>I would suspect this entire process is carbon-positive despite the atmospheric capture.
Consider the napkin math. One mole of MgSiO3 reacts with one mole of CO2 to give MgCO3 + SiO2. The embodied energy in CO2 from C + O2 is 393 kJ/mol. One mole of MgSiO3 weighs 100 grams (almost exactly) and has a specific heat of roughly 1 kJ/kg-K. That works out to roughly the amount of energy required to heat the olivine by 3930 Kelvins, although this is well beyond the point at which specific heat becomes nonlinear and would most likely melt the sample.
Since it is uncommon for rocks to melt when grinding we can conclude that the embodied energy in the carbon absorbed is way larger than the energy required to grind the material. The inefficiency of electric generation certainly comes into play but even if we use a factor of 1/5 we still find a temperature rise of 786 Kelvin which would be extremely damaging to equipment if it actually occurred, and the actual temperature rise is probably less than 100 Kelvin. This still gives a comfortable margin of inefficiency for the carbonation process. And we have assumed that all of the energy is coming from inefficient coal-burning plants, which are in reality a minority of the global energy mix.
Consequently, we can conclude unequivocally that olivine grinding absorbs more carbon than it emits even under relatively pessimistic assumptions, and dramatically more carbon than it emits under realistic assumptions. While the energy of grinding is large, the embodied energy of CO2 is very large — this is why carbonaceous fuels became popular.
There are downsides to the process — most obviously but with a distant horizon, sequestration of carbon in this manner is precisely the process expected to eventually destroy the biosphere by carbon starvation in a few hundred million years, and using olivine to stop global warming is slightly accelerating the inevitable doom of all life on Earth. Also, it takes up a lot of space and costs a lot of money. And inevitable doom. But you know, priorities.
Obviously this is not related to olivine, so we would need to call around to get the appropriate ones. This isn't like computer work where you can just google it.
You're probably looking for the fracture energy -- the energy required to create a fracture with a unit surface area.
Take the grain size you're looking to end up with, compute the surface area and mass, combine it with the fracture energy, and you should have a pretty decent estimate for the energy required to grind a particular substance to a particular size.
Your energy math, or its explanation, is incorrect. the embodied energy in CO2 is irrelevant - the comparison is of products and reactants, of which 'C' and 'O2' are neither.
Consider the napkin math. One mole of MgSiO3 reacts with one mole of CO2 to give MgCO3 + SiO2. The embodied energy in CO2 from C + O2 is 393 kJ/mol. One mole of MgSiO3 weighs 100 grams (almost exactly) and has a specific heat of roughly 1 kJ/kg-K. That works out to roughly the amount of energy required to heat the olivine by 3930 Kelvins, although this is well beyond the point at which specific heat becomes nonlinear and would most likely melt the sample.
Since it is uncommon for rocks to melt when grinding we can conclude that the embodied energy in the carbon absorbed is way larger than the energy required to grind the material. The inefficiency of electric generation certainly comes into play but even if we use a factor of 1/5 we still find a temperature rise of 786 Kelvin which would be extremely damaging to equipment if it actually occurred, and the actual temperature rise is probably less than 100 Kelvin. This still gives a comfortable margin of inefficiency for the carbonation process. And we have assumed that all of the energy is coming from inefficient coal-burning plants, which are in reality a minority of the global energy mix.
Consequently, we can conclude unequivocally that olivine grinding absorbs more carbon than it emits even under relatively pessimistic assumptions, and dramatically more carbon than it emits under realistic assumptions. While the energy of grinding is large, the embodied energy of CO2 is very large — this is why carbonaceous fuels became popular.
There are downsides to the process — most obviously but with a distant horizon, sequestration of carbon in this manner is precisely the process expected to eventually destroy the biosphere by carbon starvation in a few hundred million years, and using olivine to stop global warming is slightly accelerating the inevitable doom of all life on Earth. Also, it takes up a lot of space and costs a lot of money. And inevitable doom. But you know, priorities.