Transport in lattice fracture networks : concentration mean and variance

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 53-55).We study transport in fractured systems using a stochastic particle tracking approach. We represent a fractured system as a two-dimensional lattice network system where the transport velocity in each fracture is a random variable. Our goal is to develop an exact effective macroscopic model for the concentration mean and variance from the microscopic disorder model. Within a Lagrangian transport framework, we derive effective equations for particle transport by coarse graining and ensemble averaging of the local scale Langevin equations. The results show that the mean transport can be captured exactly by an uncoupled continuous time random walk (CTRW) and the variance of the concentration by a novel two-particle CTRW formulation. Information about variance of concentration between realizations is important for understanding predictability. Therefore, ensemble mean together with variance provide critical information for understanding and predicting transport through the lattice network.by Peter Kyungchul Kang.S.M

Anomalous transport on regular fracture networks: Impact of conductivity heterogeneity and mixing at fracture intersections

We investigate transport on regular fracture networks that are characterized by heterogeneity in hydraulic conductivity. We discuss the impact of conductivity heterogeneity and mixing within fracture intersections on particle spreading. We show the emergence of non-Fickian transport due to the interplay between the network conductivity heterogeneity and the degree of mixing at nodes. Specifically, lack of mixing at fracture intersections leads to subdiffusive scaling of transverse spreading but has negligible impact on longitudinal spreading. An increase in network conductivity heterogeneity enhances both longitudinal and transverse spreading and leads to non-Fickian transport in longitudinal direction. Based on the observed Lagrangian velocity statistics, we develop an effective stochastic model that incorporates the interplay between Lagrangian velocity correlation and velocity distribution. The model is parameterized with a few physical parameters and is able to capture the full particle transition dynamics.United States. Dept. of Energy (Grant DE-SC0003907)MISTI (Hayashi Seed Fund

Anomalous transport through porous and fractured media

Thesis: Ph. D. in Hydrology, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2014.Cataloged from PDF version of thesis.Includes bibliographical references (pages 132-144).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.by Peter Kyungchul Kang.Ph. D. in Hydrolog

Predictability of anomalous transport on lattice networks with quenched disorder

We study stochastic transport through a lattice network with quenched disorder and evaluate the limits of predictability of the transport behavior across realizations of spatial heterogeneity. Within a Lagrangian framework, we perform coarse graining, noise averaging, and ensemble averaging, to obtain an effective transport model for the average particle density and its fluctuations between realizations. We show that the average particle density is described exactly by a continuous time random walk (CTRW), and the particle density variance is quantified by a novel two-particle CTRW.United States. Dept. of Energy. Office of Science (Graduate Fellowship Program)Spain. Ministerio de Ciencia e Innovación (MICINN) (project HEART CGL2010- 18450

Stress-Induced Anomalous Transport in Natural Fracture Networks

We investigate the effects of geological stress on fluid flow and tracer transport in natural fracture networks. We show the emergence of non-Fickian (anomalous) transport from the interplay among fracture network geometry, aperture heterogeneity, and geological stress. In this study, we extract the fracture network geometry from the geological map of an actual rock outcrop, and we simulate the geomechanical behavior of fractured rock using a hybrid finite-discrete element method. We analyze the impact of stress on the aperture distribution, fluid flow field, and tracer transport properties. Both stress magnitude and orientation have strong effects on the fracture aperture field, which in turn affects fluid flow and tracer transport through the system. We observe that stress anisotropy may cause significant shear dilation along long, curved fractures that are preferentially oriented to the stress loading. This, in turn, induces preferential flow paths and anomalous early arrival of tracers. An increase in stress magnitude enhances aperture heterogeneity by introducing more small apertures, which exacerbates late-time tailing. This effect is stronger when there is higher heterogeneity in the initial aperture field. To honor the flow field with strong preferential flow paths, we extend the Bernoulli Continuous Time Random Walk model to incorporate dual velocity correlation length scales. The proposed upscaled transport model captures anomalous transport through stressed fracture networks and agrees quantitatively with the high-fidelity numerical simulations. © 2019. American GeophysicalP. K. K. acknowledges the College of Science and Engineering at the University of Minnesota and the George and Orpha Gibson Endowment for its generous support of Hydrogeology. P. K. K. also acknowledges a grant from Korea Environment Industry and Technology Institute (KEITI) through Subsurface Environmental Management (SEM) Project, funded by Korea Ministry of Environment (MOE) W12530(2018002440003). M. D. acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511). R. J. acknowledges funding by the U.S. Department of Energy Office of Science (grant DE-SC0018357). The digitized Bristol fracture network data are freely available through a data repository system at the University of Minnesota (https://doi.org/10.13020/ah7v-6n67).Peer reviewe

