The phenomenon of incomplete mixing reduces bulk effective reaction rates in reactive transport. Many existing models do not account for these effects, resulting in the overestimation of reaction rates in laboratory and field settings. To date, most studies on incomplete mixing have focused on diffusive systems; here, we extend these to explore the role that flow heterogeneity has on incomplete mixing. To do this, we examine reactive transport using a Lagrangian reactive particle tracking algorithm in two-dimensional idealized heterogeneous porous media. Contingent on the nondimensional Peclet and Damköhler numbers in the system, it was found that near well-mixed behavior could be observed at late times in the heterogeneous flow field simulations. We look at three common flow deformation metrics that describe the enhancement of mixing in the flow due to velocity gradients: the Okubo-Weiss parameter $\left(\theta \right)$, the largest eigenvalue of the Cauchy-Green strain tensor $\left({\lambda }_C\right)$, and the finite-time Lyapunov exponent $\left(\mathrm{\Lambda }\right)$. Strong mixing regions in the heterogeneous flow field identified by these metrics were found to correspond to regions with higher numbers of reactions, but the infrequency of these regions compared to the large numbers of reactions occurring elsewhere in the domain imply that these strong mixing regions are insufficient in explaining the observed near well-mixed behavior. Since it was found that reactive transport in these heterogeneous flows could overcome the effects of incomplete mixing, we also search for a closure for the mean concentration. The conservative quantity $\overline{u^2}$, where $u=C_A-C_B$, was found to predict the late time scaling of the mean concentration, i.e., $\overline{C_i}\sim \overline{u^2}$.

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• Flows in porous media
• Mixing in geophysical flows
• Reacting flows