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Emmanuel M Detournay - One of the best experts on this subject based on the ideXlab platform.
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Experimental investigation of crack Opening asymptotics for fluid-driven Fracture
Strength fracture and complexity, 2005Co-Authors: Andrew P. Bunger, Robert G. Jeffrey, Emmanuel M DetournayAbstract:Fracture Opening in the tip region of a fluid-driven Fracture is governed not only by the square-root tip asymptote, well-known from linear elastic Fracture mechanics (LEFM), but also by an intermediate tip asymptote thatis specific to fluid-driven Fracture. Additional tip asymptotes may arise when the Fracture interacts with a nearby free surface. We have explored this complex tip behavior in the laboratory by growing hydraulic Fractures in impermeable, transparent, brittle elastic materials, employing a method based on the Beer-Lambert law of optical absorption to measure the Fracture Opening. The near-tip Opening matches the fluid-driven Fracture tip asymptote when the effect of viscous dissipation is significant. Conversely, the LEFM tip asymptote matches the experimental behavior when the viscosity effects are negligible. Furthermore, when the Fracture radius is several times its depth, a third asymptote is observed that arises from the plate-like behavior of the material between the Fracture and the free-surface. The prevalence of each of the three observed asymptotes is shown to correlate with the Fracture's location in a two-dimensional parametric space.
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Crack tip behavior in near-surface fluid-driven Fracture experiments
Comptes Rendus Mécanique, 2005Co-Authors: Andrew P. Bunger, Emmanuel M Detournay, Robert G. JeffreyAbstract:Abstract This Note presents experimental results for the near-tip Fracture Opening of fluid-driven Fractures. The effect of fluid viscosity, quantified by a dimensionless parameter, was varied between tests. The tip region closely followed the classical square-root behavior from linear elastic Fracture mechanics when the viscosity parameter was small. Conversely, when the viscosity parameter was of order one and the lag between the fluid-filled region and the Fracture front accounted for less than 30% of the Fracture, the tip region behaved according to a known intermediate asymptotic solution which results from the solid/fluid coupling. To cite this article: A.P. Bunger et al., C. R. Mecanique 333 (2005).
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self similar solution of a plane strain Fracture driven by a power law fluid
International Journal for Numerical and Analytical Methods in Geomechanics, 2002Co-Authors: Jose I Adachi, Emmanuel M DetournayAbstract:This paper analyses the problem of a hydraulically driven Fracture, propagating in an impermeable, linear elastic medium. The Fracture is driven by injection of an incompressible, viscous fluid with power-law rheology and behaviour index n⩾0. The Opening of the Fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self-similar form. A solution that describes the crack length evolution, the Fracture Opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self-similar solution is obtained by expanding the Fracture Opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.
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similarity solution of a penny shaped fluid driven Fracture in a zero toughness linear elastic solid
Comptes Rendus De L Academie Des Sciences Serie Ii Fascicule B-mecanique, 2001Co-Authors: Alexei A Savitski, Emmanuel M DetournayAbstract:Abstract This note deals with the problem of a penny-shaped hydraulic Fracture propagating in an impermeable elastic solid. Growth of the Fracture is driven by injection of an incompressible Newtonian fluid at the center of the Fracture. The solution is restricted to the so-called viscosity-dominated regime where it can be assumed that the solid has zero toughness. The paper describes the construction of a semi-analytical similarity solution, which incorporates the known singularity of the fluid pressure at the center of the Fracture and at the tip and which is based on series expansions of the Fracture Opening and fluid pressure in terms of Jacobi polynomials.
Stephen E. Laubach - One of the best experts on this subject based on the ideXlab platform.
