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The energy growth paradox

Albert Einstein claimed,  “The most powerful force in the Universe is compound interest.” He referred to it as one of the greatest “miracles” known to man. And long before Einstein,  Benjamin Franklin said “Money makes money. And the money that money makes, makes money,” with reference to compound interest. It is a principle based on the Rule of 72 which says 72 divided by the interest rate of a loan equals the number of years for the investment to double in value.   

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Another quote attributed to Einstein with respect to compound interest is: "He who understands it, earns it; he who doesn't, pays it."

Clearly, it is tremendously important on which side of the debtor/creditor seesaw one is sitting.

Exponential growth, the basis of compounding, however, doesn’t apply only to interest. It is germane to viruses and even more  importantly global sustainability.

It can be insidious as has been brought home this year with COVID-19, where from a base of a single case on January 22, 2020 the cases have compounded at a rate of 4.61% a day to 118,769,551 with 2,634,414 deaths as of March 11 per the following graph.

But the insidiousness of this growth is reflected most in the daily increments. On March 9 there were 117,987,827; 781,724 less cases. And we are witnessing something similar with global warming. Although Thomas Newcomen invented the first steam engine in about 1712 to pump water out of a coal mine, ushering in the Industrial Revolution, it wasn’t until about 40 years that the Earth’s surface temperature really started rising.

And this rise can only increase in a business as usual scenario.

As awful as COVID-19 has been, no less than Bill Gates and Mark Carney, the UN’ Special Envoy on Climate Action and Finance say climate change could be worse.

Tom Murphy, professor of Physics, University of California, San Diego, in his presentation Growth has an Expiration Date and in his blog Do the Math, shows how the Earth’s physical resources—particularly energy—are also limited by exponential growth, which may prohibit continued economic growth  within centuries, or possibly earlier depending on the choices we make.

Murphy juxtaposes the issue from the viewpoint of an economist: who thinks energy will never be a limiting factor to economic growth because we can substitute non-conventional resources like tar sands, oil shale, shale gas, etc. for conventional oil and gas and when these run out, we’ll have wind, solar, and geothermal energy—plus next-generation nuclear fission and potentially nuclear fusion or even something that hasn’t even be considered.

Which is the view of the majority of us.  

And from his position as a physicist: where he says: “Sure, those things could happen, and I hope they do at some non-trivial scale. But let’s look at the physical implications of the energy scale expanding into the future. So, what’s a typical rate of annual energy growth over the last few centuries?

And he answers this question with the following graph that shows the total U.S. Energy consumption in all forms since 1650.

Source: EIA

The vertical scale of this graph is logarithmic, so the growth rate appears as a straight line. The red line corresponds to an annual growth rate of 2.9%. But linearly it is clear how aggressive this growth has been per the following.

Murphy then shows the thermodynamic impossibility of energy growth at historical levels in the following graph.

For a matter of convenience, he lowered the rate from 2.9% to 2.3% per year to show how every 100 years the growth would increases tenfold at the historical pace.  Starting  from 2012, the date of his presentation when the global rate of energy use was 12 terawatts (2,000 watts for every person on the planet).

In 400 years, we would have to cover every square meter of the  Earth’s surface to produce the requisite energy. And in 2500 years we would need the energy produced by every star in the Galaxy.

To put such a time span into perspective, 2500 years ago ancient Greek civilization was just beginning.

As Murphy points out we will soon cook ourselves with perpetual energy increase that obey the laws of thermodynamics.

In his contrived Economist/Phsycist debate, the Economist asks, “Could not technology pipe or beam the heat elsewhere, rather than relying on thermal radiation?”

The Physicist responds: “Well, we could (and do, somewhat) beam non-thermal radiation into space, like light, lasers, radio waves, etc. But the problem is that these “sources” are forms of high-grade, low-entropy energy. Instead, we’re talking about getting rid of the waste heat from all the processes by which we use energy. This energy is thermal in nature. We might be able to scoop up some of this to do useful “work,” but at very low thermodynamic efficiency. If you want to use high-grade energy in the first place, having high-entropy waste heat is pretty inescapable.”

Which is the point at which, in the humble opinion of this observer, Murphy goes off the rails.

First, there is no need to use high-grade energy and its inescapable waste heat to service a considerable portion of the energy demands of 10 billion souls.

Second, the flip side of exponential is growth is exponential depletion. The heat of global warming is a  resource going to waste that can be depleted through conversion to work in accordance with the laws of thermodynamics.  

Third, space isn’t the only place where heat can be beamed. It can be beamed into deep water with a heat pipe and converted to work and then recycled until the heat of warming has been sapped of every available watt of energy needed on landed before the waste of those conversions is dissipated to space. A process that will take upwards of 3,000 years, which make Murphy’s “total Galaxy” graphic moot.  

