Page 309 - Geology and Geochemistry of Oil and Gas

270 MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

Hydrocarbon volumes were calculated using the Monte Carlo technique at the
interval-probable setting of reservoir parameters. As discussed by Abasov et al.
(1984), such method of reserve evaluation is more preferable than evaluation using
the average parameters. This allows one to obtain not an average value of reserves
but their variation. Consequently, reliable intervals of real values of reserves (with
the reliability coefficient fixed in advance) can be obtained.

11.3.3.5. Evolution of pore-fluid (formation) pressure
The description of processes of pore-fluid pressure generation and destruction is
obtained from Eqs. 11.77, where f ðx 1 Þ ¼ p and f ðx 2 Þ ¼ p are pore-fluid pressures
1
2
1
2
in the process of being increased and decreased, respectively.
Such dynamic model can be described by a system of nonlinear differential first-
order equations as follows:
dp =dt ¼ 1 p g p p
1
12 1 2
1
dp =dt ¼ 2 p þ g p p ð11:105Þ
2
2
21 1 2
where p ¼ p ðtÞ is the pore-fluid pressure during the period of being increased,
1
1
p ¼ p ðtÞ the pore-fluid pressure during the period of being decreased, 1 and 2 are
2
2
coefficients of pore-fluid pressure change during the increasing and decreasing pe-
riods, respectively; and g 12 and g 21 are coefficients of interaction of natural factors
determining either preservation or change of the pore-fluid pressure.
The system of Eqs. 11.105 describes the processes of generation, stabilization, pres-
ervation, and dissipation of pore-fluid pressures. Due to the difficulty in simultaneous
experimental determination of the coefficients of pressure change and coefficients of
opposite influence of some natural factors, numerical simulation using the models is
possible in a practical case only when the coefficients having opposite influence may be
neglected. For g ¼ g ¼ 0, Eqs. 11.105 is reduced to two equations, one of which
12 21
describes the abnormal pore pressures, and the other, a drop to the normal hydrostatic
pressure. At actual conditions, it is necessary also to take into account the self-retarding
effect of the process, leading to the following equation:
p ¼ ½p max p expð 1 p max tފ=½p max p ð1 expð 1 p max tÞފ (11.106)
o
o
1
where p is the initial value of the pore pressure (hydrostatic pressure of water at a
o
depth where sedimentation began), p max is the maximum possible pore pressure at given
conditions, and t is the time. The coefficient of proportionality, 1 calculated for the
South Caspian Basin averages 0.02 1/(MPa/My).
The change in pressure with depth is assumed to be analogous to the change in
time and may be described by an equation similar to Eq. 11.106. This assumption is
probably true for the South Caspian Basin, taking into account a relatively young
age of rocks, absence of noticeable structuring, one-phase formation of folded
structure, normal bedding of sequential stratigraphic intervals, etc. Other factors can
also influence the development of abnormal pore pressure, but in the South Caspian
Basin they probably play a subordinate role.