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The determination of a reservoir’s mechanical properties is critical to reducing drilling risk and maximizing well and reservoir productivity. Estimates of rock mechanical properties are central to the following<ref name="r1" />:
The determination of a reservoir’s mechanical properties is critical to reducing drilling risk and maximizing well and reservoir productivity. Estimates of rock mechanical properties are central to the following<ref name="r1">Fjaer, E. et al. 1992. Petroleum Related Rock Mechanics, 1-338. Amsterdam: Developments in Petroleum Science No. 33, Elsevier, Amsterdam.</ref>:
 
*Drilling programs
*Drilling programs
*Well placement
*Well placement
*Well-completion design
*Well-completion design


[[Acoustic logging|Acoustic logging]] can provide information helpful to determining the mechanical properties of reservoir rock.
[[Acoustic_logging|Acoustic logging]] can provide information helpful to determining the mechanical properties of reservoir rock.
 
== Mechanical properties of rock ==


==Mechanical properties of rock==
Mechanical properties include:
Mechanical properties include:
*Elastic properties (Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio) [See [[Stress strain relationships in rocks]] for calculations of these properties]
 
*Inelastic properties (fracture gradient and formation strength)  
*Elastic properties (Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio) [See [[Stress_strain_relationships_in_rocks|Stress strain relationships in rocks]] for calculations of these properties]
*Inelastic properties (fracture gradient and formation strength)


Elasticity is the property of matter that causes it to resist deformation in volume or shape. Hooke’s law describes the behavior of elastic materials and states that for small deformations, the resulting strain is proportional to the applied stress.
Elasticity is the property of matter that causes it to resist deformation in volume or shape. Hooke’s law describes the behavior of elastic materials and states that for small deformations, the resulting strain is proportional to the applied stress.
*Stress is the force applied per unit area
*Stress is the force applied per unit area
*Strain is the fractional distortion that results because of the acting force
*Strain is the fractional distortion that results because of the acting force
*The modulus of elasticity is the [[Stress strain relationships in rocks|ratio of stress to strain]]
*The modulus of elasticity is the [[Stress_strain_relationships_in_rocks|ratio of stress to strain]]
 
Depending on the mode of the acting geological force and type of geological media the force is acting upon, three types of [[Compressive_strength_of_rocks|deformation]] can result as well as three elastic moduli that correspond to each type of deformation.


Depending on the mode of the acting geological force and type of geological media the force is acting upon, three types of [[Compressive strength of rocks|deformation]] can result as well as three elastic moduli that correspond to each type of deformation.
*Young’s modulus, ''E'', is the ratio of uniaxial compressive (tensile) stress to the resultant strain
*Young’s modulus, ''E'', is the ratio of uniaxial compressive (tensile) stress to the resultant strain
*Bulk modulus, ''K'', is the change in volume under hydrostatic pressure (i.e., the ratio of stress to strain) (''K'' is the reciprocal of compressibility.)  
*Bulk modulus, ''K'', is the change in volume under hydrostatic pressure (i.e., the ratio of stress to strain) (''K'' is the reciprocal of compressibility.)
*Shear modulus, ''μ'', is the ratio of shearing (torsional) stress to shearing strain.  
*Shear modulus, ''μ'', is the ratio of shearing (torsional) stress to shearing strain.
*An additional parameter, Poisson’s ratio, ''σ'', is a measure of the geometric change of shape under uniaxial stress.  
*An additional parameter, Poisson’s ratio, ''σ'', is a measure of the geometric change of shape under uniaxial stress.
These four elastic parameters are interrelated such that any one can be expressed in terms of two others and can also be expressed in terms of acoustic-wave velocity and density ('''Table 1''').
 
[[File:Elastic moduli2.jpg|alt=|thumb|Table 1|none]]
 
'''Table 1—Modulus Relations for Isotropic Solids'''
 
''E''= Young’s modulus
 
''K''= Bulk Modulus
 
''μ'' = Shear Modulus
 
''v'' = Poisson’s ratio
 
''λ'' = Lame’s parameter
{| class="wikitable"
|'''Given'''
|
|
|
|
|
|
|
|
|
|
|-
|→
|''E,K''
|''E,μ''
|''E,v''
|''E,λ''
|''K,μ''
|''K,v''
|''K,λ''
|''μ,v''
|''μ,λ''
|''λ,v''
|-
|'''''Wanted'''''
|
|
|
|
|
|
|
|
|
|
|-
|'''''E'''''
|''—''
|''—''
|''—''
|''—''
|''9K μ''
 
