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1
Zhang, Hai Yong, Shun Li He, Guo Hua Luan, Qiao Lu, Shao Yuan Mo, Zhang Zhang und Gang Lei. „Influence of Fracture Parameters on the Productivity of Fractured Horizontal Well Based on Fluid Mechanics in Tight Gas Reservoir“. Advanced Materials Research 886 (Januar 2014): 452–55. http://dx.doi.org/10.4028/www.scientific.net/amr.886.452.
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Multiple fractures are needed by hydraulic fracturing in order to improve the horizontal well productivity of a single well in tight gas reservoir. The calculation accuracy of productivity influences on the fracturing optimization results and the success ratio and effectiveness of fracturing treatment. This work focuses on analyzing the influence of fracture parameters on fractured horizontal well productivity in tight gas reservoir through establishing a productivity prediction model of fractured horizontal well, considering the interference between fracture and fracture and the wellbore pressure drop. Results show that the fracture parameters, such as fracture number, fracture interval, fracture conductivity and fracture length, have different influences on the productivity of fractured horizontal well and thus, the effects of fracture parameters should be taken into account when designing the fracturing treatment.
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Shi, Di, Liping Li, Jianjun Liu, Mingyang Wu, Yishan Pan und Jupeng Tang. „Effect of discrete fractures with or without roughness on seepage characteristics of fractured rocks“. Physics of Fluids 34, Nr. 7 (Juli 2022): 073611. http://dx.doi.org/10.1063/5.0097025.
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This study proposes a new fractal permeability model for fractured rocks that comprehensively accounts for the geometric fracture characteristics and the fluid transport mechanism. Then, the permeability changes of fractured rocks are analyzed using discrete fracture networks (DFNs) with or without roughness and different geometry parameters in the DFN modeling and finite element simulation. The results show that the proposed permeability model well agrees with the experimental data, and the established DFN numerical model more realistically reflects the fracture network in fractured rocks. Fluctuation of tortuous fracture lines (rough fractures) increases the fracture intersection probability, consequently increasing the fracture intersection area or connecting adjacent fractures. Moreover, permeability increases with the fractal dimension Df, porosity ϕ, maximum fracture length lmax, and proportionality coefficient β, and it decreases with increasing fractal dimension DTf of fracture tortuosity. When the fracture proportionality coefficient is 0.001 ≤ β ≤ 0.01, different DFNs yield similar simulation results for permeability. However, with increasing fracture network complexity, the predictive model created using conventional DFN (C-DFN) increasingly overestimates the fractured rock permeability. Thus, building a permeability model for a fractured rock using rough DFN (R-DFN) is more effective than that using C-DFN. Our findings are helpful for real permeability predictions via DFN and analytical modeling.
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VanCourt, RB, SE Byron, SJ Ali und BD Caldwell. „Fracture mechanics. A comparison study of torsional stress on bone“. Journal of the American Podiatric Medical Association 90, Nr. 4 (01.04.2000): 167–74. http://dx.doi.org/10.7547/87507315-90-4-167.
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Fractures that result from torsional loading of shafts in mechanical systems of nonbiologic materials generate a fracture line that forms a 45 degrees angle to an axis that is perpendicular to the direction of torsional loading on the shaft. As tension and compression are applied to these isotropic substances, the angle of fracture increases and decreases, respectively. Understanding how these forces, particularly compressive forces, generate elongation of a spiral fracture increases the ability to predict the extent of injury to bone. Fibular and metatarsal fractures are of primary importance to the podiatric physician, but any spiral fracture may be subject to torsional loading. Thus the principles stated here apply to the entire skeletal system. The purpose of this article is to provide a better understanding of the mechanics behind the causes and characteristics of fractures and to explore whether these same factors apply to the fracture mechanics of bone.
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Yuan, Yingzhong, Wende Yan, Fengbo Chen, Jiqiang Li, Qianhua Xiao und Xiaoliang Huang. „Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well“. International Journal of Nonlinear Sciences and Numerical Simulation 19, Nr. 3-4 (26.06.2018): 367–77. http://dx.doi.org/10.1515/ijnsns-2017-0135.
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AbstractComplex fracture systems including natural fractures and hydraulic fractures exist in shale gas reservoir with fractured horizontal well development. The flow of shale gas is a multi-scale flow process from microscopic nanometer pores to macroscopic large fractures. Due to the complexity of seepage mechanism and fracture parameters, it is difficult to realize fine numerical simulation for fractured horizontal wells in shale gas reservoirs. Mechanisms of adsorption–desorption on the surface of shale pores, slippage and Knudsen diffusion in the nanometer pores, Darcy and non-Darcy seepage in the matrix block and fractures are considered comprehensively in this paper. Through fine description of the complex fracture systems after horizontal well fracturing in shale gas reservoir, the problems of conventional corner point grids which are inflexible, directional, difficult to geometrically discretize arbitrarily oriented fractures are overcome. Discrete fracture network model based on unstructured perpendicular bisection grids is built in the numerical simulation. The results indicate that the discrete fracture network model can accurately describe fracture parameters including length, azimuth and density, and that the influences of fracture parameters on development effect of fractured horizontal well can be finely simulated. Cumulative production rate of shale gas is positively related to fracture half-length, fracture segments and fracture conductivity. When total fracture length is constant, fracturing effect is better if single fracture half-length or penetration ratio is relatively large and fracturing segments are moderate. Research results provide theoretical support for optimal design of fractured horizontal well in shale gas reservoir.
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Kubeyev, Amanzhol, Nathaniel Forbes Inskip, Tomos Phillips, Yihuai Zhang, Christine Maier, Kevin Bisdom, Andreas Busch und Florian Doster. „Digital Image-Based Stress–Permeability Relationships of Rough Fractures Using Numerical Contact Mechanics and Stokes Equation“. Transport in Porous Media 141, Nr. 2 (Januar 2022): 295–330. http://dx.doi.org/10.1007/s11242-021-01719-7.
