Page 96 - Origin and Prediction of Abnormal Formation Pressures

ORIGIN OF FORMATION FLUID PRESSURE DISTRIBUTIONS '[']

of fluid density. Thus, fluid flow in this section is presented only by free convection.
The influence of water table in the lower section is negligible due to the sealing action
of the poorly permeable formation and fluid flow is determined completely by the
processes that change the volumetric ratio of fluid and pore space volumes. Thus, only
forced convection occurs in the lower section (local fluid flows within this stage can be
considered, at a certain scale, as one of mechanisms of volume changes).
This situation can easily be described by two boundary problems. Pressure distribu-
tion in the upper stage can be described by the following boundary problem:
div lPK(-vp + --0 (3-6)

p (1-'1) =0 (3-7)
[- ]
7(-Vp + pg) (r2) - 0 (3-8)

Equations describing density and viscosity distributions, their dependence on temper-
ature and pressure, etc. may or should be added when necessary. Pressure, p, is the fluid
pressure above the atmospheric one; thus, pressure is zero at the upper boundary (water
table). There is no flow through the side and bottom boundaries: flow into the upper
section from the lower one is negligible compared to the flow in the upper section.
Solution of the above system (Eqs. 3-6, 3-7, 3-8) gives a function p(F2) for pressures
at the lower boundary of the upper section, i.e., the upper boundary of the lower section.
Then the forced convection pressure component p* can be calculated as follows:
P* = Pac -- (P -k- 7'h) (3-9)
where Y is the fluid specific weight and h is the vertical depth of the point with pressure
Pac; h is measured from the boundary surface F2. This is the p* value that should be
correlated with parameters which determine the forced convection. The error of such
a procedure of discriminating the forced convection component of pressure can be
established for each particular case by mathematical simulation. Generally, it will rarely
exceed about 25 to 30 psi.
Values of p* lower than the error should not be taken into account. For abnormalities
with p* higher than 100 psi and more such an accuracy is excellent, and correlation will
be pure from physics and geology viewpoints (free from influence of irrelevant factors)
and highly reliable.
The second case is the situation when poorly permeable formations dominate in the
whole section. Here, the boundary problem for the free convection should be solved for
the total segment of depth and resulting pressure distribution subtracted from the actual
pressure distribution. The difference p* may be assumed to be the forced convection
pressure component with approximately the same precision as in the previous case.
When a more definite evaluation is necessary, the error should be established by
simulation.
Evaluation of the error of approximation of an actual formation fluid pressure by the
sum of these two components for different geologic situations is a subject of a special
thorough analysis.