''3K + μ''
|''3K(1−2v)''
|''9K(K−λ)''
 
''3K−λ''
|''2μ(1+v)''
|''μ(3λ+μ)''
 
''λ+μ''
|''λ(1+v)(1-2v)''
 
''v''
|-
|'''''K'''''
|''—''
|''___Eμ___''
 
''3(3μ−E)''
|''____E___''
 
''3(1−2v)''
|''E+3λ+[(E+λ)<sup>2</sup> +8λ<sup>2</sup>] <sup>½</sup>''
 
''6''
|''—''
|''—''
|''—''
|''2μ(1+v)''
 
''3(1−2v)''
|''λ+  <sup>2</sup>μ''
 
  ''<sup>3</sup>''
|''λ(1+v)''
 
''3v''
|-
|'''''μ'''''
|''3EK''
 
''9K-E''
|''—''
|''____E___''


These four elastic parameters are interrelated such that any one can be expressed in terms of two others and can also be expressed in terms of acoustic-wave velocity and density ('''Table 1''').
''2(1+v)''
|''E-3λ+[(E+λ)<sup>2</sup> +8λ<sup>2</sup>]<sup>1/2</sup>''


<gallery widths=300px heights=200px>
''4''
File:Vol5 Page 0209 Image 0001.png|'''Table 1'''
|''''
</gallery>
|''3K(1−2v)''


==Computing mechanical rock properties==
''2(1+v)''
The data needed to compute mechanical rock properties are:
|''3 (K-2λ)''
*[[Compressional and shear velocities]] (slowness)
*[[Rock density and porosity|Density]]


[[Compressional and shear velocities|Shear and compressional velocities]] are a function of:
''2''
*Bulk modulus
|''—''
*Shear modulus
|''—''
*[[Rock density and porosity|Density]] of the formation being measured
|''2(1-2v)''


The ''V''<sub>''p''</sub>/''V''<sub>''s''</sub> ratio, combined with formation density, ''ρ'', is used to calculate:
''2v''
*Poisson’s ratio
|-
*Young’s modulus
|'''''v'''''
*Bulk modulus
|''1 _ E''
*Shear modulus


Whenever possible, log-derived, dynamic rock properties should be calibrated to core-derived static (laboratory) properties, because the static measurements more accurately represent the in-situ reservoir mechanical properties.<ref name="r2" /><ref name="r3" /><ref name="r4" /><ref name="r5" /><ref name="r6" /> Rock mechanical properties can be determined using either of the following:
''2   6K''
*Conventional empirical charts<ref name="r7" />
|''E _ 1''
*Computer programs


The elastic moduli and Poisson’s ratio are used in a variety of applications.<ref name="r8" /> These applications include:
  ''2μ''
*Predictions of [[Rock failure relationships|formation strength]]<ref name="r9" /><ref name="r10" /><ref name="r11" /><ref name="r12" /><ref name="r13" />
|''—''
*Well stimulation (fracture pressure and fracture height)<ref name="r14" /><ref name="r15" /><ref name="r16" /><ref name="r17" />
|''[(E+λ)<sup>2</sup> + 8λ<sup>2</sup>] <sup>½</sup> − E − h''
*Borehole and perforation stability<ref name="r18" />
*Sand production and drawdown limits in unconsolidated formations<ref name="r19" /><ref name="r20" /><ref name="r21" />
*Coal evaluation<ref name="r22" />
*Determining the roof-rock-strength index for underground mining operations.<ref name="r23" /><ref name="r24" />  


Rock mechanics applications of modern multipole tools are discussed in the article on [[Anisotropy analysis]].
''4λ''
|''3K−2μ''


==References==
''2(3K+μ)''
<references>
|''—''
<ref name="r1">Fjaer, E. et al. 1992. ''Petroleum Related Rock Mechanics'', 1-338. Amsterdam: Developments in Petroleum Science No. 33, Elsevier, Amsterdam.</ref>
|''___λ___''


<ref name="r2">Montmayeur, H. and Graves, R.M. 1985. Prediction of Static Elastic/Mechanical Properties of Consolidated and Unconsolidated Sands From Acoustic Measurements: Basic Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14159-MS. http://dx.doi.org/10.2118/14159-MS </ref>
''3K−λ''
|''—''
|''___λ___''


