Digesting ‘Quantification of energy and carbon costs for mining cryptocurrencies’

Unpacking the article in Nature

Earlier this month, Max Krause and Thabet Tolaymat published an article in the well-regarded journal Nature concerning the energy costs of mining cryptocurrencies. Unlike much of the scholarship concerning the energy costs of PoW-based cryptocurrencies, this article wasn’t immediately odious to industry practitioners — it was in fact methodologically sound, for the most part, and generally quite edifying. However, media coverage of the article was less restrained. In their coverage of the paper, the Guardian conveniently forgot to mention that the paper describes the energy cost per dollar-weighted unit, not as an aggregate like they imply:

If you still have a shred of respect for our beloved tech media, feast your eyes on this economically illiterate take:

So what is the significance of the article? Do the energy differences in per-Dollar-of-output mining costs among different metals really matter? I popped the article into Sci-Hub (information deserves to be free) and decided to find out for myself.

The article in plain language

I’d encourage you to read the paper for yourself — it’s quite accessible and not overly long. I’ll briefly summarize it here.

The authors start by describing the purpose of PoW and note that most major Proof-of-Work cryptocurrencies behave like virtual commodities or precious metals like gold. They correctly note that a comparison with Ripple is impossible because it voids the distributed trust-creation mechanism of PoW in favor of a centralized authority. The authors describe the economics of PoW and note that comparing hashrates between different hash functions is not appropriate (a common mistake made by analysts!).

They use the bottom-up estimation method used in previous analyses, dividing total hashrate by typical ASIC hashrates to find the number of operational ASICs and their resultant energy requirements. They conclude that in 2017, Bitcoin used about the same amount of energy as Angola or Panama (ranked 102–103 in the world for energy usage). They make their first slight misstep by extrapolating this figure to the whole crypto market, naively using Bitcoin’s share of total market cap to derive a general energy expenditure figure.

The market capitalization of all cryptocurrencies is approximately US$250 billion, with Bitcoin comprising approximately 50% of that value. If we assume that Bitcoin accounted for 50% of the entire crypto-energy consumed in 2017…

This isn’t appropriate, as a significant fraction of total market cap is held in assets that are not PoW mineable — Ripple, Stellar, IOTA, EOS, Cardano, BNB, NEO and Tether — just to name a few in the top 15. So Bitcoin’s energy use doesn’t generalize to the whole market. This isn’t critical to the analysis, so it’s not a big deal.

The authors helpfully tabulate other prior estimates of Bitcoin’s energy usage, demonstrating the significant challenges involved in getting plausible estimates of energy usage.

Krause and Tolaymat, 2018

Then we get to the meat of the analysis. The authors wanted to compare the energy requirements of mined cryptocurrencies to other energy-intensive commodities, so they benchmarked Bitcoin, Ethereum, Litecoin, and Monero’s energy demands against those required for aluminum, copper, gold, platinum, and rare earth metals. Importantly, they didn’t look for gross or aggregate figures, seeking instead the energy requirements to mine $1 worth of each. This gives us a stable basis for comparison.

This gives us this rather pretty chart:

Krause and Tolaymat, 2018

It’s important to note that the authors are not conducting a whole lifecycle analysis of the energy costs of extracting the commodities on the right. For instance, a complete analysis would consider the cost of paving roads to the mine, the energy costs to build the Caterpillar mining equipment, and so on. They limited themselves to the more direct energy costs as found in the literature.

The authors then attempt to determine the carbon emissions of each cryptocurrency in their sample. They already have the electricity usage numbers within a high degree to confidence, so all that remains to do is determine the energy mix responsible for that electricity. They take country-specific carbon emissions from a nine-year-old study (ok, not ideal, but I’ll let it slide), and find kilograms of CO2 emissions on a per-mined-coin basis.

Krause and Tolaymat, 2018

According to this chart, a Bitcoin mined with electricity deriving from the Indian grid (very fossil fuel intensive) would result in the release of something like 6400 kilograms of CO2. Yikes. By contrast, that number would be closer to maybe 1300 kilos of CO2 if mined with Canada’s energy mix. Better, but not… great. These countries were picked as the upper and lower bounds quite deliberately:

As the location of each miner cannot be determined, the attribution of emissions can be only broadly estimated. In this case, we estimate using the highest and lowest country-specific emission factors (India and Canada, respectively) as the upper and lower bounds…

So we have a rough order of magnitude estimate of CO2 emissions for Bitcoin mining, with the actual number presumed to be somewhere in the middle.

