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