Impact of Transient Flow on Reactive Fronts in Porous Media

Groundwater flow is subject to transients, due to natural events or human activities (recharge, tides, decontamination, etc.). The occurrence of such temporal fluctuations in the flow field can have significant impact on reactive transport processes, compared to steady flow conditions, especially in reactive fronts. These fronts manifest as localized interfacial regions where chemical reaction occurs in an ambient flow field that brings two or more reactants in contact with each other. Understanding how reaction fronts evolve during transient flows is therefore key to predicting reactive transport in the subsurface. 

In these fronts, reaction rates often depend on the local mixing state of the reactants, which in turn is controlled by the interplay between advective and diffusive processes. Under steady flow conditions, the presence of heterogeneity in the permeability fields has been shown to enhance mixing and reaction at the Darcy scale, due to stretching-enhanced mixing. In contrast, it is currently unknown how transient flows would impact reaction rates. 

Here, we conduct reactive transport experiments with transient flow in both Hele-Shaw and index-matched porous media cells. A steady mixing front is created inside the cell by two opposing injection points, creating of a stagnation point flow. Transient flow is then imposed by varying the ratio of the injection rates, causing a displacement of the stagnation point and the mixing front. A bimolecular chemiluminescent reaction is used to quantify the effective reaction rate within the mixing front at all times. We observe that transient flows increase reactivity compared to steady state conditions, both in the local maximum of reaction rates and in the size of the reactive front.

In the Hele-Shaw cell, the enhancement can be up to 3 times compared to steady conditions. The evolution of the reaction front to the new steady state occurs in a time much shorter than that required for Taylor-Aris dispersion, indicating that the reaction front remains in the ballistic shear regime when the reactivity enhancement is observed. Using the lamellar theory for sheared fronts, we find that the maximum reaction rate should scale with the transient flow strength to the power of 3/4, a prediction that compares well with the experimental observations (0.76±0.03).  

In the porous media cell, we also observe a power law scaling between the reaction rate enhancement and the transient flow magnitude, with an exponent of 0.58±0.01. In contrast to the Hele-Shaw case, we argue that the mixing enhancement is due to longitudinal hydrodynamic dispersion. Solving the advection-dispersion-reaction equation for the reaction front near the stagnation point yields a theoretical exponent of 1/2 , which agrees well with experimental observations.

These results indicate that an important part of the biogeochemical activity in the subsurface can occur during transient events. The proposed modeling framework provides a quantitative prediction of such reactive transport dynamics.