Sheng-Qing Li

SUMMARY: Natural fractured reservoirs or artificially hydraulically fractured networks typically exhibit hierarchical microstructures characterized by porous backgrounds permeated by microcracks and intersected by macroscopic fractures. Prior theoretical frameworks predominantly decouple micro- and macro-scale heterogeneities, thereby overlooking the interplay between pore-scale squirt-flow dissipation and fracture-induced wave attenuation. By integrating microcracked porous wave-motion theory with fracture scattering theory, we present a unified model for characterizing wave propagation in fluid-saturated microcracked porous rocks with intersecting fractures. Five distinct attenuation mechanisms are concurrently incorporated: squirt flow at the microcrack scale, wave-induced fluid flow (WIFF) at both fracture-background and fracture–fracture mesoscales, elastic scattering and Biot's global flow. The results show that microcrack density primarily affects matrix stiffness and shifts the attenuation of squirt flow to lower frequencies. In contrast, microcrack aspect ratios control the characteristic frequency and its coupling with fracture-related mechanisms. Fluid mobility governs the frequency range of WIFF and Biot flow, with high mobility potentially creating attenuation gaps where scattering-induced velocity drops disappear. The model also accommodates multiple-aspect-ratio microcrack systems and extends to planar fractures as linear-slip interfaces, enabling realistic characterization of anisotropic shale reservoirs. This unified approach provides a comprehensive basis for interpreting seismic dispersion and attenuation in complex fractured formations relevant to hydrocarbon exploration and reservoir monitoring. In parallel fractures and zero microcrack-limiting cases, our model predictions agree well with those of existing models.

Numerical simulation of borehole acoustic reflection imaging of far-borehole fractures requires consideration of the borehole size and the fine structure of the fractures. The 3D discretization for fine structure modeling results in a huge number of grid nodes and extremely long computational time, which severely limits the efficiency of forward modeling of far-borehole reflection wave fields in fractured reservoirs. To address this problem, an analytical method was proposed for quickly calculating snapshots of acoustic reflection imaging wave fields on both sides of a fracture using the far-field asymptotic solution of dipole radiation shear wave displacement. This method combines the angular spectrum method with the slip interface theory. The waveforms obtained are consistent with those obtained by 3D finite-difference time-domain elastic wave simulations. For the same fracture model, the computational efficiency of the analytical method is two orders of magnitude faster than that of the finite-difference numerical method. Using this method, the effect of shear stiffness changes on the real-time propagation of dipole SH wave fields in a double-fracture system was analyzed. These findings can be used to characterize and interpret multi-fracture systems in single-well reflection imaging using field data. The results show that shear stiffness changes caused by near-fracture filling materials are a prerequisite for the effective identification of far-fractures in multi-fracture systems. The analysis results provide a theoretical basis for time domain simulation and imaging analysis of dipole acoustic reflection imaging wave fields in multi-fracture systems.

Obtaining accurate shallow ultraslow formation S-wave (shear) slowness is crucial for seismic exploration and hydrocarbon reserve assessment. Dipole acoustic logging is an effective method for estimating slow formation shear slowness. However, for the large borehole and unconsolidated soft sediments of the shallow marine environment, conventional dipole logging is often ineffective. To address this issue, we develop tool eccentricity for dipole S-wave logging. This study provides the theoretical justification of our method. The dipole acoustic wavefield of an eccentric tool is studied using a dual-cylindrical coordinate system in connection with the translational addition theorem for cylindrical Bessel functions, which provide analytical solutions to analyze the effects of tool eccentricity and formation elastic property. The results indicate that tool eccentricity in such an environment can substantially increase the dipole-wave amplitude for estimating the formation shear slowness. The S-wave logging can even be conducted by positioning the dipole tool against the borehole wall. This logging configuration is tested in a shallow test well with an oversized borehole. The measurement results are compared with their centralized counterparts. The measured data indicate that compared with the centralized tool measurement, eccentering the dipole tool can greatly enhance the measured S-wave amplitude and improve the accuracy of the formation shear slowness measurement, thereby providing an effective method for obtaining formation shear slowness in shallow soft sediments.

Wave-induced fluid flow (WIFF) is a crucial mechanism influencing seismic dispersion, attenuation, and frequency-dependent anisotropy in fractured reservoirs. Most previous studies of WIFF assume an isotropic rock background. However, fractured reservoirs, such as shale, often exhibit intrinsic anisotropy in the rock background. To explore the effects of this background anisotropy on dynamic seismic signatures, we derive an analytical model for the effective elastic properties of fluid-saturated rocks with horizontal planar fractures embedded in a vertical transversely isotropic (VTI) background. This model is derived from the solution for periodically layered rocks composed of VTI layers, treating the planar fractures as thin, highly porous isotropic layers. We apply the model to a fractured tight sandstone sample with a VTI background. Our results indicate that background anisotropy significantly affects seismic wave velocities and the magnitude of velocity anisotropy. However, the impact on the magnitude of seismic dispersion and attenuation is relatively small. Correspondingly, the frequency-dependent features of velocity and attenuation anisotropy are also less influenced by background anisotropy. To validate our model, we compare our theoretical predictions with the experimental measurements on a fractured shale sample. By accounting for the background anisotropy effects, our model’s predictions agree well with the experimental data. Our model is concise and can be easily applied to characterize unconventional reservoirs with background anisotropy, such as shale reservoirs.

