SHmax from the Wellbore

Part 8, Part 8: Calibration, the Ogbon-1 Mechanical Earth Model

Learning objectives

Invert the wellbore breakout width to constrain the maximum horizontal stress, the one stress no test measures directly
Read SHmax 62 MPa on Ogbon-1 from the observed breakout width of 28 degrees, given Shmin, Pp, mud, and UCS
Carry the strength uncertainty into an SHmax band, because breakout width depends on UCS as much as on SHmax
Complete the stress tensor: five components measured, one inverted, the model ready to assemble

The Stress You Cannot Measure

Four components are placed, and one holds out. There is no leak-off test for $S_{Hmax}$ Hmax, no log that reads it, no core measurement that returns it: the maximum horizontal stress is the stress you cannot measure directly. But the wellbore itself carries the answer. Where the hoop stress exceeds the rock strength the wall spalls into breakouts, the dog-eared enlargements of Part 6.2, and the angular width of those breakouts, read from an image log or a four-arm caliper, is set by $S_{Hmax}$ Hmax. A bigger maximum stress squeezes a wider breakout. Invert the width, with everything else now known, and the last stress falls out.

On Ogbon-1 the image log shows breakouts about 28 degrees wide. With $S_{hmin}$ hmin 46, $P_p$ p 35.3, mud 36, and UCS 65 all in hand, the Kirsch hoop-stress criterion of Part 6 inverts to $S_{Hmax} = 62.0$ Hmax=62.0 MPa, the canon value. Drag the observed width and watch the stress respond: a wider breakout demands a higher $S_{Hmax}$ Hmax, a narrower one a lower. The wellbore is a stress gauge you never had to run a separate test for, which is exactly why breakout analysis is the workhorse of stress-magnitude estimation in deep wells.

The Strength Carries Through

One honesty the inversion cannot escape: $S_{Hmax}$ Hmax inherits the strength uncertainty of Section 8.3. The breakout width depends on UCS as much as on $S_{Hmax}$ Hmax, a weaker rock breaks wider at the same stress, so a bracket in strength is a bracket in $S_{Hmax}$ Hmax. Slide UCS across its 54-to-76 MPa range and the inverted $S_{Hmax}$ Hmax swings across roughly 58 to 66 MPa, while the canon 62 is the central estimate at the central strength. This is why $S_{Hmax}$ Hmax is always the least certain component of a stress model and why it is constrained last, after every input that pins it, $S_{hmin}$ hmin, $P_p$ p, mud, and strength, is already fixed. The width sensitivity is milder than the strength sensitivity, so the honest error bar on $S_{Hmax}$ Hmax is inherited, not intrinsic.

The Tensor Is Complete

With $S_{Hmax}$ Hmax inverted, all six components are in hand: $S_v$ v 67.7, $P_p$ p 35.3, $S_{hmin}$ hmin 46.0, $S_{Hmax}$ Hmax 62.0, UCS 65, and the elastic moduli. The stress tensor is complete and the ordering confirmed, $S_v$ v 67.7 above $S_{Hmax}$ Hmax 62.0 above $S_{hmin}$ hmin 46.0, a normal-faulting field. The last section of the part assembles the six into the Ogbon-1 stress model and reads its verdict: how close this field sits to the frictional edge, and what that closeness means for every well drilled through it.

References

Barton, C. A., Zoback, M. D., & Burns, K. L. (1988). In-situ stress orientation and magnitude at the Fenton Hill geothermal site, New Mexico, from wellbore breakouts. Geophysical Research Letters, 15(5), 467-470.
Zoback, M. D., Barton, C. A., Brudy, M., et al. (2003). Determination of stress orientation and magnitude in deep wells. International Journal of Rock Mechanics and Mining Sciences, 40(7-8), 1049-1076.
Zoback, M. D. (2007). Reservoir Geomechanics (ch. 8). Cambridge University Press.