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We explored the microstructure-related scale effect on the tensile failure of coal. Disc specimens with different diameters (25 mm, 38 mm, 50 mm, and 75 mm) were processed for the Brazil split test. The influence of microstructures on fracture initiation and propagation was detected and analysed by the combination of X-ray computed tomography scanning, digital image correlation approach, and acoustic emission monitoring. The investigation indicated that tensile strength decreased with increasing specimen diameter, and the relationship can be described by an exponential equation. Four tensile failure modes were observed in specimens with different diameters, namely central, non-central, central edge, and central multiple pattern. Larger specimens exhibited more complicated failure patterns (central edge and central multiple failure patterns) and a greater percentage of shear failure fractures. Strain concentration and strain reversal were observed, respectively, in mineral—inclusion-rich regions and pre-existing discontinuities regions. This possibly contributed to fracture initiation, propagation, and coalescence. Fractures tended to grow along with the interface of mineral inclusion and coal matrix, and they could have propagated into and connect the pre-existing discontinuities. The greater volume of microstructure in larger specimens resulted in fractures that were more complex and may have increased the number of shear failure cracks and led to failure modes that were more complicated.

Multi-stage plug-n-perf fracturing of horizontal wells has proven to be an effective method to develop unconventional reservoirs. Various studies have shown uneven fluid and proppant distributions across all perforation clusters. It is commonly believed that both fracturing fluid and proppant contribute to unconventional well performance. Achieving uniform fluid and proppant placement is an important step toward optimal stimulation. This paper discusses how to achieve such uniform placement in each stage via a CFD (Computational Fluid Dynamics) modeling approach. CFD models in several lab scales were built and calibrated using experimental data of proppant transport through horizontal pipes in several laboratory configurations. A field-scale model was then built and validated using perforation erosion data from downhole camera observations and the same model parameters calibrated in the lab-scale model. With the field-scale model validated, CFD simulations were performed to evaluate the impact of key parameters on fluid and proppant placement in individual perforations and clusters. Some key parameters investigated in this study included perforation parameters (size, orientation, number), cluster spacing, cluster count per stage, fluid properties, proppant properties, pumping rates, casing sizes, and stress shadow effects, etc. Both lab and CFD results show that bottom-side perforations receive significantly more proppant than top-side perforations due to gravitational effects. Lab and CFD results also show that proppant distribution is increasingly toe-biased at higher rates. Proppant concentration along the wellbore from heel to toe generally varies significantly. Gravity, momentum, viscous drag, and turbulent dispersion are key factors affecting proppant transport in horizontal wellbores. This study demonstrates that near-uniform fluid and proppant placement across all clusters in each stage is achievable by optimizing perforation, cluster, and other treatment design factors. Validated CFD modeling plays an important role in this design optimization process.

Defining the trajectory of hydraulic fractures crossing bedding planes and other fractures is a significant issue in determining the effectiveness of the stimulation. In this work, a damage evolution law is used to describe the initiation and propagation of the fracture. The model couples rock deformation and gas seepage using the finite element method and is validated against classical theoretical analysis. The simulation results define four basic intersection scenarios between the fluid-driven and preexisting fractures: (a) inserting—the hydraulic fracture inserts into a bedding plane and continues to propagate along it; (b) L-shaped crossing—the hydraulic fracture approaches the fracture/bedding plane then branches into the plane without crossing it; (c) T-shaped crossing—the hydraulic fracture approaches the fracture/bedding plane, branches into it, and crosses through it; (d) direct crossing—the hydraulic fracture crosses one or more bedding planes without branching into them. The intersection scenario changes from (a) → (b) → (c) → (d) in specimens with horizontal bedding planes when the stress ratio β ( β = σ y / σ x ) increases from 0.2 to 5. Similarly, the intersection type changes from (d) → (c) → (a) with an increase in the bedding plane angle α (0° → 90°). Stiffness of the bedding planes also exerts a significant influence on the propagation of hydraulic fractures. As the stiffness ratio E 1 ¯ / E 2 ¯ increases from 0.1 to 0.4 and 0.8, the seepage area decreases from 22.2% to 41.8%, and the intersection type changes from a T-shaped crossing to a direct crossing.

