  A new upscaling procedure that provides 1D representations of 2D
mixing-limited reactive transport systems is developed and applied. A key
complication with upscaled models in this setting is that the procedure must
differentiate between interface spreading, driven by the spatially variable
velocity field, and mixing, in which components contact one another and react.
Our model captures the enhanced mixing caused by spreading through use of a
time-dependent effective dispersion term. The early-time behavior of this
dispersion is driven by flow kinematics, while at late times it reaches a
Taylor-dispersion-like limit. The early-time behavior is modeled here using a
very fast (purely advective) particle tracking procedure, while late-time
effects are estimated from scaling arguments. The only free parameter in the
model is the asymptotic effective dispersion. This quantity is determined for a
few cases by calibrating 1D results to reference 2D results. For most cases, it
is estimated using a fit involving a dimensionless grouping of system
variables. Numerical results for bimolecular reaction systems are generated
using a pseudo-spectral approach capable of resolving fronts at high Peclet
numbers. Results are presented for two different types of 2D velocity fields
over a wide range of parameters. The upscaled model is shown to provide highly
accurate results for conversion factor, along with reasonable approximations of
the spatial distribution of reaction occurrence. The model is also shown to be
valid for non-reacting systems, and results for such cases can be used in the
calibration step to achieve computational savings.
