Early Time Effective Reactivity of Reactive Transport in Cylindrically-Advected Reaction Fronts is enhanced by Hydrodynamic Dispersion

Reaction fronts are widespread in nature and are encountered frequently in the geological context. Examples include contaminant spread, neutralization-based reservoir decontamination, biogeochemical phenomena, and many more. The complex porous structures of subsurface formations renders the flow geometry incredibly complex, which in turn can, and often does, lead to interesting and peculiar reactive transport. For instance, the stretching and folding of the reaction front due to flow shear can enhance the effective reactivity, and flow stagnation spots can serve as sites for accummulation of reactants.

At the Darcy scale, the spreading of the front is controlled by hydrodynamic dispersion, which is a continuum scale manifestation of the pore scale interaction between heterogeneous advection and molecular diffusion. When the flow field is uniform, the consequence of dispersion is only a quantitative enhancement of diffusion. However, if the flow field varies in space, as may occur for example during aquifer remediation by injection of a neutralizing agent, the effect of hydrodynamic dispersion will lead to qualitative modifications in reactive transport dynamics as compared to hypothetic scenarios where the only diffusive mechanism is molecular diffusion. Yet, despite the ubiquity of dispersion, its impact on reactive fronts in porous media has not been addressed for flows with an axisymmetrical geometry, which are typical of well injection scenarios.

Therefore, we study the impact of hydrodynamic dispersion on reactive transport in cylindrically-advected bimolecular reaction fronts. We show that, in the reaction-limited regime at early times, mechanical dispersion is the dominant transport process and augments the reaction front’s advancement (which scales as t^1/3, t being the time), the reaction rate (which scales as t^2/3) and the product mass (which scales as t^5/3), in comparison to a dispersion-free scenario (for which, the reaction front advancement, the reaction rate and the product mass scale as t^1/2, t¹ and t² respectively). On the other hand, depending on the strength of hydrodynamic dispersion, we may encounter a dispersion-dominated, mixing-limited, regime of the reactive front at large times, which exhibits a declining reaction rate. This bevahior is significantly different from the dispersion-free scenario where a declining reaction rate is never encountered. Lastly, at sufficiently long times (longer for stronger dispersion), the reaction front transitions to a behavior akin to that seen in the dispersion-free scenario, wherein the differences between the dispersive and the dispersion-free scenarios become negligible.