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Rock acoustic velocities and pressure: Difference between revisions
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Rock moduli (compressibility) and [[ | Rock moduli (compressibility) and [[Compressional_and_shear_velocities|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== | == 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 [[ | |||
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 [[Rock_acoustic_velocities_and_porosity|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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==Poorly consolidated sands== | == Poorly consolidated sands == | ||
[[ | The [[Subsurface_stress_and_pore_pressure|stress]] dependence of granular material has been examined extensively. For example, Gassmann<ref name="r1">Gassmann, F. 1951. Elastic waves through a packing of spheres. Geophysics 16 (4): 673–685. http://dx.doi.org/10.1190/1.1437718.</ref> and Duffy and Mindlin<ref name="r2">Duffy, J. and Mindlin, R.D. 1956. Stress-strain relations and vibrations of a granular medium, No. 24, 584–593. New York: Columbia University.</ref> modeled various packings of spheres. In general, they found that | ||
where ''f'' is approximately linear. This type of relation is particularly useful for poorly consolidated sands. | [[File:Vol1 page 0613 eq 001.png|RTENOTITLE]]....................(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'''). | 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'''). | ||
[[File:Vol1 page 0613 eq 002.png]]....................(2) | [[File:Vol1 page 0613 eq 002.png|RTENOTITLE]]....................(2) | ||
Examining a similar set of data allowed Eberhart-Phillips ''et al''.<ref name="r3" /> to develop a pair of relations for both ''V''<sub>''p''</sub> and ''V''<sub>''s''</sub> (see also '''Table 1a''' in [[Rock acoustic velocities and porosity]]) | Examining a similar set of data allowed Eberhart-Phillips ''et al''.<ref name="r3">Eberhart-Phillips, D., Han, D.-H., and Zoback, M.D. 1989. Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone. Geophysics 54 (1): 82–89. http://dx.doi.org/10.1190/1.1442580.</ref> to develop a pair of relations for both ''V''<sub>''p''</sub> and ''V''<sub>''s''</sub> (see also '''Table 1a''' in [[Rock_acoustic_velocities_and_porosity|Rock acoustic velocities and porosity]]) | ||
[[File:Vol1 page 0614 eq 001.png]]....................(3a) | [[File:Vol1 page 0614 eq 001.png|RTENOTITLE]]....................(3a) | ||
[[File:Vol1 page 0615 eq 001.png]]....................(3b) | [[File:Vol1 page 0615 eq 001.png|RTENOTITLE]]....................(3b) | ||
where ''P''<sub>''e''</sub> is the effective pressure. | where ''P''<sub>''e''</sub> is the effective pressure. | ||
==Carbonates== | == Carbonates == | ||
For carbonates, the explicit pressure dependence given in '''Tables 2 and 3''' allow the pressure dependence to be evaluated. | |||
For carbonates, the explicit pressure dependence given in '''Tables 2 and 3''' allow the pressure dependence to be evaluated. | |||
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The pressure dependence for carbonate ''V''<sub>''p''</sub> from Rafavich ''et al''.<ref name="r4" /> 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. | The pressure dependence for carbonate ''V''<sub>''p''</sub> from Rafavich ''et al''.<ref name="r4">Rafavich, F., Kendall, C., and Todd, T. 1984. The relationship between acoustic properties and the petrographic character of carbonate rocks. Geophysics 49 (10): 1622-1636. http://dx.doi.org/10.1190/1.1441570.</ref> 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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It is important to note that all these relations involve either differential pressure (''P''<sub>''d''</sub>) or effective pressure (''P''<sub>''e''</sub>). Pore pressure (''P''<sub>''p''</sub>) counters the influence of confining pressure (''P''<sub>''c''</sub>), so the difference between these two controls rock properties. This has been expressed simply in the Terzaghi<ref name="r5" /> relation for the pressure dependence of a given porous material property ''S'', | It is important to note that all these relations involve either differential pressure (''P''<sub>''d''</sub>) or effective pressure (''P''<sub>''e''</sub>). Pore pressure (''P''<sub>''p''</sub>) counters the influence of confining pressure (''P''<sub>''c''</sub>), so the difference between these two controls rock properties. This has been expressed simply in the Terzaghi<ref name="r5">Terzaghi, K. and Peck, R.B. 1948. Soil Mechanics in Engineering Practice. New York: John Wiley & Sons.</ref> relation for the pressure dependence of a given porous material property ''S'', | ||
[[File:Vol1 page 0615 eq 002.png]]....................(4) | [[File:Vol1 page 0615 eq 002.png|RTENOTITLE]]....................(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. | This kind of behavior has been seen in numerous cases, as in '''Fig. 4<ref name="r6">Wyllie, M.R.J., Gregory, A.R., and Gardner, G.H.F. 1958. An Experimental Investigation of Factors Affecting Elastic Wave Velocities in Porous Media. Geophysics 23 (3): 459. http://dx.doi.org/10.1190/1.1438493.</ref>'''. 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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==Nomenclature== | == Nomenclature == | ||
{| | {| | ||
|- | |- | ||
|''V''<sub>''p''</sub> | | ''C'' | ||
|= | | = | ||
|compressional velocity, m/s | | clay content | ||
|- | |||
| ''V''<sub>''p''</sub> | |||
