Effect of the Fracture Fill on the Dispersion and Attenuation of Elastic Waves in a Porous Rock with Aligned Fractures

Abstract

When a porous medium is permeated by open fractures, wave-induced flow between pores and fractures can cause significant attenuation and dispersion. Most studies of this phenomenon assume that pores and fractures are saturated with the same fluid. In some situations, particularly when a fluid such as water or carbon dioxide is injected into a tight hydrocarbon reservoir, fractures may be filled with a different fluid (with capillary forces preventing fluid mixing). Here we develop a periodic stratified poroelastic model for wave propagation in a porous medium with aligned fractures where pores and fractures are filled with different fluids. A dispersion equation for the P-wave propagating through such medium is derived by taking the simultaneous limits of zero thickness and zero normal stiffness of the thin layers. The simulation results show that in the low-frequency limit the elastic properties of such a medium can be described by Gassmann’s equation with a composite fluid, whose bulk modulus is a harmonic (Wood) average of the moduli of the two fluids. At high frequencies, the dispersion is relatively high when the fluid in both pores and fractures is liquid, and also when the pores are filled with a liquid but fractures are filled with a highly compressible gas. However, an intermediate case exists where no dispersion is observed. This can be explained by observing that when the medium is uniformly saturated with a liquid, wave-induced compression causes flow from fractures into pores due to high compliance of the fractures. Conversely, when pores are filled with a liquid but fractures are filled with gas, flow will occur from pores into fractures due to high compressibility of gas. Thus an intermediate case exists where there is no flow and hence no dispersion or attenuation.