Analysis of S waves singularity points in porous rock with two orthogonal sets of mesoscale fractures

SUMMARY The shear waves phase velocity surfaces in orthorhombic (ORT) and lower symmetry anisotropic models touch each other in one or more points resulting in so called singularity points or acoustic axes. These singularity points result in dramatic changes of velocities, amplitudes and polarizations creating problems in seismic data processing and analysis. Considering the frequency-dependent anisotropy due to mesoscale fractures in Chapman's model, we describe the singularity points in porous rock with two orthogonal sets of mesoscale fractures. First, we give the equations for frequency-dependent phase velocities of P, S1 and S2 waves in this anelastic ORT media. Then, we derive the expressions for frequency-dependent singularity points within the symmetry planes and discuss the conditions to detect the existence of singularity point. Finally, the influences of frequency, porosity, fracture density, fracture scale and saturating fluid style on the positions of singularity points within the symmetry plane are investigated.

Numerical simulation on proppant transport in fracture junctions affected by the fracture scale

The proppant distribution significantly affects the conductivity of fracture networks. However, the law of proppant transport in fracture networks is still unclear, and the influence of fracture scale on the proppant distribution has not been determined. Thus, in the present study, the influence of fracture scale was investigated, and the influences of approaching angle and width ratio on fluid split ratio were analyzed. An Eulerian–Eulerian model was utilized to simulate suspended proppant and bed load proppant migration in fracture junctions. Then, a sensitivity analysis was carried out to evaluate the parameters that may affect the proppant distribution pattern, such as injection velocity, fluid viscosity, and proppant density. The results show that the approaching angle and width ratio significantly influence the fluid split ratio in a small-scale fracture. Moreover, the effect of the approaching angle decreases with an increase in the fracture scale. The split ratio of suspended proppant increases with increasing sand ratio, fluid split ratio, and width ratio. The split ratio of bed load proppant increases with increasing injection rate, fluid viscosity, width ratio, fluid split ratio, and decreasing proppant diameter. In small-scale fracture junctions, the approaching angle affects the split ratio of suspended proppant or bed load proppant by influencing the fluid split ratio; however, the effect is inconspicuous in large-scale fractures. The increase in fluid split ratio with the fracture scale leads to an increase in the split ratio of suspended proppant or bed load proppant.

Multifractal Analysis of Acoustic Emissions during Hydraulic Fracturing Experiments under Uniaxial Loading Conditions: A Niutitang Shale Example

Fracture characterization is essential for estimating the stimulated reservoir volume and guiding subsequent hydraulic fracturing stimulations in shale reservoirs. Laboratory fracturing experiments can help provide theoretical and technical guidance for field operations. In this study, hydraulic fracturing experiments on the shale samples from Niutitang Formation in Hunan Province (China) under a uniaxial loading condition are conducted. The multifractal method is used to analyze the acoustic emission (AE) signals and characterize fracture initiation and propagation. The hydraulic fracturing process can be divided into three stages based on the characteristics of AE signals: the initial stage, the quite stage, and the fracturing stage. The multifractal analysis results showed that: (1) the value of the spectrum width, Δα, continues to increase as the energy accumulates until the fracturing stage starts; and (2) the difference in the multifractal spectrum values, Δf, reflects the relationship between small and large signal frequencies and can quantify the fracture scale, i.e., the lower the Δf, the larger the fracture scale and vice versa. The results were further verified using a time-frequency analysis of the AE signals and micro-CT scanning of the samples. This study demonstrates that the multifractal method is feasible for quantitatively characterizing hydraulic fractures and can aid field hydraulic fracturing operations.

Amputation

The decision to amputate rather than reconstruct a severely injured limb (‘mangled extremity’) has historically been one of the most difficult choices faced by a trauma surgeon. The surgeon’s responsibility is heightened by the knowledge that delayed or incorrect decision-making may lead to worse outcomes. Unfortunately, hard data upon which to base reliable decisions remain elusive. A prospective analysis of the use of scoring systems including the Limb Salvage Index, the Predictive Salvage Index, the Hanover Fracture Scale, and the NISSSA (Nerve injury, Ischaemia, Soft-tissue contamination, Skeletal damage, Shock, Age) and MESS (Mangled Extremity Severity Score) scores did not validate the clinical utility of any of the scoring algorithms.

