Effects of pore fluid pressure on the seismic response of a fractured carbonate reservoir |
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| Authors: | R Agersborg M Jakobsen B O Ruud T A Johansen |
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| Institution: | (1) Department of Earth Science, University of Bergen, Allegt. 41, 5007 Bergen, Norway;(2) Centre for Integrated Petroleum Research, University of Bergen, Allegt. 41, 5007 Bergen, Norway |
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| Abstract: | An effective medium model for the stress-dependent seismic properties of fractured reservoirs is developed here on the basis
of a combination of a general theory of viscoelastic waves in rock-like composites with recently published formulae for deformation
of communicating and interacting cavities (interconnected pores/cracks and fractures at finite concentration) under drained
loading. The inclusion-based model operates with spheroidal cavities at two different length scales; namely, the microscopic
scale of the pores and (grain-boundary) cracks, and the mesoscopic scale of the fractures (controlling the flow of fluid).
The different cavity types can in principle have any orientation and aspect ratio, but the microscopic pores/cracks and mesoscopic
fractures were here assumed to be randomly and vertically oriented, respectively. By using three different aspect ratios for
the relatively round pores (representing the stiff part of the pore space) and a distribution of aspect ratios for the relatively
flat cracks (representing the compliant part of the pore space), we obtained a good fit between theoretical predictions and
ultrasonic laboratory measurements on an unfractured rock sample under dry conditions. By using a single aspect ratio for
the mesoscopic fractures, we arrived at a higher-order microstructural model of fractured porous media which represents a
generalization of the first-order model developed by Chapman et al. (2002,2003). The effect of cavity size was here modelled
under the assumption that the characteristic time for wave-induced (squirt) flow at the scale of a particular cavity (pore/crack
vs. fracture) is proportional with the relevant scale-size. In the modelling, we investigate the effect of a decreasing pore
pressure with constant confining pressure (fixed depth), and hence, increasing effective pressure. The analysis shows that
the attenuation-peak due to the mesoscopic fractures in the reservoir will move downward in frequency as the effective pressure
increases. In the range of seismic frequencies, our modelling indicates that the P-wave velocities may change by more than
20% perpendicular to the fractures and close to 10% parallel to the fractures. In comparison, the vertical S-wave velocities
change by only about 5% for both polarization directions (perpendicular and parallel to the fractures) when the effective
pressure increases from 0 to 15 MPa. This change is mainly due to the overall change in porosity with pressure. The weak pressure
dependence is a consequence of the fact that the S waves will only sense if the fractures are open or not, and since all the
fractures have the same aspect ratio, they will close at the same effective pressure (which is outside the analysed interval).
Approximate reflection coefficients were computed for a model consisting of the fractured reservoir embedded as a layer in
an isotropic shale and analysed with respect to variations in Amplitude Versus Offset and aZimuth (AVOZ) properties at seismic
frequencies for increasing effective pressure. For the P-P reflections at the top of the reservoir, it is found that there
is a significant dependence on effective pressure, but that the variations with azimuth and offset are small. The lack of
azimuthal dependence may be explained from the approximate reflection coefficient formula as a result of cancellation of terms
related to the S-wave velocity and the Thomson’s anisotropy parameter δ. For the P-S reflection, the azimuthal dependence
is larger, but the pressure dependence is weaker (due to a single aspect ratio for the fractures).
Finally, using the effective stiffness tensor for the fractured reservoir model with a visco-elastic finite-difference code,
synthetic seismograms and hodograms were computed. From the seismograms, attenuation changes in the P wave reflected at the
bottom of the reservoir can be observed as the effective pressure increases. S waves are not much affected by the fractures
with respect to attenuation, but azimuthal dependence is stronger than for P waves, and S-wave splitting in the bottom reservoir
P-S reflection is clearly seen both in the seismograms and hodograms. From the hodograms, some variation in the P-S reflection
with effective pressure can also be observed. |
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| Keywords: | fractures cracks anisotropy fluid pressure AVOZ time-lapse |
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