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Quantum algorithms for geologic fracture networks
Abstract Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10–1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.
Laboratory system for studying cryogenic thermal rock fracturing for well stimulation
The concept of cryogenic fracturing is that a sharp thermal gradient developed by applying a cryogenic fluid on a rock surface causes a strong local tensile stress that initiates fractures. Prior field tests suggest that field application with special equipment rated for cryogenic temperatures may deliver potential benefits. The tests did not, however, identify the fracture mechanisms at work in downhole conditions. We present our laboratory designs and procedures developed for studying cryogenic fracturing mechanisms in a well environment, and examine typical data indicative of the performance of the system. The experimental apparatus and procedures were specifically designed to conduct cryogenic fracturing tests in specimens under confining stress, with integrated cryogen transport, measurements, and fracture characterization. A true-triaxial loading system was built to simulate reservoir stress levels and anisotropic stress application, and was designed to avoid thermal stresses in tests involving cryogen by arranging discrete components in an open chamber. To maximize thermal shock on the wellbore surface, tubing and wellhead are configured so that liquid nitrogen enters the borehole and flow out after contributing to thermal shock. The temperature at boreholes and along flow lines, borehole pressure, and liquid nitrogen consumption are monitored throughout treatments. Acoustic transmission and pressure-decay measurements are used to characterize fractures before and after the experiments. Breakdown tests performed on un-stimulated specimens and stimulated specimens compare breakdown pressures of the two groups and thus evaluate the performance of thermal fracturing. The laboratory design was able to effectively apply cryogenic stimulations to laboratory rock specimens. Finally, the characterization methods were able to capture fracture creation and rock property changes due to cryogenic fracturing.
Thermo-Mechanical Phase-Field Modeling of Fracture in High-Burnup UO2 Fuels Under Transient Conditions
This study presents a novel multiphysics phase-field fracture model to analyze high-burnup uranium dioxide (UO2) fuel behavior under transient reactor conditions. Fracture is treated as a stochastic phase transition, which inherently accounts for the random microstructural effects that lead to variations in the value of fracture strength. Moreover, the model takes into consideration the effects of temperature and burnup on thermal conductivity. Therefore, the model is able to predict crack initiation, propagation, and complex morphologies in response to thermal gradients and stress distributions. Several simulations were conducted to investigate the effects of operational and transient conditions on fracture behavior and the resulting cracking patterns. High-burnup fuels exhibit reduced thermal conductivity, elevating temperature gradients and resulting in extensive radial and circumferential cracks. Transient heating rates and temperatures significantly affect fracture patterns, with higher heating rates generating steeper gradients and more irregular crack trajectories. This approach provides critical insights into fuel integrity during accident scenarios and supports the safety evaluation of extended burnup limits.
Sensitivity analysis of generic deep geologic repository with focus on spatial heterogeneity induced by stochastic fracture network generation
Geologic Disposal Safety Assessment Framework is a state-of-the-art simulation software toolkit for probabilistic post-closure performance assessment of systems for deep geologic disposal of nuclear waste developed by the United States Department of Energy. This paper presents a generic reference case and shows how it is being used to develop and demonstrate performance assessment methods within the Geologic Disposal Safety Assessment Framework that mitigate some of the challenges posed by high uncertainty and limited computational resources. Variance-based global sensitivity analysis is applied to assess the effects of spatial heterogeneity using graph-based summary measures for scalar and time-varying quantities of interest. Behavior of the system with respect to spatial heterogeneity is further investigated using ratios of water fluxes. This analysis shows that spatial heterogeneity is a dominant uncertainty in predictions of repository performance which can be identified in global sensitivity analysis using proxy variables derived from graph descriptions of discrete fracture networks. New quantities of interest defined using water fluxes proved useful for better understanding overall system behavior.
Preliminary Simulation of the Corrosion Rate of Archaeological Glass
In this study, we make use of a micro-continuum modeling approach (the Kinetic-Microscopic-Continuum Model or KμC model) to capture the spatial distribution and identity of reaction products developing over time as a result of the archaeological glass corrosion, while also matching the time scales of alteration where possible. Since the glass blocks sat on the Mediterranean seafloor for 1800 years, the physical and chemical boundary conditions are largely constant. We focus on a fracture within the glass block identified by Verney-Carron et al. (2008) and simulate it as a 1D system, with a fixed concentration (Dirichlet) boundary corresponding to the interior of the fracture.
