A model to relate PWave attenuation to fluid flow in fractured tight gas sands, siliceous shales, an

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A model to relate P-Wave attenuation to fluid
flow in fractured tight gas sands, siliceous
shales, and carbonate reservoirs
Southwest Research Institute
Jorge Parra and Chris Hackert, Southwest Research
Institute Pei-Cheng Xu, Datatrends Research
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Introduction
A modeling scheme is applied for the analyses of
flow unit responses to evaluate acoustic/seismic
measurement techniques. The responses are
produced to determine the frequency band in which
flow units can be observed and distinguished from
scattering effects. The model estimates
attenuation in a large broadband frequency range
to include sonic, crosswell, VSP, and 3D seismic
scales. Since flow units in a reservoir are
characterized by permeability, porosity, and
fluid saturation and the fluids are characterized
by viscosity, density, and velocity, we use the
theory of poroelasticity. This theory provides
the physics involved in the interactions between
the fluid and the rock matrix as an acoustic wave
propagates in the medium. To represent the
energy losses due to the presence of fluids in
the formation, we use the unified Biot and
squirt-flow mechanism. This work, implemented in
a layered poroelastic medium with azimuthal
anisotropy, is used to predict whether flow units
intercepted by a borehole can be detected at
seismic scales (crosswell, VSP and 3D seismic).
To demonstrate the variability of the attenuation
profile in different rock formations, we present
attenuation profiles from fluid saturated rocks
in four fields. These fields include the Siberia
Ridge, a fractured tight gas sands in Wyoming
the Buena Vista Hills, a low permeability
diatomite shale reservoir in California the
Ropes field, a carbonate reservoir in Texas and
a high permeability carbonate aquifer in Florida.
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Figure 1. The effect of frequency and azimuths
on poroelastic attenuation for a global squirt
flow length 5 cm (representing fluid flow in
cracks) and a local squirt flow length 0.2 mm
(representing fluid flow in the matrix). This
model is for wave propagation in a fractured
tight sand unit.
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Figure 2. The effect of frequency and azimuths
on poroelastic attenuation for a global squirt
flow length 7 cm (representing fluid flow in
cracks) and a local squirt flow length 0.2 mm
(representing fluid flow in the matrix). This
model is for wave propagation in a fractured
tight sand unit. In this environment, as long as
there is fluid flow in the cracks, the fluid
motion will attenuate the acoustic waves. In the
event that there is not crack -induced fluid
flow, we cannot expect high attenuation for waves
traveling perpendicular to the fracture system.
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Application To Fractured Tight Gas Sands
The model-based scheme is applied first to data
from the Siberia Ridge field, which is a tight
gas sand reservoir located in Wyoming. The
results give responses in the frequency domain
containing the effect of scattering and intrinsic
attenuation when a sand-shale-coal sequence is
modeled. By comparing the total attenuation with
the scattering attenuation we observe the
differences associated with the flow units. Flow
units can be identified because the increase in
attenuation is due to the interaction of fluid
flow with the rock matrix. The examples show
scattering effects of shales and coals and
demonstrate that coals control the scattering
attenuation. The elastic attenuation is shown at
all frequencies and the fluid flow effects are
observed in the sonic and crosswell frequency
ranges. This model study suggests that low
frequency measurements such as 3D seismic would
not be able to map fluids through poroelasticity.
Only borehole related seismic measurements have
the potential to map the poroelastic effects of
tight gas sands at the Siberia Ridge field.
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Seismic coal-shale-sand sequence of Siberia Ridge
Figure 3a. This lithological column was
constructed from well logs to model a zone
between the measured depths of approximately
10600 to 11100 feet. We selected a stack of 114
layers representing the Almond Formation. Here
we illustrate the lithological column, well logs,
and core data. Cores were taken from the
relatively high porosity, high permeability
sandstones slightly deeper that 10,600 feet. The
final truck shows the processed NMR T2 data. In
general, the higher the T2 values, the larger the
pores and the greater the permeability. Red
indicates a high concentration of pores with that
T2 value, while blue indicate a low
concentration. Figure 3 b. A display of the
upper Almond sand showing volumes of hydrocarbon,
free water and bound water together with T2
distributions. Core measurements on plugs in the
upper Almond Formation suggest a T2 cutoff for
sandstones equal to 10 milliseconds.