<ref name="r3">Montmayeur, H. and Graves, R.M. 1986. Prediction of Static Elastic/Mechanical Properties of Consolidated and Unconsolidated Sands From Acoustic Measurements: Correlations. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October 1986. SPE-15644-MS. http://dx.doi.org/10.2118/15644-MS </ref>
''2(λ+μ)''
|''—''
|-
|'''''λ'''''
|''3K(3K−E)''


<ref name="r4">Holt, R.M., Ingsoy, P., and  Mikkelson, M. 1989. Rock Mechanical Analysis of North Sea Reservoir Formations. ''SPE Form Eval'' '''4''' (1): 33-37. SPE-16796-PA. http://dx.doi.org/10.2118/16796-PA</ref>
''9K−E''
|''μ(E−2μ''


<ref name="r5">Gatens III, J.M., Harrison III, C.W., Lancaster, D.E. et al. 1990. In-Situ Stress Tests and Acoustic Logs Determine Mechanical Propertries and Stress Profiles in the Devonian Shales. ''SPE Form Eval'' '''5''' (3): 248-254. SPE-18523-PA. http://dx.doi.org/10.2118/18523-PA</ref>
''3μ−E''
|''____vE_____''   


<ref name="r6">Yale, D.P. 1994. Static and Dynamic Rock Mechanical Properties in the Hugoton and Panoma Fields, Kansas. Presented at the SPE Mid-Continent Gas Symposium, Amarillo, Texas, 22-24 May 1994. SPE-27939-MS. http://dx.doi.org/10.2118/27939-MS </ref>
''(1+v)(1−2v)''
|''—''
|''K- <sup>2</sup> μ''


<ref name="r7">Kowalski, J.J. 1978. Formation Strength parameters from Well Logs, paper N. ''Trans.'', 1978 Annual Logging Symposium, SPWLA, 1–19.</ref>
 ''<sup>3</sup>''
|''3Kv''


<ref name="r8">Sethi, D.K. 1981. Well Log Applications in Rock Mechanics. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 27-29 May 1981. SPE-9833-MS. http://dx.doi.org/10.2118/9833-MS </ref>
''1+v''
|''—''
|''2μv''


<ref name="r9">Tixier, M.P., Loveless, G.W., and  Anderson, R.A. 1975. Estimation of Formation Strength From the Mechanical-Properties Log(incudes associated paper 6400 ). ''J Pet Technol'' '''27''' (3): 283-293. SPE-4532-PA. http://dx.doi.org/10.2118/4532-PA</ref>
''1−2v''
|''''
|''—''
|}


<ref name="r10">Stein, N. 1976. Mechanical Properties of Friable Sands From Conventional Log Data (includes associated papers 6426 and 6427 ). J Pet Technol 28 (7): 757-763. SPE-5500-PA. http://dx.doi.org/10.2118/5500-PA</ref>
== Computing mechanical rock properties ==


<ref name="r11">Onyia, E. 1988. Relationships Between Formation Strength, Drilling Strength, and Electric Log Properties. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18166-MS. http://dx.doi.org/10.2118/18166-MS </ref>
The data needed to compute mechanical rock properties are:


<ref name="r12">Stein, N. 1992. Sonic Log Data Help Determine Formation Strength. ''Oil & Gas J.'' (28 December): 96.</ref>
*[[Compressional_and_shear_velocities|Compressional and shear velocities]] (slowness)
*[[Rock_density_and_porosity|Density]]


<ref name="r13">Raaen, A.M., Hovem, K.A., Joranson, H. et al. 1996. FORMEL: A Step Forward in Strength Logging. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 6-9 October 1996. SPE-36533-MS. http://dx.doi.org/10.2118/36533-MS </ref>
[[Compressional_and_shear_velocities|Shear and compressional velocities]] are a function of:


<ref name="r14">Anderson, T. and Walker, T. 1972. Log Derived Rock Properties for Use in Well Stimulation Design. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, San Antonio, Texas, 8-11 October 1972. SPE-4095-MS. http://dx.doi.org/10.2118/4095-MS </ref>
*Bulk modulus
*Shear modulus
*[[Rock_density_and_porosity|Density]] of the formation being measured