Well Interference Diagnosis through Integrated Analysis of Tracer and Pressure Interference Tests
In ultra-low permeability reservoirs, communication between wells through connected fractures can be observed through tracer and pressure interference tests. Understanding the connectivity between fractured horizontal wells in a multi-well pad is important for infill well drilling and parent-child well interactions. Inter-well tracer and pressure interference tests involve two or more fractured horizontal wells and provide information about hydraulic fracture connectivity between the wells. In this work, we present a workflow based on combining the analysis of tracer and pressure interference data to obtain the degree of interference between fractured horizontal wells in a multi-well pad. We analyze well interference using tracer (chemical tracer and radioactive proppant tracer) and pressure data in an 11-well pad in the Permian Basin. Changes in pressure and tracer concentration in the monitor wells were used to identify and evaluate interference between the source and monitor wells. Extremely low tracer recovery and weak pressure response signify the absence of connected fractures and suggest that interference through matrix alone is insignificant. Combined tracer and pressure interference data suggest connected fracture pathways between the communicating wells. The degree of interference can be estimated in terms of pressure response times and tracer recovery. An effective reservoir model was used to simulate pressure interference between wells during production. Simulation results indicate that well interference observed during production is primarily due to hydraulically connected fractures. Combined tracer and pressure interference analysis provides a unique tool for understanding the time dependent connectivity between communicating wells, which can be useful for optimizing infill well drilling, well spacing and fracture sizing in future treatment designs.
Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling
We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.
Surface structure and stability of partially hydroxylated silica surfaces
Surface energies of silicates influence crack propagation during brittle fracture and decrease with surface relaxation caused by annealing and hydroxylation. Molecular-level simulations are particularly suited for the investigation of surface processes. In this work, classical MD simulations of silica surfaces are performed with two force fields (ClayFF and ReaxFF) to investigate the effect of force field reactivity on surface structure and energy as a function of surface hydroxylation. An unhydroxylated fracture surface energy of 5.1 J/m 2 is calculated with the ClayFF force field, and 2.0 J/m 2 is calculated for the ReaxFF force field. The ClayFF surface energies are consistent with the experimental results from double cantilever beam fracture tests (4.5 J/m 2 ), whereas ReaxFF underestimated these surface energies. Surface relaxation via annealing and hydroxylation was performed by creating a low-energy equilibrium surface. Annealing condensed neighboring siloxane bonds increased the surface connectivity, and decreased the surface energies by 0.2 J/m 2 for ClayFF and 0.8 J/m 2 for ReaxFF. Posthydroxylation surface energies decreased further to 4.6 J/m 2 with the ClayFF force field and to 0.2 J/m 2 with the ReaxFF force field. Experimental equilibrium surface energies are ~0.35 J/m 2 , consistent with the ReaxFF force field. Although neither force field was capable of replicating both the fracture and equilibrium surface energies reported from experiment, each was consistent with one of these conditions. Furthermore, future computational investigations that rely on accurate surface energy values should consider the surface state of the system and select the appropriate force field.
Numerical Simulation Applications in the Design of EGS Collab Experiment 1
The United States Department of Energy, Geothermal Technologies Office (GTO) is funding a collaborative investigation of enhanced geothermal systems (EGS) processes at the meso-scale. This study, referred to as the EGS Collab project, is a unique opportunity for scientists and engineers to investigate the creation of fracture networks and circulation of fluids across those networks under in-situ stress conditions. The EGS Collab project is envisioned to comprise three experiments and the site for the first experiment is on the 4850 Level (4,850 feet below ground surface) in phyllite of the Precambrian Poorman formation, at the Sanford Underground Research Facility, located at the former Homestake Gold Mine, in Lead, South Dakota. Principal objectives of the project are to develop a number of intermediate-scale field sites and to conduct well-controlled in situ experiments focused on rock fracture behavior and permeability enhancement. Data generated during these experiments will be compared against predictions of a suite of computer codes specifically designed to solve problems involving coupled thermal, hydrological, geomechanical, and geochemical processes. Comparisons between experimental and numerical simulation results will provide code developers with direction for improvements and verification of process models, build confidence in the suite of available numerical tools, and ultimately identify critical future development needs for the geothermal modeling community. Moreover, conducting thorough comparisons of models, modelling approaches, measurement approaches and measured data, via the EGS Collab project, will serve to identify techniques that are most likely to succeed at the Frontier Observatory for Research in Geothermal Energy (FORGE), the GTO's flagship EGS research effort. As noted, outcomes from the EGS Collab project experiments will serve as benchmarks for computer code verification, but numerical simulation additionally plays an essential role in designing these meso-scale experiments. This paper describes specific numerical simulations supporting the design of Experiment 1, a field test involving hydraulic stimulation of two fractures from notched sections of the injection borehole and fluid circulation between sub-horizontal injection and production boreholes in each fracture individually and collectively, including the circulation of chilled water. Whereas the mine drift allows for accurate and close placement of monitoring instrumentation to the developed fractures, active ventilation in the drift cooled the rock mass within the experimental volume. Numerical simulations were executed to predict seismic events and magnitudes during stimulation, initial fracture orientations for smooth horizontal wellbores, pressure requirements for fracture initiation from notched wellbores, fracture propagation during stimulation between the injection and production boreholes, tracer travel times between the injection and production boreholes, produced fluid temperatures with chilled water injections, pressure limits on fluid circulation to avoid fracture growth, temperature environment surrounding the 4850 Level drift, and fracture propagation within a stress field altered by drift excavation, ventilation cooling, and dewatering.
