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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Knowledge extraction and transfer in data-driven fracture mechanics

Significance Data-driven approaches have launched a new paradigm in scientific research that is bound to have an impact on all disciplines of science and engineering. However, at this juncture, the exploration of data-driven techniques in the century-old field of fracture mechanics is highly limited, and there are key challenges including accurate and intelligent knowledge extraction and transfer in a data-limited regime. Here, we propose a framework for data-driven knowledge extraction in fracture mechanics with rigorous accuracy assessment which employs active learning for optimizing data usage and for data-driven knowledge transfer that allows efficient treatment of three-dimensional fracture problems based on two-dimensional solutions.

Liu, Xing↗
DOE OSTI2018

An atomic-scale evaluation of the fracture toughness of silica glass

Using an atomistic technique consistent with continuum balance laws and drawing on classical fracture mechanics theory, we estimate the resistance to fracture propagation of amorphous silica. Here, we discuss correspondence and deviations from classical linear elastic fracture mechanics theory including size dependence, rigid/floppy modes of deformation, and the effects of surface energy and stress.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Silicon wafer fracture stress for tracking sensors in particle physics experiments

For the construction of the ATLAS Inner Tracker strip detector, silicon strip sensor modules are glued directly onto carbon fibre support structures using a soft silicone gel. During tests at temperatures below -35°C, several of the sensors were found to crack due to a mismatch in coefficients of thermal expansion between polyimide circuit boards with copper metal layers (glued onto the sensor) and the silicon sensor itself. While module assembly procedures were developed to minimise variations between modules, cold tests showed a wide range of temperatures at which supposedly comparable modules failed. The observed variance (fracture temperatures between -35°C and -70°C) for supposedly comparable modules suggests an undetected variation between modules suspected to be intrinsic to the silicon wafer itself. Therefore, a test programme was developed to investigate the fracture stress of representative sensor wafer cutoffs. This paper presents results for the fracture stress of silicon sensors used in detector modules.

Detector design and construction technologies and ↗
DOE OSTI2020

Estimating perturbed stress from 3-D borehole displacements induced by fluid injection in fractured or faulted shales

SUMMARY Hydrofracturing stress measurements in fractured and anisotropic shales are notoriously difficult, because opening of existing geological features tends to prevent the creation of a pure hydraulic fracture perpendicular to the least compressive principal stress. Here we show how adding 3-D borehole-displacement measurements while conducting the hydraulic injection test helps to better constrain the principal stress orientations and magnitudes. We developed a 3-D fully coupled hydromechanical numerical model to analyse the displacement, fluid pressure and injection flow-rate data measured during an injection pressure-step-rate test conducted to activate a faulted borehole interval in the Mont Terri Opalinus Clay (Switzerland). We find that injected fluids can only penetrate the fault when it is at or above the Coulomb failure pressure. Borehole displacement orientations are sensitive to a ∼15° variation in the stress–tensor orientation and a 1 MPa stress magnitude variation. Although some dispersion occurs while rupture is propagating along the fault plane ∼4 m away from the borehole, the maximum density of displacement orientations consistently informs about the stress orientation. Thus, an extended injection step-rate approach coupled with an accurate in situ measurement of the borehole wall displacements can be used to better constrain the local stress field perturbations in fractured shales and in heterogeneous rock in general.

Guglielmi, Yves↗
DOE OSTI2024

Aromatic amino acid metabolism and active transport regulation are implicated in microbial persistence in fractured shale reservoirs

