Fracture Front Research Articles

Epoxy/Graphene Nanoplatelet (GNP) Nanocomposites: An Experimental Study on Tensile, Compressive, and Thermal Properties.

This paper presents an experimental investigation of nanocomposites composed of three ratios of epoxy/graphene nanoplatelets (GNPs) by weight. The 0.1, 0.2, and 0.3 wt.% specimens were carefully manufactured, and their mechanical and thermal conductivity properties were examined. The tensile strength and modulus of epoxy/GNPs were enhanced by the large surface area of graphene nanoplatelets, causing crack deflection that created new fracture fronts and friction because of the rough fracture surface. However, the compressive strength was gradually reduced as GNP loading percentages increased. This was probably due to severe plastic yielding on the epoxy, leading to catastrophic axial splitting caused by premature fractures. Furthermore, the highest thermal conductivity was 0.1283 W/m-K, representing a 20.92% improvement over neat epoxy (0.1061 W/m-K) when 0.3 wt.% GNPs were added to the epoxy. This was because of efficient heat propagation in the GNPs due to electron movement through percolative paths. The tensile failure mode in epoxy/GNP nanocomposites showed a few deflected and bifurcated rough cracks and brittle, dimple-like fractures. Contrarily, compressive failure mode in GNP-added epoxy showed plastic flexural buckling and brittle large-axial splitting. The epoxy/GNP nanocomposites were considered a damage-tolerant material.

Propagation of extended fractures by local nucleation and rapid transverse expansion of crack-front distortion.

Fractures are ubiquitous and can lead to the catastrophic material failure of materials. Although fracturing in a two-dimensional plane is well understood, all fractures are extended in and propagate through three-dimensional space. Moreover, their behaviour is complex. Here we show that the forward propagation of a fracture front occurs through an initial rupture, nucleated at some localized position, followed by a very rapid transverse expansion at velocities as high as the Rayleigh-wave speed. We study fracturing in a circular geometry that achieves an uninterrupted extended fracture front and use a fluid to control the loading conditions that determine the amplitude of the forward jump. We find that this amplitude correlates with the transverse velocity. Dynamic rupture simulations capture the observations for only a high transverse velocity. These results highlight the importance of transverse dynamics in the forward propagation of an extended fracture.

Numerical Simulation of integrated three-dimensional hydraulic fracture propagation and proppant transport in multi-well pad fracturing

Multi-well pad fracturing is an indispensable technology for the sustainable development of unconventional oil and gas reservoirs, but the integrated simulation of fracture propagation and proppant migration in massive fracturing treatments remains challenging, including complicated numerical implementations and computational bottlenecks due to its multi-physics, fracture front propagation, size differences between proppant particles and hydraulic fractures. In this work, an integrated model of fracture propagation and proppant migration in multi-well pad fracturing was established based on the three-dimensional discontinuous displacement method for fracturing deformation computations and the Eulerian-Eulerian framework for capturing proppant concentration. The proposed simulator not only accounts for key physical processes such as stress shadow, dynamic flow rate distribution in the wellbore, fluid leak-off, perforation erosion, fractures evolution, proppant bridging, and gravitational settling, but also couples the simulation of 3D planar propagating fractures and proppant transport at well-pad scale, and presents excellent computational efficiency and promising applications than conventional fracturing models. To explore the fracture geometries and proppant distribution in typically stacked layers, single-well, multi-lateral wells, and multi-well pad fracturing are simulated from simple to complex. The findings showed that fracture propagation is jointly affected by intra-stage, inter-stage, and inter-well stress interference mechanisms, and fracture geometries are characterized by unevenness, asymmetry, and heel bias. Proppant transport is controlled by the fracture width and geometries, and most of the proppant is concentrated near the wellbore area and bridging at the narrow fractures. Fracture geometries and proppant distribution are sensitive to the landing locations of horizontal wells because hydraulic fractures always grow in the path of least resistance. Although close lateral well-spacing is beneficial to improve the stimulation efficiency, there are some challenges such as overlapped SRV, enhanced inter-well interference, and severe fracturing hits. Compared with the layout of stacked wells, staggered wells are not only beneficial to reduce the vertical inter-well interference, but also improve reservoir stimulation efficiency. Overall, the stimulated area of the high in-situ stress layers is relatively low even with intentionally landed wells.