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AbstractFlow in fractures is sensitive to their geometrical surface characteristics. The surface can undergo deformation if there is a change in stress. Natural fractures have complex geometries and rough surfaces which complicates the modelling of deformation and fluid flow. In this paper, we present a computational model that takes a digital image of a rough fracture surface and provides a stress–permeability relationship. The model is based on a first-principle contact mechanics approach at the continuum scale. Using this first principle approach, we investigate numerically the effect of fracture surface roughness and shifting of surfaces on the permeability evolution under applied stress and compare the results with laboratory experiments. A mudrock core fracture surface was digitalized using an optical microscope, and 2D cross sections through fracture surface profiles were taken for the modelling. Mechanical deformation is simulated with the contact mechanics based Virtual Element Method solver that we developed within the MATLAB Reservoir Simulation Toolbox platform. The permeability perpendicular to the fracture cross section is determined by solving the Stokes equation using the Finite Volume Method. A source of uncertainty in reproducing laboratory results is that the exact anchoring of the two opposite surfaces is difficult to determine while the stress–permeability relationship is sensitive to the exact positioning. We, therefore, investigate the sensitivity to a mismatch in two scenarios: First, we assess the stress–permeability of a fracture created using two opposing matched surfaces from the rock sample, consequently applying relative shear. Second, we assess the stress–permeability of fractures created by randomly selecting opposing surfaces from that sample. We find that a larger shift leads to a smaller drop in permeability due to applied stress, which is in line with a previous laboratory study. We also find that permeability tends to be higher in fractures with higher roughness within the investigated stress range. Finally, we provide empirical stress–permeability relationships for various relative shears and roughnesses for use in hydro-mechanical studies of fractured geological formations.
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Abass, Hazim Abass, Chris Lamei Lamei, Kaveh Amini Amini und Tadesse Teklu Teklu. „Hydraulic Fracturing Tight Reservoirs: Rock Mechanics and Transport Phenomena“. Journal of Petroleum Research and Studies 8, Nr. 2 (06.05.2021): 122–43. http://dx.doi.org/10.52716/jprs.v8i2.239.
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Conventional reservoirs have been fracture stimulated using acid fracturing and proppant fracturing.Acid fracturing is performed to improve well productivity in acid-soluble formations such aslimestone, dolomite, and chalk. Hydrochloric acid is generally used to create an etched fracture,which is the main mechanism for maintaining the fracture open during the life of a well. Proppantfracturing is an alternative option that has been applied in carbonaceous and siliceous formations.There is no quantitative method to provide an answer of whether acid fracturing or proppantfracturing is an appropriate stimulation method for a given carbonate formation. How rockmechanics can be applied to decide on what method is more effective? Laboratory experiments havebeen performed to simulate acid etched to study the effect of elastic, plastic and viscoelastic rockbehavior and their effects on fracture conductivity. Comparison of acid vs. proppant fracturingconductivity in carbonate formation is presented.Fracturing low permeability reservoirs is totally different than fracturing tight formations. Thefracture geometry required in low permeability reservoirs need to be planar, conductive andpenetrating deep in the reservoir. Fracture complexity in these reservoirs is to be avoided foroptimum stimulation treatment. However, in fracturing tight formation, a complex fracture networkis desirable for better recovery. Creating multiple fractures in horizontal wells without the use ofmechanical intervention, is becoming essential especially in tight gas reservoirs. We have learnedhow to initiate hydraulic fractures into a specific direction and place as many fractures as desired inhorizontal wells but with casing and perforation. The challenge now is to initiate weak point acrossthe horizontal well such that fracturing fluid will initiate a fracture there. How rock mechanics hasbeen applied to achieve this objective? We are fracturing tight gas sand in harsh environment, atdepth more than 18000 ft, of temperature close to 400 °F, and one can figure out the extreme in-situstresses relevant to this depth.When the reservoir pressure decreases, the elastic displacement in response to the increase ineffective stress will cause natural fractures to close leading to a decline in reservoir productivity.
The matrix medium feeds the natural tensile fractures which carry the fluids to the wellbore. Thedecline in conductivity with increasing effective stress should follow a logical declining rate tosupport a given production rate. How the concept of effective stress has been applied to understandthe stress-dependent conductivity of various conductive components of a given reservoir? Rockmechanics testing of these stress sensitive reservoirs becomes vital to optimize fracturing tightformations.Economical production from tight reservoirs, including shale gas and shale oil formations, requireshorizontal well drilling and massive proppant hydraulic fracturing stimulation. The stimulationinvolves generating sufficient fractures network or stimulated reservoir volume (SRV), which isachieved by placing optimized stimulation treatments along the horizontal section of wellboresideally drilled from multi-well pads to increase the production rate and ultimate recovery. Hydraulicfracturing in naturally fractured formations is characterized by generating a fractures’ network thatshould be designed for in extremely low permeability of unconventional reservoirs. Fractures shouldextensively reach shale matrix to achieve commercial gas production. Therefore, production rate andultimate recovery depend on the size of the created SRV.The transport phenomena controlling fluid flow through tight formation is no longer sufficient to bemodeled by Darcy’s flow. Diffusion and imbibition are important transport mechanisms. The conceptof osmosis and flow through a semi-permeable membrane component are critical. Additionally,diffusion and a special case of molecular flow due to Knudson effect will be discussed. Conventionalreservoir simulation collapses when trying to simulate fluid flow through tight reservoirs. Numericalstudies on a hydraulically fractured well to simulate the dynamic processes during fracturinginjection, following well shut-in (soaking), and production are discussed.
