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