『Abstract
　The goal of net energy analysis is to assess the amount of useful energy delivered by an energy system, net of the energy costs of delivery. The standard technique of aggregating energy inputs and outputs by their thermal equivalents diminishes the ability of energy analysis to achieve that goal because different types of energy have different abilities to do work per heat equivalent. This paper describes physical and economic methods of calculating energy quality, and incorporates economic estimates of quality in the analysis of the energy return on investment (EROI) for the extraction of coal and petroleum resources in the U.S. from 1954 to 1987. EROI is the ratio of energy delivered to energy used in the delivery process. The quality-adjusted EROI is used to answer the following questions: (1) are coal and petroleum resources becoming more scarce in the U.S.?, (2) is society's capability of doing useful economic work changing?, and (3) is society's allocation of energy between the extraction of coal and petroleum optimal? The results indicate that petroleum and coal became more scarce in the 1970s, although the degree of scarcity depends on the type of quality factor used. The quality-adjusted EROI shed light on the coal-petroleum paradox: when energy inputs and outputs are measured in thermal equivalents, coal extraction has a much larger EROI than petroleum. The adjustment for energy quality reduces substantially the difference between the two fuels. The results also suggest that when corrections are made for energy quality, society's allocation of energy between coal and petroleum extraction meets the efficiency criteria described by neoclassical and biophysical economics.』

Introduction
Accounting for energy quality in net energy analysis
Production side approaches to energy quality
End-use approaches to energy quality
　Exergy
　The economic perspective: relative prices and marginal product
　The relative price approach
　The marginal product of energy approach
　Physical versus economic perspectives of energy quality: who is right?
Data preparation
　System boundaries
　Direct energy costs
　Indirect energy costs
　Accounting for energy quality
Results
　Coal extraction
　Petroleum extraction
　Petroleum and coal compared
Discussion
　The scarcity of U.S. fossil fuel resources
　The coal-petroleum paradox
　The optimal investment of energy: economic and biophysical perspectives
Conclusion
Acknowledgements
References

Table 1 Quality factors for various enery types

Energy type		Transformitya (SEJ/joule)	Market priceb (cents/106Btu)
Coal
Bituminous		3.98×104
	mine-mouth		105
	delivered costc
Anthracite
	mine-mouth		189
Oil
	wellhead	5.3×104	265
	No.2 fuel oil		614
	gasoline	6.6×104	718
Natural gas
	wellhead	4.8×104	150
	delivered costc		285
Electricity
	leaving power plant	1.59×105
	delivered costc		1398
aSource: Odum and Odum (1983). Units are solar emjoules per joule. bSource: Department of Energy (1991). Values are 1987 prices. cCoal, price paid by electric utilities; natural gas and electricity, price paid by industrial user.

• EROI（Energy return on investment）は、次式で表される。
  EROIt＝（ΣEi,t^o）／（ΣEi,t^c）………（2）
  ここで、E^oとE^cは、熱当量（thermal equivalent）で測られた、時間（t）におけるエネルギー・タイプ（n）の入力エネルギーと出力エネルギー。E^cは、エネルギー系への直接および間接エネルギー入力の合計である。
• エネルギー・タイプの各タイプの熱当量に重みをつけて、エネルギーの質を計る必要がある。
  そのために、相対的な経済的有用性を用いる。
  新しい集合エネルギーを次式で表す。
  Et^*＝λ1t E1t＋λ2t E2t＋…＋λnt Ent………（3）
  ここで、λは個々の燃料の品質係数（quality factor）。
• 質を補正したEROIは、次式のようになる。
  EROIt^*＝（Σλi,t Ei,t^o）／（Σλi,t Ei,t^c）………（4）
  ここで、λi,t は時間（t）における燃料タイプ（i）についての品質係数であり、E^oとE^cは式（2）で定義されるようなエネルギー・コストとエネルギー出力の熱当量である。
• 品質係数をどのように求めるかが問題。
  生産側からのアプローチと利用側からのアプローチのしかたがある。
• 生産側からのアプローチ：
  燃料を生産するコスト、あるいはある形態から別の形態へ変換するコストによる。
  一つは、emergy（エメルギー）分析による（Odum and Odum, 1983; Odum et al., 1987; Odum, 1988; Huang and Odum, 1991）。あるタイプのエネルギーの質をその『transformity』により測る。『transformity』は、別のタイプのエネルギーの熱当量を生産するのに必要な、あるタイプのエネルギーの量である。基準として、太陽エネルギーが使われ、『solar emjoule（SEJ）』の単位が用いられる。
• 利用側からのアプローチ：
  物理的アプローチ：熱力学的なexergy（エクセルギー）分析など。
  経済的アプローチ：相対的な価格および限界生産物（marginal product）を用いる。

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