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Yu, Chaoyun, Bin Gong, Na Wu, Penglei Xu und Xiankai Bao. „Simulation of the Fracturing Process of Inclusions Embedded in Rock Matrix under Compression“. Applied Sciences 12, Nr. 16 (11.08.2022): 8041. http://dx.doi.org/10.3390/app12168041.
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Typical parallel fractures are often observed in the outcrops of inclusions in the field. To reveal the failure mechanism of inclusions embedded in rock matrix, a series of heterogeneous models are established and tested based on the damage mechanics, statistical strength theory, and continuum mechanics. The results show that, with the spacing between two adjacent fractures decreasing, the stress is firstly transferred from negative to positive, then from positive to negative. Stress transition is profound for the fracture spacing. Meanwhile, three types of fractures, i.e., consecutive fracture, non-consecutive fracture, and debonding fracture, are found, which are consistent with the observed modes in the field. Multiple inclusions are often fractured easier than an isolated inclusion due to the stress disturbance between inclusions and newly generated fractures. Either in single or multiple inclusions, tensile stresses inside the inclusions are the main driving force for fracture initiation and propagation. Besides, although the material heterogeneity has a small effect on the stress variation, it has an evident impact on the fracturing mode of inclusions. The stiffness ratio is critical for the stress transition and failure pattern; the interface debonding occurs earlier than the fracture initiation inside the inclusion when the stiffness ratio is relatively high. Additionally, the inclusions content only affects the sequence of fracture initiation rather than the final fracture spacing pattern.
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Melvin, J. W. „Fracture Mechanics of Bone“. Journal of Biomechanical Engineering 115, Nr. 4B (01.11.1993): 549–54. http://dx.doi.org/10.1115/1.2895538.
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This paper reviews the progress that has been made in applying the principles of fracture mechanics to the topic of fracture of long bones. Prediction of loading conditions which result in the propagation of fractures in bones has been of interest to the field of trauma biomechanics and orthopedics for over one hundred years. Independent verifications, by various investigators, of bone fracture mechanics parameters are reviewed and investigations of the effects of bone density and specimen thickness on the critical fracture mechanics parameters and of other factors such as critical crack length and plastic zone size in bovine femoral bone, and the effects of crack velocity on fracture mechanics parameters in bovine tibial bone are discussed. It took over ten years for the techniques of bone fracture mechanics to be applied to human compact bone, due primarily to geometric constraints from the smaller size of human bones. That work will be reviewed along with other continuing work to define the orientation dependence of the fracture mechanics parameters in bone and to refine the experimental techniques needed to overcome the geometric constraints of specimen size. A discussion is included of work still needed to determine fracture mechanics parameters for transverse and longitudinal crack propagation in human bone and to establish the effects of age on those parameters. Finally, a discussion will be given of how this knowledge needs to be extended to allow prediction of whole bone fracture from external loading to aid in the design of protective systems.
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McClure, Mark W., Mohsen Babazadeh, Sogo Shiozawa und Jian Huang. „Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks“. SPE Journal 21, Nr. 04 (15.08.2016): 1302–20. http://dx.doi.org/10.2118/173354-pa.
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Summary We developed a hydraulic-fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, 3D discrete-fracture networks (DFNs). The code is efficient enough to perform field-scale simulations of hydraulic fracturing in DFNs containing thousands of fractures, without relying on distributed-memory parallelization. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical properties. Fracture sliding occurs in the direction of maximum resolved shear stress. Nonlinear empirical equations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical 1D leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is modeled with linear-elastic fracture mechanics. The Forchheimer equation (Forchheimer 1901) is used to simulate non-Darcy pressure drop in the fractures because of high flow rate. A crossing criterion is implemented that predicts whether propagating hydraulic fractures will cross natural fractures or terminate against them, depending on orientation and stress anisotropy. Height containment of propagating hydraulic fractures between bedding layers can be modeled with a vertically heterogeneous stress field or by explicitly imposing hydraulic-fracture-height containment as a model assumption. Limitations of the model are that all fractures must be vertical; the mechanical calculations assume a linearly elastic and homogeneous medium; proppant transport is not included; and the locations of potentially forming hydraulic fractures must be specified in advance. Simulations were performed of a single propagating hydraulic fracture with and without leakoff to validate the code against classical analytical solutions. Field-scale simulations were performed of hydraulic fracturing in a densely naturally fractured formation. The simulations demonstrate how interaction with natural fractures in the formation can help explain the high net pressures, relatively short fracture lengths, and broad regions of microseismicity that are often observed in the field during stimulation in low-permeability formations, and that are not predicted by classical hydraulic-fracturing models. Depending on input parameters, our simulations predicted a variety of stimulation behaviors, from long hydraulic fractures with minimal leakoff into surrounding fractures to broad regions of dense fracturing with a branching network of many natural and newly formed fractures.
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Liu, Yang, Ping Chen, Bisheng Wu, Tianshou Ma, Bailin Wu, Xi Zhang und Robert G. Jeffrey. „Mechanics of Hydraulic-Fracture Growth from a Wellbore Intersecting Natural Fractures“. SPE Journal 25, Nr. 02 (09.12.2019): 646–61. http://dx.doi.org/10.2118/198890-pa.
