Page 46 - Origin and Prediction of Abnormal Formation Pressures

ORIGIN OF ABNORMAL FORMATION PRESSURES 29

the external pressure". According to him, this factor, n, is structure dependent and,
therefore, is not the same for all sediments:

Pe = Pt - npp (2-13)
Rieke and Chilingarian (1974, p. 6), however, showed that n is equal to one.
Accumulation of additional sediments upon the older sediments will cause a gradual
change in the vertical stress throughout the sediment column. The matrix pressure is
redistributed by the grains squeezing closer together so that they bear more load. Many
authors (Hubbert and Rubey, 1959; Hottman and Johnson, 1965; Powers, 1967; and
others) have stated that for thick shale sequences having low permeability, compaction
is a slow process and the fluid must support the additional load. This creates abnormally
high pore-fluid pressures, which must be balanced by a corresponding decrease in
the shale matrix pressure, because the total weight of overlying rock and water to be
supported is practically the same.

STATE OF STRESS IN COMPACTING SHALES

The lithostatic pressure (overburden weight) is probably equal to the vertical normal
component of the stress. There is the possibility, however, that the normal stress at a
point in a shale body undergoing compaction at some depth is equal to the overburden
weight per unit area plus contributions from the vertical shear components of stress (r).
A total stress field in such a sedimentary body can be specified in terms of its normal
and tangential stress components across a given plane surface (Fig. 1-2) (see Rogers,
1964, p. 25):

f x -- {Crx-Cxy-Cxz}AyAz
Fy = {72yxGy'gyz} Ax Az (2-14)
F z = {rzxrzyCrz}AxAy

where Fx, Fy, and Fz are the forces in the x-, y-, and z-directions. It should be noted
that the pressure (load per unit area) has the dimensions of stress (e.g., psf or psi). The
surface forces are measured in units of force per unit area, whereas the body forces are
measured in units of force per unit volume. Examples of these would be specific weight
and pressure. In the case of a normal stress as expressed in Eq. 2-14, the subscript refers
to the direction (axis) normal to the plane on which the stress acts. In the case of shear
stresses, the first subscript denotes the axis perpendicular to the plane in which the stress
acts, whereas the second subscript denotes the direction in which the stress acts. It is
important to note that one must be consistent in considering either (1) all forces acting
on the system or (2) all forces acting outward from the system.
If Ft is the normal component of the total force exerted on the element, and Ftt is the
tangential component of the force, then for any change in Ft or Ftt, owing to additional
overburden weight, there will be a corresponding change in the shear and tangential