Transcript A model to relate P-Wave attenuation to fluid flow in

Southwest Research Institute
Jorge Parra and Chris
Hackert, Southwest
Research Institute
Pei-Cheng Xu, Datatrends
Research
A model to relate P-Wave
attenuation to fluid flow in
fractured tight gas sands,
siliceous shales, and
carbonate reservoirs
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.
Figure
global
squirt
is for
1. The effect of frequency and azimuths on poroelastic attenuation for a
squirt flow length = 5 cm (representing fluid flow in cracks) and a local
flow length = 0.2 mm (representing fluid flow in the matrix). This model
wave propagation in a fractured tight sand unit.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
A Diatomite Shale Reservoir in
California
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.
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 (< 1000 Hz), but a very strong 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.
A Carbonate Aquifer in South
Florida (b)
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.
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, Multidisciplinary analysis of tight gas sandstone reservoirs, Almond
Formation, Siberia Ridge field, Greater Green River Basin: Gas
Research Institute, Topical Report No. GRI-00/0026.
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.