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Journal articles on the topic 'Mathematical model of fractures'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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1

Ji, Anzhao, Yufeng Wang, Youjie Xu, Guangsheng Zhang, and Xuefen Liu. "A Semianalytical Mathematical Model and Seepage Characteristics of Off-Center Fractured Vertical Wells with Multiwing Asymmetrical Fractures." Mathematical Problems in Engineering 2023 (April 21, 2023): 1–16. http://dx.doi.org/10.1155/2023/5226318.

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The complexity of formation conditions leads to multiwing asymmetric fractures after large-scale fracturing. According to a well pattern model and reservoir characteristics, a testing well is away from the center of the reservoir, and the existing well-test mathematical model cannot meet the field data analysis demand. Therefore, the mathematical model for the fractured wells with multiwing asymmetrical fractures is established. The model solution of the Laplace domain is obtained by the Laplace transform, nonuniform fracture discretization, and pressure drop superposition principle. The model

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2

Pan, Bin, and Yang Song Zhang. "Searching for the Shortest Seepage Path of 3D Network in Fractured Rock Masses." Applied Mechanics and Materials 580-583 (July 2014): 857–61. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.857.

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Fractured rock is a combination of rocks and fractures,the fractures which are ubiquitously distributed in fractured rock mass often constitute the flow and migration path of underground fluid and radionuclide.Discrete Fracture Network Model (DFN) was built with in-situ observations to evaluate the hydraulic conductivity tensor of rock masses.The fractures relation pattern with corresponding algorithm is given on the basis of computational geometric,and then the graph theory is employed as the mathematical model to represent the mutual positional relation of fractures.And then,with the use of

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3

Kasperovich, A. M., A. P. Shevelev, and A. Ya Gilmanov. "Non-isothermal mathematical model of blocking tecnogenic fractures." Vestnik of Samara University. Natural Science Series 30, no. 4 (2025): 101–15. https://doi.org/10.18287/2541-7525-2024-30-5-101-115.

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Nowadays, large oil fields have moved to the stage of declining production, to maintain reservoir pressure, it is necessary to apply flooding technologies. To maintain the previous rates of oil production, it is necessary to force selections by increasing the value of downhole pressure on the injection wells. However, the risks of exceeding the fracturing pressure are increasing, which can lead to the formation of technogenic fractures. An intensive increase in the fracture can lead to an increase in the risks of premature water reaching through it into the drainage zone of the producing wells

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4

Keshavarz, Alireza, Alexander Badalyan, Raymond Johnson, and Pavel Bedrikovetski. "Improving the efficiency of hydraulic fracturing treatment in CBM reservoirs by stimulating the surrounding natural fracture system." APPEA Journal 55, no. 1 (2015): 351. http://dx.doi.org/10.1071/aj14028.

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A method is proposed for enhancing the conductivity of micro-fractures and cleats around the hydraulically induced fractures in coal bed methane reservoirs. In this technique, placing ultra-fine proppant particles in natural fractures and cleats around hydraulically induced fractures at leak-off conditions keeps the coal cleats open during water-gas production, and this consequently increases the efficiency of hydraulic fracturing treatment. Experimental and mathematical studies for the stimulation of a natural cleat system around the main hydraulic fracture are conducted. In the experimental

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5

Chen, Zhiming, Xinwei Liao, Xiaoliang Zhao, Sanbo Lv, and Langtao Zhu. "A Semianalytical Approach for Obtaining Type Curves of Multiple-Fractured Horizontal Wells With Secondary-Fracture Networks." SPE Journal 21, no. 02 (2016): 538–49. http://dx.doi.org/10.2118/178913-pa.

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Summary In naturally fractured reservoirs, complex fracture systems can easily develop along a horizontal wellbore during hydraulic fracturing. In the fracture systems, multiple, discrete secondary fractures are connected to the multiple-fractured horizontal well (MFHW). Because of the fracture complexity, most studies about performance forecast of such MFHWs highly depend on numerical simulators. In this paper, a new semianalytical approach is proposed to overcome the challenge to analyze the pressure behavior of MFHWs in complex-fracture systems. First, a mathematical model for MFHWs with se

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6

Makeev, Maxim, Sergei Sokolov, and Anastasiya Kolmakova. "Numerical model of fracture formation in a coal seam." E3S Web of Conferences 330 (2021): 04009. http://dx.doi.org/10.1051/e3sconf/202133004009.

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The article discusses the recovery process of fracture system formation after hydraulic fracturing in a coal seam, based on the conducted seismic studies using modern mathematical software packages. Model concepts of the fractures system development under hydrodynamic impact on a rock mass are considered, which make it possible to assess the nature of fractures propagation.

