The attenuation and dispersion analyses in porous and fractured medium with arbitrary fracture fill
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To study the effect of fracture fill on the elastic anisotropy of the rock and frequency-dependent attenuation and dispersion in fractured reservoirs, a model for porous and fractured medium is developed. In this model, the fractured medium is considered 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. By taking the simultaneous limits 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 equation with a composite fluid, while the P-wave speed is relatively high at high frequencies for two layers can be treated as 'hydraulically isolated'. However, there appears to be a critical case where no dispersion is observed, which is caused by the balance of fractures compliance and fluid compressibility filling in them.
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