The attenuation of compressional (P) and shear (S) waves in dry, saturated, and frozen rocks is measured in the laboratory at ultrasonic frequencies. A pulse transmission technique and spectral ratios are used to determine attenuation coefficients and quality factor (Q) values relative to a reference sample with very low attenuation. In the frequency range of about 0.1–1.0 MHz, the attenuation coefficient is linearly proportional to frequency (constant Q) both for P‐ and S‐waves. In dry rocks, [Formula: see text] of compressional waves is slightly smaller than [Formula: see text] of shear waves. In brine and water‐saturated rocks, [Formula: see text] is larger than [Formula: see text]. Attenuation decreases substantially (Q values increase) with increasing differential pressure for both P‐ and S‐waves.

Theoretical models based on several hypothesized attenuation mechanisms are discussed in relation to published data on the effects of pressure and fluid saturation on attenuation. These mechanisms include friction, fluid flow, viscous relaxation, and scattering. The application of these models to the ultrasonic data of ToksGz et al (1979, this issue) indicates that friction on thin cracks and grain boundaries is the dominant attenuation mechanism for consolidated rocks under most conditions in the earth' s upper crust. Increasing pressure decreases the number of cracks contributing to attenuation by friction, thus decreasing the attenuation. Water wetting of cracks and pores reduces the friction coefficient, facilitating sliding and thus increasing the attenuation. In saturated rocks, fluid flow plays a secondary role relative to friction. At ultrasonic frequencies in porous and permeable rocks, however, Biot-type flow may be important at moderately high pressures. "Squirting" type flow of pore fluids from cracks and thin pores to larger pores may be a viable mechanism for some rocks at lower frequencies. The extrapolation of ultrasonic data to seismic or sonic frequencies by theoretical models involves some assumptions, verification of which requires data at lower frequencies.

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The NMR methods described here provide a rapid, nondestructive determination of porosity, movable fluid, and permeability of sandstone. Introduction Fluid flow properties of porous media have long been of interest in such varied disciplines as geology, geophysics, soil mechanics, and chemical, civil, and mechanical engineering. This interest has resulted in numerous models of porous media that have been proposed, tested, and found to be useful under, at proposed, tested, and found to be useful under, at best, only special circumstances. A critical review of most of these models is given by Scheidegger. The application of each new tool to the study of porous media has helped to test some of the existing porous media has helped to test some of the existing theories and to form neat ideas based on the new parameters being measured. In the application of parameters being measured. In the application of nuclear magnetic resonance (NMR) techniques to the study of the properties of fluids in porous media, the theoretical studies of Korringa et al. resulted in a model for the relaxation of spin polarization of protons in a hydrogenous fluid in a pore of a solid. protons in a hydrogenous fluid in a pore of a solid. Seevers verified this model, established a method for measuring the surface-to-volume-ratio distribution in a porous medium, and proposed a technique for determining specific permeability in sandstones. In the present investigation, the uses of NMR methods are extended and a simple model of porous media is developed from an analysis of pulsed NMR measurements. In tills model, the pore spaces of a porous medium are divided into three groups on the porous medium are divided into three groups on the basis of their surface-to-volume ratios. To evaluate predictions of the NMR model, laboratory predictions of the NMR model, laboratory measurements of spin-lattice relaxation time, porosity, permeability, and residual (irreducible) water saturation permeability, and residual (irreducible) water saturation were conducted on more than 150 sandstone samples obtained from four oil fields in North America. Applications are discussed for estimating the volume of movable fluid, and the specific permability, k, of sandstone samples. The former permability, k, of sandstone samples. The former parameter, which can be considered as producible porosity, parameter, which can be considered as producible porosity, is expressed by ..........................................(1) where is porosity in percent of bulk volume and Swr is the residual (irreducible) water saturation in percent of pore volume at a capillary pressure of 50 percent of pore volume at a capillary pressure of 50 psi. psi. Fast nondestructive laboratory methods are described for determining porosity, movable fluid, and permeability of sandstone samples from permeability of sandstone samples from measurements with a pulsed NNM (spin-echo) apparatus. Procedures are given for adapting these methods to Procedures are given for adapting these methods to samples of irregular shape and small size. Theory General In the Korringa, Seevers, and Torrey (KST) model the observed decrease in the spin-lattice relaxation time, T1, of protons of a hydrogenous liquid contained in the pore spaces of a porous solid is attributed to an increase in the correlation time for the random motion of the water molecules and to the presence of paramagnetic centers at the liquid-solid presence of paramagnetic centers at the liquid-solid interface. JPT P. 775

Measurements of velocity of compressional waves in consolidated porous media, conducted within a temperature range of 26 °C to −36 °C, indicate that: (1) compressional wave velocity in water‐saturated rocks increases with decreasing temperature whereas it is nearly independent of temperature in dry rocks; (2) the shapes of the velocity versus temperature curves are functions of lithology, pore structure, and the nature of the interstitial fluids. As a saturated rock sample is cooled below 0 °C, the liquid in pore spaces with smaller surface‐to‐volume ratios (larger pores) begins to freeze and the liquid salinity controls the freezing process. As the temperature is decreased further, a point is reached where the surface‐to‐volume ratio in the remaining pore spaces is large enough to affect the freezing process, which is completed at the cryohydric temperature of the salts‐water system. In the ice‐liquid‐rock matrix system, present during freezing, a three‐phase, time‐average equation may be used to estimate the compressional wave velocities. Below the cryohydric temperature, elastic wave propagation takes place in a solid‐solid system consisting of ice and rock matrix. In this frozen state, the compressional wave velocity remains constant, has its maximum value, and may be estimated through use of the two‐phase time average equation. Limited field data for compressional wave velocities in permafrost indicate that pore spaces in permafrost contain not only liquid and ice, but also gas. Therefore, before attempting to make velocity estimates through the time‐average equations, the natures and percentages of pore saturants should be investigated.