Porosity Notes

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Porosity

Courtesy J. H. Wittke & T. E. Bunch, 2004-2008

Definition of Porosity
Vv ≡ void volume
VT ≡ total volume
VV
φ≡
≡ Total Porosity
VT

Properties of Real Rocks
That Influence Porosity









Sorting
Shape
Clay minerals
Cementation
Bound water
Fracturing
Diagenesis
Solution



Particle size (only weakly)

S
Pore

Grain
Rg

Courtesy Jon Burger, UH and Chevron

Geological Classifications of Porosity
• Matrix (intergranular)
Between the grains. Think marbles.
• Fracture
Natural and induced

• Vugular

Think of a “vug” as a very small cavern.

• Fenestral

Disconnected small holes in carbonates, often due to biological action. “windows”

• Intragranular
• Intracrystaline
Think of a flaw in a diamond

Courtesy Jon Burger, UH and Chevron

Courtesy Jon Burger, UH and Chevron

Courtesy Jon Burger, UH and Chevron

Courtesy Jon Burger, UH and Chevron

How is porosity formed?
• Sediment grains are transported by water or
air
• Ensembles of packed sediment grains contain
porosity
• As sediments are compacted into rocks, the
porosity can persist

Engineering Classification of Porosity
• Total Porosity

VV
φ≡
VT
• Effective Porosity
Connected porosity that allows fluid flow
through the rock

Looks like it might be disconnected and
not contribute to “effective” porosity.
Be careful.

Looks like it might be connected and
contribute to “effective” porosity.
Be careful.

Courtesy Jon Burger, UH and Chevron

Simple Model of Matrix Porosity
Cubic Packing of Identical Spheres

Unit Cell

Calculate the porosity.
φ≡

S
Pore

Grain

Vv
VT

Rg

Vv = VT − Vg where Vg ≡ volume of grains

2D picture to aid 3D calculation

Note: You must define the unit cell in such a
way that the entire rock can be constructed
from contiguous copies of the unit cell.
However, the unit cell can be moved for
computational convenience.

Simple Model of Matrix Porosity
Cubic Packing of Identical Spheres

Unit Cell

Calculate the porosity.

S
Pore

Grain

Vv
φ≡
VT

Rg
2D picture to aid 3D calculation

Vv = VT − Vg where Vg ≡ volume of grains
1 4
3
Vg = 8( )  πR g  where R g ≡ radius of a spherical grain 8 3

VT = S 3 where S = 2R g

Simple Model of Matrix Porosity
Cubic Packing of Identical Spheres

Unit Cell

Calculate the porosity.
φ≡

S

Vv
VT

Pore

Grain
Rg

Vv = VT − Vg where Vg ≡ volume of grains

2D picture to aid 3D calculation

1 4
3
Vg = 8( )  πR g  where R g ≡ radius of a spherical grain 8 3

Note: You must define the unit cell in such a
3
VT = S where S = 2R g
way that the entire rock can be constructed
from contiguous copies of the unit cell.
However, the unit cell can be moved for
computational convenience.

1 4
3
8( )  πR g 
Vv VT − Vg
8 3
 = 1 − π ≅ 47.6%
φ≡
=
= 1−
VT
VT
6
(2Rg )3

Interpretation of Simple Model
• What is the dependence of the porosity on the
grain size?
• What effects are left out of this model?
• This model would be called “perfectly sorted”.
What does that terminology mean? Do you
expect the porosity to go up or down if the grains
are still closely packed but more poorly sorted?
• Have we calculated total porosity or effective
porosity?
• I drew a 2D picture to aid our calculation. Is a 2D
picture misleading in any way?

Pores in rocks can hold
one or more fluids






Air (very near surface typically)
Fresh water (near surface; aquifer)
Salt water (most pores in most rocks)
Oil (occasionally)
Natural Gas (occasionally)

Fluid Saturations
• Pores can contain several fluids at the same
time.
Si =

Volume of fluidi
usually expressed as a percentage
Total pore volume

For example :
Volume of oil
Total pore volume
Volume of gas
Sg =
Total pore volume
Volume of water
Sw =
Total pore volume

So =

For the usual case in which oil, gas, and...
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