Acoustic signals are used extensively in the oil industry to determine the physical properties of reservoir rock. In the interpretation of these signals empirical laws play a major role. To obtain a more fundamental interpretation of the recorded wavetrains, the need for a comprehensive theory for acoustic wave propagation and damping in rocks is obvious. In this respect, Biot's (1956a,b) theory is a straightforward and effective two‐phase theory. In contrast to Biot, who derived the macroscopic equations for wave propagation in saturated poro‐elastic material by postulating definite positive‐energy density functions, Burridge and Keller (1981), Whitaker (1986a,b,c), and Pride et al. (1992) applied rigorous averaging techniques to derive the poro‐elastic equations from a microscale. De Vries (1989) and Geerits (1996) used the averaging techniques to derive macroscopic poro‐elastic equations for the nonviscous case. The fundamental feature of all these theoretical descriptions is the existence of both a fast and slow compressional wave, as well as a shear wave. For the fast compressional wave, the pore fluid and the porous matrix are compressed simultaneously, but for the slow compressional wave, the porous matrix relaxes while the pore fluid is compressed. The attenuation mechanism for these waves is based on viscous dissipation generated by the flow of the pore fluid relative to the porous matrix. For the slow wave, the viscous dissipation results in a strong, frequency‐dependent attenuation, which makes this wave very difficult to observe in fluid‐saturated rocks. However, because the slow compressional wave is especially sensitive to certain interesting properties of the permeable material, the detection of this slow compressional wave has been one of the major issues in the acoustics of fluid‐saturated permeable solids.
A new lossless poroelastic wave propagation theory is verified by means of ultrasonic transmission measurements on artificial rock samples in a water-filled tank. The experiments involved are similar to those performed by Plona ͓Appl. Phys. Lett. 36, 259-261 ͑1980͔͒. In this physically and mathematically mutual consistent new theory the coupling terms between the fluid and solid phase of the porous medium are completely determined by the measured wave speeds and the mass densities and constitutive parameters of both constituting phases. Verification of the amplitudes of the received bulk waves in both the time domain and frequency domain provide information on the validity of the combined effect of propagation characteristics and new macroscopic fluid/ fluid-saturated-rock boundary conditions resulting from this theory. The comparison technique between theory and experiments is based on the Fraunhofer diffraction theory, and is first tested in a perfectly elastic medium transmission configuration. Subsequently, this comparison technique is used for the poroelastic medium. It is shown that this technique is very accurate and reliable. The experimental results for the compressional wave and the shear wave in the perfectly elastic medium are in excellent agreement with the theoretical predictions. For the fluid-saturated porous samples, good agreement is found only for the fast compressional wave. For both the shear wave and the slow compressional, it is obvious that there is some kind of loss mechanism involved, which cannot be explained by the current theory. Despite the fact that the bulk losses in the porous medium can be explained qualitatively by the full frequency range Biot theory, it is conjectured that even a quantitative fit is feasible if Johnson's loss model ͓D. L. Johnson et al., J. Fluid Mech. 176, 379-402 ͑1987͔͒ is applied in the lossy counterpart of the current theory
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractReservoir monitoring requires an accurate assessment of hydrocarbon saturation. As oil fields mature, reducing uncertainty in this parameter can yield major economic benefits in field development and reservoir management.Recent advancements in resistivity tool design and enhancements in pulsed neutron and NMR tools have expanded the scope of petrophysics in reservoir monitoring projects. Optimal utilization of these technologies requires an understanding of the uncertainties that are associated with these measurements in different types of environments.A new application has been developed that uses numerical analysis to compute the range of uncertainties inherent in petrophysical analysis. These uncertainties are then used as guidelines to optimize data acquisition.This methodology defines petrophysical uncertainties on a foot-by-foot basis; consequently decisions are based on prior knowledge of the uncertainty of two of the most important petrophysical parameters, water saturation and porosity.Several wells have been used in this paper to demonstrate the utility of this application and how this analysis is used to design cost-effective logging programs. Even though this technique can be used with any logging measurements, the focus of this paper will be on resistivity and pulsed neutron devices which are widely used in reservoir monitoring. The examples will show how quantifying uncertainties of key petrophysical parameters reduces reservoir management risk.
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