Strength from Logs

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

Learning objectives

Estimate UCS from sonic and porosity logs using the Chang-Zoback-Khaksar sandstone correlations
Read the honest spread: the velocity correlations bracket the Ogbon-1 main sand from 47 to 87 MPa
Explain why strength-from-logs must be bracketed and calibrated to core, not read as a single number
Place the calibrated UCS 65 as the central estimate inside the velocity cluster

Strength Is Not Logged

The vertical stress came off a density integral and the pore pressure off Eaton. Strength is harder, because no logging tool measures UCS in the ground. What the logs give is velocity, from the sonic, and porosity, from density and neutron, and rock strength correlates with both: stiff, fast, low-porosity rock is strong. Chang, Zoback and Khaksar (2006) compiled roughly thirty empirical correlations from about 260 sandstone core tests worldwide, each fitting the unconfined compressive strength to $V_p$ p, the sonic slowness $\Delta t$ , density, dynamic modulus, or porosity. The figure runs five of them on the Ogbon-1 main sand and shows what comes back.

The result is not one number. On the main sand, $V_p$ p 3378 m/s, $\Delta t$ 90.2, porosity 0.26, the velocity correlations return 87 MPa from the linear- $V_p$ p form, 47 from the McNally $\Delta t$ form, and 68 and 70 from the two density-velocity forms; the porosity correlation returns 20, though that one is out of its stated range for a sand this porous. The velocity cluster brackets the rock from about 47 to 87 MPa, a factor of nearly two. That spread is not a defect. It is the honest scatter of strength-from-logs, because the same velocity can come from many rocks, differently cemented, differently packed, differently clay-bearing, that fail at different stresses.

Bracket, Then Calibrate

So what strength does Ogbon-1 have? The disciplined answer is a bracket with a calibrated central estimate. The velocity cluster centers near 68 MPa, and the canon UCS of 65 sits squarely inside it, the value a core test on this sand would confirm and the number the rest of the model carries. Where core exists you calibrate the chosen correlation to it and carry the residual; where it does not, you carry the bracket and let the mud window and the sanding prediction inherit its width. Pretending a single log-derived curve is the truth is the classic overconfidence of a mechanical earth model, and it is why the Section 8.6 verdict is stated with a margin rather than a false decimal. Drag the porosity and watch the bracket widen as the sand weakens: a 26 percent sand is genuinely uncertain, while a 10 percent sand is not, because the correlations converge where the rock is strong.

Three of Six

Strength is the third component placed, and the first that does not land on a single clean value. $S_v$ v and $P_p$ p were an integral and a prediction; strength is a correlation with real scatter, and the elastic moduli that the same sonic and density logs give, the dynamic $E$ and $\nu$ that set stress paths and fracture widths, carry their own static-to-dynamic gap from Part 2. Four of the six inputs are now read from logs. The next two sections turn to the stresses logs cannot give directly: $S_{hmin}$ hmin from leak-off tests, and $S_{Hmax}$ Hmax from the wellbore's own failures.

References

Chang, C., Zoback, M. D., & Khaksar, A. (2006). Empirical relations between rock strength and physical properties in sedimentary rocks. Journal of Petroleum Science and Engineering, 51(3-4), 223-237.
McNally, G. H. (1987). Estimation of coal measures rock strength using sonic and neutron logs. Geoexploration, 24(4-5), 381-395.
Zoback, M. D. (2007). Reservoir Geomechanics (ch. 4). Cambridge University Press.