MOOS, DANIEL, GeoMechanics International, Palo Alto, CA
Abstract: Predicting Pore Pressure from Porosity and Velocity
Summary
Relationships between pore
pressure and velocity
are known to provide reasonable pore pressure predictions
in many sedimentary basins (e.g., Grauls et al., 1995). However, the pore
pressure predicted based on
velocity
alone may be incorrect if the elevated
fluid pressure is not a consequence of undercompaction (e.g., Bowers, 1994).
Empirical correlations between pore pressure and porosity may also give
erroneous results in similar situations. This ambiguity can be greatly
reduced if both porosity and
velocity
are measured. However, it is critically
important to account for the effect of the fluid on the P-
wave
velocity
,
as hydrocarbons in situ result in a
velocity
decrease that can be misinterpreted
as elevated pore fluid pressure. This must be done with caution, however,
because Vp/Vs is also a function of effective stress. Based on the results
presented here it is possible using velocities and porosity to determine
pore fluid pressure and its origin in sands as well as in shales.
Effects of compaction
When a confining pressure
is applied to a granular material, it will deform elastically (that is,
the strain energy will be recoverable and the sample will return to its
initial state upon release of the confining pressure) only until it reaches
some limiting effective confining stress. Increases in confining stress
beyond this limit result in permanent deformation (compaction). Relaxation
of the applied load allows recovery of the elastic deformation only. Upon
reloading the sample follows the "unloading curve" until the previous maximum
pressure is reached, and then continues along the compaction (sometimes
referred to as the "virgin") curve. Loading and unloading trends can be
separated in plots of porosity as a function of pressure. Furthermore,
by simultaneously measuring elastic properties (for example, from compressional
and shear-wave
velocities), it is possible to determine for a given material
whether it lies along a virgin curve or has been unloaded to achieve its
current state.
Laboratory data
Recently we acquired laboratory
data with which to evaluate these effects. Samples were loaded at a low
rate to a finite pressure, and pulse transmission velocity
measurements
were made at fixed pressure increments.The samples were unloaded to a fraction
of the previous maximum pressure and then reloaded at the same rate to
a higher pressure. Pulse transmission experiments to determine P- and S-
wave
velocities were repeated during the unloading and reloading segments at
the same fixed pressures. Further details of the laboratory technique can
be found in Chang et al. (1997), which also discusses frame-modulus dispersion
due to viscosity of the dry frame.
Figure 1 illustrates the
effect on sample porosity due to this deformation history. Compaction results
in a significant reduction in porosity with pressure, from approximately
0.29 (29%) to less than 0.22 (22%) accompanying loading to 30 MPa. Unloading
allows recovery of only a small fraction of the porosity loss, and the
increase in volume is largely reversible indicating that it is mostly elastic.Thus
porosity is not a single-valued function of pressure, indicating that a
measurement of porosity alone cannot provide a unique determination of
effective stress.A similar effect can be seen in velocity
data (not shown).
Therefore, pressure predictions based on
velocity
or porosity alone can
only be used if the material is on a virgin compaction curve.
Figure 2 illustrates the
relationship between velocity
and porosity. As can be seen, simultaneous
measurements of porosity (or density, if the fluid and grain densities
are known) and
velocity
can be used to determine pressure both along the
virgin compaction and the unloading trends. Furthermore, the position in
the
velocity
/porosity plane of a sample uniquely determines not only its
effective stress but also the sample history (that is, whether the sample
has been at a higher pressure, and if so, what that pressure was).
Application
These effects are utilized
in a field example in Figure 3 to determine pore fluid pressure and to
evaluate the origin of elevated pore fluid pressures in two sands in the
Gulf of Mexico. Fig. 3 superimposes well log-derived dtp (compressional-wave
slowness) and porosity for the two sands on a laboratory-determined compaction
/ unloading / reloading curve. Sand A is revealed to have elevated pore
fluid pressure but is on a virgin curve. The position of Sand B had to
be corrected for fluid effects using dts (shear-
wave
slowness) because
that sand contained compliant hydrocarbons. Once that was accomplished,
Sand B is revealed also to have elevated pore pressure, but in this case
it is likely that the cause of the elevated pressure is recharge, perhaps
accompanying influx of hydrocarbons.
AAPG Search and Discovery Article #90923@1999 International Conference and Exhibition, Birmingham, England