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1
Sil, Samik. "Fracture parameter estimation from well-log data." GEOPHYSICS 78, no. 3 (May 1, 2013): D129—D134. http://dx.doi.org/10.1190/geo2012-0407.1.
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We evaluated a method of deriving seismic fracture parameters from vertical-well-log data with the assumption that the fractured medium is transversely isotropic with a horizontal axis of symmetry (HTI). One approximation we used is that the observed vertical P-wave velocity is the same as the background isotropic P-wave velocity of the HTI medium. Another assumption was that the fractures and cracks are noninteractive and penny shaped. Using these approximations, we generated the fracture compliance matrix for each layer. Fracture parameters were then derived by constructing the HTI stiffness matrix for those layers. We tested our method using vertical-well-log data from a tight sand reservoir in Colorado, USA. “Thomsen-style” parameters were derived, and gas-filled fractures were identified on this log. The identified gas-filled fractures were compared to the production log data. The fracture density was also obtained at the well location within the depth of interest. We also found some problems and limitations caused by approximating vertical P-wave velocity the same as the background isotropic P-wave velocity.
2
Yu, Qingyan, Qi Wang, Pengcheng Liu, Jing Zhang, Qi Zhang, Xiaojuan Deng, and Kai Feng. "Theoretical Study and Application of Rate Transient Analysis on Complex Fractured-Caved Carbonate Reservoirs." Geofluids 2021 (January 23, 2021): 1–15. http://dx.doi.org/10.1155/2021/6611957.
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Carbonate reservoirs are mainly fractured-caved reservoirs with very well-developed dissolved pores, fractures, and caves. They have strong heterogeneity with various types of reservoir pore spaces. Using seismic inversion and reservoir static characterization, the result shows that the fractured-caved carbonate rocks in China are mainly caves with poor connectivity and complex oil-water distribution. Large-scale dissolved caves are mostly discrete and isolated, while the fractures are complex and various. The fracture features are observed either as a single large fractures or as a local fracture network. The characteristics of fluid flow in fracture-caved reservoirs vary as a result of the different combinations of fractures and caves. Currently, the static characterization technology of fractured-caved reservoirs is influenced by the limited resolution of seismic data, leading to large interpretation errors. In contrast, the dynamic method is a more reliable and effective method to determine reservoir parameters. However, traditional seepage equations cannot accurately characterize the flow pattern of fractured-caved carbonate reservoirs. In the case of a single large-scale dissolved fractured-caved reservoir, oil wells are usually connected to large caves through large fractures or directly drilled into large dissolved caves. In this study, the large-scale dissolved caved reservoir is simplified into two cases: (1) a single-cave and single-fracture series model composed of a single-cave and a single-fracture and (2) a composite model of dissolved caves and surrounding fracture networks. Note that the flow in a large cave is considered as free flow due to its large scale. The flow in a large fracture connected to the cave is considered as flow through porous media, and the flow in the reservoir surrounding the fracture network is considered as multiple-porosity model seepage flow. The corresponding seepage-free flow coupling mathematical model of different fractured-caved reservoirs has been established on this basis. We also obtained the rate transient analysis type curves of the oil well, conducted sensitivity analysis of each parameter, constructed the corresponding rate transient analysis curves, analyzed sensitivities of each parameter, and finally designed a dynamic evaluation method of well and reservoir parameters for different types of fractured-caved carbonate reservoirs. This study extensively applies this method in the Halahatang Oilfield of China and evaluates parameters such as reservoir reserves and physical properties to provide rational guidance for developing fractured-caved carbonate reservoirs.
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Zhang, Tingting, Ruifeng Zhang, Jianzhang Tian, Lifei Lu, Fengqi Qin, Xianzeng Zhao, and Yuefeng Sun. "Two-parameter prestack seismic inversion of porosity and pore-structure parameter of fractured carbonate reservoirs: Part 2 — Applications." Interpretation 6, no. 4 (November 1, 2018): SM9—SM17. http://dx.doi.org/10.1190/int-2018-0019.1.
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Fractures and fracture-related dissolution pores, as well as cavities, molds, and vugs, provide the major conduit and/or storage space for hydrocarbons in the deeply buried carbonate hill of Hexiwu field, Bohai Bay Basin. The fractured reservoir generally has lower porosity but better permeability than moldic/vuggy reservoir, and it consists of the major part of the buried-hill slope and buried-hill internal reservoirs. The conventional method of characterizing carbonate reservoirs, however, often mixes these two types of reservoirs together because they both have low acoustic impedance and low bulk modulus. The rock-physics analysis of two field wells indicates that a pore-structure parameter defined in a rock-physics model, the so-called Sun model, can help to distinguish the fractured reservoir zones together with porosity. Fractured zones usually have porosity of less than 5% and a pore-structure parameter of greater than six, whereas moldic/vuggy reservoirs of higher porosity have a pore-structure parameter of less than six. Field-scale application demonstrates that simultaneous prestack seismic inversion for the porosity and pore-structure parameter enables 3D mapping of fractured reservoir zones in the buried carbonate hills. It also provides an analog of detecting fractures and/or fracture-related pores in deeply buried carbonates in similar geologic settings.
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Zhou, Xin, Jianping Chen, Yunkai Ruan, Wen Zhang, Shengyuan Song, and Jiewei Zhan. "Demarcation of Structural Domains in Fractured Rock Masses Using a Three-Parameter Simultaneous Analysis Method." Advances in Civil Engineering 2018 (December 6, 2018): 1–13. http://dx.doi.org/10.1155/2018/9358098.
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A structural domain represents a volume of a rock mass with similar mechanical and hydrological properties. To demarcate structural domains (or statistically homogeneous regions) in fractured rock masses, this study proposes a three-parameter simultaneous analysis method (3PSAM) that simultaneously considers rock fracture orientation, trace length, and aperture to evaluate statistical homogeneity between two regions. First, a 102-patch three-dimensional Schmidt net, which represents a new comprehensive classification system, is established to characterize rock fractures based on their orientation and aperture. Two populations of rock fractures can then be projected to the corresponding patches. Second, the Wald–Wolfowitz runs test is used to measure the similarity between the two populations by considering the fracture trace lengths. The results obtained by applying the 3PSAM to seven simulated fracture populations show that the homogeneity is influenced by both the distributions of the fracture parameters and the sequences of the fracture parameters. The influence of a specific combination sequence makes it impractical to analyze the rock fracture parameters individually. Combined with previous methods, the 3PSAM provides reasonable and accurate results when it is applied to a fractured rock slope engineering case study in Dalian, China. The results show that each fracture population should be identified as an independent structural domain when using the 3PSAM. Only the 3PSAM identifies the west exploratory trench 2 and the east exploratory trench as being nonhomogeneous because the difference in the aperture of the two fracture populations is considered. The benefit of the 3PSAM is that it simultaneously considers three parameters in the demarcation of structural domains.
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Wang, Kang, Suping Peng, Yongxu Lu, and Xiaoqin Cui. "Full waveform inversion in fractured media based on velocity–stress wave equations in the time domain." Geophysical Journal International 227, no. 2 (July 29, 2021): 1060–75. http://dx.doi.org/10.1093/gji/ggab243.
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SUMMARY In the process of seismic wave propagation, the presence of fractures will cause a seismic wave response associated with fracture compliance. Full waveform inversion (FWI) is an effective way to quantitatively obtain fracture compliance values, which can simulate seismic wave propagation in a fractured medium and compute the gradient expression of the fracture compliance parameters. To obtain the fracture compliance parameters quantitatively, a new technique based on FWI needs to be proposed. Based on linear slip theory, a new finite-difference scheme using a rotated grid has been developed to simulate the propagation of seismic waves in fractured media. The corresponding adjoint equation for FWI and the gradient of fracture parameter expression are presented. The crosstalk between normal compliance and tangential compliance is analysed in a homogeneous background medium. Numerical simulations in double-layer media show that the new gradient equation is effective.
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Yan, Tianfan, and Yike Liu. "Fracture detection using scattered waves in the angle domain." GEOPHYSICS 86, no. 4 (June 15, 2021): S257—S269. http://dx.doi.org/10.1190/geo2020-0128.1.
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The singly and multiply scattered waves generated from interfaces of a fractured medium have strong energy, and their propagation directions contain information of fracture parameters. To exploit the useful information in the scattered waves, a fracture scattering imaging method is developed based on reverse time migration and angle decomposition. In this method, a fracture-parameter-related local image matrix is constructed in the angle domain based on the relation between the fracture parameters and the propagation angle of the scattered waves. The distribution of the scattered waves in the proposed image matrix can be used to invert for fracture parameters and identify the energy of scattered waves. Images of the fractures can be obtained by summing up the energy of the scattered waves from the proposed image matrix. Synthetic and field examples are provided to determine that the new method is effective in migrating the fracture-scattered waves at the correct spatial position and accurately extracting fracture parameters.
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Partsinevelou, Aikaterini-Sofia. "Using the SWAT model in analyzing hard rock hydrogeological environments. Application in Naxos Island, Greece." Bulletin of the Geological Society of Greece 51 (October 4, 2017): 18. http://dx.doi.org/10.12681/bgsg.11960.
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The main parameter that controls the groundwater flow regime in fractured aquifers is the fracture pattern. Its description is crucial for a hydrogeological study, as the hydraulic properties of hard rocks are mainly controlled by fracturing. The parameters of the fracture pattern that were analyzed in the study area were the frequency and spatial location of the fractures, the density of fractures and the degree of fracture intersection.Furthermore, a straight link between the fracture pattern and the hydrological conditions is important for a first analysis of the potential groundwater zones and their vulnerability in hard rock environments. To study this link, the SWAT hydrology model was applied in the study area. Using suitable territorial and meteorological data, the model simulates the parameters of the hydrological balance in each catchment of the hydrographical network.The analysis of the fracture pattern revealed that the fragmentation in all lithologies is characterized by high degree of uniformity. Very high density and interconnection density of the fractures are observed in areas where the alternations between different lithologies are very intense. Also the application of the SWAT model showed that the calculated hydrological parameters could be related to the fracture pattern, as high infiltration rates occur in areas where the density and the degree of interconnection of the fractures are also high.
