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\begin{document}

\title{Upscaling CO2 Migration Under Buoyancy and Capillary Heterogeneity
Effects -- A New Approach Using Optimization}



\author[1]{Avinoam Rabinovich}%
\author[1]{Kan Bun Cheng}%
\affil[1]{Tel Aviv University}%


\vspace{-1em}



  
  \date{May 15, 2024}


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\begin{abstract}
Coarsening a numerical mesh using methods of multiphase flow property
upscaling is essential in almost any modeling application due to
computational limits. In CO2 storage modeling, after injection wells
have been shut off or far away from the wells, CO2 migrates upwards
under the influence of gravity and capillary forces. Upscaling
permeability (k), relative permeability (kr) and capillary pressure (Pc)
is required for grid coarsening these models. However, it has been shown
that this is a difficult problem and using conventional upscaling
methods such as the common capillary limit upscaling approach leads to
large modeling errors. This work presents a new upscaling method based
on an effective property formula for k, power law averaging in the
capillary limit for kr, and an optimization approach for Pc. The new
method is tested on various example cases and coarse-grid simulations
are shown to match fine-grid ones with sufficient accuracy. The
challenge of upscaling the flows is found to be related to entry
pressure trapping and the optimization upscaled Pc is shown to have a
unique structure allowing to model the trapping. The method is global,
requiring a fine-grid simulation for calibration of the optimized
parameters. However, we show that the method reduces computational time
dramatically if calibrated parameters are used in similar cases in which
the fine-grid solution is unknown, such as for varying k realizations.%
\end{abstract}%



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