Out of Date
This article needs updating. Not chemistry or economics, but the companies named. Planetary Resources and Deep Space Industries are gone.
Keith Aug 6 2019
Mining asteroids by Keith Henson
June 9 Draft temp post as a wiki for comment!
This article provides a rough analysis of mining an asteroid for gold and other high value elements (platinum group metals) for return to an Earth market. Given serious bootstrapping at an asteroid and the development of low-cost transport to GEO in the context of a power satellite or similar very large operations in space, it appears an asteroid-mining project could make money beyond the wildest dreams of avarice.
I have not been much of a fan of mining materials off Earth for use here. (Use in space is another matter.) Still, times change and with the Planetary Resources announcement to go after water and platinum on a small scale, perhaps it is time to reconsider.
Where the gold is
There has been much talk about getting gold back to the surface of the Earth, but not a lot about the hard task of getting it out of asteroids. First, let us consider the scale of the problem.
Gold mining on Earth produces about 2700 tons per year. It's constrained by falling ore grades, now as low as 3 gm/ton. That's 3 parts per million. Part of the problem is that most of the gold in the original material that formed the Earth sank when the core differentiated. (See Goldschmidt classification ) What we mine came in with the "late heavy bombardment."
What makes ore bodies on Earth is some concentration mechanism, usually hydrothermal (read "hot salty water") that removed elements like gold, silver, copper, lead, zinc, etc. from vast amounts of rock and left them concentrated in amounts humans and their machines can mine profitably. The process continues today with the hot vents on the seafloor spreading centers.
The only certainly known mechanism that concentrates valuable elements out in the asteroids is that some asteroids melted same as the Earth. The iron part went to the center, taking nickel, cobalt, and platinum with it, including ~1-ppm gold. We see pieces of these as the iron and stony iron meteorites.
(Incidentally, gold ranges up to 5 ppm and down to .05 ppm in iron meteorites )
The very largest asteroids, Vesta and Ceres, may have both melted in the center and retained (or acquired) enough water for hydrothermal concentration of rare elements. Mining them, or even prospecting, is beyond the scope of this article.
The one I will be using (as an example) seems to be the core of an asteroid that melted, differentiated like the Earth and was later stripped down to its metal core by a cataclysmic collision. Named 1986 DA, it is possibly the most mine-able object among the asteroids, at least for heavy metals.
Income from such a venture
Gold is currently near $50,000 per kg http://goldprice.org/gold-price-per-kilo.html. The cost to mine it is around 1/3 of the sales price. The mining rate probably can't be increased much and may be at or near peak production.
$50 M/t x 2700 t is $135 B per year. As a guess, I don't think more than about a quarter of the current production could be sold without driving the price down, so $33 B per year might be a reasonable income stream (if multiple operators do not flood the market).
There is about four times as much value in platinum-group metals as gold in metal asteroids. Thus, we can multiply the above figure by five, increasing the income stream to $165 B/year. If we use a five-year return of capital from profits of 60% of sales, then the startup budget could range up to $445 B. While this is an awful lot of money, a future economy with most fossil fuel replaced by SBSP could afford it.
(The Wikipedia article on the asteroid 1986 DA estimates it is worth $11 T, mostly from high platinum prices. Eleven thousand billion dollars over 25 years is $440 B per year. Platinum is different from gold in that the market is largely industrial. Increasing the supply would drive down the price but probably not as much as gold.)
The gold and platinum returned to Earth would be in the range of 3400 tons per year. While that is a lot to just rain down, it isn't much in the context of a serious power satellite project sized to lift 500,000 tons per year of parts. At three flights per hour and 8000 hours per year, it would amount to a return load of only 140 kg per flight—a tiny fraction of the vehicle's 30-ton capacity.
Delivered to GEO instead, the metals would amount to a return traffic to LEO of less than 1%.
On the other hand, 140 kg x $50,000 per kg is $7 million per flight, and you don't have all the Skylon-derived vehicles coming back empty. In fact, the value coming back would be on a par with the initial $160 B per year from power satellite construction.
What it would cost to mine this asteroid
The next question is how much extraction plant would it take to process an asteroid such as 1986 DA.
Back in the '70s, Dr. Eric Drexler and I designed a solar-powered plant to vapor deposit aluminum or steel (See "Vapor-phase Fabrication of Massive Structures in Space "). We worked out that the plant could vaporize its own mass in aluminum every eight hours.
