Anaximenes' way

Anaximenes thought that the fundamental element was Air. He argued that rarefaction of Air produced Fire and condensation produced Water and eventually Earth. He was a predecessor of Democritus whose atomic theory of matter made possible the insights of Lavoisier and the understanding that the elements were more than four but still finite in the number of kinds.

Democritus is sometimes called the ultimate materialist but a Jungian who examined the structure of myth tagged him for including the spiritual in his theory related to his spherical and slippery soul particles. Almost, these soul atoms seem like the Chi of Lau Tzu or the breath of life of Genesis. Almost, they seem to be what Anaximenes took Air to be.

The direction of density in Anaximenes theory makes sense. Earth will silt out of a pool of Water, Air bubbles in Water and Fire rises in Air. In some ways we see Air becoming Fire as flame fills the Air. Rain also shows Air becoming Water. But what of Air becoming Earth? I'm not sure how he came to this though he is essentially correct about the formation of the Earth from a cloud of gas which at some point was entirely gas though it had already condensed out dust when the solar system formed. And, felt-like dust did play a role. One path he might have taken would be to observe a rotting log becoming soil and further observing that trees, no matter how large they grow, do not leave a depression in the soil around them. Where did the wood come from? Not from Earth. Perhaps from Water which came from Air? As we know now it comes from both water and air, but we need Lavoisier's division of air into its own elements to be clear about how.

Behind all of these ideas is the concept of conservation of matter which Democritus used to arrive at the ideas that there must be irreducible unchanging units, and which Lavoisier began to demonstrate quantitatively. A century after his false conviction and execution in the Terror of the French Revolution, we learned that there is a means of transmutation that ushered in the horrors of the nuclear age. But, even then, the core concept of conservation held but was shifted to baryons rather than elements and we were back to protons, which exist as Air as the basic unit. So, in a large sense, Anaximenes had it right to begin with.

The myth of the formation of Mankind from mud leads to the Ash Wednesday admonition: "Remember that you are dust and to dust you shall return." This is extremely helpful to set a penitent tone, and it is true that we are partly dust. But, by number, if not by mass, we are mostly hydrogen and so to Air we shall return as well whence we came for the most part. It seems fitting then that the conclusion of penitence is resurrection and ascension into Anaximenes' beloved Air.

I had originally thought to title this post Air Mining but decided to give it its present title because I think we'll be fulfilling Anaximenes' quest.

We've become troglodyte during the Stone, Bronze, Iron, Coal and Nuclear Ages, relying more and more on grubbing under the Earth for things that we use. When once the branches of trees and bones of animals were enough, we must have ever harder and hotter substitutes for our tools. But, we have not completely forsaken the air. We still get our water from it, and this, after all is the main constituent of our bodies. We get oxygen from it both to breath and to burn the coal and oil and gas that we drag up from the Earth. This is becoming a problem as last year was the second warmest on record. We get carbon from the air rather than the earth for our food at least, and to do this we also take nitrogen from the air to grow our plants, not being satisfied with the efforts of clover, beans and alder. We fill windows with argon to help with insulation. In bulk, we gather energy from its flow and rely on its mix of transparency and opacity to regulate our global temperature and let in the low entropy power of the Sun. We use its convective properties to carry away heat by constructing ugly cooling towers where even the much higher heat capacity and steady flow of a majestic river are not sufficient to deal with our wasteful methods of producing electricity. We have not forsaken the Air completely, but our deeper and deeper delving in the Earth is abusing it and unbalancing out ecosystem. The brimstone and quicksilver we dig out of the earth with our fuel spreads death through the air across our forests and waterways while the carbon itself accumulates in the atmosphere adding opacity to it, raising temperatures faster than the ecosystem can adapt.

In our discussions of Real Energy we have seen that there is no need to mine the Earth for energy; it is counter productive. And we have seen that if we do need fuel, we can make it directly from the air without burdening the ecosystem. Thus, real energy does away with the Coal and Nuclear ages. But what of the Stone, Bronze and Iron Ages? Can we similarly pull ourselves out of our shadow haunted Cave and return to the open Air? The Coal and Nuclear Ages were about the hubris of out doing the Titan Prometheus but to overcome the Bronze and Iron Ages we must propitiate the Olympian Hephaestus, because while Prometheus' stolen goods are about the means, Hephaestus' art is about the ends, the making of harder substances than wood or bones or stones. And, that is what gave us mines in the first place.

