Page 197 - Origin and Prediction of Abnormal Formation Pressures

172 F. AMINZADEH, G.V. CHILINGAR AND J.O. ROBERTSON JR.

1)2 = (-1.882 x 10-1~ 2) -+- (7.2947 • 10-6)d + 0.4267, for d > 5000 ft
(7-6)

5000 ~' - 41 O0 ~:
l) 3 = l) 1 --[- (d - 4100) , for 4100 ft > d > 5000 ft (7-7)
900
Substituting v from Eqs. 7-5 to 7-7 in Eq. 7-4, one can derive a value for K for
inclusion in Eq. 7-3.

Dutta's method

Dutta (1988, 2002) expressed effective stress as a function of temperature, shale void
ratio, and diagenetic integral depending on the time and temperature.

Fillippone formula

Fillippone (1982) developed the following formula:
Poverburden (Vp-grain - Vp-inst) (7-8a)
pp- Vp_grain- Wp_fluid
where Wp-grain is the velocity when the porosity goes to zero (approximated to matrix
velocity of the rock), Vp-nuid is the velocity when rigidity goes to zero (approximated
to pore fluid velocity), and Wp-inst is the instantaneous velocity. The Po in the above
equation is calculated from the following equation

Po (D) = PhP D (7-8b)
where hydrostatic gradient is equal to 0.465 psi/ft, fluid density is 1.073 g/cm 3, p is the
density, and D is the depth.
Eq. 7-8 is valid only in certain areas. When it is applied to other areas, errors are
usually over 10% (Fillippone, 1982).

Modified Fillippone formula

In 1982, Fillippone presented a modified formula (Fillippone, 1982):
Poverburden (Vp-grain -- Vp-inst)
pp = C Vp-~n~t (7-9)
V - r in- Vp- uid
C Vp-inst may be calibrated by well log data. In some areas,
C Vp-inst = 0.18677e ~176176176 .... (7-10)
If density logs are not available, for OBG calculation in Eqs. 7-1, 7-2 and 7-3, one has to
use synthetically derived densities. One conventional method is to use the well-known
Gardner equation (Gardner et al., 1974):
p = 0.23 V ~ (7-11)
where V is the interval velocity. Another empirical relationship to develop the rock
density curves has been reported by Traugott (1997). It is also known as the Amoco