8
Jiang, Le, Peng Gao, Jie Liu, Yunbin Xiong, Jing Jiang, Ruizhong Jia, Zhongchao Li, and Pengcheng Liu. "Simulation and Optimization of Dynamic Fracture Parameters for an Inverted Square Nine-Spot Well Pattern in Tight Fractured Oil Reservoirs." Geofluids 2020 (September 22, 2020): 1–9. http://dx.doi.org/10.1155/2020/8883803.
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Dynamic fractures are a geological attribute of water flooding development in tight fractured oil reservoirs. However, previous studies have mainly focused on the opening mechanism of dynamic fractures and the influence of dynamic fractures on development. Few attempts have been made to investigate the optimization of the dynamic fracture parameter. In this study, the inverted square nine-spot well pattern model is established by taking fractured reservoir’s heterogeneity and its threshold pressure gradients into account. This simulation model optimizes the various parameters in a tight fractured oil reservoir with dynamic fractures, that is, the intersection angle between the dynamic fractures and the well array, the number of dynamic fractures, the penetration ratio, and the conductivity of the oil well’s hydraulic fractures. The results of this optimization are used to investigate the oil displacement mechanism of dynamic fractures and to discuss a mechanism to enhance oil recovery using an inverted square nine-spot well pattern. The simulation results indicate that a 45° intersection angle can effectively restrain the increase in the water cut. A single dynamic fracture can effectively control the displacement direction of the injected water and improve the oil displacement efficiency. Moreover, the optimal penetration ratio and the conductivity of the hydraulic fracture are 0.6 and 40 D-cm, respectively.
9
ZHANG, LIMING, CHENYU CUI, XIAOPENG MA, ZHIXUE SUN, FAN LIU, and KAI ZHANG. "A FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR HISTORY MATCHING OF NATURALLY FRACTURED RESERVOIRS." Fractals 27, no. 01 (February 2019): 1940008. http://dx.doi.org/10.1142/s0218348x19400085.
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The distribution of fractures is highly uncertain in naturally fractured reservoirs (NFRs) and may be predicted by using the assisted-history-matching (AHM) that calibrates the reservoir model according to some high-quality static data combined with dynamic production data. A general AHM approach for NFRs is to construct a discrete fracture network (DFN) model and estimate model parameters given the observations. However, the large number of fractures prediction required in the AHM process could pose a high-dimensional optimization problem. This difficulty is particularly challenging when the fractures form a complex multi-scale fracture network. We present in this paper an integrated AHM approach of NFRs to tackle these challenges. Two essential ingredients of the method are (1) a 2D fractal-DFN model constructed as the geological simulation model to describe the complex fracture network, and (2) a mixture of multi-scale parameters, built according to the fractal-DNF model, as an inversion parameter model to alleviate the high-dimensional optimization burden caused by complex fracture networks. A reservoir with a multi-scale fracture network is set up to test the performance of the proposed method. Numerical results demonstrate that by use of the proposed method, the fractures well recognized by assimilating production data.
10
Geng, Yudi, and Jun Zhou. "Parameter optimization of acid fracturing in ultra-deep fault zone carbonate reservoir." E3S Web of Conferences 338 (2022): 01021. http://dx.doi.org/10.1051/e3sconf/202233801021.
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The characteristics of fracture development are complex in Shunbei area. The natural fracture development is different between different fault zones and in different locations of the same fault zone. Not all natural fractures can be activated during acid fracturing, and not all natural fractures can contribute to well productivity after acid fracturing. The use of natural fractures can not only improve the seepage capacity of the reservoir, but also improve the well productivity. Therefore, the influence of artificial fracture on the opening and fracture conductivity maintenance of natural fracture is studied, and finally the acid fracturing roceand parameters based on the change of natural fracture are formed.
11
Stadtműller, Marek. "Well logging interpretation methodology for carbonate formation fracture system properties determination." Acta Geophysica 67, no. 6 (September 9, 2019): 1933–43. http://dx.doi.org/10.1007/s11600-019-00351-w.
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Abstract The article presents the methodology for the qualitative determination of fracture zones in the profiles of carbonate formations, based on the complex fracture analysis (CFA) method. Three additive fracture ranges were distinguished, characterized by successively increasing aperture and fracture length values, operatively named micro, meso and macro. Furthermore, the quantitative characterization of fractures with different apertures was done. The methodology of laboratory data integration, fracture porosity and fracture permeability measurements performed on thin section and polished section was described as part of the quantitative well logging data interpretation procedure which uses the FPI (fracture porosity index) parameter. The research was performed in the Lower Carboniferous limestone formation that builds the Paleozoic basement of the Carpathian orogeny. An original software dedicated to the analysis of the wellbore images, obtained with the XRMI Halliburton scanner, was used to identify the presence of macro-fractures, determine their aperture and estimate fractures porosity and permeability in the profile of the analyzed rock formation. As a result of the work, postulates regarding the methodology for collecting research material were formulated, in particular: the scope of different laboratory core samples measurements and well log types. The principles of the optimal methodology for identifying fractured zones and quantitative evaluation of petrophysical parameters of recognized fracture systems were defined.
12
Ge, Zijian, Shulin Pan, and Jingye Li. "Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium." Applied Sciences 10, no. 15 (July 26, 2020): 5136. http://dx.doi.org/10.3390/app10155136.
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In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.
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Zheng, Yongxiang, Jianjun Liu, and Yun Lei. "The Propagation Behavior of Hydraulic Fracture in Rock Mass with Cemented Joints." Geofluids 2019 (June 27, 2019): 1–15. http://dx.doi.org/10.1155/2019/5406870.
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The formation of the fracture network in shale hydraulic fracturing is the key to the successful development of shale gas. In order to analyze the mechanism of hydraulic fracturing fracture propagation in cemented fractured formations, a numerical simulation about fracture behavior in cemented joints was conducted based firstly on the block discrete element. And the critical pressure of three fracture propagation modes under the intersection of hydraulic fracturing fracture and closed natural fracture is derived, and the parameter analysis is carried out by univariate analysis and the response surface method (RSM). The results show that at a low intersecting angle, hydraulic fractures will turn and move forward at the same time, forming intersecting fractures. At medium angles, the cracks only turn. At high angles, the crack will expand directly forward without turning. In conclusion, low-angle intersecting fractures are more likely to form complex fracture networks, followed by medium-angle intersecting fractures, and high-angle intersecting fractures have more difficulty in forming fracture networks. The research results have important theoretical guiding significance for the hydraulic fracturing design.
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Chen, Huaizhen, Tiansheng Chen, and Kristopher A. Innanen. "Estimating tilted fracture weaknesses from azimuthal differences in seismic amplitude data." GEOPHYSICS 85, no. 3 (May 1, 2020): R135—R146. http://dx.doi.org/10.1190/geo2019-0344.1.
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Tilted transverse isotropy (TTI) provides a useful model for the elastic response of a medium containing aligned fractures with a symmetry axis oriented obliquely in the vertical and horizontal coordinate directions. Robust methods for determining the TTI properties of a medium from seismic observations to characterize fractures are sought. Azimuthal differencing of seismic amplitude data produces quantities that are particularly sensitive to TTI properties. Based on the linear slip fracture model, we express the TTI stiffness matrix in terms of the normal and tangential fracture weaknesses. Perturbing stiffness parameters to simulate an interface separating an isotropic medium and a TTI medium, we derive a linearized P-to-P reflection coefficient expression in which the influence of tilt angle and fracture weaknesses separately emerge. We formulate a Bayesian inversion approach in which amplitude differences between seismic data along two azimuths, interpreted in terms of the reflection coefficient approximation, are used to determine fracture weaknesses and tilt angle. Tests with simulated data confirm that the unknown parameter vector involving fracture weakness and tilted fracture weaknesses is stably estimated from seismic data containing a moderate degree of additive Gaussian noise. The inversion approach is applied to a field surface seismic data acquired over a fractured reservoir; from it, interpretable tilted fracture weaknesses, consistent with expected reservoir geology, are obtained. We determine that our inversion approach and the established inversion workflow can produce the properties of systems of tilted fractures stably using azimuthal seismic amplitude differences, which may add important information for characterization of fractured reservoirs.
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Xia, Kaiwen, Cangli Liu, and Patrick Kanopoulos. "On the Energy of Dynamic Fractures." International Journal of Nonlinear Sciences and Numerical Simulation 13, no. 2 (April 1, 2012): 117–23. http://dx.doi.org/10.1515/ijnsns.2011.119.
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Abstract The validity of the constant propagation fracture energy postulation for dynamic fracture is discussed. As shown from existing direct and indirect experimental results, this assumption may not represent the physical reality. For spontaneous fractures, the fracture energy was shown to increase linearly with the crack length, and for dynamic fractures driven by known amplitude impulsive loading (generated by planar impact), the fracture energy was not a constant either. Despite of its phenomenogical origin, the Broberg's theory developed for self-similar crack growth works well for both spontaneous fractures and dynamic fractures produced by well defined dynamic loading. In this theory, the fracture energy is not a constant. Furthermore, with given far-field loading or equivalent far-field loading, the crack speed is uniquely determined by a strength-like material parameter. This parameter is related to the cohesive strength as proposed by H. J. Gao for hyperelastic materials in the crack-tip process zone. It is proposed in this work that the strength-like parameter (or equivalently the constant fracture speed) is a better material parameter to describe the dynamic fracture propagation process for most dynamic fractures.
