ON THE USE OF TRANSITION-STATE-THEORY (TST) TO PREDICT CARBONATE GROWTH IN SEDIMENTARY BASINS

The conventional way of modeling secondary carbonate formation for CO₂ storage scenarios is to employ general rate equations derived from Transition-State-Theory and the principle of detailed balancing. This offers simple equations that provide rate estimates for a range of chemical and physical conditions, and more importantly, equations that estimate precipitation rates based on far-from-equilibrium dissolution rate data.

The validity of using these equations rest on several assumptions. First, the dissolution rate coefficients used to model growth must be known and valid for the whole range of reaction affinities and hence be based on the same reaction mechanism and the same elementary reactions over the affinity region; second, growth of secondary phases must have pre-defined reactive surface areas and may form without a preceding nucleation stage; and third, the affinity term itself is based on an equilibrium surface, and hence assumes that surface defects have no impact on dissolution and growth.

We have looked into the validity of using TST derived equations to model carbonate growth and found that estimated growth rates are likely orders of magnitude overrated. First, a nucleation barrier exists at low temperatures and low supersaturations. Second, experimental data on carbonate growth appear to be explained by higher-order growth models such as Burton-Cabrera-Frank (BCF) growth, which can not be reduced to linear dependence on the reaction affinity upon approaching equilibrium, as is the requirement of TST. Third, high-resolution studies of mineral reaction rates using surface-area monitoring techniques such as AFM, suggests that both dissolution and growth are strongly dependent on non-equilibrium surface defects.

Instead of the use of TST for carbonate precipitation, we propose a model for nucleation and growth based on classical nucleation theory and second-order growth, with a minimum of adjustable parameters.

r = -kS∏a_i^vexp(-Ea/RT)(Ω-1)² - k_Nexp(-Γ(1/(T^3/2lnΩ))²)

Finally, as growth rate parameters are only known for a few minerals and nucleation rate data are mostly unknown, to successfully model carbonate growth in sedimentary basins we call for an increased effort to assemble nucleation and growth rate data.