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Quartz c-axis orientation patterns in Fracture cement as a measure of Fracture Opening rate and a validation tool for Fracture pattern models
Geosphere, 2016Co-Authors: Estibalitz Ukar, Stephen E. Laubach, Randall MarrettAbstract:We evaluate a published model for crystal growth patterns in quartz cement in sandstone Fractures by comparing crystal Fracture-spanning predictions to quartz c-axis orientation distributions measured by electron backscatter diffraction (EBSD) of spanning quartz deposits. Samples from eight subvertical Opening-mode Fractures in four sandstone formations, the Jurassic–Cretaceous Nikanassin Formation, northwestern Alberta Foothills (Canada), Cretaceous Mesaverde Group (USA; Cozzette Sandstone Member of the Iles Formation), Piceance Basin, Colorado (USA), and upper Jurassic–lower Cretaceous Cotton Valley Group (Taylor sandstone) and overlying Travis Peak Formation, east Texas, have similar quartzose composition and grain size but contain Fractures with different temperature histories and Opening rates based on fluid inclusion assemblages and burial history. Spherical statistical analysis shows that, in agreement with model predictions, bridging crystals have a preferred orientation with c-axis orientations at a high angle to Fracture walls. The second form of validation is for spanning potential that depends on the size of cut substrate grains. Using measured cut substrate grain sizes and c-axis orientations of spanning bridges, we calculated the required orientation for the smallest cut grain to span the maximum gap size and the required orientation of the crystal with the least spanning potential to form overgrowths that span across maximum measured gap sizes. We find that within a 10° error all spanning crystals conform to model predictions. Using crystals with the lowest spanning potential based on crystallographic orientation (c-axis parallel to Fracture wall) and a temperature range for Fracture Opening measured from fluid inclusion assemblages, we calculate maximum Fracture Opening rates that allow crystals to span. These rates are comparable to those derived independently from Fracture temperature histories based on burial history and multiple sequential fluid inclusion assemblages. Results support the R. Lander and S. Laubach model, which predicts that for quartz deposited synchronously with Fracture Opening, spanning potential, or likelihood of quartz deposits that are thick enough to span between Fracture walls, depends on temperature history, Fracture Opening rate, size of Opening increments, and size, mineralogy, and crystallographic orientation of substrates in the Fracture wall (transected grains). Results suggest that EBSD maps, which can be more rapidly acquired than measurement of tens to hundreds of fluid inclusion assemblages, can provide a useful measure of relative Opening rates within populations of quartz-filled Fractures formed under sedimentary basin conditions. Such data are useful for evaluating Fracture pattern development models.
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Fracturing and fluid flow in a sub-décollement sandstone; or, a leak in the basement
Journal of the Geological Society, 2015Co-Authors: John N. Hooker, Stephen E. Laubach, Peter Eichhubl, Toti E. Larson, Autumn Eakin, András Fall, Randall MarrettAbstract:Crack-seal texture within Fracture cements in the Triassic El Alamar Formation, NE Mexico, shows that the Fractures opened during precipitation of quartz cements; later, overlapping calcite cements further occluded pore space. Previous workers defined four systematic Fracture sets, A (oldest) to D (youngest), with relative timing constrained by crosscutting relationships. Quartz fluid inclusion homogenization temperatures are higher within Set B (148 ± 20°C) than in Set C (105 ± 12°C). These data and previous burial history modelling are consistent with Set C forming during exhumation. Fluid inclusions in Set C quartz have higher salinity than those in Set B (22.9 v. 14.2 wt% NaCl equivalent, respectively), and Set C quartz cement is more enriched in 18 O (20.2 v. 18.7‰ VSMOW). Under most assumptions about the true temperature during Fracture Opening, the burial duration, the amount of cement precipitated and fluid-flow patterns, it appears that the Fracture fluid became depleted in 18 O and enriched in 13 C. This isotopic evolution, combined with increasing salinity, suggests that throughout Fracture Opening there was a gravity-driven influx of fluid from upsection Jurassic evaporites, which form a regional decollement. Fracture Opening amid downward fluid motion suggests that fracturing was driven by external stresses such as tectonic stretching or unloading, rather than increases in fluid pressure.
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Non-linear growth kinematics of Opening-mode Fractures
Journal of Structural Geology, 2015Co-Authors: Yaser Alzayer, Peter Eichhubl, Stephen E. LaubachAbstract:Abstract Fracture aperture is commonly assumed to be a linear function of Fracture length, stress, and elastic material properties. Under constant stress, Fracture Opening displacement may change without concurrent length or height growth if the material effectively weakens after initial linear elastic Fracture growth by changes in elastic properties or by non-elastic deformation processes. To investigate the kinematics of Fracture Opening and its dependence on length and height growth, we reconstructed the Opening history of three Opening-mode Fractures that are bridged by crack-seal quartz cement. Similar crack-seal cement bridges had been interpreted to form by repeated incremental Fracture Opening and subsequent precipitation of quartz cement. Using scanning electron microscope cathodoluminescence imaging, we determined the thickness and number of crack-seal cement layers as a function of position along Fracture length and height. Observed trends in crack-seal cement layer thickness and number of Fracture Opening increments are consistent with non-linear Fracture growth kinematics, consisting of an initial stage of fast Fracture propagation relative to aperture growth, followed by a stage of slow propagation and pronounced aperture growth. Consistent with earlier fluid inclusion observations indicating Fracture Opening and propagation occurring over 40–50 m.y., we interpret the second stage of pronounced aperture growth and slow propagation to result from Fracture Opening strain accommodated by solution-precipitation creep and concurrent slow, possibly subcritical, Fracture propagation.