From a data visualization perspective, this chart rankles me a bit, since the authors did such a good job of standardizing earlier. Here they use the very arbitrary unit values for the four different coins (which is why Litecoin looks to have such low relative emissions — because LTC is priced more cheaply per coin!). Instead, this should have been standardized, again, by the emissions required to produce $1 worth of each cryptocurrency.

The authors conclude by estimating that Bitcoin between 2016 and 2018 accounted for between 3 to 15 million tons of CO2 emitted as an externality of mining. Let’s call it 10 million tons of CO2 per year right now, for the sake of argument. According to this dataset, the US emits 5,311 million tons of CO2 per year. So according to this paper, Bitcoin mining would represent about 0.19 percent of US yearly carbon emissions, or about one 500th.

To their credit, the authors admit that the energy mix calculation is imprecise, and that the economics of Bitcoin mining encourage the energy arbitrage:

…[S]ome industrial-scale operations are moving from China to Canada to take advantage of cheaper and cleaner energy.

Interestingly, the authors echo a common talking point in the industry that the existence of PoW-based cryptocurrencies, while a driver of externalities, may still be socially valuable.

The worldwide mining of cryptocurrencies is currently performed for self-gain but this alone does not preclude it from potentially benefiting society.

So we have a fairly sober analysis that delivers real numbers and ultimately settles on a mixed message: these things do have real externalities, but they can be mitigated by greener energy inputs.

Methodological criticisms

Now I would be remiss if I didn’t touch on a few methodological issues. First, I’d like to thank the authors for making their data available. That makes auditing the study much easier.

There are a few obvious issues. The first, as I already mentioned, is the authors’ naive extrapolation of Bitcoin’s energy demands to the broader cryptoasset market on a market cap basis. That just doesn’t work.

The second — and again, not a major issue, but a noteworthy one nevertheless— is the exclusion of fee data from miner revenue. The authors just aggregate the number of newly-minted coins as a proxy for miner revenue. While that’s ok for an approximation, fee revenue was indeed meaningful on BTC (and Ethereum, to a lesser degree) during the sample period.

The fraction of BTC miner revenue deriving from fees, Coinmetrics.io

Fees were consistently above 1% as a percentage of overall miner revenue, and indeed stretched to 20–30% for extended periods in 2017. Of course, excluding fee revenue data biases the estimates of Bitcoin carbon emissions downwards, so perhaps cryptocurrency enthusiasts should be cheering the omission. But, sound methods matter most.

I spot checked the author’s numbers on generated coins, and they were correct. I’m glad they didn’t use the naive block reward * ideal block time calculation. That trips people up quite frequently. In practice, Bitcoin issuance is slightly faster than expected, since new hashpower is almost always coming online, and it can only adjust itself every 2016 blocks.

Additionally, I’d question the author’s omission of energy from cooling in Bitcoin mining. That seems like a very direct part of the mining lifecycle and probably merits being included.

The most significant quibble I have with the paper itself is the energy mix figures. For the electricity use derivation, the authors use a bottom-up method, which grants the most accurate results. However, for the CO2 emissions section, they use a disappointing top-down method, rather bluntly assuming that miners use some variation of the average energy mix employed by Canada, Korea, Japan, USA, China, Australia, or India.

This isn’t the case, of course. Bitcoin mining is highly idiosyncratic, and it seeks out ubercheap energy sources and even liberates stranded energy assets. This stranded energy is often hydro, as is the case with the miners in Szechuan province, upstate New York, the Pacific Northwest, or Quebec. It’s well known that there are significant mines in Iceland which use geothermal energy or hydro (interestingly, repurposed from aluminium smelters!).

Increasingly, entrepreneurs are finding ways to capture even more exotic energy assets. There are multiple businesses today looking to build significant Bitcoin mining operations using waste methane emanating from oil wells which would otherwise be vented (this is often the case with off-grid wells — there is simply no ability to capture the methane). Of course, combusting methane has externalities of its own, but pure methane being vented to the atmosphere is destructive too. This is just one way in which Bitcoins location-agnosticism can make it amenable to liberate stranded energy assets.

Of course, I don’t have the numbers on Bitcoin’s actual energy mix. No one does. But using idealized, top-down estimates from a variety of countries isn’t very useful. Bitcoin has quite unique characteristics and eats up energy resources in a very peculiar way. I have heard of seasonal migrations of ASICs within China to capture hydro in one season and excess wind resources in another. There are wind farms being built in Morocco which will use Bitcoin to monetize excess energy. For a long time, Bitcoin was mined with massive quantities of grey/black market hydro in China which would have otherwise gone to waste. Plans to repurpose a massive hydro-powered former aluminum smelter in upstate NY for Bitcoin mining are underway.

