Non-constant Diffusion Behavior for CO₂ Diffusion into Brine: Influence of Density-Driven Convection

Abstract

A graphically-based analysis method used to characterize the diffusion process of carbon dioxide (CO₂) into brine conventionally assumes a constant diffusion coefficient. However, this study found that the assumption is not valid: an inflection point appeared in the calculated dimensionless pressure versus time curve separating the whole diffusion process into unsteady and steady stages, with each stage corresponding to different mechanisms. The unsteady stage, which accounts for the majority of the dissoluble CO₂ diffused into the brine, has hitherto always been neglected in calculating the diffusion coefficient. In this study, a pseudo-diffusion coefficient, which considers both the natural convection effect caused by fluid circulation due to density difference and molecule diffusion driven by the dissolved CO₂ concentration gradient, is proposed to characterize the unsteady stage of the diffusion process. Results from 21 pressure decay experiments indicate that the pseudo-diffusion coefficient of the unsteady stage varies directly with environment’s temperature and inversely with the brine concentration and pressure. The pseudo-diffusion coefficient varied in the range of 10⁻⁸–10⁻⁷ m²·s⁻¹, while the diffusion coefficient reported in the literature vary in the lower range of 10⁻¹⁰–10⁻⁸ m²·s⁻¹. The up to three orders of magnitude difference in the diffusion coefficients representing different diffusive mechanisms testifies to the importance of the unsteady stage in the diffusion of CO₂ in brine. This higher range of variation for the pseudo-diffusion coefficient now incorporating the unsteady stage has also the side effect of introducing higher uncertainties into the prediction of the concentration distribution in CO₂ sequestration calculations.