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7

Bossie-Codreanu, Dimitrie, Paul R. Bia, and Jean-Claude Sabathier. "The "Checker Model," An Improvement in Modeling Naturally Fractured Reservoirs With a Tridimensional, Triphasic, Black-Oil Numerical Model." Society of Petroleum Engineers Journal 25, no. 05 (1985): 743–56. http://dx.doi.org/10.2118/10977-pa.

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Abstract This paper describes an approach to simulating the flow of water, oil, and gas in fully or partially fractured reservoirs with conventional black-oil models. This approach is based on the dual porosity concept and uses a conventional tridimensional, triphasic, black-oil model with minor modifications. The basic feature is an elementary volume of the fractured reservoir that is simulated by several model cells; the matrix is concentrated into one matrix cell and tee fractures into the adjacent fracture cells. Fracture cells offer a continuous path for fluid flows, while matrix cello ar

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8

Muratov, Maxim V., Polina V. Stognii, Igor B. Petrov, Alexey A. Anisimov, and Nazim A. Karaev. "The study of dynamical processes in problems of mesofracture layers exploration seismology by methods of mathematical and physical simulation." Radioelectronics. Nanosystems. Information Technologies. 13, no. 1 (2021): 71–78. http://dx.doi.org/10.17725/rensit.2021.13.071.

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The article is devoted to the study of the propagation of elastic waves in a fractured seismic medium by methods of mathematical modeling. The results obtained during it are compared with the results of physical modeling on similar models. For mathematical modeling, the grid-characteristic method with hybrid schemes of 1-3 orders with approximation on structural rectangular grids is used. The ability to specify inhomogeneities (fractures) of various complex shapes and spatial orientations has been implemented. The description of the developed mathematical models of fractures, which can be used

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9

Asalkhuzina, G. F., A. Ya Davletbaev, and R. I. Nuriev. "INTERFERENCE TEST TO FRACTURED INJECTION WELLS: MATHEMATICAL MODEL AND FIELD CASE." Oil and Gas Studies, no. 6 (December 1, 2017): 56–62. http://dx.doi.org/10.31660/0445-0108-2017-6-56-62.

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This article is devoted to examine the pressure behavior during well tests at the system with two finite-conductivity vertical hydraulic fractures. An approximate numerical solution of the problem is obtained, simu-lation of studies by interference test is conducted. This was done by correlating the amplitude of the pressure in the observation well at the distance between two fractures with the fracture flow conductivity. The established mathematical model is used to interpret field case which have been get by method of interference test on a deposit with the low permeable reservoir.

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10

Zou, Yi, Desheng Zhou, Xianlin Ma, Yenan Jie, Xiaoxiang Wang, and Hongxia Liu. "Optimization of Mathematical Function-Shaped Fracture Distribution Patterns for Multi-Stage Fractured Horizontal Wells." Energies 16, no. 13 (2023): 4987. http://dx.doi.org/10.3390/en16134987.

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A conventional oil and gas well does not have a natural production capacity, which necessitates a hydraulic fracturing operation. The effectiveness of the fracturing directly impacts the economic benefit of a single well. Among the various parameters, including fracture spacing, fracture width, and conductivity, fracture half-length is one of the main influencing factors on the productivity of horizontal wells. For conventional homogeneous reservoirs, research mainly focuses on fracture patterns with equal fracture lengths. However, in actual production processes, due to mutual interference an

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11

Wang, Tong, Zhixue Sun, Kai Zhang, Chuanyin Jiang, Ying Xin, and Qiangqiang Mao. "Investigation on Heat Extraction Performance of Fractured Geothermal Reservoir Using Coupled Thermal-Hydraulic-Mechanical Model Based on Equivalent Continuum Method." Energies 12, no. 1 (2018): 127. http://dx.doi.org/10.3390/en12010127.

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Natural fractures and artificial fractures in a tight rock matrix of an enhanced geothermal system make flow and heat transfer become seriously anisotropic. In this paper, a field-scale fractured heterogeneous geothermal reservoir model is built to study the heat transfer process. Based on an equivalent continuum method and local thermal non-equilibrium model, an equivalent permeability tensor is mapped from discrete fractures and a coupled thermal-hydraulic-mechanical mathematical model is adopted in which logarithmic stress sensitivity model is used to couple effective stress and permeabilit

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12

Zhou, Ziwu, Ao Xia, Rui Guo, Lin Chen, Fengshuo Kong, and Xiaoliang Zhao. "Seepage Model and Pressure Response Characteristics of Non-Orthogonal Multi-Fracture Vertical Wells with Superimposed Sand Body in Tight Gas Reservoirs." Energies 16, no. 21 (2023): 7275. http://dx.doi.org/10.3390/en16217275.

