Shmin from the LOT Ledger

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

Learning objectives

Read the minimum horizontal stress from leak-off and extended leak-off tests, the one direct stress measurement
Fit a gradient to a ledger of closure pressures, landing Shmin 46 MPa at 3 km, a 15.3 MPa/km gradient
Distinguish the leak-off pressure, an upper bound, from the fracture closure pressure, which is Shmin itself
Place Shmin between the pore pressure and the vertical stress, the fourth component of the model

The One Stress You Can Measure

The vertical stress came from an integral, the strength from a correlation. The minimum horizontal stress is different in kind: it is the one principal stress you can measure directly, because a hydraulic fracture opens against exactly $S_{hmin}$ hmin and closes at exactly $S_{hmin}$ hmin, the result of Parts 5.4 and 7.3. Every leak-off test and extended leak-off test run while drilling is a small stress measurement, and a field accumulates a ledger of them down the section. Fit a gradient through that ledger and $S_{hmin}$ hmin becomes a continuous curve, not a guess.

On Ogbon-1 the extended-leak-off closure ledger defines a gradient of 15.3 MPa/km, and at the 3 km datum that is $S_{hmin} = 46.0$ hmin=46.0 MPa, the canon value. Drag the gradient line and watch the misfit to the closure points: the ledger pins the least stress tightly, far more tightly than any model of it could, which is why a good stress model leans on measured $S_{hmin}$ hmin wherever tests exist and models it only in the gaps between them.

Leak-off Is Not Closure

The ledger enforces one honest distinction. The leak-off pressure, where the formation first takes fluid on the pressure-up, is an upper bound on $S_{hmin}$ hmin: it carries some near-wellbore stress concentration and reads high. The closure pressure, read on the pressure falloff after shut-in, the minifrac departure of Part 7.3, is $S_{hmin}$ hmin itself. A ledger built from raw leak-off pressures reads the least stress too high; a ledger of closures reads it right. Confusing the two is among the most common errors in a stress model, and it biases the mud window, the fracture gradient, and the polygon together, because all three read from $S_{hmin}$ hmin. The figure marks the leak-off points as open bounds above the closure line so the difference is visible.

Four of Six

With $S_{hmin}$ hmin measured, the model has four components and, for the first time, a shape: $P_p$ p 35.3 below $S_{hmin}$ hmin 46.0 below $S_v$ v 67.7, the vertical stress the largest, a normal-faulting ordering. Only $S_{Hmax}$ Hmax is left, the stress no test measures directly, and the next section wrings it out of the wellbore's own breakouts, inverting the failure the Kirsch equations of Part 6 predicted.

References

Zoback, M. D. (2007). Reservoir Geomechanics (ch. 7, measuring the least principal stress). Cambridge University Press.
Raaen, A. M., Horsrud, P., Kjorholt, H., & Okland, D. (2006). Improved routine estimation of the minimum horizontal stress component from extended leak-off tests. International Journal of Rock Mechanics and Mining Sciences, 43(1), 37-48.
White, A. J., Traugott, M. O., & Swarbrick, R. E. (2002). The use of leak-off tests as a means of predicting minimum in-situ stress. Petroleum Geoscience, 8(2), 189-193.