Effect of fracture fill on seismic attenuation and dispersion in fractured porous rocks

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 model for wave propagation in a porous medium with aligned fractures where pores and fractures are filled with different fluids. The fractured medium is modelled as a periodic system of alternating layers of two types: thick porous layers representing the background, and very thin and highly compliant porous layers representing fractures. A dispersion equation for the P-wave propagating through a layered porous medium is derived using Biot's theory of wave propagation in periodically stratified poroelastic media. By taking the limit of zero thickness and zero normal stiffness of the thin layers, we obtain expressions for dispersion and attenuation of the P waves. The 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.The dispersion is relatively large 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. An intermediate case exists where the fluid in the pores is liquid while the fluid in the fractures has a bulk modulus between those of liquid and gas. In this intermediate case no dispersion is observed. This can be explained by observing that for uniform saturation, wave-induced compression causes flow from fractures into pores due to the high compliance of the fractures. Conversely, when pores are filled with a liquid but fractures are filled with gas, the fluid will flow from pores into fractures due to the high compressibility of gas. Thus, there exists an intermediate fracture fluid compressibility such that no flow can be induced and hence no dispersion or attenuation is observed.