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Lu, Le, and Dongxiao Zhang. "Assisted History Matching for Fractured Reservoirs by Use of Hough-Transform-Based Parameterization." SPE Journal 20, no. 05 (October 20, 2015): 942–61. http://dx.doi.org/10.2118/176024-pa.
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Summary Successful production in fractured reservoirs is significantly dependent on knowledge of the location, orientation, and conductivity of the fractures. Early water breakthrough can be prevented and sweep efficiency can be improved with the help of comprehensive and accurate information of fracture distributions. However, it is a challenge to estimate fracture distributions by conventional-history-matching methods because of the complexity of such reservoirs. Although there has been great progress in assisted-history-matching techniques during the last 2 decades, estimating fracture distributions in fractured reservoirs is still inefficient because of the strong heterogeneity and spatial discontinuity of model parameters. The performance of assisted-history-matching methods, such as the ensemble Kalman filter, can be significantly degraded by the non-Gaussian distributions of the parameters, such as effective permeability and porosity. On the other hand, although the geometric shapes of fractures may be generated properly at the initial step, they are difficult to preserve after updating, which results in geologically unrealistic fracture-distribution maps. In this study, we develop an assisted-history-matching method for fractured reservoirs with a Hough-transform-based parameterization. The facies maps of fractured reservoirs are parameterized into Hough-function fields in a discrete Hough space, whereas each gridblock in the Hough domain represents a fracture defined by its two Cartesian coordinates: angle θ of its normal and ρ of its algebraic distance from the origin in the flow domain. The length and axial position of the fractures are defined by two additional parameters on the same grid. The Hough-function value of each gridblock in the Hough domain is used as the indicator of the existence of the fracture in the facies map. When this parameterization is implemented in assisted history matching, the parameter fields in the Hough space, instead of the facies maps, are updated conditional on the production history. An inverse transform is performed to generate facies maps for the reservoir simulator. Pointwise prior information, such as known fractures discovered from well-log data, as well as the statistics of fracture orientation, can be honored by the inverse transform throughout the history-matching process. Applications and the effectiveness of this method are demonstrated by 2D synthetic-waterflooding examples. The fracture distributions in reference fields are identified by this method, and updated models are capable of providing improved predictions for prolonged periods of production.
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Shen, Feng, Xiang Zhu, and M. Nafi Toksöz. "Effects of fractures on NMO velocities and P‐wave azimuthal AVO response." GEOPHYSICS 67, no. 3 (May 2002): 711–26. http://dx.doi.org/10.1190/1.1484514.
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This paper attempts to explain the relationships between fractured medium properties and seismic signatures and distortions induced by geology‐related influences on azimuthal AVO responses. In the presence of vertically aligned fractures, the relationships between fracture parameters (fracture density, fracture aspect ratio, and saturated fluid content) and their seismic signatures are linked with rock physics models of fractured media. The P‐wave seismic signatures studied in this paper include anisotropic parameters (δ(v), (v), and γ(v)), NMO velocities, and azimuthal AVO responses, where δ(v) is responsible for near‐vertical P‐wave velocity variations, (v) defines P‐wave anisotropy, and γ(v) governs the degree of shearwave splitting. The results show that in gas‐saturated fractures, anisotropic parameters δ(v) and (v) vary with fracture density alone. However, in water‐saturated fractures δ(v) and (v) depend on fracture density and crack aspect ratio and are also related to Vp/VS and Vp of background rocks, respectively. Differing from δ(v) and (v), γ(v) is the parameter most related to crack density. It is insensitive to the saturated fluid content and crack aspect ratio. The P‐wave NMO velocities in horizontally layered media are a function of δ(v), and their properties are comparable with those of δ(v). Results from 3‐D finite‐difference modeling show that P‐wave azimuthal AVO variations do not necessarily correlate with the magnitude of fracture density. Our studies reveal that, in addition to Poisson's ratio, other elastic properties of background rocks have an effect on P‐wave azimuthal AVO variations. Varying the saturated fluid content of fractures can lead to azimuthal AVO variations and may greatly change azimuthal AVO responses. For a thin fractured reservoir, a tuning effect related to seismic wavelength and reservoir thickness can result in variations in AVO gradients and in azimuthal AVO variations. Results from instantaneous frequency and instantaneous bandwidth indicate that tuning can also lead to azimuthal variations in the rates of changes of the phase and amplitude of seismic waves. For very thin fractured reservoirs, the effect of tuning could become dominant. Our numerical results show that AVO gradients may be significantly distorted in the presence of overburden anisotropy, which suggests that the inversion of fracture parameters based on an individual AVO response would be biased unless this influence were corrected. Though P‐wave azimuthal AVO variations could be useful for fracture detection, the combination of other types of data is more beneficial than using P‐wave amplitude signatures alone, especially for the quantitative characterization of a fractured reservoir.
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Chichinina, Tatiana, Vladimir Sabinin, and Gerardo Ronquillo-Jarillo. "QVOA analysis: P-wave attenuation anisotropy for fracture characterization." GEOPHYSICS 71, no. 3 (May 2006): C37—C48. http://dx.doi.org/10.1190/1.2194531.
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This paper investigates [Formula: see text]-anisotropy for characterizing fractured reservoirs — specifically, the variation of the seismic quality factor [Formula: see text] versus offset and azimuth (QVOA). We derive an analytical expression for P-wave attenuation in a transversely isotropic medium with horizontal symmetry axis (HTI) and provide a method (QVOA) for estimating fracture direction from azimuthally varying [Formula: see text] in PP-wave reflection data. The QVOA formula is similar to Rüger’s approximation for PP-wave reflection coefficients, the theoretical basis for amplitude variation with angle offset (AVOA) analysis. The technique for QVOA analysis is similar to azimuthal AVO analysis. We introduce two new seismic attributes: [Formula: see text] versus offset (QVO) gradient and intercept. QVO gradient inversion not only indicates fracture orientation but also characterizes [Formula: see text]-anisotropy. We relate the [Formula: see text]-anisotropy parameter [Formula: see text] to fractured-medium parameters and invert the QVO gradient to estimate [Formula: see text]. The attenuation parameter [Formula: see text] and Thomsen-style anisotropy parameter [Formula: see text] are found to be interdependent. The attenuation anisotropy magnitude strongly depends on the host rock’s [Formula: see text] parameter, whereas the dependence on fracture parameters is weak. This complicates the QVO gradient inversion for the fracture parameters. This result is independent of the attenuation mechanism. To illustrate the QVOA method in synthetic data, we use Hudson’s first-order effective-medium model of a dissipative fractured reservoir with fluid flow between aligned cracks and random pores as a possible mechanism for P-wave attenuation.
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Far, Mehdi E., Bob Hardage, and Don Wagner. "Fracture parameter inversion for Marcellus Shale." GEOPHYSICS 79, no. 3 (May 1, 2014): C55—C63. http://dx.doi.org/10.1190/geo2013-0236.1.
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We inverted P-wave amplitude variation with offset and azimuth (AVOAz) data from the Marcellus Shale to obtain fracture parameters that can fully describe the elastic behavior of fractured rocks with overall symmetry of orthorhombic or monoclinic. AVOAz data from two interfaces, (1) the upper interface between top Marcellus and Stafford limestone and (2) the lower interface between base Marcellus and Onondaga limestone, were used for inversion. To check the validity of our inversion results, fracture parameters for the Marcellus Shale were inverted for each interface using Monte Carlo simulation to include uncertainty in our a priori information, i.e., elastic properties of unfractured rocks that are assumed to be known from well logs. Inversion results appeared robust with respect to uncertainties and converge to the same values for the two inversions. Our results were also consistent with singular value decomposition analysis (resolution matrix).
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Ren, Fengyu, Jing Zhang, Zhihua Ouyang, and Hao Hu. "Calculation of Elastic Modulus for Fractured Rock Mass Using Dimensional Analysis Coupled with Numerical Simulation." Mathematical Problems in Engineering 2021 (February 12, 2021): 1–14. http://dx.doi.org/10.1155/2021/2803837.
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Underground mining activities make the fractures in the natural rock mass develop randomly. The elastic modulus of the fractured rock mass Em is changed with the redistribution and development of the fractures. An equivalent model of fractured rock mass is structured to represent the hydraulic conductivity and the rock mass strain because of the continuum theory. Dimensional analysis is very useful to build relationship of the parameters in complex physical phenomena. Based on the engineering phenomenon of groundwater flowing into the goaf along the fracture in the rock mass, a fuzzy expression among parameters such as the parameter Em, the seepage flow Q, and the exposed area of the goaf A is obtained using dimensionless analysis. To calculate the parameter Em, the fuzzy relationship is then characterized by Darcy’s law and numerical simulation. Under the scripting environment of Python, an automated program to realize the numerical simulation of all scenarios is established, which also provides convenience for drawing the dimensionless flux charts. The results show that the parameter Em can be calculated by the dimensional analysis coupled with numerical simulation. In addition, the parameter Em decreases with the increase of the parameter Q, and the integrity of rock mass is also worse. Finally, a mine example is used to verify the feasibility of the method.
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Zhao, Zhi Hong, Jian Chun Guo, and Fan Hui Zeng. "A New Model for Predicting Productivity and Application for Fractured Horizontal Wells." Advanced Materials Research 524-527 (May 2012): 1310–13. http://dx.doi.org/10.4028/www.scientific.net/amr.524-527.1310.