It turns out that an insight of Lavoisier's allows us to break away from Bronze and Iron. He learned that diamond is actually crystallized carbon. Diamond is harder by far than bronze or iron but it is rarely formed in nature, requiring very high temperature and pressure deep in the Earth. Associated with volcanoes, it is perhaps Hephaestus' highest art. But, the feedstock, the concentrated carbon, often ultimately comes from Air unlike copper, tin or iron. Diamond is very permanently sequestered carbon dioxide, though, at a pinch, if we run low on carbon dioxide, it is possible to burn diamond in air. Diamond is also formed industrially using vapor deposition, a direct Anaximenesian approach, but here we will consider an unusual form of diamond, Lonsdaleite, which forms as meteors fall through the atmosphere, because Lavoisier's art seems to provide a simple approach to its production that might allow it to be used in structural applications. There are other forms of carbon that show promise in structural applications including nanotubes and buckyballs, but we want a direct comparison to steel for our demonstration so we'll stick with diamond.

When we looked at mining the air for fuel, we needed to obtain water and carbon dioxide. In this case we will need a supply of carbon dioxide only. The hydrogen and bromine we'll be using will be recycled in the process.

Our project is to construct a transmission line from a wind farm for lower energy cost than using steel by mining the air for our building material. We will build a GW capacity line, similar to current high voltage transmission lines. A difference though is that we will support our conductor using our building material rather than metal cable. This will allow us to change the conductor configuration, use a higher voltage and thus lower line loss.

We'll start with our conductor. High voltage transmission lines are often a composite. A strong cable is used to support the conducting material. This is because the better conductors like aluminum and copper are less strong than steel but the amount of conductor needed is not so great that it would be thick enough to hold up against its own weight and wind forces. You could space pylons more closely, but that would increase the overall use of steel. As we already saw, a conductor 6 cm in diameter (say aluminum) can be used to carry 30 GW of power at three times the voltage currently used High Voltage Direct Current transmission because the larger radius increases the limit set by corona discharge compared to a smaller radius used for the Pacific Intertie which carries 3 GW. We can retain the larger radius by making the conductor hollow. The cross sectional area of the conductor can be reduced by a factor of 30 to meet our 1 GW goal. So, the thickness of our cylindrical conductor will be about 0.5 cm. Diamond has a high tensile strength (about 95 GPa) compared to prestressed steel strands (about 1.6 GPa) so that the cross sectional area we will need will be (proportionally) less than the ratio of the radii of the hollow-to-non-hollow conductor (about a factor of three) times the ratio of steel-to-diamond tensile strengths (about 1/59). So we need about 20 times less cross sectional area compared to steel. By mass, this comes to about a factor of 44 less mass. We'll arrange this in the form of a sheath around the conductor which will need to be in the form of a woven cloth because the coefficient of thermal expansion of metals is a factor of ten or so larger than for diamond. We'll also include a few atmospheres of carbon dioxide within the supportive sheath so that in case it gets heated to 800 C, a breach of the sheath will cause any combustion to be extinguished. We'll also provide for an external conductor to avoid this situation arising from lightning.

We can largely ignore the improvements in weight that diamond conveys in the construction of our conductor because most of the weight is in the conductor itself. Also, we needn't really have gone to the trouble to improve our conductor since our wind farm may only need to build out a transmission line that is 100 miles or so long and conventional conductors using high voltage alternating current would do the job. So, this portion is mostly for fun. Much more of the embodied energy in out transmission line is in the pylons and we turn to this now.

Steel used in construction has a lower tensile strength than prestressed strands by a factor of 2 so that we can reduce the cross section of our structural members by a factor of 124 using diamond as opposed to steel and ignoring the reduced mass of the pylon itself. The amount of mass is thus a factor of 276 less. The embodied energy of steel is 32 MJ/kg so all we need to do is figure out how much energy we need to make 3.6 gm of diamond and we will be able estimate our energy savings.

We already calculated that to condense carbon dioxide from the air we need 0.77 MJ/kg so things are looking pretty good. We'll take a supply of hydrogen and form methane using the exothermic Sabatier reaction which means that we will need to recycle the water produced at this point. The energy input is about 14 MJ/kg. After these energy inputs we are basically doing room temperature chemistry (Lavoisier's specialty) producing bromoform from methane and then producing poly(hydridocarbyne) from the bromoform. We'll input about 2 MJ/kg of carbon using free radical halogenation to make the bromoform. The polymer is then painted in solution on our growing structural element and warmed using argon gas. The waste heat from the methane formation can be used for this step. To be safe, lets add another 14 MJ/kg to be sure the bromine, argon solvent and remaining hydrogen all get properly recycled. This assumes we use oxidation of hydrogen to separate our reactants but the hydrogen bromine can probably be handled with less energy input. So, in all we need about 31 MJ/kg to produce our structural element, similar to the value for steel. But, to replace the steel we need much less so we need a factor of 280 less energy to build a pylon.

