Search

We study flow and hydrodynamic transport in spatially random fracture networks.The flow and transport behavior is characterized by first passagetimes and displacement statistics, which show heavy tailsand anomalous dispersion with a strong dependence on the injectioncondition. The origin of these behaviors is investigatedin terms of Lagrangian velocities sampled equidistantly along particletrajectories, unlike classical sampling strategies at a constant rate. Thefluctuating velocity series is analyzed by its copula density, thejoint distribution of the velocity unit scores, which reveals a simple correlationstructure that can be described by a Gaussian copula. This insightleads to the formulation of stochastic particle motion in terms of aKlein-Kramers equation for the joint density of particle position andvelocity. The upscaled model captures the heavy-tailed first passagetime distribution and anomalous dispersion, and their dependence on theinjection conditions in terms of the velocity point statistics andaverage fracture length. The first passage times and displacementmoments are dominated by extremes occurring at the first step.The developed approach integrates the complex interaction of flow and structureinto a predictive model for large scale transport in random fracture networks.

Fluid flow in fractures has the potential to drastically change the economic, environmental, and safety risks associated with a subsurface operation. This work focuses on the analysis of experimental shear fracturing and subsequent shear displacement of a shale specimen that contains multiple pre-existing natural fractures. A triaxial direct shear apparatus with concurrent µCT imaging allowed continuous monitoring of sample permeability and changes in fracture geometry during fracture creation, displacement, and changes in stress. Steady-state, low Reynolds number fluid flow simulations were used to determine the changes of each individual fracture’s hydraulic aperture due to displacement and effective stress. The development of anisotropy in the hydraulic aperture of a generated shear fracture was determined for shear displacements of 0.38, 0.74, and 2.04 mm. At high confining stress (30 MPa), shear displacement significantly reduced the hydraulic aperture of the shear fracture to below flow detectable limits and X-ray imaging resolution (23 × 23 × 23 µm3). The shear generated fracture was found to be more sensitive to changes in effective stress compared to the pre-existing natural fractures. Existing models derived from fluid flow equations accounting for stochastic fracture roughness were able to partially fit the simulated flow properties of the pre-existing fractures, but no model was found to fit the flow properties of the newly formed shear fracture. These results are the first report of simultaneous changes in the geometry and flow properties of surrounding, parallel natural fractures as a shear fracture is generated with varying stress and shear displacement conditions.

We present a novel workflow for forecasting production in unconventional reservoirs using reduced-order models and machine-learning. Our physics-informed machine-learning workflow addresses the challenges to real-time reservoir management in unconventionals, namely the lack of data (i.e., the time-frame for which the wells have been producing), and the significant computational expense of high-fidelity modeling. We do this by applying the machine-learning paradigm of transfer learning, where we combine fast, but less accurate reduced-order models with slow, but accurate high-fidelity models. We use the Patzek model (Proc Natl Acad Sci 11:19731–19736, https://doi.org/10.1073/pnas.1313380110, 2013) as the reduced-order model to generate synthetic production data and supplement this data with synthetic production data obtained from high-fidelity discrete fracture network simulations of the site of interest. Our results demonstrate that training with low-fidelity models is not sufficient for accurate forecasting, but transfer learning is able to augment the knowledge and perform well once trained with the small set of results from the high-fidelity model. Such a physics-informed machine-learning (PIML) workflow, grounded in physics, is a viable candidate for real-time history matching and production forecasting in a fractured shale gas reservoir.

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Moreover, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

While several studies have linked network and in-fracture scale properties to conservative transport behavior in subsurface fractured media, studies on reactive transport cases remain relatively underdeveloped. In this study, we explore the behavior of an irreversible kinetic reaction during the interaction of two solute plumes, one consisting of species A and the other species B. When the plumes converge, these species react kinetically to form a new species C via $$A+B\xrightarrow {k} C$$ . This reactive system is studied using a three-dimensional discrete fracture network (DFN) model coupled with reactive Lagrangian particle tracking. We find that the interplay of network topology and chemical properties of the reactive solutes controls reactive transport processes. The network topology drives species A and B together, and the chemical properties dictate whether and how quickly a reaction occurs. Results demonstrate that reactions are most likely to occur in high-velocity fractures that make up the network backbone. The interplay between species’ chemical properties and transport is characterized by a non-dimensional Damkohler (Da) number. We show that the spatial distribution of reactions is sensitive to Da, which subsequently influences late-time tailing behavior in outlet breakthrough time distributions. The results of this study provide initial insights into how an irreversible reaction occurs during transport in a fracture network, using a methodology that can be applied to study reactive transport in a wide range of fractured media environments and contexts.

