Characteristics of dispersion and attenuation with a unified multiscale model in porous medium containing saturated fluid and multiscale fractures

Abstract

To analyze seismic wave field characteristics and characterize fracture (or crack) reservoirs, it is essential to build proper wave-induced fluid flow (WIFF) models of various scales. There is much research related to WIFF fractured models that are mainly suitable only for different scales of fracture (crack) medium separately, such as microscopic cracks and mesoscopic fractures. Based on previous research, it is proposed a unified multiscale (mesoscopic and microscopic) dispersion and attenuation model for the medium with fractures, cracks, pores, and fluid. The formulation uses frequency-dependent fractured (or crack) parameters expressed as the form of multiplication of fracture parameters and relaxation function. The advantage of this method is that it is convenient to build fluid porous medium with different scale fractures (or cracks) and various fracture (or crack) configurations. The numerical simulation results prove the correctness and applicability of the proposed extended WIFF dispersion and attenuation model. Based on our proposed method, the characteristics of the dispersion and attenuation of the multiscale fractured model are analyzed. The results indicate that the characteristics of velocity dispersion and wave attenuation in the medium with different scales of fractures are similar. The velocity increases with frequency and finally tends to be stable. The main difference among the different scales of models is that the frequency bands of the dispersion and attenuation occurring are different. We also discover that for multiscale fractured medium, the characteristic frequency and attenuation peaks do not necessarily correspond to each other, which makes the analysis of the dispersion and attenuation more complicated.