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Due to the differences of stress and physical property in the pay zone, the fractured horizontal well may be different in length and azimuth angle. Furthermore, because of the mutual disturbance among fractures, the accurate prediction of production of fractured horizontal wells become more complicated. This paper presents a new model to predict the production of the fractured horizontal wells by considering the effects of fracture number, fracture length, fracture interval, fracture symmetry, azimuth angle and conductivity. Compared with the numerical simulation, this model needs less parameter and calculating time, and is easy to be applied to the designs of segmentation fracturing in horizontal wells. The model in this paper has been applied to the optimizing designs of hydraulic fracturing for two horizontal wells in North China oilfield and the predicted results agree with the actual production well.
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Civan, F., and M. L. L. Rasmussen. "Parameters of Matrix/Fracture Immiscible-Fluids Transfer Obtained by Modeling of Core Tests." SPE Journal 17, no. 02 (February 8, 2012): 540–54. http://dx.doi.org/10.2118/104028-pa.
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Summary Methodology is presented and proved for determination of the best-estimate parameter values affecting the matrix/fracture-interface fluid transfer in naturally fractured reservoirs. Fracture/surface-hindered interface transfer of immiscible fluids is considered between matrix blocks and surrounding natural fractures. Improved matrix/fracture-transfer models are applied on the basis of presumed matrix-block shapes. Analytical solutions and the limiting isotropic-matrix long-time shape factors developed for special boundary conditions are used for interpretation of typical laboratory tests conducted using rectangular- and cylindrical-shaped rock samples. Workable equations and straight-line data-plotting schemes are developed for effective analysis and interpretation of laboratory data obtained from various-shaped oil-saturated reservoir-rock samples immersed into brine. Applications concerning the water/air and water/decane systems in laboratory core tests are also presented. The present approach allows rapid determination of the characteristic parameters of the matrix/fracture-transfer models for various-shaped matrix blocks, which are essential for prediction of petroleum recovery from naturally fractured reservoirs. The methodology is verified using various experimental data, and the values of the characteristic parameters (e.g., the average diffusion-coefficient and the interface-skin-mass-transfer coefficient) are determined. The Arrhenius (1889) equation is shown to represent the temperature dependency of these parameters effectively.
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Liu, Jie, Zhenhua Xu, Zhe Yuan, Hanyu Bie, and Pengcheng Liu. "Numerical Simulation Study on Fracture Parameter Optimization in Developing Low-Permeability Anisotropic Reservoirs." Geofluids 2018 (December 24, 2018): 1–9. http://dx.doi.org/10.1155/2018/1690102.
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The diamond-shape inverted nine-spot well pattern is widely used in developing low-permeability reservoirs with fractures. However, production wells with equal fracture lengths will lead to nonuniform displacement, especially in anisotropic reservoir. Previous researches mainly focused on equal-length fractures, while studies on the unequal-length fractures which can dramatically improve the development efficiency were little. In this paper, a corresponding numerical model with unequal length of fracture designed in the edge and the corner wells was built in a low-permeability anisotropic reservoir. The main objective was to examine and evaluate the effects of anisotropic permeability and fracture parameter on the waterflooding in the diamond-shape inverted nine-spot well pattern. The results indicate that different fractures penetration ratio and anisotropic permeability both result in different development efficiency. Fracture of the edge well are more easily to be water breakthrough, while the increase of penetration ratio of injection well effectively enhance oil recovery. Moreover, the most optimal penetration ratios of production well fractures under different kx : ky are determined. With the increase of kx : ky, the optimized penetration ratio of corner wells fracture decrease, while that of the edge wells increase. Setting unequal length fractures in low-permeability anisotropic reservoirs can effectively improve the oil displacement efficiency in the waterflooding process.
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Dershowitz, Bill, Paul LaPointe, Thorsten Eiben, and Lingli Wei. "Integration of Discrete Feature Network Methods With Conventional Simulator Approaches." SPE Reservoir Evaluation & Engineering 3, no. 02 (April 1, 2000): 165–70. http://dx.doi.org/10.2118/62498-pa.
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Summary The discrete feature network (DFN) approach offers many key advantages over conventional dual porosity (DP) approaches, particularly when issues of connectivity dominate recovery and reservoir stimulation in fractured and heterogeneous reservoirs. DP models have been developed for complex multiphase and thermal effects, and have been implemented for basin scale modeling. However, DP models address only the dual porosity nature of fractured reservoirs, generally simplifying connectivity and scale-dependent heterogeneity issues which are modeled efficiently and more accurately by the DFN approach. This paper describes the development of techniques to integrate DFN and DP approaches. These techniques allow the analyst to maintain many of the advantages of the DP simulator approach without losing the realism of complex fracture system geometry and connectivity, as captured by DFN models. The techniques described are currently used within a DOE funded research project for linking a DFN and a DP thermal simulation model for the Yates field, Texas. The paper describes some of the geological and engineering aspects of the Yates field and gives two examples of how DP parameters for the thermal simulation can be derived using DFN modeling techniques. Introduction Reservoir simulation can be significantly more challenging for fractured reservoirs than it is for conventional clastic reservoirs. The dual porosity (DP) approach for the simulation of fractured reservoirs adds a second interacting continuum to reflect storage and permeability characteristics but does not adequately address connectivity issues. These effects, which play a key role in fractured reservoirs, are generally better addressed by discrete feature network (DFN) models.1 Another advantage of DFN models is that they are generally implemented as stochastic models, in which multiple realizations provide a quantitative measure for uncertainty and variability. Despite the significant simplifications made regarding the geometry of the fracture network in equivalent porous medium DP models (Fig. 1) and the recent progress made in developing powerful DFN modeling software, DP models still offer advantages regarding the level of sophistication of available multiphase flow solvers. In many cases, DP models also offer advantages regarding model size and speed. As a result, there is a need to link DP and DFN models to be able to take maximum advantage of each approach. This paper presents a series of techniques, which can be used to develop DP models that more accurately reflect the anisotropy, heterogeneity, and most important, the scale-dependent connectivity structure of fractured reservoirs. These techniques will allow the DP approach to take advantage of some of the features of the DFN approach. The approach adopted is to derive grid cell and well parameters through DFN models. The first section of this paper discusses which fracture porosity parameters can be derived for DP models from DFN models and how they are derived. The second section describes different techniques that can be used to link DP and DFN models. At the end of the paper two examples are given based on data from the Yates field, Texas. DP Input Parameter from DFN Modeling Fracture System Porosity. The fracture system porosity fF can be directly calculated as the product of the fracture intensity expressed as fracture area per unit volume (P32) and the storage aperture of the fractures (e):… Because the fracture system porosity depends on the number of fractures per unit volume, the fracture size distribution and the fracture aperture distribution, a different porosity needs to be calculated for every portion of the continuum model where these parameters vary. Using a full field DFN model, the fracture system porosity can be calculated separately for each grid cell. The primary issue in definition of fracture porosity from fracture intensity P32 is the selection of an appropriate measure for storage aperture e. Possible measures include:aperture derived from transient hydraulic response,mechanical aperture,aperture derived from fracture permeability or transmissivity ("cubic law"),aperture derived from geophysical measurements (gamma density, matrix porosity), andcorrelations to fracture size and orientation. Directional Fracture System Permeability. The permeability of the fracture system depends on the fracture intensity, the connectivity of the fracture network, and the distribution of fracture transmissivities. Approaches for calculation of approximate measures of grid cell effective directional permeability include the tensor approach of Oda,2 and the use of DFN simulations with a range of orientations for a unit gradient. Oda's2 method begins by considering the orientation of fractures in a grid cell, expressed as a unit normal vector n. Integrating the fractures over all of the unit normals N, Oda obtained the mass moment of inertia of fracture normals distributed over a unit sphere: ….For a specific grid cell with known fracture areas Ak and transmissivities Tk obtained from the DFN model, an empirical fracture tensor can be calculated by adding the individual fractures weighted by their area and transmissivity:…. Oda's permeability tensor is derived from Fij by assuming that Fij expresses fracture flow as a vector along the fracture's unit normal. Assuming that fractures are impermeable in a direction parallel to their unit normal, Fij must be rotated into the planes of permeability ….
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Aghli, Ghasem, Reza Moussavi-Harami, and Ruhangiz Mohammadian. "Reservoir heterogeneity and fracture parameter determination using electrical image logs and petrophysical data (a case study, carbonate Asmari Formation, Zagros Basin, SW Iran)." Petroleum Science 17, no. 1 (December 23, 2019): 51–69. http://dx.doi.org/10.1007/s12182-019-00413-0.
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AbstractAssessment of reservoir and fracture parameters is necessary to optimize oil production, especially in heterogeneous reservoirs. Core and image logs are regarded as two of the best methods for this aim. However, due to core limitations, using image log is considered as the best method. This study aims to use electrical image logs in the carbonate Asmari Formation reservoir in Zagros Basin, SW Iran, in order to evaluate natural fractures, porosity system, permeability profile and heterogeneity index and accordingly compare the results with core and well data. The results indicated that the electrical image logs are reliable for evaluating fracture and reservoir parameters, when there is no core available for a well. Based on the results from formation micro-imager (FMI) and electrical micro-imager (EMI), Asmari was recognized as a completely fractured reservoir in studied field and the reservoir parameters are mainly controlled by fractures. Furthermore, core and image logs indicated that the secondary porosity varies from 0% to 10%. The permeability indicator indicates that zones 3 and 5 have higher permeability index. Image log permeability index shows a very reasonable permeability profile after scaling against core and modular dynamics tester mobility, mud loss and production index which vary between 1 and 1000 md. In addition, no relationship was observed between core porosity and permeability, while the permeability relied heavily on fracture aperture. Therefore, fracture aperture was considered as the most important parameter for the determination of permeability. Sudden changes were also observed at zones 1-1 and 5 in the permeability trend, due to the high fracture aperture. It can be concluded that the electrical image logs (FMI and EMI) are usable for evaluating both reservoir and fracture parameters in wells with no core data in the Zagros Basin, SW Iran.
