Page 95 - Origin and Prediction of Abnormal Formation Pressures

76 A. GUREVICH, G.V. CHILINGAR, J.O. ROBERTSON AND E AMINZADEH

characteristics, pressure should be divided into free and forced convection components
each of which can be correlated with proper parameters causing them.
Free convection pressure distribution for underground water flow, in the absence
of forced convection factors, can be easily done with reasonable approximation by
mathematical simulation. Water table position can be determined with a substantial
precision. Permeability distribution can also be assumed to be close enough to the actual
one. As a result, an error in simulated pressure distribution will be mostly within a range
of 1-2 kg/cm 2 and less.
It is not possible to calculate forced convection pressure distribution because many
values are unknown. The only way to evaluate forced convection contribution to the
total pressure value would be to subtract the free convection pressure component from
the total pressure value. This can be done only if the free and forced convection pressure
components can be considered additive. This is possible to do precisely if fluid and solid
are assumed to be incompressible (Gurevich, 1972) or with a reasonably small error for
most natural environments.
It is necessary to examine conditions under which the total pressure can be divided
into a sum of free and forced convection components with acceptable approximation.
Water constitutes more than 95 to 99% of fluid filling rock pore space. Thus, it is
possible to use equations for water only, for simplicity. Assuming that Darcy's law
is valid for water flow, the boundary problem for pressure p distribution in a basin,
formulated in general (ignoring changes in rock volume and, thus, in coordinates tied to
it) is:

div
# Ot

p(F1) = 0 (3-4)

(-Vp + pg)n = kI.t(l-"2) (3-5)
where p is the water density, K is the permeability tensor, # is the water viscosity,
g is acceleration of gravity vector, n is a normal to the boundary surface, ~b is the
rock porosity, t is the time, G is the intensity of source or sink of water, F1 is the
upper boundary (the water table), F 2 is the side and bottom boundary, and qJ(F2) is a
prescribed function. The first term in Eq. 3-1, the flow changes, can be presented as a
sum of two flows for two additive components of pressure. Boundary conditions also
can be divided into two sets for these additive boundary problems. It is obvious that
whether or not this problem for pressure p can be presented as a sum of two problems
for the free and forced convection depends only on whether fluid and rock compression
determined by the total pressure can be presented as a sum.
Two cases may be considered: (a) the fluid flow volume can be divided into two
separate volumes where free and forced convection occur separately, and (b) the actual
flow combines free and forced convection components.
The first case is the simplest one: a poorly permeable clayey or salt formation
divides the geologic section into two hydraulic sections. The fluid dynamics in the upper
section depends mostly on the water-table relief and, often negligibly, on heterogeneity