Frequency-dependent characteristics of P-wave in fractured porous media

Most studies on seismic wave attenuation in anisotropic media only focus on transversely isotropic media containing a set of fractures. Since there are often several sets of orthogonal or oblique fractures developed in actual reservoirs, it is necessary to study the seismic wave dispersion and attenuation of reservoirs with multiple sets of fractures. Chapman builds a mesoscale squirt flow model including two sets of fractures but does not discuss the influence of those fractures on the characteristic frequency, dispersion, and attenuation magnitude. Therefore, a method for calculating the P-wave frequency-dependent characteristics of reservoirs with multiple sets of fractures is proposed. Firstly, the Chapman model is numerically simulated, and the effects of fracture parameters on characteristic frequency, dispersion, and attenuation amplitude are discussed. Then, the relationship between the Chapman model and the standard linear solid model is analyzed. Finally, a method is developed to calculate the frequency-dependent P-wave modulus of reservoirs with multiple sets of fractures by the generalized standard linear solid model. This means that the low-frequency modulus is obtained by the Chapman model and anisotropic Gassmann equation, and the high-frequency modulus is obtained by the Chapman model. The proposed method employs the low-frequency and high-frequency limit modulus and modulus loss to characterize the frequency dispersion and attenuation properties of seismic waves. The modulus loss can represent the contribution of each set of fractures, and the following conclusions are obtained. ① Fracture orientations and seismic wave incident direction only affect the velocity (frequency dispersion) and attenuation magnitude but do not affect the frequency dispersion and attenuation frequency band. ② The P-wave velocity VP (or P-wave inverse quality factor QP-1) curves of different fracture development conditions have some algebraic relationship. Therefore, the VP (or QP-1) curves of a single set of fractures can be utilized to represent the VP (or QP-1) curves of two or more sets of fractures. ③ When the propagation direction of seismic waves is parallel to the fractures, the variation of VP with frequency is slight, and the attenuation of P-wave is the smallest. The proposed method is of practical significance for studying the seismic wave field characteristics and seismic response mechanism of anisotropic media. © 2022, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.