True Triaxial Stress Conditions Research Articles

Crack mode-changing stress level in porous rocks under polyaxial stress conditions

As the global push towards clean energy intensifies, the demand for critical minerals has driven deep excavation in hard rock formations, posing significant challenges related to rockburst and spalling. Spalling refers to explosion-like rock fractures under high geo-stresses. Despite several successful studies and practical models, the mechanisms governing spalling propagation under polyaxial stress states remain inadequately understood, particularly in weaker and high-porosity rocks. This study introduces a novel Crack Mode-Changing Stress (CMCS) concept, which defines the minimum principal stress required to change the crack mode from shear to tensile failures when rock spalls. The concept was validated using cubed sandstone samples containing centric circular holes subjected to a range of loading conditions including uniaxial, biaxial, generalized triaxial compression, generalized triaxial tensile, and true triaxial loading stress states. Our results highlight the significance of the out-of-plane minor principal stress on the crack initiation threshold and the CMCS, emphasizing the need for careful consideration when designing openings in highly stressed environments.

Hydraulic fracture morphology and conductivity of continental shale under the true-triaxial stress conditions

Continental shale oil formations generally exhibit more complex lithology and stronger heterogeneity than marine shale. The coexistence of dense laminas, lithologic interfaces (LIs), and mineral-filled natural fractures (NFs) in such formations can cause complex mechanisms of hydraulic fracture (HF) growth, proppant placement, and conductivity evolution. To obtain an intuitive understanding of this problem, a series of comprehensive laboratory sand fracturing experiments and fracturing conductivity tests were carried out innovatively on downhole shale cores using an improved small-size true triaxial fracturing simulation system combined with multiple examination methods in this work. HF morphology and proppant distribution were characterized through the high-precision CT scanning technique. Moreover, HF conductivity was tested on the cylindrical cores drilled from the fractured specimens. Experimental results show that high breakdown pressure and volatile wellbore pressure during the sand-adding stage were likely presented in the relatively rigid formations. HF growth path is likely to be deflected and bifurcated by the NFs laterally and by the oblique laminas vertically. “╪”-shaped HF also tends to be created due to the interaction of HF with dense horizontal laminas. The local heterogeneity in the continental shale formation can cause significant complexity and uncertainty in HF. The dominant HF nearby the wellbore contains most of the proppant, and the activated laminas, NFs, or/and branches are short of proppant. The volume and area of the proppant-filled HF can only account for less than 20% of the total HF volume and less than 65% of the total HF area, respectively. The distribution of relatively small-size proppant is more uniform and broader than that of large ones. There is a positive correlation between fracture conductivity and the proppant concentration. The conductivity of no proppant-filled fractures (including the HF, activated lamina, and NF) is low and unstable, and can almost be neglected under closure stress beyond approximately 20–25 MPa. The findings in this work are expected to provide practitioners with a bigger map of the performance and effectiveness of the hydraulic fracture they created.

Experimental investigation on the propagation of hydraulic fractures in massive hydrate-bearing sediments