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Huang, Shijun, Jiaojiao Zhang, Sidong Fang, and Xifeng Wang. "An Analytical Method for Parameter Interpretation of Fracture Networks in Shale Gas Reservoirs considering Uneven Support of Fractures." Geofluids 2021 (October 14, 2021): 1–15. http://dx.doi.org/10.1155/2021/3800525.
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In shale gas reservoirs, the production data analysis method is widely used to invert reservoir and fracture parameter, and productivity prediction. Compared with numerical models and semianalytical models, which have high computational cost, the analytical model is mostly used in the production data analysis method to characterize the complex fracture network formed after fracturing. However, most of the current calculation models ignore the uneven support of fractures, and most of them use a single supported fracture model to describe the flow characteristics, which magnifies the role of supported fracture to a certain extent. Therefore, in this study, firstly, the fractures are divided into supported fractures and unsupported fractures. According to the near-well supported fractures and far-well unsupported fractures, the SRV zone is divided into outer SRV and inner SRV. The four areas are characterized by different seepage models, and the analytical solutions of the models are obtained by Laplace transform and inverse transform. Secondly, the material balance pseudotime is introduced to process the production data under the conditions of variable production and variable pressure. The double logarithmic curves of normalized production rate, rate integration, the derivative of the integration, and material balance pseudotime are established, and the parameters are interpreted by fitting the theoretical curve to the measured data. Then, the accuracy of the method is verified by comparison the parameter interpretation results with well test results, and the influence of parameters such as the half-length and permeability of supported and unsupported fractures on gas production is analyzed. Finally, the proposed method is applied to four field cases in southwest China. This paper mainly establishes an analytical method for parameter interpretation after hydraulic fracturing based on the production data analysis method considering the uneven support of fractures, which is of great significance for understanding the mechanism of fracturing stimulation, optimization of fracturing parameters, and gas production forecast.
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Huang, Shijun, Jiaojiao Zhang, Sidong Fang, and Xifeng Wang. "An Analytical Method for Parameter Interpretation of Fracture Networks in Shale Gas Reservoirs considering Uneven Support of Fractures." Geofluids 2021 (October 14, 2021): 1–15. http://dx.doi.org/10.1155/2021/3800525.
Full textAbstract:
In shale gas reservoirs, the production data analysis method is widely used to invert reservoir and fracture parameter, and productivity prediction. Compared with numerical models and semianalytical models, which have high computational cost, the analytical model is mostly used in the production data analysis method to characterize the complex fracture network formed after fracturing. However, most of the current calculation models ignore the uneven support of fractures, and most of them use a single supported fracture model to describe the flow characteristics, which magnifies the role of supported fracture to a certain extent. Therefore, in this study, firstly, the fractures are divided into supported fractures and unsupported fractures. According to the near-well supported fractures and far-well unsupported fractures, the SRV zone is divided into outer SRV and inner SRV. The four areas are characterized by different seepage models, and the analytical solutions of the models are obtained by Laplace transform and inverse transform. Secondly, the material balance pseudotime is introduced to process the production data under the conditions of variable production and variable pressure. The double logarithmic curves of normalized production rate, rate integration, the derivative of the integration, and material balance pseudotime are established, and the parameters are interpreted by fitting the theoretical curve to the measured data. Then, the accuracy of the method is verified by comparison the parameter interpretation results with well test results, and the influence of parameters such as the half-length and permeability of supported and unsupported fractures on gas production is analyzed. Finally, the proposed method is applied to four field cases in southwest China. This paper mainly establishes an analytical method for parameter interpretation after hydraulic fracturing based on the production data analysis method considering the uneven support of fractures, which is of great significance for understanding the mechanism of fracturing stimulation, optimization of fracturing parameters, and gas production forecast.
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Ding, Benjamin T. K., Kaamini Pillay, and Sreedharan Sechachalam. "Radial shaft fracture obliquity as a predictor of distal radioulnar joint instability." Journal of Hand Surgery (European Volume) 43, no. 7 (February 21, 2018): 732–38. http://dx.doi.org/10.1177/1753193418756591.
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We assessed whether radial shaft fracture obliquity measurements on radiographs could predict intra-operative distal radioulnar joint instability. We also clinically validated previously described predictors of distal radioulnar joint instability, which included a fracture line within 7.5 cm of the lunate fossa, radial shortening >5 mm, and ulna styloid fracture. We retrospectively analysed the radiographs of all surgically managed patients in our unit with radial shaft fractures from 2006 through 2016. The degree of obliquity was analysed on the basis of the maximum fracture-line angle in either the coronal or the sagittal plane. A radial shaft fracture obliquity >30° is predictive of distal radioulnar joint instability ( P = 0.001). Radial fracture shaft obliquity >30° was the most sensitive radiological parameter (76%) for predicting distal radioulnar joint instability. Oblique radial shaft fractures appear to be associated with increased incidence of distal radioulnar joint instability. This radiologic parameter may be used together with established parameters in predicting distal radioulnar joint instability for surgical treatment. Level of evidence: III
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Malikova, Lucie, Hana Simonova, Barbara Kucharczykova, and Petr Miarka. "Multi-parameter fracture mechanics." Frattura ed Integrità Strutturale 13, no. 49 (June 25, 2019): 65–73. http://dx.doi.org/10.3221/igf-esis.49.07.
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Wagner, D. A., and J. C. Simo. "Fracture parameter for thermoinelasticity." International Journal of Fracture 56, no. 2 (July 1992): 159–87. http://dx.doi.org/10.1007/bf00015598.
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ZHANG, KAI, XIAOPENG MA, YANLAI LI, HAIYANG WU, CHENYU CUI, XIAOMING ZHANG, HAO ZHANG, and JUN YAO. "PARAMETER PREDICTION OF HYDRAULIC FRACTURE FOR TIGHT RESERVOIR BASED ON MICRO-SEISMIC AND HISTORY MATCHING." Fractals 26, no. 02 (April 2018): 1840009. http://dx.doi.org/10.1142/s0218348x18400091.
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Hydraulic fracturing is an important measure for the development of tight reservoirs. In order to describe the distribution of hydraulic fractures, micro-seismic diagnostic was introduced into petroleum fields. Micro-seismic events may reveal important information about static characteristics of hydraulic fracturing. However, this method is limited to reflect the distribution area of the hydraulic fractures and fails to provide specific parameters. Therefore, micro-seismic technology is integrated with history matching to predict the hydraulic fracture parameters in this paper. Micro-seismic source location is used to describe the basic shape of hydraulic fractures. After that, secondary modeling is considered to calibrate the parameters information of hydraulic fractures by using DFM (discrete fracture model) and history matching method. In consideration of fractal feature of hydraulic fracture, fractal fracture network model is established to evaluate this method in numerical experiment. The results clearly show the effectiveness of the proposed approach to estimate the parameters of hydraulic fractures.
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Matvienko, Yu G. "Two-parameter elastic-plastic fracture criterion and corrected fracture toughness." Industrial laboratory. Diagnostics of materials 88, no. 8 (August 21, 2022): 59–69. http://dx.doi.org/10.26896/1028-6861-2022-88-8-59-69.
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The basic aspects of the J-A concept of elastic-plastic two-parameter fracture mechanics, based on a three-term asymptotic description of the stress field at the crack tip are presented. It is noted that the field of elastic-plastic stresses at the crack tip is controlled by two parameters of fracture mechanics, namely, J-integral and parameter A. Parameter A is a measure of the deviation of the stress field from the HRR-stress field and can be considered a parameter of elastic-plastic constraint at the crack tip both under conditions of small- and large-scale yielding. The results of studying the influence of the exponent of the strain hardening of the material, crack aspect ratio and the thickness of standard specimens with a crack on the elastic-plastic stress intensity factor and parameter A are presented. A two-parameter elastic-plastic J-A fracture criterion based on the relationship between J-integral and strain(stress) on the surface of the crack-notch and the principle of linear summation of damage is formulated. To reflect the crack-tip constraint, the parameter A is introduced into the criterion equation as a function of applied failure stresses. The elastic-plastic fracture toughness as a function of the crack-tip constraint in the fracture criterion is interpreted as the corrected elastic-plastic fracture toughness of a specimen with the corresponding constraint parameters A. The results of studying the normalized corrected fracture toughness as a function of failure stresses, crack aspect ratio and strain hardening exponent of the material are presented.
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Fleischhacker, Evi, Georg Siebenbürger, Johannes Gleich, Wolfgang Böcker, Fabian Gilbert, and Tobias Helfen. "The Accuracy of Distal Clavicle Fracture Classifications—Do We Need an Amendment to Imaging Modalities or Fracture Typing?" Journal of Clinical Medicine 11, no. 19 (September 24, 2022): 5638. http://dx.doi.org/10.3390/jcm11195638.
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Background: Despite its fair-to-moderate reliability, the “modified Neer classification” is widely accepted and used. The purpose of this study was to reevaluate its applicability. Methods: Of n = 59 patients with distal clavicle fractures, fractures were classified on standard radiographs. Afterwards, an MRI examination was performed, and fractures reclassified. The primary outcome parameter was quantifying the rate of misclassification. The secondary outcome parameters were the evaluation of the ligamentous injury constellations. Results: In all cases, the fracture course and ligamental integrity could be assigned to the fracture type. Correction of the classification was necessary in n = 5 (8.5%) cases. In n = 3 (5%) cases, a correction was necessary from Neer I to Craig IIc and thus from conservative to operative treatment. Mean coracoclavicular distance (CCD) in Neer I was 10.2 ± 2.1 mm versus 14.2 ± 3.9 mm in Craig IIc (p = 0.02). The mean fracture angle in Neer I was 25.1 ± 3.3° versus 36.8 ± 4.4° in Craig IIc (p = 0.02). Conclusion: Cross-sectional imaging resulted in higher precision. Nevertheless, recommendations remain for standard radiographs. The CCD and fracture angle should be considered. An angle of >30° can be assumed as a parameter of instability. A previously undescribed fracture type does not seem to exist. The modified Neer classification is an appropriate and complete fracture classification.
