at the
pithead is also the only commodity with EIRp>40 before the 1940s. Thus, the post-World War II era
is unique in having high EIRpenergy that is not coal.
In comparing the long-term EIR (left of Figure 6) to the more recent one (right of Figure 6), we
can more clearly distinguish meaningful differences in the prices of the IEA and Fouquet. Fouquet’s
energy prices are largely those for the end-consumer. Thus, the EIRp,Coal for average coal is similar to
the EIRp,Coal,Res using IEA residential prices. The same holds true for the EIR using Fouquet’s average
gas (town and natural gas) and electricity prices, as they match best with EIRp,NG,Res and EIRp,Elec,Res
using IEA data. The one meaningful difference in the time series is that for all commodities (coal, gas
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Energies 2015,8, 12949–12974
and electricity), EIRs using Fouquet’s prices are lower in the 1980s–mid-1990s than those using IEA’s
residential prices. After around 1995, all EIRs (e.g., prices) seem to agree relatively well.
Everyone alive today has lived in a time of generally decreasing economic energy intensity (for
developed countries), but this has not always been the case, as Figure 9a shows for England and the
U.K. While describing the full history of energy and technology in the U.K. is beyond the scope of
this paper (see [53–55] for more details), we make a few general statements. For our purposes, the
broad trends are most important rather than debating the annual variations in data (which Fouquet
also notes imply greater accuracy than exist). Suffice it to say that energy, combined with prime
movers and other technologies providing energy services, is key to a modern economy and defines
the structure of the economy to a large degree. Over the course of 700 years, the energy intensity of
England and the United Kingdom has varied by nearly ±80% relative to the pre-industrial average.
U.K. industrialization in the 1800s coincided with increasing energy intensity as an increasing rate of
energy consumption outpaced economic output, which also increased rapidly. Ever since the 1870s,
the U.K.’s economy has restructured to produce more value from less (domestic) energy consumption.
It is only since the 1870s that the effective power return ratio of coal, using EIRp,coal as a proxy,
began to rise again. Thus, over the history of the U.K., real energy prices (and hence, PRRs and ERRs)
have fluctuated in the context of available energy, technology and labor. As such, the EIRpof energy
commodities fluctuated, as well. While we do not perform a causal analysis relating high energy
and power return resources, we can map the structure of the economy to EIR and prices to provide
a conceptual understanding.
ViewingEngland/U.K.EIREnergy
Intensityover7centuries
Data:RogerFouquet(2011)REEP.
Year Toe/year2000
pound
1300 0.00064
1560 0.00039
1820 0.0007
1870 .001
1930 0.00062
2008 0.00015
0
200
400
600
800
1000
1200
1300 1400 1500 1600 1700 1800 1900 2000
Mtoe/£(2000)
Yea r
(a)
0
50
100
150
200
250
300
350
400
450
500
0 10203040
Price(£(2000)pertoe)
EIRp
Firewoods(1300‐1869)
Coal(1300‐1869)
Coal(post‐1869)
ViewingEngland/U.K.EIRofcoaland
Firewoodover7centuries
Data:RogerFouquet(2011)REEP.
1300
1820
1873
2007
1979
1995
1966
1750
1560
1868
Year Toe/year2000
pound
1300 0.00064
1560 0.00039
1820 0.0007
1870 .001
1930 0.00062
2008 0.00015
1420
(b)
Figure 9. (a) England’s/the U.K.’s economy energy intensity; (b) price vs. EIRpfor 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].
Figure 9b plots coal (average) and wood prices versus EIRpof each. If it were not for a changing
structure in the economy, here characterized by the country energy intensity (e= TPES/GDP), then
all points in Figure 9b would lie on a single inverse curve. By presenting the EIR, price and energy
intensity data as shown, we gain a historical perspective on how energy return ratios (ERRs) and
power return ratios (PRRs) might have related to prices, as discussed in Section 4.1.
For example, population pressure in pre-industrial England was relatively high during the time
periods of high energy intensity in Figure 9a (see [33]). This population pressure affected farm wages
that were low from 1250 to 1350, high from 1400 to 1500 and again lower from 1550 to 1650 [65].
