Page 30 - Applied Petroleum Geomechanics

20 Applied Petroleum Geomechanics

Figure 1.13 Lab experimental results of horizontal and vertical Young’s moduli in the
Haynesville and Bossier shales.

bedding direction. The shale will be stiffer if it is loaded parallel to the
bedding direction than that loaded perpendicular to the same direction. For
instance, uniaxial compression tests in shale core samples were performed
with weak plane laminations orientated different angles to the loading
direction, the anisotropic strength ratio (the ratio of the maximum to the
minimum compressive strengths) could be > 3. The anisotropic ratios in
Young’s moduli of the loading parallel to the bedding direction to the
loading perpendicular to the bedding direction are also very different. For
example, the compression test results in core samples show that the ratios
of the horizontal to vertical Young’s moduli vary from 1 to 4.2 in the
Haynesville and Bossier shale gas formations (Fig. 1.13).
To model anisotropic elastic media, stressestrain relation with thermal
effect can be written in a more compact matrix form to account for the
anisotropy (Bower, 2010):

s ¼ Cðε þ a T DTÞ (1.35)