Separating metals might take a two or three times larger plant, especially given the weaker sunlight in the asteroid belt. I have previously considered a 50,000-ton processing plant able to provide power-satellite Invar (35% nickel) construction sheet. I sized it to produce its own mass in nickel every 50 days processing a metal asteroid such as 1986 DA  and slide 90 [www.nss.org/settlement/ssp/library/CO2andSpaceResources.ppt]. The delta V between GEO and this asteroid can be as low as 140 m/s.
(The high mass estimate was due to including a full-scale power satellite and a substantial habitat for several hundred plant operators and their families.)
The assumed market was Invar for second-generation power satellites. It's a tiny 10,000-ton per day pilot plant by comparison to a serious gold mining project. Out of ten million kg/day, it would recover ~7.5 kg of gold and around 30 kg of platinum group elements worth about $700 million a year. That's just noise in the context of $700 B per year from power satellite construction.
To recover 625 tons of gold per year given gold at 0.75 ppm would mean processing 900 million tons per year or about 2.5 million tons per day. 1986 DA with a mass of 22,000 million tons would last at that rate for 24 years.
This is about the right project size for 1986 DA given that processing plants for mines usually use up an ore body in 25-30 years. For example 
(I am familiar with the history of this mine, having run geophysics in the area in 1964. It has had an on-and-off history  because a higher-grade ore body was worked out and the mine closed for some years during low copper prices. It currently processes a lower-grade ore at four times the rate the higher grade was processed.)
The first step in concentrating metals from low-grade ores is often the most expensive. The amount of valuable metals in an asteroid is not much different from a current gold mine processing 3-ppm ore. It will take a different method from crushing rock; asteroid iron is on a par with giant anvils.
By rough analogy to the work Drexler and I did, the processing plant might mass 2.5 million tons (i.e., it process the plant mass in a day). That's a lot. Even by the standard of a half-million-ton-per-year power-satellite project, it would take 5 years to lift that much off the Earth.
Still, we can plug in numbers. A scheme I have worked on is to lift power parts to GEO using a combination of air-breathing rocket planes (Skylon) followed by arcjet tugs powered by small power satellites. The arcjet tugs lift 15,000-ton cargo blocks from LEO to GEO. The proposed cost is slightly under $200/kg. This is a LEO-to-GEO velocity change of about 4 km/s. It's probably possible (especially at this scale) to get the cost for transporting a mining and processing plant to 1986 DA down to ~$300/kg (for a delta-V of around 7.1 km/s from LEO).
That would cost $750 B for a 2.5-million-ton processing plant. Just for the transport cost, that's already twice the permitted capital budget.
Actually, $750 B is not bad for a first cut.
It's going to take bootstrapping, but not an absurd amount. In this context, a 90% bootstrap seems feasible, especially starting from a plant sized to make Invar for power- satellite parts and already returning a few thousand tons per day of power satellite parts to GEO.
That much bootstrapping reduces the transport cost to $75 B for the startup. Of course, a technology that allowed a smaller starting mass would be even less expensive.
To analyze further, we have to assume a particular process. One proposed by Alexis Gilliland in the Rosanante book series was to use zone refining for the initial concentration step. (If you have never read them, the Rosanante books are the best fiction ever written about both space colonies and AI.)
I will assume for this article melting the asteroid with an open-ended induction furnace, rolling the hot metal into thin sheet metal, followed by dissolving the metal in carbon monoxide under high pressure (i.e., the Mond process). The iron and nickel carbonyls will have to be reduced back to metals to recover the carbon monoxide.
How to separate the liquid carbonyls in zero-g is a so far unsolved question. It may require artificial gravity (discussed below).
The local structure could be made of iron or unprocessed metal or any alloy available from the output of the plant.
The power plant size depends on the heat capacity of iron at 25 J per mol per deg K. Iron is 56 g/mol, so to heat a gram of iron a degree K would take about 0.46 J, or 0.45 kJ/kg. The asteroid metal needs to be heated (1811 –164) deg K which takes ~741 kJ/kg. Iron takes 13.8 kJ/mol to melt it, adding 246 kJ/kg for 987 kJ/kg. Round up to 1 MJ/kg. (A million watt-seconds per kg.)
2.5 million tons per day is about 29,000 kg/s. Melting this flow would take 29 GW, round to 30 GW. That is a lot of power, equal to three 5 GW power satellites before you take the 50% loss in transmitting power to the ground. A while ago I was in a Nucor minimill. The main melting furnace was 50 MW making this musing roughly 500 times larger.