Since farming was a large part of the pre-industrial economy, as a part of the energy sector in
providing fodder and food for animate (animal and human) power, there is a relationship between
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Energies 2015,8, 12949–12974
farm wages (e.g., costs) for the energy sector and the energy intensity of the economy overall that
needs exploration. That is to say, when farm (e.g., energy) wages were high, the pre-industrial English
energy intensity was low, and vice versa. Since farm wages were the major input to the pre-industrial
energy sector (e.g., agriculture), they translated to more expensive energy (e.g., food and fodder)
that incentivized more efficient consumption. It is precisely this type of relationship that we need to
understand for modeling future energy scenarios from both economic and biophysical perspectives.
We cannot separate the combination of high ERR fuels and new conversion technologies (e.g., steam
engines) from the feedbacks within the overall economy. As Figure 9b shows, over time, a given EIRp
was not associated with a single price. It is left to future work to understand this relationship of prices
to ERRs and PRRs based on the information of the actual wood and coal life cycle processes.
5. Conclusions
We believe that to make net energy analysis relevant to decision-making, one approach is to
translate between economic and biophysical descriptions of energy systems and technologies. In
taking this approach, it is important to make sure one is linking the proper metrics. Thus, the
metrics must be clearly defined as described in this paper. The energy intensity ratio calculated (EIR)
in this paper is one metric to translate between economic (e.g., prices of energy commodities) and
biophysical (e.g., power and energy return ratios) descriptions of the value of energy commodities.
The EIR is based on annual energy price data, but scaled via the energy intensity (total primary energy
supply/GDP) to translate to the power return ratios of a biophysical or net energy modeler. EIR is
a proxy for the gross external power ratio (for primary energy commodities) and the net external
power ratio (for delivered energy commodities). Levelized costs of energy best translate to energy
return ratios (ERR), such as the net external energy ratio (NEER) calculated using information over
the entire life cycle of the energy system. We find it important to distinguish among the mathematical
definitions of these terms, and we use a unique terminology for each equation so as not to confuse
a single term (e.g., energy return on energy invested, EROI) with more than one definition.
For any calculated value for an ERR, there is not a single cost of energy. Likewise, for any
given calculated power return ratio (PRR), there is not a single price of energy. In order to more
fully translate between prices and power return ratios, or levelized costs and energy return ratios, it
is necessary to consider the structure of the investments for an energy technology or system. This
structure can be measured by the energy intensity of the life cycle inputs. We expect energy systems
and technologies with a high proportion of capital and services inputs to have lower energy intensity
of investment (e.g., lower MJ/$ for inputs), which translates to a higher cost or price at a constant
ERR or PRR, respectively. Examples of these kinds of technologies are wind and photovoltaic
power, which have no fuel costs and low operating costs. Conversely, we expect energy systems
and technologies with a high proportion of direct energy inputs (e.g., fuels) to have higher energy
intensity of investment (e.g., higher MJ/$ for inputs), which translates to a lower cost or price at
a constant ERR or PRR, respectively.
Just as the structure of investments for an energy technology can help link its ERR to its cost, the
structure of the economy overall affects the underlying assumptions for the calculations. We showed
that the calculated EIRpnfor global oil, coal, natural gas and electricity prices all show a similar trend:
increasing from 1978 to around the year 2000, then decreasing to 2008 before rebounding up slightly to
2010. During this short time span, many economies changed their structure significantly by becoming
more efficient in the use of energy. However, the changes pale in comparison to the structure changes
that morphed the pre-industrial England economy to that of the United Kingdom today. For over five
centuries (1300–1800), the EIR of English coal was always higher than the EIR of wood, even though
the EIR of coal slowly declined over that time.
If an overall economy has high energy intensity, then this might be linked to its ability to produce
high ERR energy, as we show occurred during industrialization in the United Kingdom in the 1800s.
Conversely, a country that cannot produce high ERR energy (e.g., due to lack of quality resources)
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Energies 2015,8, 12949–12974
is more incentivized to reduce energy intensity to make the most economic use of produced and
imported energy. Future research should strive for better models to link ERRs to costs and PRRs to
marginal prices.
Acknowledgments: This work was partially supported by, and the authors thank, the Jackson School of
Geosciences Energy Theme at The University of Texas at Austin.
Author Contributions: Carey W. King designed and structured the research. Alyssa Donovan, John P. Maxwell,
Carey W. King obtained and organized the data from the various sources while performing calculations for
the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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