An implicit level set algorithm for hydraulic fracturing with a stress-layer asymptote

The capability to simulate a hydraulic fracturing process is an essential tool that can be used to optimize treatment design and increase the efficiency of field operations. In most practical cases, hydraulic fractures propagate in a multi-layered rock formation. As a result, there is a need to incorporate the effect of such heterogeneities in fracturing models to achieve an accurate prediction. To capture the layered structure of rocks, a hydraulic fracture simulator typically requires a fine mesh, which leads to a drastic reduction in computational performance. An alternative is to use more sophisticated models that are capable of providing reasonably accurate predictions even on a relatively coarse mesh. In the case of fracture growth modeling, the pivotal component of the simulation is a fracture front tracking algorithm that accounts for the layered structure of the formation. Consequently, this paper aims to extend the established Implicit Level Set Algorithm (ILSA) to account for the effect of multiple stress layers within the tip asymptote. The enhanced front tracking algorithm involves the stress-corrected asymptote that incorporates the influence of stress layers within the near-tip region. To further increase the validity region of the stress-corrected asymptote, the stress relaxation factor is introduced, and its accuracy is examined. The numerical algorithm is validated against the reference semi-analytical solutions as well as experimental observations. In addition, we investigate the sensitivity of the fracture geometry to mesh size to demonstrate that the front tracking algorithm based on the stress-corrected asymptote retains its accuracy on a coarse mesh.

Simulation of 3D fracture propagation under I-II-III mixed-mode loading

Fracture propagation under mixed-mode loading conditions prevails in many natural geological processes and deep engineering projects, while the corresponding numerical simulation is very challenging in rock mechanics, especially in 3D cases. In most previous studies, the complexity of 3D fracture geometry was over-simplified, and model III loading was often not considered. In this study, we propose to use an efficient stress-based Schöllmann criterion combined with Displacement Discontinuity Method (DDM) to model 3D fracture propagation under arbitrary I ​+ ​II ​+ ​III mixed-mode loading conditions. A novel curve-smoothing algorithm is developed to smoothen the fracture front during propagation, which significantly enhances the model's ability in dealing with complex 3D fracture geometry. In particular, we adopt two different solution schemes, namely staggered and monolithic, to simulate mode I fracture propagation in the case of hydraulic fracturing. The accuracy, efficiency and convergency of the two solution schemes are compared in detail. Our research findings suggest that the degree of coupling between fracture aperture and fluid pressure in hydraulic fracturing lies somewhere between one-way and two-way, which favors the staggered solution scheme. To further test our new model, we provide three additional numerical examples associated with 3D fracture propagation under various mixed-mode loading conditions. Our model shows excellent performance in efficiently locating the new fracture front and reliably capturing the complex 3D fracture geometry. This study provides a generic algorithm to model high-fidelity 3D fracture propagation without simplifying fracture geometry or loading conditions, making it widely applicable to fracture-propagation-related problems.

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

AbstractRecently, a fluid volume enrichment strategy based on the asymptotic solutions near the crack tip was proposed for fluid‐driven fracture propagation problems. Despite its successes in various benchmark and field‐scale problems of hydraulic fracturing simulations, the aforementioned enrichment strategy has the following limitations. First, the tightly coupled solid‐fluid nonlinear system cannot be consistently linearized due to the fast marching method applied to solve the Eikonal equation for fracture tracking. As a result, an approximated Jacobian had to be deployed for the Newton‐Raphson iterations. This is particularly troublesome when the fracture front propagates into newly fractured cells, since a large number of nonlinear iterations are required for convergence because of the inconsistent linearization. Second, the existing method only focused on the viscosity‐dominated fracture propagation regime. Even though the extension of the method to the toughness‐dominated regime could be relatively straightforward, it is not immediately clear how to apply the enrichment technique to the transition regime. This work is dedicated to address the above two limitations. Specifically, a unified fracture propagation criterion is proposed, which not only works for the viscosity‐dominated regime, but also for the toughness‐dominated regime and the transition regime in between. The techniques to consistently linearize the coupled solid‐fluid system and properly initialize the primary unknowns are demonstrated, which result in the significant reduction of required number of nonlinear iterations for convergence. The proposed technique is demonstrated in the context of the Khristianovic‐Geertsma‐de Klerk (KGD) problems due to its relative simplicity.

