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\begin{document}

\title{Rayleigh invariance allows the estimation of effective CO2 fluxes due to
convective dissolution into water-filled fractures}



\author[1]{Leon Keim}%
\author[1]{Holger Class}%
\affil[1]{University of Stuttgart, Institute for Modelling Hydraulic and Environmental Systems}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
Convective dissolution of CO2 is a well-known mechanism in geological
storage of CO2 . 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 CO2 concentration were used to compute
scenario-specific results for effective CO2 entry rates into an
idealized fracture with varying aperture, temperature, and CO2
concentration at the gas-water interface. The results were analyzed in
terms of dimensionless quantities. They revealed a Rayleigh invariance
of the effective CO2 flux after the complete formation of a
quasi-stationary velocity profile, i.e. after a certain entry length.
Hence, this invariance can be exploited to estimate the effective CO2
entry rates, which can then be used, in perspective, in upscaled
models.\\
We have studied convective CO2 dissolution for two different fracture
settings; the first one relates to karstification scenarios, where CO2
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 CO2 storage, where the literature provides only
studies on convective CO2 dissolution for porous-media flow with Darcy
regimes.%
\end{abstract}%



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