Page 126 - Well Logging and Formation Evaluation

116 Well Logging and Formation Evaluation

K b = stress strain = P overburden - P formation (d V dry V).

d V = d V m + d V dry = P formation . VK m +( P overburden - P formation ). VK b (7.3)

The strain is given by:

dVV = P formation K m +( P overburden - P formation ) K b . (7.4)

The true effective rock stress is given by K b * strain:

* )
= K b (P formation K m +(P overburden - P formation ) K b
- (1 - K K m * (7.5)
) P formation .
= P overburden b
The factor (1 - K b /K m ) is usually denoted by a and called the poroelas-
tic constant. As long as K m >> K b , then a~ 1 and the net effective stress
is a good approximation of the true effective stress.
This assumption may break down if soft shales are present as part of
the matrix. Experiments on North Sea samples from the Fulmar forma-
tion have shown that values of a as low as 0.7 may be encountered. Where
stress issues are likely to be important, such as where compaction and
subsidence are likely to have an impact, it is recommended to make
measurements of a on representative core samples.
For reasons that will be explained, s z is not the pressure that should be
used for SCAL (special core analysis) measurements at in-situ conditions.
Because the rock is constrained laterally, there are also lateral stresses
(s x and s y ), which, because of the firmness of the rock, will be less than
the vertical stress. In a normal reservoir, where there is no significant
difference in s x or s y , they are given by:

s x = s y = s z * m (1 - m) (7.6)

where m is Poisson’s ratio of the rock, related to V p and V s via:
2
)
m= ( [ VV s 21 p ) - ] 1 . (7.7)
- ] ( [ VV s
p
The average stress (s iso ) experienced by the rock is given by:
s iso = ( s x + s y + s z ) 3 = * + m) [3* (1 - m)]. (7.8)
s z (1
In a laboratory SCAL experiment, any confining stress is applied evenly
over the sample, hence “isostatic” (or “hydrostatic”) conditions apply.