Due to overburden and tectonic stresses, many deep formation rocks contain vertically oriented fractures, resulting in significant seismic S-wave anisotropy and attenuation, as commonly observed from borehole acoustic anisotropy measurements in deep wells. Understanding the fracture-induced phenomena is of theoretical interest and practical importance. By applying a fracture scattering theory to a fluid-saturated rock containing vertical fractures, we investigate the fracture-induced effects on dynamic S-wave moduli, anisotropy, and attenuation anisotropy in the rock medium. This includes the effects of fracture-background wave-induced fluid flow and elastic scattering on the fractured rock’s stiffness. The results indicate that fracture elastic scattering has a significant influence on the S-wave moduli and attenuation anisotropy. Compared with the velocity response of elastic scattering, Rayleigh scattering increases the S-wave anisotropy, whereas Mie scattering decreases it. The elastic scattering-dominated S-wave anisotropy and attenuation anisotropy are significantly affected by fracture size (diameter) and density. We use the theoretical results to interpret field acoustic anisotropy and attenuation anisotropy data acquired in a deep well, wherein the theory and measured data are in good agreement.

The increasing use of cluster wells in recent oil and gas drilling has raised concerns about well collisions. Although the successful application of single-well acoustic reflection imaging for nearby well detection has made it a potential ranging technique for collision prevention, further analyses are needed to demonstrate its utility for detecting multiple target wells around the measurement well. We develop a multiple-well acoustic ranging method that uses 4C dipole logging data to azimuthally scan multiple nearby wells and determine their distances and directions. To this aim, we develop a fast analytical method to model elastic wave radiation from the measurement well and wave scattering from multiple nearby wells and analyze the sensitivity and effectiveness of the 4C dipole tool in the generation of the transmitted wave and detection of the scattered waves. By means of 4C rotation and migration, the scattered wave data, as measured by the tool, are used to image the targeted wells and determine their distance and azimuth relative to the measurement well. Field data application is presented to demonstrate the effectiveness of this multiple-well acoustic ranging technique.

Fractures are widely distributed underground. The stiffness matrix of fractured rocks has been extensively investigated in a fluid-saturated porous background medium. However, the existing stiffness models only incorporate the attenuation mechanism of wave-induced fluid flow (WIFF). For macroscopic fractures, the elastic scattering (ES) of fractures cannot be ignored. To alleviate this issue, a frequency-dependent stiffness matrix model is developed, including the mesoscopic WIFF between fractures and background (FB-WIFF), the microscopic squirt flow, and the macroscopic ES from the fractures. By combining the far-field scattered wavefields of normal incident P and SV waves with the linear slip theory, the dynamic full-stiffness matrices for fracture-induced effective vertically transversely isotropic rocks in a fluid-saturated porous and microcracked background are derived. Then, the P, SV, and SH-wave velocities and attenuation can be obtained through the Kelvin-Christoffel equation. The results indicate that the FB-WIFF mechanism significantly affects the velocities and attenuation of the P and SV waves but has almost no effect on the SH wave, whereas the squirt flow and ES mechanisms affect the velocities and attenuation of all the P, SV, and SH waves. For validation, the model is compared with existing models and previous experimental ultrasonic data.

Owing to the complex structural characteristics of aligned fractured rocks with a fluid-saturated porous background, many existing single-wave attenuation mechanism models cannot accurately characterize measuring multiband shear vertical (SV) wave data. Moreover, the coupled effect of wave-induced fluid flow between fractures and the background (FB-WIFF) and elastic scattering (ES) from the fractures leads to ambiguity in the elastic response of the SV wave. Using Biot’s theory and mixed boundary constraints, the exact solutions of the scattering problem for a single penny-shaped fracture with an obliquely incident SV wave are derived. Furthermore, a theoretical model for a set of aligned fractures is developed by using Foldy’s scheme. The numerical results indicated that the FB-WIFF, ES of fractures, and their coupling effects were mainly responsible for wave dispersion and attenuation. The FB-WIFF occurs primarily in the low-frequency seismic exploration frequency band, whereas the ES of the fracture surface depends on the relationship between the wavelength and fracture size. In addition, by comparing our model with an existing interpolation approximation model and previous experimental measurements, the accuracy and effectiveness of the model was validated. The results of this work can explain the acoustic response of SV-wave experimental data in different frequency bands and theoretically support fracture detection and characterization.