Page 51 - Origin and Prediction of Abnormal Formation Pressures

34 G.V. CHILINGAR, J.O. ROBERTSON JR. AND H.H. RIEKE III

with each other and the fluid wetting the clay-particle surfaces and filling the pore space
between the particles. If the mechanical model were sealed in such a manner that no
fluid could escape through the plate, then the total applied pressure to the system would
be carried by the fluid and none by the spring (Fig. 2-5B). The compressibility of the
spring is assumed to be so great that the strains produced in the fluid and in the cylinder
walls are negligible in comparison (Taylor, 1948, p. 223). Fig. 2-5C shows that if the
fluid is allowed to escape through the perforations, then the overburden pressure is
carried both by the spring and the fluid. As the fluid escapes, the plate sinks lower and
lower, compressing the metal spring. The length of time required for the spring to pass
from one state of compaction to the next depends on how rapidly the water escapes;
this is determined by the size of the perforations in the plate. Equilibrium is reached at
a point where none of the overburden stress is borne by the fluid (Fig. 2-5D); however,
any additional applied loads cause the plate to compact the spring still further, expelling
additional fluid. In this manner the clay layers are thought to be compacted under the
weight of the overlying sediments.
In the spring analogy of the compaction, the following relationship (static equilib-
rium) must exist at any particular time:
Ft = Fs + Fw (2-31)
where Ft is the total overburden force applied to the system, Fs is the force carried by
the spring, and Fw is the force applied to the fluid. If these forces are divided by the total
cross-sectional area, A, of the enclosing cylinder, then:
Pt or o- = Ft/A (2-32)

Pe or or'= lS~/A (2-33)
pp or aw = Fw/A (2-34)

where pt or cr is the total stress applied to the system, Pe or a' is the effective stress, and
pp or cr w is the pore-water pressure. Thus, Eq. 2-31 can be rewritten as:
cr = o-' + aw (2-35)

As expressed in Eq. 2-35, the total stress, or, normal to any plane in the skeletal
structure consists of two components: (1) the pore fluid pressure, Crw; and (2) the
effective stress component, or', which is 'effectively' carried by the skeletal structure.
The spring analogy fails to agree with the actual compaction of clay in that the
pressure conditions are not the same throughout the thickness of the clay mass as they
are in the cylinder. In compacting saturated clay at a given pressure, the water pressure
at its surface is atmospheric (0 psig), whereas at short distances inside the clay sample
the water pressure is equal to o- - or'. Fig. 2-6 illustrates a void space surrounded by a
shale matrix. In this figure, the total weight of the overburden, which acts downward,
and the vertical and horizontal portions of the effective stress are shown. The high
fluid-pressure gradient at the clay's surface is caused by the rapid expulsion of the
fluid from the pores near the surface. Under a constant overburden pressure, the water
pressure decreases with time, whereas the intergranular pressure increases.