Hydraulic fracturing is regarded as one of the potential technical means to realize efficient development of natural gas hydrate. Massive-distributed hydrates are widespread around the world, although the solid fluidization method has been proposed to develop this kind of reservoir, the process of this method is complex, and there are still a lot of key problems need to be solved. Meanwhile, when the hydrate decomposed during production, how to maintain formation stability is still an unsolved key problem. Therefore, we consider using hydraulic fracturing technology to exploit this kind of reservoir. On the one hand, the fractures formed by high viscosity fracturing fluid can improve the reservoir permeability. On the other hand, the proppant added during fracturing can play a good supporting role to the formation. In this work, a series of large-size (300 × 300 × 300 mm) hydraulic fracturing physical simulation experiments were conducted under true triaxial stress states to investigate hydraulic fracture propagation law in massive-distributed hydrate-bearing reservoir. The effects of massive hydrate size, approaching angle and fracturing fluid displacement on the fracture propagation were studied. The experimental results indicated that massive hydrate exerts an important influence on hydraulic fracture propagation. Two main massive hydrate-hydraulic fracture interaction modes were observed in our experiments: (a) When the massive hydrate size is small, the hydraulic fractures mainly propagated along the interface between the sediment matrix and the massive hydrate. (b) The hydraulic fractures penetrated the massive hydrate, which usually occurs when hydraulic fracture encountered large-size massive hydrate, and the penetrated position moves from both sides to the central position of the massive hydrate. The approaching angle has a significant effect on the massive hydrate-hydraulic fracture interaction law. Under the condition of high approaching angle, hydraulic fractures easily penetrated the massive hydrate. The influence of fracturing fluid displacement on massive hydrate-hydraulic fracture interaction is closely related to massive hydrate size. When hydraulic fractures encountered the small-size massive hydrate, increasing the displacement has a limited effect on massive hydrate-hydraulic fracture interaction, and the hydraulic fractures still mainly propagated along the interface. When large-size massive hydrates are distributed in the sample, increasing the displacement has a significant effect on the massive hydrate-hydraulic fracture interaction, and hydraulic fractures tend to branch, the complex fracture geometry would be formed. In this study, a new large-size massive hydrate sample preparation method was proposed, and the effects of various factors on the hydraulic fracture propagation law were investigated experimentally, which can provide guidance for the fracturing design of massive hydrate-bearing reservoir.

Ductile–brittle quantitative evaluation of rock based on post-peak properties under true triaxial stress

To quantitatively evaluate the influence of high true three-dimensional stresses on the ductile–brittle behaviours of rock in deep underground engineering, a series of true triaxial compression tests with different stress levels were carried out on marble and four kinds of granite. The influences of true triaxial stress states (σ2, σ3) on the post-peak characteristics were analysed, and a new normalized ductile–brittle evaluation index was proposed based on post-peak energy conversion characteristics of rock under true triaxial stresses. The ductile–brittle behaviours of rock were divided into four qualitative levels, namely, ductile-brittleness, transitional, brittleness and super-brittleness, and the influences of true triaxial stress states on the ductile–brittle behaviours of rock were quantitatively investigated. The research shows that as σ2 increases or σ3 decreases (that is, the differential stress between σ2 and σ3 increases), the brittleness of rock increases, and its increase rate gradually decreases and tends to be stable, transforming from ductile-brittleness to transitional, brittleness and super-brittleness and resulting in super-brittleness being easily induced by low-σ3 and high-σ2 conditions. When the differential stress between σ2 and σ3 is small, the intrinsic characteristics of rock itself have an obvious influence on ductile–brittle behaviours. When the differential stress between σ2 and σ3 is large, all kinds of rocks can exhibit super-brittle behaviour. The change of stress controls the evolution of rock ductile–brittle behaviours, and high-stress controls rock brittleness. The rock brittleness under true triaxial stress is significantly higher than that under conventional triaxial stress at the same σ3. σ2 induces an increase in rock brittleness and causes the decay rate of brittleness to decrease with increasing σ3, and σ2 increases the upper limit of σ3 for brittle failure of rock. The enhancement effect of σ2 on rock brittleness must be considered when evaluating the brittle failure of deep surrounding rock under high-stress conditions; otherwise, the risk of brittle failure may be underestimated.

Influence of intermediate principal stress ratio on strength and deformation characteristics of frozen sandy soil under different moisture contents

Frozen ground often contain non-uniform moisture content and are under true triaxial stress state and their practical engineering application are still explored. The present study is carried out to investigate the strength and deformation characteristics of frozen soil with different moisture contents under true triaxial stress state conditions. A series of true triaxial tests were conducted on frozen soil specimens having constant minimum principal stress (σ3) and constant intermediate principal stress ratio (b). The experimental test results showed that the stress-strain curves represent the strain-hardening characteristics under different test conditions. The intermediate principal stress ratio (b) has a dual effect of strengthening and weakening on the strength of frozen sandy soil. When 0 ≤ b ≤ 0.5, the strengthening effect was found to be dominant in the frozen soil specimen, whereas, the weakening effect was dominant when 0.5 < b ≤ 1. The strength of frozen soil under true triaxial stress state is 8.18% to 36.33% higher under different water content conditions, compared to that under generalized triaxial compression stress state. The difference in deformation between the direction of the intermediate principal stress and the minimum principal stress increased with the increment in the intermediate principal stress ratio value. The volumetric strain in the soil sample initially exhibited the characteristics of shear contraction and then shear dilation.