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Summary The creation and propagation of hydraulic fractures (HFs) emanating from a well in a naturally fractured rock is important not only to the success of fracturing treatments, but also for interpretation of the data from diagnostic fracture injection tests (DFITs). In this paper, we consider the reservoir rock to consist of an impermeable rock matrix and a system of discrete natural fractures (NFs) that are permeable. The well is assumed to intersect two sets of NFs at their midpoints, and injection into the wellbore might open the NFs and/or create new fractures that extend along the maximum-principal-stress direction. Both new fractures and pre-existing NFs can act as either a main HF or a fluid-loss path. In this near-well transient-fracture analysis, the NFs are short segments characterized by size, orientation, and aperture. A fully coupled HF model is used to investigate the interaction between the fractures to determine how the fluid injected is distributed to the fractures for a range of stress, fluid-injection-rate, and NF-geometry conditions. We find that a more-isotropic stress condition and a lower value of the fluid-viscosity/injection-rate product favor propagation of NFs. These conditions cause the NFs to accept more fluid, and, as a result, the growth of new fractures is suppressed. The post-shut-in pressure responses for the cases with propagating new fractures and nonpropagating NFs are studied.
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Rice, J. R. „Fracture Mechanics“. Applied Mechanics Reviews 38, Nr. 10 (01.10.1985): 1271–75. http://dx.doi.org/10.1115/1.3143689.
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Fracture mechanics is an active research field that is currently advancing on many fronts. This appraisal of research trends and opportunities notes the promising developments of nonlinear fracture mechanics in recent years and cites some of the challenges in dealing with topics such as ductile-brittle transitions, failure under substantial plasticity or creep, crack tip processes under fatigue loading, and the need for new methodologies for effective fracture analysis of composite materials. Continued focus on microscale fracture processes by work at the interface of solid mechanics and materials science holds promise for understanding the atomistics of brittle vs ductile response and the mechanisms of microvoid nucleation and growth in various materials. Critical experiments to characterize crack tip processes and separation mechanisms are a pervasive need. Fracture phenomena in the contexts of geotechnology and earthquake fault dynamics also provide important research challenges.
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Erdogan, F. „Fracture mechanics“. International Journal of Solids and Structures 37, Nr. 1-2 (Januar 2000): 171–83. http://dx.doi.org/10.1016/s0020-7683(99)00086-4.
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Aliabadi, M. „Fracture mechanics“. Engineering Analysis with Boundary Elements 6, Nr. 2 (Juni 1989): 114. http://dx.doi.org/10.1016/0955-7997(89)90009-x.
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Parker, A. P. „Fracture mechanics“. Journal of Mechanical Working Technology 18, Nr. 1 (Januar 1989): 123. http://dx.doi.org/10.1016/0378-3804(89)90115-0.
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OHJI, Kiyotsugu. „Fracture Mechanics“. Journal of the Society of Mechanical Engineers 90, Nr. 823 (1987): 706–7. http://dx.doi.org/10.1299/jsmemag.90.823_706.
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Ferri Aliabadi, M. H. „Fracture mechanics“. Engineering Analysis with Boundary Elements 20, Nr. 3 (Oktober 1997): 269–71. http://dx.doi.org/10.1016/s0955-7997(97)00053-2.
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Wang, Wenhai, Yang Zhao, Lishuai Jiang, Jiacheng Zuo, Guangsheng Liu und Hani S. Mitri. „Preliminary Study on Size Effect of Fractured Rock Mass with Sand Powder 3D Printing“. Processes 10, Nr. 10 (30.09.2022): 1974. http://dx.doi.org/10.3390/pr10101974.
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The size effect has a significant effect on the mechanical behavior of rock, thereby fundamentally influencing the stability of rock excavations. The main challenge associated with the experimental research on the size effect of fractured rock mass lies in the difficulty of specimen preparation to represent the influence of size and fracture on the mechanical behavior of the rock material. In order to preliminarily explore the feasibility of 3D printing technology in the field of rock mechanics, fractured rock specimens of different sizes and different fracture characteristics were produced using sand powder 3D printing technology. The uniaxial compression test was combined with the digital image correlation method (DIC) technology to study the influence of the size effect on the mechanical properties and deformation and failure of different fractured specimens. The research finds that: (1) The elastoplastic mechanical characteristics of the sand powder 3D printed specimens are similar to soft rock. Specimen size and fracture angle have significant effects on the mechanical properties of specimens. Under different fracture conditions, the uniaxial compressive strength (UCS) and Elasticity Modulus of sand powder 3D specimens should be decreased with the increase of the specimen size, and the size effect has different influences on the specimens with different fracture characteristics. (2) Under different fracture conditions, the crack initiation position and failure mode of specimens of various sizes are affected by the fracture inclination to varying degrees. (3) The size effect of fractured rock mass is closely related to the defect level inside the rock mass. The size effect originates from the heterogeneity inside the material. The research results verify the feasibility of applying sand powder 3D printing technology to study the size effect of fractured rock masses and provide an innovative test method for the size effect test study. Preliminary exploration of the size effect of fractured rock masses provides a powerful reference for related research in this field. The study proves the feasibility of applying sand powder 3D printing technology in similar rock mechanics tests and contributes to understanding the size effect of a fractured rock mass.
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Xu, Qianghui, Xiongyu Chen, Junyu Yang, Zhiying Liu und Lin Shi. „Pore-scale study of coke combustion in a matrix-fracture system based on the micro-continuum approach“. Physics of Fluids 34, Nr. 3 (März 2022): 036603. http://dx.doi.org/10.1063/5.0082518.
