  Motivated by CO2 capture and sequestration (CCS) design considerations, we
consider the coupled effects of permeability heterogeneity and background flow
on the dissolution of a supercritical CO2 lens into an underlying deep,
confined aquifer. We present the results of a large-scale Monte Carlo
simulation study examining the interaction of background flow rate and three
parameters describing multi-Gaussian log-permeability fields: mean, variance,
and correlation length. Hundreds of high-resolution simulations were performed
using the PFLOTRAN finite volume software to model CO2 dissolution in a
kilometer-scale aquifer over 1000 y. Predictive dimensionless scaling
relationships relating CO2 dissolution rate to heterogeneity statistics,
Rayleigh (Ra) and Peclet (Pe) numbers were developed for both gravitationally
dominated free convection to background flow-dominated forced convection
regimes. An empirical criterion, $\rm Pe\ = Ra^{3/4}$, was discovered for
regime transition. All simulations converged quickly to a quasi-steady,
approximately linear dissolution rate. However, this rate displayed profound
variability between permeability field realizations sharing the same
heterogeneity statistics, even under mild permeability heterogeneity. In
general, increased heterogeneity was associated with a lower mean and higher
variance of dissolution rate, undesirable from a CCS design perspective. The
relationship between dissolution rate and background flow was found to be
complex and nonlinear. Dimensionless scaling relationships were uncovered for a
number of special cases. Results call into question the validity of the
Boussinesq approximation in the context of modest-to-high background flow rates
and the general applicability of numerical simulations without background flow.