Simulation of fracture propagation law in fractured shale gas reservoirs under temporary plugging and diversion fracturing

Natural fractures (NFs) are developed in shale gas reservoirs, which can easily cause frac hits during hydraulic fracturing and reduce the productivity of infill wells and parent wells. Temporary plugging diverting fracturing (TPDF) can hinder the single forward extension of fracture transition and avoid the communication of hydraulic fractures (HFs) or NFs adjacent to wells. In order to explore the fracture propagation law of TPDF in fractured shale gas reservoirs, this study systematically evaluates the main factors such as stress difference, displacement, and fracturing fluid viscosity on the fracture temporary plugging diversion (TPD) law by means of true triaxial hydraulic fracturing simulation device and cohesive element model in ABAQUS. The findings reveal that (1) the law of fracture initiation and propagation at the engineering scale is similar to that in indoor experiments. Upon the primary fracturing (PF), the smaller the horizontal stress difference, the larger the pumping displacement, and the smaller the viscosity of the fracturing fluid is, the greater the corresponding fracture breakdown pressure and the stronger the rock compression resistance. (2) After TPD secondary fracturing, a small horizontal stress difference and a large pumping displacement facilitate the formation of a vertical complex fracture network structure on the primary fracture. Because of the small size of the indoor rock, viscosity has little effect on the fracture propagation of the TPDF, but the numerical simulation results reveal that the higher the viscosity, the greater the width of the new fracture. In addition, (3) the smaller the angle between the new fracture opened after PF and TPDF, the better the propagation effect of the new fracture. Meanwhile, the farther the temporary plugging zone is from the fracture front end, the wider the new fracture opened after TPDF. The field construction results reveal that the TPDF technology can avoid the effect of HFs, thus preventing frac hits during shale gas reservoir reconstruction. This study not only posits a physical and numerical simulation method for simulating the fracture propagation law of TPDF in fractured shale gas reservoirs but also provides theoretical guidance for applying TPDF to field construction.

Formulation optimization of materials used in temporary plugging diversion between fracture front end and cluster in shale gas: From laboratory research to field application

The staged and multi-cluster fracturing of horizontal wells is the main fracturing technology used for shale gas reservoir development. Temporary plugging diversion (TPD) is an important technical means to realize a uniform propagation of hydraulic fractures and avoid problems such as frac hits (i.e., well-to-well interference). Although this technology has been extensively used worldwide, field monitoring results have shown that temporary plugging cannot effectively improve the nonuniform propagation of multiple fractures. The fundamental reason is the lack of an organic combination of laboratory research and field application. To solve this problem, this study investigated the reservoir adaptability and plugging performance of three types of temporary plugging agent (TPAs), namely, powder, particle, and fiber, used in the fracturing of wells in the Weiyuan (WY) shale gas field, Sichuan, China, using a pressure-bearing capacity test device for three dimensional (3D)-printing-simulated TPA. A calculation method for the plugging efficiency of the TPA was established, and the ratio and concentration of the TPA were optimized under different fracture widths. The similarity criterion was used to calculate the amount of TPA required for different fracture widths. A field application chart of the TPA was formulated, and a method that connects laboratory research and field application was established. The results showed that the three TPAs have good reservoir adaptability and degradation performance. It is recommended to use 200–400 mesh powder + 6 mm fiber with different concentrations and dosages when performing temporary plugging and fracturing at the front end of 1–3 mm fractures. In the case of inter-cluster TPD for a fracture width of 4–6 mm, a combination of 20 mesh powder + 6 mm fiber + 1–3 mm particles is recommended. The field application results showed that the pressure increased significantly at the front end of the fractures and during inter-cluster temporary plugging when the plugging agent was in place, and there were no frac hits in the adjacent wells. This paper provides a practical research method for hydraulic fracturing involving temporary plugging, from laboratory research to engineering application.

