Basic Porosity Concept1

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Porosity

Fundamentals:

Porosity is one of the most important rock properties in describing porous media. It is

defined as the ratio of pore volume to bulk volume of a rock sample. The porosity of a

rock is the fraction of the volume of space between the solid particles of the rock to the

total rock volume. The space includes all pores, cracks, vugs, inter- and intra-

crystalline spaces. The porosity is conventionally given the symbol f, and is expressed

either as a fraction varying between 0 and 1, or a percentage varying between 0% and

100%.

∅ =

Even though it is a dimensionless quantity, expressed either in decimal or percentage,

it is best to remember that it represents a volume ratio of pore space to the bulk space.

Figure below illustrates a simple example of porosity for a granular media.

Figure - Cross-sectional view of a porous media (white areas are pore space, pattern areas are grains)






It is within these pore spaces that the oil, gas and/or water reside. Therefore a primary

application of porosity is to quantify the storage capacity of the rock, and subsequentlydefine the volume of hydrocarbons available to be produced. From a drilling

perspective, the rate of penetration and the volume of drilling fluid lost to a formation

by invasion are related to porosity. Consider the following example of the effect of

porosity on fluid loss.

Several types of porosity have been defined based on the degree of connectivity or the

time of pore development. Total porosity is the ratio of the total pore space of themedia to the total bulk volume. Effective porosity is the ratio of interconnected pore

space to the bulk volume of the rock. Figure 2.3 is an example of total vs. effective

porosity in a vuggy rock. Notice the pathway for fluid to migrate in connected pores

and the isolated nature of others. Production of hydrocarbons is dependent upon the

fluid to flow in the porous media.

Grain Packing: Textural parameter of importance is the packing or arrangement ofgrains. As shown in Figure below, for uniform grains the porosity will be different for

cubic vs. rhombohedral structures, with the cubic packing the maximum for

uncompacted sand grains.

Question 1: Determine the porosity for the cubic packing arrangement in Figure

above.

Solution:

Define the unit cell with sides equal to twice the radius of the sand grain, 2r. The bulk

volume of the cell becomes,

Vb = (2r) 3 = 8r3






Figure - Example of cubic and rhombohedral packing

The volume of an individual sand grain is, Vg = 4/3 π r3. Within the unit cell there are

8 – 1/8 sand grain spheres, or one grain volume. Porosity can now be determined from

basic equation.

∅ = − =

−

= − =.

Notice the radius of the sand grains cancel and therefore porosity is a function of

packing. The theoretical porosities for various grain packing arrangements can be

calculated. The theoretical maximum porosity for a cubic packed rock made of

spherical grains of a uniform size is 0.4764, and is independent of grain size. The

maximum porosity of other packing arrangements is shown in Table below. The

calculations of these ideal porosities is relatively simple.






Figure – Porosities of different ordered packing arrangements

Question 2: Routine core analysis use core with cross section area of 3 cm2 and

length of the core is 5 cm. Dry core weighing 50 grams saturated for 24 hours in

saline water of density 1.02 gm/cc. Weight of saturated core is measured 56 grams.

Calculate the porosity of the system?

A. 38.2 %

B. 39.2 %

C.

59.2 %

D. 41.2 %

Solution:

∅ =

When core is saturated with water, volume of absorbed water is equal to pore

volume of core sample.

= −






= −

= = ∗

= (−). = .

∅ = . ∗=.%

Reference –

1. Petrophysics MSc Course Notes by Dr. Paul Glover

2. Horgan, G. W.; B. C. Ball (1994). "Simulating diffusion in a Boolean model of soil pores". European

Journal of Soil Science.

3. Glasbey, C. A.; G. W. Horgan; J. F. Darbyshire (September 1991). "Image analysis and three-

dimensional modelling of pores in soil aggregates". Journal of Soil Science

4. SPE Handbook

Basic Porosity Concept1

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