Ebrom, Daniel^{1}, Philip D. Heppard^{1}, Michael Tompkins^{1},
Leon Thomsen^{1}

(1) BP Amoco, Houston, TX

ABSTRACT: Compaction, Stresses, and Velocity in High Overpressure

An approximation in analyzing pore pressure is to assume that effective stress (stress
supported by the rock matrix) is equal to the differential stress (overburden stress minus
pore pressure). This is Terzaghi’s relation, and there are good theoretical reasons
to expect Terzaghi’s relation to be modified for large effective stresses.
Biot’s theory predicts that the ability of pore pressure to reduce effective stress
is governed by a multiplier n, equal to (1 – Kb/Kg). Here Kb is the matrix bulk
modulus, and Kg is the grain bulk modulus.

If n were equal to 1 regardless of depth, then it would be possible for primary
overpressure to maintain a shale in a compaction state corresponding to a very shallow
depth. Analysis of a suite of shale P-wave stacking-velocity-derived interval velocities
from Tertiary clastic basins distributed around the globe tells a different story.
Specifically, the minimum P-wave velocity of shales is given by a best fit relation of
1500 m/s + 0.239 m/s/m*(depth in meters).

If we assume that the lowest shale velocities correspond to sediments with pore pressures
almost at the fracture gradient, then we are led to the conclusion that n must be less
than 1 in real sediments at depths of interest to the petroleum community. The practical
conclusion is that shales can be at a higher pore pressure than we might have predicted
based on the assumption of effective stress being equal to differential stress.

AAPG Search and Discovery Article #90026©2004 AAPG Annual Meeting, Dallas, Texas, April 18-21, 2004.