<ref name="r15">Anderson, R.A., Ingram, D.S., and  Zanier, A.M. 1973. Determining Fracture Pressure Gradients From Well Logs. J Pet Technol 25 (11): 1259-1268. SPE-4135-PA. http://dx.doi.org/10.2118/4135-PA</ref>
The ''V''<sub>''p''</sub>/''V''<sub>''s''</sub> ratio, combined with formation density, ''ρ'', is used to calculate:


<ref name="r16">Newberry, B.M., Nelson, R.F., and  Ahmed, U. 1985. Prediction of Vertical Fracture Migration Using Compression and Shear Wave Slowness. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 19–22 May. SPE-13895-MS. http://dx.doi.org/10.2118/13895-MS </ref>
*Poisson’s ratio
*Young’s modulus
*Bulk modulus
*Shear modulus


<ref name="r17">Stein, N. 1988. How to Calculate Fracture Pressures from Well Logs. ''Petroleum Engineer Intl.'' '''60''' (8): 36–38.</ref>
Whenever possible, log-derived, dynamic rock properties should be calibrated to core-derived static (laboratory) properties, because the static measurements more accurately represent the in-situ reservoir mechanical properties.<ref name="r2">Montmayeur, H. and Graves, R.M. 1985. Prediction of Static Elastic/Mechanical Properties of Consolidated and Unconsolidated Sands From Acoustic Measurements: Basic Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14159-MS. http://dx.doi.org/10.2118/14159-MS</ref><ref name="r3">Montmayeur, H. and Graves, R.M. 1986. Prediction of Static Elastic/Mechanical Properties of Consolidated and Unconsolidated Sands From Acoustic Measurements: Correlations. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October 1986. SPE-15644-MS. http://dx.doi.org/10.2118/15644-MS</ref><ref name="r4">Holt, R.M., Ingsoy, P., and Mikkelson, M. 1989. Rock Mechanical Analysis of North Sea Reservoir Formations. SPE Form Eval 4 (1): 33-37. SPE-16796-PA. http://dx.doi.org/10.2118/16796-PA</ref><ref name="r5">Gatens III, J.M., Harrison III, C.W., Lancaster, D.E. et al. 1990. In-Situ Stress Tests and Acoustic Logs Determine Mechanical Propertries and Stress Profiles in the Devonian Shales. SPE Form Eval 5 (3): 248-254. SPE-18523-PA. http://dx.doi.org/10.2118/18523-PA</ref><ref name="r6">Yale, D.P. 1994. Static and Dynamic Rock Mechanical Properties in the Hugoton and Panoma Fields, Kansas. Presented at the SPE Mid-Continent Gas Symposium, Amarillo, Texas, 22-24 May 1994. SPE-27939-MS. http://dx.doi.org/10.2118/27939-MS</ref> Rock mechanical properties can be determined using either of the following:


<ref name="r18">Bruce, S. 1990. A Mechanical Stability Log. Presented at the SPE/IADC Drilling Conference, Houston, Texas, 27 February-2 March 1990. SPE-19942-MS. http://dx.doi.org/10.2118/19942-MS </ref>
*Conventional empirical charts<ref name="r7">Kowalski, J.J. 1975. Formation Strength parameters from Well Logs, paper N. Trans., 1975 Annual Logging Symposium, SPWLA, 1–19.</ref>
*Computer programs


<ref name="r19">Stein, N. and Hilchie, D.W. 1972. Estimating the Maximum Production Rate Possible from Friable Sandstones Without Using Sand Control. ''J Pet Technol'' '''24''' (9): 1157-1160. SPE-3499-PA. http://dx.doi.org/10.2118/3499-PA</ref>
The elastic moduli and Poisson’s ratio are used in a variety of applications.<ref name="r8">Sethi, D.K. 1981. Well Log Applications in Rock Mechanics. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 27-29 May 1981. SPE-9833-MS. http://dx.doi.org/10.2118/9833-MS</ref> These applications include:


<ref name="r20">Edwards, D.P., Sharma, Y., and Charron, A. 1983. Zones of Sand Production Identified by Log-Derived Mechanical Properties—A Case Study, paper S. ''Trans.'', 1983 European Formation Evaluation Symposium, SPWLA, London Chapter, 1–23.</ref>
*Predictions of [[Rock_failure_relationships|formation strength]]<ref name="r9">Tixier, M.P., Loveless, G.W., and Anderson, R.A. 1975. Estimation of Formation Strength From the Mechanical-Properties Log(incudes associated paper 6400 ). J Pet Technol 27 (3): 283-293. SPE-4532-PA. http://dx.doi.org/10.2118/4532-PA</ref><ref name="r10">Stein, N. 1976. Mechanical Properties of Friable Sands From Conventional Log Data (includes associated papers 6426 and 6427 ). J Pet Technol 28 (7): 757-763. SPE-5500-PA. http://dx.doi.org/10.2118/5500-PA</ref><ref name="r11">Onyia, E. 1988. Relationships Between Formation Strength, Drilling Strength, and Electric Log Properties. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18166-MS. http://dx.doi.org/10.2118/18166-MS</ref><ref name="r12">Stein, N. 1992. Sonic Log Data Help Determine Formation Strength. Oil & Gas J. (28 December): 96.</ref><ref name="r13">Raaen, A.M., Hovem, K.A., Joranson, H. et al. 1996. FORMEL: A Step Forward in Strength Logging. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 6-9 October 1996. SPE-36533-MS. http://dx.doi.org/10.2118/36533-MS</ref>
*Well stimulation (fracture pressure and fracture height)<ref name="r14">Anderson, T. and Walker, T. 1972. Log Derived Rock Properties for Use in Well Stimulation Design. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, San Antonio, Texas, 8-11 October 1972. SPE-4095-MS. http://dx.doi.org/10.2118/4095-MS</ref><ref name="r15">Anderson, R.A., Ingram, D.S., and Zanier, A.M. 1973. Determining Fracture Pressure Gradients From Well Logs. J Pet Technol 25 (11): 1259-1268. SPE-4135-PA. http://dx.doi.org/10.2118/4135-PA</ref><ref name="r16">Newberry, B.M., Nelson, R.F., and Ahmed, U. 1985. Prediction of Vertical Fracture Migration Using Compression and Shear Wave Slowness. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 19–22 May. SPE-13895-MS. http://dx.doi.org/10.2118/13895-MS</ref><ref name="r17">Stein, N. 1988. How to Calculate Fracture Pressures from Well Logs. Petroleum Engineer Intl. 60 (8): 36–38.</ref>
*Borehole and perforation stability<ref name="r18">Bruce, S. 1990. A Mechanical Stability Log. Presented at the SPE/IADC Drilling Conference, Houston, Texas, 27 February-2 March 1990. SPE-19942-MS. http://dx.doi.org/10.2118/19942-MS</ref>
*Sand production and drawdown limits in unconsolidated formations<ref name="r19">Stein, N. and Hilchie, D.W. 1972. Estimating the Maximum Production Rate Possible from Friable Sandstones Without Using Sand Control. J Pet Technol 24 (9): 1157-1160. SPE-3499-PA. http://dx.doi.org/10.2118/3499-PA</ref><ref name="r20">Edwards, D.P., Sharma, Y., and Charron, A. 1983. Zones of Sand Production Identified by Log-Derived Mechanical Properties—A Case Study, paper S. Trans., 1983 European Formation Evaluation Symposium, SPWLA, London Chapter, 1–23.</ref><ref name="r21">Ong, S., May, A., George, I. et al. 2000. An Accurate Characterization of Sand Strength in Weak and Unconsolidated Formations Aids Offshore Production Test Designs - A Bohai Bay Case Study. Presented at the International Oil and Gas Conference and Exhibition in China, Beijing, China, 7-10 November 2000. SPE-64738-MS. http://dx.doi.org/10.2118/64738-MS</ref>
*Coal evaluation<ref name="r22">Fertl, W.H. and DeVries, M.R. 1997. Coal Evaluation Using Geophysical Well Logs, paper F. Trans., 1997 Formation Evaluation Symposium, Canadian Well Logging Society, 1–17.</ref>
*Determining the roof-rock-strength index for underground mining operations.<ref name="r23">Bond, L.O., Alger, R.P., and Schmidt, A.W. 1971. Well Log Applications in Coal Mining and Rock Mechanics. Trans., AIME 250: 355–362.</ref><ref name="r24">Kowalski, J. and Fertl, W.H. 1977. Application of Geophysical Well Logging to Coal Mining Operations. Energy Sources 3 (2): 133–147.</ref>


<ref name="r21">Ong, S., May, A., George, I. et al. 2000. An Accurate Characterization of Sand Strength in Weak and Unconsolidated Formations Aids Offshore Production Test Designs - A Bohai Bay Case Study. Presented at the International Oil and Gas Conference and Exhibition in China, Beijing, China, 7-10 November 2000. SPE-64738-MS. http://dx.doi.org/10.2118/64738-MS </ref>
Rock mechanics applications of modern multipole tools are discussed in the article on [[Anisotropy_analysis|Anisotropy analysis]].


