Analytical solutions for an extended overcore stress measurement method based on a thermo-poro-elastic analysis

Abstract A theoretical generalized plane-strain thermo-poro-elastic (THM) wellbore model is developed for application to the conventional overcore stress measurement method, under the situations when the thermal effect cannot be decoupled from the measured strains on the borehole walls. The THM theory developed by Coussy is used to describe the effects of both the pore pressure and the temperature on the stress and strain distributions around an inclined wellbore, which is assumed to be drilled instantly and subjected to initial stresses with arbitrary directions. The Laplace transformation is used to obtain the temperature, pressure, displacement, strain and stresses in the three-dimensional state around the wellbore. As special cases, the solutions of the above field variables are also provided for the poro-elastic (HM), thermo-elastic (TM) and pure elastic (CM) cases. Based on the THM solutions obtained, the stresses at the borehole wall, which vary with time, provide a bridge to find the in situ stresses from the measured strains at the wellbore surface. In this THM overcore stress measurement method, the temperature and the pressure (if a fluid is present) at the wellbore wall are another two parameters that need to be measured for stress inversion.

[1]  Robert G. Jeffrey,et al.  A semi-analytic solution of a wellbore in a non-isothermal low-permeability porous medium under non-hydrostatic stresses , 2012 .

[2]  Marcel Crochet,et al.  ON CONSTITUTIVE EQUATIONS FOR FLOW OF FLUID THROUGH AN ELASTIC SOLID. , 1966 .

[3]  N. Cook,et al.  Analysis of borehole breakouts , 1989 .

[4]  P. A. Domenico,et al.  Characterization of drained and undrained response of thermally loaded repository rocks , 1982 .

[5]  Younane N. Abousleiman,et al.  Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium , 2005 .

[6]  Y. Abousleiman,et al.  Poroelastic solutions in transversely isotropic media for wellbore and cylinder , 1998 .

[7]  J. Sherwood,et al.  Swelling of shale around a cylindrical wellbore , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[8]  Y. Abousleiman,et al.  Poromechanics Response of Inclined Wellbore Geometry in Chemically Active Fractured Porous Media , 2009 .

[9]  R. Ewy,et al.  Thermoporoelastic Effect on Wellbore Stability , 2005 .

[10]  X. Li,et al.  Stress and displacement fields around a deep circular tunnel with partial sealing , 1999 .

[11]  Jean-Herve Prevost,et al.  Thermoporoelastic response of a fluid-saturated porous sphere: An analytical solution , 2011 .

[12]  D. F. McTigue,et al.  Thermoelastic response of fluid‐saturated porous rock , 1986 .

[13]  S. Shadizadeh,et al.  A transient fully coupled thermo-poroelastic finite element analysis of wellbore stability , 2015, Arabian Journal of Geosciences.

[14]  Olivier Coussy,et al.  A general theory of thermoporoelastoplasticity for saturated porous materials , 1989 .

[15]  E. R. Leeman,et al.  A Technique For Determining the Complete State of Stress In Rock Using a Single Borehole , 1966 .

[16]  Mark D. Zoback,et al.  Compressive and tensile failure of inclined well bores and determination of in situ stress and rock strength , 1995 .

[17]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[18]  Y. Abousleiman,et al.  Poromechanics Response of Inclined Wellbore Geometry in Fractured Porous Media , 2005 .

[19]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[20]  D. Mctigue.  Flow to a heated borehole in porous, thermoelastic rock: Analysis , 1990 .

[21]  N. Cook,et al.  BOREHOLE BREAKOUT AND STRESS MEASUREMENTS , 1988 .

[22]  J. P. Henry,et al.  Laboratory investigation of the mechanical behaviour of Tournemire shale , 1997 .

[23]  Euripides Papamichos,et al.  THERMAL EFFECTS ON FLUID FLOW AND HYDRAULIC FRACTURING FROM WELLBORES AND CAVITIES IN LOW?PERMEABILITY FORMATIONS , 1999 .

[24]  M. Biot.  General solutions of the equations of elasticity and consolidation for a porous material , 1956 .

[25]  Larry G. Mastin,et al.  Well bore breakouts and in situ stress , 1985 .

[26]  Harald Stehfest,et al.  Remark on algorithm 368: Numerical inversion of Laplace transforms , 1970, CACM.

[27]  R.K.N.D. Rajapakse,et al.  Coupled consolidation of a porous medium with a cylindrical or a spherical cavity , 1998 .

[28]  Bernt S. Aadnøy,et al.  STABILITY OF HIGHLY INCLINED BOREHOLES. , 1987 .

[29]  Euripides Papamichos,et al.  Conductive heat flow and thermally induced fluid flow around a well bore in a poroelastic medium , 1994 .

[30]  Yukitoshi Oka,et al.  Determination of the stress in rock unaffected by boreholes or drifts, from measured strains or deformations , 1968 .

[31]  A. Cheng,et al.  Fundamentals of Poroelasticity , 1993 .

[32]  F. J. Santarelli,et al.  Analysis of Borehole stresses using pressure-dependent, linear elasticity , 1986 .

[33]  D. Ask.  Measurement-related uncertainties in overcoring data at the Äspö HRL, Sweden. Part 2: Biaxial tests of CSIRO HI overcore samples , 2006 .

[34]  John P. Carter,et al.  Elastic consolidation around a deep circular tunnel , 1981 .

[35]  A. Cheng,et al.  Poroelastic Solution for an Inclined Borehole , 1997 .

[36]  W. B. Bradley.  Failure of Inclined Boreholes , 1979 .

[37]  Per Horsrud,et al.  Sand Stresses Around a Wellbore , 1982 .

[38]  Guangjing Chen,et al.  Consolidation around a tunnel in a general poroelastic medium under anisotropic initial stress conditions , 2015 .

[39]  Musharraf Zaman,et al.  Applications of time-dependent pseudo-3D stress analysis in evaluating wellbore stability , 1997 .

[40]  Emmanuel M Detournay,et al.  Poroelastic response of a borehole in a non-hydrostatic stress field , 1988 .

[41]  R. Rajapakse,et al.  Stress Analysis of Borehole in Poroelastic Medium , 1993 .

[42]  Michio Kurashige,et al.  A thermoelastic theory of fluid-filled porous materials , 1989 .

[43]  Y. Abousleiman,et al.  Porochemothermoelastic Solution for an Inclined Borehole in a Transversely Isotropic Formation , 2005 .

[44]  Maurice B. Dusseault,et al.  A coupled conductive–convective thermo-poroelastic solution and implications for wellbore stability , 2003 .

[45]  H. Jalalifar,et al.  Analysis of vertical, horizontal and deviated wellbores stability by analytical and numerical methods , 2014, Journal of Petroleum Exploration and Production Technology.

[46]  E. R. Leeman.  The determination of the complete state of stress in rock in a single borehole—Laboratory and underground measurements , 1968 .

[47]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[48]  Y. Hiramatsu,et al.  Stress around a shaft or level excavated in ground with a three-dimensional stress state. , 1962 .

[49]  Musharraf Zaman,et al.  ANALYSES OF INCLINED BOREHOLES IN POROELASTIC MEDIA , 2004 .