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Faced with difficulties stemming from the complex interactions between tight gas sand bodies and fractures, when describing and identifying reservoirs, a composite reservoir model was established. By setting the supply boundary to characterize the superposition characteristics of sand bodies, a mathematical model of unstable seepage in fractured vertical wells in tight sandstone gas reservoirs was developed, considering factors such as stress sensitivity, fracture density and fracture symmetry. The seepage law and pressure response characteristics of gas wells in tight sandstone discontinuous

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13

Abdel Azim, Reda, Saad Alatefi, and Ahmad Alkouh. "A Coupled Poro-Elastic Fluid Flow Simulator for Naturally Fractured Reservoirs." Energies 16, no. 18 (2023): 6476. http://dx.doi.org/10.3390/en16186476.

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Naturally fractured reservoirs are characterized by their complex nature due to the existence of natural fractures and fissures within the rock formations. These fractures can significantly impact the flow of fluids within the reservoir, making it difficult to predict and manage production. Therefore, efficient production from such reservoirs requires a deep understanding of the flow behavior via the integration of various geological, geophysical, and engineering data. Additionally, advanced simulation models can be used to predict reservoir behavior under different production scenarios and ai

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14

Jonoud, S., O. P. P. Wennberg, G. Casini, and J. A. A. Larsen. "Capturing the Effect of Fracture Heterogeneity on Multiphase Flow During Fluid Injection." SPE Reservoir Evaluation & Engineering 16, no. 02 (2013): 194–208. http://dx.doi.org/10.2118/147834-pa.

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Summary Carbonate fractured reservoirs introduce a tremendous challenge to the upscaling of both single- and multiphase flow. The complexity comes from both heterogeneous matrix and fracture systems in which the separation of scales is very difficult. The mathematical upscaling techniques, derived from representative elementary volume (REV), must therefore be replaced by a more realistic geology-based approach. In the case of multiphase flow, an evaluation of the main forces acting during oil recovery must also be performed. A matrix-sector model from a highly heterogeneous carbonate reservoir

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15

Ali, Mahmoud T., Ahmed A. Ezzat, and Hisham A. Nasr-El-Din. "A Model To Simulate Matrix-Acid Stimulation for Wells in Dolomite Reservoirs with Vugs and Natural Fractures." SPE Journal 25, no. 02 (2019): 609–31. http://dx.doi.org/10.2118/199341-pa.

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Summary Designing matrix-acid stimulation treatments in vuggy and naturally fractured carbonate reservoirs is a challenging problem in the petroleum industry. It is often difficult to physically model this process, and current mathematical models do not consider vugs or fractures. There is a significant gap in the literature for models that design and evaluate matrix-acid stimulation in vuggy and naturally fractured carbonate reservoirs. The objective of this work is to develop a new model to simulate matrix acidizing under field conditions in vuggy and naturally fractured carbonates. To obtai

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16

Yu, Qingyan, Qi Wang, Pengcheng Liu, et al. "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 frac

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17

Pankov, I.O., V.L. Ogarkova, S.D. Sirazitdinov, and A.L. Emelin. "ABOUT THE SHIFT MECHANISM DISLOCATION AT THE ABDUCTION FRACTURES OF DISTAL DEPARTMENT OF OSSES CRURIS." Annali d'Italia 41 (March 27, 2023): 69–73. https://doi.org/10.5281/zenodo.7774338.

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Pronation fractures of the distal tibial articular department are among the most common types of injuries. With this mechanism of injury usually takes place outside of the ankle transsyndesmosis fracture, fracture of the internal malleolus or deltoid ligament rupture, partial or total damage to the distal tibiofibular syndesmosis. Complications usually associated with errors in diagnosis and the wrong choice of treatment. It is often not detected distal tibiofibular syndesmosis injury and neglected features of lateral malleolus fractures. The mathematical model of a pronational fracture of the

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18

Hosseini, Erfan, Mohammad Sarmadivaleh, and Zhongwei Chen. "Developing a new algorithm for numerical modeling of discrete fracture network (DFN) for anisotropic rock and percolation properties." Journal of Petroleum Exploration and Production Technology 11, no. 2 (2021): 839–56. http://dx.doi.org/10.1007/s13202-020-01079-w.

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AbstractThe role of natural fractures in future reservoir performance is prominent. The fractured porous media is composed of an interconnected network of fractures and blocks of the porous medium where fractures occur in various scales and have a strong influence either when most of the flow is concentrated and them or when they act as barriers. A general numerical model for discrete fracture networks (DFN) is usually employed to handle the observed wide variety of fracture properties and the lack of direct fracture visualization. These models generally use fracture properties’ stochastic dis

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19

Tang, Chao, Xiaofan Chen, Zhimin Du, Ping Yue, and Jiabao Wei. "Numerical Simulation Study on Seepage Theory of a Multi-Section Fractured Horizontal Well in Shale Gas Reservoirs Based on Multi-Scale Flow Mechanisms." Energies 11, no. 9 (2018): 2329. http://dx.doi.org/10.3390/en11092329.