<ref name="r22">Fertl, W.H. and DeVries, M.R. 1997. Coal Evaluation Using Geophysical Well Logs, paper F. ''Trans.'', 1997 Formation Evaluation Symposium, Canadian Well Logging Society, 1–17.</ref>
== References ==


<ref name="r23">Bond, L.O., Alger, R.P., and Schmidt, A.W. 1971. Well Log Applications in Coal Mining and Rock Mechanics. ''Trans.'', AIME '''250''': 355–362.</ref>
<references />


<ref name="r24">Kowalski, J. and Fertl, W.H. 1977. Application of Geophysical Well Logging to Coal Mining Operations. ''Energy Sources'' '''3''' (2): 133–147.</ref>
== Noteworthy papers in OnePetro ==
</references>


==Noteworthy papers in OnePetro==
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read


==External links==
== External links ==
 
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro


==See also==
== See also ==
[[Acoustic logging]]
 
[[Acoustic_logging|Acoustic logging]]
 
[[Acoustic_logging_tools|Acoustic logging tools]]


[[Acoustic logging tools]]
[[Stress_strain_relationships_in_rocks|Stress strain relationships in rocks]]


[[Stress strain relationships in rocks]]
[[Rock_failure_relationships|Rock failure relationships]]


[[Rock failure relationships]]
[[Compressive_strength_of_rocks|Compressive strength of rocks]]


[[Compressive strength of rocks]]
[[Compressional_and_shear_velocities|Compressional and shear velocities]]


[[Compressional and shear velocities]]
[[Acoustic_velocity_dispersion_and_attenuation|Acoustic velocity dispersion and attenuation]]


[[Acoustic velocity dispersion and attenuation]]
[[Rock_acoustic_velocities_and_porosity|Rock acoustic velocities and porosity]]


[[Rock acoustic velocities and porosity]]
[[Rock_acoustic_velocities_and_pressure|Rock acoustic velocities and pressure]]


[[Rock acoustic velocities and pressure]]
[[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]]
[[PEH:Acoustic_Logging]]


[[PEH:Acoustic Logging]]
[[PEH:Rock_Properties]]


[[PEH:Rock Properties]]
==Category==
[[Category:1.2.3 Rock properties]]
[[Category:YR]]

Latest revision as of 14:29, 9 March 2020

The determination of a reservoir’s mechanical properties is critical to reducing drilling risk and maximizing well and reservoir productivity. Estimates of rock mechanical properties are central to the following[1]:

  • Drilling programs
  • Well placement
  • Well-completion design

Acoustic logging can provide information helpful to determining the mechanical properties of reservoir rock.

Mechanical properties of rock

Mechanical properties include:

  • Elastic properties (Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio) [See Stress strain relationships in rocks for calculations of these properties]
  • Inelastic properties (fracture gradient and formation strength)

Elasticity is the property of matter that causes it to resist deformation in volume or shape. Hooke’s law describes the behavior of elastic materials and states that for small deformations, the resulting strain is proportional to the applied stress.

  • Stress is the force applied per unit area
  • Strain is the fractional distortion that results because of the acting force
  • The modulus of elasticity is the ratio of stress to strain

Depending on the mode of the acting geological force and type of geological media the force is acting upon, three types of deformation can result as well as three elastic moduli that correspond to each type of deformation.

  • Young’s modulus, E, is the ratio of uniaxial compressive (tensile) stress to the resultant strain
  • Bulk modulus, K, is the change in volume under hydrostatic pressure (i.e., the ratio of stress to strain) (K is the reciprocal of compressibility.)
  • Shear modulus, μ, is the ratio of shearing (torsional) stress to shearing strain.
  • An additional parameter, Poisson’s ratio, σ, is a measure of the geometric change of shape under uniaxial stress.

These four elastic parameters are interrelated such that any one can be expressed in terms of two others and can also be expressed in terms of acoustic-wave velocity and density (Table 1).