Abstract Hydraulic fracturing has unlocked vast amounts of hydrocarbons trapped within unconventional shale formations. This large-scale engineering approach inadvertently introduces microorganisms into the hydrocarbon reservoir, allowing them to inhabit a new physical space and thrive in the unique biogeochemical resources present in the environment. Advancing our fundamental understanding of microbial growth and physiology in this extreme subsurface environment is critical to improving biofouling control efficacy and maximizing opportunities for beneficial natural resource exploitation. Here, we used metaproteomics and exometabolomics to investigate the biochemical mechanisms underpinning the adaptation of model bacterium Halanaerobium congolense WG10 and mixed microbial consortia enriched from shale-produced fluids to hypersalinity and very low reservoir flow rates (metabolic stress). We also queried the metabolic foundation for biofilm formation in this system, a major impediment to subsurface energy exploration. For the first time, we report that H. congolense WG10 accumulates tyrosine for osmoprotection, an indication of the flexible robustness of stress tolerance that enables its long-term persistence in fractured shale environments. We also identified aromatic amino acid synthesis and cell wall maintenance as critical to biofilm formation. Finally, regulation of transmembrane transport is key to metabolic stress adaptation in shale bacteria under very low well flow rates. These results provide unique insights that enable better management of hydraulically fractured shale systems, for more efficient and sustainable energy extraction.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2016

Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry

Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass, and the notch radius ρ. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation time scale τ$ ^{pl}_0 $ and an effective loading time scale τ ext ($ \dot{K} $ I , ρ ), where KI is the tensile stress-intensity-factor rate. The toughness is predicted to scale with ρ independently of ξ≡τ ext /τ$ ^{pl}_0 $ for ξ «1, to scale as T$ \sqrt{ρ} $log(ξ) for ξ«1 (related to thermal activation, where T is the temperature), and to feature a nonmonotonic behavior in the crossover region ξ~ O (1) (related to plastic yielding dynamics). These predictions are verified using 2D computations, providing a unified picture of the notch fracture toughness of glasses. Here, the theory highlights the importance of time-scale competition and far-from-steady-state elasto-viscoplastic dynamics for understanding the toughness and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented, and possible implications for applications are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Universality and Stability Phase Diagram of Two-Dimensional Brittle Fracture

The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here, we highlight the universal character of this instability by showing that it is present in materials exhibiting widely different near crack tip elastic nonlinearity, and by demonstrating that the oscillations wavelength follows a universal master curve in terms of dissipation-related and nonlinear elastic intrinsic length scales. Moreover, we show that upon increasing the driving force for fracture, a high-velocity tip-splitting instability emerges, as experimentally demonstrated. The analysis culminates in a comprehensive stability phase diagram of two-dimensional brittle fracture, whose salient properties and topology are independent of the form of near tip nonlinearity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fracture mechanisms of sodium silicate glasses

Reactive classical molecular dynamics simulations of sodium silicate glasses, xNa 2 O–(100 – x)SiO 2 (x = 10–30), under quasi-static loading, were performed for the analysis of molecular scale fracture mechanisms. Mechanical properties of the sodium silicate glasses were consistent with experimentally reported values, and the amount of crack propagation varied with reported fracture toughness values. The most crack propagation occurred in NS20 systems (20-mol% Na 2 O) compared with the other simulated compositions. Dissipation via two mechanisms, the first through sodium migration as a lower activation energy process and the second through structural rearrangement as a higher activation energy process, was calculated and accounted for the energy that was not stored elastically or associated with the formation of new fracture surfaces. Here, a correlation between crack propagation and energy dissipation was identified, with systems with higher crack propagation exhibiting less energy dissipation. Sodium silicate glass compositions with lower energy dissipation also exhibited the most sodium movement and structural rearrangement within 10 Å of the crack tip during loading. Therefore, high sodium mobility near the crack tip may enable energy dissipation without requiring formation of structural defects. Therefore, the varying mobilities of the network modifiers near crack tips influence the brittleness and the crack growth rate of modified amorphous oxide systems.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Dynamic fracture of tantalum under extreme tensile stress

