Fracture Propagation Model Research Articles

Geometric characteristics of diverting fractures for multi-stage dynamic temporary plugging and diverting fracturing in fractured reservoir

Temporary plugging and diverting fracturing (TPDF) technology constitutes a pivotal stimulation methodology in the advancement of unconventional resources, given its efficacy in establishing communication with natural fractures (NFs). Presently, the comprehension of TPDF is primarily confined to laboratory-scale experiments, with a notable dearth of accurate knowledge regarding the diverting law and geometric characteristics of diverting fractures at the field scale. This study introduces a hydro-mechanical-damage model for hydraulic fracture (HF) propagation, developed through the derivation and refinement of the phase field method. The model integrates the dynamic flow distribution process among multi-perforation clusters under stress interference, alongside the construction of a dynamic transportation and plugging model for the temporary plugging agent in TPDF. Subsequently, a coupled model encompassing multi-cluster and multi-stage dynamic TPDF is established using the finite element method. Utilizing this model, an exploration of the diverting fracture's opening and propagation mechanisms, as well as the impact of stimulation and reservoir factors on geometric characteristics, is conducted at the field scale. The results show that the TPDF model has high accuracy, and for the first time, it realistically simulates the gradual increase and decrease in fracturing pressure in the field after temporary plugging. The diverting fracture propagation is affected by the stress interference from the initial HF (ini HF), NF, and horizontal stress difference. The energy required to open NFs to form a diverting fracture is higher than that to cross NFs after temporary plugging, and there is a strong positive correlation between the energy rise and the approach angle and the horizontal stress difference. The use of multi-scale plugging agents can promote a more uniform distribution of diverting fractures. When the NF angle is near 60°, the diverting fracture has a larger fracture control volume. The NF distribution and the interaction between NF and HF are of great significance to the opening position of diverting fractures in TPDF. According to the propagation pattern of diverting fractures, they can be divided into five categories. The temporary plugging agent can alleviate the directional propagation of HFs caused by NF induction. The alleviating effect is not only controlled by the interaction mode between HF and NF but also related to the NF density. The propagation distance of the diverting fracture formed by the inferior fracture will be about 50% farther compared with the superior fracture. The diverting fractures are mainly interfered by the stress of the HFs in the same perforation cluster at the early stage and mainly interfered by the HFs of different perforation clusters at the middle and late stages.

Numerical Simulation of the Simultaneous Development of Multiple Fractures in Horizontal Wells Based on the Extended Finite Element Method

Simultaneous multiple-fracture treatments in horizontal wellbores have become an essential technology for the economic development of shale gas reservoirs. During hydraulic fracturing, fracture initiation and propagation always induce additional stresses on the surrounding rock. When multiple fractures develop simultaneously, the development of some fractures is limited due to the stress-shadow effect. An in-depth understanding of the multiple-fracture propagation mechanism as reflected by fracture morphology and flow rate distribution can help to set reasonable operation parameters for improving the uniformity of multiple fractures and forming a complex fracture network according to the different in situ stress conditions in a reservoir to increase the shale gas recovery and reduce the cost. In this study, a two-dimensional (2D) fracture propagation model was developed based on the extended finite element method (XFEM). Then, the influences of various factors, including geological and operational factors, on the development of multiple fractures were studied. The results of numerical simulations showed that increasing the cluster spacing or injecting fracturing fluid with lower viscosity can help reduce the stress-shadow effect. In the case of smaller in situ stress differences, the deflection of the fractures was larger due to the stress-shadow effect. As the stress difference increased, the direction of the propagation of the fracture was gradually biased towards the direction of maximum horizontal stress. In addition, the injection rate had some effects on the fracture morphology and flow rate distribution. However, as the injection rate increased, the dominant fracture developed rapidly, and the fracture length significantly increased.

Research on the data-driven inter-well fracture channeling identification method for shale gas reservoirs

