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and all the stress increase takes place in the horizontal direction, with increases that range between 40 and 80 percent of the pore pressure increase.

The expansion of the reservoir as a whole also alters the stress state in the surrounding rock, in particular inducing a decrease of the horizontal stress above and below a thin reservoir. These stress variations could in principle also trigger normal faulting in these regions; however, the combination of stress and pore pressure change caused by fluid injection is more likely to trigger seismicity in the reservoir rather than outside. The reverse is true for fluid extraction.

FLUID INJECTION IN A FRACTURED IMPERMEABLE ROCK

Unlike fluid injection in permeable rocks, the injection of fluid in fractured impermeable rock is essentially inducing an increase of fluid pressure in the fractures, with negligible concomitant changes in the stress. It is therefore a worst case compared to the permeable rock case, where the increase of pore pressure is in part offset by an increase of the compressive stress, which is a stabilizing factor. (In other words, factor m introduced in Figure G.1 is about equal to zero.) Because fractures can be very conductive and offer less storage compared to a permeable rock, the pore pressure perturbations can travel on the order of kilometers from the point of injection.

Coulomb Criterion and Effective Stress

For slip to take place on a fault, a critical condition involving the normal stress σ (the force per unit area normal to the fault), the shear stress τ (the force per unit area parallel to the fault), and the pressure ρ of the fluid on the fault plane, must be met (see Figure G.2 for a representation of σ and τ). This condition is embodied in the Coulomb criterion, |τ| = μ(σ – ρ) + c, which depends on two parameters: the coefficient of friction μ, with values typically in the narrow range from 0.6 to 0.8, and the cohesion c, equal to zero, however, for a frictional fault.

The Coulomb criterion simply expresses that the condition for slip on the fault is met when the magnitude of the “driving” shear stress, |τ|, is equal to the shear resistance μ(σ – ρ) + c. The quantity (σ – ρ) is known as the effective stress, a concept initially introduced by Terzaghi (1940) in the context of soil failure. It captures the counteracting influence of the fluid pressure ρ on the fault to the stabilizing effect of the compressive stress σ acting across the fault.

As long as the shear resistance is larger than the shear stress magnitude, the fault is stable. However, an increase of the shear stress magnitude or a decrease of the shear strength would cause the fault to slip if the two quantities become equal. For example, an increase of the fluid pressure induced by injection could be responsible for a drop of shear strength large enough to reach the critical conditions.



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