Maximizing the value of pressure data in saline aquifer characterization

The injection and storage of freshwater in saline aquifers for the purpose of managed aquifer recharge is an important technology that can help ensure sustainable water resources. As a result of the density difference between the injected freshwater and ambient saline groundwater, the pressure field is coupled to the spatial salinity distribution, and therefore experiences transient changes. The effect of variable density can be quantified by the mixed convection ratio, which is a ratio between the strength of two convection processes: free convection due to the density differences and forced convection due to hydraulic gradients. We combine a density-dependent flow and transport simulator with an ensemble Kalman filter (EnKF) to analyze the effects of freshwater injection rates on the value-of-information of transient pressure data for saline aquifer characterization. The EnKF is applied to sequentially estimate heterogeneous aquifer permeability fields using real-time pressure data. The performance of the permeability estimation is analyzed in terms of the accuracy and the uncertainty of the estimated permeability fields as well as the predictability of breakthrough curve arrival times in a realistic push-pull setting. This study demonstrates that injecting fluids at a rate that balances the two characteristic convections can maximize the value of pressure data for saline aquifer characterization. Keywords: Managed aquifer recharge; Density-dependent flow; Inverse modeling; Ensemble Kalman filter; Value of information; Permeability estimatio

Coupled Flow Processes in Fractured Media Across Scales: Experimental and Modeling Advances II

International audienceIn fractured media, fluid flow depends on and induces coupled processes (hydrogeological-mechanical-chemical-biological-thermal) across a wide range of time and length scales. Understanding fluid flow and its coupling with different processes is critical for numerous subsurface applications including petroleum and geothermal reservoir management, environmental remediation, carbon sequestration, and long-term radioactive waste isolation. This session focuses on recent research that provides mechanistic understanding and predictive capability of physical processes in fractured media including coupled flow and geomechanics, non-Fickian transport, colloid and bacterial transport, mixing and reaction, fluid/mineral interactions, and biofilm formation. In particular, we encourage submissions related to (1) experiments and field observations, (2) new theoretical and numerical modeling approaches (direct simulation in single fractures, discrete fracture network modeling, upscaling methodologies, and multi-scale methods), and (3) the integration of data and models for observational interpretation and model validation

Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks

We study first passage behaviors in the flow through three-dimensional random fracture networks. Network and flow heterogeneity lead to the emergence of heavy-tailed first passage time distributions that evolve with increasing distance between the start and target planes, and transition toward stable laws. Analysis of the spatial memory of the first passage process shows that particle motion can be quantified stochastically by a time domain random walk conditioned on the initial velocity data. This approach identifies advective tortuosity, the velocity point distribution and the average fracture link length as key quantities for the prediction of first passage times. Using this approach, we develop a theory for the evolution of first passage times with increasing distance between the start and target planes and the convergence towards stable laws. © 2019 American PhysicalJ.D.H. and A.H. are thankful for support from the US Department of Energy through the Los Alamos National Laboratory. Specifically, support through the Laboratory-Directed Research and Development Program grants 20180621ECR and 20170103DR. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). J.D.H. also thanks the partial support of DOE’s Office of Science Basic Energy Sciences E3W1. M.D. gratefully acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511). P.K.K. acknowledges a grant from the Korea Environment Industry & Technology Institute (KEITI) through Subsurface Environmental Management (SEM) Project, funded by the Korea Ministry of Environment (MOE) (2018002440003).Peer reviewe