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Aimed at the multi-scale fractures for stimulated reservoir volume (SRV)-fractured horizontal wells in shale gas reservoirs, a mathematical model of unsteady seepage is established, which considers the characteristics of a dual media of matrix and natural fractures as well as flow in the large-scale hydraulic fractures, based on a discrete-fracture model. Multi-scale flow mechanisms, such as gas desorption, the Klinkenberg effect, and gas diffusion are taken into consideration. A three-dimensional numerical model based on the finite volume method is established, which includes the construction

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20

Pankov, I.O., V.L. Ogarkova, S.D. Sirazitdinov, and A.L. Emelin. "ABOUT THE SHIFT MECHANISM DISLOCATION AT THE ADDUCTION FRACTURES OF DISTAL DEPARTMENT OF OSSES CRURIS." Annali d'Italia 41 (March 27, 2023): 74–78. https://doi.org/10.5281/zenodo.7774353.

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Supination fractures of the distal tibial articular department are among the gravest types of injuries of the ankle joint. With this mechanism of injury usually takes place fracture of the internal malleolus or internal margin of the tibia, subsyndesmosis fracture of the external malleolus, damage of the distal tibiofibular syndesmosis is not vision. Complications usually associated with graves of damage of the articular surface of tibia, errors in diagnosis and the wrong choice of treatment. The mathematical model of a supinational fracture of the distal department of the curries illustrated

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21

Zhao, Xing, Jin Zhao, Hehua Wang, and Yuandong Liu. "Study on the Influence of Perforating Parameters on the Flow Rate and Stress Distribution of Multi-Fracture Competitive Propagation." Processes 12, no. 4 (2024): 839. http://dx.doi.org/10.3390/pr12040839.

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It is of great significance to investigate the flow rate and stress distribution of multi-fracture propagation for the optimization of perforation parameters and fracture parameters. Considering the coupling of rock deformation, fracture direction and fluid flow in multi-fracture scenarios, a mathematical model and solution program for the flow and stress distribution of multiple fractures are established, and the analytical model is used for comparison and verification. The effects of perforation cluster number, cluster spacing, perforation diameter on fracture extension trajectory, fracture

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22

Shevelev, Alexander P., Alexander Ya Gilmanov, and Anton M. Kasperovich. "Simulation of blocking of hydraulic fracture near injector in a reservoir simulator." Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy 9, no. 1 (2023): 78–91. http://dx.doi.org/10.21684/2411-7978-2023-9-1-78-91.

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Mature fields, as a rule, are developed using flooding technology. During long-term operation of field, in order to maintain the fluid flow rate at the same level, it is necessary to increase the bottom-hole pressure of the injector, which, when the pressure of the fracturing is exceeded, leads to the formation of fractures near the injectors. Uncontrolled growth of these fractures can lead to a breakthrough of water through it into the drainage zone of the producer and increase in the water cut of the production. This phenomenon has been observed in several fields, so the task of blocking of

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23

XU, PENG, HAICHENG LIU, AGUS PULUNG SASMITO, SHUXIA QIU, and CUIHONG LI. "EFFECTIVE PERMEABILITY OF FRACTURED POROUS MEDIA WITH FRACTAL DUAL-POROSITY MODEL." Fractals 25, no. 04 (2017): 1740014. http://dx.doi.org/10.1142/s0218348x1740014x.

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As natural fractures show statistically fractal scaling laws, fractal geometry has been proposed and applied to model the fracture geometry and to study the hydraulic properties of fractured porous media. In this paper, a fractal dual-porosity model is developed to study the single-phase fluid flow through fractured porous media. An analytical expression for effective permeability of fractured porous media is derived, which depends on the fractal dimension and fracture aperture. The effect of fractal dimensions for fracture aperture distribution and tortuosity, the ratio of minimum to maximum

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24

Wang, Yong, and Xiangyi Yi. "Flow Modeling of Well Test Analysis for a Multiple-fractured Horizontal Well in Triple Media Carbonate Reservoir." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 5 (2018): 439–57. http://dx.doi.org/10.1515/ijnsns-2016-0075.

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AbstractCarbonate reservoir is one kinds of important reservoir in the world. Because of the characteristics of carbonate reservoir, horizontal well, and acid fracturing became a key technology for efficiently developing carbonate reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A coupling mathematical model for a fractured horizontal well in triple media carbonate reservoir with t

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25

Ke, Xijun, Yunxiang Zhao, Jiaqi Li, Zixi Guo, and Yunwei Kang. "Production Simulation of Oil Reservoirs with Complex Fracture Network Using Numerical Simulation." Energies 15, no. 11 (2022): 4050. http://dx.doi.org/10.3390/en15114050.

