Compaction and Subsidence

Part 10, Part 10: The Producing Field

Learning objectives

Compute reservoir compaction from depletion, the uniaxial thinning h alpha dPp over the modulus M
Propagate compaction to the surface as a Geertsma subsidence bowl
Read the canon Geertsma ratio 0.44, center subsidence over compaction, for a reservoir as wide as it is deep
Understand the Ekofisk case: meters of subsidence and the platforms jacked up

The Reservoir Thins

The stress path showed the effective and differential stresses rising as a reservoir depletes. The rock responds by compacting: the reservoir thins. For uniaxial, laterally confined, compaction the thinning is $\Delta h = h\,\alpha\,\Delta P_p / M$ p/M, with $h$ the reservoir thickness, $\alpha$ the Biot coefficient, $\Delta P_p$ p the pressure drop, and $M$ the uniaxial modulus. A 100 m sand of modulus 36 GPa depleted 20 MPa compacts about 6 cm. Soft, high-porosity reservoirs, chalks and weak sands, compact far more, because their modulus is low.

Compaction is not only a reservoir problem; it reaches the surface. The rock above the shrinking reservoir sags into the void, and the sag spreads and shallows on its way up, arriving at the surface as a broad, smooth subsidence bowl. Geertsma (1973) solved its shape for a disk-shaped reservoir in an elastic half-space: the center subsidence is a fraction of the reservoir compaction, and that fraction depends only on the reservoir's radius-to-depth ratio and Poisson's ratio. For a reservoir as wide as it is deep, the canon case, the ratio is 0.44, the surface subsiding a little under half of what the reservoir compacts.

Wide and Shallow Sinks Most

The geometry is intuitive once seen. A reservoir much wider than its depth transmits nearly all its compaction to the surface, the ratio approaching $2(1-\nu)$ , about 1.5, because the surface sits within reach of the whole compacting disk. A narrow, deep reservoir barely dimples the surface, its compaction diffused through the intervening rock. Drag the radius-to-depth ratio and watch the bowl deepen and widen. This is why the great subsidence disasters are shallow, wide, soft fields. The most famous is Ekofisk, a North Sea chalk field where decades of depletion compacted a soft, thick reservoir and sank the seafloor about nine meters, enough that the production platforms had to be physically jacked up to keep their decks above the waves. Wilmington, beneath Long Beach, California, subsided nearly nine meters too before water injection arrested it. These are the surface signature of the stress path, integrated over a field's life.

From Bowl to Monitoring

The subsidence bowl is also a measurement. Its shape and rate, tracked by GPS, InSAR satellite radar, and seafloor gauges, invert back to the reservoir compaction and thus to the pressure change and the modulus, a surface window on a reservoir kilometers down. And the same compaction that sinks the surface also shears the wells that pass through the compacting interval, the subject of the next section, and generates the time-lapse seismic signal of Section 10.4. Compaction is the hinge of the producing field: it connects the reservoir pressure to the surface, to the wells, and to the repeated seismic survey.

References

Geertsma, J. (1973). Land subsidence above compacting oil and gas reservoirs. Journal of Petroleum Technology, 25(6), 734-744.
Nagel, N. B. (2001). Compaction and subsidence issues within the petroleum industry: from Wilmington to Ekofisk and beyond. Physics and Chemistry of the Earth, Part A, 26(1-2), 3-14.
Zoback, M. D. (2007). Reservoir Geomechanics (ch. 12). Cambridge University Press.