The effects of pore pressure penetration and time-dependent rock strength on the growth of the yielded (plastic) zone around a wellbore are analyzed using an elastic-brittle-plastic model. Solutions for two possible cases are developed: (1) no increase in permeability, and (2) a significant increase in permeability upon yielding. The extent of the yielded zone is sensitive to a number of mechanical parameters, of which the residual strength of the rock is most critical. In both cases, the rate of yielded zone growth depends strongly on formation permeability (both prior to and after yielding) and mud filtrate viscosity. In case (2), the stiffness of the rock and the extent of the yielded zone are also critical.
Wellbore instability in shales is one of the more important problems experienced during drilling. Although the potential destabilizing effects of clay hydration and swelling have long been known and accepted, it is now recognized that wellbore instability in shale sections is also strongly dependent on mechanical parameters, i.e. the state of effective stress around the wellbore and the strength of the shale. The following discussion describes the mechanical factors affecting wellbore stability. Hydration effects are only considered indirectly, as they may affect the strength of the rock.
A number of non-linear wellbore stability models have previously been developed. These include damage mechanics models (e.g. Cheng and Dusseault 1993, Shao and Khazrai 1994), bifurcation models (e.g. Papamichos et al. 1994), non- continuum models (e.g. Thallak et al. 1991, Rawlings et al. 1993), linear elastic borehole breakout models (e.g. Zheng et al. 1989), strain- hardening elastoplastic models (e.g. Bradford and Cook 1994) and strain-weakening, elastic-brittle- plastic models (e.g. Ladanyi 1974, Kennedy and Lindberg 1978, Wang and Dusseault 1991). The defining feature of the elastic-brittle-plastic model is the assumption that, once a rock's peak compressive strength has been exceeded as stresses around the wellbore increase during excavation, the rock yields but does not fall into the wellbore. Instead, an annulus of weakened rock (referred to as the yielded or plastic zone) develops around the well, peak stress is redistributed away from the wellbore surface, and eventually a stable configuration is achieved (Figure 1). Since the yielded zone will be susceptible to spalling due to pressure surges during trips and mechanical erosion by the drillstring, the larger this zone is the greater the likelihood that instability-related problems will occur. In order to develop a closed-form solution to this problem, it necessary to make a number of assumptions concerning the mechanical behaviour of the rock. Firstly, it is assumed that deformation is linear elastic until peak stress is reached, then strain weakening occurs instantaneously and stress is reduced to a residual level (Figure 2). It is also assumed that peak and residual strength of the rock can be represented by linear Mohr-Coulomb criteria, plane strain conditions prevail, the material is homogeneous and isotropic, and boundary stresses are uniform so that the problem is axisymmetric.
