## Simulation Of Porefluid Formation Pressure

The description of processes of pore-fluid pressure generation and destruction is obtained from Equations 89, where f1(x1) = p1 and f2(x2) = p2 are pore-fluid pressures in the process of their increase and decrease, respectively. This dynamic model satisfied the following conditions:

1. A current pore-fluid pressure at any moment of time is a result of dynamic equilibrium among the synchronous processes of generation/dissipation of these pressures in a given geologic object.

2. Natural factors affecting generation/dissipation of pore-fluid pressures are permanent.

3. The rate of change in pore-fluid pressure in a given geologic object is proportional to the current pore-fluid pressure.

4. Pore-fluid pressures increase/decrease so that a constant portion of the current pore-fluid pressure increases/decreases per unit of time (the given condition is not obligatory).

5. Factors of pressure drop act so that a portion of pressure decrease per unit of time is equal to the product of increasing portion of the pressure by its decreasing portion.

Dynamic models can be described by a system of nonlinear differential first-order equations as follows:

where p1 = p1(t) is the pore-fluid pressure during the period of its increase; p2 = p2(t) is the pore-fluid pressure during the period of its decrease; e1 and e2 are coefficients of pore-fluid pressure change during the periods of its increase and decrease, respectively; and y12

and y21 are coefficients of interaction of natural factors determining either preservation or change of the pore-fluid pressure.

The system of Equations 134 describe the theoretical processes of generation, stabilization, preservation, 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 y12 = Y21 = 0, Equations 134 are reduced to two equations, one of which describes the abnormal pore pressures, and the other, a drop to 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:

p1 = [pmaxpo^p^pmaxOMpmax " Po(1 - e^^»] (135)

where po is the initial value of the pore pressure (hydrostatic pressure of water at a depth where sedimentation began), pmax is the maximum possible pore pressure at given conditions, and t is time. The coefficient of proportionality calculated for the South Caspian Basin averages 0.02 (MPa per million years)-1.

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 Equation 135. This assumption is probably true for the South Caspian Basin, taking into account a relatively young age of rocks, absence of noticeable faulting, 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 (Buryakovsky et al., 1986c).

Using Equation 135, it is possible to describe the dynamics of the pore-fluid pressure (Figure 12-7a) and to forecast the pore pressure in the reservoir rocks and caprocks at various depth (Figure 12-7b) for the various regions of the South Caspian petroleum province (Buryakovsky and Chilingarian, 1991c).

Fertl (1976), Fertl and Chilingarian (1976), and Magara (1982) pointed that the abnormally-high pore pressures have different origin and can be caused by various natural factors superimposed upon each other. In the South Caspian Basin, for example, with accumulation of

Pressure, MPa

0 20 40 60 80 100 120

0 20 40 60 80 100 120

thick sand-shale sequences (mainly shales), the most probable mechanism for abnormally-high pore pressure development is gravitational consolidation with upward filtration of fluids. Gravitational consolidation prevails over the upward flow of fluids at rapid rates of sedimentation. This leads to a considerable undercompaction of sediments (mainly shales) and development of abnormally high pore pressures.

It has been shown (Buryakovsky et al., 1986c) that hydrostatic pressure gradients in shales at the depth interval of 1,000-6,000 m

(over 2,000 determinations by well-logging) range from 0.012 to 0.024 MPa/m with an average value of 0.018 MPa/m (Figure 12-8).

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