Fracture network characterization is an important yet intractable task in many subsurface applications related to energy recovery, storage, and waste disposal. A major challenge is the lack of advanced methods for parameterizing complex fracture networks within low-dimensional parameter spaces to address the ill-posedness caused by the inherent complexity of subsurface fractures and pervasive data scarcity. In this work, we propose a deep-learning-assisted, projection-based approach to generate high-fidelity three-dimensional (3D) discrete fracture networks (DFNs) from low-dimensional latent spaces. Since directly generating 3D DFNs is computationally prohibitive, we decompose the task into two more tractable ones: generating two-dimensional (2D) DFNs and establishing the projection relationship between 2D and 3D DFNs. We treat a 2D DFN as the projection of its 3D counterpart on a 2D plane, introducing two parameters, fracture dip angle and projection distance, to describe the projection relationship. We first develop three generative models to generate 2D DFNs, dip angle maps, and projection distance maps from low-dimensional latent spaces through Wasserstein generative adversarial networks with gradient penalty (WGAN-GP), and then construct 3D DFNs via reverse projection of these three 2D components. We demonstrate that the proposed approach faithfully generates 50-fracture 3D DFNs (300 parameters via conventional methods) from a 40-dimensional latent space, and 100-fracture 3D DFNs (600 conventional parameters) from a 72-dimensional space. Fracture connectivity and fluid flow characteristics in the generated 3D DFNs are also comprehensively analyzed to illustrate the approach’s effectiveness and robustness in generating high-fidelity 3D DFNs while maintaining substantial diversity to facilitate subsequent DFN inversion.

Cold fluid injection in various subsurface applications may induce thermal fracturing, which is a coupled process of fracture propagation, heat conduction and convection, and fluid flow in the fractures and reservoir. While most existing studies employ a thermoelastic model, their accuracy may be compromised by thermoporoelastic effects. This study aims to systematically investigate the thermoporoelastic effects in thermal fracturing using numerical models of varying complexity. We first developed a fully coupled model incorporating all relevant physical processes including fracture propagation and arrest, heat and fluid transport in fractures and reservoir. A novel dimensionless framework with five key parameters is introduced to elucidate the thermo-hydromechanical coupling. Additionally, three partially coupled models are developed to isolate the effects of diffusion- and deformation-induced back stress, pore water contraction, and heat convection. Extensive numerical simulations indicate that (1) diffusion-induced back stress minimally impedes the fracture propagation in case of nonnegligible permeability and pressure differential, (2) deformation-induced back stress and pore water contraction primarily affect fracture growth in low-permeability rock, reducing and increasing fracture length by 3.81 %- 18.61 % and 15.51 %-49.99 %, respectively, under undrained condition, (3) heat convection is the dominant thermoporoelastic effect under high permeability and pressure differential, significantly promoting fracture propagation, and (4) thermoporoelastic effects have negligible influence on thermal fracturing for permeability between 10-18 m2 and 10-15 m2.

The Kozeny-Carman (K-C) equation and its variants have been widely used for permeability prediction in geotechnical engineering, but their prediction accuracy is often compromised by the assumption of circular pore shape. To enhance the accuracy of the K-C equation and clarify the influences of structural parameters on the porous media permeability, we derive a novel fractal analytical model for permeability and K-C constant, which incorporates irregular pore shape and contains no empirical constants. The fractal analytical model for permeability and K-C constant is related to parameters including the average pore shape factor, the pore size distribution fractal dimension, the tortuosity fractal dimension, the maximum pore diameter, and porosity. Based on the publicly available digital core data, the predictions of the new model were compared with those of other permeability equations, validating the effectiveness and applicability of the proposed model. We analysed the influence of the average pore shape factor on dimensionless permeability and K-C constant. An increase in the average pore shape factor leads to a nonlinear decrease in K-C constant and a nonlinear increase in dimensionless permeability. The influence of pore shape irregularity on permeability aligns with physical principles. Sensitivity analysis using the Sobol method was conducted on the parameters affecting permeability and K-C constant. The results indicate that accurately determining K-C constant by obtaining precise values for the pore size distribution fractal dimension, the average pore shape factor, and the tortuosity fractal dimension is key to reducing permeability prediction errors. In summary, the novel fractal analytical model established in this study can enhance the prediction accuracy of permeability for porous media with non-circular pores, further reveal the fluid transport mechanisms in such media, and provide a more solid theoretical foundation for geotechnical engineering and related fields.

