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 volume 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,