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Insights into rates of Fracture growth and sealing from a model for quartz cementation in Fractured sandstones
Geological Society of America Bulletin, 2014Co-Authors: R. H. Lander, Stephen E. LaubachAbstract:A new model accounts for crystal growth patterns and internal textures in quartz cement in sandstone Fractures, including massive sealing deposits, thin rinds or veneers that line open Fracture surfaces, and bridge structures that span otherwise open Fractures. High-resolution cathodoluminescence imaging of bridge structures and massive sealing deposits indicates that they form in association with repeated micron-scale fracturing of growing quartz crystals, whereas thin rinds do not. Model results indicate that the three morphology types develop in response to (1) the ratio of the rates of quartz growth to Fracture Opening and (2) the substantially faster growth rate that occurs on noneuhedral surfaces in certain crystallographic orientations compared to euhedral crystal faces. Rind morphologies develop when the Fracture Opening rate exceeds two times the fastest rate of quartz growth (along the c axis on noneuhedral surfaces) because growing crystals develop slow-growing euhedral faces. Massive sealing, on the other hand, develops where the net rate of Fracture Opening is less than twice the rate of quartz growth on euhedral faces because all quartz growth surfaces along the Fracture wall seal the Fracture between fracturing events. Bridge structures form at Fracture Opening rates that are intermediate between the massive sealing and rind cases and are associated with crystallographic orientations that allow growth to span the Fracture between fracturing events. Subsequent Fractures break the spanned crystal, introducing new, fast-growing noneuhedral growth surfaces where quartz grows more rapidly compared to the euhedral faces of nonspanning crystals. As the ratio of Fracture Opening to quartz growth rate increases, the proportion of overgrowths that span the Fracture decreases, and the range in c -axis orientations for these crystals comes progressively closer to perpendicular to the Fracture wall until the maximum spanning limit is reached. Simulation results also reproduce “stretched crystal,” “radiator structure,” and “elongate blocky” textures in metamorphic quartz veins. The model replicates a well-characterized quartz bridge from the Cretaceous Travis Peak Formation as well as quartz cement abundances, internal textures, and morphologies in the sandstone host rock and Fracture zone using the same kinetic parameters while honoring fluid-inclusion and thermal-history constraints. The same fundamental driving forces, in both in the host rock and Fracture system, are responsible for quartz cementation, with the only significant difference within the Fracture zone being the creation of new pore space as well as new noneuhedral surfaces for cases where overgrowths span Fractures between fracturing events. Rates of Fracture growth and sealing may be inferred from Fracture cement textures using model results.
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a 48 m y history of Fracture Opening temperature and fluid pressure cretaceous travis peak formation east texas basin
Geological Society of America Bulletin, 2010Co-Authors: Stephen P Becker, R. H. Lander, Robert M. Reed, Stephen E. Laubach, Peter Eichhubl, Robert J BodnarAbstract:Quartz cement bridges across Opening-mode Fractures of the Cretaceous Travis Peak Formation provide a textural and fluid inclusion record of incremental Fracture Opening during the burial evolution of this low-porosity sandstone. Incremental crack-seal Fracture Opening is inferred based on the banded structure of quartz cement bridges, consisting of up to 700 cement bands averaging ∼5 μm in thickness as observed with scanning electron microscope–cathodoluminescence. Crack-seal layers contain assemblages of aqueous two-phase fluid inclusions. Based on fluid inclusion microthermometry and Raman microprobe analyses, we determined that these inclusions contain methane-saturated brine trapped over temperatures ranging from ∼130°C to ∼154°C. Using textural crosscutting relations of quartz growth increments to infer the sequence of cement growth, we reconstructed the fluid temperature and pore-fluid pressure evolution during Fracture Opening. In combination with published burial evolution models, this reconstruction indicates that Fracture Opening started at ca. 48 Ma and above-hydrostatic pore-fluid pressure conditions, and continued under steadily declining pore-fluid pressure during partial exhumation until present times. Individual Fractures opened over an ∼48 m.y. time span at rates of 16–23 μm/m.y. These rates suggest that Fractures can remain hydraulically active over geologically long times in deep basinal settings.
Nicolas J Huerta - One of the best experts on this subject based on the ideXlab platform.
