Simulation of borehole acoustic wavefields in fractured media by combining the spectral element method and linear-slip model

We use the spectral element method (SEM) to simulate 3D acoustic wavefields in the fluid-filled borehole embedded in the fractured media. The fractures are characterized by the linear-slip model (LSM), which is incorporated into the surface integral of the SEM weak form, avoiding meshing individual fractures, thus reducing the degrees of freedom of the fractures comparing with meshing each fracture directly. For the fracture-free case, we validate SEM through the comparison with the real-axis integration (RAI) method for both monopole and dipole sources. For the case with a fracture, we compare the SEM-LSM solutions with the reference numerical solutions of a thin layer model using finite-difference method. Good agreement is achieved between the results from the proposed method and the reference finite-difference solutions. We find that the acoustic wavefields excited by a dipole source are more sensitive to the fractures than those by a monopole source. To show the ability of the approach to handle complex problems, we simulate the cases with a tilted fracture and multiple fractures. Based on the simulated results, we investigate the influence of the fracture parameters (e.g., stiffness, tilt angle, azimuth, thickness, number and spatial intervals of fractures) on the scattered wavefields. We find that the tilt angle has an obvious influence on the scattered waveforms and amplitudes. The results also demonstrate that the wavefields are quite sensitive to the number of fractures. The magnitudes of the horizontal-components transmitted wavefields decrease linearly with the number of the fractures. Through analyzing the synthetic data in time and frequency domains, we discuss how to evaluate the properties of fractures intersected by a borehole.

Spectral element simulation of elastic wave propagation through fractures using linear slip model: microfracture detection for CO2 storage

SUMMARY Simulation of seismic wave propagation through fracture has a wide range of applications in environmental sciences. In this paper, we propose an efficient tool to compute accurate seismic response from a fracture within a reasonable time frame. Its theoretical formulation is based on the spectral element method (SEM) and extended to Schoenberg’s linear slip model (LSM). SEM is very effective in terms of accuracy and stability criteria. LSM is treated as a boundary condition and perfectly fits for modelling fractures with a small aperture. The method is implemented for 3-D heterogeneous media on GPU, which allows calculating the tasks with large and complex geometries. The validation of the numerical method shows good agreement with the theory. Finally, we applied the method to the task that illustrates the possibility of the proposed solution to handle real problems. We model sonic logging for a well with a microfracture in a cement sheath. Based on synthetic seismograms, strong connections between wave mode parameters and the fracture parameters were established. This task is of high importance for carbon capture and storage, as microfractures provide the path for long-term CO2 migration.

Fracture detection and fluid identification based on anisotropic Gassmann equation and linear-slip model

Detection of fracture and fluid properties from subsurface azimuthal seismic data improves our abilities to characterize the saturated porous reservoirs with aligned fractures. Motivated by the fracture detection and fluid identification in a fractured porous medium, we have developed a feasible approach to perform a rock physics model-based amplitude variation with offset and azimuth (AVOAz) inversion for the fracture and fluid parameters in a horizontal transversely isotropic (HTI) medium using the PP-wave angle gathers along different azimuths. Based on the linear-slip model, we first use anisotropic Gassmann’s equation to derive the expressions of saturated stiffness components and their perturbations of first-order approximation in terms of elastic properties of an isotropic porous background and fracture compliances induced by a single set of rotationally invariant fractures. We then derive a linearized PP-wave reflection coefficient in terms of fluid modulus, dry-rock matrix term, porosity, density, and fracture compliances or quasi-compliances for an interface separating two weakly HTI media based on the Born scattering theory. Finally, we solve the AVOAz inverse problems iteratively constrained by the Cauchy-sparse regularization and the low-frequency regularization in a Bayesian framework. The results demonstrate that the fluid modulus and fracture quasi-compliances are reasonably estimated in the case of synthetic and real seismic data containing moderate noise in a gas-filled fractured porous reservoir.

Low-cycle fatigue test and life assessment of carbon structural steel GB Q235B butt joints and cruciform joints

Axial low-cycle fatigue tests are conducted on transverse butt joint specimens and cruciform joint specimens made of carbon structural steel GB Q235B. The effect of slip between the specimens and the grips of the test machine is considered by the proposal of a linear slip model. The cyclic softening properties are studied by observing the variation of stress amplitude with cycles. The cyclic stress–strain curve and the strain–life curve for both kinds of specimens are obtained based on the fatigue test data, and the corresponding coefficients are fitted. In order to verify the fatigue test results, finite element models of specimens are established and the corresponding fatigue life assessment is conducted using the local stress–strain approach and the equivalent structural stress approach, respectively. The results show that the effect of slip is unneglectable and the established linear slip model is reasonable. The two kinds of specimens both show a strain softening property, but cruciform joint specimens experience sudden falls of stress amplitude during the test due to the damage of welded lines; cruciform joint specimens show an either one-side failure mode or two-side failure mode while butt joint specimens only show a one-side failure mode; the two-side failure mode tends to lead to shorter fatigue life, so in the design of cruciform joint, such failure mode should be avoided.

Experimental verification of spatially varying fracture-compliance estimates obtained from amplitude variation with offset inversion coupled with linear slip theory

The elastic compliance of a fracture can be spatially varying, reflecting the variation of microscale properties of the fracture, e.g., aperture, contact asperities, and fracture infill. Characterizing the spatial heterogeneity of a fracture is crucial in explaining the apparent frequency dependence of fracture compliance and in addressing the spatially varying mechanical and hydraulic properties of the fractured medium. Apparent frequency dependence of the estimated fracture compliance is caused when the used seismic wavelength is very large compared to the scale of heterogeneity. We perform ultrasonic laboratory experiments, and characterize the spatially varying compliance along a fluid-filled fracture. We simulate a horizontal fracture, and introduce heterogeneous fluid distribution along the fracture. We perform amplitude variation with offset (AVO) inversion of the P-P reflections, in which we obtain the theoretical angle-dependent reflection responses by considering the linear-slip model. The estimated compliance distribution clearly separates the dry region from the wet region of the fracture. The effective bulk modulus of the fluid is estimated using the derived values of the compliance. We find that the obtained bulk modulus is well-explained by the presence of minute quantity of air bubbles in the water. We also find new evidence of the existence of scattered waves generated at the boundary representing a sharp change in fracture compliance. The estimated boundary between the dry and the wet regions of the fracture, which is detected by AVO inversion, is slightly shifted compared with the actual location. This is possibly due to the interference of the scattered waves that are generated at the boundary. The linear-slip model can represent thin structures in rocks in a wide range of scale. Therefore, our methodology, results, and discussion will be useful in developing new applications for assessing laterally varying mechanical and hydraulic properties of thin nonwelded discontinuities, e.g., fractures, joints, and faults.