A model to relate P-Wave attenuation to fluid flow in fractured tight gas sands, siliceous shales, and carbonate reservo

1. 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

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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).

14. A Diatomite Shale Reservoir in California

15. 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.

16. 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.

17. A Carbonate Aquifer in South Florida (b)

18. 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.

19. 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.

20. 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.