Page 297 - Geology and Geochemistry of Oil and Gas

MODELS OF DYNAMIC GEOLOGIC SYSTEMS 259
This problem is solved by making three assumptions and using their implications:
(1) The process of postsedimentary changes and consolidation of sediments is
affected by many natural factors.
(2) The effect of each factor is unique and differs from those of other factors.
(3) The final result is the sum of individual influences of all natural factors on the
sediments during their transformation into rocks.
Thus:
(A) Assumptions (1) and (2) indicate that the individual influences of any factor on
the overall result of consolidation are small and are inversely proportional to
the number of factors.
(B) Assumption (2) indicates that the influence of each factor is not equal to that of
others.
The above discussion allows one to reach the following conclusions:
(1) Small influences of each ith factor resulting in a relative change in the volume
of consolidating sediments, U, can be represented as dU i /U i , whereas the cumulative
R
influences of all the factors can be represented by dU i /U i . This expression is some-
what analogous to Hooke’s law: dU i /U i ¼ bs, where b is the modulus of elasticity
and s is the affecting stress. If bs is understood not only as the effect of static load,
but also as the influence of any ith factor, one would obtain:

U n
Z
X
dU i =U i ¼ c i (11.91)
U o i¼1
where U o is the rate of initial compaction and c i the influence of ith factor.
Hence, one can derive the following equations:

!
n
X
U t ¼ U o exp c i (11.92)
i¼1
and

n
Y
(11.93)
U t ¼ U o x i
i¼1
where U t is the rate of compaction at the present moment of time, x i ¼ expðc i Þ, and
Q n
i¼1 i is a generalized measure of a change in parameter U.
x
(2) Differences in the physicogeological nature of factors affecting the rock con-
solidation require their presentation in the form of relative dimensionless values that
correspond to a formal type of individual influence dU i /U i . The influence of the ith
factor (dU i =U i c i ) is evaluated (a) from the results of direct laboratory measurements
on cores (reproduction of Hooke’s law), (b) by using analogies when the direct phys-
ical simulation is impossible, or (c) by actual field observations and measurements.
Based on the above assumptions, a multivariable model was proposed for eval-
uation of the rate of compaction and diagenetic changes of sediments after their