Analysis of the Influence of Hydraulic Fracturing Fluid Velocity on Fracture Propagation

To reveal the influence of fracturing fluid velocity on hydraulic fracturing fracture propagation, a hydraulic fracturing numerical model was established based on a coalbed methane (CBM) field in the northeast of China. The influence of fracturing fluid velocity on hydraulic fracturing fracture propagation is mainly investigated, and the relationship between fracturing fluid velocity and fracture tip displacement is obtained. The results show that the fracture front presents different morphological characteristics at different times of fracturing. The larger the fracturing fluid velocity, the larger the fracture length and width after the same time of hydraulic fracturing. However, the fracture length will not increase indefinitely; the fracture will stop spreading when the injected fluid reaches a balance with the fluid that is permeated or filtered from the fracture surface. With the increase in fracturing fluid velocity, the fracture length increases logarithmically and gradually flattens out. The research conclusion provides a certain reference for improving the fracture propagation effect of hydraulic fracturing.

Geometric rules for the annihilation dynamics of step lines on fracture fronts.

The roughness of a fracture surface records a crack's complex path through a material and can affect the resultant frictional or fluid transport properties of the broken medium. For brittle fractures, some of the most prominent surface features are long, step-like discontinuities called step lines. In heterogeneous materials, the mean crack surface roughness created by these step lines is well captured by a simple, one-dimensional ballistic annihilation model, which assumes the creation of these steps is a random processes with a single probability that depends on the heterogeneity of the material, and that their destruction occurs via pairwise interactions. Here, through an exhaustive study of experimentally generated crack surfaces in brittle hydrogels, we examine step interactions and show that interaction outcomes depend on the geometry of the incoming steps. The rules that govern step interactions can be categorized into three unique classes and are fully described, providing a complete framework for predicting fracture roughness.

Interpretation of Fracture Initiation Points by In-Well Low-Frequency Distributed Acoustic Sensing in Horizontal Wells

Summary Low-frequency distributed acoustic sensing (LF-DAS) exploits the optical phase shift of Rayleigh backscatter in fiber-optic cables to obtain distributed measurements of changes in strain and temperature. Fiber-optic cables are often installed for multistage hydraulic fracture diagnostics in horizontal wells. LF-DAS in an untreated well provides far-field strain measurements, while offset wells are hydraulically fractured. Such a configuration is called crosswell LF-DAS sensing. Crosswell LF-DAS measurements have proved useful in diagnosing fracture hits, fracture azimuth, planarity, cluster efficiency, fracture propagation rates, and the dynamic distance to the fracture front. In contrast, in-well LF-DAS is conducted on the actively fractured well. Due to cool fracture fluid being injected at high injection rates, the strain component of the LF-DAS response is largely obscured by temperature changes. In permanent fiber-optic cable installations, distributed temperature sensing (DTS) is often conducted simultaneously with LF-DAS. An opportunity exists to decouple the temperature and strain components of LF-DAS sensors to observe strain changes on in-well LF-DAS. The LF-DAS response is modeled as linearly dependent on strain and temperature changes. Theoretical LF-DAS temperature and strain sensitivity coefficients are derived based on the changes to the index of refraction and length of the fiber. Using the DTS measurements, temperature changes are computed, smoothed, filtered, and compared to the LF-DAS response. Crossplots of the in-well LF-DAS measurements and temperature changes from DTS measurements far from the actively fractured region are used to validate the theoretical sensitivity coefficients. Uncertainty in the temperature component of the LF-DAS response is quantified. The difficulty in corresponding the different spatial and temporal resolutions of the DTS and LF-DAS measurements is overcome by comparing the responses over a moving temporal and spatial window. If the LF-DAS response at the center of the window agrees with the DTS response within uncertainty, the measurement is filtered out. After filtering, the remaining nonzero in-well LF-DAS measurements are due to changes in strain. The data are then visualized in waterfall plots. The results indicate that the theoretical and observed strain and temperature coefficients agree within 10%. After the temperature component of the in-well LF-DAS response is extracted, the remaining nonzero measurements are located primarily within the actively treated region. Locations with peaks in the strain response are interpreted to indicate fracture initiation points. These fracture initiation points are compared with in-well DTS and high-frequency DAS noise measurements across multiple stages to better understand fracture initiation along the horizontal well.