Non-aqueous or gaseous stimulants are alternative working fluids to water for hydraulic fracturing in shale reservoirs, which offer advantages including conserving water, avoiding clay swelling and decreasing formation damage. Hence, it is crucial to understand fluid-driven fracture propagation and morphology in shale formations. In this research, we conduct fracturing experiments on shale samples with water, liquid carbon dioxide, and supercritical carbon dioxide to explore the effect of fluid characteristics and in situ stress on fracture propagation and morphology. Moreover, a numerical model that couples rock property heterogeneity, micro-scale damage and fluid flow was built to compare with experimental observations. Our results indicate that the competing roles between fluid viscosity and in situ stress determine fluid-driven fracture propagation and morphology during the fracturing process. From the macroscopic aspect, fluid-driven fractures propagate to the direction of maximum horizontal stress direction. From the microscopic aspect, low viscosity fluid easily penetrates into pore throats and creates branches and secondary fractures, which may deflect the main fracture and eventually form the fracture networks. Our results provide a new understanding of fluid-driven fracture propagation, which is beneficial to fracturing fluid selection and fracturing strategy optimization for shale gas hydraulic fracturing operations.

We explore microstructure-related effects of loading direction and specimen size on the anisotropy of uniaxial compressive strength in coal. We measure uniaxial compressive strength on coal samples of four different diameters (25 to 75 mm) and with varied dip of the bedding plane with respect to loading direction (0°, 15°, 30°, 45°, 60° and 90°) including characterizing the variation of microstructures in the specimens by X-ray imaging. The uniaxial compressive strength for each specimen size exhibits a unique U-shape curve against the angle of anisotropy ( Jaeger, 1971 ). The degree of the strength anisotropy decreases with increasing specimen size, principally due to the enhanced microstructural volume of a larger specimen. The contribution of microstructures on uniaxial compressive strength differs for different orientations of loading relative to anisotropy. The rate of decline of the average uniaxial compressive strength with increasing specimen size is greatest when loading is parallel to bedding (anisotropic angle of 0°) and is the most moderate at 45°. An empirical equation relating specimen diameter with uniaxial compressive strength is proposed and verified against the experimental data. Based on this equation, the UCS of coal samples with different orientations relative to the anisotropy are predicted for the limiting sizes of zero and ∞. The anisotropy of the scale effect is also explored. Meanwhile, it is verified that a cosine relation between anisotropy angle and uniaxial compressive strength is applicable to coal specimens of different sizes. This demonstrates that the strength anisotropy in coal will remain constant when the specimen diameter is larger than a critical threshold. Based on these two observations/equations, a universal equation relying on the minimum strength angle, friction angle and Weibull coefficients is proposed and verified against experimental data to describe the relationship among anisotropy angle, specimen size, and uniaxial compressive strength in coal.

