The present theoretical study analyzes the kinetic characteristics of precipitation of magnesite and lizardite as a result of hydrothermal alteration of olivine under high carbonate alkalinity. It makes use of a simulation strategy in which, both the chemical evolution of the aqueous solution and the solid phases are considered. The simulation is performed with the help of the NANOKIN code. It includes a full treatment of speciation processes in the aqueous solution, a rate equation for the dissolution of olivine, and a full account of nucleation and growth processes during the formation of secondary particles. The comparison between experimental (Lafay et al., 2014) and simulation results puts strong constraints on the simulation parameters, in particular those related to the nucleation and growth of the particles. Modeling points to an incongruent olivine dissolution and reveals a transitory precipitation of SiO2, not detected experimentally, showing that the fate of Si is more complex than a mere incorporation in lizardite. It highlights how lizardite, magnesite and SiO2 compete for the incorporation of silicon and magnesium released by the olivine dissolution.