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Research Papers

Cylindrical Borehole Failure in a Transversely Isotropic Poroelastic Medium

[+] Author and Article Information
Yue Gao, Zhanli Liu

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Zhuo Zhuang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: zhuangz@tsinghua.edu.cn

Deli Gao

MOE Key Laboratory of Petroleum Engineering,
China University of Petroleum,
Beijing 102249, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Keh-Chih Hwang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: huangkz@tsinghua.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 22, 2017; final manuscript received September 10, 2017; published online September 26, 2017. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 84(11), 111008 (Sep 26, 2017) (17 pages) Paper No: JAM-17-1395; doi: 10.1115/1.4037880 History: Received July 22, 2017; Revised September 10, 2017

Rocks underground often have pores and bedding planes, which are appropriate to be described by the transversely isotropic poroelastic constitutive model. Drilling boreholes in these rocks must be careful, since stresses and pore pressure would change with time, because of the inherent time dependent property of poroelasticity as well as pore fluid diffusion. In order to correlate the behavior of transversely isotropic poroelastic model of borehole in plane strain with the behavior of isotropic poroelastic model, an equivalent isotropic material is built with carefully chosen material constants, and correlation rules are successfully developed. With the solutions for the borehole problem in an isotropic model obtained previously, the solutions to transversely isotropic model can be obtained. Two cases of tensile failure and six cases of shear failure for the borehole are considered. As a result, the allowable borehole working pressure range is formulated by explicit expressions. The failure case, time, and location could also be obtained for any given drilling pressure. Results obtained from the Hooke’s traditional elastic model are compared, and it is found that poroelastic model is necessary in borehole safety check, while Hooke’s model is not on the safe side.

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References

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Figures

Grahic Jump Location
Fig. 1

A schematic diagram of the borehole section

Grahic Jump Location
Fig. 2

Loading decomposition of the borehole problem

Grahic Jump Location
Fig. 3

Allowable borehole pressure for P0/σV∈[0,2]. Eight lines indicate the tensile and shear failure criteria, respectively. Different Poisson’s ratio off the isotropic plane are used: (i) ν′=0.2 and (ii) ν′=0.6.

Grahic Jump Location
Fig. 4

Comparison of allowable borehole pressure regions obtained by (i) Hooke’s elastic model, and (ii) Biot’s poroelastic model, with the same in situ stresses. The criterion (2) is absent in Hooke’s model due to the absence of pw in Eq. (111).

Grahic Jump Location
Fig. 5

Numerical results to be checked on the Mohr plane for case (a). Six curved lines denote different time story with respect to dimensionless time t* from 10−5 to 100. Every point in a curve denotes a specific point in the rock, from the borehole boundary (r = a, the upper right end of each curve in the figure), to infinity (r→∞, bottom left end, dot D). Any point above the Mohr–Coulomb criterion, i.e., the straight line on the upper side of the figure, will lead to the shear failure on the horizontal plane, which is described in Sec. 8.1. Two examples are given in this figure, which have the same loading conditions and the same material constants, but a different ν′ only, where (i) ν′=0.246, and the borehole is in the critical shear failure state; (ii) ν′=0.4, and the borehole is far away from shear failure. Two dashed lines indicate the whole domain solutions, respectively, for the instantaneous solution (t=0+, Eq. (62)) and the long-time solution (t→∞, Eq.(63)). The elastic solution does not touch M–C criterion in the two examples, while the poroelastic result in (i) shows that the shear failure would occur near the borehole boundary at a very short time (r≈a, t≈0+). Therefore, for a poroelastic medium, the safety check based on the poroelasticity is necessary, instead of the traditional Hooke’s elastic model.

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