The Stress Path

Part 10, Part 10: The Producing Field

Learning objectives

Define the depletion stress path: the horizontal stress falls at gamma, two-thirds, the rate the pore pressure falls
Walk the Mohr circle under depletion and watch the effective and differential stresses grow
Read the operational consequence: the fracture gradient falls as the reservoir depletes
Understand why depletion mildly stabilizes the reservoir interior but loads compaction and the flanks

Depletion Moves the Stresses

Part 9 perturbed the stress model with injection; Part 10 does the opposite and inevitable thing, production. Every producing reservoir loses pore pressure, and that pressure drop moves the stresses. The vertical stress does not change, the overburden is still there, but the horizontal stress falls: as the pore pressure drops the rock wants to contract horizontally, the surrounding rock resists, and the horizontal stress relaxes. The stress-path coefficient sets the rate, $\gamma = dS_h/dP_p = \alpha(1-2\nu)/(1-\nu)$ , which for the canon $\alpha = 1$ and $\nu = 0.25$ is exactly two-thirds. Deplete the pressure by 15 MPa and $S_{hmin}$ hmin falls by 10.

Watch the Mohr circle walk. Both effective stresses rise as pressure falls, $S_v'$ v′ faster than $S_{hmin}'$ hmin′ because the horizontal stress is dropping too, so the circle moves right and grows: the differential stress increases. On the stress-path line the state slides down the two-thirds slope from the initial point, $P_p$ p 35.3 and $S_{hmin}$ hmin 46, toward lower pressure and lower stress. Two consequences follow, one operational and one structural.

The Fracture Gradient Falls

The operational consequence is immediate and costly: because $S_{hmin}$ hmin falls with depletion, the fracture gradient of the reservoir falls too. A hydraulic fracture opens against $S_{hmin}$ hmin (Part 7), so a depleted reservoir fractures at a lower pressure, and its safe mud window (Part 6) narrows from the top. Infill wells drilled into a depleted zone lose circulation more easily and must run lighter mud; a frac job in a depleted layer stays in that layer more readily, because the surrounding un-depleted rock now carries a higher $S_{hmin}$ hmin and contains the fracture. Depletion rewrites the mud-weight window and the completion design of every well drilled after it, which is exactly why a mechanical earth model is dated: the stresses it reports are the stresses at that pressure, and production moves them.

Stabilize Inside, Load the Edges

The structural consequence is subtler. Inside the reservoir the mobilized friction barely changes, drifting slightly toward stability as both effective stresses rise together, so the reservoir interior does not usually fail in normal faulting from depletion alone. But the growing differential stress compacts the reservoir, the subject of the next section, and the stress change does not stay inside the reservoir: it loads the bounding faults and the rock above and below, where the geometry can drive reverse slip or shear. The largest depletion-induced earthquakes have come not from the reservoir interior but from its edges and bounding faults. The stress path is the opening move for everything Part 10 examines: compaction, subsidence, well damage, and the time-lapse signal that lets you watch it happen.

References

Hettema, M. H. H., Schutjens, P. M. T. M., Verboom, B. J. M., & Gussinklo, H. J. (2000). Production-induced compaction of a sandstone reservoir: the strong influence of stress path. SPE Reservoir Evaluation & Engineering, 3(4), 342-347.
Segall, P., & Fitzgerald, S. D. (1998). A note on induced stress changes in hydrocarbon and geothermal reservoirs. Tectonophysics, 289(1-3), 117-128.
Zoback, M. D. (2007). Reservoir Geomechanics (ch. 12). Cambridge University Press.