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This paper established a numerical simulation model to analyze the pressure transient and rate transient behaviors in reservoir with complex fracture network. Firstly, the fractures are introduced into the coordinate system through the position, angle, and length. Secondly, a mathematical model is established by using unstable seepage model. Thirdly, the central difference method was used to solve the model and local grid refinement method is introduced to describe the network fractures. Finally, we compared the results obtained from this paper’s model with the production data. The results sho

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26

Bashmakov, R. A., D. A. Nasyrova, and Z. R. Khakimova. "Natural vibrations of fluid in a well connected with the reservoir by a system of radial fractures." Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza, no. 2 (October 19, 2024): 126–34. http://dx.doi.org/10.31857/s1024708424020115.

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The problem of natural vibrations of a fluid in a horizontal well with multiple fractures obtained by hydraulic fracturing is considered. A mathematical model of the natural vibrations of fluid in a horizontal oil well connected to the reservoir by a system of radial hydraulic fractures is constructed and the frequency characteristics of the natural vibrations of fluid as functions of the hydraulic fracture and reservoir parameters are determined. Using a numerical analysis of the frequency characteristics of vibrations, the effect of changes in the fracture width, the number of fractures, and

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27

Bobreneva, Yu O., P. I. Rahimly, Yu A. Poveshchenko, V. O. Podryga, and L. V. Enikeeva. "Numerical modeling of multiphase mass transfer processes in fractured-porous reservoirs." Journal of Physics: Conference Series 2131, no. 2 (2021): 022002. http://dx.doi.org/10.1088/1742-6596/2131/2/022002.

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Abstract The paper presents an algorithm for solving the problem of the process of mass transfer of a two-phase fluid in a fractured-porous reservoir in a one-dimensional formulation. The presence of natural fractures in such reservoirs impedes various types of exploration and field development. Fractured-porous reservoirs are characterized by intense exchange fluid flow between fractures and porous blocks. Each system has its own individual set of filtration-capacity parameters, and this fact complicates the problem under consideration. To study the mass transfer of a two-phase fluid in a med

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28

Bobreneva, Yulia Olegovna, Parvin Ilgar gizi Rahimly, Victoria Olegovna Podryga, Svetlana Sergeevna Bazhitova, Ahmed Elsaid Ezeldin Bakeer Ali Bakeer, and Ahmed Kamal Ibrahim Abu-Nab. "On one method of numerical modeling of a two-phase fluid system in a fractured-porous reservoir." Keldysh Institute Preprints, no. 38 (2021): 1–20. http://dx.doi.org/10.20948/prepr-2021-38.

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In this work, the authors propose an algorithm for solving the problem of the process of mass transfer of a two-phase fluid in a fractured-porous reservoir in a one-dimensional formulation. The presence of natural fractures in such reservoirs impedes various types of exploration during field development. Fractured porous reservoirs are characterized by intense exchange fluid flow between fractures and porous blocks. Each system under consideration has its own individual set of filtration-capacity parameters that complicates the problem. To study the mass transfer of a two-phase liquid in a med

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29

Both, Jakub Wiktor, Bergit Brattekås, Eirik Keilegavlen, Martin Fernø, and Jan Martin Nordbotten. "High-fidelity experimental model verification for flow in fractured porous media." InterPore Journal 1, no. 3 (2024): IPJ271124–6. http://dx.doi.org/10.69631/ipj.v1i3nr31.

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Mixed-dimensional mathematical models for flow in fractured media have been prevalent in the modeling community for almost two decades, utilizing the explicit representation of fractures by lower-dimensional manifolds embedded in the surrounding porous media. In this work, for the first time, direct qualitative and quantitative comparisons of mixed-dimensional models are drawn against laboratory experiments. Dedicated displacement experiments of steady-state laminar flow in fractured media are investigated using both high-resolution PET images as well as state-of-the-art numerical simulations.

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Keshavarz, Alireza, Kate Mobbs, Aditya Khanna, and Pavel Bedrikovetsky. "Stress-based mathematical model for graded proppant injection in coal bed methane reservoirs." APPEA Journal 53, no. 1 (2013): 337. http://dx.doi.org/10.1071/aj12028.

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A technology called graded proppant (propping agent) injection that consists of the injection of proppant particles, with increasing sizes and decreasing concentrations, into a naturally fractured reservoir results in deeper percolation of the particles into the natural fracture system, and thus expansion of the stimulated reservoir area. The placement of graded proppant particles keeps the fractures open, even after pressure decline due to production. There is, therefore, an enhancement in the well productivity. This proposed technology could be used to improve the productivity of CSG wells a

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Yuan, Yingzhong, Wende Yan, Fengbo Chen, Jiqiang Li, Qianhua Xiao, and Xiaoliang Huang. "Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 3-4 (2018): 367–77. http://dx.doi.org/10.1515/ijnsns-2017-0135.