The understanding of fracture phenomena of a material at extremely high strain rates is a key issue for a wide variety of scientific research ranging from applied science and technological developments to fundamental science such as laser-matter interaction and geology. Despite its interest, its study relies on a fine multiscale description, in between the atomic scale and macroscopic processes, so far only achievable by large-scale atomic simulations. Direct ultrafast real-time monitoring of dynamic fracture (spallation) at the atomic lattice scale with picosecond time resolution was beyond the reach of experimental techniques. We show that the coupling between a high-power optical laser pump pulse and a femtosecond x-ray probe pulse generated by an x-ray free electron laser allows detection of the lattice dynamics in a tantalum foil at an ultrahigh strain rate of Embedded Image ~2 × 10 8 to 3.5 × 10 8 s -1 . A maximal density drop of 8 to 10%, associated with the onset of spallation at a spall strength of ~17 GPa, was directly measured using x-ray diffraction. The experimental results of density evolution agree well with large-scale atomistic simulations of shock wave propagation and fracture of the sample. Our experimental technique opens a new pathway to the investigation of ultrahigh strain-rate phenomena in materials at the atomic scale, including high-speed crack dynamics and stress-induced solid-solid phase transitions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Kink bands promote exceptional fracture resistance in a NbTaTiHf refractory medium-entropy alloy

Single-phase body-centered cubic (bcc) refractory medium- or high-entropy alloys can retain compressive strength at elevated temperatures but suffer from extremely low tensile ductility and fracture toughness. We examined the strength and fracture toughness of a bcc refractory alloy, NbTaTiHf, from 77 to 1473 kelvin. This alloy’s behavior differed from that of comparable systems by having fracture toughness over 253 MPa·m 1/2 , which we attribute to a dynamic competition between screw and edge dislocations in controlling the plasticity at a crack tip. Whereas the glide and intersection of screw and mixed dislocations promotes strain hardening controlling uniform deformation, the coordinated slip of <111> edge dislocations with {110} and {112} glide planes prolongs nonuniform strain through formation of kink bands. These bands suppress strain hardening by reorienting microscale bands of the crystal along directions of higher resolved shear stress and continually nucleate to accommodate localized strain and distribute damage away from a crack tip.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Sulfide Generation by Dominant Halanaerobium Microorganisms in Hydraulically Fractured Shales

ABSTRACT Hydraulic fracturing of black shale formations has greatly increased United States oil and natural gas recovery. However, the accumulation of biomass in subsurface reservoirs and pipelines is detrimental because of possible well souring, microbially induced corrosion, and pore clogging. Temporal sampling of produced fluids from a well in the Utica Shale revealed the dominance of Halanaerobium strains within the in situ microbial community and the potential for these microorganisms to catalyze thiosulfate-dependent sulfidogenesis. From these field data, we investigated biogenic sulfide production catalyzed by a Halanaerobium strain isolated from the produced fluids using proteogenomics and laboratory growth experiments. Analysis of Halanaerobium isolate genomes and reconstructed genomes from metagenomic data sets revealed the conserved presence of rhodanese-like proteins and anaerobic sulfite reductase complexes capable of converting thiosulfate to sulfide. Shotgun proteomics measurements using a Halanaerobium isolate verified that these proteins were more abundant when thiosulfate was present in the growth medium, and culture-based assays identified thiosulfate-dependent sulfide production by the same isolate. Increased production of sulfide and organic acids during the stationary growth phase suggests that fermentative Halanaerobium uses thiosulfate to remove excess reductant. These findings emphasize the potential detrimental effects that could arise from thiosulfate-reducing microorganisms in hydraulically fractured shales, which are undetected by current industry-wide corrosion diagnostics. IMPORTANCE Although thousands of wells in deep shale formations across the United States have been hydraulically fractured for oil and gas recovery, the impact of microbial metabolism within these environments is poorly understood. Our research demonstrates that dominant microbial populations in these subsurface ecosystems contain the conserved capacity for the reduction of thiosulfate to sulfide and that this process is likely occurring in the environment. Sulfide generation (also known as “souring”) is considered deleterious in the oil and gas industry because of both toxicity issues and impacts on corrosion of the subsurface infrastructure. Critically, the capacity for sulfide generation via reduction of sulfate was not detected in our data sets. Given that current industry wellhead tests for sulfidogenesis target canonical sulfate-reducing microorganisms, these data suggest that new approaches to the detection of sulfide-producing microorganisms may be necessary.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2023

Influence of extreme fracture flow channels on the thermal performance of open-loop geothermal systems at commercial scale