The issue of inter-well fracture channeling in shale reservoirs is becoming increasingly prominent, significantly impacting the production of nearby wells. Therefore, it is crucial to accurately determine the location of fracture channeling in order to effectively design anti-channeling measures and optimize reservoir fracturing. In this paper, a data-driven fracture propagation model and fracture channeling identification method are established. In the model, the fracture morphology is fitted by the bottom-hole flowing pressure constraint. The bottom-hole flowing pressure (pwp) calculated by the construction pump pressure and the fluid wellbore flow is mainly considered as the real solution. The bottom-hole flowing pressure (pwf) calculated by the construction displacement and the fracture morphology is used as the constraint variable, and the fracture parameters are changed using the SPSA optimization algorithm to realize the dynamic fitting of the fracture morphology. In order to accurately describe the position of fracture channeling, the seepage radius of the fracture boundary is introduced to calculate the volume of fracture reconstruction. The volume coefficient of repeated reconstruction is used as the quantitative evaluation index of fracture channeling. This approach enables an accurate depiction of the position of fracture channeling. Finally, the model method is applied to the actual fracture channeling well. The study shows that the fracture length of the well inversion is greater than the well spacing, and there is a possibility of inter-well fracture channeling. The volume coefficient of repeated reconstruction is 8%, similar to the critical fracture channeling index. There are nine fracturing sections with fracture channeling, and the maximum fracture channeling coefficient is 14.2%. This paper successfully explains the reason for cross-well fracture channeling, and its conclusion aligns with the actual monitoring results. The proposed method in this paper effectively identifies the location of fracture channeling and offers guidance for optimizing channeling prevention in subsequent designs.

Efficient optimization of fracturing parameters with consideration of fracture propagation and heterogeneity in tight gas reservoirs

The parameters of fractures, such as fracture geometries, placement, and conductivity, are critical for the production of horizontal wells in tight gas reservoirs. Current studies on fracture parameter optimization, especially those using the optimization algorithms, are often based on the assumptions that the fractures are uniformly placed with equal length and conductivity. However, non-uniform designs of fracture spacing have been proved to be effective in reducing fracture interference as well as increasing the well production, especially with strong rock heterogeneity. In addition, most of the current literature focuses on identifying optimal hydraulic fracture geometries without considering the fracture propagation process, which may oversimplify the evaluation of completion cost and result in fracture geometries that cannot be realized in practice.In this paper, an automatic optimization process, which could efficiently couple the fracture propagation, is proposed to optimize the fracture parameters. The genetic algorithm (GA) with penalty function method is used to optimize the constraint and non-linear problem. A modified PKN fracture propagation model is established to quickly predict the hydraulic fracture geometries. Fracture locations and fluid injection volume are sequentially optimized with consideration of heterogeneous rock properties. Model parameters are taken from typical tight gas horizontal wells in Jinqiu gas field in Sichuan Province, China. The results show the importance of permeability on both fracture length and production in tight gas well. The lower the permeability, the more significant the production increase after fracture location optimization. More fractures tend to be placed in area with small permeability and fewer fractures are required in highly permeable regions. With an increase in rock heterogeneity, the distribution of fractures becomes more uneven. Conversely, increasing the number of fractures can lead to a more even distribution of fractures. More fluid should be injected in low-permeability regions according to the optimization results. The optimization method is applied to a practical tight gas well in Sichuan Basin and the cumulative gas production can be increased by 6.5% to 8% when compared with the initial uniform designs.

Discrete Lattice Element Model for Fracture Propagation with Improved Elastic Response

This research presents a novel approach to modeling fracture propagation using a discrete lattice element model with embedded strong discontinuities. The focus is on enhancing the linear elastic response within the model followed by propagation of fractures until total failure. To achieve this, a generalized beam lattice element with an embedded strong discontinuity based on the kinematics of a rigid-body spring model is formulated. The linear elastic regime is refined by correcting the stress tensor at nodes within the domain based on the internal forces present in lattice elements, which is achieved by introducing fictitious forces into the standard internal force vectors to predict the right elastic response of the model related to Poisson’s effect. Upon initiation of the first fractures, the procedure for the computation of the fictitious stress tensor is terminated, and the embedded strong discontinuities are activated in the lattice elements for obtaining an objective fracture and failure response. This transition ensures a shift from the elastic phase to the fracture propagation phase, enhancing the predictive capabilities in capturing the full fracture processes.

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.

Dynamic strain gradient brittle fracture propagation: comparison with experimental evidence

<p>This paper presented a physico-mathematical model for dynamic fracture propagation in brittle materials with a purely continuum mechanics hemi-variational-based strain gradient theory. As for the quasi-static case, the simulation results, obtained by means of finite elements, revealed that strain gradient effects significantly affected the fracture propagation, leading to finite fracture thickness that was independent of the mesh size. It was also observed that nonsymmetric loading rate lead to a deviation from standard mode-Ⅰ crack propagation that cannot be revealed in the quasi-static case. The model results were compared against experimental data from fracture tests on notched specimens taken from the literature. The comparison showed good agreement between the model predictions and the experimental measurements. The presented model and simulation results can be useful in the design and optimization of structural components subjected to dynamic loading conditions.</p>

Study on rock fracture mechanism and hydraulic fracturing propagation law of heterogeneous tight sandstone reservoir.