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In situ combustion is an advanced recovery technique used to exploit heavy oil in the fractured reservoirs that make up approximately one-third of global heavy-oil resources. However, the mesoscopic mechanisms of coke combustion in the multiscale matrix-fracture system are not well understood because of the difficulty of performing pore-resolved simulations. In the present study, a pore-resolved micro-continuum approach was used to investigate fully coupled thermal and reactive flows through fractured media that contain nanometer-range coke pores, micrometer-range matrix pores, and sub-millimeter range natural fractures. Image-based simulations were implemented using synthetic geological models to mimic coke deposition patterns based on tomography images. The combustion regime diagram for the fractured media was mapped based on the ignition temperature and the air flux to exhibit three combustion regimes. The regime diagram was compared with that for unfractured media to address the impact of natural fractures on oxygen transport and the burning temperature. The oxygen diffusion mechanism dominated oxygen transport from the fracture into the matrix and led to a desirable smoldering combustion temperature regardless of the air injection rate. Effects of fracture geometries were quantified to demonstrate tortuous and discrete fractures, and matching air injection rates with fracture apertures can suppress air-channeling risk effectively. Possible discrepancies between lab measurements and field operations were demonstrated, and their potential to drive misinterpretation of experimental results was considered. The present pathway from tomography images to synthetic images and numerical simulations extends the “image and compute” technique to resolution of multiscale and nonlinear reactive transport.
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Sakamoto, Haruo. „Fracture Mechanics in Design Guidance and Practice“. Key Engineering Materials 353-358 (September 2007): 182–85. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.182.
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This paper describes the state of the art in design codes and guidance using fracture mechanics. In Germany, a railroad accident occurred in June, 1998, which resulted in about 100 passenger deaths due to a wheel fracture. In September, 1999, a water leak accident due to a crack in a pipe happened at the Tsuruga nuclear plant in Japan. Such serious accidents are the result of fracture events. Fracture mechanics is thought to be a tool to avoid such catastrophic fracture accidents. The state of the art in designing mechanical components or structures applying fracture mechanics was reviewed. The American Society of Mechanical Engineer, the Japanese Society of Mechanical Engineers, the Japanese Welding Society, and the Japanese Industrial Standard were mainly surveyed. This report suggests that a more consideration of fracture mechanics in the design codes and guidance is needed for avoiding fracture accidents in components or structures.
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Wu, Kan, und Jon E. Olson. „Simultaneous Multifracture Treatments: Fully Coupled Fluid Flow and Fracture Mechanics for Horizontal Wells“. SPE Journal 20, Nr. 02 (29.05.2014): 337–46. http://dx.doi.org/10.2118/167626-pa.
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Summary Successfully creating multiple hydraulic fractures in horizontal wells is critical for unconventional gas production economically. Optimizing the stimulation of these wells will require models that can account for the simultaneous propagation of multiple, potentially nonplanar, fractures. In this paper, a novel fracture-propagation model (FPM) is described that can simulate multiple-hydraulic-fracture propagation from a horizontal wellbore. The model couples fracture deformation with fluid flow in the fractures and the horizontal wellbore. The displacement discontinuity method (DDM) is used to represent the mechanics of the fractures and their opening, including interaction effects between closely spaced fractures. Fluid flow in the fractures is determined by the lubrication theory. Frictional pressure drop in the wellbore and perforation zones is taken into account by applying Kirchoff's first and second laws. The fluid-flow rates and pressure compatibility are maintained between the wellbore and the multiple fractures with Newton's numerical method. The model generates physically realistic multiple-fracture geometries and nonplanar-fracture trajectories that are consistent with physical-laboratory results and inferences drawn from microseismic diagnostic interpretations. One can use the simulation results of the FPM for sensitivity analysis of in-situ and fracture treatment parameters for shale-gas stimulation design. They provide a physics-based complex fracture network that one can import into reservoir-simulation models for production analysis. Furthermore, the results from the model can highlight conditions under which restricted width occurs that could lead to proppant screenout.
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FAN, L. F., X. W. YI und G. W. MA. „NUMERICAL MANIFOLD METHOD (NMM) SIMULATION OF STRESS WAVE PROPAGATION THROUGH FRACTURED ROCK MASS“. International Journal of Applied Mechanics 05, Nr. 02 (Juni 2013): 1350022. http://dx.doi.org/10.1142/s1758825113500221.
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The present work is devoted to the simulation of stress wave propagation through fractured elastic media, such as rock mass, by using the numerical manifold method (NMM). A single fracture is used to verify the capability and accuracy of the NMM in modeling fractured rock mass. The frequency-dependence on stress wave transmission across a fracture is analyzed. The influence of the fracture specific stiffness on the wave attenuation and effective wave velocity is discussed. The results from the NMM have a good agreement with those obtained from a theoretical displacement discontinuity method (DDM). Taking the advantage that the NMM is able to simulate highly fractured elastic media with a consistent mathematical cover system, a numerical example of stress wave propagation through a fractured rock mass with numerous inherent fractures is presented. It is showed that the results are reasonable and the NMM has a high efficiency in simulating stress wave propagation through highly fractured rock mass. A safety assessment of a tunnel under blast is conducted by using the NMM subsequently. The potential application of the NMM to a more complex fractured rock mass is demonstrated.
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Dubey, Prashant K., Sushil Kumar, Khushboo Havelia und Savitri Yadav. „Integrated deterministic and predictive discrete fracture network modeling for an Eocene carbonate reservoir, Bengal Basin, India“. Leading Edge 38, Nr. 4 (April 2019): 274–79. http://dx.doi.org/10.1190/tle38040274.1.
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Prediction of fracture porosity and permeability remains a challenge for fractured carbonate reservoirs. As natural fractures are heterogeneous and subseismic in scale, core data and image logs only provide partially sampled data, leading to sparse information on fracture length, height, orientation, spacing, and aperture. In the present study, an integrated discrete fracture network was generated that is capable of predicting fracture porosity in Eocene carbonates of the Bengal Basin in northeastern India. The predictive fracture modeling method used 3D kinematic and geomechanical restoration of interpreted seismic horizons to estimate infinitesimal stress and strain values and to characterize associated fracture sets. Seismic attribute analysis was used to extract faults and fractures from an ant-track cube, which provided sharper definition of discontinuities seen in conventional curvature attribute data. An integrated discrete fracture model was created using information from seismic attributes, seismic inversion, and strain distribution to determine fracture intensity. Faults and fractures that are seismically resolved were statistically analyzed, which indicated that spatial distribution of fracture length follows a power law. Based on theoretical concepts of fracture mechanics, linear aperture-to-length scaling was used to characterize aperture population. A present-day geomechanical earth model was used to identify open fracture sets. This model shows that northeast–southwest-oriented fracture sets are critically stressed and will contribute to porosity and permeability. Criticality of fractures to shear failure was analyzed by computing geomechanical parameters — slip stability and dilation tendency, based on the direction and magnitude of far-field stresses. Fractures with slip and dilation tendencies greater than 0.6 in the modeled discrete fracture network were taken as inputs for porosity and permeability estimation.
