Dupont, Koppelaar and Jeanmart (Applied Energy 257:113968, 2020) quantified the globally available solar energy under land-use, irradiation, technology and net-energy constraints and found the result acutely sensitive to the assumed minimum energy return on investment (EROI, the ratio of energy delivered over a system's lifetime to the life-cycle energy invested in it): of a constrained potential of about 1098 EJ per year, 98%, 75% and only 15% can be extracted if the system must deliver an EROI of at least 5, 7.5 and 9, respectively. Which cut-off is correct is unknown, and the paper's explicit open question is what EROI level is sustainable for society and what befalls an energy system that falls below it. This problem record poses that question: determine, at an explicitly justified system boundary, the minimum EROI a sustainable society must maintain, with uncertainty, determined rather than assumed from prior literature; and quantify the implications — how much of the physical solar resource should be counted as available to society under the determined threshold, and what changes in the energy sector's claim on economic output, in net energy delivered to end uses, and in transition feasibility follow for a system operating below the cut-off. The question remains open: proposed thresholds span roughly 3:1 to beyond 15:1, depend on contested boundary conventions, and recent work (useful-stage and societal EROI accounting, dynamic transition models) has sharpened but not settled it.

Background

Every energy-conversion system spends energy to deliver energy: manufacturing, transporting, maintaining and decommissioning solar panels, wind turbines or fuel-extraction infrastructure all consume energy. The energy return on investment (EROI) is the ratio of the energy a system delivers over its lifetime to this life-cycle energy investment, accounted cradle to grave from raw-material extraction to decommissioning; the net energy is the surplus that remains available to the rest of society once the energy sector's own consumption is paid. Because society runs on net rather than gross energy, several authors have proposed a law of minimum EROI: below some threshold, the share of economic activity that must be diverted to obtaining energy grows so large that the structure of the economy changes. Hall, Balogh and Murphy (2009) made a first quantitative estimate of about 3:1 at the point of extraction for oil and corn ethanol; Hall, Lambert and Balogh (2014) reviewed the implications of declining EROI for society; Lambert et al. (2014) found correlations between national EROI and quality-of-life indicators and speculated that values near 15 would be needed to support arts and leisure activities; Fizaine and Court (2016) connected the minimum EROI of society to energy-expenditure and economic-growth constraints. A persistent complication is that EROI values depend strongly on where the system boundary is drawn — at the point of extraction, at the delivery of final energy to consumers, or at useful energy after end-use conversion — so any threshold must be defined jointly with its boundary.

Dupont, Koppelaar and Jeanmart (2020) assessed the global solar resource under these net-energy constraints. They used a global grid-cell methodology (dividing the land surface into cells and applying land-use, slope, protected-area and irradiation constraints), life-cycle energy-input inventories for the main commercial photovoltaic (PV) technologies and for concentrated solar power (CSP, in which mirror fields concentrate direct sunlight to drive a thermal power cycle, optionally with molten-salt thermal energy storage), and produced a potential-EROI curve: the amount of electricity extractable as a function of the minimum EROI demanded of the system. The constrained global potential is about 1098 EJ per year (1 EJ = 101810^{18} J), several times current annual world final-energy use, but 98%, 75% and only 15% of it survives if the system must deliver an EROI of at least 5, 7.5 and 9, respectively. The sensitivity is strongest in low-irradiation regions, and Europe holds only about 2% of the global net solar potential. The nonlinearity is intrinsic: the net energy delivered per unit of gross output scales as 1−1/EROI1-1/\mathrm{EROI}, which steepens sharply at low EROI, so modest changes in the cut-off swing the counted resource by large factors.

The parameter that decides this result — the minimum EROI that a sustainable society actually requires — was left open. The paper's concluding open question is what EROI cut-off would be sustainable from a societal perspective, and what the implications are of an energy system falling below this cut-off. Subsequent work has sharpened the surrounding debate — useful-stage EROI accounting, societal EROI measurements, dynamic net-energy transition models — but the threshold itself remains an assumed, contested parameter, so the amount of solar energy that should be counted as genuinely available to society is still undetermined.

Problem Statement

What EROI (energy return on investment: the ratio of the energy a system delivers over its lifetime to the life-cycle energy invested in building, operating and decommissioning it) cut-off level is sustainable for society, and what happens when an energy system falls below it? A complete answer must (i) determine, at an explicitly stated and justified system boundary (point of extraction, final energy delivered to consumers, or useful energy after end-use conversion) and under an explicitly stated and justified criterion for societal sustainability, the minimum EROI that a sustainable society must obtain from its energy system, with its uncertainty, determined rather than assumed from prior literature (for example through derivation from energy-system and economy models or empirical calibration against historical energy-economy data); and (ii) quantify the implications of this threshold: how much of the physically constrained global solar resource (the roughly 1098 EJ/yr potential, of which 98%, 75% and 15% survive at EROI cut-offs of 5, 7.5 and 9) should be counted as available to society under the determined threshold, and what changes — in the fraction of economic output absorbed by the energy sector, in the net energy delivered to end uses, and in the feasibility of the energy transition — are implied for a system operating below the cut-off.

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