Experimental and Numerical Simulation of Interlayer Propagation Path of Vertical Fractures in Shale

The complex fracture network formed by volume fracturing of shale gas reservoir is very important to the effect of reservoir reconstruction. The existence of bedding interface will change the propagation path of the hydraulic fracture in the vertical direction and affect the reservoir reconstruction range in the height direction. The three-point bending test is used to test and study the mechanical parameters and fracture propagation path of natural outcrop shale core. On this basis, a two-dimensional numerical model of hydraulic fracture interlayer propagation is established based on the cohesive element. Considering the fluid-solid coupling in the process of hydraulic fracturing, the vertical propagation path of hydraulic fracture under different reservoir properties and construction parameters is simulated. According to the results, the strength of the bedding interface is the weakest, the crack propagation resistance along the bedding interface is the smallest, and the crack propagation path is straight. When the crack does not propagate along the bedding interface, the fracture propagation resistance is large, and the fracture appears as an arc propagation path or deflection. The difference between vertical stress and minimum horizontal stress difference, interlayer stress difference and interface stiffness will have a significant impact on the propagation path of vertical fractures. Large injection rate and high viscosity fluid injection are helpful for vertical fractures to pass through the bedding interface, and low viscosity fracturing fluid is helpful to open the bedding interface. This research work is helpful to better understand the characteristics of bedding shale and the interlayer propagation law of vertical fractures, and to form the stimulation strategy of shale gas reservoir.

Experimental Study on the Fracture Distribution Characteristics of the Overlying Strata in an Abandoned Gob

A lot of gas resources remain in the abandoned gob. The overlying strata of the abandoned gob are the main places for gas storage and flow. The fracture distribution characteristics of the overlying strata have a significant impact on the gas migration. The mining similarity simulation test device of a plane stress was used to study the deformation and failure characteristics of overlying strata in an abandoned gob. The caved strata of the abandoned gob formed a trapezoidal distribution, and the caving range decreased gradually with an increase in distance from the coal seam. The strata collapsed in the caved zone, whereas the strata collapsed mainly on the bending subsidence in fractured zone. The subsidence curves of caved strata showed a lower concave shape, and the maximum subsidence existed in the middle of the abandoned gob. The caved strata subsidence decreased with an increase in distance from the coal seam. The horizontal fractures were dominant in the fractured zone. The abscission rate of the end mining position was greater than that of the start mining position. Large numbers of vertical fractures existed in the caved zone. The development degree of vertical fractures near the end mining position were larger than that of the start mining position, and the width of the gas-conducting fracture was more than three times that of the start mining position. The development degree, quantity and connectivity of the fracture in the end mining position were better than those in the start mining position.

Propagation of Cryogenic Thermal Fractures from Unconfined PMMA Boreholes

In cryogenic fracturing, a rock surface exposed to cryogenic fluids undergoes a large thermal gradient, and the resultant local tensile stress overcomes rock strength and initiates fractures. This study investigates the development of cracks generated from the cryogenic treatment of a borehole under no external confining stress on specimens. The experiments were performed on transparent PMMA specimens to observe fracture proliferation around boreholes. Liquid nitrogen was flowed through the boreholes to cool the borehole surface. The results show that initial fracture growth is characterized by abrupt starts and stops, and as the fracture propagates outward, the growth appears more continuous. In an early stage, horizontal/radial fractures and vertical fractures are the defining patterns. Horizontal fractures tend to be separated by a specific exclusion distance (i.e., spacing between cracks). While distinct horizontal/vertical fractures and exclusion distance manifest themselves at an early stage, fractures resulting from fracture interactions and curvatures can develop into complex shapes at later stages. Cryogenic thermal loading induces distinctively curved fractures. The tendency of curvature may prevent greater penetration. An increase in the borehole pressure during liquid nitrogen flow, however, can lessen fracture tortuosity and facilitate radial propagation. A high flow pressure and rate are also advantageous in that they accelerate cooling and fracture propagation.