Abstract Adequate stewardship of geothermal resources requires accurate forecasting of long-term thermal performance. In enhanced geothermal systems and other fracture-dominated reservoirs, predictive models commonly assume constant-aperture fractures, although spatial variations in aperture can greatly affect reservoir permeability, fluid flow distribution, and heat transport. Whereas previous authors have investigated the effects of theoretical random aperture distributions on thermal performance, here we further explore the influence of permeability heterogeneity considering field-constrained aperture distributions from a meso-scale field site in northern New York, USA. Using numerical models of coupled fluid flow and heat transport, we conduct thermal–hydraulic simulations for a hypothetical reservoir consisting of a relatively impervious porous matrix and a single, horizontal fracture. Our results indicate that in highly channelized fields, most well design configurations and operating conditions result in extreme rates of thermal drawdown (e.g., 50% drop in production well temperatures in under 2 years). However, some other scenarios that account for the risks of short-circuiting can potentially enhance heat extraction when mass flow rate is not excessively high, and the direction of geothermal extraction is not aligned with the most permeable features in the reservoir. Through a parametric approach, we illustrate that well separation distance and relative positioning play a major role in the long-term performance of highly channelized fields, and both can be used to help mitigate premature thermal breakthrough.

Rangel-Jurado, Nicolás↗
DOE OSTI2017

Washington Geothermal Play Fairway Analysis Heat, Permeability, and Fracture Model Data

This submission contains raster and vector data for the entire state of Washington, with specific emphasis on the three geothermal play fairway sites: Mount St. Helens seismic zone (MSHSZ), Wind River valley (WRV), and Mount Baker (MB). Data are provided for 3 major geothermal models: heat, permeability, and fluid-filled fractures, and an additional infrastructure model. Both of the permeability and fluid-filled-fracture models are produced at 200 m and at 2 km depths; the heat model is only produced at the 200 m depth. Values are provided for both model favorability and model confidence. A combined model at 200m and 2 km depths is provided for favorability, confidence, and exploration risk. Raster data are provided in GeoTiff format and have a statewide coverage. Cell size is 104.355 ft; file type is unsigned 8-bit integer (0-255); 0 represents no favorability or confidence; 255 represents maximum favorability or confidence. The NAD83(HARN)/Washington South (ftUS) projection is used (EPSG:2927). Vector data are provided in shapefile or comma-delimited text file formats. Geographic coordinates, where provided, are in WGS84. A readme file accompanies each folder and provides an overview and description of the enclosed data. The heat model combines 5 intermediate raster layers (which are included in the download package): temperature gradient wells, young volcanic vents, hot springs, young intrusive volcanic rocks, and geothermometry. The permeability model combines 8 intermediate raster layers: density of mapped faults, 2D dilation tendency of mapped faults, 2D slip tendency of mapped faults, seismicity, 3D dilation tendency, 3D slip tendency, 3D maximum coulomb shear stress, and 3D slip gradients. The fluid-filled fracture model combines up to 4 intermediate rasters: resistivity from magneto-telluric 3D inversions, seismicity, Vp/Vs anomalies from passive seismic tomography, and Vs anomalies from ambient-noise tomography. A statewide infrastructure model is also provided that formalizes land-use constraints and restrictions relevant for geothermal prospecting and development. This model combines 10 intermediate rasters: areas off limits to drilling, existing or proposed geothermal leases, DNR-owned land, land-use restrictions along the Columbia River Gorge, areas inundated by water, availability of potential process water, proximity to existing roads, proximity to transmission lines, distance from urban areas, and snow-related elevation restrictions. Supporting vector data for the development of each raster layer is provided. For details on the areas of interest and modeling process please see the 'WA_State_Play_Fairway_Phase_2_Technical_Report' in the download package.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Key Learnings from Hydraulic Fracturing Test Site - 2 (HFTS-2), Delaware Basin

