Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background  

作　　者：Zheng-Qian Ma Xing-Yao Yin Zhao-Yun Zong Yuan-Yuan Tan Ya-Ming Yang 

机构地区：[1]National Key Laboratory of Deep Oil and Gas,China University of Petroleum(East China),Qingdao,266580,Shandong,China [2]School of Geosciences,China University of Petroleum(East China),Qingdao 266580,Shandong,China [3]Pilot National Laboratory for Marine Science and Technology(Qingdao),Qingdao,266200,Shandong,China

出　　处：《Petroleum Science》2024年第1期221-243,共23页石油科学（英文版）

基　　金：We would like to acknowledge all the reviewers and editors and the sponsorship of National Natural Science Foundation of China(42030103);the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(2021QNLM020001-6);the Laoshan National Laboratory of Science and Technology Foundation(LSKJ202203400).

摘　　要：Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

关 键 词：Effective elastic property Tilted crack Transverse isotropy Analytical solution Crack opening displacement 

分 类 号：TE31[石油与天然气工程—油气田开发工程]