Page 301 - Geology and Geochemistry of Oil and Gas

262 MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

TABLE 11.12

Equations of normalization for natural factors (see Table 11.11)
Factor Equation of normalization
Absolute geological age, A t (My) T A ¼ 0.002A t
Dynamic deformation, N (tectonic-strat. units) T N ¼ 0.2+1.46 log N
Depth of burial, D (km) T D ¼ 0.167D
o
Formation temperature, T ( C) T t ¼ 0.005T
Rate of sedimentation, R d (m/My) T V ¼ 0.5(log R d 1.3)
Content of quartz in sandstones, Q (wt%) T Q ¼ 1 0.01Q
Content of smectites in clays, M (wt%) T M ¼ 0.02M
Cementation index, C (wt%) T C ¼ 0.033C
T ss ¼ 0.1(S ss 1)
Sorting coefficient of sandstones, S ss
T sh ¼ 0.1(11 S sh )
Sorting coefficient of shales, S sh
Homogeneity of carbonates, S cr T cr ¼ 0.1S cr

Only five natural factors affect the compaction of carbonate rocks. The ‘‘strong’’
factors: geologic age, the number of tectonic cycles, depth of burial, and temper-
ature. The ‘‘moderate’’ factor is the homogeneity level.
For shales, there are eight natural factors. The ‘‘strong’’ factors: geological age,
depth of burial, and rate of sedimentation. The ‘‘moderate’’ factors: the number of
tectonic cycles, content of smectites (montmorillonite), and cementation. The
‘‘weak’’ factors: the sorting coefficient and temperature.
Modeling coefficients are calculated using the following equation:
x i ¼ expð a j T i Þ (11.95)

where a j is the coefficient of influence of normalized value T i of any natural factor on
the various rock properties x i . Coefficients a j were obtained by examining numerous
experimental data (Buryakovsky et al., 1982; Chilingar et al., 1979) and are pre-
sented in the following table:

Rock type Degree of influence of natural factors, a j coefficient (Eq. 11.95)

Strong Moderate Weak
Reservoir rock 0.968 0.714 0.511
Caprock 2.996 1.833 1.309

Using modeling coefficients, one can calculate the Z factor:
n
Y
Z ¼ U t =U o ¼ x i (11.96)
i¼1
The Z factor characterizes the relative compaction and other diagenetic changes of
sediments, i.e., the relative consolidation of rocks. This factor is used for calculating