Anomalous transport through porous and fractured media

Abstract

Anomalous transport, understood as the nonlinear scaling with time of the mean square displacement of transported particles, is observed in many physical processes, including contaminant transport through porous and fractured geologic media, animal and human foraging patterns, tracer diffusion in biological systems, and transport in complex networks. Understanding the origin of anomalous transport is essential, because it determines the likelihood of high-impact, low-probability events and therefore exerts a dominant control over the predictability of a system. The origin of anomalous transport, however, remains a matter of debate. In this thesis, we first investigate the pore-scale origin of anomalous transport through sandstone. From high-resolution (micron-scale) 3D numerical flow and transport simulation, we find that transport at the pore scale is markedly anomalous. We demonstrate that this anomalous behavior originates from the intermittent structure of the velocity field at the pore scale, which in turn emanates from the interplay between velocity heterogeneity and velocity correlation. Finally, we propose a continuous time random walk (CTRW) model that honors this intermittent structure at the pore scale and captures the anomalous 3D transport behavior at the macroscale. To show the generality of our finding, we study transport through lattice networks with quenched disorder. We again observe anomalous transport originating from the interplay between velocity heterogeneity and velocity correlation. We extend the developed CTRW model to capture the full multidimensional particle transport dynamics for a broad range of network heterogeneities and for both advection- and diffusion-dominated flow regimes. We then study anomalous transport through fractured rock at the field-scale. We show that the interplay between heterogeneity and correlation in controlling anomalous transport can be quantified by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity heterogeneity. Our transport model captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Moreover, the inferred flow correlation length shows qualitative agreement with geophysical measurements. Thus, the proposed correlated CTRW modeling approach furnishes a simple yet powerful framework for characterizing the impact of flow correlation and heterogeneity on transport in porous and fractured media. Finally, we propose a joint flow-seismic inversion methodology for characterizing fractured reservoirs. Traditionally, seismic interpretation of subsurface structures is performed without any account of flow behavior. With the proposed methodology, we reduce the uncertainty by integrating dynamic flow measurements into the seismic interpretation, and improve the predictability of reservoir models by this joint use of seismic and flow data. This work opens up many possibilities of combining geophysical and flow information for improving subsurface characterization.