Page 79 - Petroleum Geology

58

This is a dimensionless parameter representing the proportion of the total
overburden supported by fluid pressure. Its value ranges from about 0.45
under normal hydrostatic conditions to near 1 when pore pressures are severe-
ly abnormal. Rearranging eq. 3.13 and substituting eq. 3.14, we obtain:

0 = s-p z (1 -A) Tbw 2- (3.15)
From this we see that as the pore pressure approaches the overburden pres-
sure at depth z, h + 1 and u -+ 0; that is, the effective stress that tends to
compact a sedimentary rock decreases as the pore pressure increases relative
to the overburden pressure, and the rock's compaction is retarded.
This value of effective stress, however, corresponds with that of a normally
compacted but otherwise identical rock at a shallower depth, ze (Fig. 3.13).
At this shallower depth (using the suffix e to denote equilibrium compaction
conditions*) :

= (1 - he) "/bw 2,. (3.16)
Equating eq. 3.15 and 3.16 and accepting that for practical purposes the value
of 'ybw above depth ze does not differ significantly from that above depth 2,
we obtain:
ze/z = (1 - h)/(l - he). (3.17)
This quantity has been assigned the symbol 6 (Chapman, 1972), so:
2, = 6 2. (3.18)
The parameter 6 is a dimensionless quantity that takes pore-fluid pressures
into account. Its value varies from 1 (when X = he) to 0 (when X = 1) and it
may be regarded as a non-linear measure of the extent to which mechanical
compaction equilibrium has been achieved by the expulsion of pore water.
For example, the water pressure measured in a thin sandstone lens within
a thick mudstone was found to be 62 MPa (632 kgf cm-2; 8992 psi) at 3250
m (10,660 ft). Assuming an overburden pressure gradient of 22 kPa/m (0.24
kgf cm-2 m-'; 0,97 psilft) and a normal hydrostatic pressure gradient of 10
kPa/m (0.102 kgf cm-2 m-'; 0.442 psilft) we compute:

S = 22 X lo3 X 3250 = 71.5 MPa
pe = 10 X lo3 X 3250 = 32.5 MPa
he = 0.45
X = 62 X 106/71.5 X lo6 = 0.87
F = (1 - 0.87)/(1 - 0.45) = 0.24.
So, ze = 0.242 = 768 m (2520 ft).

* Strictly, he is the proportion of the overburden supported by the ambient fluid -air, if
subaerial; water, if submarine - but almost all, if not all abnormal pressures are below sea
level, so we may take normal hydrostatic pressures to define he (see Chapman, 1979).