(U) Marker Lagrangian Simulations using Geometry from CAD Assembly Files [Slides]
The Eulerian code PAGOSA now contains an option for the forward time integration of any user selected material in the Lagrangian frame of reference. This option is accomplished using a Multifield version of Brackbill’s FLIP plus Sulsky’s MPM. FLIP+MPM is a Marker Lagrangian scheme that is not to be confused with well known Grid Lagrangian schemes. This Marker Lagrangian method allows materials to undergo completely arbitrary deformation, up to and including fracture and separation. Using this option makes PAGOSA into a mixed frame simulation tool such that fluids can be integrated in the Eulerian frame and solids integrated in the Lagrangian frame. Boundaries between the fields are said to be ’immersed’ in the computational domain, and their nature is formulated using Multifield Theory. Each Marker in a field of FLIP+MPM material tracks the thermodynamic state of a small (but finite) piece of mass. Initiation of the Markers using the geometry and material information from CAD Assembly files is the subject of the talk. The ease and speed with which the dynamics of the assembly can be studied is demonstrated.
DEM Particle Fracture Model
An adaptive particle fracture model in poly-ellipsoidal Discrete Element Method is developed. The poly-ellipsoidal particle will break into several sub-poly-ellipsoids by Hoek-Brown fracture criterion based on continuum stress and the maximum tensile stress in contacts. Also Weibull theory is introduced to consider the statistics and size effects on particle strength. Finally, high strain-rate split Hopkinson pressure bar experiment of silica sand is simulated using this newly developed model. Comparisons with experiments show that our particle fracture model can capture the mechanical behavior of this experiment very well, both in stress-strain response and particle size redistribution. The effects of density and packings o the samples are also studied in numerical examples.
ICAT: A numerical scheme to minimize numerical diffusion in advection-dispersion modeling and its application in identifying flow channeling
The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. We report discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.
An IIPG-based finite element framework in MOOSE for modeling fiber reinforced composite failure governed by extrinsic cohesive laws
Fiber reinforced composites (FRC) are widely applied to many important engineering structures such as silicon carbide ceramic matrix composite (SiC CMC) of nuclear fuel claddings. Many material and structure failures are initiated at the interface between two distinctive materials, such as the debonding of interfaces of matrix/fiber of composites or bulk matrix/inclusion in metals at micro-scales. Accurate and robust modeling of these interface failures is critical to the development of novel material and structure with improved functionality. This paper presents a discontinuous Galerkin (DG) finite element method based on the Incomplete Interior Penalty scheme and its implementation in MOOSE for modeling material interface behaviors. The proposed method naturally accommodates important extrinsic cohesive zone material models and is capable of modeling the failures of material interfaces across which material properties are highly distinctive. We demonstrate a good performance of the proposed method using single fiber and multiple fiber debonding problems.
Corrosion of Metal Inclusions In Bulk Vitrification Waste Packages. Erratum
This report refers to or contains K g values for glasses LAWA44, LAWB45 and LAWC22 affected by calculations errors as identified by Papathanassiu et al. (2011). The corrected K g values are reported in an erratum included in the revised version of the original report. The revised report can be referenced as follows: Pierce E. M. et al. (2004) Waste Form Release Data Package for the 2005 Integrated Disposal Facility Performance Assessment. PNNL-14805 Rev. 0 Erratum. Pacific Northwest National Laboratory, Richland, WA, USA.
