Predicting Anomalous Reactive Transport in Rough Fractures: Pore-scale Simulation and Stochastic Upscaling

Abstract:

Mixing and reaction in rough channel flows are ubiquitous phenomena occurring in numerous engineering applications and natural processes including microfluidics, biomedical devices, heat exchangers, and fractured geological media. The classic Taylor–Aris approach based on the concept of effective diffusivity has been proven useful for capturing spreading in channel flows. However, in pre-asymptotic regimes, the approach breaks down and anomalous transport has been observed in channel flows. Furthermore, the interplay between wall roughness and inertia causes recirculating flows which have been shown to cause anomalous transport. However, the effects of recirculating flows on mixing and reactive transport in channel flows, especially in pre-asymptotic regimes, are poorly understood. In pre-asymptotic regimes, solute particles have not yet sampled the full velocity spectrum and mixing and reaction dynamics are spatially heterogeneous, leading to complex reactive transport behavior. Currently, we do not have comprehensive understanding of anomalous reactive transport in rough channel flows limiting our predictive capability.

We investigate the compound effects of roughness, inertia, and diffusion on the emergence of anomalous reactive transport in rough channels. We consider instantaneous bimolecular reaction (A + B → C) and solve for advection–diffusion–reaction over wide ranges of roughness, Reynolds number (Re), and Peclet number (Pe), using a random walk based reactive particle tracking method. With extensive numerical simulations and stochastic modeling, we show that the complex reactive transport behavior is encoded in Lagrangian velocity statistics. We propose a parsimonious upscaled reactive transport model that is fully parameterized with the Lagrangian velocity statistics and find that the model can capture reactive transport over wide ranges of roughness, inertia, and diffusion.