Hydraulic fracturing technology is an effective way to develop tight sandstone reservoirs with low porosity and permeability. The tight sandstone reservoir is heterogeneous and the heterogeneity characteristics has an important influence on fracture propagation. To investigate hydraulic fracture performance in heterogeneous tight reservoir, the X-ray diffraction experiments are carried out, the Weibull distribution method and finite element method are applied to establish the uniaxial compression model and the hydraulic fracture propagation model of heterogeneous tight sandstone. Meanwhile, the sensitivity of different heterogeneity characterization factors and the multi-fracture propagation mechanism during hydraulic fracture propagation is analyzed. The results indicate that the pressure transfer in the heterogeneous reservoir is non-uniform, showing a multi-point initiation fracture mode. For different heterogeneity characterization factors, the heterogeneity characteristics based on elastic modulus are the most sensitive. The multi-fracture propagation of heterogeneous tight sandstone reservoir is different from that of homogeneous reservoir, the fracture propagation morphology is more complex. With the increase of stress difference, the fracture propagation length increases. With the increase of injection rate, the fracture propagation length increases. With the increase of cluster spacing, the propagation length of multiple fractures tends to propagate evenly. This study clarifies the influence of heterogeneity on fracture propagation and provides some guidance for fracturing optimization of tight sandstone reservoirs.

Material point method to simulate the evolution characteristics of loading damage in fractured sandstone

Cracks in rocks can lead to different load responses and mechanical properties. Primary and secondary cracks are altered during loading, with varying degrees of impact on the failure of underground engineering rock masses. However, the precise modeling of fracture initiation and propagation resulting in failure remains challenging, and the macroscopic evolution characteristics of cracks and stress fields have not been accurately described. In this study, a numerical simulation tool based on the material point method (MPM) and a strain softening model were used to establish a plane loading model with different cutting angles. A simulation of the damage evolution of fractured sandstone under constant-rate loading was conducted for different confining pressures and cutting angles. The results show the following. 1) A comparison of the simulation and experimental results indicates that the proposed numerical method accurately simulates the macroscopic crack generation and the complex physical processes of fractured sandstone during loading. 2) The stress concentration area originates from both ends of the crack and extends toward the edge in a diagonal direction until the crack has penetrated the rock. 3) The ranking of the cutting angle based on the sandstone strength is 0° > 90° > 60° > 30°. The cumulative dissipated energy exhibits an inflection point near the peak stress, and the increase after this point is primarily attributed to friction at the crack surface. The damage degree and dissipated energy of the rock in different stages correspond to the rock’s strength.

Main Control Factors of Fracture Propagation in Reservoir: A Review.

The fracture distribution and internal control factors after the fracturing of unconventional oil and gas reservoirs determine the reservoir reforming effect to a large extent. Based on the research of global scholars on the influencing factors of fracture propagation, comprehensive theoretical model, and numerical simulation, this Review systematically discusses the influence of internal geological factors and external engineering factors of unconventional oil and gas reservoir on fracture propagation behavior and summarizes the current problems and development trends in fracture research. The results show the following: (1) The fracture propagation is a comprehensive process constrained by lithology and mineral composition, water saturation, nonhomogeneity, natural weak surface, and ground stress. (2) External engineering factors have a meaningful control effect on fracture propagation; the type and temperature of fracturing fluids can also change the mechanical properties of different rocks, thus affecting the fracture propagation pattern. (3) The existing fracture propagation models have certain limitations, and their computational reliability still needs to be further verified. (4) Numerical simulation can break through the limitations of physical simulation, but different simulation methods have different shortcomings and applicability. In the future, we should focus on: (1) finding parameters to quantitatively characterize heterogeneity at the 3D level, which is an important direction to study the effect of heterogeneity on fracture propagation; (2) introducing computerized methods to establish a geological model that considers multiple factors and combining it with numerical simulation software to study fracture propagation; (3) considering the characteristics of fluid-liquid-solid phase comprehensively, establishing a suitable THL coupling equation; (4) how the interaction mode of fracturing fracture is combined with the natural fracture geometry, and how the fracture is affected by fracturing engineering parameters such as fluid injection rate and viscosity of fracturing fluid; and (5) geology-engineering dynamic integration, which is an important direction to be carried out in the future.

