Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks

Abstract

Seismic velocities in rocks at ultrasonic frequencies depend not only on the degree of saturation but also on the distribution of the fluid phase at various scales within the pore space. Two scales of saturation heterogeneity are important: (1) saturation differences between thin compliant pores and larger stiffer pores, and (2) differences between saturated patches and undersaturated patches at a scale much larger than any pore. We propose a formalism for predicting the range of velocities in partially saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry rock porosity versus pressure. The pressure dependence contains all of the necessary information about the distribution of pore compliances for estimating effects of saturation at the finest scales where small amounts of fluid in the thinnest, most compliant parts of the pore space stiffen the rock in both compression and shear (increasing both P-and S-wave velocities) in approximately the same way that confining pressure stiffens the rock by closing the compliant pores. Large-scale saturation patches tend to increase only the high-frequency bulk modulus by amounts roughly proportional to the saturation. The pore-scale effects will be most important at laboratory and logging frequencies when pore-scale pore pressure gradients are unrelaxed. The patchysaturation effects can persist even at seismic field frequencies if the patch sizes are sufficiently large and the diffusivities are sufficiently low for the larger-scale pressure gradients to be unrelaxed.

Estimating rock porosity and fluid saturation using only seismic velocities

“…The methods will apply to low frequency (seismic) data whether or not they fit Gassmann's model (Gassmann, 1951) or a patchy saturation model (Berryman et al, 1988;Endres and Knight, 1989;Mavko and Nolen-Hoeksema, 1994;Dvorkin and Nur, 1998). At these low frequencies, the type of saturation present (well-segregated liquids and gases, homogeneous fluid mixtures, or some patchy saturation state intermediate between these two extremes) determines the location of data points on the ( , )-plane.…”

“…If all the other assumptions of the Gassmann model are satisfied, but the liquid and gas are not distributed uniformly (so that different pores have different saturation levels), then we have the circumstances that may better fit the "patchy saturation" model (Berryman et al, 1988;Endres and Knight, 1989;Mavko and Nolen-Hoeksema, 1994;Dvorkin and Nur, 1998). In that case, for the plot of vs. , instead of data following a horizontal line with a jump up at the high saturation end (e.g., Figure 1b), the ideal patchy saturation model (for completely segregated liquid and gas pockets) would predict that the data should lie on another straight line connecting to the two end points (dry and saturated) on this plot.…”

“…This is especially so for partial saturation conditions (i.e., when the fluid in each pore is a mixture of gas and liquid). In some cases these deviations can be attributed (Berryman et al, 1988;Endres and Knight, 1989;Mavko and Nolen-Hoeksema, 1994;Dvorkin and Nur, 1998) to "patchy saturation," meaning that some void regions are fully saturated with liquid and others are filled with gas. When the concept of patchy saturation is applicable, Gassmann's formulas apply locally (but not globally) and must be averaged over the volume to obtain the overall seismic velocity of the system.…”

Analysis of rock physics response of gas-bearing volcanic reservoir based on three-phase poroelastic theory

“…For the study of rock physics in a medium permeated by two fluids, a simple method is to extend Biot's poroelastic theory or the Gassmann model by replacing model parameters with ones modifi ed for the fl uid-fl uid or gas-fluid mixtures (Mochizuki, 1982;Mavko and Nolen-Hoeksema, 1994;Nie et al, 2004). White (1975) proposed the fi rst model of patchy saturation consisting of a periodic ensemble of cubic cells.…”

Wavefield simulation in porous media saturated with two immiscible fluids

“…For the aspect of studying the wave propagation mechanism in a porous medium saturated by two fl uids, a simplified method is the equivalent fluid method, which is an expansion of Biot's theory for two-phase media by substituting the equivalent parameters of a fluid-fluid or fluid-gas mixture for the corresponding parameters in Biot's or Gassman's model (Mochizuki, 1982;Mavko and Nolen-Hoeksema, 1994;Lee, 2004;Chao et al, 2006). Santos et al (1990aSantos et al ( , 1990b proposed a wave theory for porous media saturated by a two-phase fl uid with different viscidity based on the compensation work and Lagrangian variation principles and forecasted that there are four types of bulk waves, three kinds of compressional waves and one shear wave in the multiphase medium.…”