Engineering topics

Dentz, Marco

Publications and source records attributed to Dentz, Marco.

14 records

DOE OSTI2023

The hidden structure of hydrodynamic transport in random fracture networks

We study the large-scale dynamics and prediction of hydrodynamic transport in random fracture networks. The flow and transport behaviour is characterized by first passage times and displacement statistics, which show heavy tails and anomalous dispersion with a strong dependence on the injection condition. The origin of these behaviours is investigated in terms of Lagrangian velocities sampled equidistantly along particle trajectories, unlike classical sampling strategies at a constant rate. The velocity series are analysed by their copula density, the joint distribution of the velocity unit scores, which reveals a simple, albeit hidden, correlation structure that can be described by a Gaussian copula. Based on this insight, we derive a Langevin equation for the evolution of equidistant particle speeds. In this framework, particle motion is quantified by a stochastic time-domain random walk, the joint density of particle position, and speed satisfies a Klein–Kramers equation. The upscaled theory quantifies particle motion in terms of the characteristic fracture length scale and the distribution of Eulerian flow velocities. That is, it is predictive in the sense that it does not require the a priori knowledge of transport attributes. The upscaled model captures non-Fickian transport features, and their dependence on the injection conditions in terms of the velocity point statistics and average fracture length. It shows that the first passage times and displacement moments are dominated by extremes occurring at the first step. The presented approach integrates the interaction of flow and structure into a predictive model for large-scale transport in random fracture networks.

42 ENGINEERING↗

DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially-saturated conditions flows in fractures, percolating fracture networks, and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components and hence the bulk flow velocity and dispersion of fracture networks. In this work, we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The developed transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows to efficiently simulate flow through fracture networks with simple cubic structure and arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a non-dimensional bulk flow velocity ($\widetilde{v}$) and dispersion coefficient ($\widetilde{D}$) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales $\tau_m$ and $\tau_0$. The dispersion coefficient is shown to strongly depend on the horizontal time scale and converges towards a constant value of $0.08$ within reasonable fluid and geometrical parameter ranges, while the non-dimensional velocity exhibits a characteristic $\widetilde{v} \sim \tau_m^{-1/2}$ scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer system, such as boreholes or springs, our study intends to provide a rudimentary analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, e.g., the dispersive properties of discharge (groundwater level fluctuations).

42 ENGINEERING↗

DOE OSTI2020

Anomalous Transport in Three-Dimensional Discrete Fracture Networks: Interplay Between Aperture Heterogeneity and Injection Modes

In this work, we study how the interplay between fracture aperture heterogeneity and tracer injection mode controls fluid flow and tracer transport in three-dimensional (3D) discrete fracture networks (DFNs). The direct 3-D DFN simulations show that tracer injection mode has substantial effects on tracer spreading across all levels of aperture heterogeneity. The key controlling factor for effective transport is the initial Lagrangian velocity distribution, which is determined by the interplay between injection mode and aperture heterogeneity. The fundamental difference between initial Lagrangian velocity distribution and domain-scale Eulerian velocity distribution plays a vital role in determining anomalous transport. We effectively capture the observed anomalous transport using an upscaled transport model that incorporates initial velocity distribution, stationary velocity distribution, velocity correlation length, and average advective tortuosity. With the upscaled transport model, we accurately capture the evolution of Lagrangian velocity distribution and predict longitudinal spreading in 3-D DFN.

58 GEOSCIENCES↗

DOE OSTI2019

Characterizing the Influence of Fracture Density on Network Scale Transport

The topology of natural fracture networks is inherently linked to the structure of the fluid velocity field and transport therein. Here we study the impact of network density on flow and transport behaviors. We stochastically generate fracture networks of varying density and simulate flow and transport with a discrete fracture network model, which fully resolves network topology at the fracture scale. We study conservative solute trajectories with Lagrangian particle tracking and find that as fracture density decreases, solute channelization to large local fractures increases, thereby reducing plume spreading. Furthermore, in sparse networks mean particle travel distance increases and local network features, such as velocity zones where flow is counter to the primary pressure gradient, become increasingly important for transport. As the network density increases, network statistics homogenize and such local features have a reduced impact. We quantify local topological influence on transport behavior with an effective tortuosity parameter, which measures the ratio of total advective distance to linear distance at the fracture scale; large tortuosity values are correlated to slow-velocity regions. Additionally, these large tortuosity, slow-velocity regions delay downstream transport and enhance tailing on particle breakthrough curves. Finally, we predict transport with an upscaled, Bernoulli spatial Markov random walk model and parameterize local topological influences with a novel tortuosity parameter. Furthermore, Bernoulli model predictions improve when sampling from a tortuosity distribution, as opposed to a fixed value as has previously been done, suggesting that local network topological features must be carefully considered in upscaled modeling efforts of fracture network systems.

58 GEOSCIENCES↗

DOE OSTI2019

Stress-Induced Anomalous Transport in Natural Fracture Networks

In this work 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.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Linking structural and transport properties in three-dimensional fracture networks

Here, we investigate large scale particle motion and solute breakthrough in sparse three-dimensional discrete fracture networks (DFN) characterized by power-law distributed fracture lengths. The three networks we consider have the same fracture intensity values but exhibit different percolation densities, geometric properties and topological structures. We considered two different average transport models to predict solute breakthrough, a streamtube model and a Bernoulli CTRW model, both of which provide insights into the flow fields within the networks. The streamtube model provides acceptable predictions at short distances in two of the networks, but fails in all cases to predict breakthrough times at the outlet plane, which indicates that particle motion in such fracture networks cannot be characterized by a constant velocity between the inlet and control plane at which the breakthrough curve is detected. Rather the structure of the network requires that frequent velocity transitions be made as particles move through the system. Despite the relatively broad distribution of fracture radii and relatively small number of independent velocity transitions, the CTRW approach conditioned on the initial velocity distribution provides reasonable predictions for the breakthrough curves at different distances from the inlet. The application of these averaged transport models provides a richer understanding of the link from the fracture network structure to ow and transport properties.

