The Useful Concept of “Thermodynamic Rarity”   The Useful Concept of “Thermodynamic Rarity” Mark Lindley, 15 July 2016 International Exergy Economics Workshop, University of Sussex

Antonio and Alicia Valero at the University of Zaragoza make quanti­tative assessments of each kind of mineral commodity in terms of its “thermodynamic rarity”, defined as the amount of exergy that would have to be expended, using the best available tech­niques, to extract the desired mineral from ordinary rock (i.e. not from ore) and then to purify it to the desired extent.

With this concept they reckon (1) the “natural bonus” of having ores (i.e. concentrated mineral deposits) in the first place, as well as (2) the “exergy cost” (i.e. expendi­ture of con­sumable energy) of the mining, bene­ficia­tion and purifica­tion processes. And, they calculate good theoretical (3) allocations, to different eco­nomic­ally useful elements in one and the same ore, of the elements’ respective natural-bonus values and exergy costs.

They estimate the exergy cost of an object by calculating how much consumable energy (paid for) has actually been expended for the production pro­cess.   If trustworthy data for this are lacking, they recom­mend reverting to an “embodied-energy” estimate as a surrogate for a proper exergy-cost estim­ate. Both kinds of estimate are based on material-flow-analysis (MFA) data, but analytical vagueness often lurks in “embodied-energy” estimates. (How far back should you go to look for expenditures of energy that you are going to suppose to be “embodied” in the thing or service?)

The Valeros’ reckoning of exergy expenditures is based on clear accounts of (a) the process from a given point forward and (b) how each part of it has been done. In order to en­sure clarity of analysis, no economic procedures prior to extraction from the mine(s) are covered; the view (for this purpose) is from the natural “cradle” (i.e. the ore) forward, as repre­sented by the bold-font items in the fol­lowing diagram (of my devising). The arrows in the dia­gram repre­sent economic deci-sions.

The following figure puts this in a broader context and shows how the theoretical “replacement exergy cost” (which is how the natural bonus is calculated) fits into the theory. In this figure, most of the thin arrows repre-sent “natural” expenditures of exergy, i.e. not due to human decisions. (Don’t lose sleep about in­crease of entropy due to cosmic expendi-ture of exergy. The Sun will swell up and swallow the Earth long before the Universe might approach a con­dition of “heat death”, i.e. of uniform temperature etc. throughout.)

The “grave” in the Valeros’ theoretical scheme would be a demise, not of Humankind, but only of a kind of economy that depends on extract­ing abiotic (i.e. not living) nonrenew­able mineral resources and fossil fuels from the Earth.

A century or two ago, when the quantity and quality of the ores in the cradle were very good, the exergy value of the natural bonus was a lot more than the exergy cost of extracting and re­fining the valuable minerals. Let me show you a graph repre­sent­ing such a state of affairs. Exergy will be plotted vertically, while the economic quality of some mineral element of direct eco­nomic value is plotted hori-zon­tally; and, “xC” refers to the eco­nomic qual­ity of what there is of it in ordinary, non-ore rock. (This qual­ity is like in the theoretical grave at the end of the pro­jected “crepus-­cular” phase – i.e. “dusk” – of modern economic history.)

(With a graph miles high we might chart the exergy expenditures of the Big Bang etc., but we don’t want to do that; we’re econo­mists, not cos­molo­gists.) Meanwhile, “xM” refers to the valuable stuff in the mine (i.e. with the bene­fit of the natural bonus of having it concen­trated there), and “xB” to the situ-ation after bene­ficiation. Here is the same graph again:

Mining causes the historically remaining amount of the bonus to decline; this tends to jack up the cost of sub-sequent mining (a fact which is one of several reasons why the Valeros’ meth­od of assessment can help har­mon­ize the thinking of exergy eco­nomists with that of main­stream econo­mists). The following graph represents this fact:

But, if more efficient techniques are developed, then the curve is low­ered as this and/or that improvement in the quality of the stuff is achieved with a smaller expendi-ture of exergy than with the earlier, less efficient cor­responding techniques:

Here is an interesting way in which the Valeros’ theoretical reckonings can be useful in the short-to-medium term:

While defining a “thermo­dynamic­ally ‘rare’ chemical element” as one which is naturally scarce (in the crust of the Earth) and /or costly energy-wise to process, they assess, in collab­oration with Nadja von Gries, the “com­posed thermo­­dynamic rarities” of the sets of materials used in this and that kind of electric and electronic appli­ance. This kind of assessment is relevant to setting wise priorities (a) in the design of such appliances and (b) in regard to recycling them when the consumers are ready to discard them.

I reckon there won’t be time here to go into detail about this. Thank you for your attention.