Hydraulic fracturing is a key method in the stimulation of shale gas reservoirs. Shale gas formations often contain natural fractures which are fluid-pressure sensitive and dilate in response to the inflation of the fracture, increasing fluid loss and slowing down and potentially prematurely arresting fracture propagation. Models typically assume 1-D single-porosity/permeability (Carter) leakoff perpendicular to the hydraulic fracture. However, the leakoff process in naturally fractured formations is considerably more complex. In this study, we present an hydraulic fracturing model based on the PKN-formalism which accommodates leakoff into a pressure-sensitive dual porosity medium. Proppant transport is accommodated by introducing empirical constitutive equations to determine the proppant distribution during the hydraulic fracturing treatment. The model is solved numerically and is validated against known small and large time asymptotic solutions. The model is capable of providing a rapid estimation of the morphology of hydraulic fractures in naturally fractured formations and the corresponding proppant distribution. The simulation results illustrate that the leakoff into a dual porosity medium, where fracture permeability is a strong function of applied fluid pressure, results in a reduced length of the propagating fracture due to the fugitive fluid leakoff from the fracture into the surrounding formation and that this in turn results in a reduced maximum width during the treatment. The ability to infuse proppants in fluid-driven fractures penetrating large distances from the injection wellbore is further limited by premature screen-out. This may compromise the ultimate efficiency of the final hydraulic fracture regarding gas recovery. Reduced propagation and premature screen-out are limited by low permeability and large spacing of the natural fractures. The presence of an existing network of natural fractures, including those adjacent to the hydraulic fracture that may become propped, aids in the recovery of the resource by reducing diffusion lengths of the hydrocarbon to the main fracture.

The residual opening of fluid-driven fractures is conditioned by proppant distribution and has a significant impact on fracture conductivity - a key parameter to determine fluid production rate and well performance. A 2D model follows the evolution of the residual aperture profile and conductivity of fractures partially/fully filled with proppant packs. The model accommodates the mechanical response of proppant packs in response to closure of arbitrarily rough fractures and the evolution of proppant embedment. The numerical model is validated against existing models and an analytic solution. Proppant may accumulate in a bank at the fracture base during slick water fracturing, and as hydraulic pressure is released, an arched zone forms at the top of the proppant bank as a result of partial closure of the overlaying unpropped fracture. The width and height of the arched zone decreases as the fluid pressure declines, and is further reduced where low concentrations of proppant fill the fracture or where the formation is highly compressible. This high-conductivity arch represents a preferential flow channel and significantly influences the distribution of fluid transport and overall fracture transmissivity. However, elevated compacting stresses and evolving proppant embedment at the top of the settled proppant bed reduce the aperture and diminish the effectiveness of this highly-conductive zone, with time. Two-dimensional analyses are performed on the fractures created by channel fracturing, showing that the open channels formed between proppant pillars dramatically improve fracture transmissivity if they are maintained throughout the lifetime of the fracture. However, for a fixed proppant pillar height, a large proppant pillar spacing results in the premature closure of the flow channels, while a small spacing narrows the existing channels. Such a model provides a rational means to design optimal distribution of the proppant pillars using deformation moduli of the host to control pillar deformation and flexural spans of the fracture wall.

Conventional water-based fracturing treatments may not work well for many shale gas reservoirs. This is due to the fact that shale gas formations are much more sensitive to water because of the significant capillary effects and the potentially high contents of swelling clay, each of which may result in the impairment of productivity. As an alternative to water-based fluids, gaseous stimulants not only avoid this potential impairment in productivity, but also conserve water as a resource and may sequester greenhouse gases underground. However, experimental observations have shown that different fracturing fluids yield variations in the induced fracture. During the hydraulic fracturing process, fracturing fluids will penetrate into the borehole wall, and the evolution of the fracture(s) then results from the coupled phenomena of fluid flow, solid deformation and damage. To represent this, coupled models of rock damage mechanics and fluid flow for both slightly compressible fluids and CO2 are presented. We investigate the fracturing processes driven by pressurization of three kinds of fluids: water, viscous oil and supercritical CO2. Simulation results indicate that SC-CO2-based fracturing indeed has a lower breakdown pressure, as observed in experiments, and may develop fractures with greater complexity than those developed with water-based and oil-based fracturing. We explore the relation between the breakdown pressure to both the dynamic viscosity and the interfacial tension of the fracturing fluids. Modeling demonstrates an increase in the breakdown pressure with an increase both in the dynamic viscosity and in the interfacial tension, consistent with experimental observations.

