A transient fully coupled thermo-poroelastic finite element analysis of wellbore stability

Abstract

Stress variations around wellbores and in the reservoirs are of much interest in subsequent drilling operations, future production, and petroleum reservoir development. Stress variations induced by in situ stresses, pore pressure, and temperature changes during drilling operations may lead to various modes of instabilities in forms of induced fractures and borehole breakouts. Previous studies of thermally induced stresses were primarily based on either assumptions of heat conduction through rock matrix or heat convection, in this case, without considering the effect of solid grain thermal conductivity. To analyze wellbore stability, in the present work, a thermo-poro-mechanical model that is fully coupled to conductive and convective transport processes is employed. Then using a two-dimensional finite element method, the stress distribution around an open borehole is investigated. Further, four rock strength criteria, Mohr–Coulomb, Drucker–Prager, modified Lade, and Mogi–Coulomb, are used to examine wellbore stability of both vertical and inclined boreholes. Results show that there are considerable differences between radial and tangential stresses simulated from models containing coupled conductive and conductive-convective transport processes. Shear stress distribution around borehole, resulted from interaction of borehole inclination and in situ stresses, is found to be an important factor affecting stability conditions of inclined wellbore. In the case of rock failure criteria, Mohr–Coulomb results in the highest values of the minimum mud weight required for wellbore stability; Drucker–Prager gives the lowest values, modified Lade, and Mogi–Coulomb result in mean values for the minimum mud weight required for wellbore stability.

Appendix

$$ \begin{array}{l}X={\displaystyle \underset{\varOmega }{\int }{\varPi}^{\mathrm{T}} D\varPi d\varOmega}\hfill \\ {}{R}_1=-\alpha {\displaystyle \underset{\varOmega }{\int }{\varPi}^{\mathrm{T}} mNd\varOmega}\hfill \\ {}{R}_2=-{\displaystyle \underset{\varOmega }{\int }{\varPi}^{\mathrm{T}}K{\beta}_{\mathrm{s}} mNd\varOmega}\hfill \\ {}Q=\frac{k}{\mu}\left(-{\displaystyle \underset{\varOmega }{\int}\nabla {N}^{\mathrm{T}}\nabla Nd\varOmega}+{\displaystyle \underset{\mathrm{s}}{\int }{N}^{\mathrm{T}}\nabla N{n}_{\mathrm{i}} ds}\right)\hfill \\ {}{\varGamma}_1=-\beta {\displaystyle \underset{\varOmega }{\int }{N}^{\mathrm{T}} Nd\varOmega}\hfill \\ {}{\varGamma}_2=\alpha {\displaystyle \underset{\varOmega }{\int }{N}^{\mathrm{T}} mBNd\varOmega}\hfill \\ {}{\varGamma}_3=-{\beta}_{\mathrm{m}}{\displaystyle \underset{\varOmega }{\int }{N}^{\mathrm{T}} Nd\varOmega}\hfill \\ {}W=\frac{k_{\mathrm{m}}}{{\left(\mu c\right)}_{\mathrm{m}}}\left(-{\displaystyle \underset{\varOmega }{\int}\nabla {N}^{\mathrm{T}}\nabla Nd\varOmega}+{\displaystyle \underset{\mathrm{s}}{\int }{N}^{\mathrm{T}}\nabla N{n}_{\mathrm{i}} ds}\right)\hfill \\ {}{\varLambda}_1=-{\displaystyle \underset{\varOmega }{\int }{N}^{\mathrm{T}} Nd\varOmega}\hfill \\ {}{\varLambda}_1=-\frac{{\left(\rho c\right)}_{\mathrm{f}}}{{\left(\rho c\right)}_{\mathrm{m}}}v{\displaystyle \underset{\varOmega }{\int }{N}^{\mathrm{T}} Nd\varOmega}\hfill \end{array} $$