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Kumar, Ashish, and Mukul M. Sharma. "Diagnosing Hydraulic Fracture Geometry, Complexity, and Fracture Wellbore Connectivity Using Chemical Tracer Flowback." Energies 13, no. 21 (October 28, 2020): 5644. http://dx.doi.org/10.3390/en13215644.
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The productivity of a hydraulically fractured well depends on the fracture geometry and fracture–wellbore connectivity. Unlike other fracture diagnostics techniques, flowback tracer response will be dominated only by the fractures, which are open and connected to the wellbore. Single well chemical tracer field tests have been used for hydraulic fracture diagnostics to estimate the stagewise production contribution. In this study, a chemical tracer flowback analysis is presented to estimate the fraction of the created fracture area, which is open and connected to the wellbore. A geomechanics coupled fluid flow and tracer transport model is developed to analyze the impact of (a) fracture geometry, (b) fracture propagation and closure effects, and (c) fracture complexity on the tracer response curves. Tracer injection and flowback in a complex fracture network is modeled with the help of an effective model. Multiple peaks in the tracer response curves can be explained by the closure of activated natural fractures. Low tracer recovery typically observed in field tests can be explained by tracer retention due to fracture closure. In a complex fracture network, segment length and permeability are lumped to define an effective connected fracture length, a parameter that correlates with production. Neural network-based inverse modeling is performed to estimate effective connected fracture length using tracer data. A new method to analyze chemical tracer data which includes the effect of flow and geomechanics on tracer flowback is presented. The proposed approach can help in estimating the degree of connectivity between the wellbore and created hydraulic fractures.
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Qin, Xilin, Zhixian Gui, Fei Yang, Yuanyuan Liu, Wei Jin, and Jian Xiong. "Prediction of sweet spots in tight sandstone reservoirs based on anisotropic frequency-dependent AVO inversion." Journal of Geophysics and Engineering 18, no. 5 (September 14, 2021): 664–80. http://dx.doi.org/10.1093/jge/gxab044.
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Abstract The frequency-dependent amplitude-versus-offset (FAVO) method has become a practical method for fluid detection in sand reservoirs. At present, most FAVO inversions are based on the assumption that reservoirs are isotropy, but the application effect is not satisfactory for fractured reservoirs. Hence, we analyse the frequency variation characteristics of anisotropy parameters in tight sandstone reservoirs based on a new petrophysical model, and propose a stepwise anisotropic FAVO inversion method to extract frequency-dependent attributes from prestack seismic field data. First, we combine the improved Brie's law with the fine-fracture model to analyse frequency-dependent characteristics of velocities and Thomsen anisotropy parameters at different gas saturations and fracture densities. Then, we derive an anisotropic FAVO inversion algorithm based on Rüger's approximation formula and propose a stepwise anisotropic FAVO inversion method to obtain the dispersions of anisotropy parameters. Finally, we propose a method that combines the inversion spectral decomposition with the stepwise anisotropy FAVO inversion and apply it to tight sand reservoirs in the Xinchang area. We use P-wave velocity dispersion and anisotropy parameter ε dispersion to optimise favourable areas. Numerical analysis results show that velocity dispersion of the P-wave is sensitive to fracture density, which can be used for fracture prediction in fractured reservoirs. In contrast, anisotropic parameter dispersion is sensitive to gas saturation and can be used for fluid detection. The seismic data inversion results show that velocity dispersion of the P-wave and anisotropic parameter dispersion are sensitive to fractured reservoirs in the second member of Xujiahe Group, which is consistent with logging interpretation results.
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Bakulin, Andrey, Vladimir Grechka, and Ilya Tsvankin. "Estimation of fracture parameters from reflection seismic data—Part II: Fractured models with orthorhombic symmetry." GEOPHYSICS 65, no. 6 (November 2000): 1803–17. http://dx.doi.org/10.1190/1.1444864.
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Existing geophysical and geological data indicate that orthorhombic media with a horizontal symmetry plane should be rather common for naturally fractured reservoirs. Here, we consider two orthorhombic models: one that contains parallel vertical fractures embedded in a transversely isotropic background with a vertical symmetry axis (VTI medium) and the other formed by two orthogonal sets of rotationally invariant vertical fractures in a purely isotropic host rock. Using the linear‐slip theory, we obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media. Under the assumptions of weak anisotropy of the background medium (for the first model) and small compliances of the fractures, all effective anisotropic parameters reduce to the sum of the background values and the parameters associated with each fracture set. For the model with a single fracture system, this result allows us to eliminate the influence of the VTI background by evaluating the differences between the anisotropic parameters defined in the vertical symmetry planes. Subsequently, the fracture weaknesses, which carry information about the density and content of the fracture network, can be estimated in the same way as for fracture‐induced transverse isotropy with a horizontal symmetry axis (HTI media) examined in our previous paper (part I). The parameter estimation procedure can be based on the azimuthally dependent reflection traveltimes and prestack amplitudes of P-waves alone if an estimate of the ratio of the P- and S-wave vertical velocities is available. It is beneficial, however, to combine P-wave data with the vertical traveltimes, NMO velocities, or AVO gradients of mode‐converted (PS) waves. In each vertical symmetry plane of the model with two orthogonal fracture sets, the anisotropic parameters are largely governed by the weaknesses of the fractures orthogonal to this plane. For weak anisotropy, the fracture sets are essentially decoupled, and their parameters can be estimated by means of two independently performed HTI inversions. The input data for this model must include the vertical velocities (or reflector depth) to resolve the anisotropic coefficients in each vertical symmetry plane rather than just their differences. We also discuss several criteria that can be used to distinguish between the models with one and two fracture sets. For example, the semimajor axis of the P-wave NMO ellipse and the polarization direction of the vertically traveling fast shear wave are always parallel to each other for a single system of fractures, but they may become orthogonal in the medium with two fracture sets.
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Han, Tongcheng, and Sam Yang. "Dielectric properties of fractured carbonate rocks from finite-difference modeling." GEOPHYSICS 84, no. 1 (January 1, 2019): MR37—MR44. http://dx.doi.org/10.1190/geo2018-0003.1.
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Fractures are common features in virtually all types of geologic rocks and tend to dominate their mechanical and hydraulic properties. Detection and characterization of fractures in rocks are of interest to a variety of geophysical applications. We have investigated the frequency-dependent dielectric properties of fractured porous carbonate rocks in the frequency range [Formula: see text] and their relationships with different types of fluids filling the fractures, fracture connectivity, and directions of electrical field applied to the rocks using numerical simulation methods based on a 3D finite-difference model. We tested the validity of the modeling method on a spherical-shell model with the theoretical analytical solutions. The two fractures in the two digital carbonate rocks have the same length, but in one rock, they intersect and in the other sample they do not. The fractures in the brine-saturated digital rocks are filled either with oil or with the same brine as in the background rock. We found that although conductivity and relative permittivity are sensitive to the fracture-filling fluids, the dielectric loss factor is the best parameter discriminating the fluids. When filled with brine, the fracture connectivity does not affect the dielectric properties of the rocks. When filled with oil, the fracture connectivity can only be detected if the electrical field is parallel to the longer fracture orientation. The results provide new insights into the frequency-dependent dielectric responses of fractured sedimentary rocks and will help with the interpretation of the dielectric data acquired from rocks with fractures.
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Hu, Hao, Yingcai Zheng, Xinding Fang, and Michael C. Fehler. "3D seismic characterization of fractures with random spacing using the double-beam method." GEOPHYSICS 83, no. 5 (September 1, 2018): M63—M74. http://dx.doi.org/10.1190/geo2017-0739.1.
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Obtaining information on the spatial distribution of subsurface natural and induced fractures is critical in the production of geothermal or hydrocarbon fluids. Traditional seismic characterization methods for subsurface fractures are based on the assumption of effective anisotropy medium theory, which may not be true in reality when the fracture distribution is random. We have tested the recently proposed double-beam method to characterize nonuniformly distributed fractures. We built a 3D layered reservoir model; the reservoir layer was geometrically irregular, and it contained a set of randomly spaced fractures with spatially varying fracture compliances. We used an elastic full-wave finite-difference method to model the wavefield, where we treat the fractures as linear-slip boundaries and the data include all elastic multiple scattering. Taking the surface seismic data as input, the double-beam method forms a focusing source beam and a focusing receiver beam toward the fracture target. The fracture information is derived from the interference pattern of these two beams, which includes fracture orientation, fracture spacing, and fracture compliance as a function of spatial location. The fracture orientation parameter is the most readily determined parameter even for multiple nonorthogonal coexistent fracture sets. The beam-interference amplitude depends on the fracture spacing and compliance in a local average sense for random fractures. The beam-interference amplitude is large when there are many fractures or the compliance value is large, which is important in the interpretation of the fluid-transport properties of a reservoir.
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Chen, Li, Sun Lichun, Sun Hansen, Feng Ruyong, Wang Cunwu, and Zhang Fang. "A Method to Improve Computational Efficiency of Productivity Evaluation with Rectangular Coalbed Methane Reservoir." Geofluids 2022 (March 11, 2022): 1–11. http://dx.doi.org/10.1155/2022/3558643.