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AbstractComplex fracture systems including natural fractures and hydraulic fractures exist in shale gas reservoir with fractured horizontal well development. The flow of shale gas is a multi-scale flow process from microscopic nanometer pores to macroscopic large fractures. Due to the complexity of seepage mechanism and fracture parameters, it is difficult to realize fine numerical simulation for fractured horizontal wells in shale gas reservoirs. Mechanisms of adsorption–desorption on the surface of shale pores, slippage and Knudsen diffusion in the nanometer pores, Darcy and non-Darcy seepag

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32

Jiang, Liwu, Tongjing Liu, and Daoyong Yang. "A Semianalytical Model for Predicting Transient Pressure Behavior of a Hydraulically Fractured Horizontal Well in a Naturally Fractured Reservoir With Non-Darcy Flow and Stress-Sensitive Permeability Effects." SPE Journal 24, no. 03 (2019): 1322–41. http://dx.doi.org/10.2118/194501-pa.

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Summary Non-Darcy flow and the stress-sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for fractured wells. The main object of this work is to establish a semianalytical solution to quantify the combined effects of non-Darcy flow and stress sensitivity on the transient pressure behavior for a fractured horizontal well in a naturally fractured reservoir. More specifically, the Barree-Conway model is used to quantify the non-Darcy flow behavior in the hydraulic fractures (HFs), while the permeability modulus is incorporated into math

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33

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 (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

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34

Chen, Zhiming. "Technology Focus: Formation Evaluation (August 2023)." Journal of Petroleum Technology 75, no. 08 (2023): 38–39. http://dx.doi.org/10.2118/0823-0038-jpt.

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Fractures, whether natural or hydraulic, serve as crucial pathways for fluid flow within rock formations. Because natural and hydraulic fractures are generated hundreds of meters underground, their parameters always seem to be a black box. Their influence on pressure propagation and well productivity, however, cannot be overstated. So how well are we doing in fracture evaluation and modeling? Fracture evaluation can be regarded as an inverse problem, wherein the structural characteristics of a system are deduced based on input and output signals. Our objective is to ascertain the distribution,

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35

Gu, Shaohua, Yunqing Shi, and Zhangxin Chen. "Numerical Simulation of Fracture Permeability Change in Production of Pressure-sensitive Reservoirs with In-situ Stress Field." Open Petroleum Engineering Journal 8, no. 1 (2015): 440–50. http://dx.doi.org/10.2174/1874834101508010440.

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In pressure sensitive reservoirs, interaction effects among the porous media flow field, the fracture field and the stress field can cause some specific flow characteristics entirely different from those in conventional reservoirs. Dynamic fracture behavior is one of them, which generates a change in the value of fracture aperture and even a variation in the anisotropy of permeability. In this paper, we focus on the dynamic behavior of fractures and some affecting factors, including driving pressure and in-situ stress. Numerical discrete fracture network (DFN) models are built and solved by th

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Valov, A. V. "On the simultaneous growth of multiple hydraulic fractures emanating from an inclined well." Journal of Physics: Conference Series 2057, no. 1 (2021): 012079. http://dx.doi.org/10.1088/1742-6596/2057/1/012079.

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Abstract The primary focus of this paper is to investigate the interaction between simultaneously propagating multiple fractures, initiated from an inclined well. In particular, the aim is to better understand the influence of the well inclination angle on the stress shadow between the fractures and on the overall resulting geometry of individual cracks. To simplify the analysis, the paper assumes the limit of large perforation friction, which leads to a uniform flux distribution between the fractures. The mathematical model for multiple hydraulic fractures is constructed by coupling together

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Kozhevnikova, P., P. Kovalenko, S. Glukhova, I. Dydykina, and A. Lila. "POS1108 THE ACCURACY OF OSTEOPOROTIC FRACTURE RISK PREDICTION IN PATIENTS WITH RHEUMATOID ARTHRITIS USING THE PREDICTIVE MODEL DEVELOPED AT V.A. NASONOVA REASEARCH INSTITUTE OF RHEUMATOLOGY (RUSSIA) AND FRACTURE RISK ASSESSMENT TOOL (FRAX)." Annals of the Rheumatic Diseases 80, Suppl 1 (2021): 834.2–835. http://dx.doi.org/10.1136/annrheumdis-2021-eular.1717.

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Background:FRAX is a computer-based algorithm that calculates the 10-year probability of a major osteoporotic fracture and the 10-year probability of hip fracture. However, FRAX has several limitations in assessing the risk of fracture in patients with rheumatoid arthritis (RA).In 2013 V.A. Nasonova Reasearch Institute of Rheumatology (Russia) developed a predictive mathematical model for assessing the risk of osteoporotic fractures in RA, which includes 2 main risk factors: cumulative glucocorticoid dose (GC), decrease in BMD in the femoral neck to osteoporosis, and 2 additional factors: for

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Li, Kewen, Yuanping Gao, Youchang Lyu, and Man Wang. "New Mathematical Models for Calculating Proppant Embedment and Fracture Conductivity." SPE Journal 20, no. 03 (2015): 496–507. http://dx.doi.org/10.2118/155954-pa.

