Page 50 - Origin and Prediction of Abnormal Formation Pressures

ORIGIN OF ABNORMAL FORMATION PRESSURES 3 3

where crl is the total major stress, ~r2 is the total intermediate stress and or3 is the total
minor stress.
According to Lo (1969), the physical justification for Eq. 2-30 lies in the fact that un-
der ambient stress, the induced pore pressure corresponds almost exactly to the applied
pressure, because the compressibility of the pore water and argillaceous sediment grains
are much lower than that of the sediment structure. Most of the pore-pressure equations
presented in literature give almost identical results providing they are properly used. For
further detailed discussion see Rieke and Chilingarian (1974).

Spring models of compaction

The concept of the shale-compaction process can be best explained by a mechanical
model which is composed of a perforated, round metal plate and the enclosing cylinder
which contains a metal spring and water (Fig. 2-5). In this analogy, the spring represents
the compressible clay particles, the water represents the fluid in the pore space, and the
size of the perforations in the metal plate determines the permeability.
Using this model, well-saturated clay can be treated mathematically, as a two-phase
continuum. The hydrated clay is envisioned as clean clay plates in mechanical contact

A B C D
Overburden Pressure Overburden Pressure
0 psig 25 psig Overburden Pressure
= 9 25 psig
Overburden Pressure
25 psig
Perforated plate
/ /
/ t.t
Manometer

or'= 0psig ~'= 0psig or'= 3psig ~'= 25psig
~w = 0 psig crw = 25 psig ~ = 22 psig crw = 0 psig
)~ =infinity ~L = I )~ - 0.875 X = 0
Fig. 2-5. Compaction analogy using a spring and perforated plate, o -t is the effective (intergranular) stress,
~w is the pore-water stress and X is the ratio of the pore-water stress to the overburden stress on the system
(c~ t and Crw are in psig). (Case A) Initial conditions; tightly fitted, frictionless metal plate seals the water in
the cylinder. There is no overburden load on the system and perforations of plate are sealed. (Case B) A
25-psig load is imposed on the model. This load is entirely carried by the water. Perforations in the plate
are sealed. (Case C) The fluid is allowed to flow out through the perforations. The plate descends as the
fluid escapes. The spring carries a portion of the load. (Case D) The spring now carries the entire 25 psig
load. The system is in equilibrium and there is no water outflow. (Modified after Taylor, 1948; in Rieke and
Chilingarian, 1974, fig. 49, p. 90.)