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Gong, Diguang, Junbin Chen, Cheng Cheng, Yuanyuan Kou, Haiyan Jiang und Jianhong Zhu. „Numerical Simulation on Radial Well Deflagration Fracturing Based on Phase Field Method“. Energies 16, Nr. 12 (16.06.2023): 4758. http://dx.doi.org/10.3390/en16124758.
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A radial well has a unique wellbore configuration. Fracture propagation in radial well deflagration fracturing is studied rarely. The mechanism of interaction between deflagration fractures, natural fractures, and micro-fractures is still unknown. Based on continuum mechanics, damage mechanics, and variational principles, a numerical model of fracture propagation in deflagration fracturing is established with the Hamilton principle and phase-field fracture theory. The effects of horizontal principal stress difference, natural fracture distribution, and micro-fractures around the wellbore on fracture propagation in deflagration fracturing are studied. First, when no natural fractures are developed around the radial well, fractures are initiated at both ends of the radial well. Second, when there are three natural fractures around the radial well, the created fractures have the morphology of shorter fractures in the middle and longer fractures on both sides under stress interference mechanisms. Third, a larger density of natural fractures causes obvious stress superposition, changes the initiation points of radial wells and fracture morphology, and increases fracture width and reservoir stimulation volume. Fourth, as the micro-fractures increase, their interference and induction effects on deflagration fractures are enhanced gradually, and the deflection angle of fractures increases by 38.7%. The study provides a reference for optimizing deflagration fracturing in a radial well.
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Zhao, Xueping, und R. Paul Young. „Numerical modeling of seismicity induced by fluid injection in naturally fractured reservoirs“. GEOPHYSICS 76, Nr. 6 (November 2011): WC167—WC180. http://dx.doi.org/10.1190/geo2011-0025.1.
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The interaction between hydraulic and natural fractures is of great interest for the energy resource industry because natural fractures can significantly influence the overall geometry and effectiveness of hydraulic fractures. Microseismic monitoring provides a unique tool to monitor the evolution of fracturing around the treated rock reservoir, and seismic source mechanisms can yield information about the nature of deformation. We performed a numerical modeling study using a 2D distinct-element particle flow code ([Formula: see text]) to simulate realistic conditions and increase understanding of fracturing mechanisms in naturally fractured reservoirs, through comparisons with results of the geometry of hydraulic fractures and seismic source information (locations, magnitudes, and mechanisms) from both laboratory experiments and field observations. A suite of numerical models with fully dynamic and hydromechanical coupling was used to examine the interaction between natural and induced fractures, the effect of orientation of a preexisting fracture, the influence of differential stress, and the relationship between the fluid front, fracture tip, and induced seismicity. The numerical results qualitatively agree with the laboratory and field observations, and suggest possible mechanics for new fracture development and their interaction with a natural fracture (e.g., a tectonic fault). Therefore, the tested model could help in investigating the potential extent of induced fracturing in naturally fractured reservoirs, and in interpreting microseismic monitoring results to assess the effectiveness of a hydraulic fracturing project.
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Bart, M., J. F. Shao, D. Lydzba und M. Haji-Sotoudeh. „Coupled hydromechanical modeling of rock fractures under normal stress“. Canadian Geotechnical Journal 41, Nr. 4 (01.08.2004): 686–97. http://dx.doi.org/10.1139/t04-018.
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In this paper, a nonlinear poromechanical model is developed for a single rock fracture under normal stress. The fracture is represented by a set of voids, and the progressive fracture displacement is considered as a modification process of void space. Based on experimental data obtained from three representative rock fractures, the constitutive model is formulated through an extension of Biot poroelasticity theory to a saturated fracture. A generalized poroelastic coupling coefficient is introduced to describe the interaction between pore fluid pressure and fracture deformation. This coefficient is expressed as a function of fracture aperture. Five parameters involved in the model have been determined from mechanical and poromechanical compression tests. The validity of the model is checked on fluid flow tests under different normal stresses. Comparisons between numerical simulations and experimental data are provided.Key words: hydromechanical coupling, interfaces, joints, poroelasticity, rock mechanics, fractures.
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Li, Xin, Xiang Li, Dongxiao Zhang und Rongze Yu. „A Dual-Grid, Implicit, and Sequentially Coupled Geomechanics-and-Composition Model for Fractured Reservoir Simulation“. SPE Journal 25, Nr. 04 (10.06.2020): 2098–118. http://dx.doi.org/10.2118/201210-pa.