The phenomenon of flow-channeling, or the existence of preferential pathways for flow in fracture networks, is well known. Identification of the channels (“backbone”) allows for system reduction and computational efficiency in simulation of flow and transport through fracture networks. However, the purpose of machine learning techniques for backbone identification in fractured media is two-pronged system reduction for computational efficiency in simulation of flow and transport as well as physical insight into the phenomenon of flow channeling. The most critical aspect of this problem is the need to have a truly “physics-informed” technique that respects the constraint of connectivity. We present a method that views a network as a union of connected paths with each path comprising a sequence of fractures. Thus, the fundamental unit of selection becomes a sequence of fractures, classified based on attributes that characterize the sequence. In summary, this method represents a parametrization of the sample space that ensures every selected sample sub-network (which is the union of all selected sequences of fractures) always respects the constraint of connectivity, demonstrating that it is a truly physics-informed method. The algorithm has a user-defined parameter which allows control of the backbone size when using the random forest or logistic regression classifier. Even when the backbones are less than 30% in size (leading to computational savings), the backbones still capture the behavior of the breakthrough curve of the full network. Moreover, there is no need to check for path connectedness in the backbones unlike previous methods since the backbones are guaranteed to be connected.

We introduce an innovative ensemble analysis framework for organizing, searching, and comparing results produced by hundreds of physical simulations. Our web-based approach is built on standard technologies, utilizes a scalable and modular design, and is suitable for displaying the results of in situ analysis and extreme-scale simulations.

Fractures form the main pathways for flow of fluids and transport of constituents carried by these fluids in fractured subsurface media. The majority of flow and transport occurs in the primary sub...

We develop a computational geometry-based upscaling approach to accurately capture the dynamic processes occurring within and between subsurface fracture networks and the surrounding porous matrix named the Upscaled Discrete Fracture Matrix model (UDFM). Fracture attributes (orientations and apertures) are upscaled and combined with matrix attributes (permeability and porosity) into properties of an unstructured spatially variable Delaunay tetrahedral continuum mesh. The resolution of the mesh depends on proximity to the fractures to preserve the geometric and topological integrity of the underlying fracture network as well as increasing the accuracy of gradients in the dynamics between the fractures and matrix. The UDFM Delaunay mesh and its dual Voronoi mesh can be used in existing multiphysics simulators for flow, solute/heat mass transport, and geomechanics, thereby eliminating the need for the additional development of numerical methods to couple processes in fracture/matrix systems. The model is verified by comparing flow, transport, and coupled heat-mass flow simulations on the provided meshes against analytical and numerical benchmarks. We also provide an additional example to demonstrate the applicability of the UDFM to complex heteregenous fractured media. Overall, the UDFM is accurate in all of the cases considered here and presents an attractive alternative to other modeling strategies that require novel numerical methods or multi-dimensional meshes.

Quantitative prediction of natural and induced phenomena in fractured rock is one of the great challenges in the Earth and Energy Sciences with far-reaching economic and environmental impacts. Frac...

We present a set of multiphase flow simulations where supercritical CO$$_2$$ (scCO$$_2$$) displaces water at hydrostatic conditions within three-dimensional discrete fracture networks that represent paths for potential leakage through caprock above CO$$_2$$ storage reservoirs. The simulations are performed to characterize and compare the relative impact of hydraulic and structural heterogeneity in fractured media on the initial movement of scCO$$_2$$ through these caprock formations. In one scenario, intrinsic fracture permeabilities are varied stochastically within a fixed network structure. In another scenario, we generate multiple independent, identically distributed network realizations with varying fracture network densities to explore a wide range of geometric and topological configurations. Analysis of the simulations indicates that network structure, specifically connectivity and the presence of hanging fractures, plays a larger role in controlling the displacement of water by scCO$$_2$$ than variations in local hydraulic properties. We identify active surface area of the network as a single-phase feature that could provide a lower bound on the percentage of the network surface area reached by scCO$$_2$$.

