Olivine Carbonation

What is modelled

A spherical grain of olivine reacts with dissolved CO2 from the outside in. The unreacted core shrinks, the carbonate and silica it leaves behind form an ash layer, and the CO2 has to cross the water film, diffuse through that ash and then react on the core surface. The three steps work in series.

Equations

• Reaction Mg2SiO4 + 2 CO2 → 2 MgCO3 + SiO2.
• Time to reach conversion X: t = τf X + τa [1 − 3(1−X)2/3 + 2(1−X)] + τr [1 − (1−X)1/3].
• Characteristic times τf = ρBR/(3 b kg C), τa = ρBR2/(6 b De C), τr = ρBR/(b ks C).
• Arrhenius law for the surface rate constant and the diffusivity; dissolved CO2 concentration taken proportional to the pressure.

Checks run in the page

• The rate law integrated step by step against the closed form.
• The pure reaction-controlled limit.
• CO2 uptake from the atomic masses.
• Scaling with grain radius and temperature.

Honest simplifications

The rate constants, the Henry-law concentration and the activation energies are illustrative round numbers, not a fit to a particular rock. Real olivine carbonation also depends on pH, passivation by silica, salt content and the dissolution of the mineral, none of which is in this model.

• Press Coarse grain and see the ash layer take over as the slow step.
• Press Fine grind and watch the time drop by orders of magnitude.
• Raise the CO2 pressure and see all three resistances shrink together.