Injection, Depletion, and the Stress They Leave

The Reservoir Talks Back

Deplete a reservoir and the obvious thing happens: pore pressure falls, so effective stress rises. But a reservoir laterally pinned by its non-depleting surroundings is in exactly the uniaxial-strain geometry of section 2.3, and that constraint has a consequence people miss. As the depleting rock tries to shrink horizontally, its confinement resists, and the total horizontal stress falls too. The bookkeeping is the same K0 algebra run on a pressure change instead of a burial increment, and it delivers the stress-path coefficient $\gamma = \dfrac{\Delta S_h}{\Delta P_p} = \alpha\,\dfrac{1-2\nu}{1-\nu}$=alpha,dfrac1−2nu1−nu. For the canon rock, $\alpha = 1$ and $\nu = 0.25$, this is $\gamma = 2/3$ exactly, and it is the single most-used number in the back half of this course.

Deplete the reservoir in the figure and watch two bars move in opposite directions. Drop the pore pressure by 10 MPa and the total minimum horizontal stress falls by $\tfrac{2}{3}\times 10 = 6.7$ MPa, from 46 to about 39.3, while the effective horizontal stress rises, because pore pressure fell faster than total stress did. Total stress follows the fluid; effective stress fights it. Injection runs the same arithmetic in reverse: raise the pressure and the total stresses swell, which is precisely why repeated injection can lift the fracture gradient and why a depleted zone becomes a fracture-trap that steers later fracs toward it.

Two Thirds, Everywhere Downstream

This one coefficient is load-bearing for the rest of the book, so it earns a careful statement of its reach. In Part 7, the falling total stress means the fracture gradient drops as a field is produced, so infill wells fracture at lower pressures than the discovery well did. In Part 9, the same drop changes the total clamping stress on nearby faults even as the effective stress rises, and which effect wins decides whether depletion stabilizes or reactivates a fault, a genuinely two-sided question. In Part 10, gamma sets the reservoir's march around the Mohr diagram, the stress path that can walk a producing field into its own failure envelope. The number is not universal, stiff rocks and different Poisson ratios shift it, and a real study measures it from repeat stress tests, but two thirds is the canon's value and the anchor every later calculation returns to. Part 2 closes here; Part 3 turns from how rock deforms to when it breaks.

References

• Fjaer, E., Holt, R. M., Horsrud, P., Raaen, A. M., & Risnes, R. (2008). Petroleum Related Rock Mechanics (2nd ed.). Elsevier.
• Zoback, M. D. (2007). Reservoir Geomechanics. Cambridge University Press.
• Segall, P. (1989). Earthquakes triggered by fluid extraction. Geology, 17(10), 942-946.