Ah, Terry beaten me to it! Indeed, it'd be huge lot of olivine required; something on the order of 1.000.000.000.000 tons of it to make any serious cut to the present CO2 athmopsheric content of nearly 2.054.000.000.000 tons of CO2. Assuming heavy-duty rail cars each carrying 100 tons, and assuming each cart doing a trip every week year-round (a week, in terms of rail transport, is VERY fast for a round), and assuming the project would aim to drop enough matherial in a matter of 10 years, we'd need:
1.000.000.000.000 / 100 / 52 / 10 = 19.230.769 cars, rolling non-stop for 10 years. In reality, for repairs, wear and tear, logistics and other reasons, the fleet of cars gotta be at least twice as big - 40 millions of 'em. Assuming length of each being 20 meters, 40 millions of them put one after another would circle the Earth at equator some 20 times; in other words, if we'd make a train made out of 40 millions of 20-meter-long train cars, and then send it steaming right straight to the moon, and after reaching the moon we'd send it right back to Earth - then by the time the 1st rail car would get back to Earth from the moon - the last car of the train would not yet have been departed from Earth, so the whole train itself would be like a double thread, tying Earth and Moon together.
Now that's indeed a lot of rail cars, eh.
As of now, there are approximatly 14500 trains in the world, if to trust wiki answers. Even if we'd assume average length of a train being 100 cars, which is alot, it then would be 1.450.000 train cars - that's for all purposes, passenger, all freight, oil cisterns - everything. That's how much mankind managed to built so far; 40 millions train cars is thus quite unrealistic, eh. Even if built somehow, it'd then be required to build corresponding rail roads on which 20 millions cars would be moving nearly 24/7 for 10 years, with all the required infrastructure - existing rail roads wouldn't suffice for even a tenth of required capacity, probably...
And rail cars is least of problems, yet. The energy to get enough sufficiently pure olivine is not a joke either - extraction operation would be astronomically costly, considering the amount needed. Then most likely it'll have to be crushed into small enough pieces, and all the machinery needed for that ain't no joke either. And then it'll have to be distributed properly - can't just drop 100-ton piles of it right into the shallow waters, as that much would simply form a pile, and only small fraction of the matherial would actually do any chemical reaction, the rest would be just "buried". So most likely it'll have to be special ships, going along coasts, spreading the matherial around.
Although those flows do not in any way discredit the idea itself! Perhaps with time solutions could be found to circumvent all the problems of "usual" way. I'm just affraid such solutions may perhaps create further massive trouble, though. Like, if they at some point would decide to use some fraction of existing nuclear weapons to "blow" large masses of olivine into the ocean (from known large deposits of this mineral underwater, for example). Or if they'd just blow a hole to olivine magmas with those same weapons, and let some few thousands gigatons of the staff to enter top layers of the ocean. On 1st glimpse it could work in practice, but i really wouldn't try to get tectonic... We might well end up eventually blowing ourselves up if we'd start to look that direction; after all, Earth crust is indeed like a very thin, tender, weak "skin" of the core mass of Earth - which is red- or white-molten, radioactive, rather poisonous mass of molten rocks and heavy molten metals (at the core).
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As for the other project, - capturing CO2 at the exit pipe of power stations, - it has some serious flaws too:
- R&D cost 15 billions USD for 5-year program. Not a problem for a proven technology - but a problem for any technology not confirmed by a full-scale pilot project. Uncertain if any investor willing to risk 15B for a something which is, seemingly, only a lab-tested idea. The thing needs much more humble "proof of concept" 1st if it's any serious, imho;
- is not quick enough: 5+ years for required R&D, then some 10-15 years at very least to implement the technology to the majority of world coal and gas power stations. So ~20 years even in the best case before it starts to make any practical and significant difference. Those are 20 years we do not have, because
- too late for the idea itself, too. Already existing levels of CO2, which is 400 ppm, is likely to lead to +6 or so degrees C warming. Was the case ~3 millions years ago - was +6 warmer with some 340...400 ppm CO2 in the air. At the moment, most of the warming is yet not realized due to thermal inertia of the world ocean, which is few decades long process; however, as additional thermal forcing from alread-yemitted CO2 stays around for centuries, the world ocean will continue to be filled with heat, and as it does, more and more surface increase of temperatures will realize as well - even with constant CO2 levels. And 2nd, there is massive man-made dimming (aka "global dimming"), from all the aerosols emitted by fossil fuel combustion, deforestation (often made by fire), increasingly powerful forest fires, cement production, airliners, etc. Most of those aerosols settle down in a matter of a 1...3 years. Sooner or later fossil fuel burning will stop (one way or another - it's not infinite in any case), aerosols wil lthen go down, but CO2 will still be around - which will result in further and large increase of radiative forcing, and then 2nd "act" of additional warming, comparable in scale to what was before that moment. There are, however, some few places on Earth which are quite far from any major sources of aerosols even nowadays; one such place is a little city of Petropavlovsk-Kamchatsky in Russia's far east. Well guess what, during last decade, average monthly temperatures for all 12 months there have increased by 2.2...3.6 degrees C (iirc, last time i checked). So almost +3 degrees C average annual temperature during last decade. And it ain't polar region, with that (so no strong polar amplification);
- even if all above would not be a problem, there is one more thing: nowadays, and as it have always been since industrial revolution, power plants emit less than a half of man-made CO2. Significantly less than a half. The rest is being emitted by a sum of emissions from transport, direct home heating (by the way, peat, which is used to heat homes in poor regions, is VERY dirty thing as a fuel), agriculture machinery, cement production, intentional deforestation and other sources. And, it'd be quite problematic to install the technology proposed to every car, plane, ship, diesel locomotive, helicopter, truck, agriculture vehicle, i guess. Thus, it could, at best, only slow further increase of CO2 in the athmosphere a bit, but nothing more. To illustrate how relatively insignificant the reduction would be, suffice to compare the reduction expected (as they say on the page you linked), which is 0.7 GT CO2/yr, to the total amount of CO2 emitted by mankind: ~35GT CO2/yr. In other words, a reduction of annual emissions of 2.0%. Is this a big deal to you? To me, it's not; regular and still ongoing growth of CO2 emissions would completely negate this reduction in a matter of less than 2 years - which is 10 times shorter than the realistic timeframe of installing the technology.
So in the essense, this carbon capture scheme is, imho, nothing else than partial, inapproriate, insignificant and outdated solution to the problem. I am really sorry to say that. But it'd be even worse to be silent about that. Still, i am sorry.
And that's even before any consideration for the process itself, technologically. That 20-30$ a ton look good on paper, but i just bet the figure will be increased much, perhaps even 10-fold, after the technology gets from laboratory into the real world. To provide all the vast masses of compounds needed, to combat corrosion (inevitable, since the process involves water, hot gases and metallic constructions), to remove and properly dispose of the products, and to do all that in economically deteriorating world (which it most likely will be by the time R&D phase would be done for this tech) - will be expensive.
This was a long and sad message i piled up here, paragraph by paragraph. But it's how things are, imho. Say, if you didn't read James Lovelock's "Vanishing face of Gaia" yet, may be it's the time to. HEre it is:
http://esotericonline.net/docs/library/Philosophy/Environmental%20philosophy/Environmental%20Issues/Lovelock%20-%20The%20Vanishing%20Face%20of%20Gaia.pdf .