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Fracture Opening or self sealing critical residence time as a unifying parameter for cement co2 brine interactions
International Journal of Greenhouse Gas Control, 2016Co-Authors: Jeanpatrick Leopold Brunet, Zuleima T Karpyn, Nicolas J HuertaAbstract:Abstract Understanding long-term property evolution of cement Fractures is essential for assessing well integrity during geological carbon sequestration (GCS). Cement Fractures represent preferential leakage pathways in abandoned wells upon exposure to CO 2 -rich fluid. Contrasting self-sealing and Fracture Opening behavior have been observed while a unifying framework is still missing. Here we developed a process-based reactive transport model that explicitly simulates flow and multi-component reactive transport in Fractured cement by reproducing experimental observation of sharp flow rate reduction during exposure to carbonated water. The simulation shows similar reaction network as in diffusion-controlled systems without flow. That is, the CO 2 -rich water accelerates the portlandite dissolution, releasing calcium that further reacted with carbonate to form calcite. The calibrated model was used for CO 2 -flooding numerical experiments in 250 cement Fractures with varying initial hydraulic aperture ( b ) and residence time ( τ ) defined as the ratio of Fracture volume over flow rate. A long τ leads to slow replenishment of carbonated water, calcite precipitation, and self-sealing. The opposite occurs when τ is small with short Fracture and fast flow rates. Simulation results indicate a critical residence time τ c – the minimum τ required for self-sealing – divides the conditions that trigger the Opening and self-sealing behavior. The τ c value depends on the initial aperture size through τ c = 9.8 × 10 −4 × b 2 + 0.254 × b . Among the 250 numerical experiments, significant changes in effective permeability – self-healing or Opening – typically occur within hours to a day, thus providing supporting argument for the extrapolation of short-term laboratory observation (hours to months) to long-term prediction at relevant GCS time scales (years to hundreds of years).
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Fracture Opening or self-sealing: Critical residence time as a unifying parameter for cement–CO2–brine interactions
International Journal of Greenhouse Gas Control, 2016Co-Authors: Jeanpatrick Leopold Brunet, Zuleima T Karpyn, Nicolas J HuertaAbstract:Abstract Understanding long-term property evolution of cement Fractures is essential for assessing well integrity during geological carbon sequestration (GCS). Cement Fractures represent preferential leakage pathways in abandoned wells upon exposure to CO 2 -rich fluid. Contrasting self-sealing and Fracture Opening behavior have been observed while a unifying framework is still missing. Here we developed a process-based reactive transport model that explicitly simulates flow and multi-component reactive transport in Fractured cement by reproducing experimental observation of sharp flow rate reduction during exposure to carbonated water. The simulation shows similar reaction network as in diffusion-controlled systems without flow. That is, the CO 2 -rich water accelerates the portlandite dissolution, releasing calcium that further reacted with carbonate to form calcite. The calibrated model was used for CO 2 -flooding numerical experiments in 250 cement Fractures with varying initial hydraulic aperture ( b ) and residence time ( τ ) defined as the ratio of Fracture volume over flow rate. A long τ leads to slow replenishment of carbonated water, calcite precipitation, and self-sealing. The opposite occurs when τ is small with short Fracture and fast flow rates. Simulation results indicate a critical residence time τ c – the minimum τ required for self-sealing – divides the conditions that trigger the Opening and self-sealing behavior. The τ c value depends on the initial aperture size through τ c = 9.8 × 10 −4 × b 2 + 0.254 × b . Among the 250 numerical experiments, significant changes in effective permeability – self-healing or Opening – typically occur within hours to a day, thus providing supporting argument for the extrapolation of short-term laboratory observation (hours to months) to long-term prediction at relevant GCS time scales (years to hundreds of years).
Andrei Kotousov - One of the best experts on this subject based on the ideXlab platform.
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Controlling the Height of Multiple Hydraulic Fractures in Layered Media
SPE Journal, 2016Co-Authors: Aditya Khanna, Andrei KotousovAbstract:Summary Fracture-height containment is desirable in hydraulic-fracturing treatments because it can result in better efficiency of oil or gas recovery and have less impact on the environment. Several mechanisms of the containment of a single hydraulic Fracture were investigated in the past, and the outcomes of these studies are now well-documented in the open literature. However, the effectiveness of these mechanisms in the case of multiple closely spaced hydraulic Fractures has not received much attention. The latter situation typically arises in the case of multiple transverse Fractures emanating from a single horizontal wellbore. In this paper, we develop a mathematical model that one can use to assess the Fracture-interaction phenomenon as well as the effect of the modulus contrast between adjacent rock layers. We consider the situation in which one must contain the hydraulic Fractures entirely in the pay zone and investigate fracturing-fluid-pressure control as a possible mechanism of height containment. It is demonstrated that when the Fracture spacing becomes comparable with the Fracture height, the interaction between the Fractures produces a shielding effect. In this case, the fracturing-fluid pressure that ensures Fracture containment is greater in comparison with the case of a single isolated Fracture. However, the Fracture Opening is also smaller in the case of closely spaced Fractures. The dependence of the fracturing-fluid pressure and Fracture Opening on the Fracture spacing needs to be taken into consideration during the selection of Fracture spacing for a particular treatment.