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Computational efficiency is the key factor to be considered in the productivity evaluation of rectangular coalbed methane reservoir. There are three main factors affecting the calculation speed: the nonlinearity of the material balance equation of coalbed methane reservoir, the poor conductivity of fractures cannot be considered as infinite conductivity fractures, and the Duhamel convolution is needed in history fitting and boundary image inversion. At present, there is no method to quickly evaluate the productivity of finite conductivity fracture model in rectangular coalbed methane reservoir. Diffusion equation of matrix is generated by the Fick diffusion law. The Darcy seepage law is used to build the seepage equation of fractured system in coalbed methane reservoir. In order to transform the calculation result of infinite conductivity fracture into finite conductivity fracture, fracture conductivity factor is employed in this paper. The applicability of fracture conductivity factor in the whole production process is clarified. It is clear that the factor is prone to calculation errors when the time is small, and the calculation fluctuates greatly. According to the characteristics of the Riley method and discrete method, an accurate and efficient analytical solution calculation process is designed. This will make the calculation results accurate. A production evaluation method of rectangular coalbed methane reservoirs with fractured vertical well and finite conductivity fracture is proposed. The purpose of quickly and accurately predict well production capacity is reached. The geological parameters are recombined, and new coalbed methane reservoir flow parameters are defined. Through parameter sensitivity analysis, the influence of different flow characteristic parameters on gas production is clarified. The dimensionless transfer constant and dimensionless storage capacity affect the appearance time of desorption and diffusion and the storage capacity of the fracture system, respectively. The dimensionless desorption constant describes the strength of desorption and diffusion. The influence of fracture conductivity factor on production is studied. It is clarified that its impacts are different in the early stage and the later stage of production. There is a limit to the fracture conductivity factor. When the limit is exceeded, the fracture conductivity factors no longer affect the production of a single well. The findings of this study can understand the percolation stage of finite conductivity fractured wells with rectangular coalbed methane reservoir and can also guide fracturing design and writing in the field. The research results enrich the productivity evaluation model of coalbed methane reservoir. In the end, a set of production evaluation method is put forward suitable for the well in rectangular coalbed methane reservoirs with fractured vertical well and finite conductivity fracture. In this paper, the influence of fracture conductivity on single well productivity in rectangular coalbed methane reservoir is quantitatively evaluated for the first time. By improving the calculation method and optimizing the calculation path, the productivity evaluation calculation speed of finite conductivity fractured wells in rectangular coalbed methane reservoir is optimized without affecting the calculation accuracy. The new method can be applied directly to productivity evaluation software, which has the significance of popularization.
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Zhang, Ruiduo, Yonggang Duan, and Mingqiang Wei. "Temperature Prediction Model for Two-Phase Flow Multistage Fractured Horizontal Well in Tight Oil Reservoir." Geofluids 2021 (June 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/9949977.
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Distributed temperature sensing (DTS) has been used for fracture parameter diagnosis and flow profile monitoring. In this paper, we present a new model for predicting the temperature profile of two-phase flow multistage fractured horizontal wells in the tight oil reservoirs. The homogeneous reservoir flow/heat transfer model is extended to the tight oil reservoir-fracture-wellbore coupled flow/thermal model. The influence of SRV area on reservoir and wellbore is considered, and the Joule-Thomson effect, heat convection, heat conduction, and other parameters are introduced into the improved model. The temperature distributions of reservoir and wellbore with different production times, water cut, and locations of water entry are simulated. The simulated results indicate that the Joule-Thomson effect will cause wellbore temperature to rise; the temperature of fractures with more water production is significantly lower than that of other fractures, and the water outlet location can be judged according to the temperature change of the wellbore. By using the improved temperature prediction model, the DTS monitoring data of two-phase flow multistage fractured horizontal well in the tight reservoir has been calculated and analyzed, and the accurate production profile has been obtained.
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Ouyang, Chengsheng, Tianxi Tang, and Surendra P. Shah. "Relationship between fracture parameters from two parameter fracture model and from size effect model." Materials and Structures 29, no. 2 (March 1996): 79–86. http://dx.doi.org/10.1007/bf02486197.
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Alvarez, Leidy Laura, Leonardo José do Nascimento Guimarães, Igor Fernandes Gomes, Leila Beserra, Leonardo Cabral Pereira, Tiago Siqueira de Miranda, Bruno Maciel, and José Antônio Barbosa. "Impact of Fracture Topology on the Fluid Flow Behavior of Naturally Fractured Reservoirs." Energies 14, no. 17 (September 2, 2021): 5488. http://dx.doi.org/10.3390/en14175488.
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Fluid flow modeling of naturally fractured reservoirs remains a challenge because of the complex nature of fracture systems controlled by various chemical and physical phenomena. A discrete fracture network (DFN) model represents an approach to capturing the relationship of fractures in a fracture system. Topology represents the connectivity aspect of the fracture planes, which have a fundamental role in flow simulation in geomaterials involving fractures and the rock matrix. Therefore, one of the most-used methods to treat fractured reservoirs is the double porosity-double permeability model. This approach requires the shape factor calculation, a key parameter used to determine the effects of coupled fracture-matrix fluid flow on the mass transfer between different domains. This paper presents a numerical investigation that aimed to evaluate the impact of fracture topology on the shape factor and equivalent permeability through hydraulic connectivity (f). This study was based on numerical simulations of flow performed in discrete fracture network (DFN) models embedded in finite element meshes (FEM). Modeled cases represent four hypothetical examples of fractured media and three real scenarios extracted from a Brazilian pre-salt carbonate reservoir model. We have compared the results of the numerical simulations with data obtained using Oda’s analytical model and Oda’s correction approach, considering the hydraulic connectivity f. The simulations showed that the equivalent permeability and the shape factor are strongly influenced by the hydraulic connectivity (f) in synthetic scenarios for X and Y-node topological patterns, which showed the higher value for f (0.81) and more expressive values for upscaled permeability (kx-node = 0.1151 and ky-node = 0.1153) and shape factor (25.6 and 14.5), respectively. We have shown that the analytical methods are not efficient for estimating the equivalent permeability of the fractured medium, including when these methods were corrected using topological aspects.
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Griffiths, S. K., and R. H. Nilson. "Similarity Analysis of Condensing Flow in a Fluid-Driven Fracture." Journal of Heat Transfer 110, no. 3 (August 1, 1988): 754–62. http://dx.doi.org/10.1115/1.3250556.
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Similarity solutions are derived for some fundamental problems of condensing flow in a hydraulically driven fracture. The governing equations describe one-dimensional homogeneous turbulent flow along a wedge-shaped hydraulic fracture in an elastic medium. The instantaneous fracture speed is determined as an analytical function of fracture length, material properties, process parameters, and a single eigenvalue, which is calculated by solving a system of ordinary differential equations for the variation of pressure, energy, velocity, and opening displacement along the fracture. Results are presented for abrupt condensation of a pure substance and for gradual condensation of air/water mixtures. The rate of condensation is controlled by the rate of heat transfer to the fracture wall, which depends upon a single dimensionless parameter. For small and large values of this parameter the present multiphase solutions are in agreement with previous solutions for single-phase flows of vapors and liquids. Although most of the results are presented in dimensionless form, some numerical examples are given for steam-driven fractures emanating from the cavity resulting from an underground nuclear explosion.
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Chen, Xiaozhong. "Parametric design of patient-specific fixation plates for distal femur fractures." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 232, no. 9 (August 13, 2018): 901–11. http://dx.doi.org/10.1177/0954411918793668.
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To facilitate the creation, modification, and optimization of patient-specific plates for distal femur fractures, a novel approach was proposed for the rapid and convenient design of patient-specific plates for patients’ fractured femurs using feature parameterization. First, several femur parameter values were obtained for a specific patient and used to construct a restored surface model of the fractured femur. Next, combined with the particular femur anatomy and the fracture, a parameterized plate with a suitable shape was created automatically based on the parameter maps between the femur and plate. Finally, using finite-element analysis, the Von Mises stresses of the plate under human gait loads were calculated to evaluate the biomechanical performance of the plate, and the plate was optimized for specific patients by recursively adjusting the parameter values. Case results indicate that patient-specific plate models can be created rapidly based on the fractured femur modes of patients and can be optimized efficiently with high-level semantic parameters. Therefore, the proposed approach may be used as a basic tool for the design and modification of patient-specific plates for use in orthopedic operations.
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Li, Jianxiong, Wen Xiao, Guanzhong Hao, Shiming Dong, Wen Hua, and Xiaolong Li. "Comparison of Different Hydraulic Fracturing Scenarios in Horizontal Wells Using XFEM Based on the Cohesive Zone Method." Energies 12, no. 7 (March 31, 2019): 1232. http://dx.doi.org/10.3390/en12071232.
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Multistage hydraulic fracturing is a highly effective method for creating multiple transverse fractures to improve gas and oil reservoir production. It is critical to minimize the fracture spacing while also ensuring transverse propagation of fractures in multi-fractured horizontal wells. In this paper, a 3D fully coupled pore pressure-stress model based on the extended finite element method (XFEM) combined with the cohesive zone method is established to simulate five different fracturing scenarios in close spacing. The sensitivity of mesh size and the integration method are optimal, which are verified by the highly accurate traditional cohesive zone method. Then, the effect of five different fracturing scenarios on fracture geometries is compared. It is shown that spacing is a key parameter controlling fracture geometries in all fracturing scenarios. Alternative sequential and modified two-step fracturing can significantly reduce the influence of stress shadowing to generate more transverse fractures and form longer effective fractures. The sequential and two-step fracturing see an obvious improvement with increased fracture effective length when the spacing increases. The simultaneous fracturing technique can result in excessive closure of the middle fractures, which causes serious insertion of proppants. These results offer a new insight on optimization of hydraulic fracturing and can be a guidance for typical field cases.
