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...