Page 106 - Physical Principles of Sedimentary Basin Analysis

88 Compressibility of rocks and sediments

Solution: We have
V s (V b − V p ) V b V p
= = − (4.56)
V s V b − V p V b − V p V b − V p

V b V b V p V p
= − (4.57)
(V b − V p ) V b (V b − V p ) V p
1 V b φ
V p
= − (4.58)
(1 − φ) V b 1 − φ V p
which is relationship (4.48).

4.4 Effective pressure coefficients
The compressibilities were defined by relative changes of the bulk volume and the pore
volume in response to changes in the bulk pressure and the pore fluid pressure, as given by
equations (4.5) and (4.6). These equations can also be written as
V b
=−α bc ( p b − γ b p f ) (4.59)
V b
V p
=−α pc ( p b − γ p p f ) (4.60)
V p
in terms of the effective pressure coefficients

α bp K
γ b = = 1 − (4.61)
α bc K s
α pp K p
γ p = = 1 − . (4.62)
α pc K φ
It turns out that the effective pressure coefficients often have values close to 1, which

implies that 1/K
1/K and 1/K φ
1/K p . Effective pressure coefficients close to 1
s
can also be written as α bp ≈ α bc and α pp ≈ α pc , which means that the rock then is equally
compressible with respect to the (confining) bulk pressure as to the (pore) fluid pressure.
Effective pressure coefficients can also be introduced for the porosity and the solid volume.

4.5 Compaction of sediments
Soils are different from rocks by being loose aggregates of particles. Different types of
soil can be grouped with respect to their mineral content and the size of the particles. For
instance (clean) sand is comprised of quartz grains of a relatively large size, while clay is
comprised of very fine particles. Although there is a great difference between soils like sand
and clay all soils are found to compact by loss of void space caused by a rearrangement and
crushing of the grains. The compressibility of the mineral grains themselves is considered
negligible. A direct way to measure compaction of soils is to use an oedometer test, where