Saturday, March 17, 2012

17 November 2010 – Econothermodynamics, or why cheetahs can never prosper


While trolling the intertubes yesterday, I happened across a post on a website I check regularly -, run by former meteorologist Anthony Watts - that had been submitted by a regular guest-blogger, Willis Eschenbach.  

I was mildly surprised to come across a chart that looked a little familiar:

The chart, which Eschenbach linked to a Lockheed Martin site (although I didn't see any data there), reminded me an awful lot of a very similar chart that I had put together for a draft paper a year and a half ago:

(Source: Author, April 2009)

In drawing up this chart, I had used data from the BP Statistical Survey of World Energy (June 2008) and the online CIA Factbook.  For those unfamiliar with the terminology, KgOE/yr is “kilograms of oil-equivalent per year".

The two charts are essentially the same.  What they show, more or less, is a correlation between the amount of energy consumed per capita by a country, and its per-capita GDP.  They also show that, ceteris paribus, countries with equivalent per-capita GDPs may consume radically different amounts of energy, reflecting different geographic and environmental realities.  France and Canada, for example, have equivalent per-capita GDPs, but Canadians consume roughly twice as much energy per capita as the French.  One can speculate about the reasons for that, of course (three which come to mind are that Canadians have to deal with a harsher climate, have to cover longer distances for every conceivable purpose related to maintaining our civilization, and have a resource-intensive economy; Russia and Brazil share a similar apparent similarity) but it doesn't change the broad correlation.  The poorest countries consume the least energy per person; the richest countries consume the most.  That's a fact that's so commonly bandied about by politicians and bureaucrats at international shindigs that nobody spends a lot of time thinking either about the why and how of those consumption patterns, or about the arrow of causality - i.e., do rich countries consume a lot of energy because they're rich? Or, are they rich because they consume a lot of energy?

Most of the explanations of this phenomenon tend to be economic, with an exploitation/class-struggle flavour to them, i.e., rich countries supposedly consume a lot of energy because they exploit the efforts of the downtrodden.  I don't know about that.  The US buys more oil from us than from any other single country, and I don't feel particularly exploited by Washington, except that I would really like it if they let the Olive Garden came back to Ottawa.

What made Eschenbach's chart interesting was the fact that it was accompanied by a couple of citations from a paper thattakes a different approach to explaining the correlation between energyconsumption and wealth, focusing instead on biology, machinery, thermodynamics and the unifying property of the 'constructal law'.

The 'constructal law', according to Bejan and Lorente, the authors of the paper, derives from constructal theory, which is "the view that (1) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered b a principle (the constructal law): 'for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it'."  The authors, incidentally, are referring to real currents - water, blood, electrical, air, and so forth - and not some sort of para-psychological nonsense.  The constructal law accordingly has two "useful sides" - it can be used to predict natural phenomena; and it can be used to strategically engineer new architectures that are designed not to mimic nature, but rather to optimize evolutionary design through maximization of flow.

Thermodynamics comes into the equation by virtue of the fact that the authors are, more or less, proposing to replace the old thermodynamic model of systems stability and evolution (i.e., the eternal, and losing, struggle of order vs. entropy) by replacing the key criterion, order, with flow, and the process of building order out of disorder (which is what life does) with the process of producing 'configuration'.  'Configuration' is a more appropriate measure, since it covers things that order does not.  For example, tree branches may look disorderly as they grow sunwards, but they are producing a predictable configuration in response to biological imperatives deriving from plant DNA.

The generation of 'configuration', the authors argue, "is ubiquitous", and "unites the animate with the inanimate".  This reworking of the paradigm, they suggest, will "cover all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes."  All of nature, they argue, can be visualized as a mechanism for maximizing flow optimization, conglomerating all geophysical and biological systems into an "engine and brake" design.

Trust me, it makes more sense when you read the paper.  A little bit, anyway.

How on Earth does all of this bear on socio-cultural metrics like per-capita GDP?  Back to thermodynamics for a moment.  The traditional understanding of a power plant is one of the oldest thermodynamic constructs.  Basically, a power plant can be visualized as a mechanism for turning heat energy into some sort of work.  The heat content of the system is represented by the equation Qh=W+Ql, where Qh is the heat content of the heat reservoir, W is the work done, and Ql is the waste heat lost to the environment.  The Second Law of thermodynamics states that entropic transfer out of the system will always exceed entropic transfer into the system, which is usually paraphrased as "disorder always increases".  Or to put it another way, the total amount of energy produced by burning coal and using it to create steam to drive a turbine will always be less than the energy it would take to turn water vapour, smoke, ash, waste heat from the boiler, the condenser, and the bearings, and rotational momentum back into anthracite.

(For those unfamiliar with the laws of thermodynamics, they are, in a nutshell, (1) the energy in a closed system remains constant, (2) the entropy in a closed system never decreases, and (3) as temperature approaches absolute zero, entropy approaches absolute minimum.  As far as using energy to generate power to do work is concerned, these laws are often super-summarized as "You can't win, you can't break even, and you can't quit.")