After over 50 years of exploration and practice, enhanced geothermal systems (EGS) have become a key technology to harness the abundant geothermal energy in the shallow crust of the Earth. The continuous discovery of promising high-temperature EGS sites and technological breakthroughs in drilling and fracturing have led to the successful implementation of several EGS projects, demonstrating the strong commercialization prospects of EGS over the next decade. Despite these progresses, a major operational challenge still remains, i.e., fracture flow channeling, which has been identified a primary risk in many EGS projects for premature thermal breakthrough and reduced thermal longevity. In this review, we first describe fracture flow channeling within and among fractures, and then summarize various physical and chemical processes that dynamically modify fracture aperture and flow patterns. In particular, we comprehensively discuss processes that interact with fracture flow channeling in a feedback loop manner, either exacerbating or mitigating flow channeling. We also develop a thermo-hydro-mechanical-chemical (THMC) coupled model to quantitatively analyze how these effects jointly modify fracture aperture distribution and affect long-term thermal performance. Afterward, we introduce current techniques for fracture flow tuning in EGSs, including proppants/gels/polymers to plug preferential flow channels, working fluid with more temperature-sensitive viscosity, downhole flow control and injection optimization. Finally, we offer an outlook on future research directions and highlight the importance of subsurface fracture characterization techniques and advanced THMC coupled models. We also propose a potential physical-chemical-biological synergistic technique for fracture flow tuning that might be worth investigating and applying in the future.

The increase in CO2 injectivity and shifting of CO2-absorbing layers in multilayered geological CO2 sequestration (GCS) reservoirs in Ordos, China indicate significant permeability variations in certain layers. To capture these system changes, a numerical model incorporating all 21 aquifers and internal aquitards was developed. The monitored pressure was well matched through multiphase and thermal-hydraulic-mechanical (THM) coupling numerical simulations by introducing permeability variations. The results revealed that the permeability in the second layer increased on approximately day 13 due to the abrupt pressure buildup and temperature decrease. Even such a low rate of CO2 (2.8 kg/s) injected into the low permeability system initiated some fractures and the permeability in the second layer around the wellbore increased by 722 times. The second critical system change occurred on approximately day 386. As demonstrated in the numerical simulation, the substantial injection of cold CO2 induced strong thermal stress, leading to rock contraction and the initiation of several cracks. The permeability of the first layer around the wellbore unexpectedly increased by 4 orders of magnitude. Since no additional pressure could drive the CO2 into the remaining 17 layers, the total storage capability of the multilayered system was reduced. A whole picture of the system variation is fully presented and the underlying mechanisms are analyzed. It is believed that the phenomenon of thermal-hydraulic fracturing observed in this field and the simulation procedures will benefit other fluid injection and production works in various geotechnical settings.

High-speed projectile impact is a promising approach for assisting hard-rock fragmentation; however, the coupled effects of projectile geometry and impact velocity on crater formation and penetration behavior under lateral confinement remain insufficiently understood. In this study, seven granite penetration tests were conducted using a biomass-fueled combustion-driven gas gun system coupled with a biaxial lateral confinement device, including one unconfined case and six cases under 2 MPa lateral confinement. Equal-mass YG20 cemented carbide projectiles with cone angles of 60°, 90°, and 120° were tested at nominal velocities of approximately 220 and 400 m/s. The results show that the two velocity levels produced different crater morphologies, and cone angle regulated the relative development of axial penetration and transverse crater expansion. At the lower velocity level, surface crushing dominated, with penetration depth decreasing from 13.5 to 10.5 mm and equivalent crater diameter decreasing from 74.5 to 44.4 mm as cone angle increased. At the higher velocity level, funnel-shaped craters were formed, with penetration depth decreasing from 45.0 to 30.0 mm, while equivalent crater diameter exhibited a non-monotonic variation. Dynamic strain measurements revealed coupled radial compression and circumferential tensile responses, with more complex transient fluctuations observed for the 120° projectile at high velocity. Based on the Young/Sandia framework, a condition-specific penetration-depth correlation was established. The full seven-test calibration gave an in-sample RMSE of 1.87 mm and R2 = 0.977, while leave-one-condition-out evaluation of the five conditions not used to define the paired-test boundary-state reduction ratio K2 yielded an RMSE of 3.40 mm and R2 = 0.937. The held-out analysis is interpreted as an internal stability check rather than independent external validation. These findings provide insights into the coupled influence of projectile cone angle and impact velocity on granite crater formation under controlled lateral confinement.

