Rock acoustic velocities and pressure

Rock moduli (compressibility) and elastic velocities are strongly influenced by pressure. With increasing effective pressure, compliant pores within a rock will deform, contract, or close. The rock becomes stiffer, and, as a result, velocities increase.

Effect of pressure

Two examples are shown in Fig. 1. The typical behavior is rapid increase in velocity, with increasing pressure at low pressures, followed by a flattening of the curve at higher pressures. Presumably, compliant pores and cracks are closed at higher pressure, and velocities asymptotically approach a relatively constant velocity. This specific behavior at high pressures leads to the simple velocity-porosity transforms and probably is responsible for our ability to use sonic tools as in-situ porosity indicators with little regard to local pressures.

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  Fig. 1 – Examples of dry and water-saturated sandstone velocities as a function of hydrostatic differential pressure. As pressure increases, compliant pores close, making the rock stiffer with higher velocity and lower pore fluid sensitivity.

Poorly consolidated sands

The stress dependence of granular material has been examined extensively. For example, Gassmann and Duffy and Mindlin modeled various packings of spheres. In general, they found that

....................(1)

where f is approximately linear. This type of relation is particularly useful for poorly consolidated sands.

Sandstones

Although the absolute pressure dependences shown in Fig. 1a vs 1b are in significant contrast, for most sandstones, relative changes are more consistent. By normalizing the velocities to those at high pressure (40 MPa), we get a much more consistent behavior (Fig. 2).

....................(2)

Examining a similar set of data allowed Eberhart-Phillips et al. to develop a pair of relations for both V_p and V_s (see also Table 1a in Rock acoustic velocities and porosity)

....................(3a)

....................(3b)

where P_e is the effective pressure.

Carbonates

For carbonates, the explicit pressure dependence given in Tables 2 and 3 allow the pressure dependence to be evaluated.

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  Table 2

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  Table 3

The pressure dependence for carbonate V_p from Rafavich et al. is shown in Fig. 3. Note that pressure sensitivity increases with increasing porosity. These types of relations permit velocity changes associated with pressure changes in the reservoir to be modeled.

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  Fig. 2 – Compressional velocities normalized by the velocity at 40 MPa. For many sandstones, the average trend can be used.

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  Fig. 3 – Generalized compressional velocities dependence on pressure seen in carbonates by Rafavich et al. Pressure dependence is a function of porosity.

It is important to note that all these relations involve either differential pressure (P_d) or effective pressure (P_e). Pore pressure (P_p) counters the influence of confining pressure (P_c), so the difference between these two controls rock properties. This has been expressed simply in the Terzaghi relation for the pressure dependence of a given porous material property S,

....................(4)

This kind of behavior has been seen in numerous cases, as in Fig. 4. This is one reason why properties such as density, resistivity, and velocity can decrease with increasing depth when "overpressure" or when increased pore pressure is encountered. Changes in reservoir pore pressure will have a similar influence. More precisely, it is the effective pressure that controls properties rather than just the differential. However, the magnitude of effective pressure is often found to be close to the simpler differential pressure.

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  Fig. 4 – Compressional velocities through a water-saturated oil-wet sandstone sample at various confining and pore pressures. When confining and pore pressures are varied together to give constant differential pressure, the velocity stays almost constant (after Wylie et al.).

Nomenclature

C	=	clay content
Vp	=	compressional velocity, m/s
Vp	=	compressional velocity, m/s
Φ	=	porosity
P	=	pressure, MPa
Pc	=	confining pressure, MPa
Pd	=	differential pressure, MPa
Pe	=	effective pressure, MPa
Pp	=	pore pressure, MPa

Noteworthy papers in OnePetro

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External links

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See also

Compressional and shear velocities

Rock acoustic velocities and porosity

Rock acoustic velocities and temperature

Rock acoustic velocities and in-situ stress

Seismic attributes for reservoir studies

Seismic time-lapse reservoir monitoring

PEH:Rock_Properties