We address the theoretical possibility of drilling with mud weights in excess of the least principal stress for cases of particularly severe wellbore instability. Tensile fractures initiate at the wellbore wall at Pfrac, they link up to form large axial fracturesub-parallel to the wellbore axis at Plink,?, and they propagate away from the wellbore at Pgrow. In general, our modeling shows that Pfrac and Plink,? can be maximized by drilling the wellbore in an optimally stable orientation, and Pgrow,? can be maximized by using "non-invading" drilling muds, that is, those that prevent fluid pressure from reaching the fracture tip (i.e., if solids in the mud form bridges within the fracture).
In this paper we investigate theoretically the circumstances under which it may be possible to drill with mud weights in excess of the least principal stress in extreme drilling environments. To accomplish this we must avoid lost circulation due to the initiation and propagation of hydraulic fractures. We consider the case of an arbitraryoriented well with a perfect mud cake such that in the absence of hydraulic fracturing, no drilling fluids leave the wellbore. We consider a three fold strategy to increase, to the greatest degree possible, wellbore pressure during drilling. To accomplish this we utilize the facts that: (i) Wellbore pressure at fracture initiation varies with wellbore orientation, i.e., inclination and azimuth (Daneshy 1973, Hayashi et al. 1985, 1997, Peska & Zoback 1995). (ii) As deviated wells are generally not parallel to one of the principal stresses, multiple tensile fractures form at the wellbore wall in "en-echelon" pattern on opposite sides of the wellbore wall (Brudy & Zoback 1993). Wellbore pressure and wellbore orientation determine whether these multiple fractures link up or not (Weng 1993). (iii) When drilling with "high solids" water-based muds, pressures in the wellbore may not reach the fracture tip due to the narrow width of fracture and the bridging of solids within it (Black 1986, Fuh et al. 1992, Morita et al. 1996). Taking account of these facts, we show a theoretical model to estimate the critical pressures which dominate hydraulic fracture initiation and propagation. First, the pressure necessary to initiate fractures at the wellbore wall. Second, that required to link the inclined tensile fractures near the wellbore wall. Third, that required to extend the fracture unstably away from the wellbore. To the degree to which we can identify conditions which raise these pressures above the least principal stress, we can raise mud weights to deal with problems of extreme wellbore instability or in cases of extremely high pore pressure where the difference between the pore pressure and fracture gradient is quite small.