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246    Reservoir geomechanics



        a.                                   b.                   c.
           160                         180
                                                     ∆P = 0               ∆P = 15MPa
           140
                                   w
           120
           100
            80
           s min  60                s tmin
            40
            20
            0
           −20                          0
              0     90   q t  180  270   360         q t                  q t

               Figure 8.7. Theoretical illustration of the manner of formation of en echelon drilling-induced
               tensile fractures in a deviated well. (a) The fracture forms when σ tmin is tensile. The angle the
               fracture makes with the axis of the wellbore is defined by ω, which, like σ tmin varies around the
               wellbore. (b) The en echelon fractures form over the angular span θ t , where the wellbore wall is in
               tension. (c) Raising the mud weight causes the fractures to propagate over a wider range of angles
               because σ tmin is reduced around the wellbore’s circumference.



               grows, σ tmin becomes compressive. Raising the wellbore pressure (Figure 8.7c) allows
               the fracture to propagate further around the wellbore because the σ tmin is decreased
               by the amount of 
P, thus increasing the angular span (θ t ), where tensile stress are
               observed around the wellbore circumference.




               Confirming that S  Hmax  and S hmin  are principal stresses

               Drilling-induced tensile fractures were ubiquitous in the KTB pilot hole and main
               borehole. As mentioned above, along most of the well path, the tensile fractures are
               axial. As this is a near-vertical borehole, it indicates that there is a near-vertical principal
               stress. However, in a few sections of the wellbore, the state of stress is locally perturbed
               by slip on faults and is rotated away from a horizontal and vertical orientation (Brudy,
               Zoback et al. 1997). Over the entire depth interval studied in detail in the KTB boreholes
               (from ∼ 1kmto ∼8km depth), axial drilling-induced tensile fractures indicate that one
               principal stress is nearly always vertical and the cases where this is not true is limited
               to zones of locally anomalous stress (Brudy, Zoback et al. 1997). Near vertical drilling-
               induced tensile fractures were observed to ∼7km depth in the Siljan wells drilled
               in Sweden (Lund and Zoback 1999). A similar situation was encountered by Wiprut,
               Zoback et al.(2000) who documented both axial and en echelon fractures in a suite of
               five oil wells in the Visund field of the northern North Sea. While the stress field is well-
               characterized by a near-vertical and two horizontal principal stresses, there are zones
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