Discrete fracture networks (DFN) are often used to model flow and transport in fractured porous media. The accurate resolution of flow and transport behavior on a large DFN involving thousands of fractures is computationally expensive. This makes uncertainty quantification studies of quantities of interest such as travel time through the network computationally intractable, since hundreds to thousands of runs of the DFN model are required to get bounds on the uncertainty of the predictions. Prior works on the subject demonstrated that the complexity of a DFN could be reduced by considering a sub-network of it (often termed a “backbone” sub-network), one whose flow and transport properties were then shown to be similar to that of the full network. The technique is tantamount to partitioning the complete set of fractures of a network into two disjoint sets, one of which is the backbone sub-network while the other its complement. It is in this context that we present a system-reduction technique for DFNs using supervised machine learning via a Random Forest Classifier that selects a backbone sub-network from the full set of fractures. The in-sample errors (in terms of precision and recall scores) of the trained classifier are found to be very accurate indicators of the out-of-sample errors, thus exhibiting that the classifier generalizes well to test data. Moreover, this system-reduction technique yields sub-networks as small as 12% of the full DFN that still recover transport characteristics of the full network such as the peak dosage and tailing behavior for late times. Most importantly, the sub-networks remain connected, and their size can be controlled by a single dimensionless parameter. Furthermore, measures of KL-divergence and KS-statistic for the breakthrough curves of the sub-networks with respect to the full network show physically realistic trends in that the measures decrease monotonically as the size of the sub-networks increase. The computational efficiency gained by this technique depends on the size of the sub-network, but large reductions in computational time can be expected for small sub-networks, yielding as much as 90% computational savings for sub-networks that are as small as 10-12% of the full network.

We investigate large-scale particle motion and solute breakthrough in sparse three-dimensional discrete fracture networks 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 continuous time random walk 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 continuous time random walk 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 flow and transport properties. ©2019. American Geophysical Union. All Rights Reserved., J. D. H. and A. H. are thankful for support from Department of Energy at Los Alamos National Laboratory under contract DE-AC52-06NA25 396 through the Laboratory-Directed Research and Development Program. J. D. H. acknowledges support from the LANL LDRD program office Grant 20180621ECR. M. D. gratefully acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511). P. K. K. acknowledges a grant from Korea Environment Industry & Technology Institute(KEITI) through Subsurface Environmental Management (SEM) Project, funded by Korea Ministry of Environment(MOE; 2018002440003). dfnworks can be obtained at https://github.com/lanl/dfnWorks and run files for simulations can obtained at https://gitlab.com/hymanjd/ hyman-jgr-2018.git.

We present a comprehensive workflow to simulate single-phase flow and transport in fractured porous media using the discrete fracture matrix approach. The workflow has three primary parts: (1) a method for conforming mesh generation of and around a three-dimensional fracture network, (2) the discretization of the governing equations using a second-order mimetic finite difference method, and (3) implementation of numerical methods for high-performance computing environments. A method to create a conforming Delaunay tetrahedralization of the volume surrounding the fracture network, where the triangular cells of the fracture mesh are faces in the volume mesh, that addresses pathological cases which commonly arise and degrade mesh quality is also provided. Our open-source subsurface simulator uses a hierarchy of process kernels (one kernel per physical process) that allows for both strong and weak coupling of the fracture and matrix domains. We provide verification tests based on analytic solutions for flow and transport, as well as numerical convergence. We also provide multiple expositions of the method in complex fracture networks. In the first example, we demonstrate that the method is robust by considering two scenarios where the fracture network acts as a barrier to flow, as the primary pathway, or offers the same resistance as the surrounding matrix. In the second test, flow and transport through a three-dimensional stochastically generated network containing 257 fractures is presented.

The publication of this article unfortunately contained a mistake. The assignment to the affiliations of author Satish Karra was not correct

International audience; Fractured rocks are often modeled as multiscale populations of interconnected discrete fractures (discrete fracture network, DFN). Graph representations of DFNs reduce their complexity to their connectivity structure by forming an assembly of nodes connected by links (edges) to which physical properties, like a conductance, can be assigned. In this study, we address the issue of using graphs to predict flow as a fast and relevant substitute to classical DFNs. We consider two types of graphs, whether the nodes represent the fractures (fracture graph) or the intersections between fractures (intersection graph). We introduce an edge conductance expression that accounts for both the portion of the fracture surface that carries flow and fracture transmissivity. We find that including the fracture size in the expression improves the prediction of flow compared to expressions used in previous studies that did not. The two graph types yield very different results. The fracture graph systematically underestimates local flow values. In contrast, the intersection graph overestimates the flow in each fracture because of the connectivity redundancy in fractures with multiple intersections. We address the latter issue by introducing a correction factor into the conductances based on the number of intersections on each fracture. We test the robustness of the proposed conductance model by comparing flow properties of the graph with high-fidelity DFN simulations over a wide range of network types. The good agreement found between the intersection graph and test suite indicates that this representation could be useful for predictive purposes.

We describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the $O({10}^{4})$ speedup that was obtained for steady-state flows earlier. However, the transient flows considered here involve an additional degree of complexity that was not present in the steady-state flows considered previously with a graph-based approach, that of time marching and solution of the flow equations within a time-stepping scheme. We verify our method with an analytical test case and demonstrate its use on a practical problem related to fluid flows in hydraulically fractured reservoirs. By enabling the study of transient flows, we create an opportunity for a wide set of possibilities where a steady-state approximation is not sufficient, such as the example motivated by hydraulic fracturing that we present here. This work validates the concept that graphs are able to reliably capture the topological properties of the fracture network and serve as effective surrogates in an uncertainty-quantification framework.

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., PKK acknowledges the College of Science & Engineering at the University of Minnesota and the George and Orpha Gibson Endowment for its generous support of Hydrogeology. PKK and WSH acknowledge a grant from Korea Environment Industry and Technology Institute (KEITI) through Subsurface Environmental Management (SEM) Project, funded by the Korea Ministry of Environment (MOE) (2018002440003). MD acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511), and the support of the Spanish Ministry of Science and Innovation through a Severo Ochoa project (No. CEX2018324 000794‐S), and the project HydroPore (PID2019‐106887GB‐C31). JDH acknowledges support from the LANL LDRD program office Grant 20180621ECR and thanks to the Department of Energy (DOE) Basic Energy Sciences program (LANLE3W1) for support as well.

A quantitative assessment of how faults control the migration of geofluids is critical in many areas of geosciences. We integrated geological fieldwork, quantitative analysis of the fractures distribution and numerical modeling to build a geometrical representation of a fault zone and to characterize its hydraulic properties. Our target is a fault located in the Majella Mountain (Italy). We collected 21 scan lines across the fault profile in order to characterize its architecture. The numerical modeling of the fracture network of the damage zones and their hydraulic parameters was performed using both commercial (Move®) and open source software (dfnWorks and PFLOTRAN). Move® was used to build a representative model of the fault zone using fracture spacing as a proxy, and to model the hydraulic parameters of the different fault domains. dfnWorks and PFLOTRAN were employed to infer the hydraulic parameters of the damage zones of the fault and then upscale these properties to an equivalent continuum domain, suitable for fluid flow simulations through the whole fault zone. Our findings show how even in a relatively small area it is possible to describe changes in terms of hydraulic properties of a fault zone and to build models capable to represent these variations.

This is primarily an account of the role of machine learning, including the role played by graph theory, in the development of reduced-order models (ROM) of flow and transport through fractured media that are modeled with the DFN approach. We describe the construction of a DFN, the necessary governing equations for flow and transport through DFN and various graph representations of it. The development of ROMs in DFN is then traced and divided into different unifying themes. We set out, in general terms, the role of machine learning in constructing reduced-order models of DFN, place three different machine learning approaches that have been developed in this context into an abstract perspective, and explain the fundamental ideas of each approach. We show that the approaches differ in the identity of the elements being classified, and the rule for assigning labels to elements. By choosing the elements as paths, rather than fractures, a truly physics-informed machine learning method results that preserves network connectivity in the reduced networks.

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.

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. 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. 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., T. S. is supported by the National Science Foundation Graduate Research Fellowship under Grant DGE‐1841556. D. B. was supported by the US Army Research Office under Contract/Grant W911NF‐18‐1‐0338 and by the National Science Foundation under award CBET‐1803989. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract 89233218CNA000001). J. D. H. acknowledges support from the LANL LDRD program office Grant 20180621ECR and DOE's Office of Science Basic Energy SciencesE3W1: LA‐UR‐19‐27671. M. D. acknowledges funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007‐2013)/ ERC Grant Agreement 617511 (MHetScale). DFNWORKS and and simulation data can be obtained at GitHub (https://github.com/lanl/dfnWorks and https://github.com/tjsherman24/FractureNetworkDensity, respectively).

Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Current models either ignore or idealize microscale information at these larger scales because we lack a framework that efficiently utilizes it in its entirety to predict macroscale behavior in brittle materials. We propose a method that integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning. Our method has been shown to improve accuracy of predictions with up to four orders of magnitude speedup.

Motivated by a triaxial coreflood experiment with a sample of Utica shale where an abrupt jump in permeability was observed, possibly due to the creation of a percolating fracture network through the sample, we perform numerical simulations based on the experiment to characterize how the effective permeability of otherwise low-permeability porous media depends on fracture formation, connectivity, and the contrast between the fracture and matrix permeabilities. While a change in effective permeability due to fracture formation is expected, the dependence of its magnitude upon the contrast between the matrix permeability and fracture permeability and the fracture network structure is poorly characterized. We use two different high-fidelity fracture network models to characterize how effective permeability changes as percolation occurs. The first is a dynamic two-dimensional fracture propagation model designed to mimic the laboratory settings of the experiment. The second is a static three-dimensional discrete fracture network (DFN) model, whose fracture and network statistics are based on the fractured sample of Utica shale. Once the network connects the inflow and outflow boundaries, the effective permeability increases non-linearly with network density. In most networks considered, a jump in the effective permeability was observed when the embedded fracture network percolated. We characterize how the magnitude of the jump, should it occur, depends on the contrast between the fracture and matrix permeabilities. For small contrasts between the matrix and fracture permeabilities the change is insignificant. However, for larger contrasts, there is a substantial jump whose magnitude depends non-linearly on the difference between matrix and fracture permeabilities. A power-law relationship between the size of the jump and the difference between the matrix and fracture permeabilities is observed. The presented results underscore the importance of fracture network topology on the upscaled properties of the porous medium in which it is embedded.

We present a graph-based method to identify primary flow and transport sub-networks in three-dimensional discrete fracture networks (DFNs). The structure of a DFN lends itself to the use of graphs ...

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., JDH thanks the Department of Energy Basic Energy Sciences program (LANLE3W1), and the Spent Fuel and Waste Science and Technology Campaign, Office of Nuclear Energy, of the U.S. Department of Energy under contract number 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). This work was prepared as an account of work sponsored by an agency of the United States Government. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, its contractors or subcontractors. MD gratefully acknowledges the support of the Spanish Ministry of Science and Innovation through the project HydroPore (PID2019-106887GB-C31). Los Alamos National Laboratory unclassified release number: LA-UR-21-22994.

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. We compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km 3 ) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. We identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.

We present an analysis and visualization prototype using the concept of a flow topology graph (FTG) for characterization of flow in constrained networks, with a focus on discrete fracture networks (DFN), developed collaboratively by geoscientists and visualization scientists. Our method allows users to understand and evaluate flow and transport in DFN simulations by computing statistical distributions, segment paths of interest, and cluster particles based on their paths. The new approach enables domain scientists to evaluate the accuracy of the simulations, visualize features of interest, and compare multiple realizations over a specific domain of interest. Geoscientists can simulate complex transport phenomena modeling large sites for networks consisting of several thousand fractures without compromising the geometry of the network. However, few tools exist for performing higher-level analysis and visualization of simulated DFN data. The prototype system we present addresses this need. We demonstrate its effectiveness for increasingly complex examples of DFNs, covering two distinct use cases - hydrocarbon extraction from unconventional resources and transport of dissolved contaminant from a spent nuclear fuel repository.

Shale gas and hydraulic refracturing has revolutionized the US energy sector in terms of prices, consumption, and CO2 emissions. However, key questions remain including environmental concerns and extraction efficiencies that are leveling off. For the first time, we identify key discoveries, lessons learned, and recommendations from this shale gas revolution through extensive data mining and analysis of 23 years of production from 20,000 wells. Discoveries include identification of a learning-by-doing process where disruptive technology innovation led to a doubling in shale gas extraction, how refracturing with emerging technologies can transform existing wells, and how overall shale gas production is actually dominated by long-term tail production rather than the high-profile initial exponentially-declining production in the first 12 months. We hypothesize that tail production can be manipulated, through better fracturing techniques and alternative working fluids such as CO2, to increase shale gas recovery and minimize environmental impacts such as through carbon sequestration.