The Effects of Confining Pressure and Fluid Saturation on Ultrasonic Velocities in Rocks

Laboratory measurements of ultrasonic pand S-wave velocities were made as a function of confining pressure for vacuum dry, benzene-, and water-saturated samples of Westerly granite, Bedford limestone, and Weber, Navajo, Berea, and Kayenta sandstones. The measurements indicate: 1) water-saturated bulk moduli are higher than benzene-saturated values, 2) fluid-saturated shear moduli are always greater than or equal to dry values, and 3) water-saturated shear moduli for the sandstones are higher than benzene values at low pressure while lower than both benzene and dry values at higher pressure, Indicating that an apparent watersoftening effect Is concentrated In the shear modulus. Modelling of the velocity measurements with the Blot (1956a) and Gassmann (1951) equations for static effective bulk modulus Indicates that It underestimates the Increase In bulk modulus and velocities caused by fluid saturation. Inertial effects of the pore fluid as treated by Blot (1956a, 1956b) are also shown to 91ve minimal improvement to predicted velocities, which are underestimated. Velocity measurements are modelled with the Cheng-Kuster-Toksoz ellipsoidal pore and crack model using the inversion technique developed by Cheng (1978). Fits of dry and benzene-saturated velocities are shown along with pore aspect ratio distributions at zero pressure. Water-saturated velocity data and measured porosity reductions with pressure are compared with predictions of the model. INTRODUCTION Compressional and shear wave seismic velocities and attenuations in a rock depend on properties of both the rock and the seismic wave. For the rock these Include mineralogy of the solid phase, porosity, and pore fluid type. Particularly Important Is the distribution of porosity, or pore shapes, as this Influences how pressure and fluid saturation affect seismic propagation. Important properties of the seismic wave Include Its frequency, strain amplitUde, and whether It Is compressional or shear. Many details of these factors have been Identified and Isolated with laboratory measurements. Two valuable techniques include measurements as a function of stress, thereby changing the distribution of pore shapes while keeping mineralogy constant, and as a function of pore fluid saturation, changing overall acoustic response by Introducing fluid with readily defined compressibility, viscosity, and density. A number of experimental studies have documented these effects (Hughes 331 332 Coyner and Cheng and Cross, 1951; Wyllie et al., 1956, 1958; Birch, 1960, 1961; Simmons, 1964; King, 1966; Nur and Simmons, 1969; Gregory, 1976; Winkler and Nur, 1979; Spencer, 1981; Jones and Nur, 1983; Murphy, 1984). There are several general conclusions from these studies. The effect of confining pressure Is to Increase velocities, an effect which has been interpreted In terms of the closure of small cracks (Birch, 1960; Simmons, 1964; Nur and Simmons, 1969; Toksoz et aI., 1976). In all cases, the Introduction of full saturation Into dry rocks results In higher P-wave velocities while the S-wave velocities behave less regular. Differences between dry and saturated velocities are more pronounced at lower pressure. Measurements at ultrasonic frequencies which have shown higher S-wave velocities In fluid-saturated rock samples over the corresponding dry samples have been reported by Wyllie et al., 1958; Gregory, 1963; King, 1966; Nur and Simmons, 1969; Murphy, 1984). In addition, Wyllie et al. (1958) and KIng (1966) have reported on the effects of different types of pore fluids. King (1966) Interpreted the results at low pressures as due to "relaxation effects" and also noted several Instances where water saturated S-wave velocities were lower than the kerosene saturated velocities, indicating an effect of water on softening the quartz grain contacts. In this paper we present some new measurements of ultrasonic velocities In a suite of dry and saturated rocks and interpret and model the data with various theoretical models. The experimental data presented In the first part of this paper focuses on the effects of confining pressure and saturation on pand S-wave ultrasonic velocities for dry, benzeneand water-saturated rock samples. The definition of "dry" Is a 20 jJJTl Hg vacuum continuously applied to the sample for at least 24 hours before and as measurements were taken. The definition of "saturated" Is benzene at 100 bars Introduced through the pore pressure system Into the sample under vacuum. Additional measurements with distilled water at 100 bars are also shown for most of the samples. In the second part, the measured seismic velocities are compared with three theoretical models: 1) simplified Blot (1956a) or Gassmann (1951), hereafter referred to as Blot-Gassmann, 2) the hlghfrequency approximations for Inertial effects of the pore fluid as treated by Blot (1956b), and 3) the Cheng-Kuster-Toksoz elliptical pore model. Benzene In addition to water was chosen as the pore fluid In these measurements in order to compare the effects of water, particularly in the higher porosity rocks at high confining pressures. An example of what happens when water versus benzene Is added at these high pressures Is shown In Fig. 1. Plotted Is a set of stress-strain relations for a vacuum dry, water saturated, and benzene saturated sample of Berea sandstone. The Introduction of water Into the sample under pressure "softens" the rock so that linear strain Increases, owing to fluid interaction with the quartz grains or Interstitial cements. Note that the three curves are pretty much parallel after a few hundred bars, so that the nature of porosity at low pressures are at least partially modified In the rock over the whole pressure range. This effect of water on static strain Is contrasted with the presence of benzene as the pore flUid, which has little effect on strain except for a slight Increase. Wyllie et al. (1 958) also report similar effects for a sample of Berea sandstone saturated altemately with dry air, oil, silicone fluid, and water. Maximum strain was measured with water as the pore fluid; minimum strain was measured for the dry sample. Significantly, the silicone measurements were nearly as high as those with water, Indicating that perhaps the solubility or wetting properties are not as Important as the lubricating properties of the pore fluid. Similar strain measurements of dry and water saturated samples were made by Mann and Fatt (1960) for a number of sandstones. They too observed the large Increase of water-saturated strain.