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Summary Proppant embedment plays a significant role in decreasing fracture aperture and conductivity, especially for weakly consolidated sandstones, shale (oil and gas) rock, and coalbeds. Empirical and semiempirical models were usually used to calculate the embedment of proppants. However, the accuracy of matching or predicting the proppant embedment with these existing models may not be satisfactory in some cases. On the other hand, it is difficult to determine the coefficients of these models. In this study, analytical models were derived to compute proppant embedment and fracture conductiv

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Krupin, K. N., M. A. Kislov, V. I. Bahmetev, and E. M. Kildyushov. "Mathematical Modeling and Visualization of a Complex Stress State in Case of a Fracture of the Femoral Diaphysis." Scientific Visualization 16, no. 1 (2024): 112–23. http://dx.doi.org/10.26583/sv.16.1.10.

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The purpose of this work is to establish the possibility of using the finite element analysis method to study complex stress states in case of a femur fracture with subsequent data visualization. Experimental data were obtained on a solid-state mathematical parametric model of the femur, created on the basis of computer tomogram data, and repeating studies on native biological objects. As a result of mathematical modeling, oblique transverse and helical fractures of the diaphysis of the femur with elements of helical deformation were studied. The application of finite element analysis made it

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HUANG, NA, RICHENG LIU, and YUJING JIANG. "EVALUATING THE EFFECT OF APERTURE VARIATION ON THE HYDRAULIC PROPERTIES OF THE THREE-DIMENSIONAL FRACTAL-LIKE TREE NETWORK MODEL." Fractals 28, no. 06 (2020): 2050112. http://dx.doi.org/10.1142/s0218348x20501121.

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Hydraulic properties of rock fractures are important issues for many geoengineering practices. Previous studies have revealed that natural rock fractures have variable apertures that could significantly influence the permeability of single rock fractures, yet the effect of aperture variation on the hydraulic properties of fractured rock masses has received little attention. The present study implemented a series of flow calculations on two kinds of 3D fractal-like tree network models constituted by fractures with heterogeneous aperture distributions and parallel plates with uniform apertures t

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Han, Lili, Yanyan Li, Wei Hu, et al. "Numerical Study on Hydraulic Fracture Propagation in a Layered Continental Shale Reservoir." Energies 15, no. 23 (2022): 8840. http://dx.doi.org/10.3390/en15238840.

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The distribution of beddings varies greatly in shale reservoirs. The influence of beddings on hydraulic fracture propagation has often been studied using simplified geological models, i.e., uniformly distributed bedding models. However, the propagation processes of hydraulic fractures in shale reservoirs with complicated distributed beddings remains unclear. In this research, an outcrop-data-based bedding model of a continental shale formation in the Ordos Basin, China, is built. A mathematical model for fracture propagation is built using the discrete element method and is then verified by a

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Delprete, C., and M. M. Gola. "Mechanical Performance of External Fixators With Wires for the Treatment of Bone Fractures—Part I: Load-Displacement Behavior." Journal of Biomechanical Engineering 115, no. 1 (1993): 29–36. http://dx.doi.org/10.1115/1.2895467.

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Using matrix algebra, a mathematical model is formulated for a particular type of external fixator with wires (system developed by Ilizarov) for the treatment of bone fractures. The mathematical model is used to give a linear estimate of the stiffness under lateral and axial loads in a representative number of practical conditions. Relative displacements of the bone ends at the fracture site are calculated not only in the common case of a gap, but also for various angles of inclined sliding contact; in this case, a realistic load is applied and nonlinear stiffening of the wires under transvers

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Fyodorov, Konstantin M., Aleksandr P. Shevelev, Aleksandr Ya Gil’manov, Aleksey A. Izotov, and Aleksandr V. Kobyashev. "A NEW APPROACH FOR MODELING THE DEVELOPMENT OF INJECTION-INDUCED HYDRAULIC FRACTURES." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 91 (2024): 125–40. http://dx.doi.org/10.17223/19988621/91/11.

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A new approach for modeling the development of injection-induced hydraulic fractures is proposed in this paper. The fracture is assumed to be elliptical in the crosssection. The initial fracture length is determined by the mass conservation law and Darcy's law. A quasi-stationary mathematical model of injection-induced hydraulic fracture growth is based on the specification of two characteristic areas of the fracture: in the first, the dispersed particles settle down near the boundaries of the developed fracture; in the second, the fracture expands with the retarded motion of the suspension fr

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Wang, Guiqin, Rui Zhang, and Liangliang Cui. "Transient Pressure Behavior of a Horizontal Well in a Naturally Fractured Gas Reservoir with Dual-Permeability Flow and Stress Sensitivity Effect." Geofluids 2022 (April 30, 2022): 1–11. http://dx.doi.org/10.1155/2022/5993701.