Hybrid Analytical and Numerical Approach for Modeling Fluid Flow in Simplified Three-Dimensional Fracture Networks

Modeling fluid flow in three-dimensional fracture networks is required in a wide variety of applications related to fractured rocks. Numerical approaches developed for this purpose rely on either simplified representations of the physics of the considered problem using mesh-free methods at the fracture scale or complex meshing of the studied systems resulting in considerable computational costs. Here, we derive an alternative approach that does not rely on a full meshing of the fracture network yet maintains an accurate representation of the modeled physical processes. This is done by considering simplified fracture networks in which the fractures are represented as rectangles that are divided into rectangular subfractures such that the fracture intersections are defined on the borders of these subfractures. Two-dimensional analytical solutions for the Darcy-scale flow problem are utilized at the subfracture scale and coupled at the fracture-network scale through discretization nodes located on the subfracture borders. We investigate the impact of parameters related to the location and number of the discretization nodes on the results obtained, and we compare our results with those calculated using reference solutions, which are an analytical solution for simple configurations and a standard finite-element modeling approach for complex configurations. This work represents a first step towards the development of 3D hybrid analytical and numerical approaches where the impact of the surrounding matrix will be eventually considered.

Multi-Scale Simulation of Hydraulic Fracturing and Production: Testing with Comprehensive Data from the Hydraulic Fracturing Test Site in the Permian Basin

<p>The Hydraulic Fracturing Test Site (HFTS) project, fielded a few years ago within the Wolfcamp Formation in the Permian Basin in the United States, provides an excellent opportunity to further develop our understanding of the geomechanical response to hydraulic stimulation and associated production in shale lithologies. In addition to a full set of geophysical and tracer observations, the project obtained core samples from wells drilled through the stimulated region, characterizing the propagation of fractures, reactivation of pre-existing natural fractures, and placement of proppant. In addition to providing an overview of the available field data from the field test, we describe here a multi-scale modeling effort to investigate the hydrologic, mechanical and geochemical response of the Wolfcamp Formation to stimulation and production. The ultimate outcome of this project is the application and validation of a new framework for microscopic to reservoir scale simulations, built upon a fusion of existing high performance simulation capabilities.</p><p>The modeling occurs across two spatial domains – the “reservoir scale”, which encompasses the intra- and inter-well regions, and the “inter-fracture scale”, which is the region between stimulated fractures. Physics-based simulations of the fracture network evolution upon stimulation at the reservoir scale using the simulator GEOS provide input for reservoir-scale production simulations conducted with the TOUGH family of codes. At the inter-fracture scale, the fluid dynamics and reactive transport Chombo-Crunch code is used simulate the micro-scale pore-resolved physical processes occurring at the fracture and rock interfaces upon stimulation and production, tested against laboratory studies of proppant transport and pore-scale reactions. Micro-scale modeling and imaging provides upscaled flow and transport parameters for larger-scale reservoir modeling and production optimization.</p>

Perturbative corrections for the scaling of heat transport in a Hele-Shaw geometry and its application to geological vertical fractures

In this work, we investigate numerically the perturbative effects of cell aperture in heat transport and thermal dissipation rate for a vertical Hele-Shaw geometry, which is used as an analogue representation of a planar vertical fracture at the laboratory scale. To model the problem, we derive a two-dimensional set of equations valid for this geometry. For Hele-Shaw cells heated from below and above, with periodic boundary conditions in the horizontal direction, the model gives new nonlinear scalings for both the time-averaged Nusselt number $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}$ and dimensionless mean thermal dissipation rate $\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}$ in the high-Rayleigh regime. We demonstrate that $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}$ and $\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}$ depend upon the cell anisotropy ratio $\unicode[STIX]{x1D716}$, which measures the ratio between the cell gap and height. We show that $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}$ values in the high-Rayleigh regime decrease when $\unicode[STIX]{x1D716}$ grows, supporting the field observations at the fracture scale. When $\unicode[STIX]{x1D716}\ll 1$, our results are in agreement with the scalings found using the Darcy model. The numerical results satisfy the theoretical relation $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}=Ra\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}$, which is obtained from the model. This latter relation is valid for all values of Rayleigh number considered. The perturbative effects of cell aperture are observed only in the exponents of the scalings $\langle Nu\rangle _{\unicode[STIX]{x1D70F}}\sim Ra^{\unicode[STIX]{x1D6FE}(\unicode[STIX]{x1D716})}$ and $\langle \unicode[STIX]{x1D717}\rangle _{\unicode[STIX]{x1D70F}}\sim Ra^{\unicode[STIX]{x1D6FE}(\unicode[STIX]{x1D716})-1}$.