Table 1

Table 1—Modulus Relations for Isotropic Solids

E= Young’s modulus

K= Bulk Modulus

μ = Shear Modulus

v = Poisson’s ratio

λ = Lame’s parameter

Given
E,K E,μ E,v E,λ K,μ K,v K,λ μ,v μ,λ λ,v
Wanted
E 9K μ

3K + μ

3K(1−2v) 9K(K−λ)

3K−λ

2μ(1+v) μ(3λ+μ)

λ+μ

λ(1+v)(1-2v)

v

K ___Eμ___

3(3μ−E)

____E___

3(1−2v)

E+3λ+[(E+λ)2 +8λ2] ½

6

2μ(1+v)

3(1−2v)

λ+ 2μ

  3

λ(1+v)

3v

μ 3EK

9K-E

____E___

2(1+v)

E-3λ+[(E+λ)2 +8λ2]1/2

4

3K(1−2v)

2(1+v)

3 (K-2λ)

2

2(1-2v)

2v

v 1 _ E

2  6K

E _ 1

 

[(E+λ)2 + 8λ2] ½ − E − h

3K−2μ

2(3K+μ)

___λ___

3K−λ

___λ___

2(λ+μ)

λ 3K(3K−E)

9K−E

μ(E−2μ

3μ−E

____vE_____   

(1+v)(1−2v)

K- 2 μ

 3

3Kv

1+v

2μv

1−2v

Computing mechanical rock properties

The data needed to compute mechanical rock properties are:

Shear and compressional velocities are a function of:

  • Bulk modulus
  • Shear modulus
  • Density of the formation being measured

The Vp/Vs ratio, combined with formation density, ρ, is used to calculate:

  • Poisson’s ratio
  • Young’s modulus
  • Bulk modulus
  • Shear modulus

Whenever possible, log-derived, dynamic rock properties should be calibrated to core-derived static (laboratory) properties, because the static measurements more accurately represent the in-situ reservoir mechanical properties.[2][3][4][5][6] Rock mechanical properties can be determined using either of the following:

  • Conventional empirical charts[7]
  • Computer programs

The elastic moduli and Poisson’s ratio are used in a variety of applications.[8] These applications include:

Rock mechanics applications of modern multipole tools are discussed in the article on Anisotropy analysis.