Low-frequency distributed acoustic sensing shape factors for fracture front detection

Accurate knowledge of fracture extents generated in multistage unconventional completions remains elusive. Crosswell low-frequency distributed acoustic sensing (LF-DAS) measurements can determine the time and location of a frac hit. Knowing where and when a frac hit occurs constrains the fracture extent but does not estimate it quantitatively. A recent study on crosswell LF-DAS demonstrated a simple method to rapidly determine the instantaneous fracture propagation rate when a frac hit occurs. This method, the zero strain-rate location method (ZSRLM), is based on laboratory experiments and numerical modeling assuming a radial fracture geometry. The method estimates a fracture propagation velocity that is used to extrapolate the final fracture extent. The propagation rate is calculated based on dynamic estimates of the nearest distance from the fiber to the front of a propagating fracture. The ZSRLM is adapted to estimate the distance to the fracture front based on rectangular fracture geometries. A 3D displacement discontinuity method program generates crosswell LF-DAS strain-rate waterfall plots considering a single, rectangular fracture of constant height. Over 150 different simulations were conducted varying formation mechanical properties, fracture height, and the vertical and horizontal offset between the treatment and monitor well. For each simulated case, the ZSRLM is used to estimate the distance to the fracture front based on the simulated waterfall plots. The difference between the estimated and actual distance to the front is corrected by a shape factor. The relationship among the shape factor, fracture height ratio, and vertical offset ratio is determined. Using a shape factor improves the performance of the ZSRLM by up to a factor of two for rectangular fractures. The updated ZSRLM is applied to extrapolate final fracture extents in two field cases: a single cluster stage in the Montney Formation and a multicluster stage of an Austin Chalk completion.

A hydro‐mechanically‐coupled XFEM model for the injection‐induced evolution of multiple fractures

AbstractIn this paper, a two‐dimensional eXtended Finite Element Method (XFEM) solution is presented for the hydro‐mechanically coupled hydro‐frac‐induced propagation of multiple fractures in rocks. Fractures are considered one‐dimensional objects, and the rock matrix is regarded as a two‐dimensional medium. Rules for improving the accuracy of the solution are included to deal with the transfer of variables between fractures and matrix in the coupling process. The main variables include fluid pressure and fracture aperture. The following assumptions are made: (1) the fluid pressure inside a fracture is applied as a net pressure; (2) fluid leak‐off is ignored; (3) the fluid front is regarded as a fracture front provided that the area of fluid lag has a small effect on fracture propagation compared to the area at which the fluid pressure is applied. The fluid flow is governed by the lubrication equation, while the XFEM is used to describe the behaviour of the elastic medium. The simulation results are compared with analytical solutions for a single hydraulic fracture model to verify and validate the proposed algorithm. A simulation with multiple hydraulic fractures is also performed to investigate the interference effect of multiple fractures and fracture propagation. The shadow effect caused by multiple fractures is analysed to manifest the stress variation along the propagation path.

Early-Time Shut-In for Plane-Strain Hydraulic Fractures

One investigates the post-shut-in growth of a plane-strain hydraulic fracture in an impermeable medium while accounting for the possible presence of a fluid lag. After the stop of fluid injection, the fracture may present three distinct propagation patterns: an immediate arrest, a temporary arrest with delayed propagation, and a continuous fracture growth. These three patterns are all followed by a final fracture arrest yet the fracture behaviour prior to that results from the interplay between the dimensionless toughness mathcal {K}_m, the shut-in time t_s/t_{om}, and the propagation time t/t_s. mathcal {K}_m characterizes the energy dissipation ratio between fracture surface creation and viscous fluid flow under constant rate injection. t_s and t_{om} represent respectively the timescale of shut-in and the coalescence of the fluid and fracture fronts. The immediate arrest occurs when the fracture toughness dominates the fracture growth at the stop of injection (mathcal {K}_m gtrapprox 4.3). It may also occur upon an early shut-in at low dimensionless toughness associated with an overshoot of fracture extension and a significant fluid lag. For intermediate values of mathcal {K}_m and t_s/t_{om}, the fracture may experience a temporary arrest followed by a restart of fracture propagation. The period of the temporary arrest becomes shorter with higher dimensionless toughness and later shut-in until it drops to zero. The fracture behaviour after shut-in then transitions from temporary arrest to continuous propagation. These propagation patterns result in different evolution of fracture dimensions which possibly explains the various emplacement scaling relations reported in magmatic dikes.

