Page 36 - Applied Petroleum Geomechanics

26 Applied Petroleum Geomechanics

where a h and a V are Biot’s coefficients in the horizontal and vertical direc-
tions, respectively.
Eqs. (1.48) and (1.49) are similar to the ones presented by Thiercelin and
Plumb (1994), where they did not consider thermal effects. If E h ¼ E V ¼ E,
n h ¼ n V ¼ n, a h ¼ a V ¼ a, a Th ¼ a T , Eqs. (1.48) and (1.49) can be
simplified to the isotropic case, as follows:

n E Ea T
s h ¼ ðs V ap p Þþ ap p þ ðε h þ nε H Þþ DT (1.50)
1 n 1 n 2 1 n
n E Ea T
s H ¼ ðs V ap p Þþ ap p þ ðε H þ nε h Þþ DT (1.51)
1 n 1 n 2 1 n
If ε h ¼ ε H ¼ 0, then Eqs. (1.48) and (1.49) can be simplified to the case
of the TI rocks in the uniaxial strain condition:

E h n V Ea Th
s h ¼ ðs V a V p p Þ þ a h p p þ DT (1.52)
E V ð1 n h Þ 1 n h

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