Restimulation of previously hydraulically-fractured wells can restore productivity to near original levels. Understanding the stress state resulting from the original hydraulic fracturing and subsequent depletion is vital for a successful refracuring treatment. The stress obliquity in the vicinity of the wellbore, due to production from a previously introduced hydraulic fracture, promotes a new concept – that of altered-stress refracuring which allows fractures to propagate into previously unstimulated or understimulated areas and therefore enhancing recovery. In this study, a coupled poromechanical model is used to define stress redistribution and to define optimal refrac timing as defined by maximizing the size of the stress reversal region. Key factors include the time dependency of the stress reorientation, the threshold stress ratio σ h max / σ h min and the influences of permeability anisotropy/heterogeneity, pressure drawdown and rock-fluid properties. The results show that stress reorientation develops immediately as the reservoir begins to produce. This stress reversal region extends to a maximum extent before retreating as the direction of the maximum principal stress gradually returns to the initial state. The optimal refrac timing and the size of the stress reversal region are positively correlated with pressure drawdown and Biot coefficient, negatively correlated with stress ratio σ h max / σ h min ratio and Poisson’s ratio and ambiguously correlated with permeability anisotropy. Permeability magnitude and porosity have no influence on the size of the resulting zone but are negatively and positively correlated to the timing, respectively. Permeability heterogeneity has no influence on the size nor the timing. Coupled fluid flow and damage-mechanics simulations follow fracture propagation under the effect of stress redistribution during refracturing treatments. These results define the evolving path of secondary refracture as it extends perpendicular to the initial hydrofracture and ultimately turns parallel to the hydrofracture as it extends beyond the stress-reversal region. This discrete model confirms the broader findings of the continuum model.

Water-based hydraulic fracturing for the exploitation of shale gas reservoirs may be limited by two main factors: (1) water pollution and chemical pollution after the injection process and (2) permeability decrease due to clay mineral swelling upon contact with the injection water. Besides, shale rock nearly always contains fractures and fissures due to geological processes such as deposition and folding. Based on the above, a damage-based coupled model of rock deformation and gas flow is used to simulate the fracturing process in jointed shale wells with CO2 fracturing. We validate our model by comparing the simulation results with theoretical solutions. The research results show that the continuous main fractures are formed along the direction of the maximum principal stress, whilst hydraulic fractures tend to propagate along the preexisting joints due to the lower strength of the joints. The main failure type is tensile damage destruction among these specimens. The preexisting joints can aggravate the damage of the numerical specimens; the seepage areas of the layered jointed sample, vertical jointed sample, and orthogonal jointed sample are increased by 32.5%, 29.16%, and 35.05%, respectively, at time t=39 s compared with the intact sample. The preexisting horizontal joints or vertical joints promote the propagation of hydraulic fractures in the horizontal direction or vertical direction but restrain the expansion of hydraulic fractures in the vertical or horizontal direction.

Acoustic emission (AE) in coal is anisotropic. In this paper, we investigate the microstructure-related scale effect on the anisotropic AE feature in coal at unconfined loading process. A series of coal specimens were processed with diameters of 25 mm, 38 mm, 50 mm, and 75 mm (height to diameter ratio of 2) and anisotropic angles of 0°, 15°, 30°, 45°, 60°, and 90°. The cumulative AE counts and energy dissipation increase with the specimen size, while the energy dissipation per AE count behaves in the opposite way. This may result from the increasing amount of both preexisting discontinuities and cracks (volume/number) needed for specimen failure and the lower energy dissipation AE counts generated by them. The effect of microstructures on the anisotropies of AE weakens with the increasing specimen size. The TRFD and its anisotropy reduce as the specimen size increases, and the reduction of fractal dimension is most pronounced at the anisotropic angle of 45°. The correlation between TRFD and cumulative AE energy in the specimens with different sizes are separately consistent with the negative exponential equation proposed by Xie and Pariseau. With the specimen size gain, the reduction of the TRFD weakens with the increasing amount of cumulative absolute AE energy.