Discrete modeling of concrete failure and size-effect

Size-effect in concrete and other quasi-brittle materials defines the relation between the nominal strength and structural size when material fractures. The main cause of size-effect is the so-called energetic size-effect which results from the release of the stored energy in the structure into the fracture front. In quasi-brittle materials and in contrast to brittle materials, the size of the fracture process zone is non-negligible compared to the structural size. As a consequence, the resulting size-effect law is non-linear and deviates from the response predicted by linear elastic fracture mechanics. In order to simulate the size-effect, one needs to rely on numerical modeling to describe the formation, development and propagation of the fracture process zone. Although a number of models have been proposed over the years, it transpires that a correct description of the fracture and size-effect which accounts for boundary effects and varying structural geometry remains challenging. In this study, the Lattice Discrete Particle Model (LDPM) is proposed to investigate the effects of structural dimension and geometry on the nominal strength and fracturing process in concrete. LDPM simulates concrete at the aggregate level and has shown superior capabilities in simulating complex cracking mechanisms thanks to the inherent discrete nature of the model. In order to evaluate concrete size-effect and provide a solid validation of LDPM, one of the most complete experimental data set available in the literature was considered and includes three-point bending tests on notched and unnotched beams. The model parameters were first calibrated on a single size notched beam under three-point bending and on the mechanical response under unconfined compression. LDPM was then used to perform blind predictions on the load-crack mouth opening displacement curves of different beam sizes and notch lengths. Splitting test results on cylinders were also predicted. The results show a very good agreement with the experimental data. The quality of the predictions was quantitatively assessed. In addition, a discussion on the fracturing process and dissipated energy is provided. Last but not least, the Universal Size-Effect Law proposed by Bažant and coworkers was used to estimate concrete fracture parameters based on experimental and numerical data.

A pseudo-transient-based staggered algorithm for hydraulic fracturing simulations in the absence of a fluid lag

In the present work we propose a novel approach to the simulation of fluid-driven fracture propagation in the absence of a fluid lag. The presented algorithm relies on a staggered treatment of the coupling between the fluid and solid equations describing the viscous fluid flow driving the solid deformation and fracture propagation, allowing the use of optimal solution techniques for each individual problem. Standard finite elements are employed for the discretization of the fluid equation while a hybrid Discontinuous Galerkin/cohesive zone model formulation is chosen for modeling the solid response. Under zero fluid lag conditions, coalescence of the fluid and fracture fronts results in a Neumann elliptic boundary value problem for the fluid, exhibiting non-uniqueness as well as potentially being ill-posed. We show how a false-transient treatment of the fluid equation enables the prescription of full Neumann boundary conditions without the need to resort to intermediate pressure boundary conditions, owing to the coupling with the solid problem. Stability and convergence conditions are derived under simplifying hypotheses. The performance of the algorithm is verified against known analytical solutions, with very good results.

Modeling of dynamic bridging of solid particles in multiple propagating fractures

During multi-cluster fracturing, solid particles are widely used to alleviate the non-uniform fluid distribution and fracture growth. Even though diversion technology has been applied and proved effective in numerous field applications, many involved physical mechanisms, such as solid diverters transport, settling, bridging, and packing in multiple propagating fractures, remain unclear. In this work, a computational mechanics system is developed to interpret the coupling process of fluid flow, fracture propagation, and particle transport. The moving fracture front is located using the implicit level set algorithm (ILSA) and tip asymptotic solution. The diverter particle transport model can capture the settling, bridging, and packing of particles; thus the slurry flow in the fracture can transit from Poiseuille flow to Darcy flow naturally. Application of the developed system to simulate a single stage of three equally spaced clusters indicates that it is possible to create multiple fractures with uniform length using diversion technology, but their widths are non-uniform. Instead, they demonstrate pinched or ballooned shapes, because of the stress interference. An extensive parametric study is also performed to investigate how various parameters affect diversion efficiency.