Effects of intermediate stress on deep rock strainbursts under true triaxial stresses

The effect of intermediate stress (in situ tunnel axial) on a strainburst is studied with a three-dimensional (3D) bonded block distinct element method (DEM). A series of simulations of strainbursts under true triaxial in situ stress conditions (i.e. high tangential stress, moderate intermediate stress and low radial stress) of near-boundary rock masses are performed. Compared with the experimental results, the DEM model is able to capture the stress-strain response, failure pattern and energy balance of strainbursts. The fracturing processes of strainbursts are also numerically reproduced. Numerical results show that, as the intermediate stress increases: (1) The peak strain of strainbursts increases, the yield stress increases, the rock strength increases linearly, and the ratio of yield stress to rock strength decreases, indicating that the precursory information on strainbursts is enhanced; (2) Tensile and shear cracks increase significantly, and slabbing and bending of rock plates are more pronounced; and (3) The stored elastic strain energy and dissipated energy increase linearly, whereas the kinetic energy of the ejected rock fragments increases approximately exponentially, implying an increase in strainburst intensity. By comparing the experimental and numerical results, the effect of intermediate stress on the rock strength of strainbursts is discussed in order to address three key issues. Then, the Mogi criterion is applied to construct new strength criteria for strainbursts by converting the one-face free true triaxial stress state of a strainburst to its equivalent true triaxial stress state. In summary, the effect of intermediate stress on strainbursts is a double-edged sword that can enhance the rock strength and the precursory information of a strainburst, but also increase its intensity. ©2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Anisotropic Poroelastic Modelling of Depletion-Induced Pore Pressure Changes in Valhall Overburden

Stress and pore pressure changes due to depletion of or injection into a reservoir are key elements in stability analysis of overburden shales. However, the undrained pore pressure response in shales is often neglected but needs to be considered because of their low permeability. Due to the anisotropic nature of shales, the orientation of both rock and stresses should be considered. To account for misalignment of the medium and the stress tensor, we used anisotropic poroelasticity theory to derive an angle-dependent expression for the pore pressure changes in transversely isotropic media under true-triaxial stress conditions. We experimentally estimated poroelastic pore pressure parameters of a shale from the Lista formation at the Valhall field. We combined the experimental results with finite element modelling to estimate the pore pressure development in the Valhall overburden over a period of nearly 40 years. The results indicate non-negligible pore pressure changes several hundred meters above the reservoir, as well as significant differences between pore pressure and effective stress estimates obtained using isotropic and anisotropic pore pressure parameters. We formulate a simple model approximating the undrained pore pressure response in low permeable overburden. Our results suggest that in the proximity of the reservoir the amplitude of the undrained pore pressure changes may be comparable to effective stresses. Combined with the findings of joint analysis of locations of casing deformation and total and effective stresses, the results suggest that pore pressure modelling may become an important element of casing collapse and caprock failure risk analysis and mitigation.

Validation of the Crack Mode-Changing Stress in Circular Tunnels Under Generalized Triaxial Tensile Stress States

In the past century, mining depths have increased profoundly from a few hundred meters to several kilometres following improvements in drilling techniques and instrumentation methods. In highly-stressed tunnels, the predominant failure mechanism of underground rock is controlled by stress-induced fractures parallel to the excavation boundaries in terms of spalling failures or, in some severe cases, a violent slab ejection that forms a V-shaped notch around the excavation walls. Such failures can seriously affect production and shut down the operation temporarily or even permanently. To better characterize, predict, and prevent these catastrophic failures, many laboratory tests and scaled model tunnels have been conducted under uniaxial and biaxial loading conditions, with limited studies also available under true triaxial stress states. This paper extends the previous studies on the impact of true triaxial loading conditions on the spalling failure in high porosity sandstone and investigates further the validation of a new Crack Mode-Changing Stress (CMCS) parameter, defined as the minimum principal stress required to change rock fracturing from splitting to a sliding failure mode. The results revealed that the minor principal stress can significantly affect the propagation of the stress-induced fractures of spalling failure along the tunnel sidewall.

