SHmax: The Hardest Number
Learning objectives
- Explain why no test measures the maximum horizontal stress directly
- Use the stress polygon as a solution space and shrink it with independent constraints
- Combine the measured Shmin, the observed breakouts, and the absence of tensile fractures into overlapping bounds
- Box in the canon SHmax to a narrow band around 62 MPa
The Stress You Cannot Measure
The minimum horizontal stress had a test that reads it off a chart. The maximum horizontal stress has none: no fracture opens against it, no simple pressure equals it, and this is the central difficulty of in-situ stress determination. What we have instead is indirect constraint, and the tool that turns scattered indirect evidence into a number is the stress polygon of section 5.3. Treat the polygon not as a picture but as a solution space: every allowable pair the crust could hold. Each independent observation carves away part of that space, and where the surviving constraints overlap, is pinned.
Toggle the constraints in the figure and watch the box shrink. First, the measured from the last section is a vertical line through the polygon: it fixes one coordinate, leaving free only up the line. Second, if the wellbore shows breakouts, the hoop stress at the wall reached the rock strength, which the Kirsch equations of Part 6 turn into a relation between , , the mud weight, and the UCS, an upper bound: cannot be so high that the breakouts would be wider than observed. Third, if no drilling-induced tensile fractures appeared, cannot be so high that the wall would have gone tensile, another bound from the same equations. Overlay the three and the allowable segment collapses to a short interval. For the canon well, the breakout and no-tensile-fracture constraints bracket between about 58 and 66 MPa, with a midpoint of 62, the canon value.
Honest Numbers Have Error Bars
The lesson is methodological and it is one the whole course has been building toward: the hardest quantities are constrained, not measured, by intersecting independent evidence, and an honest is reported as a range, not a point. The width of that range is real uncertainty, driven by how well the breakout width is picked, how confidently the UCS is known, and whether tensile fractures were truly absent or merely unimaged. A geomechanicist who quotes to three digits without an error bar is hiding the physics. This constraint-intersection method, polygon plus wellbore observations, is exactly the machinery Part 8 will run on the Ogbon-1 well to build its mechanical earth model, and it depends entirely on the Kirsch equations that translate wellbore failure into stress, which is where Part 6 now takes us. First, one more piece of context: how the stress field looks across whole continents.
References
- Zoback, M. D. (2007). Reservoir Geomechanics. Cambridge University Press.
- Moos, D., & Zoback, M. D. (1990). Utilization of observations of well bore failure to constrain crustal stresses. Journal of Geophysical Research, 95(B6), 9305-9325.
- Zoback, M. D., 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.