Updated Lagrangian nonlocal general particle dynamics for large deformation problems

The traditional general particle dynamics (GPD) has been successfully applied in modeling fracture propagation, frictional contact and stick–slip problems in rocks. In this study, the updated Lagrangian nonlocal general particle dynamics (UL-NGPD) method is proposed to solve large deformation problems. In the UL-NGPD, the continuity equation and momentum equation are reformulated in the integro-differential formulation by introducing nonlocal theories in the updated Lagrangian framework. The artificial viscosity and artificial force state are utilized to enhance the numerical stability and accuracy in modeling large deformation. The nonlocal velocity gradient in the deformed configuration is used to update the Cauchy stress rate from the Drucker-Prager elasto-plastic constitutive model with strain-softening behaviour for solids. The UL-NGPD paradigm is numerically implemented through an explicit Predictor-Corrector scheme for high-performance computing. The stability and accuracy of the UL-NGPD are verified by numerical tests on compression test, slope stability analysis and aluminum bar collapse experiment. Thereafter, simulations of granular soil collapse and retrogressive landslide in sensitive clays are presented to demonstrate its efficacy and robustness in modeling challenging geotechnical problems involving large deformation. The numerical results show that the proposed UL-NGPD is powerful and suitable for analyzing large deformation problems in geotechnical engineering.

A Semi-Analytical Model for Studying the Transient Flow Behavior of Nonuniform-Width Fractures in a Three-Dimensional Domain

In the fracture propagation model, the assumption that hydraulic fractures with non-uniform widths have been successfully utilized to predict fracture propagation for decades. However, when one conducts post-fracture analysis, the hydraulic fracture is commonly simplified with a uniform width, which is contradictory to the real fracture models. One of the reasons for over-simplifying the fracture geometry in the post-fracture analysis can be ascribed to the fact that we are still lacking a model to characterize the pressure transient behavior of the nonuniform-width fractures which can induce three-dimensional flow around the fractures. In this work, on the basis of the Green function and Newman product method, the authors derived a semi-analytical model to account for the effect of non-uniform width distribution of the hydraulic fractures in a three-dimensional domain. In addition, the effect of the fracturing strategies on the well performance is investigated based on the developed semi-analytical model. The calculated results from the developed model show that the vertical flow in the vicinity of the fracture cannot be neglected if the fracture height is sufficiently small (e.g., hf = 10 m), and one can observe vertical elliptical flow and vertical pseudo-radial flow during the production. A nonuniform-width fracture can penetrate further into the reservoir with a lower injection rate (e.g., qi = 1.44 × 103 md). For the scenarios of high fracture permeability (i.e., kf = 1 × 105 md), a smaller fracture height, lower injection rate, and larger Young’s modulus can be more favorable for enhancing the well productivity. Compared to the influence of fracture height, the influences of injection rate and Young’s modulus on the well performance are less pronounced.

Crustal Conditions Favoring Convective Downward Migration of Fractures in Deep Hydrothermal Systems

AbstractCooling magma plutons and intrusions are the heat sources for hydrothermal systems in volcanic settings. To explain system longevity and observed heat transfer at rates higher than those explained by pure conduction, the concept of fluid convection in fractures that deepen because of thermal rock contraction has been proposed as a heat‐source mechanism. While recent numerical studies have supported this half a century old hypothesis, understanding of the various regimes where convective downward migration of fractures can be an effective mechanism for heat transfer is lacking. Using a numerical model for fluid flow and fracture propagation in thermo‐poroelastic media, we investigate scenarios for which convective downward migration of fractures may occur. Our results support convective downward migration of fractures as a possible mechanism for development of hydrothermal systems, both for settings within active zones of volcanism and spreading and, under favorable conditions, in older crust away from such zones.

Investigation of fracture behavior and deformation capacity of high-strength steel butt-welded joints

Performance-based design of high-strength steel welded structures requires accurate prediction of their load-bearing capacity as well as deformation capacity. There have been several studies undertaken on the load-bearing capacity of high-strength steel butt-welded (HSSBW) joints, but very few studies are performed on their deformation capacity. This study investigates the fracture behavior as well as the deformation capacity of double-V HSSBW joints with strength-matching welding materials, taking into account the effects of different heat inputs, steel strengths, and steel processing methods. To evaluate the deformation capacity, fracture initiation criterion, and fracture propagation model of four zones within the butt-welded joints, including hardened heat-affected zone (HHAZ), softened heat-affected zone (SHAZ), welding material zone (WM), and base metal zone (BM), are first calibrated from experimental results and numerical analysis results. The calibrated material models are validated against the test data. Numerical analyses are then performed to predict the fracture behavior and deformation capacities of the welded joints utilizing the verified material models. According to the analysis results, heat inputs no more than 1.9 kJ/mm impose a limited influence on the fracture behavior of each zone within the double-V HSSBW joints. If the heat input is below 1.9 kJ/mm, QT steel welded joints exhibit a higher deformation capacity than TMCP steel welded joints. When compared to the tension specimens made of pure base metal, the reduction of the deformation capacity of the double-V HSSBW joints was even more than 30 % and it is more significant than the reduction of load-bearing capacity, therefore, evaluation of the deformation capacity of the welded joints is very essential for the performance-based design of high-strength steel welded structures.