Investigation of Coupled Processes in Argillite Rock: FY18 Progress
The report presents the current status of the TOUGH-FLAC and TOUGH-RBSN simulators for modeling of coupled THM processes in argillite, including fracturing, and verification of the TOUGH-FLAC model against major in situ heater experiments at the Mont Terri Underground Research Laboratory (URL) in Switzerland and at the URL in Bure, France. The heater experiments modeled are the Mont Terri FE (Full-scale Emplacement) Experiment, conducted as part of the Mont Terri Project, and the TED and ALC experiments conducted in Callovo-Oxfordian claystone (COx) at the Meuse/Haute-Marne (MHM) URL in Bure, France. The modeling of the TED and ALC heater experiments is part of a modeling task (Task E) of the international DECOVALEX-2019 project. DECOVALEX, which stands for DEvelopment of COupled Models and their VALidation against EXperiments, is an international collaborative activity, in which DOE and LBNL gain access to unique laboratory and field data defined as modeling test cases. DECOVALEX tasks are studied collectively among several international groups to better understand the processes and to improve numerical models that could eventually be applied in the performance assessment for nuclear waste disposal in clay host rocks and bentonite backfill. The report also includes a description of LBNL’s activities for modeling gas migration in bentonite related to Task A of the international DECOVALEX project, and presents new FY2018 work related to monitoring and characterization of faults using a unique borehole tool.
3D orthorhombic earth model effects on seismic source characterization
Most earth materials are anisotropic with regard to seismic wave-speeds, especially materials such as shales, or where oriented fractures are present. However, the base assumption for many numerical simulations is to treat earth materials as isotropic media. This is done for simplicity, the apparent weakness of anisotropy in the far field, and the lack of well-characterized anisotropic material properties for input into numerical simulations. One approach for addressing the higher complexity of actual geologic regions is to model the material as an orthorhombic medium. We have developed an explicit time-domain, finite-difference (FD) algorithm for simulating three-dimensional (3D) elastic wave propagation in a heterogeneous orthorhombic medium. The objective of this research is to investigate the errors and biases that result from modeling a non-isotropic medium as an isotropic medium. This is done by computing “observed data” by using synthetic, anisotropic simulations with the assumption of an orthorhombic, anisotropic earth model. Green’s functions for an assumed isotropic earth model are computed and then used an inversion designed to estimate moment tensors with the “observed” data. One specific area of interest is how shear waves, which are introduced in an anisotropic model even for an isotropic explosion, affect the characterization of seismic sources when isotropic earth assumptions are made. This work is done in support of the modeling component of the Source Physics Experiment (SPE), a series of underground chemical explosions at the Nevada National Security Site (NNSS).
Field Laboratory for Emerging Stacked Unconventional Plays in Central Appalachia
The goal of the Field Laboratory for Emerging Stacked Unconventional Plays (ESUP) in Central Appalachia project was to investigate and characterize the resource potential for multi-play production of emerging unconventional reservoirs in Central Appalachia. Project activities included drilling, logging and coring of a vertical characterization well drilled to basement to approximately 15,000 feet in depth. The data from drilling and well logs as well recovered core samples were used by the research team to support characterization of the geology and potential pay zones within the Nora Gas Field of southwestern Virginia and the greater Central Appalachian Basin. This project was led by Dr. Nino Ripepi of the Virginia Center for Coal and Energy Research (VCCER) in close collaboration with EnerVest Operating LLC (EnerVest). VCCER is housed in the Department of Mining and Minerals Engineering at Virginia Tech and was created by an Act of the Virginia General Assembly on March 30, 1977, as an interdisciplinary study, research, information, and resource facility for the Commonwealth of Virginia. EnerVest is a top tier, low-cost oil and natural gas company with a long history of traditional operating relationships with institutional investors as well as public and private companies. This report summarizes two major research activities: 1) Log and Core Analysis and 2) Numerical Modeling. Core analysis comprises the characterization efforts of the ESUP Field Laboratory and includes a discussion of the well logs run in the deep characterization wells, an initial analysis of those, the number, size and location of cores recovered, core testing and analysis done to date as well as plans for future analysis. Numerical modeling is comprised of seven major modeling efforts, including (1) Multiphysics shale transport modeling work, (2) the developed in-house compositional simulator studies, (3) reservoir modeling studies using GEM software, (4) fracture modeling work using EFRAC3D software and (5) numerical modeling efforts with ABAQUS software, (6) Numerical modeling efforts using FLAC3D and PFC3D, and (7) Automatic Machine Learning (AutoML) Studies.