Page 298 - Geology and Geochemistry of Oil and Gas

260 MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

deposition in the sedimentary basin. The general form of this model is
n
Y
(11.94)
U t ¼ U o x i
i¼1
where U o is the rate of initial compaction of sediments and U t is the rate of com-
paction at a given depth and at a certain geologic time t, and x i is the modeling
coefficient.
In selecting the modeling coefficients, one must consider: (1) conditions of accu-
mulation of terrigenous or carbonate sediments, (2) their postsedimentary changes
(diagenesis and catagenesis or epigenesis), and (3) the structural evolution of the
region. One should recognize the role of different factors, such as external (pressure,
temperature, etc.) and internal (lithology, mineralogic composition, cementation, etc.).
The characteristic feature of coefficients x i is their independence, which is a nec-
essary condition for the model (Eq. 11.94). Numerical values of x i coefficients cor-
responding to the c i factors are given in Table 11.11. Their evaluation is carried out
according to the initial data of experimental and field studies (Buryakovsky et al.,
1982, 1990).
Modeling coefficients take into account the influence of major geological (natural)
factors on compaction and other diagenetic and catagenetic changes of rocks. These
factors are as follows:
(1) geologic age (in million years — My),
(2) number of tectonic (orogenic) cycles (in dimensionless tectonic-stratigraphic
units),
(3) depth of burial (in km),
(4) temperature (in 1C),
(5) rate of sedimentation (in m/My),
(6) content of quartz in sandstones (in wt%),
(7) content of smectites (montmorillonite) in shales (in wt%),
(8) degree of cementation (content of CaCO 3 in wt%),
(9) sorting coefficient of Trask, and
(10) degree of homogeneity of carbonate rocks (dimensionless).
Ranges in the absolute values of natural factors are shown in Table 11.11. Scales
of absolute values of natural factors are presented in this table. Model (Eq. 11.94)
requires a normalized form of natural factors. Normalization equations for natural
factors are shown in Table 11.12. These equations, which relate the absolute and the
normalized scales, were obtained from data in Table 11.11.
The number of natural factors used in Eq. 11.94 varies depending on the type of
rocks. The influence of a particular factor is also different for each type of rocks.
There are three types of natural factors with a different influence on rocks: strong,
moderate, and weak.
The ‘‘strong’’ factors affecting the compaction of sandstones are as follows: ge-
ologic age and depth of burial. The factors of ‘‘moderate’’ influence: the number of
tectonic cycles (epochs), quartz content, and cementation (CaCO 3 content). The
‘‘weak’’ factors: rate of sedimentation, sorting coefficient of Trask, and formation
temperature. Thus, eight natural factors affect compaction of sandstones.