Hydraulic fractures (HF) play a dominant role in oil and gas production from unconventional reservoirs, fracture characteristics, geometry, and extent are generally not well known and are typically inferred from various monitoring methods or subsurface models. The Hydraulic Fracturing Test Site-2 (HFTS-2) is a field-based research experiment performed in the Wolfcamp formation of the Permian (Delaware) Basin. HFTS-2, a unique joint industry program (JIP) that brings together government, academia, and industry, focused on field data acquisition and interpretation. The project has built a comprehensive HF research dataset that includes microseismic (MS), 1,500 ft of core, diagnostic formation injection tests (DFIT), fluid characterization, advanced logs, geochemistry, downhole gauges, varying completions, and permanent fiber optic (FO) cable in vertical and horizontal wells. These data were integrated and used to characterize HF geometry/dimensions and resulting depletion profiles, gain insights for completion design, and achieve a better understanding of parent well depletion effects on child well performance. The analysis and integration of the comprehensive HFTS-2 diagnostics dataset provide insights for optimal well placement and completions and improves understanding about the effects of parent well depletion. Furthermore, this dataset can be used to blind test and develop subsurface workflows for unconventional resources. Key learnings from HFTS-2 and the new technologies tested can easily be transferred to other unconventional plays.

58 GEOSCIENCES↗
DOE OSTI2021

Analysis and Integration of the Hydraulic Fracturing Test Site-2 (HFTS-2) Comprehensive Dataset

Hydraulic Fracturing Test Site-2 (HFTS-2) is a field-based research experiment performed in the Permian (Delaware) Basin. The unique aspect of this program was the acquisition of a unique, comprehensive, diagnostic dataset. Additionally, shorter parent wells drilled three years before the child wells offered clear distinction between the stages influenced by parent-child effects and the stages without any effects. The goal of this study was to analyze and integrate this comprehensive diagnostic dataset to understand the areal and vertical extent of hydraulic fractures (HF). The paper also provides insights on the effects of parent wells’ depletion on child well HF geometry based on various monitoring methods and subsurface models. Areal and vertical coverage for all HFTS-2 wells during stimulation and depletion was estimated based on analysis and interpretation of diagnostics and advanced modeling results. HFTS-2 diagnostics included microseismic (MS), pre- and post-stimulation logs and cores, bottomhole gauges, and fiber optic (FO) data. The diagnostics results (MS, FO, image logs) were integrated and used to calibrate subsurface models. Additional field tests were designed and implemented for depletion monitoring. The tailored program for monitoring depletion included vertical and slant well pressures, interference testing, and a vertical strain depletion trial. Areal Coverage: Conventional MS (and FO MS) were used to compute HF dimensions, which were compared with diagnostics (FO strain, gauge, image logs) observations and calibrated subsurface models. A post-production interference test did not show offset well communication. Vertical Coverage: Vertical coverage during stimulation was monitored using a vertical monitoring well. The stronger mechanical strain signals showed good correlation with MS event intensities, geomechanical properties, and gauge inferences. Vertical depletion was estimated based on vertical/slant well gauges and strain depletion tests. Parent-Child Effects: Diagnostics and calibrated subsurface models show asymmetry in child well fracture geometries for stages that overlap parent wells. Child well image logs serve as a good indicator for parent Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/2-21URTC/D021S031R004/2477423/urtec-2021-5241-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5241 well HF tracking. Child well MS events had an eastward bias, in line with pre-stimulation image logs, and was confirmed by parent well frac hits. Novel/Additive Information: The dataset presents a unique, over-constrained problem space to compare independent techniques to arrive at HF metrics (i.e., stimulation height and/or half-length), unlike a single source dataset, in which calibration is done using available data to guide predictions. Here, the asymmetry in HF geometry seen in the stages influenced by parent-child effects offers unique insights into well spacing and landing, which are key capital decisions the unconventional resources industry is seeking to optimize.

