Page 209 - Applied Petroleum Geomechanics
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204   Applied Petroleum Geomechanics


             Therefore, Eq. (6.27) can be rewritten as follows:
                            n                      E
                     s h ¼     ðs V   ap p Þþ ap p þ   ðε h þ nε H Þ  (6.29)
                          1   n                  1   n 2
          where E is Young’s modulus of the rock; ε h and ε H are the tectonic strains
          or excess applied strains in the minimum and maximum horizontal stress
          directions, respectively. Eq. (6.29) can be derived from Hooke’s law (refer
          to Eq. (1.50) in Chapter 1 with thermal effect or Warpinski (1989)).
             To apply the above method the tectonic strains have to be obtained,
          which can be back-calculated either from in situ stress measurements or
          from calibrations of observed wellbore shear and tensile failures. Dolinar
          (2003) presented how to use the measured horizontal stress results to obtain
          the excess applied strain in mining areas for the eastern United States. He
          considered that the excess strains could be obtained from Eq. (6.29) after
          the effects of gravity (effect of Eq. 6.26) were removed from the measured
          horizontal stresses. The stress measurements were mainly obtained by
          overcoring method from 37 sites in the northern (7 sites) and central (19
          sites) Appalachian regions as well as from the eastern Mid-Continent region
          (11 sites) with the depths ranging from 275 to 2500 feet. Examining the
          excess strains obtained from the stress measurements indicates that for most
          of the eastern United States the maximum applied excess or tectonic strain
          (ε H ) ranges from 300 to 550 micro strains (Table 6.1). However, in a high
          strain zone in the central Appalachian region, the maximum applied tec-
          tonic strains range from 700 to 1000 micro strains.


          Table 6.1 Average excess applied horizontal strain by region for the eastern United
          States (Dolinar, 2003).
                                     Max.      Max. Strain  Min.    Strain
                            Number   Strain ε H  range     Strain ε h  ratio
                                                              6
                                         6
                                                   6
          Region            of sites  (10 )    (10 )       (10 )    ε H /ε h
          Northern           7       440       300e540     260      1.69
          Appalachian
          Central            7       370       300e480     170      2.17
          Appalachian: Low
          strain zone
          Central           12       760       550e970     410      1.85
          Appalachian: High
          strain zone
          Eastern Mid-      10       370       240e530      80      4.6
          Continent
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