Geoscience Reference
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injection
withdrawal
FIGURE G.1
Effective stress change in a reservoir induced by injection or withdrawal of fluid.
pressure perturbation in an infinite reservoir, one simply takes the length of the reservoir
to infinity, which causes the reference time scale to go to infinity.
FLUID INJECTION AND EXTRACTION IN A (PERMEABLE)
RESERVOIR ROCK
An increase of pore pressure in a permeable rock that is free to deform induces an
increase of volume. This physical phenomenon is akin to thermal expansion (i.e., the vol-
ume increase experienced by an unconstrained material when subjected to a temperature
increase). However, because the deformation of the rock is inhibited by the surrounding
material, an increase of pore pressure induces a volume change that is smaller than the
unconstrained volume change that would have been for the same pore pressure increase.
In addition the compressive stresses in the rock are increased by an amount proportional
to the pore pressure increase (see Box 2.3). But for very specific situations, the compressive
stress increases in the vertical and in the horizontal directions are unequal, the stress ratio
being a function of the shape of the reservoir and the contrast in elastic properties between
the reservoir and the surrounding rocks (Rudnicki, 1999, 2002). In particular, the ratio
of the induced vertical stress to the induced horizontal stress decreases with the aspect
ratio of the reservoir (i.e., the ratio of the reservoir thickness to the lateral extent). For a
“thin” reservoir, characterized by a small aspect ratio, the vertical stress change is negligible,
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