Page 74 - Petroleum Geology

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Figure 3-8 shows the family of curves of At for various values of scale length.
It will be noted that departure from linearity (log At with depth) is slight at
shallow depths and with larger values of b. The scale length is therefore inter-
preted as a parameter that takes time, temperature, and the compressibility
of the mineral grains and the bulk material into account.
It is possible that the compaction of sandstones can be described by similar
equations with a scale length so large that the porosity-depth relationship
is almost linear.

PORE-WATER EXPULSION

Sediments and sedimentary rocks can only compact if a commensurate
volume of pore water can be expelled. Compaction leads to a reduction of
bed thickness as well as a reduction of porosity. Earlier in this chapter we
noted that very large volumes of water must be expelled during compaction of
mudstones, and it is becoming increasingly important for quantitative geolog-
ical and geochemical studies of source rocks and primary migration to be
able to assess the quantities of pore fluids expelled, and to reconstruct the
stratigraphic thicknesses and depths at earlier stages of the accumulation of a
sequence of sedimentary rocks.
The volume of pore water expelled during compaction from fractional
porosity fl to f2, expressed as a proportion of the bulk volume at porosity fit
is approximated by:
(3.10)
4 = (f2 - fl)/(l - fl)
assuming constant volume of solids and incompressibility of water. (This
equation is quite generai: if f2 is larger than fl, q is positive and represents
the additional proportional volume required for porosity fl to be increased to
f2.)
To estimate the thickness at porosity fl when the present thickness at fz is
known, the known thickness is multiplied by the compaction factor, 1 - 4.
Equations 3.7 permit us to estimate these quantities from the sonic log
data. For example, compaction from At, = 120 ps/ft to At2 = 100 ps/ft
corresponds with compaction from fl = 0.295 to fz = 0.205. The change of
volume, as a proportion of the volume at At2 and f2, is -0.13. This amounts
to 130,000 m3 km-’ per metre of thickness at 20.5% porosity. The original
thickness was greater by a factor of 1.1 3.
Conversely, when mudstones are undercompacted for their depth, there is
a volume of water that has not been expelled. The resulting porosity is greater
than normal for that depth, and the transit time longer than normal. For ex-
ample, the sonic log shows a transit time of 115 ps/ft in mudstone at a depth
at which the normal transit time (from eq. 3.8) would have been 90 ps/ft.
So fl = 0.159 and fz = 0.273. The proportion of the present volume at