Page 365 - Numerical Analysis and Modelling in Geomechanics

346 RESERVOIR COMPACTION, SUBSIDENCE AND WELL DAMAGE
in only “one direction,” since pore pressures change the state of stress, but the
pressures are not affected by the change in stress. This approach also reduces
significantly the number of material model input data required for the
geomechanical modeling, and a full transient analysis is not required. The
computations using this decoupled approach were shown to agree well with
subsidence measurements, as will be shown later in this chapter. Yale et al. 86
compared this technique of decoupled geomechanical analysis, using
independently computed pore pressure, with full coupling in the simulation of
production from a single well in a compacting reservoir to determine the
magnitude of approximation from decoupling. The magnitude of the differences
in the pore pressures and the overall stress state is dependent on many factors,
including reservoir dimensions, fluid and rock compressibilities, and overburden
rock mechanical properties.

Modeling rock discontinuities
Geologic discontinuities such as faults, fractures and weak rock layers have a
finite, measurable thickness which can lead to casing damage up to tens of feet.
However, on the scale of the thickness of most highly compactive hydrocarbon
reservoirs, which is on the order of hundreds to thousands of feet, the
discontinuities can be reasonably approximated as zero-thickness, frictional
sliding, surfaces. Shear deformations of discontinuities can be modeled generally
as frictional slip or sliding between the surfaces. The slip can be episodic (i.e.,
stick-slip) or continuous sliding, depending on the constitutive behavior of the
frictional surface. A simple model for such frictional sliding is Coulomb’s law,
typically written as:
(11.43)

where τ is the shear stress acting on the layer or surfaces, γ is the relative shear
f
displacement or slip across the surfaces, and µ is a friction factor. Thin layers of
weak rock and gauge-filled faults actually have constitutive behavior, 2,90 which
governs the amount of shear deformation. Most frequently, however, such
constitutive behavior is modeled by the friction factor. Thus, the magnitude of
the friction factor should be correlated from measurements of slip obtained
during actual field operations. As will be shown later, the magnitude of the
friction factor has been found to range from 0.2 to 0.6.

Initial geostatic field

The geologic process of lithifaction results in a tectonic stresses below the
surface. This state of stress changes with depth, the vertical component being, of
course, zero at the surface. Geologic processes determine the other stress tensor
components. One of the most important and principal complications of