In The Motion of the Ocean segment of his blog, Murphy considers ocean thermal energy conversion (OTEC) and concludes, “I’m not sure why we’d waste our time on OTEC when there are better (cheaper) ways to collect the abundant energy of the Sun. OTEC has some advantage in not having to build the collector, and in the fluid delivery system, but this would seem to be a minor plus stacked against the operational disadvantages. OTEC deserves a spot in the abundant box, but practicalities limit its likely role.”

So, lets consider the operational disadvantage of OTEC as Murphy sees them:

  1. By his reckoning, the maximum thermodynamic efficiency tops out at 10%, and in practice we might get half of this in a real application. Which is true for conventional OTEC but not for a deep water condenser design where the 1000 meter long column of gas in the heat pipe gains about 5 degrees Celsius due to influence  of gravity. Which another physicist, Melvin Prueitt of Los Alamos Labs, makes for a real application thermodynamic efficiency of 7.6 percent for an ammonia working fluid.  
  2. How much energy is available? The corrected version of the Nature paper Quantification of ocean heat uptake from changes in atmospheric O2 and CO2 composition by Resplandy et al. shows that between 1991 and 2016 the change is ocean heat content was 1.29 ± 0.79 × 1022  Joules per year, which equates to 409 terawatts converted at an efficiency of 7.6 percent equals 31 terawatts, which is over twice what we are getting from fossil fuels. (As an aside, the Resplandy paper quantified ocean heat uptake on the basis of oxygen and carbon dioxide content. The cooler the ocean the less gas is vented to the atmosphere. The paper Negative-CO2-emissions ocean thermal energy conversion  shows for each gigawatt of continuous electric power generated over one year with NEOTEC roughly 13 GW of surface ocean heat would be directly removed to deep water which has ramification for cost. All other CO2 removal schemes are energy intensive (zero sum), produce waste heat, and are costly. Whereas Thermodynamic Geoengineering, sequesters atmospheric CO2, , produces energy, and depletes the heat of global warming at no additional cost.
  3. Since the energy produced is a quadratic function of ΔT, a temperate OTEC plant becomes seriously impaired in the winter.  Thermodynamic Geoengineering plants are heat grazers that move with the seasons to convert heat at the highest surface temperatures available.
  4. Operating and maintaining an offshore power plant in seawater, transmitting the power to land, dealing with storms and other mishaps are serious challenges. The petroleum industry has been operating in deep water for decades. The mass of Thermodynamic Geoengineering plants makes them stable in rough water, which is less problematic in the  Intertropical Convergence Zone where cyclones don’t form and where the conditions for producing power are best and abundant.
  5. He totally disregards the exponential nature of heat conversion; a significant benefit.

In Murphy’s Physicist/Economist scenario the debate goes:

Physicist: “Then in order to have real GDP growth on top of flat energy, the fractional cost of energy goes down relative to the GDP as a whole.”

Economist: Correct.

Physicist: How far do you imagine this can go? Will energy get to 1% of GDP? 0.1%? Is there a limit?

The better question the physicist might have asked is, what is GDP?

The IMF says we spend $5.3 trillion a year on fossil fuel subsidies. Here is costed 31,000 1 GW Thermodynamic Geoengineering plants which can be had for less that $5.3 trillion a year. Are these not therefore too cheap to meter. And what’s more Delton Chan  has devised a trackable digital currency, produced when a ton of carbon is eliminated from the atmosphere—when, for example, oil companies leave their reserves in the ground, forests are re-established, or machines filter carbon from the air.

In other words when we do the right thing, which requires producing energy that negates all of the problems produce by the production of energy.

As Murphy has observed, “we can not decouple from energy.”  Economic growth started outpacing energy growth around about 70 years ago but efficiency, a service sector, innovation, and information technology etc. can never become 100 percent of the economy as the following graphic demonstrates.

The green curve represents the scale of raw energy available each year, while the blue curve is the effective energy available through gains in efficiency. Regardless of timescale, the key feature is that the fraction of the economy that is independent of energy availability must grow to dominate all other activities in order to keep growth alive, here reaching 98% by the end of the century. This is an untested—and possibly physically untenable—economic state.

Instead of reducing energy consumption, according to .digitalinformationworld, the energy required by digital devices is much more (7%) than the global energy consumption all over the world (3%) and that the production and operation of Information and Communications Technology will rise to about 21% in 2030.

In other words, unstable growth.

Below left, graphically, Murphy questions what lays beyond fossil fuels?


Below right, this piece postulates that for at least the next 3,000 years we can derive twice the energy of fossil fuels, potentially at little to no cost, while setting the preindustrial clock back to zero.


Clearly, it is tremendously important on which side of the debtor/creditor equation one sits. The surest way to become a debtor is to be a consumer of fossil fuels or investor in existing carbon dioxide schemes.  Conversely, the planet prospers when it capitalizes on the most powerful force in the Universe and the energy paradox that the more energy is produced, the surface is cooled by converting the heat of global warming to the work planet requires with Thermodynamic Geoengineering.

It is the only energy that ticks all of the boxes : abundant, potent, and a mass market.

Jim Baird's picture
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