Take a deep refreshing breath. Anaximenes would say "I told you so."

Now, world steel production is only 1.3 billion metric tons per year and to replace that we would need only 4.7 million metric tons of diamond compared to about 3 billion metric tons of carbon in our fossil fuel pollution. But, there are probably other materials that could be replaced as well. Concrete production comes to around 12 billion metric tons and wood is harvested at 3 billion metric tons per year. So, we might begin to sequester a few percent of our carbon emissions by mining the air for carbon. Leaving the trees alone might have the largest effect, since this would both take up carbon in forests and help to bring our estuaries back into balance.

We've been looking at Energy Returned on Energy Invested (EROEI) recently. How would replacing the steel in a wind turbine with diamond affect this value? The amount of steel used in 3 MW wind turbine is described in this life cycle analysis which estimates the EROEI to be 20. Assuming 10% steel by mass for the reinforced concrete foundation, the structure contains about 460 metric tons of steel/iron. Using our conversion factor of 32 MJ/kg, this is about 14 million MJ of embodied energy and about 55% of the 7405 MWh of energy used in construction of the turbine. So, replacing steel with diamond would give 3333 MWh instead. Thus the EROEI would be boosted by a factor of 2.2 to 44.

Back in our pylon, we would want to use the same method for protecting against combustion that we used in our conductor, namely, filling hollow structural elements with several atmospheres of carbon dioxide so that a combustion rupture would be self-extinguishing. This probably has fabrication advantages as well. The thermal conductivity of diamond is quite high and we need to build our tubes by painting layers which are warmed using argon gas to remove the hydrogen in the poly(hydridocarbyne) and the solvent. Thus, having heat flow down the tube once this is done will allow us to rapidly paint on the next layer. Arranging our painting and warming heads periodically around the growing mouth of the tube would essentially have us spinning the tube into existence. At a rate of tens of microns per second growth, we can grow a meter long tube in about a day. Our manufacturing facility would bear an uncanny resemblance to a uranium centrifuge enrichment facility with all that spinning going on, but would not be prone to seismic risk since the rotational frequencies would be much lower, in the neighborhood of tens of Hertz.

Lonsdaleite, our chosen form of diamond, has still not been characterized fully experimentally and the samples studied so far show a hardness somewhat lower than common diamond. Thus, we might have to use more than we have anticipated. Theoretical study suggests that the Lonsdaleite structure may be slightly stronger than regular diamond and that present samples are affected by defects and impurities. In any case, other carbon structures are even stronger. Fullerite may be twice as strong as regular diamond. The choice of what to mine the air for will likely come down to ease of fabrication and required energy. But, our passage through our troglodyte phase and our flirtation with Hephaestus would seem to be ending and drawing to a close the Ages with which we understand history. For our new Age, the name Carboniferous has already been taken and Anthropocene seems too ominous. Let's just call it the restoration of the Holocene instead.

EROEI

Energy returned on energy invested (EROEI) is a measure of the feasibility of an energy source and so it should be useful for comparing different energy sources to try to pick which one to use. Here we are mainly concerned with real energy, but from time to time I get into discussions with people who feel that nuclear power is a good thing because it is suppose to have a high EROEI. They are deceiving themselves but they are being encouraged by the nuclear industry in this self-deception so lets look at the numbers. We won't do a full life cycle analysis, just find a few of the problems.

EROEI can be calculated as (net energy out)/(energy expended)+1. We can see that EROEI=1 is the break even point because if you are not getting any net energy out then you have zero in the numerator of the fraction and you are left with 1 in the sum. This is the situation where it takes just as much energy to get energy as you actually get. The classic example would be when an oil well needs a barrel of oil to extract a barrel of oil. Oil wells shut down before this happens. If an oil well gets two barrels of oil gross for every one used to run it then the EROEI(thermal) for the well is 2. We have pumped two barrels total to get one barrel net: 1/1+1. We are tagging the EROEI as thermal because that will be important later. Now let's consider an oil field where the output of half the wells are used to run the whole field. We'll consider this from the perspective of the oil input. The oil input produces itself in half the wells leaving an equal amount to take away (net). So, EROEI(thermal)=1/1+1, the same result as you might guess. For a similar system using nuclear power with half the reactors enriching uranium to power all the reactors we have net thermal energy from half the reactors (Eu/2) and energy input from half the reactors (Eu/2) so again we get EROEI(thermal)=(Eu/2)/(Eu/2)+1=2.

