Dynamic gassmann's equation: Effects of permeability and partial saturation

Abstract

BASIC ASSUMPTIONS AND DEFINITIONS The viscoelastic response of rock to seismic waves depends on the relative motion of pore fluid with respect to the solid phase. The fluid motion depends , in part, on the internal wave-induced pore pressure dist ribution whi ch depends on the pore microstructure of rock, and on the scales of saturation. We consider wave-induced fluid flow at two scales: (1) local microscopic (squirt) flow at the smallest scale of saturation heterogeneity (e.g., within a single pore) and (2) macroscopic flow at the large scale of saturated and dry patches.The main goal of this paper is to explore the circumstances under which each of these mechanisms dominates the viscoelastic behavior of a. porous material. We examine such flows under the conditions of uniform confining (bulk) compression and obtain a dynamic extension of the Gassmann formula which is applicable to velocity and attenuation estimates at all frequencies and all types of saturation. The important results of our theoretical modeling are: (1) a. hysteresis of seismic velocity versus saturation at imbibition and drainage, and (2) two peaks of acoustic wave attenuation one at low frequency (due to the global squirt flow) and another at higher frequency (due to the local flow). Both theoretical results are well supported by experimental data. Microscopic Squirt Flow refers to the fluid motion at the smallest scale of heterogeneity in a porous material. The material is represented by elementary microscopic units (Figure 1) composed of thin conduits and stiff equidimensional pores (Murphy et al., 1986). The thin conduits connect the large pores and thus provide the paths for macroscopic fluid flow (Figure lb,c).