Page 595 - Petrophysics

562 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

parameters to accurately simulate the in-situ condition. Three measuring
and loading techniques are commonly used: hydrostatic, uniaxial, and
triaxial. These techniques, which are discussed later, essentially involve
applying a specified load and measuring the corresponding strain
according to the theory of linear elasticity.

HOOKE’S LAW

If a rock body is subjected to directed forces lasting for a few minutes,
hours, or days, it usually passes through four stages of deformation:
elastic, elastico-viscous, plastic, and rupture. The stages are dependent
upon the elasticity, viscosity, and rigidity of the rock, as well as on its
stress history, temperature, time, pore pressure, and anisotropy.
At first, the deformation is elastic-that is, if the stress is withdrawn,
the body returns to its original shape and size. With purely elastic
deformation, the strain is a linear function of stress, i.e., the material
obeys Hooke’s law, as shown in Figure 9.6.

CJ = EE (9.19)
where E is the modulus of elasticity. E, which is also known as Young’s
modulus, is a measure of the property of the rock to resist deformation.
If a cylindrical rock sample is subjected to stress parallel to its long axis,
it will lengthen and the diameter of the cylinder becomes smaller under
tension as shown in Figure 9.7. Under compression parallel to the axis,
the rock sample wiII shorten while its diameter becomes greater. The
ratio of transverse or lateral strain to axial strain is known as Poisson’s
ratio, v, or:

(9.20)

where: do = original diameter of cylindrical core sample.
Ad = change in diameter.
Lo = original length of core.
AL = change in length.
Elat = strain in the lateral direction.
= strain in the axial direction.

Using these terms, Young’s modulus can be expressed as:

<T
E=-- - F/A (9.21)
Eax AL/L
where F/A is the load per unit area. Another important elastic constant is
the modulus of rigidity, G, which is a measure of the resistance of a body