Page 98 - Physical Principles of Sedimentary Basin Analysis

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Compressibility of rocks and sediments

4.1 Rock compressibility
Volume changes of a porous rock are linearly related to the pore pressure and the bulk
pressure changes within certain bounds. For large variations in the pressure a rock volume
may behave non-linearly or eventually fracture. The bulk pressure is defined as the mean
normal stress acting on the surface of the rock sample, and it is taken to be the same as the
confining pressure in poroelasticity. It is now possible to define four rock compressibilities
in terms of the bulk volume V b and the pore volume V p with respect to the bulk pressure
p b and pore pressure p f , and they are
1 ∂V b
α bc =− (4.1)
V b ∂ p b
p f
1 ∂V b
α bp =+ (4.2)
V b ∂ p f
p b
1 ∂V p
α pc =− (4.3)
V p ∂ p b
p f
1 ∂V p
α pp =+ . (4.4)
V p ∂ p f
p b
These compressibilities are given the following names: α bc is the drained bulk compress-
ibility, α bp is the bulk volume expansion coefficient, α pc is the drained pore compressibility
and α pp is the pore volume expansion coefficient. A drained compressibility is measured at
a constant pore fluid pressure, because the fluid must be allowed to leave or enter (drain)
the sample in order to keep the pressure constant. Another way to express these compress-
ibilities is to write down the linear relationships between volume changes and pressure
changes:

V b
=−α bc p b + α bp p f (4.5)
V b
V p
=−α pc p b + α pp p f . (4.6)
V p

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