The Iron Law Of Power Density, Part 2

A look at EROEI and material intensity per megawatt-hour

Discarded wind turbine blades near Sweetwater, Texas, in 2021. Photo by author.

My August 13 article, “The Power Of Power Density,” is the second most popular article I have published here on Substack. The article struck a chord. Why? I suspect that lots of people want to have a better grasp of the physics that rule our energy and power systems.

As I explained last week, power density is perhaps the most important — and yet least understood — metric in physics. Indeed, many people who work in the energy and power sectors don’t understand it. In addition, the Iron Law of Power Density  — which says the lower the power density, the greater the resource intensity — helps us understand why wind and solar energy cannot, will not, ever be able to power our society. In addition to their incurable intermittency and dependence on the weather, they require too much land and other resources.

Given the favorable response to last week’s posting, I am going to expand on it here. First, I’ll explore another key metric: energy return on energy invested or EROEI. Like power density, EROEI is a critical tool for understanding why our energy and power systems continue to be dominated by hydrocarbons and why we should be focusing our efforts on natural gas and nuclear energy.

In addition, I am publishing two new graphics. The first is an updated resource intensity graphic that looks at electricity generation capacity, measured in kilograms per megawatt. The second graphic looks at the resource intensity of electricity production by measuring it in kilograms per megawatt-hour of energy produced. Spoiler alert: the new graphic shows even more clearly why offshore wind is such a loser.

Before diving into EROEI, a quick refresher: power density is a measure of energy flow that can be harnessed from a given area, volume, or mass. Thus, power density can be measured in watts per square meter, per liter, or per kilogram. I largely focus on areal power density — measured in watts per square meter — because it is the key to understanding land use and why the paltry power density of wind and solar has led to land-use conflicts from Erie County, Ohio to the Golan Heights. If you want to dive into volumetric and gravimetric power density — measured in watts per liter or watts per kilogram, which are essential to understanding motors and engines — I suggest you read my fifth book, Smaller Faster Lighter Denser Cheaper: How Innovation Keeps Proving the Catastrophists Wrong.)

Now, EROEI.  The importance of this metric is obvious: we want maximum return on the cash we put in the bank or the stock market. We also want maximum return on the energy we spend. Just as it takes money to make money, producing energy always requires using energy. Whether it’s chopping wood for the fireplace, the diesel fuel needed to run the generators that power a drilling rig, or the electricity needed to spin the centrifuges that enrich the uranium fuel that we put in our nuclear reactors, we have to spend energy to get energy. And the less we have to spend, the better.

As can be seen in the graphic above, wind and solar have a woefully low EROEI of 3.5:1, that is, for every unit of energy put into wind and solar, you get 3.5 units of energy out. Meanwhile, nuclear has an EROEI of 100 to 1.

Many analysts and scientists have written about EROEI, but one of the best explorations of the topic was published last year by Leigh Goehring and Adam Rozencwajg. In their essay, “The Distortions of Cheap Energy,” which is the source of the numbers in the graphic, Goehring and Rozencwajg wrote that the explosion in global economic growth that has occurred over the past 140 years or so “was entirely driven by improving EROEI. The modern world we enjoy today is the direct result of efficient and abundant sources of energy.” (Adam Rozencwajg was on the Power Hungry Podcast on January 17 talking about EROEI and other topics.)

Goehring and Rozencwajg, who run a New York-based investment firm of the same name, regularly publish analyses on trends in energy and natural resources. They continued their essay by listing the enormous amount of stuff needed to make a 1.5-megawatt wind turbine: 235 tons of steel, 600 tons of concrete, 15 tons of carbon fiber, and nine tons of copper. They sum up the problem by concluding that it would take 10 wind turbines to replace the energy produced by a single oil well in the Permian Basin. They go on:

Much of Europe’s energy crisis today is related to their massive renewable investment, all of which sports an extremely low EROEI. The questions we get asked the most are: “How could renewables possibly have such poor EROEI without anyone realizing it, and how could so much renewable investment be made with so little recognition of the problem?”

They then talk about the factors that are now coming back to haunt the wind sector, and in particular, offshore wind:

Our modeling suggests that declining (and cheap) energy prices have distorted and partially hidden the true costs of wind and solar over the last decade. Now that energy costs have surged, the true cost of installing and operating renewables are obvious. The relationship between energy input costs and the cost to produce renewable electricity is based upon our propriety research. We have not seen this argument laid out anywhere before, but the more we study the issues the more we’re convinced we are correct... Amazingly, no one has connected declining energy costs and cheap capital with the proliferation over the last decade of energy-hungry, capital-intensive projects such as wind, solar, and lithium-ion battery manufacturing. We think the two are fundamentally linked. What will happen when energy prices normalize and interest rates rise — as is happening right now?