Mechanical characteristics and reservoir stimulation mechanisms of the Gulong shale oil reservoirs, the northern Songliao Basin

Shale oil of the Qingshankou Formation of the Gulong Sag, the northern Songliao Basin, represents the first attempt at large-scale development of pure-shale-type shale oil in China. By integrating the multi-scale refined reservoir characterization with macro-micro-scale mechanical testing, it is clarified that the Gulong shale is characterized by high clay mineral content, high rock plasticity, highly-developed bedding, and prominent mechanical anisotropy. A three-dimensional (3D) fracture propagation model of hydraulic fracturing was built for the Gulong shale, which fully captures the hydraulic fracture distribution pattern affected by the high bedding density, in-situ stress, and fracturing treatment parameters. Our research showed that due to influences of bedding, hydraulic fracturing in the Gulong shale forms a complex fracture morphology featuring the main fracture with multiple perpendicular branches that have different lengths (like the outdoor directional TV antenna); however, the vertical propagation of fractures is inhibited, and the fracture height is commonly less than 10 m. The limited stimulated reservoir volume (SRV) is the main problem facing the fracturing stimulation of the Gulong shale oil. Bedding density has vital effects on fracture morphology, so case-specific fracturing designs shall be developed for shale intervals with different bedding development degrees. For reservoirs with well-developed bedding, it is suggested to properly increase the perforation cluster spacing and raise the volume and proportions of viscous fluids of the pad, so as to effectively promote vertical fracture propagation and improve reservoir stimulation performance. This study integrates multi-scale fine reservoir characterization and macro-micro-scale mechanical testing, as well as the construction and numerical simulation of hydraulic fracturing models for high-density layered shale reservoirs, providing a new approach and methodological framework for the fracturing research of high-density layered shale reservoirs.

Adaptive phase-field modeling of fracture in orthotropic composites

An adaptive phase-field method is developed and applied to model fracture propagation in orthotropic composites. The proposed approach extends the work of Muixí et al. (2020) to orthotropic composites through following modifications: (a) elastic tensor is evaluated in the global coordinate system from a given engineering stiffness matrix in the principal material coordinates, (b) strain energy density is additively decomposed into fiber and matrix-dominated modes, and (c) a penalized second-order structural tensor is introduced in the phase-field equation facilitating preferential damage growth along the fiber orientation. The developed approach is validated through several benchmark examples and available experimental results.Several numerical failure experiments are conducted varying fiber orientation, adhesive layer thickness, shear modulus, and fracture toughness. A large increase in ductility and peak-load carrying capacity is observed for laminate configurations where the fibers are oriented such that the principal material coordinates and the global coordinates are aligned. An increase in the adhesive layer’s fracture toughness increases the macroscopic ductility and prevents catastrophic failure of laminate. The results of this study provide valuable insights into the failure mechanisms in orthotropic composites.

Adaptive phase-field modeling of fracture propagation in bi-layered materials

We study fracture propagation in bi-layered materials using an adaptive phase-field method. The method combines a phase-field representation of fracture with spatial adaptivity to provide mesh refinement in the smeared zone of damage, where higher accuracy is needed to resolve the solution. We place a particular emphasis on studying the competition between crack arrest, deflection, and penetration at the interface of two dissimilar materials. To explore this competition, we perform tension tests on various models with different combinations of material and geometric properties. We begin by validating the adaptive phase-field model through a uniaxial tension test. The material mismatch and locations of the initial damage for this example are chosen such that the fracture propagation behavior is identical to that in a homogeneous material. Next, we independently vary the mismatches in elastic stiffness and critical energy release rate to study their influence on crack growth. Our observations show that both mismatches contribute to an effective toughening of the model, but in different ways. Critical energy release rate mismatch causes crack deflection along the interfaces, while elastic stiffness mismatch results in retardation of crack growth. We also note that for a specific combination of material mismatch and location of initial damage, crack nucleation in the adjacent material is preferred over propagation from the existing notch. Finally, through models with inclined interfaces, we demonstrate the effect of the relative orientation between the approaching crack and the material interface on crack penetration, deflection, and nucleation. The numerical results from this study provide valuable insight into the various failure mechanisms in bi-layered materials.