A three-dimensional (3D) mathematical model was established, coupling the large eddy simulation (LES) turbulence model, heat transfer model, solidification model, discrete phase model (DPM), and dynamic mesh model. Based on the actual continuous casting (CC) end process, the numerical simulation was divided into 4 stages. A method for calculating the motion velocity of the dynamic wall and the solidified shell was proposed to achieve the coupled simulation of transient flow, heat transfer, and solidification. In stage 1, molten steel speed and jet depth decreased as casting speed reduced, while the shell thickness steadily increased. In stage 2, after the submerged entry nozzle (SEN) removal, the molten steel speed and temperature dropped rapidly, and the circulation flow dissipated. In stage 3, the remaining molten steel region gradually decreased, and complete solidification occurred at approximately 4 647.5 s, with the final solidification position located about 0.28 m below the end of the last slab. Based on the actual CC end stages and the entrapped positions of inclusions, a method for calculating the actual positions of inclusions was introduced to predict the 3D spatial distribution of inclusions in a CC end slab. The normalized number (NN) of inclusions exhibited a fluctuating downward trend with the increasing distance below the end of the last slab. It was recommended to cut the last slab at 4 m to ensure cleanliness, while the 3D normalized number density (NND) of inclusions in regions beyond 7 m below the end of the last slab reached a lower stable value.

Transverse thermal fractures in horizontal wells can be induced by cold fluid injection into high-temperature formations during drilling, geothermal production, CO2 storage, etc. As these fractures propagate, some are arrested due to stress interaction, resulting in a hierarchical fracture pattern. This study investigates the propagation and arrest of radial transverse thermal fractures in a horizontal well driven by 1-D radial heat conduction using an axisymmetric model. We derived a new elasticity equation for multiple radial thermal fractures in a horizontal well, and developed the dimensionless governing equations, in terms of dimensionless fracture penetration depth L, spacing D, aperture Omega, time z, and two model parameters (dimensionless net confining stress T and wellbore radius A) through parameter scaling. Displacement discontinuity method was employed to discretize the governing equations and the dimensionless solutions [L(z, T , A ), D (z, T , A ), Omega(z, T , A )] for the critical states at fracture arrests were solved through stability analysis. The fully transient solutions with stepwise fracture spacing were then obtained to predict the hierarchical fracture pattern. Our findings indicate that the solutions for the radial transverse fractures are asymptotic to those for half-plane thermal fractures at early time and the evolution of fracture penetration depth approaches to a scaling lawL = f (T , A)tau((1-T)/2) at late time. Application to a real geothermal site showed that thermal fractures reach depths of 0.48, 3.48, and 28.29 m, spacings of 0.46, 2.34, and 13.20 m, and apertures (at the wellbore wall) of 0.37, 1.53, and 6.15 mm at 1, 100 and 10,000 days of cooling, respectively.

The filter layer is a crucial component in preventing internal erosion in earth-rockfill dams. Its design typically replies on the particle size distribution of the filter material and base soil, with the ratio between them (i.e., interlayer coefficient) playing a critical role in controlling the blockage and interception process of eroding particles. To better understand how the interlayer coefficients affect subsoil erosion and the retention capacity of filter material, we simulate a reverse filtration system under varying interlayer coefficients using a novel 3D coupled computational fluid dynamics-discrete element method (CFD-DEM) that incorporates irregularly shaped particles. The numerical results indicate that: (1) A smaller interlayer coefficient more effectively inhibits base soil erosion, with the erosion process progressing through three stages: rapid erosion, slow erosion, and stability; (2) The interlayer coefficient significantly influences the transport behavior of soil particles. Interlayer coefficients above 6 weaken the retention capacity of the filter material, causing noticeable subsurface suffusion and damage to the base soil. In contrast, Coefficients below 4 result in the accumulation of fine soil particles at the interface, forming a weakly permeable layer resembling a “filter cake”. A new filter layer design criterion is proposed based on the numerical tests above and is validated through experimental results from the literature. This study provides valuable insights into the microscopic characteristics and suffusion mechanisms of the base soil-filter system, offering practical guidance for the design of filtration systems.