Fracture Evolution Analysis of Rock Bridges in Hard Rock with Nonparallel Joints in True Triaxial Stress States

Fracture Evolution Analysis of Rock Bridges in Hard Rock with Nonparallel Joints in True Triaxial Stress States

Experimental study on stress and permeability response with gas depletion in coal seams

The gas extraction environment in coal seam exhibits uniaxial strain condition with constant overlying strata stress and horizontal strain. Simulating this environment in laboratory often ignores true triaxial stress state, so the difference in horizontal stresses reduction and the accompanying permeability evolution remain ambiguous. Therefore, this study conducted the true triaxial stress and permeability response tests simulating gas extraction environment under shallow and deep in-situ stress conditions. To quantify gas adsorption effect, the adsorbed (CO2) and non-adsorbed (He) gases were also used. The results indicated that the intermediate and minimum principal stresses, i.e., σ2 and σ3, exhibited a linear decreasing trend during gas depletion, but showed more decreases in stress when the intermediate and minimum principal strains, i.e., ε2 and ε3, recover under high gas pressure depletion. High true triaxial stress enhanced the compressibility of pores and fractures in coal, resulting in low horizontal deformation and stress reduction gradient during gas depletion. Similarly, the reduction gradient of σ2, mσ2, was less than that of σ3. This suggested that the difference between horizontal stresses also increased during coalbed methane (CBM) extraction, which exacerbated the risk of coal body damage. For different gas depletion, the stress reduction gradient exhibited mHe < 1 and mCO2 > 1, which was related to the relative affinity of different gas species for the adsorption medium. A significant matrix shrinkage effect resulted in a more pronounced stress reduction. For permeability, the permeability increased exponentially during CO2 depletion, while the permeability of helium exhibited a decreasing followed by an increase with decreasing gas pressure. This is related to the competing mechanism and synergistic effect of the adsorptive gas desorption, effective stress effect, and slippage effect. We quantified the contribution and mechanism of the three to the permeability separately. The permeability anisotropy ratio (Ar) decreased exponentially during gas depletion.

A modified rigid-body-spring method for modeling damage and failure of brittle rocks subjected to triaxial compression

A three-dimensional modified rigid-body-spring method (3D mRBSM) is presented to simulate the progressive damage and failure process of rocks under triaxial compressive conditions. Different from the original RBSM model, the mRBSM employs spring-set groups distributed on interfaces between blocks to approximately describe the progressive failure process of micro-cracks without increasing the size of governing equations. Firstly, the basic equations of 3D mRBSM are derived. A new randomly distributed Voronoi-based mesh technique is proposed to reproduce homogeneous and isotropic rock materials. Then, relationships between macro and micro elastic parameters are established, and a calibration procedure for parameters of failure criterion is adopted based on the trial-and-error procedure. Lastly, the new model is applied to simulate pseudo triaxial and true triaxial compression tests on brittle rocks. Results show that the proposed model correctly captures common mechanical properties of brittle rocks, such as nonlinear stress–strain relationship, brittle-ductile transition, confining pressure dependence of failure mode and medium principal stress effect. The above research demonstrates that the mRBSM is successfully upgraded to three-dimensional version. The new method is a promising tool for simulation of deformation and failure process of rocks under true triaxial stress conditions.