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Kottwitz, Maximilian O., Anton A. Popov, Tobias S. Baumann, and Boris J. P. Kaus. "The hydraulic efficiency of single fractures: correcting the cubic law parameterization for self-affine surface roughness and fracture closure." Solid Earth 11, no. 3 (May 29, 2020): 947–57. http://dx.doi.org/10.5194/se-11-947-2020.
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Abstract. Quantifying the hydraulic properties of single fractures is a fundamental requirement to understand fluid flow in fractured reservoirs. For an ideal planar fracture, the effective flow is proportional to the cube of the fracture aperture. In contrast, real fractures are rarely planar, and correcting the cubic law in terms of fracture roughness has therefore been a subject of numerous studies in the past. Several empirical relationships between hydraulic and mechanical aperture have been proposed based on statistical variations of the aperture field. However, often, they exhibit non-unique solutions, attributed to the geometrical variety of naturally occurring fractures. In this study, a non-dimensional fracture roughness quantification scheme is acquired, opposing effective surface area against relative fracture closure. This is used to capture deviations from the cubic law as a function of quantified fracture roughness, here termed hydraulic efficiencies. For that, we combine existing methods to generate synthetic 3-D fracture voxel models. Each fracture consists of two random, 25 cm2 wide self-affine surfaces with prescribed roughness amplitude, scaling exponent, and correlation length, which are separated by varying distances to form fracture configurations that are broadly spread in the newly formed two-parameter space (mean apertures in submillimeter range). First, we performed a percolation analysis on 600 000 synthetic fractures to narrow down the parameter space on which to conduct fluid flow simulations. This revealed that the fractional amount of contact and the percolation probability solely depend on the relative fracture closure. Next, Stokes flow calculations are performed, using a 3-D finite differences code on 6400 fracture models to compute directional permeabilities. The deviations from the cubic law prediction and their statistical variability for equal roughness configurations were quantified. The resulting 2-D solution fields reveal decreasing cubic law accordance down to 1 % for extreme roughness configurations. We show that the non-uniqueness of the results significantly reduces if the correlation length of the aperture field is much smaller than the spatial extent of the fracture. An equation was provided that predicts the average behavior of hydraulic efficiencies and respective fracture permeabilities as a function of their statistical properties. A model to capture fluctuations around that average behavior with respect to their correlation lengths has been proposed. Numerical inaccuracies were quantified with a resolution test, revealing an error of 7 %. By this, we propose a revised parameterization for the permeability of rough single fractures, which takes numerical inaccuracies of the flow calculations into account. We show that this approach is more accurate compared to existing formulations. It can be employed to estimate the permeability of fractures if a measure of fracture roughness is available, and it can readily be incorporated in discrete fracture network modeling approaches.
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Xie, Jun, Haoyong Huang, Yu Sang, Yu Fan, Juan Chen, Kan Wu, and Wei Yu. "Numerical Study of Simultaneous Multiple Fracture Propagation in Changning Shale Gas Field." Energies 12, no. 7 (April 8, 2019): 1335. http://dx.doi.org/10.3390/en12071335.
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Recently, the Changning shale gas field has been one of the most outstanding shale plays in China for unconventional gas exploitation. Based on the more practical experience of hydraulic fracturing, the economic gas production from this field can be optimized and gradually improved. However, further optimization of the fracture design requires a deeper understanding of the effects of engineering parameters on simultaneous multiple fracture propagation. It can increase the effective fracture number and the well performance. In this paper, based on the Changning field data, a complex fracture propagation model was established. A series of case studies were investigated to analyze the effects of engineering parameters on simultaneous multiple fracture propagation. The fracture spacing, perforating number, injection rate, fluid viscosity and number of fractures within one stage were considered. The simulation results show that smaller fracture spacing implies stronger stress shadow effects, which significantly reduces the perforating efficiency. The perforating number is a critical parameter that has a big impact on the cluster efficiency. In addition, one cluster with a smaller perforating number can more easily generate a uniform fracture geometry. A higher injection rate is better for promoting uniform fluid volume distribution, with each cluster growing more evenly. An increasing fluid viscosity increases the variation of fluid distribution between perforation clusters, resulting in the increasing gap between the interior fracture and outer fractures. An increasing number of fractures within the stage increases the stress shadow among fractures, resulting in a larger total fracture length and a smaller average fracture width. This work provides key guidelines for improving the effectiveness of hydraulic fracture treatments.
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Li, Jianxiong, Shiming Dong, Wen Hua, Yang Yang, and Xiaolong Li. "Numerical Simulation on Deflecting Hydraulic Fracture with Refracturing Using Extended Finite Element Method." Energies 12, no. 11 (May 28, 2019): 2044. http://dx.doi.org/10.3390/en12112044.
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Refracturing is a key technology in enhancing the conductivity of fractures from hydraulically-fractured wells. However, the deflecting mechanism of the diverting fracture is still unclear. In this paper, a fully coupled seepage-stress model based on the extended finite element method (XFEM) was developed to realize the deflection mechanism of the refracturing fractures. The modified construction of refracturing was then verified by laboratory experiments. Furthermore, two new deflection angles considering the influence area along initial fracture length were introduced to evaluate the refracturing. The numerical results demonstrated that: (1) lower stress difference, larger perforation angle and longer perforation depth can lead to a higher deflection angle, thereby a more curving propagation path of the diverting fracture; (2) increasing injection rate or fluid viscosity can significantly enhance the diverting behavior; and (3) an initial location near the root of the initial fracture results in a larger value of the deflection angle, which is preferred for far-field refracturing. The conclusions in this study can be a systematic guide for the parameter optimization in refracturing treatment.
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Luo, Erhui, Yongle Hu, Zifei Fan, Wenqi Zhao, Chenggang Wang, Meng Sun, and Xuanran Li. "Pressure transient analysis of a vertical well with multiple etched fractures in carbonate reservoirs." Energy Exploration & Exploitation 38, no. 3 (November 11, 2019): 591–612. http://dx.doi.org/10.1177/0144598719885066.
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Acid fracturing has been widely used as an industry practice in explored and developed carbonate reservoirs. It is very important to understand responses of reservoirs and improve production performance of a well due to the presence of fracture networks by stimulation treatments. Pressure transient analysis is one of the most effective diagnostic techniques available to enhance our understanding of natural and artificial-etched fracture behavior. This work presented a novel mathematical model for unsteady state flow of naturally fractured porous medium into multiple etched fractures intersecting a vertical well, and three different geometric shapes of matrix blocks containing slabs, cylinders and spheres were considered. The new solution was derived by using the Laplace transformation and the point source function integral approach. The polar coordinate transformation was used to deal with the radial distribution of arbitrary fracture number and angle. Then the model was validated by comparison with three published cases. Finally, type curves were plotted to identify flow regimes: linear flow, transitional flow, pseudoradial flow, and boundary dominant flow if the closed or constant pressure boundary exists. Furthermore, sensitivity analysis was investigated. The results showed that the acid-etched fracture parameters containing fracture number, fracture distribution and conductivity had a significant impact on pressure behavior at early times. However, natural fracture storativity coefficient and interporosity flow parameter mainly affected the transitional flow at intermediate times. Moreover, the shape of matrix blocks had a little influence on transient responses at intermediate times. It is found that multiple etched fractures existing near the wellbore consume less pressure drop and increase the productivity of a well as a whole.
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Agten, Christoph A., Stephen Honig, Punam K. Saha, Ravinder Regatte, and Gregory Chang. "Subchondral bone microarchitecture analysis in the proximal tibia at 7-T MRI." Acta Radiologica 59, no. 6 (September 12, 2017): 716–22. http://dx.doi.org/10.1177/0284185117732098.
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Background Bone remodels in response to mechanical loads and osteoporosis results from impaired ability of bone to remodel. Bone microarchitecture analysis provides information on bone quality beyond bone mineral density (BMD). Purpose To compare subchondral bone microarchitecture parameters in the medial and lateral tibia plateau in individuals with and without fragility fractures. Material and Methods Twelve female patients (mean age = 58 ± 15 years; six with and six without previous fragility fractures) were examined with dual-energy X-ray absorptiometry (DXA) and 7-T magnetic resonance imaging (MRI) of the proximal tibia. A transverse high-resolution three-dimensional fast low-angle shot sequence was acquired (0.234 × 0.234 × 1 mm). Digital topological analysis (DTA) was applied to the medial and lateral subchondral bone of the proximal tibia. The following DTA-based bone microarchitecture parameters were assessed: apparent bone volume; trabecular thickness; profile-edge-density (trabecular bone erosion parameter); profile-interior-density (intact trabecular rods parameter); plate-to-rod ratio; and erosion index. We compared femoral neck T-scores and bone microarchitecture parameters between patients with and without fragility fracture. Results There was no statistical significant difference in femoral neck T-scores between individuals with and without fracture (–2.4 ± 0.9 vs. −1.8 ± 0.7, P = 0.282). Apparent bone volume in the medial compartment was lower in patients with previous fragility fracture (0.295 ± 0.022 vs. 0.317 ± 0.009; P = 0.016). Profile-edge-density, a trabecular bone erosion parameter, was higher in patients with previous fragility fracture in the medial (0.008 ± 0.003 vs. 0.005 ± 0.001) and lateral compartment (0.008 ± 0.002 vs. 0.005 ± 0.001); both P = 0.025. Other DTA parameters did not differ between groups. Conclusion 7-T MRI and DTA permit detection of subtle changes in subchondral bone quality when differences in BMD are not evident.