Mechanisms of anomalous dispersion in flow through heterogeneous porous media

2017

Eur. Phys. J. B

Self Cite

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of heterogeneity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials. arXiv:1707.05560v2 [physics.flu-dyn]

Section: Disorder Modelmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

Comolli

2017

Eur. Phys. J. B

Self Cite

“…(), and Tyukhova et al. () investigated the relation between the hydraulic conductivity distribution and advective travel times for heterogeneous porous media. Edery et al.…”

Section: Introductionmentioning

confidence: 99%

Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media

Comolli

Hakoun

Water Resources Research

2019

Self Cite

We study the upscaling and prediction of large‐scale solute dispersion in heterogeneous porous media with focus on preasymptotic or anomalous features such as tailing in breakthrough curves and spatial concentration profiles as well as nonlinear evolution of the spatial variance of the concentration distribution. Spatial heterogeneity in the hydraulic medium properties is represented in a stochastic modeling approach. Direct numerical Monte Carlo simulations of flow and advective particle motion combined with a Markov model for streamwise particle velocities give insight in the mechanisms of preasymptotic and asymptotic solute transport in terms of the statistical signatures of the medium and flow heterogeneity. Based on the representation of equidistantly sampled particle velocities as a Markov process, we derive an upscaled continuous time random walk approach that can be conditioned on the flow velocities and thus hydraulic conductivity in the injection region. In this modeling framework, we identify the Eulerian velocity distribution, advective tortuosity, and the correlation length of particle velocities as the key quantities for large‐scale transport prediction. Thus, the upscaled model predicts the spatial concentration profiles, their first and second centered moments, and the breakthrough curves obtained from direct numerical Monte Carlo simulations in spatially heterogeneous conductivity fields. The presented approach allows to relate the medium and flow properties to large‐scale preasymptotic and asymptotic solute dispersion.

“…The continuous time random walk (CTRW) model has become a growingly popular framework for predicting anomalous transport in heterogeneous media [ Dentz and Berkowitz , ; Berkowitz et al , ; de Anna et al , ; Kang et al , ; Le Borgne et al , ; Holzner et al , ; Le Borgne et al , ; Sund et al , ; Tyukhova et al , ]. At its core, CTRW models describe effective transport by discretizing the solute into a large number of particles that move as a sequence of transitions in space and time.…”

Section: Introductionmentioning

confidence: 99%

Stochastic dynamics of intermittent pore‐scale particle motion in three‐dimensional porous media: Experiments and theory

Morales

Geophysical Research Letters

Willmann

et al. 2017

We study the evolution of velocity in time, which fundamentally controls the way dissolved substances are transported and spread in porous media. Experiments are conducted that use tracer particles to track the motion of substances in water, as it flows through transparent, 3‐D synthetic sandstones. Particle velocities along streamlines are found to be intermittent and strongly correlated, while their probability density functions are lognormal and nonstationary. We demonstrate that these particle velocity characteristics can be explained and modeled as a continuous time random walk that is both Markovian and mean reverting toward the stationary state. Our model accurately captures the fine‐scale velocity fluctuations observed in each tested sandstone, as well as their respective dispersion regime progression from initially ballistic, to superdiffusive, and finally Fickian. Model parameterization is based on the correlation length and mean and standard deviation of the velocity distribution, thus linking pore‐scale attributes with macroscale transport behavior for both short and long time scales.