A chemical kinetics algorithm for geochemical modelling

Abstract

A chemical kinetics algorithm is presented for geochemical applications. The algorithm is capable of handling both equilibrium- and kinetically-controlled reactions in multiphase systems. The ordinary differential equations (ODEs) are solved using an implicit multistep backward differentiation formula (BDF) algorithm to ensure efficiency and stability when integrating stiff ODEs. An adaptive control scheme of the time step is adopted to guarantee small steps in steeper regions and large steps in smoother regions of the integration. Analytical derivatives of the reaction rates and species activities are used to permit the use of larger time steps, and to increase the robustness of the calculations. The chemical equilibrium calculations are performed using a Gibbs free energy minimisation algorithm, which is based on a trust-region interior-point method adapted with a watchdog strategy that yields quadratic rates of convergence near the solution. The chemical kinetics algorithm is applied to geochemical problems relevant to carbon storage in saline aquifers. The calculations assume aqueous, gaseous and mineral phases, where the kinetics of the water–gas–rock interactions are investigated. The results allow us to estimate the time frames at which brine of different salinities and supercritical CO2 attains equilibrium with a carbonate rock, as well as the amount of carbon dioxide trapped by solubility and mineralisation mechanisms.