You must log in to edit PetroWiki. Help with editing

Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. More information


Difference between revisions of "Rock acoustic velocities and pressure"

PetroWiki
Jump to navigation Jump to search
 
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
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.  
+
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 [[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.  
+
 
 +
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.
  
 
<gallery widths="300px" heights="200px">
 
<gallery widths="300px" heights="200px">
Line 8: Line 9:
 
</gallery>
 
</gallery>
  
==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" /> and Duffy and Mindlin<ref name="r2" /> modeled various packings of spheres. In general, they found that
 
  
[[File:Vol1 page 0613 eq 001.png]]....................(1)
+
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 ==
  
==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.
  
 
<gallery widths="300px" heights="200px">
 
<gallery widths="300px" heights="200px">
Line 36: Line 40:
 
</gallery>
 
</gallery>
  
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.
  
 
<gallery widths="300px" heights="200px">
 
<gallery widths="300px" heights="200px">
Line 44: Line 48:
 
</gallery>
 
</gallery>
  
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.
  
 
<gallery widths="300px" heights="200px">
 
<gallery widths="300px" heights="200px">
Line 54: Line 58:
 
</gallery>
 
</gallery>
  
==Nomenclature==
+
== Nomenclature ==
 +
 
 
{|
 
{|
|''C''
 
|=
 
|clay content
 
 
|-
 
|-
|''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>
 
<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>
 
  
<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>
+
== References ==
  
<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>
+
<references />
  
<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>
+
== Noteworthy papers in OnePetro ==
  
<ref name="r5">Terzaghi, K. and Peck, R.B. 1948. ''Soil Mechanics in Engineering Practice''. New York: John Wiley & Sons.</ref>
+
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
  
<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>
+
== External links ==
</references>
 
  
==Noteworthy papers in OnePetro==
+
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
 
  
==External links==
+
== See also ==
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
 
  
==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 Properties]]
+
[[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.

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

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).

RTENOTITLE....................(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)

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

RTENOTITLE....................(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.

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.

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,

RTENOTITLE....................(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.

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

  1. Gassmann, F. 1951. Elastic waves through a packing of spheres. Geophysics 16 (4): 673–685. http://dx.doi.org/10.1190/1.1437718.
  2. Duffy, J. and Mindlin, R.D. 1956. Stress-strain relations and vibrations of a granular medium, No. 24, 584–593. New York: Columbia University.
  3. 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. 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.
  5. Terzaghi, K. and Peck, R.B. 1948. Soil Mechanics in Engineering Practice. New York: John Wiley & Sons.
  6. 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

Seismic time-lapse reservoir monitoring

PEH:Rock_Properties