Development of an Orthotropic 3D Elastoplastic Material Model for Shale

Abstract

Abstract Shales encountered in the overburden above hydrocarbon reservoirs often pose challenges to the stability of boreholes.Consequently, there is a keen interest in borehole stability prediction, which is complicated by the laminated structure of shale that arises as a consequence of the depositional environment. A combined experimental/numerical investigation is being undertaken to address how the directional properties of shale impact borehole stability in weak shale formations.Within this paper an advanced finite element procedure for simulation of progressive damage of orthotropic pressure-sensitive materials is presented, which includes bifurcation and post-bifurcation analysis.This constitutive model is based on critical state theory and is specifically designed to represent the characteristic deformation of weak shale formations. It includes orthotropic elasticity and an orthotropic pressure-dependent yield surface that is curved in the p-q plane, and which intercepts the hydrostatic axis in both tension and compression. A regularization procedure is also presented that ensures mesh invariance and correctly reproduces the dependence of strength on the size of the test specimen. Calibration of the model parameters is also discussed and the model is validated by comparison with the results of uniaxial and triaxial compression tests for Pierre I Shale performed at different bedding plane orientations. Introduction Despite significant advances in prediction in recent years, wellbore instability can still occur in shales during drilling. While instability in homogeneous shales can largely be avoided by using an adequate mud weight, attention is now focusing on predicting instability in shales with a more pronounced ‘fabric’ or fissile character. This anisotropy in mechanical and strength properties is usually neglected in conventional analyses. However, shales usually possess a laminated structure as a consequence of the depositional environment, and therefore exhibit a directional variation in elastic properties, yield strength and post-yield behaviour. Conventional approaches - assuming transverse isotropic elastic properties with isotropic failure surfaces - are typically unable to properly reproduce the complex yield and deformation behaviour of these materials.This deficiency is most pronounced in highly laminated and fissile shales, which are the most likely to cause drilling problems. The low permeability of shale may also complicate the stability assessment by necessitating a coupled poroelastic formulation. Extensive research has been carried out on the formulation of appropriate failure criteria for orthotropic and transversely isotropic materials, see [4] for a recent review. Early work focused on empirical failure criteria that account for the continuous variation of compressive strength with orientation for transversely isotropic rock [5,6]. Subsequently Tsai and Wu [7] and Pariseau [8] extended Hill's criterion [9] for orthotropic metal plasticity to pressure sensitive materials, and Ong and Roegiers [10] employed these theories in horizontal wellbore stability predictions. Nova [11] proposed a generalised failure condition that describes failure of transversely isotropic rocks in compression and Nova and Zaninetti [12] established a failure criterion in tension based on similar concepts. Cazacu and Critescu [13] show that an anisotropic Mises-Schleicher (AMS) criterion can accurately fit the failure strength for transversely isotropic rocks, including the directional character of transversely isotropic materials under general loading conditions, and the dependence on the intermediate principal stress.