Now, we've introduced the tag thermal. This is important. The net energy is not really net until we figure out how its is used. For the example of nuclear power just now, we know that the power plants that are not used for enrichment will be producing electricity with a fairly low thermal to electric conversion factor near 30%. So, we should account for this by applying this to the net energy. We get EROEI(actual)=(Eu/2*0.3)/(Eu/2)+1=1.3. For the oil, it may be used in a furnace in which case EROEI(thermal) is just fine, or it may be used in an engine in which case we would have a similar conversion factor: EROEI(actual)=(1*0.3)/1+1=1.3. Or, it might be stored until fuel cells are available to use it in which case EROEI(actual)=1.7 might be about right. Because of this ambiguity, we want to know the scope of our calculation. Are we ending at the well head, at the furnace or at the wheels? In the case of electricity, we always end at the toaster so when comparing sources, this is where we want to set our scope.

Let's look at the EROEI of the French nuclear program. The French have 58 reactors of which three are devoted to uranium enrichment so we can estimate the EROEI(thermal)=55/3+1=19.3 and the EROEI(actual)=(55*0.3)/3+1=6.5. Because we are only looking at the energy input for uranium enrichment and ignoring the energy inputs for mining, ore processing, plant construction and decommissioning, and unmaking of the nuclear waste this is really an upper limit on the EROEI(actual) of the French nuclear program even if our method of estimating is a little imprecise.

We can use our estimate of the EROEI of the French nuclear program to make another estimate. Suppose that instead of enriching uranium from 0.7% U235 to 3% U235 for fuel, it is enriched to 25% U235 and then diluted this back down to 3% as the US is now doing. Since the US is using cold war enriched uranium, the process used in France, gaseous diffusion, is an appropriate model. Assuming that the depleted uranium that is a product of the enrichment process has a U235 content of 0.3%, Then one unit of natural uranium becomes about 0.14 units of 3% enriched uranium or 0.016 units of 25% enriched uranium with the remainder being depleted uranium. It takes about 1.55 times more energy to get to the higher level of enrichment. So, if France were following the US example, we'd have five of 58 reactors carrying out enrichment rather than three; EROEI(thermal) would be 53/5+1=11.6 and EROEI(actual) would be 4.2. Again, these are upper limits owing to neglect of other energy inputs.

The problem that we run into with the nuclear industry is that they will sometimes admit that the EROEI values they calculate are thermal values, but then they will compare these with actual values from real energy sources which power the toaster without conversion. So, if they calculate an EROEI(thermal) of 20 for nuclear power they'll compare this with an EROEI(actual) of 12.5 for silicon solar panels and say "Hey, nuclear is better!" But, as we have seen, the EROEI(actual) for nuclear power is less than 7 and thus lower than for the solar panels. We've noted before that extending the use of silicon to 100 years gives an EROEI(actual)=33 and recycling makes it approach 99 eventually. The reported values for the EROEI of wind power are also actual and they come in near 20 or above, again better than nuclear power.

The World Nuclear Association has put together a table (2) of estimates of EROEI from a number of sources but they are comparing thermal figures with non-thermal figures in many cases. Let's summarize their table here making the following corrections: for nuclear power we'll use a conversion of 30%, for coal, 40% and for gas 60% assuming a combined cycle:

Power Source	EROEI(actual)
Hydro	50, 43 and 205
Nuclear (centrifuge)	18.1, 18.4, 14.5, 13.6 and 14.8
Nuclear (diffusion)	6.0, 6.7, 5.8, 7.9, 5.3, 5.6 and 3.9
Coal	12.2, 7.4, 7.32, 3.4 and 14.2
Gas (piped)	16
Gas (piped a lot or liquefied)	3.4, 3.76 and 4
Solar	10.6
Solar PV	12-10, 7.5 and 3.7
Wind	12, 6, 34, 80 and 50

Here we also have corrections to their table 2 to be consistent with their table 1 for their own calculations. Their calculations are the first listed in each nucelar row and the rest are taken in the order they give them as well. I have not checked that they copied correctly from the references they cite (they left the referernces out) but the solar PV values look familiar and are somewhat out-of-date now. In all, nuclear power does not look as good as wind, even with centrifuge enrichment and with current solar EROEI for thin film PV around 30 in 2009, it does not look good in comparison there either. If the row marked just solar is concentrated solar thermal power, then a commenter below has kindly provided a reference which did not fear to look at conversion to electricty, finding an EROEI of 27 with thermal storage and 34 without (this last is a correction spotted by Brad F at TOD). And, it should be remembered that silicon can get to 30 if you are willing to wait just a little longer than the warrantee duration. It is notable also that present day coal does better than present day (diffusion sourced) nuclear power in most estimates. In all, the renewable sources of electricity, hydro, wind and solar do better than the non-renewable sources, which is pretty much what you would expect since they don't need fuel.

