# INTRODUCTION TO PHYSICAL PROPERTIES OF ROCKS

Document Sample

```					GOPH365 – JM MAILLOL - 2001

OVERVIEW OF PHYSICAL PROPERTIES OF EARTH MATERIALS

1. Geophysics and rock physical properties
All geophysical methods are indirect ways of determining the physical properties of rocks
The flowchart below is a representation of the concept of geophysical surveying from
data acquisition to the end product in the form of geological interpretation.

Field Survey                           Physical Measurement

Translation of physical
Processing
measurements into physical
Geophysical Interpretation
property distribution

Translation of physical property
Geological Interpretation
distribution into geological information

2. Homogeneity and Inhomogeneity - Isotropy and Anisotropy
Homogeneity or inhomogeneity of a particular volume indicates whether or not a property
is a function of local coordinates.
Homogeneity: The property is the same at every point.
Inhomogeneity: The property varies depending on the measurement location

Isotropy or inosotropy in a particular volume indicates whether or not a property is
function of the direction in which it is measured.
Investigation of anisotropy show a strong correlation of this phenomenon with structural
or textural properties. For example elastic properties depend on crack o r fracture
orientation, grain or mineral anisotropy. It is currently a very important subject of study.
Homogeneity and isotropy also depend on the scale at which the properties are
considered.

1
GOPH365 – JM MAILLOL - 2001

Illustration of the terms isotropy - anisotropy and homogeneity - inhomogeneity;
(Gassmann 1964)

3. Pore space properties

Porosity
The fraction of the entire volume of material occupied by pores, cracks, etc. (= voids)

VP       V
Total porosity: Φ =     = 1− m        Vp = volume of pores; Vm = volume of matrix
V       V
It is a dimensionless number.

Definition of porosity
Various kinds of porosity: primary, secondary, intergranular, intercrytalline, fissures,
vugular, …

2
GOPH365 – JM MAILLOL - 2001

Interconnected porosity: It lets fluids or electrical current flow
Porosity is extremely variable and hardly systematic, but a general trend can be observed
among earth materials:

HIGH                 Highly porous marine sediments
POROSITY
Unconsolidated sediments (porosity decreases from clay to silt to
sand to gravel)
sandstones
Carbonate rocks
LOW                  Fractured igneous rocks and other initially “dense” rock types
POROSITY
Porosity generally decreases with increasing age and depth

3.2 Permeability
The ability of a fluid under pressure to flow through the pores of a material.
u
Darcy’s law: k = −η
∇P
Units: Darcy (d), in SI it’s m2 (µm2), 1d = 0.9869µm2
In most practical cases 1d ≈ 1µm2
Permeability depends on porosity, pore size and distribution, pore shape, arrangement of
pores and pore throats. It can vary by 13 orders of magnitude.
k increases with increasing porosity, increasing grain size, it decreases with increasing
degrees of compaction and cementation.

3
GOPH365 – JM MAILLOL - 2001

Range of permeability values in rocks (cited by Hearst , Nelson 1985). Note that the scale
spans 13 orders of magnitude.

4. Density
It is the ratio mass/volume: ρ = M/V, in kg/m3 (SI) or g/cm3 . Sometimes the Mg/m3 is
used as it gives the same numerical values as the g/cm3.
1 kg/m3 = 10-3 g/cm3
The bulk density is the average density including voids: ρ; matrix density = ρm; pore-fluid
density: ρp
It has a relatively narrow range of variation (1-3.4). The bulk density depends on mineral
composition, porosity, and contents of voids.
In igneous and metamorphic rocks it is essentially a function of the mineral density and it
increases from acid to basic rocks. In sedimentary rocks it is essentially a function of the
porosity and of the saturation.

4
GOPH365 – JM MAILLOL - 2001

Mean density range of sedimentary rocks; data after Wohlenberg 1982

5. Magnetic properties

5.1 Susceptibility
κ = M/H where M= induced magnetization, H= applied magnetic field strength
It is dimensionless
It is a function of % of ferromagnetic minerals (magnetite…) present in the rock and it is
one of the most variable physical
properties.

5
GOPH365 – JM MAILLOL - 2001

It results from the spontaneous decay of atoms of certain isotopes. The activity is the
number of decays/unit time and is measured in Curie (Ci)
The most common radioactive isotopes are: 235,238U, 232Th, 40K.

7. Elastic properties
Experiments performed to measure seismic velocities show that they depend on the
density and elastic moduli (elastic coefficients).
Elasticity:    Hooke’s law σ = C ε where σ = stress, ε = strain, C = tensor of elasticity
When the stress is removed, the material returns to its original state (=elastic behavior).

For a uniaxial compression or tension:

σ
ε2
ε1

σ = E ε1, E = Young’s modulus
µ = - ε2/ε1 , Poisson’s ratio always <=0.5
Two other elastic coefficients are important:
If an isotropic elastic material is subjected to a change of pressure, a change in volume
results:
∆P
K=           = bulk modulus or incompressibility modulus.
∆V
V
Finally, it is possible to deform a solid by simple shear. The shear strain τ is induced by
applying a shear stress σs .

6
GOPH365 – JM MAILLOL - 2001

τ = tan Ψ
Ψ

G = σσ /τ = shear modulus or rigidity modulus.

These 4 quantities reasonably well define the elastic behavior of a material and they are
important factors governing the speeds of seismic waves. Not all 4 coefficients are
mutully independent.
In rocks, the speed of seismic waves is controlled by the elastic moduli of the minerals,
the nature of contact, cementation of grains and bonding properties.
In igneous rocks the composition (mineralogy) is the main controlling factor; in
sedimentary rocks it is again mostly the porosity and pore content.

8. Electrical Properties

8.1 Electrical conduction
Ohm’s law describes conduction currents: E = ρ J
E= electric field, J=current density, ρ = electrical resistivity
It can also be written: J = σ E where σ is the electrical conductivity (σ = 1/ρ );
ρ is expressed in Ohm-m (Ω-m) and σ is expressed in Siemens/meter (S/m)

Resistivity has a broad range of variation. Minerals are generally very resistive so the
resistivity of rocks is essentially controlled by water, especially in sedimentary rocks and
unconsolidated sediments. In the latter, direct relationships exist between porosity and
resistivity/conductivity (Archie’s “law”). In general resistivity increases when porosity
increases.

7
GOPH365 – JM MAILLOL - 2001

Range of resistivities for rocks and sediments

8.2 Dielectric polarization
When displacement currents are involved the physical property of importance is the
dielectric permittivity ε.
D = ε E where D = electric displacement, E= electric field
Water has also an “anomalous” dielectric permittivity compared to other earth material
constituents: dielectric constant of 80 compared to less than 10 for most minerals.
Therefore the dielectric permittivity of rocks is again essentially controlled by the amount
of water.
Material           ε                  V (m/ns)
Air                1                  0.30
Ice                3-4                0.16
Fresh water        80                 0.033
Salt water         80                 0.01
Dry sand           3-5                0.15
Wet sand           20-30              0.06
Shales and clays 5-20                 0.08
Silts              5-30               0.07
Limestone          4-8                0.12
Granite            4-6                0.13
(dry) salt         5-6                0.13

8

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 21 posted: 2/16/2010 language: English pages: 8