| = | |||
| compressional velocity, m/s | |||
|- | |- | ||
|''V''<sub>''p''</sub> | | ''V''<sub>''p''</sub> | ||
|= | | = | ||
|compressional velocity, m/s | | compressional velocity, m/s | ||
|- | |- | ||
|''Φ'' | | ''Φ'' | ||
|= | | = | ||
|porosity | | porosity | ||
|- | |- | ||
|''P'' | | ''P'' | ||
|= | | = | ||
|pressure, MPa | | pressure, MPa | ||
|- | |- | ||
|''P''<sub>''c''</sub> | | ''P''<sub>''c''</sub> | ||
|= | | = | ||
|confining pressure, MPa | | confining pressure, MPa | ||
|- | |- | ||
|''P''<sub>''d''</sub> | | ''P''<sub>''d''</sub> | ||
|= | | = | ||
|differential pressure, MPa | | differential pressure, MPa | ||
|- | |- | ||
|''P''<sub>''e''</sub> | | ''P''<sub>''e''</sub> | ||
|= | | = | ||
|effective pressure, MPa | | effective pressure, MPa | ||
|- | |- | ||
|''P''<sub>''p''</sub> | | ''P''<sub>''p''</sub> | ||
|= | | = | ||
|pore pressure, MPa | | pore pressure, MPa | ||
|} | |} | ||
== References == | |||
< | <references /> | ||
== Noteworthy papers in OnePetro == | |||
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | |||
== External links == | |||
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | |||
Use this section to | |||
== | == See also == | ||
[[Compressional_and_shear_velocities|Compressional and shear velocities]] | |||
[[Compressional and shear velocities]] | |||
[[Rock acoustic velocities and porosity]] | [[Rock_acoustic_velocities_and_porosity|Rock acoustic velocities and porosity]] | ||
[[Rock acoustic velocities and temperature]] | [[Rock_acoustic_velocities_and_temperature|Rock acoustic velocities and temperature]] | ||
[[Rock acoustic velocities and in-situ stress]] | [[Rock_acoustic_velocities_and_in-situ_stress|Rock acoustic velocities and in-situ stress]] | ||
[[Seismic attributes for reservoir studies]] | [[Seismic_attributes_for_reservoir_studies|Seismic attributes for reservoir studies]] | ||
[[Seismic time-lapse reservoir monitoring]] | [[Seismic_time-lapse_reservoir_monitoring|Seismic time-lapse reservoir monitoring]] | ||
[[PEH:Rock | [[PEH:Rock_Properties]] | ||
[[Category:1.2.3 Rock properties]] [[Category:YR]] | |||
Latest revision as of 16:09, 25 June 2015
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.
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[1] and Duffy and Mindlin[2] 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.[3] to develop a pair of relations for both Vp and Vs (see also Table 1a in Rock acoustic velocities and porosity)
....................(3a)
....................(3b)
where Pe is the effective pressure.
Carbonates
For carbonates, the explicit pressure dependence given in Tables 2 and 3 allow the pressure dependence to be evaluated.
Table 2
Table 3
The pressure dependence for carbonate Vp from Rafavich et al.[4] 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.
Fig. 2 – Compressional velocities normalized by the velocity at 40 MPa. For many sandstones, the average trend can be used.
![Fig. 3 – Generalized compressional velocities dependence on pressure seen in carbonates by Rafavich et al.[4] Pressure dependence is a function of porosity.](/w/images/thumb/b/bc/Vol1_Page_620_Image_0001.png/188px-Vol1_Page_620_Image_0001.png)
Fig. 3 – Generalized compressional velocities dependence on pressure seen in carbonates by Rafavich et al.[4] Pressure dependence is a function of porosity.
![Fig. 3 – Generalized compressional velocities dependence on pressure seen in carbonates by Rafavich et al.[4] Pressure dependence is a function of porosity.](/File:Vol1_Page_620_Image_0001.png)
It is important to note that all these relations involve either differential pressure (Pd) or effective pressure (Pe). Pore pressure (Pp) counters the influence of confining pressure (Pc), so the difference between these two controls rock properties. This has been expressed simply in the Terzaghi[5] 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[6]. 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.
![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.[6]).](/w/images/thumb/6/6e/Vol1_Page_621_Image_0001.png/299px-Vol1_Page_621_Image_0001.png)
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.[6]).
![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.[6]).](/File:Vol1_Page_621_Image_0001.png)
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 |
References
- ↑ Gassmann, F. 1951. Elastic waves through a packing of spheres. Geophysics 16 (4): 673–685. http://dx.doi.org/10.1190/1.1437718.
- ↑ Duffy, J. and Mindlin, R.D. 1956. Stress-strain relations and vibrations of a granular medium, No. 24, 584–593. New York: Columbia University.
- ↑ Eberhart-Phillips, D., Han, D.-H., and Zoback, M.D. 1989. Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone. Geophysics 54 (1): 82–89. http://dx.doi.org/10.1190/1.1442580.
- ↑ 4.0 4.1 Rafavich, F., Kendall, C., and Todd, T. 1984. The relationship between acoustic properties and the petrographic character of carbonate rocks. Geophysics 49 (10): 1622-1636. http://dx.doi.org/10.1190/1.1441570.
- ↑ Terzaghi, K. and Peck, R.B. 1948. Soil Mechanics in Engineering Practice. New York: John Wiley & Sons.
- ↑ 6.0 6.1 Wyllie, M.R.J., Gregory, A.R., and Gardner, G.H.F. 1958. An Experimental Investigation of Factors Affecting Elastic Wave Velocities in Porous Media. Geophysics 23 (3): 459. http://dx.doi.org/10.1190/1.1438493.
Noteworthy papers in OnePetro
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
External links
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
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