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Method
To simulate fractured zones containing fluids we
use a poroelastic model characterized by the
tensor permeability and the squirt-flow tensor.
The model is based on the work given by Parra
(1997) and Dvorkin and Nur (1993). We simulate a
system of cracks by assuming that the horizontal
x-axis is the axis of symmetry. To relate
attenuation and dispersion to the presence of
cracks embedded in tight sands, we define the
plane of the cracks as a plane of large
permeability and the direction perpendicular to
the cracks as having the low permeability of the
tight sand. To simulate the crack system we
consider two scales squirt-flow length of the
order of centimeters to represent cracks, and
squirt-flow length less than or equal to 1 mm to
represent grain scales. These scales add some
degree of anisotropy to simulation that include
directional attenuation. We calculated
dispersion and attenuation curves for the
fractured sand units to analyze the applicability
of acoustic/seismic techniques to detect the
presence of fractures. The model parameters are
given in Table 1. The core data provided the
grain density, permeability, and porosity.
Dipole sonic logs provided the velocities. The
fracture orientation and apertures were derived
from the FMI data. The squirt-flow lengths were
estimated from thin section analysis. Fracture
permeability is chosen from the high end of the
estimated fracture permeabilities at Siberia
Ridge (Sturm et al., 2000). In this way, we are
predicting the response of the most productive
formations. Following this, we constructed a
plane layered model based on typical sand, shale,
and coal properties. We measured the attenuation
of plane waves traveling through the medium with
a poroelastic modeling program.
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Method, Figure 4
Figure 4. Elastic attenuation for the layered
model at normal incidence. Green line is
elastic, red line is stochastic medium
prediction. This is a full model with coal
layers. The coals cause a large increase in
attenuation, but are too sparse and too different
to have a good match from stochastic theory.
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Method, Figure 5
Figure 5. Elastic attenuation of a plane wave at
normal incidence. Green line is elastic, red
line is stochastic medium prediction. This is a
modified model without coal layers. This model
(using sand and shale only) shows a good match
with a stochastic medium theory result.
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Method, Figure 6
Figure 6. Attenuation of plane wave at normal
incidence to the Siberia Ridge Almond Formation.
Green line is elastic only, red line is
poroelastic. Vertical incidence is parallel to
fractures, so the only real effect is at high
frequencies.
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Method, Figure 7
Figure 7 Attenuation of plane wave at oblique
incidence to the Siberia Ridge Almond Formation.
Green line is elastic only, red line is
poroelastic. As the angle of incidence moves
away from vertical, the effect of the fractures
can be seen in the attenuation at moderate
frequencies for the 0 degree azimuth.
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Application to Siliceous Shales and Carbonate
Reservoirs
These applications include the Buena Vista Hills,
a low permeability diatomite shale reservoir in
California the Ropes field, a carbonate
reservoir in Texas and a high permeability
carbonate aquifer in Florida. The following
figures present some information on the rock
properties in these formations, and the
associated predicted attenuation response. These
results show that, in general, any attempt to use
attenuation or dispersion to predict fluid
effects must be based on relatively high
frequency information. the presence of fractures
may allow lower frequency seismic information to
be used, as demonstrated in the Siberia Ridge
data. Nevertheless, while surface seismic data
may identify impedance contrasts associated with
fluids, or anisotropy associated with fractures,
it appears that in most cases this low frequency
data will not be useful in identifying the
poroelastic response of a fluid-saturated
formation.
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A Diatomite Shale Reservoir in California
Figure 8 Lithology from core and well logs from
a 30 m section of the Buena Vista Hills,
California reservoir. The lithology here is
predominantly diatomite shale, with many thin
sand beds. The sand is the source of much of the
lateral field permeability. The simulated
poroelastic attenuation profile is shown in red.
The average elastic scattering background is
shown as a green line. The predicted poroelastic
attenuation profile based on an analytic solution
incorporating the medium properties is shown as a
blue curve. Details of these calculations are in
Hackert and Parra (2000).
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A Diatomite Shale Reservoir in California
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A Carbonate Reservoir in Ropesville, Texas
Figure 9 Well logs and attenuation profile for
500 feet (150 m) of the Cisco formation at the
Ropes field in west Texas. The poroelastic
attenuation (red) shows a significant increase
over the elastic scattering attenuation (green).
