Page 196 - Origin and Prediction of Abnormal Formation Pressures

SEISMIC METHODS OF PRESSURE PREDICTION 171

depth:

Pp -- Po -- (Po -- Ph) ~o (7-1)
where pp is the predicted pore pressure, Ph is the normal hydrostatic pressure, Atn
is the normal shale travel time, Ato is the observed shale travel time, and N is an
experimental coefficient. This method of predicting pore pressure is based upon the
assumption of sediment compaction; thus, it is appropriate in sand-shale sequences
only. The exponential coefficient, N, is determined for different regions (geological
basins) and for offset wells. A typical N value in the Gulf of Mexico is 3.

Eaton's exponent for pore pressure determination from resistivity logs

Eaton's transient time equation can also be expressed in terms of resistivities:

Pp -- Po -- (Po -- Ph) Rn (7-2)
where Ro is the observed shale resistivity and Rn is the resistivity of normally compacted
shale. The exponent M is usually chosen to be 1.2 for the Gulf of Mexico.

Eaton's fracture pressure gradient equation

In Eqs. 7-1 and 7-2, the overburden pressure is critical to the accuracy of prediction
of overpressures. In vertical wells, the fracture pressure is related to the overburden
pressure, horizontal stress and pore pressure. To fracture a formation would require a
drilling mud weight pressure at least equal to the formation pressure. Any additional
required pressure must be related to overcoming the horizontal stress and/or the
cohesive strength of the rock matrix. Eaton's fracture gradient equation (Eaton and
Eaton, 1977) is based on the equation developed by Mathews and Kelly (1967) to
calculate the fracture pressure:

pf = pp n L K (Po - Pp) (7-3)
where pf is the fracture pressure, and K is the coefficient describing horizontal
stress/vertical stress.
Eaton used the following expression in terms of the empirical depth-dependent
Poisson's ratio, v, to calculate K:
v
K = (7-4)
1--v
From the data collected worldwide by Eaton, he was able to generate depth-dependent
heuristic equations for v. This was done through a multi-segmented regression analysis
of the empirical relationship between v and the depth below the mud line in feet (d and
d2). For deep water, the fit was reasonable in many cases. The following are expressions
for v:
Vl = (-6.0893 x 10-9d 2) -k- (8.0214 x i0-5)d + 0.2007, for d < 4100 ft
(7-5)