58 GEOSCIENCES↗
DOE OSTI2012

Self-decomposable Fibrous Bridging Additives for Temporary Cementitious Fracture Sealers in EGS Wells

This study evaluates compatibility of a self-degradable temporary fracture sealer with the drilling mud and plugging and self-degrading performance of different fibers to be used in combination with the sealer. The sodium silicate-activated slag/Class C fly ash (SSASC) cementitious sealer must plug fractures at 85oC to allow continuous well drilling and it must degrade and leave the fractures open for water at later times when exposed to temperatures above 200oC. The sealer showed good compatibility with the mud. Even the blend of 80/20 vol.% of sealer/mud reached a compressive strength of more than 2000 psi set as one of the material criteria, mostly due to the additional activation of the slag and Class C fly ash by the alkaline ingredient present in the drilling fluid. In contrast, the drilling fluid was detrimental to the compressive strength development in conventional Class G well cement, so that it failed to meet this criterion. Among several organic fibers tested both polyvinyl alcohol (PVA)-and nylon-based fibers showed adequate plugging of the sealer in slot nozzles of 1-in. wide x 6-in. long x 0.08 in. and 0.24 in. high under pressures up to 700 psi. PVA fibers displayed better compressive toughness and self-degrading properties than nylon. The compressive toughness of sealers made by adding 1.0 wt% 6 mm-length PVA and 0.5 wt% 19 mm-length PVA was 9.5-fold higher than that of a non-bridged sealer. One factor governing the development of such high toughness was an excellent adherence of PVA to the SSASC cement. The alkali-catalyzed self-decomposition of PVA at 200°C led to the morphological transformation of the material from a fibrous structure to a microscale flake-like structure that helped the desirable conversion of the sealer into small fragments. In contrast, nylon’s decomposition provided a reticular network structure in the self-degraded sealer resulting in bigger fragments compared against the sealer with PVA. The PVA fiber has a high potential as a self-decomposable bridging additive in the SSASC cement sealer.

15 GEOTHERMAL ENERGY↗
DOE OSTI2013

Training and Research on Probabilistic Hydro-Thermo-Mechanical Modeling of Carbon Dioxide Geological Sequestration in Fractured Porous Rocks

Colorado School of Mines conducted research and training in the development and validation of an advanced CO 2 GS (Geological Sequestration) probabilistic simulation and risk assessment model. CO 2 GS simulation and risk assessment is used to develop advanced numerical simulation models of the subsurface to forecast CO 2 behavior and transport; optimize site operational practices; ensure site safety; and refine site monitoring, verification, and accounting efforts. As simulation models are refined with new data, the uncertainty surrounding the identified risks decrease, thereby providing more accurate risk assessment. The models considered the full coupling of multiple physical processes (geomechanical and fluid flow) and describe the effects of stochastic hydro-mechanical (H-M) parameters on the modeling of CO 2 flow and transport in fractured porous rocks. Graduate students were involved in the development and validation of the model that can be used to predict the fate, movement, and storage of CO 2 in subsurface formations, and to evaluate the risk of potential leakage to the atmosphere and underground aquifers. The main major contributions from the project include the development of: 1) an improved procedure to rigorously couple the simulations of hydro-thermo-mechanical (H-M) processes involved in CO 2 GS; 2) models for the hydro-mechanical behavior of fractured porous rocks with random fracture patterns; and 3) probabilistic methods to account for the effects of stochastic fluid flow and geomechanical properties on flow, transport, storage and leakage associated with CO 2 GS. The research project provided the means to educate and train graduate students in the science and technology of CO 2 GS, with a focus on geologic storage. Specifically, the training included the investigation of an advanced CO 2 GS simulation and risk assessment model that can be used to predict the fate, movement, and storage of CO 2 in underground formations, and the evaluation of the risk of potential CO 2 leakage to the atmosphere and underground aquifers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Development of an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs

In this study, we have developed an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs where fluid flow through the fracture is radial. The dimensionless forms of the governing equations and the initial and boundary conditions in the radial flow system can be written in a form identical to those in the linear flow system developed by Jung and Pruess [Jung, Y., and K. Pruess (2012), A Closed-Form Analytical Solution for Thermal Single-Well Injection-Withdrawal Tests, Water Resour. Res., 48, W03504, doi:10.1029/2011WR010979], and therefore the analytical solutions developed in Jung and Pruess (2012) can be applied to compute the time dependence of temperature recovery at the injection/withdrawal well in a horizontally oriented fracture with radial flow.

54 ENVIRONMENTAL SCIENCES↗