Understanding hydraulic fracture mechanisms: From the laboratory to numerical modelling

The development of fracture networks associated with hydraulic fracturing operations are extremely complex multiphysics processes and there is still no accepted methodology for mapping or realistic recreating such fracture networks. This is an issue especially for modeling purposes, as, ideally, an accurate numerical representation, and subsequent numerical model, should be able to honor the trajectory, type, connectivity, and geometric properties of the complex fracture network generated. This research proposes a novel framework capable of conducting fluid flow numerical simulations based on mapped fracture networks induced during hydraulic fracturing laboratory experiments where a shale sample, under true triaxial reservoir stress conditions, is subjected to fluid injection to mimic a single stage open-hole in-situ hydraulic fracture operation. The resulting post-test fracture network of the shale sample is filled with fluorescent dyed epoxy and subsequently imaged. The images are segmented, and individual fractures are classified based on their geometrical characteristics, as parted bedding planes, opened natural fractures, and newly generated hydraulic fractures. The digital fracture network is numerically represented for fluid flow simulation using a dual-porosity model within the finite volume method. In the numerical reconstruction, fractures are implicitly represented in a set of cells with virtual fracture aperture. The properties of each grid cell are assigned based on fracture classification, and flow between grid cells is explicitly assigned based on the connectivity of the grid cells. Findings show faster fluid drainage parallel to bedding planes (horizontal) than in the vertical direction, indicating strong fluid flow anisotropy. Cited as: Abdelaziz, A., Ha, J., Li, M., Magsipoc, E., Sun, L., Grasselli, G. Understanding hydraulic fracture mechanisms: From the laboratory to numerical modelling. Advances in Geo-Energy Research, 2023, 7(1): 66-68. https://doi.org/10.46690/ager.2023.01.07

A new fractional-order model for time-dependent damage of rock under true triaxial stresses

To reasonably describe the time-dependent characteristics of rock under true triaxial stresses and analyze the long-term stability of deep underground engineering, based on the understanding of time-dependent mechanical properties of rock under true triaxial stresses, a new fractional-order damage element and the method in which the crack initiation stress is taken as the starting point of creep and the crack damage stress as the starting point of creep accelerating stage were established. Then, combined with the Mogi-Coulomb strength criterion, a fractional-order creep damage model of rock under true triaxial stresses was proposed. The proposed model was further verified based on uniaxial, conventional triaxial and true triaxial creep test results. The theoretical curves of the model are highly consistent with the test curves, indicating that the proposed model has wide applicability and rationality. Meanwhile the sensitivity of true triaxial stress states and model parameters to the creep characteristics was further investigated. Finally, based on the proposed creep model, the time-dependent characteristics of rock under untested true triaxial stress levels were predicted. The research provides a theoretical basis for the prediction of time-dependent disasters and the long-term stability analysis of surrounding rock in deep engineering.

Experimental study on mechanics and seepage of coal under different bedding angle and true triaxial stress state

Experimental study on mechanics and seepage of coal under different bedding angle and true triaxial stress state

Experimental study on deformation and fracture characteristics of coal under different true triaxial hydraulic fracture schemes

Hydraulic fracturing techniques are often applied to form permeability enhancement zones near boreholes and/or wellbores in tight low-permeability reservoirs to improve their extraction efficiency. As conventional hydraulic fracturing techniques often generate high breakdown pressure and induced seismic potential, novel alternative production enhancement techniques (such as pulse hydraulic pressurization) have been proposed. However, their applicability requires further verification. Therefore, this study conducted hydraulic fracturing tests of coal under three test schemes: conventional hydraulic fracturing (CHF), stepwise pressurization hydraulic fracturing (SPHF), and stepwise pulse pressurization hydraulic fracturing (SPPHF), considering the true triaxial stress state of an actual coal seam. The results showed that the breakdown pressure of coal decreased with an increase in the horizontal stress difference (σ2-σ3). Moreover, the pulse pressurization produced more intergranular fractures and caused a large number of particles to be conducted as a stress concentrator at the fracture tip spalling, which promoted the unstable propagation of fractures, which decreased the breakdown pressure of coal. The abnormally high breakdown pressure in the SPHF experiments is likely due to the obstruction of high σ2 to the fracture propagation rate and fluid injection, which intensifies the fluid hysteresis effect and the stable fracture development and expansion during the pressure-maintaining stage, thus increasing the breakdown pressure. To describe the relationship between the variation in the breakdown pressure and fracture evolution characteristics, we introduced the equivalent characteristic length l and established a breakdown pressure prediction model based on the tensile stress criterion, which shows effective prediction of the breakdown pressure in different test schemes. Anisotropic principal strain appeared under different injection schemes. During the CHF and SPHF experiments, fluid injection deformed the σ1 direction by compression and the σ3 direction by expansion. In the σ2 direction, the deformation transitioned from expansion at a low stress level to compression at a high stress level. The deformation in the σ2 direction was always compressive in the SPPHF experiments. Continuous and pulse pressurizations can promote the deformation and fracture development. For the fracture morphology, the coal in the CHF experiments was dominated by a single tensile fracture, and macroscopic shear fractures were formed in the SPHF and SPPHF experiments owing to the continuous stimulation of fluid pressure to the bonding of particles and the weak surface structure, such as bedding and cleats during the pressure maintenance and pulse, and the fragmentation effect was significant and accompanied by obvious particle spalling.