Separation of Split Shear Waves in Two Non-orthogonal Sets of Vertical Fractures

The phenomenon of S-wave splitting indicates the development of fractures in the shallow crust. Therefore, methods based on S-wave splitting have been established to predict the development of one set of parallel fractures. However, for rocks containing two non-orthogonal sets of vertical fractures, the mechanism of S-wave splitting is more complex, and the available methods cannot be applied. To resolve this inadequacy, we propose a two-way rotation method to separate split S-waves with the aim of restoring the split S-wave polarizations and predicting the fracture azimuths. First, we calculate the stiffness matrix of fractured media based on the linear slip theory and derive the phase velocities and polarizations of split S-waves induced by fractures using the Christoffel equation. Second, we clarify the S-wave splitting mechanism in this media by employing velocity analysis and deconstruct the S-wave polarizations on the horizontal components. Third, we deduce a two-way rotation matrix obtained by the S-wave splitting modes to separate the split S-waves. To solve for the angle parameters related to the fracture azimuths in the two-way rotation matrix, we superpose the subspace polarizations in two dimensions to determine the polarization azimuths of the split S-waves. Numerical model tests demonstrate that the proposed method is stable under noisy conditions. Finally, we apply the proposed method to real near-offset and walkaround VSP data, and the predicted fracture results are verified by imaging logs and prior knowledge.

A vertical fracture cluster embedded into thinly layered medium

<p>The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium, according to Schoenberg and Helbig, 1997), the effective medium becomes orthorhombic.  The vertical fractures may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures’ azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the (x<sub>2</sub>; x<sub>3</sub>) plane than that in the (x<sub>1</sub>; x<sub>3</sub>) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium. Assuming that the fracture cluster has a preferred azimuth angle and other fractures are statistically distributed around it, we define the effective compliance matrix by a Gaussian function,  the Bond transformation matrix and  the excess compliance matrix of the vertical fractures in the eigen-coordinate system. The resulting effective medium possess the monoclinic symmetry. The monoclinic anisotropy parameters (Stovas, 2021) can easily be defined from the effective stiffness coefficients.</p><p> </p><p>Schoenberg, M. and Helbig K., 1997, Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth, Geophysics, <strong>62</strong>(6), 1954-1974.</p><p>Stovas, A., 2021, On parameterization in monoclinic media with a horizontal symmetry plane, Geophysics (early online).</p>

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures' azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the ( x2, x3) plane than that in the ( x1, x3) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium.

Evolution Mechanism of Interconnected Vertical Fractures in the Overburden of Longwall Coal Mining

Whether a tensile failure fracture will penetrate a stratum is difficult to ascertain at present. In view of this, the method of similar simulation and field verification are used to carry out a systematic study. Similar simulations show that tensile failure fractures will penetrate the layered strata if the compressive stress is greater than the compressive strength. Theoretical analysis points out that whether the tensile failure fractures will penetrate the layered strata can be expressed by the value of criterion of interconnected vertical fractures and the compression-tension ratio. When the value of criterion of interconnected vertical fractures is greater than the compression-tension ratio, the layered strata will break. This criterion was qualitatively verified with a field test. The results of this paper are of great significance for the prevention of water inrush in coal mines, and it can also promote the understanding of the law of strata movement.

Azimuthal Fourier coefficient inversion for horizontal and vertical fracture characterization in weakly orthorhombic media

Horizontally and vertically aligned fractures (joints) permeated in an isotropic background can give rise to a long-wavelength equivalent orthorhombic medium, which is common for naturally fractured reservoirs. We have developed a feasible approach to characterize the horizontal and vertical fractures using observed azimuthal seismic reflection data. For weak anisotropy, we assume that the horizontal and vertical fractures are decoupled. Using a linear-slip orthorhombic model, we first obtain analytic expressions for the effective elastic stiffness matrix and the corresponding perturbed matrix of an effective orthorhombic anisotropic elastic medium. Combining the scattering function and the perturbed matrix of the orthorhombic medium, we then derive a linearized PP-wave reflection coefficient of effective orthorhombic medium in terms of compressional-wave (P-wave) and shear-wave (S-wave) moduli, density, and horizontal- and vertical-fracture-induced normal and tangential weaknesses. To handle the inverse problem for multiple model parameters in an orthorhombic medium, we reexpress the linearized PP-wave reflection coefficient as a Fourier series. According to the sensitivity analysis of Fourier coefficients (FCs) to isotropic background elastic parameters and four fracture weaknesses, we finally establish a three-step inversion approach to describe the orthorhombic model, which involves (1) estimation of the FCs at different incidence angles from observed azimuthal seismic data and determination of the symmetry axis azimuth, (2) an iterative Bayesian inversion for isotropic background elastic parameters and fracture weaknesses of horizontal fractures from the zeroth-order FC, and (3) an iterative Bayesian inversion for fracture weaknesses of vertical fractures from the second-order FC. The proposed approach is validated by tests on synthetic and field data sets, which demonstrates that the inversion results of P- and S-wave moduli, density, and four fracture weaknesses are robust and reasonable for gas-bearing fractured reservoir characterization with orthorhombic symmetry.