On the Relationship between Embodied Energy, Maintenance Power and EROEI for Energy Generation
Some time ago my article Efforts to Maintain a Material World pondered on the energy expenditure per annum, or maintenance power, to sustain a certain material standard of living characterised by the embodied energy of all its material assets. Related to that subject, I recently came across the article Lotka’s wheel and the long arm of history: how does the distant past determine today’s global rate of energy consumption? by Timothy Garrett, Matheus Grasselli, and Stephen Keene. The paper posits a proportional relationship between annual energy consumption and historically cumulative production. This story tries to combine both articles with the concept of Energy Return on Energy Invested (ERoEI) all for energy generation infrastructure in order to derive the limits of economic growth given diminishing ERoEI due to environmental degradation, resource depletion and waste production.
Garrett et al claim: “a new macroeconomic quantity — historically cumulative production — that we demonstrated to have had a quantifiable constant relationship with world primary energy resource demands, or civilization’s collective power.” It was found that the historically cumulative production expressed in a currency appears to be proportional to civilisation’s power consumption, the average power measured in Terra-Watts, or Exa-Joules per annum; conversely, civilisation’s power consumption is proportional to the historically cumulative production and not, as one would have thought, to the annual production, e.g. the global gross domestic product (GDP). There are interesting consequences for capital creation, capital creation rate, economic growth and inflation as well as to the limits of growth. I had to read the paper several times to understand all the subtleties.
Material Decay Equals Power
My interpretation of historically cumulative production is that of the historically cumulative material items, as an integral, the sum total of all of civilisation’s efforts that have used energy to transform matter into items, i.e. ore into metals and metals into goods, or clay to bricks and bricks to buildings, but also wheat into flour and flour into bread. Continuous production throughout our civilisation’s history resulted thus in material items such as industrial and domestic infrastructure, assets proper, but also more volatile items such as consumables, all with an embodied energy: bricks, mortar, concrete, steel, cars, trains, computers down to bread and butter. With Eᵢ(t) being the embodied energy in Joules of each item at a given point of time t, the total embodied energy of all conceivable items can be expressed in a thought experiment as:
All these material items are subject to a certain decay, either naturally through wear & tear or simply by consumption. Iron rusts, wood rots, stone withers and glass shatters, bearings, joints and tyres wear, and bread & butter get eaten. Some material items enjoy a long life time, others, such as consumables, have a very short life time; it is all a matter of time constants associated with every material item. Assuming some form of decay or use, the amount of embodied energy in any material item decreases according to functions that govern the loss of embodied energy. For simplicity, let’s assume some kind of linear decay as a function of time t over the life time Tᵢ for each item with an initial embodied energy of Eᵢ⁰. This loss in embodied energy can be expressed as a change of energy equally distributed over its life time as “loss power”:
Should a certain material status quo have to be maintained, a commensurate amount of power is needed to keep the level of embodied energy constant, i.e. to compensate material decay, e.g. repair, refurbishment, recycle, or replacement. That said, the world’s power consumption, or the world primary energy resource demands (energy per annum = average power) are related to the energetic decay of all accumulated items, i.e. the historically cumulative production. In such a stationary state, all economic activity (GDP) then serves the maintenance of a status quo. Only surplus power leads to true GDP growth, i.e. growth rate above inflation rate; true GDP growth is proportional to the difference of civilization’s collective power and material asset decay (energy dissipation). As for the world, Garrett et al quantify their claim:
in each of the 50 years following 1970 for which reliable data are available, 1 exajoule of world energy was required to sustain each 5.50 ± 0.21 trillion year 2019 US dollars of a global wealth quantity defined as the cumulative inflation-adjusted economic production summed over all history.
Eventually, the accumulated material wealth for a complex civilisation network reaches a limit when the available power equals the decay (and dissipation) of the embodied energy; there is only enough power available to keep things the way they are. No surplus energy per time unit is available for real systemic growth any more. This is akin to a thermal problem: given a certain amount of heating power, the maximum temperature of matter is reached when the power input compensates the thermal losses, i.e. the system is balanced. Another example could be a leaky bucket: at low filling levels, a certain influx will increase the water level; the maximally attainable filling level is reached if the influx compensates the losses such as consumption, evaporation or leaks.
The Limits of Loss and to Growth
How does the previous section on material decay and power loss relate to ERoEI? Well, given its definition, the ratio between energy return Eᵣ to energy invested Eᵢ, or ERoEI = η = Eᵣ/Eᵢ, the net energy Eₙ can be obtained for an installed energy generation capacity Eᵣ as:
To present some concrete values, in the early days of oil production an ERoEI of 100 and above was not uncommon; however, with more recent enhanced recovery techniques for shale oil and fracking, the ERoEI has fallen to values as low as 5. Renewable energy sources in contrast have an ERoIE of about 10–20, depending if energy storage is accounted for or not. On the other hand, bio energy like bio diesel or corn ethanol achieve an ERoEI of about 0.8–1.6; for instance, an ERoEI of 1.2= 6/5 translates in needing 5 units of energy to produce 6 units in total with 1 unit net energy. If the ERoEI falls below the break-even point of 1, then more energy needs to be spent than can be returned, e.g. 0.1–0.7 for algae derived energy.
In a stationary state, the net energy Eₙ over the energy production asset’s life time T has to equal the power requirement in order to maintain a status quo as stated above for the embodied energy of all items:
Combining all equations, the installed power production capability required to maintain the status quo becomes:
The required energy generation capability is proportional to:
- the sum of all material items (assets and consumables) weighted by the inverse of their time constants; this means, a) the fewer and smaller items the better (e.g. fewer cars, small cars and by no means SUVs!), i.e. reduce & reuse, and b) long life time, i.e. longevity by design.
- the ratio of η/(η-1) is critical; a small value of η, the ERoIE, perhaps close to 1 means that the amount of installed power becomes infinite; in other words, the smaller η, the more energy generation capacity.
The bottom line is, with resource depletion for important materials such as copper or lithium as well as oil & gas, the ERoIE becomes smaller, requiring even more energy generation assets that need more resources, resulting in more depletion and consequently in a decreasing ERoEI: energy requirements spirals out of control and are likely to lead to a Seneca collapse, similar to an outcome predicted in the Business-as-usual model in Limits To Growth (original and updated versions). This happens through an initial positive feedback mechanism coupled with a combination of delayed negative feedback (pollution) and non-linear elements in the loop such as saturation (depletion puts a clamp on resources).
Since renewable resources on the planet are limited, the consequence is that the total amount of material assets that can sensibly be maintained has to decrease at least in step with an ERoEI decrease. In other words, the total amount of material assets available to our civilisation is limited by the ERoEI; we’d better get used to that idea and evolve humanity towards a much smaller footprint. This would require unlikely societal changes.