At 3 kg/kW, a power plant masses 3000 tons per GW. The asteroid 1986 DA swings out further than Mars, which would reduce the sunlight intensity to 1/4. The power output would swing over the same range. Using the same kg/kW as near Earth, the power plant would mass 30 GW x 3000 t/GW or 90,000 tons. Virtually all of the mass could come from the asteroid.
Assuming asteroid metal rolled thin enough to dissolve in a day, the high-pressure chamber will need to hold 2.5 million tons of crinkled-up sheet metal. At a density of 1000/kg/m^3, the reaction chamber would be 2.5 million cubic meters. As a cube, it would be around 136 meters on a side.
Moving high-pressure CO through a reaction vessel at a meter per second would be a path length of 86,400 m. It would require an area of 28.9 square meters, or 5.4 meters inside diameter. The pressure inside at 50 bar (~750 psi) would generate a hoop tension per meter would be 5.4/2 x 100,000 Pa/bar x 50 bar or 13.4 MPa. This is a large reaction vessel, but it's not completely beyond what has been constructed (on earth).
The yield strength of steel is up to 500 MPs. Stressed to 200 MPa, the wall thickness would be 1/15th of a meter thick, and the mass per meter would be ~5.4 m x pi x 1/15 x 7800 kg / m or 8.8 tons per meter. The whole pressure chamber would mass 762,000 tons, all of it from the local source. This is by far the largest piece of the processing plant and about 3 times the initial plant mass estimate.
While steel can hold the pressure, the inside lining can't be iron or nickel. Gold perhaps-- or plastic.
The rotation of 1986 DA is 0.149 day, making the period 12873.6 s. Omega is .0000488 radians per second. The outward end of an 86.4 km long object would be subject to an acceleration of ~0.02 m/s^2 or about 1/500th of a g, not useful.
I am assuming the asteroid has north and south polar boom stems installed and a C shaped structure to hold the induction furnace in place as it peels the slowly rotating asteroid. The sheet metal would go through rolling seals into the high-pressure processing chamber.
For the acceleration at the end of the pressure chamber to be raised to a g would take a rotational speed of omega2 = 10/86400. That gives a period of about 9.7 minutes. The dust, everything plus the iron and nickel carbonyls, would fall outward against the countercurrent flow of CO.
Excess CO would go out the inward end, possibly with some dust, and against the flow of new metal ribbons. The outward end would provide a 1 g environment in which to sort out the liquid carbonyls by fractional distillation.
Reducing the size by half and using the pressure chambers in pairs would reduce the bearing forces on the asteroid coupling to near zero. Angular momentum balance will be part of the design, probably by pumping liquid from one side to the other of the center bearing
Depending on the exact composition of the asteroid, the CO dissolution step will reduce the processing stream by ~98% (90% iron, 8% nickel typical). The main element left will be cobalt (up to 1/2). The process will enrich gold to 50 ppm, platinum to 500 ppm and copper to 5000 ppm.
A byproduct is finely powdered iron. An efficient way to use this as reaction mass would lower the cost of cargo return to the Earth. A co-product could be Invar, but in amounts far beyond what the largest possible power-satellite project could use.
After removing the iron and nickel, sorting out the valuable elements from the stream will not be particularly challenging or energy intense, i.e., wet chemistry, electrowinning, ion exchange, etc. Of course, the plant will have to be configured to regenerate acids or other reagents needed in the process.
While this looks like an extremely profitable mining operation, many questions need to be researched to refine the design and economic analysis. For example, at what rate does high-pressure carbon monoxide eat away the surface of asteroid metal? Do the other elements, particularly cobalt, retard the attack?
Back in 1990 Dr. John Lewis (now Chief Scientist for Deep Space Industries) did extensive experiments on digesting iron meteorite specimens in a CO pressure bomb, including the catalytic effects of adding other gases to the CO. (The work was done by Muralidharan and Freiser in the UofA's Strategic Metals Recovery Research Facility under funding from our Space Engineering Research Center.)
While I think asteroid mining for gold and platinum is a ways off, it also seems to be a natural outgrowth of a large power satellite program. Indeed, it could provide some or all of the motivation to build the transport system for power satellites, if solving energy and carbon problems isn't enough.
This related article, "How Many Ore-Bearing Asteroids?"
by Martin Elvis came out in Nov. 2013