Page 295 - Geology and Geochemistry of Oil and Gas

MODELS OF DYNAMIC GEOLOGIC SYSTEMS 257
The second model is derived from the equality of absolute change in the variable y
to the value of this variable reached by a certain moment of time, i.e.,
dy ¼ cy (11.84)
resulting in an exponential dependence of the variable y on the factor of propor-
tionality c:
y ¼ y e c (11.85)
o
If the process is affected by the sum of different factors, then the equation becomes
n !
X
y ¼ y exp c i (11.86)
o
i¼1
This model can be transformed into a model of multiplication
n
Y
y ¼ y (11.87)
o X i
i¼1
where X i ¼ expðc i Þ, and Q n X i is a generalized measure of the change in variable y.
i¼1
Based on the principle of equality of the rate of evolution of compaction process
to the obtained value of some parameter characterizing this process, the writers
obtained a number of models:
(a) Model of sediment compaction (compaction model by Terzaghi, 1961):

U t ¼ 1 h t =h o ¼ 1 f½h min expðc h h min tފ=½h min h o ð1 expðc h h min tÞފg
(11.88)
where U t is the relative compaction of sediments, h o , h t , and h min are the thicknesses
of the layer before compaction, at time t, and for the completely compacted rock
(lowest, minimum value), respectively; and c h is the factor of proportionality.
(b) Model of density:
g ¼ ½g g expðc g g tފ=½g g ð1 expðc g g tÞފ (11.89)
t o max max max o max
where g , g , and g max are rock densities at time t, before compaction, and for the
t
o
completely compacted rock, respectively; and c g is the factor of proportionality.
(c) Model of porosity:
f ¼ ½f expð c f tފ=½1 f ð1 expð c f tÞފ (11.90)
t o o
where f and f are porosities before and at a certain time during the process of
o t
compaction of sediments; and c f is the factor of proportionality.
Models based on Eq. 11.87 were widely used in predicting reservoir-rock
properties and physical properties of terrigenous rocks at different geological and
physical environments of the South Caspian Basin, Daghestan Plain, and the Middle
Caspian Basin at depths of 6–9 km. Many examples are given by Buryakovsky et al.
(1982, 1990, 2001).

11.3.3.2. Simulation of rock properties
The main factor of postsedimentary changes of any deposits is the compaction of
overlying strata, resulting in the continuous decrease of the initial porosity of