Effect of the phase-transition fluid reaction heat on wellbore temperature in self-propping phase-transition fracturing technology

The key to the success of self-propping phase-transition fracturing (SPF) technology using two immiscible fluids to generate proppants in-situ in a reservoir lies in accurate calculations of temperature distribution. As the reaction heat of phase-transition fluid (PF) significantly affects wellbore temperature, reaction kinetic parameters were fitted by experimental data based on the Arrhenius equation, and the transient temperature model considering the reaction heat is established based on the first law of thermodynamics. This model is discretized by the finite difference method and solved by the successive over-relaxation iteration method. The results show that the reaction heat effect on wellbore temperature cannot be ignored. A temperature value and a phase transition time at the well bottom are the largest in the whole wellbore, so the phase transition ratio at the well bottom is the largest. Moreover, since the PF with incomplete phase transition in a wellbore is easier to enter fractures and prop fracture fronts, it is recommended to inject a pre-pad fracturing fluid before injecting PF to reduce wellbore temperature and prevent premature phase transition in the wellbore. These findings can help reveal the action mechanisms of different injection methods and parameters in a heat transfer process, which is of great significance for the theoretical research and field implementation of SPF technology.

Damage and failure mechanism of sapphire under ballistic loading based on a modified bond‐based peridynamic model

AbstractTo investigate the dynamic mechanical behaviors of c‐plane and a‐plane sapphire, a novel anisotropic constitutive model and fracture criterion are constructed on the basis of bond‐based peridynamics (BB‐PD) theory. And the concept of strain is introduced in the framework of BB‐PD. After that, the simulations of a‐ and c‐planes of sapphire under spherical and cylindrical impact are conducted. In addition to capturing the distribution of strain and damage, the histories of various fracture types such as the primary fracture front and cracks are monitored for quantitative analysis. The numerical predictions are shown to agree well with previous experimental results, and further reveal the damage and failure mechanisms of sapphire. The different forms of contact between the projectile and the target strongly influence the stress waves generated and energy transferred ultimately affecting the damage development process. The crystal orientation dominates the appearance of anisotropic crack modes. Crack bending and deflection, as well as spalling‐like fracture, are associated with wave reflection and intersection. Moreover, an in‐depth examination of the observed wave splitting phenomenon is performed.

Laboratory Investigation of Hydraulic Fracture Growth in Zimbabwe Gabbro

AbstractDirect measurement of the apparent toughness evolution during hydraulic fracture growth remains challenging in rocks due to the difficulty of measuring the time evolution of the fracture geometry. We report hydraulic fracturing tests performed in 250 × 250 × 250 mm Zimbabwe gabbro under different confining stress. Using time‐lapse active acoustic surveys, we reconstruct the fracture front and fracture width using scattered and transmitted waves. After verifying that hydraulic fracture growth is dominated by the energy dissipated in fracture creation such that the fluid pressure can be considered spatially uniform in the fracture (negligible viscous flow energy dissipation), we estimate the apparent fracture toughness, using the theory of linear hydraulic fracture mechanics, by combining fracture geometry and pressure data. The apparent fracture energy is higher than that measured from semicircular bending tests. The created fractures evolve in a planar and radial geometry at the macroscopic scale, but we observe overlapping segments and bridges at the millimetric scale. This complex segmentation at a scale on par with the rock grain size is likely responsible for the observed higher fracture energy at centimetric scale. Such fracture segmentation and bridging will necessarily occur when encountering heterogeneities and result in a further increase of fracture energy at a larger scale even if the overall macroscopic geometry remains planar. The experimental data set reported here should guide modeling efforts necessary to better predict hydraulic fracture growth in rock masses.