Multiaxial Damage Ratio Strength Criteria for Fiber-Reinforced Concrete

Based on the damage ratio strength theory, a dimensionless damage ratio strength criterion for fiber-reinforced concrete (FRC) under true triaxial stress states was established under the assumption of small strains. Based on the experimental data of steel fiber–reinforced concrete (SFRC), polypropylene fiber–reinforced concrete (PFRC), hybrid fiber–reinforced concrete (HFRC), and steel fiber–reinforced high-performance lightweight concrete (SFRHLC), parameters for the damage ratio criterion were recommended. The damage ratio values were verified by SFRC experimental results under uniaxial, biaxial, and triaxial loading conditions, and the damage ratio values of SFRC under uniaxial tension, uniaxial compression, and biaxial equal compression stress conditions were compared with those of plain concrete. The true triaxial damage ratio strength criterion can be reduced to the conventional triaxial criterion and biaxial criterion, and the corresponding simplified strength criteria were proposed. The proposed dimensionless six-parameter criterion agrees well with the experimental results of the aforementioned materials for true triaxial, conventional triaxial, and biaxial loading conditions. Compared with the strength criteria in other studies, the proposed criterion can accurately represent the strength characteristics of FRC.

Study on Failure Difference of Hard Rock Based on a Comparison Between the Conventional Triaxial Test and True Triaxial Test

The study on the failure difference of deep hard rock based on the comparison between conventional and true triaxial tests can help us better understand the fracture processes and failure characteristics of the deep rock mass. Therefore, this article carries out a comparative analysis of the failure of hard rock under conventional and true triaxial stress states. Within the scope of this study, it is found that the brittle–ductile transformation properties can be intuitively reflected in the rock stress–strain curve and failure mode. The brittle–ductile transition point of rock can also be determined by the difference between peak and residual strengths. The rock failure strength increases with the increase of σ2, the peak strain decreases with the increase of σ2, the stress drop of the post-peak curve becomes more obvious with the increase of σ2, and the rock tends toward Class II brittle failure after the peak with the increase of σ2. When σ3 is relatively high, the rock fracture angle increases with the increase of σ2 with obvious regularity. Compared with conventional triaxial stress conditions, the differential stress-induced anisotropy failure is the biggest difference in rock fracture characteristics between true and conventional triaxial stress states. This study can supply useful references to the study of failure properties of hard rock under complex stress states.

Strength characteristics of brittle rocks under multi-stage intermediate principal stress loading

A series of single-stage true triaxial compression (TTC) tests and multi-stage intermediate principal stress (σ2) loading tests were carried out on three types of brittle rock specimens in this study to examine the influence of σ2 and the validity of obtaining strength parameters by using a multi-stage loading method under true triaxial stress conditions. There exists a critical σ2 at which the rock strength attains its ultimate value under both loading conditions. Under the same σ3 level, the critical σ2 is much smaller under the multi-stage σ2 loading compared with under the single-stage TTC. The test results also show that the strength determined under multi-stage σ2 loading is much smaller than that determined under single-stage TTC. The strength difference can attain 39%. A lower strength is measured under multi-stage σ2 loading because the local fracture plane induced by true triaxial stress is parallel to the σ2, and the strength of the rock specimen containing this type of local fracture plane is not affected by σ2. On the contrary, rock damage accumulates during multiple loading and unloading cycles. The current testing results indicate that the multi-stage loading test is not suitable for determining the strength envelope of brittle rock under true triaxial conditions.

