Rayleigh Invariance Allows the Estimation of Effective CO2 Fluxes Due To Convective Dissolution Into Water-Filled Fractures

Abstract

Convective dissolution of ${\text{CO}}_2$ is a well-known mechanism in geological storage of ${\text{CO}}_2$. It is triggered by gravitational instability which leads to the onset of free convection. The phenomenon is well studied in porous media, such as saline aquifers, and the literature provides substantial evidence that onset times and effective flux rates can be estimated based on a characterization of instabilities that uses the Darcy velocity. This work extends the study of convective dissolution to open water-filled fractures, where non-Darcy regimes govern the induced flow processes. Numerical simulations using a Navier-Stokes model with fluid density dependent on dissolved ${\text{CO}}_2$ concentration were used to compute scenario-specific results for effective ${\text{CO}}_2$ entry rates into an idealized fracture with varying aperture, temperature, and ${\text{CO}}_2$ concentration at the gas-water interface. The results were analyzed in terms of dimensionless quantities. They revealed a Rayleigh invariance of the effective ${\text{CO}}_2$ flux after the complete formation of a quasi-stationary velocity profile, that is, after a certain entry length. Hence, this invariance can be exploited to estimate the effective ${\text{CO}}_2$ entry rates, which can then be used, in perspective, in upscaled models. We have studied convective ${\text{CO}}_2$ dissolution for two different fracture settings; the first one relates to karstification scenarios, where ${\text{CO}}_2$ is the dominant driving force, and were stagnant-water conditions in fractures have not yet received attention to date. The second setting is inspired from geological ${\text{CO}}_2$ storage, where the literature provides only studies on convective ${\text{CO}}_2$ dissolution for porous-media flow with Darcy regimes.