Annotation:
Summary In the development of fractured reservoirs, geomechanics is crucial because of the stress sensitivity of fractures. However, the complexities of both fracture geometry and fracture mechanics make it challenging to consider geomechanical effects thoroughly and efficiently in reservoir simulations. In this work, we present a coupled geomechanics and multiphase-multicomponent flow model for fractured reservoir simulations. It models the solid deformation using a poroelastic equation, and the solid deformation effects are incorporated into the flow model rigorously. The noticeable features of the proposed model are it uses a pseudocontinuum equivalence method to model the mechanical characteristics of fractures; the coupled geomechanics and flow equations are split and sequentially solved using the fixed-stress splitting strategy, which retains implicitness and exhibits good stability; and it simulates geomechanics and compositional flow, respectively, using a dual-grid system (i.e., the geomechanics grid and the reservoir-flow grid). Because of the separation of the geomechanics part and the flow part, the model is not difficult to implement based on an existing reservoir simulator. We validated the accuracy and stability of this model through several benchmark cases and highlighted the practicability with two large-scale cases. The case studies demonstrate that this model is capable of considering the key effects of geomechanics in fractured-reservoir simulation, including matrix compaction, fracture normal deformation, and shear dilation, as well as hydrocarbon phase behavior. The flexibility, efficiency, and comprehensiveness of this model enable a more realistic geocoupled reservoir simulation.
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Men, Xiaoxi, und Jiren Li. „Numerical Investigation of Fracture Network Formation under Multiple Wells“. Mathematical Problems in Engineering 2020 (20.08.2020): 1–11. http://dx.doi.org/10.1155/2020/1763713.
Annotation:
A two-step fracturing method is proposed to investigate the hydraulic fracture evolution behavior and the process of complex fracture network formation under multiple wells. Simulations are conducted with Rock Failure Process Analysis code. Heterogeneity and permeability of the rocks are considered in this study. In Step 1, the influence of an asymmetric pressure gradient on the fracture evolution is simulated, and an artificial structural plane is formed. The simulation results reflect the macroscopic fracture evolution induced by mesoscopic failure; these results agree well with the characteristics of the experiments. Step 2, which is based on the first step, investigates the influence of preexisting fractures (i.e., artificial structural planes) on the subsequent fracturing behavior. The simulation results are supported by mechanics analysis. Results indicated that the fracture evolution is influenced by pressure magnitude on a local scale around the fracture tip and by the orientation and distribution of pore pressure on a global scale. The constant pressure in wellbore H2 can affect fracture propagation by changing the water flow direction, and the hydraulic fractures will propagate to the direction of higher local pore pressure. Furthermore, the artificial structural planes influence the stress distribution surrounding the wellbores and the hydraulic fracture evolution by altering the induced stresses around the preexisting fractures. Finally, fracture network is formed among the artificial structural planes and hydraulic fractures when multiple wells are fractured successively. This study provides valuable guidance to unconventional reservoir reconstruction designs.
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Atluri, S. N., M. H. Aliabadi und D. P. Rooke. „Numerical Fracture Mechanics.“ Mathematics of Computation 63, Nr. 208 (Oktober 1994): 825. http://dx.doi.org/10.2307/2153308.
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Sih, G. C., L. Faria und C. H. Popelar. „Fracture Mechanics Methodology“. Journal of Applied Mechanics 52, Nr. 2 (01.06.1985): 500. http://dx.doi.org/10.1115/1.3169086.
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Kanninen, Melvin F., Carl H. Popelar und A. J. McEvily. „Advanced Fracture Mechanics“. Journal of Engineering Materials and Technology 108, Nr. 2 (01.04.1986): 199. http://dx.doi.org/10.1115/1.3225862.
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Lewandowski, John J. „Modern fracture mechanics“. Philosophical Magazine 93, Nr. 28-30 (30.09.2013): 3893–906. http://dx.doi.org/10.1080/14786435.2013.812811.
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Kanninen, M. F., C. A. Popelar und H. Saunders. „Advanced Fracture Mechanics“. Journal of Vibration and Acoustics 110, Nr. 3 (01.07.1988): 419–20. http://dx.doi.org/10.1115/1.3269540.
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Newman, J. C., und Uwe Zerbst. „Engineering Fracture Mechanics“. Engineering Fracture Mechanics 70, Nr. 3-4 (Februar 2003): 367–69. http://dx.doi.org/10.1016/s0013-7944(02)00124-8.
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Freund, L. B., und John W. Hutchinson. „Dynamic Fracture Mechanics“. Journal of Applied Mechanics 59, Nr. 1 (01.03.1992): 245. http://dx.doi.org/10.1115/1.2899458.
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Pugno †, Nicola M., und Rodney S. Ruoff ‡. „Quantized fracture mechanics“. Philosophical Magazine 84, Nr. 27 (21.09.2004): 2829–45. http://dx.doi.org/10.1080/14786430412331280382.
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Sollberger, J. B. „Hinge Fracture Mechanics“. Lithic Technology 19, Nr. 1 (März 1994): 17–20. http://dx.doi.org/10.1080/01977261.1994.11720903.
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Cherepanov, G. P. „Quantum fracture mechanics“. Strength of Materials 22, Nr. 2 (Februar 1990): 155–63. http://dx.doi.org/10.1007/bf00773232.
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Aliabadi, M. H. „Dynamic fracture mechanics“. Engineering Analysis with Boundary Elements 9, Nr. 3 (Januar 1992): 279–80. http://dx.doi.org/10.1016/0955-7997(92)90111-j.
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Delima-Silva, W. „Engineering fracture mechanics“. Engineering Analysis with Boundary Elements 9, Nr. 1 (Januar 1992): 106–7. http://dx.doi.org/10.1016/0955-7997(92)90135-t.
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Deighton, M. „Fracture mechanics methodology“. Materials & Design 6, Nr. 2 (April 1985): 95. http://dx.doi.org/10.1016/0261-3069(85)90171-2.
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Altiero, N. J. „Advanced fracture mechanics“. Materials Science and Engineering 94 (Oktober 1987): 268. http://dx.doi.org/10.1016/0025-5416(87)90344-2.
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Mielke, Steven L., Ted Belytschko und George C. Schatz. „Nanoscale Fracture Mechanics“. Annual Review of Physical Chemistry 58, Nr. 1 (Mai 2007): 185–209. http://dx.doi.org/10.1146/annurev.physchem.58.032806.104502.