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Dual-permeability flow and stress sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for horizontal wells. However, few attempts have been made to simulate the combined effects of dual-permeability flow and stress-dependent fracture permeability on the pressure transient dynamics of a horizontal well in a naturally fractured gas reservoir. In this approach, an analytical model is proposed to integrate the complexities of pressure-dependent PVT properties, dual-permeability flow behavior, and stress-dependent fracture permeability cha

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Li, J., S. J. Feng, and Q. T. Zheng. "Simulation of microbial transport and petroleum hydrocarbon compound biodegradation in a fracture–matrix coupled system." IOP Conference Series: Earth and Environmental Science 1335, no. 1 (2024): 012025. http://dx.doi.org/10.1088/1755-1315/1335/1/012025.

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Abstract In-situ bioremediation technology is considered an ideal and environment-friendly approach for the largescale treatment of petroleum-contaminated soil. Most earlier studies on bioremediation have focused on the biostimulation techniques, which can enhance the biodegradation capabilities of indigenous bacteria, rather than on bioaugmentation involving the introduction of exogenous microorganisms. Additionally, contaminated soil sites typically contain both natural and artificial fractures. These fractures serve as preferential transport pathways, complicating the transport of bacteria

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Dou, Bin, Hui Gao, Gang Zhou, and Lei Ren. "Numerical Simulation of Heat Transfer from Hot Dry Rock to Water Flowing through a Circulation Fracture." Advanced Materials Research 852 (January 2014): 831–34. http://dx.doi.org/10.4028/www.scientific.net/amr.852.831.

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This paper presents an advanced computational modeling of natural fracture networks in hot dry rock (HDR) reservoirs. A mathematical model is developed for describing the heat energy extracted from a HDR in a multi-well system. The model stochastically simulates discrete properties of natural fractures, utilizing multi-set orientation and fractal mathematics. The simulated fracture networks are essential for further stimulation and fluid flow studies. The results show that the heat extraction effectiveness is affected significantly by the well spacing, well radius, reservoir thickness, and pum

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Weijermars, Ruud, and Aadi Khanal. "Flow in Fractured Porous Media Modeled in Closed-Form: Augmentation of Prior Solution and Side-Stepping Inconvenient Branch Cut Locations." Fluids 5, no. 2 (2020): 51. http://dx.doi.org/10.3390/fluids5020051.

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Carefully chosen complex variable formulations can solve flow in fractured porous media. Such a calculus approach is attractive, because the gridless method allows for fast, high-resolution model results. Previously developed complex potentials to describe flow in porous media with discrete heterogeneities such as natural fractures can be modified to expand the accuracy of the solution range. The prior solution became increasingly inaccurate for flows with fractures oriented at larger angles with respect to the far-field flow. The modified solution, presented here, based on complex analysis me

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Guk, Vyacheslav, Mikhail Tuzovskiy, Don Wolcott, and Joe Mach. "Optimizing the Number of Fractures in a Horizontal Well." SPE Journal 24, no. 03 (2019): 1364–77. http://dx.doi.org/10.2118/174772-pa.

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Summary Horizontal wells with multiple hydraulic fractures have become a standard completion for the development of tight oil and gas reservoirs. Successful optimization of multiple-fracture design on horizontal wells began empirically in the Barnett Shale in the late 1990s (Steward 2013; Gertner 2013). More recently, research has focused on further improving fracturing performance by developing a model-derived optimum. Some researchers have focused on an economic optimum on the basis of multiple runs of an analytical or numerical model (Zhang et al. 2012; Saputelli et al. 2014). With such an

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Bortolan Neto, Luiz, Aditya Khanna, and Andrei Kotousov. "A new approach to evaluate the performance of partially propped hydraulic fractures." APPEA Journal 53, no. 1 (2013): 355. http://dx.doi.org/10.1071/aj12030.

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A new approach for evaluating the performance of hydraulic fractures that are partially packed with proppant (propping agent) particles is presented. The residual opening of the partially propped fracture is determined as a function of the initial fracture geometry, the propped length of the fracture, the compressive rock stresses, the elastic properties of the rock, and the compressibility of the proppant pack. A mathematical model for fluid flow towards the fracture is developed, which incorporates the effects of the residual opening profile of the fracture and the high conductivity of the u

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Khanna, Aditya, and Andrei Kotousov. "Controlling the Height of Multiple Hydraulic Fractures in Layered Media." SPE Journal 21, no. 01 (2016): 256–63. http://dx.doi.org/10.2118/176017-pa.

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Summary Fracture-height containment is desirable in hydraulic-fracturing treatments because it can result in better efficiency of oil or gas recovery and have less impact on the environment. Several mechanisms of the containment of a single hydraulic fracture were investigated in the past, and the outcomes of these studies are now well-documented in the open literature. However, the effectiveness of these mechanisms in the case of multiple closely spaced hydraulic fractures has not received much attention. The latter situation typically arises in the case of multiple transverse fractures emana

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