Sv and Pp on Ogbon-1

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

Learning objectives

Integrate a density log to the vertical stress, Sv the integral of density times gravity over depth, landing 67.7 MPa at 3 km
Explain why the unlogged shallow section dominates Sv and must come from a compaction trend
Place the hydrostatic pressure 30.3 and the Eaton overpressure 35.3 MPa on the same depth axis
Read the effective vertical stress 32.4 MPa that the rest of the model will use

The Overburden Is an Integral

The vertical stress is the simplest component to state and the easiest to get quietly wrong. It is the weight of everything above a point, per unit area: $S_v(z) = \int_0^z \rho(z')\, g\, dz'$ rho(z′),g,dz′. On Ogbon-1 we integrate the density log from the surface down to the 3 km datum and land on 67.7 MPa, the canon overburden, the very number the Rock Physics pressure ladder used at the same depth. The figure puts density on the left track and the running $S_v$ v integral on the right; move through depth and read both. The logged reservoir section carries the real Ogbon-1 density, the same log the Petrophysics course reads; above it the profile follows a compaction trend.

Here is the catch every log analyst knows: you never log density from the surface. The Ogbon-1 tool runs over the reservoir only, and the roughly 2.8 km of rock above it is unlogged, yet that unlogged section is most of $S_v$ v. So the vertical stress is only as trustworthy as the compaction trend you assume for the shallow rock. Drag the shallow-trend slider and watch $S_v$ v at the datum swing by several MPa for a tenth of a g/cc, the single largest uncertainty in the vertical stress and the reason overburden is calibrated to offset wells and checkshots, not just read off one log.

Pore Pressure on the Same Axis

Now overlay the pore pressure. A hydrostatic brine column at 1.03 g/cc reaches 30.3 MPa at 3 km. But the Ogbon-1 sonic trend of Part 4 showed the reservoir mildly overpressured: Eaton returned 35.3 MPa, five MPa above hydrostatic. That five MPa is not an accounting nicety. It sets the effective stress that governs friction, failure, and the mud window. Subtract it: the effective vertical stress is $S_v - P_p = 67.7 - 35.3 = 32.4$ 67.7−35.3=32.4 MPa, with Biot $\alpha = 1$ for the total-overburden bookkeeping. That 32.4 is the number Section 8.6 will hand to the frictional check, and it is why the field sits where it does inside the polygon.

The First Course of the Model

Two of the six components are now in place, $S_v$ v at 67.7 and $P_p$ p at 35.3, both read from logs and a trend, both landing on the canon. They were the tractable ones: a density integral and a pressure prediction the course already built. The next section reads rock strength from the same sonic and porosity logs, and it will not land as cleanly, because strength-from-logs is a correlation carrying real scatter, and honest calibration means bracketing it rather than pretending a single curve is the truth.

References

Zoback, M. D. (2007). Reservoir Geomechanics (ch. 4, vertical stress and pore pressure). Cambridge University Press.
Traugott, M. (1997). Pore/fracture pressure determinations in deep water. World Oil, 218(8), 68-70.
Plumb, R., Edwards, S., Pidcock, G., Lee, D., & Stacey, B. (2000). The mechanical earth model concept. IADC/SPE Drilling Conference, SPE 59128.