ABSTRACT For unconventional reservoirs, hydraulic fracturing is a common development method. Casing deformation occurs frequently during fracturing operations. Severe casing deformation will block the fracturing tool from reaching the designed position, due to the subsequent fracturing operation between the casing deformation position and the fracturing stage cannot be carried out. According to the statistical results of various oilfields, at least half of casing deformation cases are related to the faults across the well trajectory. Classic theory presumed that the normal stress and friction coefficient of the fault surface will decrease after the high-pressure fluid of the fracturing operation flows into the fault. When the friction stress is less than the shear stress of the fault surface, the fault is activated to slip and cause deformation of the casing passing through the fault. However, the research results based on numerical simulation in this paper show that even if the fracturing fluid does not communicate the fault, the change of the shear stress field at the tip of the artificial fracture also can cause the local fault to slip, especially those faults which the shear stress and friction stress are relatively close. This result can better explain some casing deformation cases far from the fracturing operation stage. In this paper other results indicate that: (1) Unlike the classical theory that the fluid flow into the fault causes the slip of all the fault area, the change of local shear stress field by fracturing operation will only cause the local fault slip; (2) Because only local fault slips, the influence of fault length on fault slip is not obvious, but the fault length and fault slip are still in a positive correlation; (3) The short fault located in the extension line area of the artificial fracture can make the artificial fracture more inclined to propagation to the fault area, and the length difference between the half artificial fracture length of the same fracturing stage is about 20%. Based on the research results, the fault area intersected by the artificial fracture extension line is the most dangerous fault. For the well trajectory that must cross fault, adjusting the design scheme to cross the area with a small fault slip is one of the feasible means to reduce the fracturing casing deformation probability.

Effective elastic properties of porous media are known to be significantly influenced by porosity. In this paper, we investigated the influence of another critical factor, the inter-grain cementation stiffness, on the effective elastic properties of a granular porous rock (Bentheim sandstone) using an advanced numerical workflow with realistic rock microstructure and a theoretical model. First, the disparity between the experimentally tested elastic properties of Bentheim sandstone and the effective elastic properties predicted by empirical equations was analysed. Then, a micro-computed tomography (CT)-scan based approach was implemented with digital imaging software AVIZO to construct the 3D (three-dimensional) realistic microstructure of Bentheim sandstone. The microstructural model was imported to a mechanics solver based on the 3D finite element model with inter-grain boundaries modelled by cohesive elements. Loading simulations were run to test the effective elastic properties for different shear and normal inter-grain cementation stiffness. Finally, a relation between the macroscale Young's modulus and inter-grain cementation stiffness was derived with a theoretical model which can also account for porosity explicitly. Both the numerical and theoretical results indicate the influence of the inter-grain cementation stiffness, on the effective elastic properties is significant for porous sandstone. The calibrated normal and shear stiffnesses at the inter-grain boundaries are 1.2 × 105 and 4 × 104 GPa/m, respectively.

The continuous migration and loss of small particles in fractured rock mass with water flow is the main cause of water inrush in fault zones. In this study, a fluid–solid coupling model for fault zone was established to study the complex coupling between the groundwater seepage and migration of broken rock mass, and reveal the mechanism of erosion-induced water inrush. The rock skeleton and broken rock mass in the fault zone were modelled by large skeleton particles and small filling particles, respectively, in 3D particle flow software while the fluid flow through the fault was modelled by the built-in computational fluid dynamics module. The numerical results show that: (1) with the increase of water pressure, the loss of filling particles increases continuously, and the whole seepage process can be divided into three stages: slow seepage, abrupt seepage and steady seepage, (2) the mass loss, porosity and permeability first increase slowly, then increase rapidly, and finally tend to be stable, (3) higher fine particle content are more likely to cause structural instability due to mass loss, thus increases the risk of water inrush and mud outburst.

Pore pressure is disregarded in traditional laboratory rock hydraulic fracturing experiments, and the effect of pore pressure is not clear. An integrated experiment for seepage and hydrofracturing was established and used to perform sandstone hydraulic fracturing experiments under an initial evenly distributed pore pressure. The experimental results show that there is a positive correlation between the breakdown pressure and the pore pressure at the initiation stage. The data fitting results show that the breakdown pressure and pore pressure follow a linear growth trend. As the pore pressure increases, the acoustic emission energy at the moment of borehole wall fracturing correspondingly increases. After borehole wall fracturing, the reduced magnitude of the pumping pressure also increases, indicating that the initial rupture range is positively correlated with pore pressure. During fracturing propagation, the propagation range and opening of the fracture increase as the initial pore pressure increases within the same pumping time. During hydraulic fracturing, a pore pressure gradient is generated on both sides of the mineral particles. When the tensile stress or shear stress induced by the pore pressure gradient reaches the ultimate strength of the mineral particle bonding surface, the particle bonding surface breaks and opens. This experimental process is more similar to the actual hydraulic fracturing process of oil and gas reservoirs. These results provide a more comprehensive theoretical basis for resolving technical problems of unconventional oil and gas resource exploitation.