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Neale, K. W. „Dynamic fracture mechanics“. Canadian Journal of Civil Engineering 18, Nr. 3 (01.06.1991): 535. http://dx.doi.org/10.1139/l91-065.
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Tuck, M. A. „Hydraulic fracture mechanics“. Engineering Structures 18, Nr. 11 (November 1996): 886–87. http://dx.doi.org/10.1016/0141-0296(96)84813-9.
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Kussmaul, K. „Advanced Fracture Mechanics“. Nuclear Engineering and Design 91, Nr. 3 (Februar 1986): 391. http://dx.doi.org/10.1016/0029-5493(86)90089-0.
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Mecholsky, John J. „Fracture mechanics principles“. Dental Materials 11, Nr. 2 (März 1995): 111–12. http://dx.doi.org/10.1016/0109-5641(95)80044-1.
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Tikalsky, P. J. „Dynamic fracture mechanics“. Mechanism and Machine Theory 28, Nr. 1 (Januar 1993): 179. http://dx.doi.org/10.1016/0094-114x(93)90056-2.
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Liu, Hong, Lin Wang, Yu Wu Zhou und Xi Nan Yu. „A Mathematical Model for Natural Fracture Evolution in Water-Flooding Oil Reservoir“. Advanced Materials Research 868 (Dezember 2013): 535–41. http://dx.doi.org/10.4028/www.scientific.net/amr.868.535.
Annotation:
The fractured low permeability reservoirs develop complex fracture network. As the of waterflooding recovery heightens, excessive high injection pressures and excessive water injection rate will result in open, initiation, propagation and coalescence of micro-fracture, connecting injection with production form the high permeability zone, which results in a one-way onrush of waterflooding, water cut in oil well water rise quickly, causing a severe oil well flooding and channeling, thereby reducing the ultimate oil recovery efficiency. The effect of the waterflooding seepage within natural fracture on fracture initiation is studied and analyzed here, applying the theory of rock fracture mechanics to analyze the interaction of fracture system for naturally fractured reservoirs in waterflooding developing process, studying the mechanical mechanism of opening, initiation, propagation and coalescence of natural fracture under injection pressure, which is important theoretical significance for studying the distribution law of fracture and defining appreciate water injection mode and injection pressure in the process of injection development of the naturally fractured reservoir and for delaying the directivity water break-through and water flooding rate of oil well in the process of injection development.
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Mehrabian, Amin. „The Stability of Inclined and Fractured Wellbores“. SPE Journal 21, Nr. 05 (29.03.2016): 1518–36. http://dx.doi.org/10.2118/180910-pa.
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Summary The theory of linear-elastic fracture mechanics is used to develop an analytical solution for a wellbore in an isotropic elastic medium when drilled inclined to a general state of 3D far-field stress, and attached to which are an arbitrary number of N straight and axially aligned fractures. Axial alignment refers to the special case where the borehole axis is the existing common interface of all planes defined by the fracture faces. The solution uses a familiar load decomposition and coordinate-transform scheme. Within the fracture-mechanics context of the analysis, this scheme translates into a set of three fundamental subproblems comprising a uniaxial stress problem, together with an in-plane mixed mode (Modes I and II), and a Mode III antiplane-crack/cavity-interaction problem. The overall solution is obtained by superposing the solutions to these subproblems. A numerical example is presented to demonstrate its usefulness in the stability analysis of inclined and fractured wellbores. Attention has been directed toward the underlying significance that the results would bring in fundamental understanding of lost-circulation events. For this purpose, the criteria for a possible extended margin of the mud weight that secures stable states of a fractured wellbore are recognized and quantified. These criteria include the wellbore-wall refracturing and the existing fractures propagation.
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Liu, Piyang, Chaoping Huang, Lijing Jia, Weijing Ji, Zhao Zhang und Kai Zhang. „Numerical Simulation of the Wormhole Propagation in Fractured Carbonate Rocks during Acidization Using a Thermal-Hydrologic-Mechanics-Chemical Coupled Model“. Water 14, Nr. 24 (16.12.2022): 4117. http://dx.doi.org/10.3390/w14244117.
Annotation:
Acidizing is a widely adopted approach for stimulating carbonate reservoirs. The two-scale continuum (TSC) model is the most widely used model for simulating the reactive process in a carbonate reservoir during acidizing. In realistic cases, there are overburden pressure and pore pressure at present. When the injected acid reacts with the rock, the dissolution of the rock and the consumption of the acid in the pore will break the mechanical balance of the rock. Many experimental studies show that cores after acidizing have lower strength. However, it is still not clear how the deformation of rocks by the change of ground stress influences the acidizing dynamics. For fractured carbonate reservoirs, fractures play a leading role in the flow of injected acid, which preferentially flows into the fractures and dissolves the fracture walls. The effect of the combined action of rock mechanical balance broken and fracture wall dissolution on the formation of wormholes in fractured carbonate reservoirs remains to be studied. To address the above-mentioned issues, a thermal-hydrologic-mechanical-chemical coupled model is presented based on the TSC model for studying the wormhole propagation in fractured carbonate reservoirs under practical conditions. Linear and radial flow cases are simulated to investigate the influences of fracture distribution, reaction temperature, and effective stress on acidizing dynamics. The simulation results show that more wormhole branches are formed by acidizing if the fractures are perpendicular to the flow direction of acid. Temperature is a key parameter affecting the acidification dissolution patterns, so the influence of temperature cannot be ignored during the acidification design. As the effective stress of the formation increases, the diameter of the wormhole gradually decreases, and the branching decreases. More acid is needed for the same stimulation result under higher effective stress.