They continued, writing. “It is no coincidence that the proliferation of renewable energy occurred during a decade of abundant cheap energy and abundant cheap capital. As both resources become scarcer and more expensive, the inherent limitation of renewable energy (i.e., its significantly worse EROEI) will come to the fore.”

By now, it should be easy to see how the Iron Law of Power Density and EROEI fit together. Low power density sources like ethanol, biomass, wind, and solar, require more resources like steel, concrete, copper, and zinc. All of those resources require expending energy. Therefore, EROEI can be interpreted as a way to prove the Iron Law of Power Density. Why? The greater the resource intensity (read: energy-hungry ingredients) the worse the EROEI.

Goehring and Rozencwajg concluded their essay with a point that I have been making since 2008: we need to embrace nuclear energy. They wrote, “We have long argued that nuclear must be part of any energy future — green or otherwise. No other energy source offers superior energy return on energy investment…than nuclear power. Furthermore, no other energy source can dispatch the carbon free baseload power needed to run the modern world.”

Now, to the graphics. I updated the graphic above, a version of which was published last week. As you can see, I added a call-out bubble to underscore the 13 times difference between offshore wind and natural gas-fired generation.

After getting some constructive criticism about that graphic, which uses a screen grab from this 2021 International Energy Agency report, I decided to take another stab at the resource intensity of electricity generation by calculating the amount of metals and minerals that are needed per unit of energy produced. I discussed this idea with my friend, Roger Pielke Jr. (who coined the Iron Law of Climate Change). Roger, who holds a degree in mathematics, agreed to combine the IEA’s numbers of resources with the capacity factors for those forms of electricity generation.

Capacity factor is another critical metric needed to understand our energy and power systems. Capacity factor measures how much energy is produced by a given power plant relative to how much it can produce at peak capacity. Solar plants have relatively low capacity factors because the sun doesn’t shine at night. Coal and nuclear plants generally have high capacity factors because they often provide baseload power and their output doesn’t depend on the weather. The capacity factors used in the graphic came from a paper published last year in the Proceedings of the National Academy of Sciences that was authored by Natanael Bolson, Pedro Prieto, and Tadeusz Patzek.

As can be seen above, when you include capacity factors for the various forms of generation, offshore wind looks even worse than before, requiring about 27 times more metals and minerals per unit of energy produced than gas-fired generation and more than 10 times more than what’s needed for coal and nuclear plants. This helps explain why so many offshore projects are now in financial trouble.

In their paper, “Capacity factors for electrical power generation from renewable and nonrenewable sources,” Bolson and his co-authors write that “capacity factors are needed for an accurate quantification of the nominal generation capacity needed to replace and expand the current electricity infrastructure.” They looked at global capacity factors for “biomass, fossil fuels, geothermal heat, water, uranium, solar light, and wind over the period 2000–2017. Global and regional values are estimated to highlight the differences in the performance of different technologies. These average CF values are then used to calculate the required nominal capacity to be installed in the future for our unavoidable energy transition.”

Using the capacity factors from the PNAS paper, Roger made a couple of assumptions. The first: gas-fired generation requires one kilogram of metals and minerals per megawatt-hour. He also assumed 1,000 megawatts of capacity for each technology with the power plants operated for one year. The results are eye popping. Solar energy requires about 27 times more metals and minerals than gas and onshore wind requires about 19 times more. Even if these calculations overstate the differences among the different energy sources by 20% or 30%, they still show why solar and wind are the wrong way to go.

In summary, whether we are looking at our energy and power systems through the lens of EROEI, or material intensity of generation capacity, or material intensity of electricity production, the conclusions are irrefutable: the Iron Law of Power Density will not be repealed. If we are serious about cutting emissions, land sparing, preventing the industrialization of our oceans, saving the North Atlantic Right Whale, saving Bald and Golden Eagles, protecting bats, and reducing the amount of mining we have to do to produce the metals, minerals, and magnets needed for our energy and power systems, the way forward is now — and always will be — N2N: natural gas to nuclear.

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2. A personal note: Check your smoke detectors, y’all. On August 2, at about 3 am, Mary’s house in Los Angeles burned. Thankfully, miraculously, she and Jake Miles were not injured. They were able to save some things, including their passports, wallets, and guitars, but they lost a lot of possessions. That fire, and the deadly fire in Maui, are a reminder that we need to be prepared. I just installed two new smoke detectors and a new CO detector. I also got two fire extinguishers and put them in places where they are easily reached. Test your detectors. Make sure they have fresh batteries. Thousands of people die every year in house fires. Many others die of carbon monoxide poisoning. Don’t be one of them.