An analysis that we would all benefit from, skeptics and proponents alike, would be an honest, bottom-up effort, which captures data from actual miners in the field. These top down assessments are interesting thought experiments, but have no plausible justification.

General comments

Overall, I found the study very interesting, and I’m glad it was written. I have certainly been critical of some of the scholarship and amateur blogging which targets Bitcoin or Proof of Work in the past, but the authors in this case were arguing in good faith, with the best available data.

However, the same cannot be said for the media, which picked up the story with aplomb. The futurism article linked at the beginning of this piece relies on a simple misunderstanding of how these industrial processes work. Yes, Bitcoin uses more energy, per dollar of the commodity mined, than gold, but that doesn’t make Bitcoin any more or less efficient than gold. It just means that the energy-related variable costs involved in Bitcoin mining are proportionately higher than those in gold. Energy resources aren’t globally fungible, and commodities aren’t uniformly distributed, so you cannot simply repurpose energy resources for Bitcoin and extract gold instead.

The Guardian article was particularly entertaining.

They conveniently omit the most energy-hungry resource of them all, aluminum, from the chart! It uses a mammoth 110 megajoules to create $1 worth of the metal. (A quick note on aluminum: it’s not the mining of the bauxite ore which is expensive, but rather than smelting technique involved in actually creating aluminum from the ore. So to say that aluminum mining is energy intensive is a bit misleading.)

My general response to the media coverage of this topic is bemusement. All the authors proved in their study is that Bitcoin has a high opex-to-capex ratio, relative to some of its commodity peers (but not aluminum). I’ve summarized the data in the below chart.

Source: Krause and Tolaymat, own calculations

According to this chart, if you have access to electricity at 4 cents per kilowatt hour, you could mine $1 worth of Bitcoin for 21 cents! Not a bad deal, eh? Well, you also have to acquire the hardware, pay maintenance staff, cool the rigs, build housing, and so on. Since mining occurs close to breakeven today, it’s fair to assume that these non-electricity costs make up most of the difference. Assuming that the average Bitcoin is mined at 5 cent-per-kilowatt hour electricity, we arrive at a 1:3 ratio of pure electricity cost to capex/admin cost. In fact, this is in line with what I had heard anecdotally, so it is interesting to see the numbers apparently demonstrate this.

This is certainly interesting information, but it doesn’t tell us much about Bitcoin’s sustainability, per se. What absolutely matters is the energy mix used to find the energy, and this article didn’t make a concerted effort to find those real-world numbers.

A note on aluminum

The aluminum case study is interesting. Converting bauxite to refined aluminum is an expensive, energy-intensive process. Historically, aluminum catalyzed the same global energy arbitrage that Bitcoin now benefits from — for a while, Iceland was a net energy exporter to China through the medium of aluminum. A much larger fraction of the cost to create one kilogram of aluminum consists of electricity than other metals, and so smelters adapted to locate themselves in areas with abundant or cheap energy. At maturity, I’d expect Bitcoin to look a lot like this.

Moreover, since Bitcoin doesn’t require heavy equipment, land management, smelting/refining, or physical transportation, it is utterly unsurprising that energy costs are a higher share of the total cost to create than its tangible peers. As Bitcoin matures, and ASICs become more commoditized, the electricity cost input will rise relative to the other overheads (hardware, admin, staff, etc).

The important thing to keep in mind here is that if something is worth $1 on the open market, absent barriers to entry, roughly $1 will be expended to acquire it. Bitcoin is a very free market; all you need to participate is electricity and an ASIC. Margins, as a consequence, are quite thin. Most commodities are similar, although their industrialization allows for potentially fatter margins. But the core identity is much the same. Of the ~$1 which is spent to acquire that $1, some amount will be energy, and some amount will be other costs. Bitcoin happens to be tilted more heavily to the energy side rather than the physical overhead side of the continuum, since Bitcoin is a relatively pure process of transmuting hashes into value.

At 5 cents per kilowatt hour, one quarter of Bitcoin miner expenditure will be spent on electricity; is this high? Relative to gold, yes. Relative to aluminum, no. To conclude: while the study was quite edifying, I wasn’t impressed with the carbon emissions conclusion, which was a rather haphazard top-down analysis. I’m still waiting eagerly for a bottom-up analysis of miner energy sources; that will be a tremendously useful study, and free us from relying on proxies. In general, it’s important to consider the full context when reading these articles, and where possible, to go right to the source.

Thanks to Hugo Uvegi for the feedback.