Rock brittleness is a crucial mechanical property and essential for fracability evaluation and fracturing scheme design in unconventional reservoirs. However, the influence of inherent anisotropy on deep laminated sandstone’s mechanical properties and brittleness characteristics is rarely investigated. The energy transformation and damage evolution reflected by complete stress-strain curves are analyzed during the entire process of rock rupture under compressions. A new brittleness index is established based on energy evolution during sandstone failure. Its advantages involve comprehensively considering the energy transformation characteristics at both pre-peak and post-peak stages and the capability to characterize the effect of confining pressure and bedding plane (BP) geometry on sandstone brittleness. The triaxial compression tests on sandstones are conducted to validate the reliability and accuracy of the new brittleness index. Numerical simulations are then performed to further investigate the manner in which BP angle, BP density, and confining pressure control the brittleness anisotropy of deep laminated sandstones based on the finite element method. Then the acoustic emission (AE) characteristics of anisotropic sandstone and correlations between AE mode and brittleness index are discussed. The results indicated that the anisotropy of mechanical properties and brittleness of deep laminated sandstones were significantly affected by BP angle, BP density, and confining pressure. With the increase of BP angle, the brittleness index of deep laminated sandstone decreases first and then increases, showing a U-shape variation law, whose maximum and minimum values are obtained at φ =0° and φ =45°, respectively. The AE characteristics were closely related to rock brittleness, which was jointly controlled by BP geometry and confining pressure. The results provide a basis for the brittleness and fracability evaluation and optimum hydraulic fracturing design in deep laminated sandstones.

Understanding the microstructure–property relationships of porous media is of great practical significance, based on which macroscopic physical properties can be directly derived from measurable microstructural informatics. However, establishing reliable microstructure–property mappings in an explicit manner is difficult, due to the intricacy, stochasticity, and heterogeneity of porous microstructures. In this paper, a data-driven computational framework is presented to investigate the inherent microstructure–permeability linkage for natural porous rocks, where multiple techniques are integrated together, including microscopy imaging, stochastic reconstruction, microstructural characterization, pore-scale simulation, feature selection, and data-driven modeling. A large number of 3D digital rocks with a wide porosity range are acquired from microscopy imaging and stochastic reconstruction techniques. A broad variety of morphological descriptors are used to quantitatively characterize pore microstructures from different perspectives, and they compose the raw feature pool for feature selection. High-fidelity lattice Boltzmann simulations are conducted to resolve fluid flow passing through porous media, from which reliable permeability references are obtained. The optimal feature set that best represents permeability is identified through a performance-oriented feature selection process, upon which a cost-effective surrogate model is rapidly fitted to approximate the microstructure-permeability mapping via data-driven modeling. This surrogate model exhibits great advantages over empirical/analytical formulas in terms of prediction accuracy and generalization capacity, which can predict reliable permeability values spanning four orders of magnitude. Besides, feature selection also greatly enhances the interpretability of the data-driven prediction model, from which new insights into the mechanism of how microstructural characteristics determine intrinsic permeability are obtained.

PurposeAccurate presentation of the rock microstructure is critical to the grain-scale analysis of rock deformation and failure in numerical modelling. 3D granite microstructure modelling has only been used in limited studies with the mineral pattern often remaining poorly constructed. In this study, the authors developed a new approach for generating 2D and 3D granite microstructure models from a 2D image by combining a heterogeneous material reconstruction method (simulated annealing method) with Voronoi tessellation.Design/methodology/approachMore specifically, the stochastic information in the 2D image is first extracted using the two-point correlation function (TPCF). Then an initial 2D or 3D Voronoi diagram with a random distribution of the minerals is generated and optimised using a simulated annealing method until the corresponding TPCF is consistent with that in the 2D image. The generated microstructure model accurately inherits the stochastic information (e.g. volume fraction and mineral pattern) from the 2D image. Lastly, the authors compared the topological characteristics and mechanical properties of the 2D and 3D reconstructed microstructure models with the model obtained by direct mapping from the 2D image of a real rock sample.FindingsThe good agreements between the mapped and reconstructed models indicate the accuracy of the reconstructed microstructure models on topological characteristics and mechanical properties.Originality/valueThe newly developed reconstruction method successfully transfers the mineral pattern from a granite sample into the 2D and 3D Voronoi-based microstructure models ready for use in grain-scale modelling.

