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)
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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
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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.
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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.
= −
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= −
= = ∗
= (−). = .
∅ = . ∗=.%
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