对比研究KGD、PKN与改进的P3D模型
A Comparative Analysis of KGD, PKN, and a Modified P3D Model
DOI: 10.12677/AAM.2023.1211448, PDF,   
作者: 刘广涛：数学地质四川省重点实验室，成都理工大学，四川 成都
关键词: PKN；KGD；二维断裂模型；改进的P3D断裂模型；椭圆断裂；PKN； KGD； 2-Dimensional Fracture Model； Improved P3D Fracture Model； Elliptic Fracture
摘要: 本文的目的是表征一个裂缝在特定时间的生长到其最终形状。对设计早期水力裂缝的二维模型KGD和模型PKN进行了分析、比较，并求解。并对P3D三维模型进行了修正，给出了真实的三维结果。通过假设裂缝的椭圆生长而不是圆形生长，产生了更真实的结果。特别要注意的是，由于断裂而形成的椭圆轨迹的参数在任何时刻都是变化的，这意味着在特定时间内的断裂轨迹，也不能用一个简单的数学方程来描述。使用MATLAB进行编程得出KGD、PKN和改进的P3D模型，并展示可视化后的结果。
Abstract: The paper is aiming to represent the growth of a fracture to its final shape at a specific time. 2D models i.e. KGD and PKN which most of the early hydraulic fractures were designed by applying one of these models were analyzed, compared and their equations solved. Moreover a P3D model is modified to give true 3D results. By assuming elliptical growth of the fracture and not the circular growth, a more realistic results generated. It is prudent to notice that the elliptic behavior which the fracture growing is representing has changing parameters at any moment, means the growth of a fracture in a specific period of time even in its simplest form does not obey a simple mathematical equation. Programming using MATLAB to derive KGD, PKN and improved P3D models and display visualized results.
文章引用：刘广涛. 对比研究KGD、PKN与改进的P3D模型[J]. 应用数学进展, 2023, 12(11): 4570-4579. https://doi.org/10.12677/AAM.2023.1211448

参考文献

[1] Eaton, D.W. and Schultz, R. (2018) Increased Likelihood of Induced Seismicity in Highly Overpressured Shale For-mations. Geophysical Journal International, 214,751-757. [Google Scholar] [CrossRef] 
[2] Schultz, R., Stern, V., Novakovic, M., Atkinson, G. and Gu, Y.J. (2015) Hydraulic Fracturing and the Crooked Lake Sequences: In-sights Gleaned from Regional Seismic Networks. Geophysical Research Letters, 42, 2750-2758. [Google Scholar] [CrossRef] 
[3] Schultz, R., Wang, R.J., Gu, Y.J., Haug, K. and Atkinson, G. (2017) A Seismological Overview of the Induced Earthquakes in the Duvernay Play Near Fox Creek, Alberta. Journal of Geo-physical Research: Solid Earth, 122, 492-505. [Google Scholar] [CrossRef] 
[4] 惠钢, 陈胜男, 顾斐. 流体-地质力学耦合建模表征水力压裂诱发地震: 以加拿大Fox Creek地区为例[J]. 地球物理学报, 2021, 64(3): 864-875.
[5] Hui, G., Chen, S.N., Chen, Z.X. and Gu, F. (2021) An Integrated Approach to Characterize Hydraulic Fracturing-Induced Seismicity in Shale Reservoirs. Journal of Petroleum Science and Engineering, 196, Article ID: 107624. [Google Scholar] [CrossRef] 
[6] Settari, A. and Cleary, M.P. (1986) Development and Testing of a Pseudo-Three-Dimensional Model of Hydraulic Fracture Geometry. SPE Production Engineering, 1, 449-466. [Google Scholar] [CrossRef] 
[7] Xu, J.X., Ding, Y.H., Yang, L.F., Liu, Z., Gao, R., Yang, H.X. and Wang, Z. (2019) Effect of Proppant Deformation and Embedment on Fracture Conductivity after Fracturing Fluid Loss. Journal of Natural Gas Science and Engineering, 71, Article ID: 102986. [Google Scholar] [CrossRef] 
[8] 潘英. 矿山提升机械设计[M]. 徐州: 中国矿业大学出版社, 2001.
[9] 王志甫. 矿山固定机械与运输设备[M]. 徐州: 中国矿业大学出版社, 2006.
[10] 于励民, 仵自连. 矿山固定设备选型使用手册(下册) [M]. 北京: 煤炭工业出版社, 2007.
[11] Zeng, Q.L., Liu, Z.L., Xu, D.D. and Zhuang, Z. (2014) Modeling Stationary and Moving Cracks in Shells by X-FEM with CB Shell Elements. Science China Technological Sciences, 57, 1276-1284. [Google Scholar] [CrossRef] 
[12] 景东阳, 李治平, 赵晓红, 等. 致密薄互层水力压裂裂缝垂面扩展施工因素数值模拟[J]. 科学技术与工程, 2023, 23(14): 5988-5994.
[13] 李小波, 史英, 张修明, 等. 水力压裂裂缝模拟研究[J]. 西安石油大学学报(自然科学版), 2009, 24(3): 52-55.
[14] 魏海峰. 非均质性页岩水力压裂裂缝扩展形态研究进展[J]. 油气地质与采收率, 2023, 30(4): 156-166.
[15] Warpinski, N.R., Abou-Sayed, I.S., Moschovidis, Z. and Parker, C. (1993) Hydraulic Fracture Model Comparison Study: Complete Results. Technical Re-port.
[16] Esfandiari, M. and Pak, A. (2023) XFEM Modeling of the Effect of in-Situ Stresses on Hydraulic Fracture Characteristics and Comparison with KGD and PKN Models. Journal of Petroleum Exploration and Production Tech-nology, 13, 185-201. [Google Scholar] [CrossRef] 
[17] Haddad, M. and Eichhubl, P. (2020) Poro-elastic Models for Fault Reactivation in Response to Concurrent Injection and Production in Stacked Reservoirs. Geo-mechanics for Energy and the Environment, 24, Article ID: 100181. [Google Scholar] [CrossRef] 
[18] Qu, Z.Q., Wang, J.W., Guo, T.K., Shen, L., Liao, H.L., Liu, X.Q., Fan, J.C. and Hao, T. (2021) Optimization on Fracturing Fluid Flowback Model after Hydraulic Fracturing in Oil Well. Journal of Petroleum Science and Engineering, 204, Article ID: 108703. [Google Scholar] [CrossRef] 
[19] Gao, F.Q., Stead, D. and Kang, H.P. (2015) Numerical Simula-tion of Squeezing Failure in a Coal Mine Roadway Due to Mining-Induced Stresses. Rock Mechanics and Rock Engi-neering, 48, 1635-1645. [Google Scholar] [CrossRef] 
[20] Guo, J.C., Luo, B., Lu, C., Lai, J. and Ren, J.C. (2017) Numerical Investigation of Hydraulic Fracture Propagation in a Layered Reservoir Using the Cohesive Zone Method. Engineering Fracture Mechanics, 186, 195-207. [Google Scholar] [CrossRef] 
[21] Bakhshi, E., Rasouli, V., Ghorbani, A., Marji, M.F., Damjanac, B. and Wan, X. (2019) Lattice Numerical Simulations of Lab-Scale Hydraulic Fracture and Natural Interface Interaction. Rock Mechanics and Rock Engineering, 52, 1315- 1337. [Google Scholar] [CrossRef] 

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