Purpose Thermal fractures initiated under cooling at the surfaces of a 2-D or 3-D structure propagate, arrest and coalesce, leading to its structural failure and material-property changes, while the same processes can happen in the rock mass between parallel hydraulic fractures filled with cold fluid, leading to enhanced fracture connectivity and permeability. Design/methodology/approach This study used a 2-D plane strain fracture model for mixed-mode thermal fractures from two parallel cooling surfaces. Fracture propagation was governed by the theory of linear elastic fracture mechanics, while the displacement and temperature fields were discretized using the adaptive finite element method. This model was validated using two numerical benchmarks with strong fracture curvature and then used to simulate the propagation and coalescence of thermal fractures in a long rock mass. Findings Modeling results show two regimes: (1) thermal fractures from a cooling surface propagate and arrest by following the theoretical solutions of half-plane fractures before the unfractured portion decreases to 20% rock-mass width and (2) some pairs of fractures from the opposite cooling surfaces tend to eventually coalesce. The fracture coalescence time is in a power law with rock-mass width. Originality/value These findings are relevant to both subsurface engineering and material engineering: structure failure is a key concern in the latter, while fracture coalescence can enhance the connectivity of thermal and hydraulic fractures and thus reservoir permeability in the former.

Water jet drilling (WJD) is an effective technique for drilling micro-holes in the subsurface for reservoir stimulation . This study aims to investigate numerically the failure mechanism of rock during WJD and to assess the WJD performance before drilling. A 3D fluid-solid coupling model is developed for simulating WJD by coupling a mechanical solver based on the combined finite-discrete element method (FDEM) with a fluid solver using an immersed-body method. The new numerical model is capable of simulating crack initiation and propagation and fragment removal under the impact load of a high-speed water jet. The poroelastic effect is implemented via Biot's theory of poroelasticity . The numerical results show that: (1) rock failure is only observed in the Gildehaus sandstone with the lowest strengths among the three types of rock tested, (2) most of the cracks are tensile failures and pure shear cracks are rare, mixed mode cracks account for 15%∼40% of the total crack number depending on the mechanical boundary conditions , (3) increased water back pressure significantly suppresses jet erosion. The poroelastic effect on the rock failure is insignificant in the mesoscale simulations and will be further investigated using a microscale model in future.

Abstract The effect of pore pressure on rock damage is a core problem in underground engineering. In this paper, the pseudotriaxial hydromechanical coupling experiment system is utilized to carry out the physical model experiment of the pore pressure on the rock damage, and the effect of evenly distributed pore pressure on rock strength and pore structure is analyzed. Compared with natural rock sample before the pore pressure effect, the uniaxial compressive strength is reduced by about 35.24%. Pore pressure decreases the strength of the rock and reduces its ability to resist deformation. The stress growth rate at the prepeak stage of the stress-strain curve for rock sample after pore pressure effect decreases. The peak strength decreases, and the strain corresponding to the peak stress increases. The plastic deformation characteristics of the sample are obvious. After the sample has macroscopically broken, the decline rate of postpeak stress slows down, and the residual strength decreases. The rock gradually changes from brittle failure mode to ductile failure mode. Through scanning electron microscopy (SEM) test and comparison analysis, it is found that after the pore pressure effect, the surface of the rock sample becomes rougher. There are multiple pore and fissure concentrated areas in the rock sample. Compared with the sample before the pore pressure effect, the number of pores with an equivalent diameter in the range of 2 μm-3 μm increases significantly. The proportion has increased from 7.7% to 19.1%, and the number has increased from 1468 to 4454. A large number of small-sized pores (less than 3 μm) are generated in the rock sample after the pore pressure effect. Therefore, the overall pore content of the rock sample increases.

Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low-permeability formations under one-dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture l....ength., ap....erture O, sp....acing....., time...., and effective confining stress....., were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fra....cture,.(.......) increases nonlinearl....y with v.... and then transitions to scaling law..... =.... (.)v...., indicating that late-time fracture length increases linearly with the square root of cooling time. For constantly spaced frac....tures,.(.......,.) deviates from the single-fracture solution at....a later.... for a....larger., showing slower propagation under inter-fracture stress interaction. For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scalin....g law,. =.... '(.)v........with.... '(.) <....(.), obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter...... Application to a geothermal sit....e with. = 0.11 demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and