Experimental study on deformation and permeability enhancement of oil sand reservoir by hydraulic fracturing technique under true triaxial stress

AbstractHydraulic fracturing technology is often applied to form a permeable zone for geothermal resources near the borehole in tight reservoirs to improve the permeability and extraction efficiency. Steam or hot water is often injected to dissolve the heavy oil to increase its fluidity during the extraction. As the numerical simulation or two‐dimensional physical experiments have great limitations to simulate hydraulic fracturing of oil sand reservoirs, this study conducted a large‐scale three‐dimensional physical simulation experimental study of hydraulic fracturing with high temperature of oil sand reservoir under true triaxial stress state and monitored the water pressure change at various points inside the box during the hydraulic fracturing by laying pressure sensors. The experimental results showed that the hydraulic breakdown pressure of oil sands increases with the increase in σ2, which is related to the increase in σ2 limiting the fracture growth and the decrease in effective stress during fluid injection. To better describe the breakdown pressure variation, we developed a new oil sand breakdown pressure prediction model considering the true triaxial stress condition, which showed a good prediction effect. Due to the formation of fluid hysteresis zone during the fracture expansion, the fluid pressure recorded by the internal pressure sensor lagged behind the injection pressure. Hydraulic fracturing produced shear fractures inside the oil sands under low σ2 conditions and tensile fractures under high σ2 conditions, and the permeability was significantly increased after hydraulic fracturing, in which the shear fractures formed under low σ2 showed a better permeability enhancement effect than the tensile fractures formed under high σ2. The research and analysis in this study can provide reasonable suggestions and feasibility analysis for the design and construction of heavy oil extraction.

Stress and pressure dependent permeability of shale rock: Discrete element method (DEM) simulation on digital core

Shale permeability will change with the variation of reservoir pressure and formation stress, especially when natural fractures occur failure due to pressure and stress perturbation during hydraulic fracturing, the permeability will change dramatically. So far, however, there is no comprehensive theoretical method could estimate the rock permeability change with natural fractures failure under true-triaxial stress condition. This paper aims to propose a numerical method to investigate the influence of pore pressure, triaxial stress, and natural fractures failure on the shale rock permeability. Firstly, this paper built a digital shale core cylinder by combining the discrete element method (DEM) and fluid-solid coupling model. Then, all the micro parameters of the digital rock were delicately calibrated according to the quasi-triaxial compression tests data of real rock core collected from Bakken shale formation, making the macro-mechanical property and seepage characteristic of digital rock are consistent with real shale rock. Then, based on the calibrated micro-parameters, we constructed a digital core cube to simulate the permeability test under true triaxial conditions. Finally, some natural fractures, as the weak planes, were preset in digital core, and the shale rock permeability change was analyzed with natural fractures failure. It shows that the intact shale permeability will decrease with triaxial stress increasing or pore pressure decreasing. Besides, the permeability of shale will be affected by the natural fractures’ property and failure states. In general, as the triaxial stress increases, the natural fractures in shale rock cube will occur failure gradually, meanwhile, its permeability will rise remarkably in the beginning. However, after most of the natural fractures have occurred failure under high-stress or high-pressure, shale permeability will turn to decrease as the stress continues to increase. This paper explores the inner mechanism and exterior behavior of shale permeability dependence on triaxial stress, pore pressure, and natural fractures failure. • A digital core modeling method is proposed based on the discrete element method. • The digital shale core is constructed and it is identical to a real shale core from Bakken formation. • A series of permeability tests simulation are conducted on the digital shale core cube under true-triaxial stress conditions. • The mechanism of shale permeability dependence on stress, pressure, and natural fractures failure is explored. • This research is beneficial to the fracturing design in shale reservoirs.