# Rock mechanical properties

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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[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
à E,K E,μ E,v
 Given à 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 [null 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   2μ — [(E+λ)2 + 8λ2] ½ − E − h 4λ 3K−2μ 2(3K+μ) — ___λ___ 3K−λ — ___λ___ 2(λ+μ) — [null 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.