References

  1. Fjaer, E. et al. 1992. Petroleum Related Rock Mechanics, 1-338. Amsterdam: Developments in Petroleum Science No. 33, Elsevier, Amsterdam.
  2. Montmayeur, H. and Graves, R.M. 1985. Prediction of Static Elastic/Mechanical Properties of Consolidated and Unconsolidated Sands From Acoustic Measurements: Basic Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14159-MS. http://dx.doi.org/10.2118/14159-MS
  3. Montmayeur, H. and Graves, R.M. 1986. Prediction of Static Elastic/Mechanical Properties of Consolidated and Unconsolidated Sands From Acoustic Measurements: Correlations. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October 1986. SPE-15644-MS. http://dx.doi.org/10.2118/15644-MS
  4. Holt, R.M., Ingsoy, P., and Mikkelson, M. 1989. Rock Mechanical Analysis of North Sea Reservoir Formations. SPE Form Eval 4 (1): 33-37. SPE-16796-PA. http://dx.doi.org/10.2118/16796-PA
  5. Gatens III, J.M., Harrison III, C.W., Lancaster, D.E. et al. 1990. In-Situ Stress Tests and Acoustic Logs Determine Mechanical Propertries and Stress Profiles in the Devonian Shales. SPE Form Eval 5 (3): 248-254. SPE-18523-PA. http://dx.doi.org/10.2118/18523-PA
  6. Yale, D.P. 1994. Static and Dynamic Rock Mechanical Properties in the Hugoton and Panoma Fields, Kansas. Presented at the SPE Mid-Continent Gas Symposium, Amarillo, Texas, 22-24 May 1994. SPE-27939-MS. http://dx.doi.org/10.2118/27939-MS
  7. Kowalski, J.J. 1975. Formation Strength parameters from Well Logs, paper N. Trans., 1975 Annual Logging Symposium, SPWLA, 1–19.
  8. Sethi, D.K. 1981. Well Log Applications in Rock Mechanics. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 27-29 May 1981. SPE-9833-MS. http://dx.doi.org/10.2118/9833-MS
  9. Tixier, M.P., Loveless, G.W., and Anderson, R.A. 1975. Estimation of Formation Strength From the Mechanical-Properties Log(incudes associated paper 6400 ). J Pet Technol 27 (3): 283-293. SPE-4532-PA. http://dx.doi.org/10.2118/4532-PA
  10. Stein, N. 1976. Mechanical Properties of Friable Sands From Conventional Log Data (includes associated papers 6426 and 6427 ). J Pet Technol 28 (7): 757-763. SPE-5500-PA. http://dx.doi.org/10.2118/5500-PA
  11. Onyia, E. 1988. Relationships Between Formation Strength, Drilling Strength, and Electric Log Properties. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18166-MS. http://dx.doi.org/10.2118/18166-MS
  12. Stein, N. 1992. Sonic Log Data Help Determine Formation Strength. Oil & Gas J. (28 December): 96.
  13. Raaen, A.M., Hovem, K.A., Joranson, H. et al. 1996. FORMEL: A Step Forward in Strength Logging. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 6-9 October 1996. SPE-36533-MS. http://dx.doi.org/10.2118/36533-MS
  14. Anderson, T. and Walker, T. 1972. Log Derived Rock Properties for Use in Well Stimulation Design. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, San Antonio, Texas, 8-11 October 1972. SPE-4095-MS. http://dx.doi.org/10.2118/4095-MS
  15. Anderson, R.A., Ingram, D.S., and Zanier, A.M. 1973. Determining Fracture Pressure Gradients From Well Logs. J Pet Technol 25 (11): 1259-1268. SPE-4135-PA. http://dx.doi.org/10.2118/4135-PA
  16. Newberry, B.M., Nelson, R.F., and Ahmed, U. 1985. Prediction of Vertical Fracture Migration Using Compression and Shear Wave Slowness. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 19–22 May. SPE-13895-MS. http://dx.doi.org/10.2118/13895-MS
  17. Stein, N. 1988. How to Calculate Fracture Pressures from Well Logs. Petroleum Engineer Intl. 60 (8): 36–38.
  18. Bruce, S. 1990. A Mechanical Stability Log. Presented at the SPE/IADC Drilling Conference, Houston, Texas, 27 February-2 March 1990. SPE-19942-MS. http://dx.doi.org/10.2118/19942-MS
  19. Stein, N. and Hilchie, D.W. 1972. Estimating the Maximum Production Rate Possible from Friable Sandstones Without Using Sand Control. J Pet Technol 24 (9): 1157-1160. SPE-3499-PA. http://dx.doi.org/10.2118/3499-PA
  20. Edwards, D.P., Sharma, Y., and Charron, A. 1983. Zones of Sand Production Identified by Log-Derived Mechanical Properties—A Case Study, paper S. Trans., 1983 European Formation Evaluation Symposium, SPWLA, London Chapter, 1–23.
  21. Ong, S., May, A., George, I. et al. 2000. An Accurate Characterization of Sand Strength in Weak and Unconsolidated Formations Aids Offshore Production Test Designs - A Bohai Bay Case Study. Presented at the International Oil and Gas Conference and Exhibition in China, Beijing, China, 7-10 November 2000. SPE-64738-MS. http://dx.doi.org/10.2118/64738-MS
  22. Fertl, W.H. and DeVries, M.R. 1997. Coal Evaluation Using Geophysical Well Logs, paper F. Trans., 1997 Formation Evaluation Symposium, Canadian Well Logging Society, 1–17.
  23. Bond, L.O., Alger, R.P., and Schmidt, A.W. 1971. Well Log Applications in Coal Mining and Rock Mechanics. Trans., AIME 250: 355–362.
  24. Kowalski, J. and Fertl, W.H. 1977. Application of Geophysical Well Logging to Coal Mining Operations. Energy Sources 3 (2): 133–147.

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

Acoustic logging

Acoustic logging tools

Stress strain relationships in rocks

Rock failure relationships

Compressive strength of rocks

Compressional and shear velocities

Acoustic velocity dispersion and attenuation

Rock acoustic velocities and porosity

Rock acoustic velocities and pressure

Rock acoustic velocities and temperature

Rock acoustic velocities and in-situ stress

PEH:Acoustic_Logging

PEH:Rock_Properties

Category