Fracture propagation laws of staged hydraulic fracture in fractured geothermal reservoir based on phase field model

Hydraulic fracturing is widely used in geothermal resource exploitation, and many natural fractures exist in hot dry rock reservoirs due to in-situ stress and faults. However, the influence of natural fractures on hydraulic fracture propagation is not considered in the current study. In this paper, based on the phase field model, a thermo-hydro-mechanical coupled hydraulic fracture propagation model was established to reveal the influence of injection time, fracturing method, injection flow rate, and natural fracture distribution on the fracture propagation mechanism. The results show that fracture complexity increases with an increase in injection time. The stress disturbance causes the fracture initiation pressure of the second cluster significantly higher than that of the first and third clusters. The zipper-type fracturing method can reduce the degree of stress disturbance and increase fracture complexity by 7.2% compared to simultaneous hydraulic fracturing. Both low and high injection flow rate lead to a decrease in fracture propagation time, which is not conducive to an increase in fracture complexity. An increase in the natural fracture angle leads to hydraulic fracture crossing natural fracture, but has a lesser effect on fracture complexity. In this paper, we analyzed the influence of different factors on initiation pressure and fracture complexity, providing valuable guidance for the exploitation of geothermal resources.

Criteria for discriminating layer-penetration fracturing considering pressure drop and interfaces

Accurately predicting fracture height growth in a stratified reservoir presents a significant challenge. In this study, we have developed a semi-analytical prediction model for fracture height growth that accounts for pressure drop effects and considers the influence of bedding interfaces, all based on the principles of equilibrium height theory. The methodology involves solving intricate nonlinear equations and generating fracture height profiles, systematically investigating the effects of various factors: in-situ stress, fracture toughness, fluid density, and perforation location on fracture height. Sensitivity analysis of the model has revealed findings: (1) The presence of a stress barrier leads to a substantial increase in the induced stress required for fracture height growth. In particular, the stress barrier inhibits growth on one side while promoting it on the opposite side. (2) The influence of the fracture toughness barrier on fracture height growth, while significant, is overshadowed by that of the stress barrier. An increase in the fracture toughness of the rock decelerates the rate of fracture height growth but simultaneously raises the required induced stress for layer penetration. (3) Increasing the density of the fracturing fluid exerts a dual effect, slowing the growth rate of the upper fracture tip while accelerating the advancement of the lower fracture tip. Higher fluid density, under constant perforating pressure, results in a noticeable reduction in overall fracture height. (4) Fracture growth from the low-stress layer to the high-stress layer required an increase in induced stress. The research findings not only provide essential data on fracture height profiles, enhancing the applicability of the pseudo-3D hydraulic fracture propagation model, but also contribute to the refinement of governing equations within hydraulic fracture modeling.

A novel hydraulic fracturing model for the fluid-driven fracture propagation in poroelastic media containing the natural cave

Hydraulic fracturing is an efficient technology to extract hydrocarbon within natural caves. However, these caves can markedly affect the fracture propagation behavior. This paper proposes a novel hydraulic fracturing model to simulate the fracture propagation in poroelastic media containing the natural cave, utilizing the strengths of the phase-field method. By coupling the Reynolds flow with cubic law in fracture domain, free flow in cave domain, and low-permeability Darcy flow in reservoir domain, the fracture-cave-reservoir flow governing equations are established. The Biot poroelasticity theory and fracture width are the links of hydro-mechanical coupling. The smooth phase-field is introduced to diffuse not only the sharp fracture but also the sharp cave edge. The fully coupling model is solved by a staggered scheme, which independently solves the pressure field and displacement field in inner cycle, and then independently solves the phase field in outer cycle. The proposed model is verified by comparing with the Khristianovic–Geertsma–de Klerk (KGD) model and Cheng's hydraulic fracturing model. Then, the interaction between hydraulic fracture and natural cave is investigated through several two-dimensional and three-dimensional cases. The result shows that the cave effect can make the hydraulic fracture deflect and raise its propagation velocity. Increasing the fracture-cave distance, injection rate, and in situ stress difference can all decline the cave effect. The displayed cases also substantiate the capability and efficiency of the proposed model.