Some poroelastic effect is seen at all
frequencies, although the dominant poroelastic
attenuation is above 10 kHz. Because of the
limited spatial resolution of sonic logs, elastic
scattering attenuation cannot be accurately
predicted for frequencies higher than about 3
kHz. The attenuation profile was obtained for
oil saturated carbonated in the zone of
permeability greater than 1 millidarcy near
9640-9730 feet. As was expected, the attenuation
shifts somewhat toward lower frequencies.
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A Carbonate Aquifer in South Florida (a)
Figure 10 (a) Well logs and (b) attenuation
profile for 200 feet (60 m) of a Florida
carbonate aquifer. Elastic scattering
attenuation (green) dominates at the lower
frequencies (poroelastic attenuation (red) is visible at the
higher frequencies. In the sonic logging
frequency range a Q of about 14 is predicted.
Because of the limited spatial resolution of
sonic logs, elastic scattering attenuation cannot
be accurately predicted for frequencies higher
than about 3 kHz.
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A Carbonate Aquifer in South Florida (b)
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Conclusion
The modeling results in the Siberia Ridge field
indicate that cracks in tight gas sands may be
detected using seismic methods in the range of 10
to 1000 Hz at azimuths less than 30ø and angles
of incidence near 90ø. Also, the results suggest
that attenuation is sensitive to fluid flow in
the tight sands above 1000 Hz at azimuths greater
than 60ø. These results indicate that any attempt
to map fractures in low permeability and low
porosity environments will require multiple
frequency measurements in the range of sonic logs
and long-space logging or high frequency VSP
measurements. To separate intrinsic effects from
scattering effects associated with the
shale-sand-coal layer sequence in the Siberia
Ridge field it will require measurements at a
minimum of two frequencies (e.g., sonic and VSP
data). The results of the an analysis
provide a modeling approach based on borehole
data to predict whether flow units can be
detected at acoustic and seismic scales. The flow
units were constructed using core and borehole
data. The model based on these two scales
predicts attenuation responses at the borehole
and crosswell scales. The modeling approach can
be applied to other reservoirs with different
petrophysical characteristics and reservoir
parameters. In this application, permeability and
porosity were derived from NMR well logs that
were calibrated with core data. The
attenuation profiles based on Buena Vista Hills
lithology suggests that fluid flow effects
associated with oil saturated sands may be
captured by borehole related measurements such as
long-space sonic and high-resolution cross well
seismics. In a similar way, the results in Ropes
field show that the viscosity of the saturating
fluid (oil) have an effect on the Biot/squirt
flow attenuation. This suggest that borehole
related measurements may be used to map the
presence of oil saturation at Ropes field.
However, in Florida aquifer the attenuation
profiles at frequencies greater that 400 Hz show
that P-wave attenuation can be used to map
intrinsic properties associated with water flow
effects.
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References
Dvorkin, J., and Nur, A., 1993, Dynamic
poroelasticity a unified model with the squirt
and the Biot mechanisms Geophysics, 58, pp.
523-533.   Hackert, C.L., and Parra, J. O., 2000,
Analysis of multi-scale scattering and
poroelastic attenuation in a real sedimentary
sequence, J. Acoust. Soc. Am., 107, pp.
3028-3034.   Parra, J.O., 1997, The transversely
isotropic poroelastic wave equation including
the Biot and the squirt mechanisms Theory and
application Geophysics, 62, pp. 309-318.
  Parra, J.O., 2000, Poroelastic model to relate
seismic wave attenuation and dispersion to
permeability anisotropy Geophysics, 65, pp.
202-210.   Sturm, S.D., Evans, W.L., Keusch,
B.F., and William, J.C., 2000, Multi- disciplinary
analysis of tight gas sandstone reservoirs,
Almond Formation, Siberia Ridge field, Greater
Green River Basin Gas Research Institute,
Topical Report No. GRI-00/0026.
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Acknowledgements
This work was performed with support from the
U.S. Department of Energy (DOE), under contract
no. DE-AC26-99BC15203. The assistance of Mr.
Purna Halder is gratefully appreciated.
We thank Springfield Exploration, especially Ms.
Mary Irwin de Mora, for providing the Ropes field
data as in-kind contribution to the project. We
thank, Chevron Production U.S.A., in particular
Dr. M. Morea for his contribution of the Buena
Vista Hills field data. We also thank M. Bennett
from South Florida Water Management District.
Finally, we thank Schlumberger-Holditch-Reservoir
Technologies for providing the Siberia Ridge
data.