In common-sense terms, the second law means that burning fuel to do work - either moving a car, generating electrical power, or making your neurons fire when writing a particularly scintillating TM - is always a losing proposition.  Waste heat is constantly being lost to the environment (that's the Second Law at work), and you can never get as much out of the system as you put into it.  Where Bejan and Lorente break some new ground is in departing from the traditional thermodynamic paradigm by considering the heat-to-work equation under constructal law, where "flow" dynamics are used to describe not just the delta between input energy and output entropy and work, but rather the ultimate fate of all energy in the macroscopic view of the system.  In the flow paradigm, for example, an animal burning sugar from food to generate muscular action and waste heat is coupled not only to the atmosphere (which absorbs the waste heat radiated by the animal) but also to the ground.  The animal's motion, though presumably useful to the animal itself (e.g., in the context of a cheetah chasing a gazelle in searching of lunch, and the gazelle doing its best to avoid becoming tomorrow's waste heat), when considered under the constructal paradigm, is simply entropy generated and contained within the larger terrestrial macrosystem.  From a point of view of physics, the animal transfers momentum to the planet; each thrust of its legs in a given direction (referring to Newton's Third Law, now) generates an "equal and opposite reaction", imparting momentum to the Earth proportional to the animal's mass and the impulse of its thrust, with an opposing vector.  The overall energy of the terrestrial macrosystem remains constant, and entropy increases.

This is where what the authors call the "engine and brake design of nature" comes in.  Every system comes with its own engine and brake; even at the macro level, the cheetah (and the gazelle) are engines, while the Earth's environment - the air that absorbs their radiated waste heat, the earth that absorbs their other generated waste products, and the the planet itself as a physical object that absorbs the momentum imparted by their movement - is the brake.  Both living flow systems (animals, people, trees) and inanimate flow systems (rivers, plate tectonics, landslides) move mass, reordering the Earth's surface, and expending energy in doing so [note 1].  The "exergy" (the energy emitted by a system) used in the reordering equals the mass moved times the horizontal displacement.  The same principle, the authors argue, is true for all human activities, including, for example, vehicles, where "the spent fuel is proportional to the weight of the vehicle times the distance travelled." (Mass times distance, incidentally, is the equation for "work").  In other words, where artificial engines for producing work from heat are concerned, the authors argue that "all high-temperature heating that comes from burning dissipated into the environment.  The need for higher efficiencies in power generation [by which they mean a better ratio of W/Qh, work produced per unit of heat energy consumed] is the same as the need to do more Work [W] overall, i.e., the need to move more weight on the surface of the Earth, which is the natural tendency summarized in the constructal law."

Their key conclusion of interest, at least from a strategic analysis point of view, is this: from a constructal law perspective, because all energy consumed in the course of generating work from heat is eventually dissipated through interaction with the environment, the ultimate destination and/or use of the work itself is irrelevant ("There is no taker for the W produced"); all that matters is that work is proportional to the exergy of the system, i.e., to the heat energy, which is to say the fuel, consumed in producing the work.  "This," they argue, "is why the GNP of a country should be roughly proportional to the amount of fuel burned in that country." (Bejan & Lorente, 1341).  This also implies that attempts to increase the efficiency of heat engines (e.g., through "less dissipation in the bio, geo and engineered flow architectures") are from a macro perspective ultimately futile, because striving for less dissipation in the system architecture "is equivalent to pursuing more dissipation in the 'brake' that connects the constructal architecture to its environment."  In other words, even if we were to succeed in getting 99.999% efficiency out of our fuel (the Second Law, and for that matter the Third, says we can't get 100%), all of that energy eventually ends up in the environment anyway, in all manner of different forms, from waste heat radiated by the cheetah through exhalation and evaporation of its perspiration, to the heat generated by his gastrointestinal flora and fauna, to the coprophages engaged in breaking down his scats, to the energy dissipated by the impact of his paws on the soil, to the slowing of the Earth's rotational velocity due to transfer of momentum when the cheetah runs east, and its acceleration when he runs west.

This is not, of course, to suggest that we shouldn't strive for ever-greater fuel efficiency; we absolutely should, because the more efficiently we use fuel, the less we use of it, the less we pay for it, and the more useful work we can get out of it.  What matters to us is how much we can do with the power that is produced from fuel before that power ends up in the form of waste heat and/or momentum in the macroenvironment.  The constructal law, therefore, doesn't displace (much less replace) the laws of thermodynamics so much as offer a mental construct enabling us to visualize holistically the interconnections between ourselves and other "bio" critters; the "geo" structures all around us; the heat engines that we design and build to do work; and the larger macroenvironment where everything from coal to cheetahs to us ends up as entropy anyway.

For anyone who's interested in more on this subject, go read the paper.  Don't say I didn't warn you, though.




[1] The authors argue that they do this "by destroying exergy that originates from the Sun", which is not entirely accurate; the residual heat of aggregation remaining from the formation of the solar system is not solar-derived, nor is the thermal energy generated by nuclear fission in the Earth's core, except to the extent that the fissile elements were formed in supernova explosions billions of years before our Solar System was born.