Page 24 - Physical Principles of Sedimentary Basin Analysis

6 Properties of porous media

(a) (b)
Figure 2.4. Regular porous media. (a) Two grain sizes. (b) Rhombohedral packing.

scale. We will meet the Athy porosity function later since it is a convenient function to
work with.
Exercise 2.1 What is the porosity and the void ratio of a medium with exactly the same
amount of void space as solid volume?

Exercise 2.2 Derive relationship (2.3).

Exercise 2.3 Calculate the porosity of the regular porous medium shown in Figure 2.1a,
where all grains have equal size. Is the porosity dependent on the grain size (the radius)?

Exercise 2.4 Calculate the porosity of the porous medium shown in Figure 2.4. Notice
that grains of different sizes allow for denser packing.

Exercise 2.5 The porosity of a dry rock sample can be measured from the increase in
weight by filling the pore space by a wetting fluid. What is the porosity of a sample if its
mass increases with m, when it is filled with a fluid of density , and it has the total
volume V t ?

2.2 The correlation function and specific surface
A porous medium can specified by the characteristic function f defined as

0, when x is in a grain
f (x) = (2.5)
1, when x is in the pore space
where the porosity of the volume V is seen to be
1
φ = f (x) dV. (2.6)
V V
The characteristic function can be used to define the two-point correlation function

1
C(r 1 , r 2 ) = f (x + r 1 ) f (x + r 2 ) dV (2.7)
V V