Do you know where I can find reaction rate constants? I tried the NIST reaction kinetics database, but H2O + CO2 -> H2CO3 is not even listed... I have implemented chemical reaction simulations before (gillespie and normal differential equations), the hard part is not the theory of simulating reactions but knowing how to determine the needed reaction rates for small inorganic reactions...

I read the paper you referenced, but it does not really add much? The key takeaway you refer to is probably the exothermic reaction enthalpy... we were discussing equilibria before this, so while a profound one, it is still a plattitude to point just at the exothermic nature as if at equilibrium all matter will be in the lowest energy state. It's still ~300K out there...

Somewhat less of a plattitude is to look at such a reaction and pretend we have a 2 level system (i.e. no other reactions occuring, no substep reactions). Let's take reaction number 2 on page 4 you mention:

1 / 3 Mg3Si2O5(OH)4 + CO2 → MgCO3 + 2 / 3 SiO2 + 2 / 3 H2O + 64 kJ/mole.

So lets call the energy of the "excited" LHS(left-hand-side)-state E1 and the RHS-state E0 the ground state.

Now to make a physical calculation we need integral numbers of molecules so I multiply both sides with 3:

Mg3Si2O5(OH)4 + 3CO2 → 3MgCO3 + 2SiO2 + 2H2O + 192 kJ/mole.

(The enthalphy per mole of reactions tripled because a single new reaction now converts 3 times the reagents as the original reaction)

So the LHS is 192kJ / N_avogadro higher in energy than the RHS for the specified number of molecules.

So for a simple 2 level System the partition function is Z = exp(-beta E_lhs)+exp(-beta E_rhs), from here on I will write B for beta...

The probability of finding the molecules in the LHS-state is P(LHS)=exp(-B E_lhs) / Z and similar for RHS...

The ratio LHS:RHS at equilibrium is P(LHS)/P(RHS) = exp(-B E_lhs) / exp(-B E_rhs) = exp(-B DeltaE) = exp(-B 192kJ / N_a)

= exp(-192kJ / mole / (N_a k_B T))

since B = 1 / ( k_B T ),

= exp(-192kJ / mole / (R T))

since ideal gas constat R = N_a * k_B = 8.314 J / mole / K

= exp(-192kJ / mole / (8.314 J / mole / K * 300K) )

= 3.7E-34

So the right hand side does indeed look very much preferred

But this calculation assumes not dissolving in water.

This paper does not propose dissolving the resulting mineral carbonate in water, they propose burying it in the same mine the igneous rock was found!

I am still worried that simply dissolving it in surface water of the oceans means the CO2 can be released, or at the very least the CO2 in one of the dissolved species CO2, HCO3- or CO3(2-) are too bio-available... this may sound good, but if it is captured back into the biosphere it will be exhaled again by the organism (or its predator) pretty soon... grass clippings can be considered carbon sequestration, until you feed it to the organisms in your composting heap!

I would love to see numerical simulations of the chemical reactions, it would help sway those of us who understand how to simulate a set of reactions but have insufficient domain knowledge to know which reactions should be kept in mind.

The different competing entities that wish to get sponsored for such activities have a common interest to produce such a model or at least a list of relevant chemical reactions in the ocean and their kinetic rate constants. They could pool their resources to build this model.