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# Difference between revisions of "Rock mechanical properties"

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:

• 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—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   2μ — [(E+λ)2 + 8λ2] ½ − E − h 4λ 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. Rock mechanical properties can be determined using either of the following:

• Conventional empirical charts
• Computer programs

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

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