There are some, particularly nuclear power proponents, who might object to my procedure here saying that EROEI should only be applied to the energy source itself and not compared with other sources in this manner. We can easily overcome these objections by subtracting one from each of the numbers in the table. This gives us a new measure which we can call Energy Delivered on Energy Expended (EDOEE). For this measure, break even occurs at the value zero (it was at the value 1 previously). This allows us to look at another set of issues. Two sources in the table require primarily electrical energy be expended to make them work. For nuclear power, enrichment is done using electricity and for solar power refining silicon is also done in this manner. This means that the mix of generating sources is essentially the same for both. Nuclear proponents will often try to hide this by saying that enrichment of uranium is done using nuclear power, but electricity is fungible so this is quite dishonest. But, since both produce electricity, they have the potential to change the mixture of generating sources. Which can do this producing the least amount of emissions? Here we are talking about future growth so we should use the high numbers for nuclear power (around 14) since enrichment capacity is currently inadequate to supply even the current set of nuclear reactors to the end of their design lifetimes so new enrichment facilities would need to be built. Enrichment causes deaths owing to criticality accidents. And, we should take at least the EDOEE for thin film solar (29) (which also uses electricity) since competition will drive out the low EDOEE producers. By taking the ratio, we see that solar power can make electricity generation free of carbon dioxide emissions with half the associated emissions to get the job done. For a utility scale solar installation at an average US location, the two are about equal.

The emissions associated with either are not that large though, and so the largest gain comes in doing the job quickly so that fossil fuel use for general consumption is eliminated. Here, wind has an advantage. 20 GW were installed in 2007. For nuclear power, it is not clear that new construction can keep up with the retirement of existing reactors. With 30 reactors under construction and a ten year construction timescale, that comes to about 3 GW/year of new nuclear power without accounting for retirement of old reactors. So, the pace of nuclear energy is slow. In fact, it is even slow compared to solar which produced 3.8 GW of new capacity in 2007. With growth rates for wind at 30% and solar at 50% annually, both are faster off the block than the essentially replacement level activity in nuclear power. Now, these are all nameplate capacities and we do need to look at the capacity factors which are 82% for nuclear power worldwide, about 35% for wind and about 20% for solar, so wind is ahead of solar by a factor of nine. New nuclear power, not adjusted for retirements, is ahead of solar by a factor of three or less and wind is ahead of nuclear by a factor of three or more. At the present rates of growth, solar will match wind in adding capacity factor adjusted new capacity in 15 years at which point is would be adding 1920 GW of namplate and 384 GW of adjusted capacity. It seems unlikely that that nuclear power will be adding that much capacity in fifteen years while the growth of solar power seems sustainable over the next decade or so owing to the rapidly falling cost of production.

Comparing EROEI(actual) or EDOEE shows us that less effort is needed to eliminate fossil fuel use in electricity generation using wind and solar power compared to nuclear power. This probably partly explains why both wind and solar are doing so much better than nuclear power in getting the job done. It also tells us how much of our time we'll be spending on paying our energy bill rather than say educating our children or improving our health. Those sources which require more effort will be more expensive and a greater drain on our resources. Since nuclear power appears to have little to contribute to accomplishing what we need to do to reduce fossil fuel emissions, it can be viewed as a wasted effort which hinders that accomplishment. Such wasted efforts generally lead to financial losses so it would seem prudent to avoid placing public money at risk in such ventures.

On critic of this entry (mcrab) has proposed a Virtual EROEI (VEROEI) which, instead of adjusting the output of thermal sources of electricity by their conversion efficiency to electricity, one would multiply the outputs of the electricity only sources, hydro, wind and PV solar by factor of three to make a comparison. This is an interesting suggestion and it would provide a fair comparison of relative EROEI between the thermal and more direct sources, giving simliar results to what we have just done using EDOEE. In a way this is a fair thing to do since, if we are to electrify transportation, a wind mill only needs to put in a third as much energy as a gas pump. So, the virtual thermal energy returned is quite a bit more. And, it is true that one can get 4 times as much low grade heat with electricity as with, say, heating oil using a heat pump. But, we can only get a one-to-one conversion when we make fuel using electricity and then only if we have a use for the process heat. Further, to intercompare thermal sources, VEROEI is not all that useful since gas produces twice as much electricity as nuclear power for the same thermal input (one does not want the nuclear fuel to melt). VEROEI may be useful for comparing oranges to oranges, but for apples-to-apples, the method adopted here seems clearer and more physical.