Elastic
Properties of sedimentary Anisotropic Rocks
(Measurements and Applications)
by
Franklin J. Ruiz Peña
Submitted
to the Department of Earth, Atmospheric, and Planetary Sciences on October
9, 1998 in partial fulfillment of the requirements for the
degree of Masters of Science
ABSTRACT
In multidisciplinary studies carried out in the Budare Oil Field of the Great
Oficina Oil Field, there was difficulty in matching well log synthetic seismograms
with 2D and 3D seismic data. In addition, the seismically determined depths
of reservoir horizons are greater than the well sonic log depths. To examine
this discrepancy we conducted an experimental study of dynamic elastic parameters
of the rocks in the oil field. We chose core representative samples of the
lower Oficina Formation, the main reservoir of the field. The rocks selected
were sandstones, sandy shales and dolomite shales.
For the velocity measurements, we used the ultrasonic transmission method
to measure P-, SH- and Sv-wave traveltimes as function of orientation, and
pore and confining pressures to 60 and 65 Mpa, respectively. We found that,
in room dry condition, most of the rocks studied are transversely isotropic.
The stiffness constants, Young"s moduli, Poisson"s ratios, and bulk moduli
of these rocks, were also calculated.
The velocity anisotropies, together with the behavior of the elastic constants
for dry rocks, indicate that: 1) the elastic anisotropy of the sandstones
and sandy shales is due to the combined effects of pores, cracks, mineral
grain orientation, lamination and foliation. The velocity anisotropies caused
by the preferred oriented cracks decrease with increasing confining pressure.
2) For the dolomitized shales, the elastic anisotropy is due to mineral orientation
and microlamination. In these cases the very high intrinsic anisotropy does
not decrease with increasing confining pressure. 3) The velocities of the
compressional waves are greater in sandstones saturated with water than in
the dry specimens, but the opposite behavior was found for shear waves. 4)
The P-wave velocity anisotropy decreases after saturation; the magnitude of
the decrease depends on the crack density and on the abundance and distribution
of clay. 5) The Vsh-anisotropy does not show a pronounced change
after saturation, and it is only slightly affected by confining pressure.
Visual description, petrography and mineralogical analysis from thin sections
and x-ray diffractions revealed the vertical and lateral heterogeneous nature
of sandstones and sandy shales, whereas the dolomitized shale specimens looked
homogeneous.
The results of laboratory measurements are consistent with an elastic model,
using the equivalent medium theory for fine-layered isotropic and anisotropic
media. However, in order to do reliable seismic migration and solve the problem
of thickness calculations and time-to-depth conversion of surface seismic
data, the ultrasonic data need to be extrapolated to low frequencies.
Determining rock mechanical properties in situ is important in many
applications in the oil industry such as reservoir production, hydraulic fracturing,
estimation of recoverable reserves, and subsidence. Direct measurement of
mechanical properties in situ is difficult. Nevertheless, experimental
methods exist to obtain these properties, such as measurements of the stress-strain
relationships (static) and elastic wave velocities (dynamic).
We investigate the static and dynamic elastic behavior of sedimentary, anisotropic
rock specimens over a range of confining and pore pressures up to 70 Mpa, the
original reservoir conditions. The static and dynamic properties are simultaneously
measured for room dry shales, room dry sandstones, and brine saturated sandstones.
We found that (1) All the ratios of dynamic to static velocities and of dynamic
to static elastic parameters in all directions, Rm(O) {O = Theta}, decrease
with increasing confining pressure. However, the rate of decrease is greater
in the vertical direction than in the horizontal direction. 2) After saturation,
all the ratios of dynamic to static velocities, Rm(O), decrease, except the
bulk compressibility ratio, Rkb, which increases. 3) All the ratios of dynamic
to static moduli, Rm(O), decreases when the pore pressure is raised, except
Rkb which increases. 4) The magnitude of the ratio of dynamic to static velocities
or moduli, Rm(O), depends on the direction of the measurements. Not all the
ratios Rm(O) are equally affected. The ratio of dynamic to static P-wave velocity,
Rp(O), is greater in the vertical direction than in the horizontal direction.
On the other hand, the ratio of dynamic to static SH-wave velocity, Rsh(O),
does not depend on the direction of propagation. 5) The modulus determined from:
uniaxial stresses, hydrostatic compression or any other stress system yields
different values. This is because of the rock porosity. 6) All the static and
dynamic velocities and elastic parameters decrease with increasing confining
pressure. 7) The static velocity anisotropies and static modulus anistropies
are always greater than the corresponding dynamic anisotropies, over the entire
range of confining pressure and directions. 8) After saturation, the dynamic
Vp-anisotropy, Ed, decrease, while the dynamic Vsh-anisotropy, (gamma)d, is
affected much less. The static anisotropy also decreases after saturation. 9)
Both Vp(dyn)and Vp(stat) increase after saturation and with increasing pore
pressure. However, the increase is more pronounced in the Vp(stat). 10) Vs(dyn)
decreases after saturation and with increasing pore pressure. On the other hand,
Vs(stat) increases both after saturation and with increasing pore pressure.
11) The increase of elastic moduli with confining pressure is much larger than
the increase in the corresponding dynamic ones.
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