58 GEOSCIENCES↗

DOE OSTI2017

Effect of Unsaturated Flow Modes on Partitioning Dynamics of Gravity-Driven Flow at a Simple Fracture Intersection: Laboratory Study and Three-Dimensional Smoothed Particle Hydrodynamics Simulations

In this work, we study unsaturated gravity-driven free-surface flows on a synthetic surface intersected by a horizontal fracture and the importance of flow modes (droplet; rivulet) on the partitioning behavior at the fracture intersection. We present laboratory experiments, three-dimensional smoothed particle hydrodynamics (SPH) simulations using a heavily parallelized code, and an analytical solution. The flow-rate-dependent mode switching from droplets to rivulets is reproduced by the SPH model, and the transition ranges agree with the laboratory experiments. We show that flow modes heavily influence the bypass behavior. Flows favoring the formation of droplets exhibit a much stronger bypass capacity compared to rivulet flows, where nearly the whole fluid mass is initially stored within the horizontal fracture. This behavior is demonstrated for a multi-inlet laboratory setup where the inlet- specific flow rate is chosen so that either a droplet or rivulet flow persists. The effect of fluid buffering within the horizontal fracture is presented in terms of dimensionless fracture in- flow so that characteristic scaling regimes can be recovered. For both cases (rivulets and droplets), the flow within the horizontal fracture transitions into a Washburn regime until a critical threshold is reached and the bypass efficiency increases. For rivulet flows, the initial filling of the horizontal fracture is described by classical plug flow. Meanwhile, for droplet flows, a size-dependent partitioning behavior is observed, and the filling of the fracture takes longer. For the case of rivulet flow, we provide an analytical solution that demonstrates the existence of classical Washburn flow within the horizontal fracture.

unsaturated flow, fractured media, smoothed partic↗

DOE OSTI2017

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

Here we investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that—even if the Eulerian fluid velocity is steady—the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

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

We investigate here 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.

58 GEOSCIENCES↗

DOE OSTI2014

Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model

Flow and transport through fractured geologic media often leads to anomalous (non-Fickian) transport behavior, the origin of which remains a matter of debate: whether it arises from variability in fracture permeability (velocity distribution), connectedness in the flow paths through fractures (velocity correlation), or interaction between fractures and matrix. Here we show that this uncertainty of distribution- versus correlation-controlled transport can be resolved by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on velocity correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity distribution. We build on this insight, and propose a Lagrangian statistical model that takes the form of a continuous time random walk (CTRW) with correlated particle velocities. In this framework, velocity distribution and velocity correlation are quantified by a Markov process of particle transition times that is characterized by a distribution function and a transition probability. Our transport model accurately captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Thus, the proposed correlated CTRW modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media.

58 GEOSCIENCES↗

DOE OSTI2014

The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows

We investigate the effective kinetics of a reaction front for mixing limited bimolecular reaction $A+B\rightarrow C$ in a porous medium. While Fickian diffusion predicts a scaling of the cumulative mass produced as $M_C \propto t^{1/2}$, we observe two time regimes in which the total product mass evolves faster then $t^{1/2}$. At early times the invading solute is organized in fingers of high velocity. Reactions take place only at the fingers boundaries whose surface grows linearly in time. We show that this configuration leads to a mass scaling $M_C \propto t^2$. When diffusion mixes reactants and destroy these finger structures, the effective reaction rate slows down and we relate it to the longitudinal advective spreading providing $M_C \propto \sigma_x$. The transition time between these two regimes is characterized by the diffusion time over the transverse fingers cross section.

reactive transport, multiscale methods, smoothed p↗

DOE OSTI2013

Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media

We study the intermittency of fluid velocities in porous media and its relation to anomalous dispersion. Lagrangian velocities measured at equidistant points along streamlines are shown to form a spatial Markov process. As a consequence of this remarkable property, the dispersion of fluid particles can be described by a continuous time random walk with correlated temporal increments. This new dynamical picture of intermittency provides a direct link between the microscale flow, its intermittent properties, and non-Fickian dispersion.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2012

Linearized Functional Minimization for Inverse Modeling

Heterogeneous aquifers typically consist of multiple lithofacies, whose spatial arrangement significantly affects flow and transport. The estimation of these lithofacies is complicated by the scarcity of data and by the lack of a clear correlation between identifiable geologic indicators and attributes. We introduce a new inverse-modeling approach to estimate both the spatial extent of hydrofacies and their properties from sparse measurements of hydraulic conductivity and hydraulic head. Our approach is to minimize a functional defined on the vectors of values of hydraulic conductivity and hydraulic head fields defined on regular grids at a user-determined resolution. This functional is constructed to (i) enforce the relationship between conductivity and heads provided by the groundwater flow equation, (ii) penalize deviations of the reconstructed fields from measurements where they are available, and (iii) penalize reconstructed fields that are not piece-wise smooth. We develop an iterative solver for this functional that exploits a local linearization of the mapping from conductivity to head. This approach provides a computationally efficient algorithm that rapidly converges to a solution. A series of numerical experiments demonstrates the robustness of our approach.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