Study on wellbore stability considering rock matrix and weak plane of porous shale subjected to polyaxial compression and different time-domain poroelastic solutions

Abstract

Deep hydrocarbon exploration of shale gas and oil resources meets weak planes (bedding, micro-fractures) with strong anisotropic strength compared to the rock matrix and the time-dependent borehole collapse during the drilling operation. These two factors consist of the internal control factor of frequent wellbore instability and seriously restrict the improvement of drilling quality and efficiency. Based on the fundamental theory of elastic mechanics, this work derives the weak plane strength criterion under polyaxial compression (three-dimensional stress), and the Mogi-Coulomb strength criterion is also introduced to evaluate the failure of the rock matrix. Primarily, one derives a strength expression depending on the dip angle and direction to assess the failure characteristics of the weak plane and reformulates the Mogi-Coulomb criterion to obtain the strength expression of the rock matrix in terms of intermediate and minimum principal stress loadings. These two strength expressions are expected to guide the experiment design and study the strength variation of laminated rock developed weak plane when the stress loading magnitude and direction are applied under polyaxial compression. Besides, to avoid the inversion operation after the Laplace transformation to the isotropic poroelastic solutions, one provides analytical poroelastic solutions for arbitrarily inclined boreholes, including five-time domains related to instantaneous, modified instantaneous, short-time, long-time, and time-independent elastic ones. Thus, the variation of the equivalent density of collapse pressure is analyzed considering the new strength criterion for the weak plane and different time-domain poroelastic solutions drilled through the shale formation. The apparent influence of intermediate principal stress on the rock matrix and weak plane shows that the strength of the rock matrix increases first and then decreases with the increasing intermediate principal stress. The strength of the weak plane does not change with the increasing intermediate principal stress where the applied direction of intermediate principal stress parallels the plane of the weak plane structure. Given intermediate principal stress, the failure angle range of the weak plane gradually increases with the increasing dip direction angle of the weak plane. Given a weak plane occurrence and the intermediate principal stress, the apparent strength of the rock increases with the increase of the minimum principal stress. The equivalent density magnitude of collapse pressure is arranged in descending order when short-time, modified instantaneous, long-time, instantaneous, and elastic solutions are adopted. Severe wellbore instability occurs at a larger angle between the wellbore axis line and the normal line of the weak plane. Studying the influence of three-dimensional stress on the strength of the weak plane and rock matrix is conducive to improving the prediction accuracy of collapse pressure equivalent density. It can help solve the problem of wellbore collapse in troublesome shale formations.