Page 127 - Well Logging and Formation Evaluation

Rock Mechanics Issues 117

This means that less pressure need be applied than the s z calculated in the
reservoir by a factor given by equation 7.4. A typical value for m for sand-
stones is 0.3. This means that the stress needed in the laboratory is only
0.63*s z. Often confusion arises about the relation between the different
types of compressibility measured in the lab on rock samples, so this will
be explained. First of all bear in mind that when compressing a sample
by applying an external stress, the pore pressure may be either kept
constant or allowed to vary. The pore compressibility at constant pore
pressure, denoted by C pc (= 1/Kf), is given by:

C pc =-(1 V pore ) ∂ V pore ∂ P c (7.9)
*
where V pore is the pore volume and P c is the confining stress. The bulk
compressibility at constant confining pressure, denoted by C bp, is given
by:

*
C bp =-(1 V bulk ) ∂ V bulk ∂ P p (7.10)

where V bulk is the bulk volume and P p is the pore pressure. The bulk com-
pressibility at constant pore pressure, denoted by C bc (= 1/K dry), is given
by:

*
C bc =-(1 V bulk ) ∂ V bulk ∂ . (7.11)
P c
The pore compressibility at constant confining pressure, denoted by C pp,
is given by:

*
C pp =-(1 V pore ) ∂ V pore ∂ P p . (7.12)

If modeling compaction effects arising from depletion, one is typically
concerned with C bp, since the confining pressure (the overburden) will stay
constant while the pore pressure drops. In a reservoir simulation, one is
typically concerned with C pp. For measurement of porosity, cementation
exponent, and permeability “at overburden,” one will typically supply the
core contractor with the pressures to use. While the most important pres-
sure is the one corresponding to the initial uniaxial stress conditions,
measurement should also be extended beyond the pressure to cover any
uncertainty in Poisson’s ratio and the expected conditions at abandonment.
Note that the leak-off test, commonly conducted after first drilling out
a casing shoe, may also provide useful information about the weakest