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228    Reservoir geomechanics


              used variations of the occurrence of breakouts (as indicated by wellbore spalling) with
              changes in mud weight to make an estimate of the maximum horizontal stress, after first
              constraining the other parameters associated with wellbore failure as described above.
              While no detailed observations of the shape of breakouts were available to them, the
              approach they used was fundamentally similar to that described above.



              Drilling-induced tensile fractures and the magnitude of S  Hmax


              As discussed in Chapter 6, drilling-induced tensile fractures occur in vertical wells
              whenever there is a significant difference between the two horizontal stresses. From
              equation (6.8), it can easily be shown that the condition for tensile fracture formation
              in the wellbore wall in a vertical well leads to
                                                
T
              S Hmax = 3S hmin − 2P p − 
P − T 0 − σ                              (7.8)
              As mentioned in Chapter 6,itis straightforward to show that the conditions for the
              occurrence of drilling-induced tensile fractures (the light diagonal line in Figure 7.10)
              around a vertical wellbore are essentially the same as the values of S hmin and S Hmax
              associated with a strike-slip faulting regime in frictional equilibrium (the upper left
              periphery of the polygon). Following the logic used in the discussion of wellbore
              breakouts, the value of S Hmax required to explain the occurrence of drilling induced
              tensile fractures in the well considered in Figure 7.10 requires a value of S Hmax to be
              approximately 130 MPa. A lower value of S Hmax would not have been sufficient for the
              tensile fractures to form. A higher value is not reasonable as it would imply a value of
              S Hmax that exceeds the frictional strength of the earth’s crust. Thus, the observations
              of breakout width and occurrence of tensile fractures in this well yield the same values
              of S Hmax (about 130 MPa) and indicate a strike-slip stress state in frictional equilibrium.
              Note that we assumed T 0 = 0in this analysis. As noted in Chapter 4, T 0 is always quite
              small (a few MPa, at most), so drilling-induced tensile fractures can initiate at small
              flaws on the wellbore wall and the influence of T 0 on the computed value of S Hmax
              (equation 7.8)is quite small (Figure 6.13). In Figure 7.5, the impact of a finite T 0 of
              2 MPa, for example, would be to shift the light-diagonal line down by that amount such
              that uncertainty in tensile strength has a comparable (but relatively very small) effect
              on the estimated value of S Hmax .
                Mud weights during drilling (i.e. that which correspond to the Equivalent Circulating
              Density, or ECD) above the pore pressure also encourage the formation of drilling-
              induced tensile fractures. Because of this, it is necessary to assure that the occurrence
              of drilling-induced tensile fractures is not significantly influenced by increases in mud
              pressure associated with such drilling activities as running in the hole (potentially
              resulting in a piston-induced increase in mud pressure at the bottom of the well),
              surges in mud pressure associated with wash and reaming operations or pack-off events
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