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effect of residual Opening on the inflow performance of a hydraulic Fracture
International Journal of Engineering Science, 2014Co-Authors: Aditya Khanna, Luiz Bortolan Neto, Andrei KotousovAbstract:Abstract The problem of steady state fluid production from a hydraulic Fracture subject to remote compressive stresses is considered. The Fracture is partially filled with proppant and the distribution of proppant is symmetric about the wellbore. The unpropped Fracture segments can provide additional length to the Fracture and highly conductive pathways for fluid flow. However, these Fracture segments are susceptible to closure due to the confining stresses. The governing equations for Fracture Opening and fluid flow into the Fracture are solved numerically using the Gauss–Chebyshev quadrature technique and a sensitivity study is conducted to investigate the effect of the residual Opening of the unpropped Fracture segments on the performance of a hydraulic Fracture. The range of governing parameters is identified for which the residual Opening of a Fracture leads to production enhancement.
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A New Approach to Hydraulic Stimulation of Geothermal Reservoirs by Roughness Induced Fracture Opening
Effective and Sustainable Hydraulic Fracturing, 2013Co-Authors: Nima Gholizadeh Doonechaly, S. Rahman, Andrei KotousovAbstract:Hydraulic fracturing by shear slippage mechanism (mode II) has been studied in both laboratory and field scales to enhance permeability of geothermal reservoirs by numerous authors and their success stories have been reported. Shear slippage takes place along the planes of pre-existing Fractures which causes Opening of the Fracture planes by the Fracture asperities (roughness induced Opening). Simplified empirical relationships, which are derived based on simple Fracture experiments or best guess, are used to calculate compressive normal surface traction, residual aperture and shear displacement. This introduces ambiguity into the simulation results and often leads to erroneous predictions of reservoir performance. In this study an innovative analytical approach based on the distributed dislocation technique is developed to simulate the roughness induced Opening of Fractures in the presence of compressive and shear stresses as well as fluid pressure inside the Fracture. This provides fundamental basis for computation of aperture distribution for all parts of the Fracture which can then be used in the next step of modeling fluid flow inside the Fracture as a function of time. It also allows formulation of change in aperture due to thermal stresses. The stress distribution and the fluid pressure are calculated using the fluid flow modeling inside the Fracture in a numerical framework in which thermo-hydro mechanical effects are also consid‐ ered using finite element methods (FEM). In this study, Fractures with their characteristic properties are considered to simulate rock deformation. This new approach is applied to the Soultz-Sous-Forets geothermal reservoir to study changes in permeability and its impact on temperature drawdown. It has been shown that the analytical © 2013 Doonechaly et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. approach provides a more realistic prediction of residual Fracture aperture which agrees well with the experience of existing EGS trials around the world. An average increase in aperture due to fluid induced shear dilation has been found to be lower and time required to obtain a sizeable reservoir volume is greater than those previously estimated.
Zhihong Dong - One of the best experts on this subject based on the ideXlab platform.
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Study on the influence of Fracture flow on the temperature field of rock mass with high temperature
Case Studies in Thermal Engineering, 2020Co-Authors: Qifeng Guo, Meifeng Cai, Yu Zhu, Jie Zhang, Zhihong DongAbstract:Abstract For the development of deep resources, the temperature field of deep rock mass is an unavoidable problem. In order to understand the law of redistribution of temperature field in deep rock mass disturbed by fissure water, this paper simulates the heat transfer process of smooth and rough Fractured rock mass with groundwater flow, and analyzes the influence of Fracture Opening, seepage velocity and roughness on the redistribution of temperature field. The results show that: the larger the Fracture Opening is, the smaller the growth rate of rock wall temperature is, and the larger the range of slow increase is of water temperature; seepage velocity has a gradual effect on the increase of rock wall temperature, the greater the seepage speed is, the smaller the water temperature is at the same position; when the roughness is between 0% and 20%, the rock wall temperature has a sudden drop, and the maximum rock wall temperature decreases by 20.56%. Compared with the flow velocity, changing the Fracture roughness can improve the cooling efficiency of rock wall. With the increase of roughness, the water temperature in the same position is lower.
