Stress Shadow Research Articles

The 12 October 2021, MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document}=6.4, Zakros, Crete earthquake

We study the strong 12 October 2021, MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_W$$\\end{document}=6.4, offshore Zakros, Crete earthquake, and its seismotectonic implications. We obtain a robust location (azimuthal gap equal to 17∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}) for the mainshock by combining all freely available local, regional and teleseismic phase arrivals (direct and depth phase arrivals). Based on our location and the spatial distribution of the poor aftershock sequence we parameterise the fault area as a 30 km ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} 20 km planar surface, and using three-component strong motion data we calculate slip models for both earthquake nodal planes. Our preferred solution shows a simple, single slip episode on a NE-SW oriented, NW shallow-dipping fault plane, instead of a N-S oriented, almost vertical nodal plane. An anti-correlation of the aftershocks spatial distribution versus the maximum slip (∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document} 27 cm) of our model further supports this, although the accuracy of the aftershock hypocentral locations could be somewhat questionable. Coulomb stress changes calculated for both kinematic models do not show substantial differences, as the aftershock seismicity within the first 3 months after the mainshock is distributed along the stress shadow zone and over the stress enhanced areas developed at the southern fault edge, induced by the mainshock. The Kasos island tide gauge record analysis shows a small signal after the earthquake, but it can hardly demonstrate the existence of tsunami waves due to the low signal-to-noise ratio. Tsunami simulations computed for the two nodal planes do not yield conclusive evidence to highlight whether the causative fault plane is NE-SW oriented, NW shallow-dipping plane, or the N-S oriented plane, nevertheless, the power spectrum analysis of the NW shallow-dipping nodal plane matches the spectral peak at 8 s period and is overall closer to the spectrum of the tide gauge record. A USGS Shakemap was also produced with all available local strong motion data and EMSC testimonies. This was also investigated in an effort to document the responsible fault. The overall analysis in this study, slightly suggests a rather westward, shallow-dipping offshore fault zone, being antithetic to the main Zakros almost vertical normal fault which shapes the coast of eastern Crete and is perpendicular to the direction of Ptolemy Trench in this area. This result agrees with seismotectonic and bathymetric evidence which support the existence of approximately N-S trending grabens, east and northeast of Crete.

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.

Stress Evolution of the Main Himalayan Thrust Fault Induced by the Mw 7.8 Gorkha Earthquake

ABSTRACT The Mw 7.8 Gorkha earthquake that occurred in 2015 is the largest thrust event in the middle of the main Himalayan thrust fault zone (MHT) in the past 81 yr. Its impact on the regional tectonic stress state and future seismic risks is a significant scientific issue worthy of in-depth analyses. In this study, we inverted the planar fault-slip model (the planar model), the flat-ramp fault-slip model (the flat-ramp model) and the double flat-ramp fault-slip model (the double flat-ramp model) to analyze the effect of the fault geometry, based on the steepest descent method (SDM) and the layered earth model. Compared with the flat-ramp model, the planar model exhibits a wider slip distribution in the down-dip direction of the main rupture zone, whereas the double flat-ramp model shows a larger coseismic slip on the middle ramp at the depth of 7.5–11.5 km. Those slip differences produce larger stress shadow areas in the above models, but for a blind thrust event induced by a low-dip thrust fault, this does not significantly change the distribution mode of coseismic Coulomb stress change (ΔCFS) in the three models. Namely, there is an obvious stress release in the main rupture but an obvious stress loading in the up-dip and down-dip directions of the main rupture zone. Based on the Burgers rheological model, we calculated the postseismic viscoelastic Coulomb stress change (V−ΔCFS) and the cumulative Coulomb stress change (C−ΔCFS) induced by the Gorkha earthquake in the flat-ramp model and comparatively analyzed the evolution pattern of coseismic and postseismic stresses. Our results indicate that the variation trend of postseismic stress in the lithosphere is opposite to that of the coseismic ΔCFS. The postseismic viscoelastic relaxation promotes the slip of the flat-ramp structure at the depth of 10–25 km, and the stress unloads in the shallow and deep part simultaneously. As a blind thrust event, the coseismic ΔCFS still plays a dominant role in the shallow part after 50 yr, whereas the loading C−ΔCFS in the deep part of the MHT is greatly weakened by the postseismic V−ΔCFS. Seismic risks still exist in the unruptured area on the west side of the mainshock and the shallow Main Frontal thrust.

Study on the Impact of Flow Dynamic Allocation Mechanism on the Balanced Propagation of Multicluster Fractures in Horizontal Wells

Abstract The implementation of the multicluster fracturing technique in horizontal wells is crucial to the economic development of shale gas reservoirs. The stress shadow area generated by them suppresses the effective expansion of fractures, leading to lower construction quality. Numerous well logging and production data indicate that dynamic flow allocation is also an important mechanism restricting oil and gas production. To reveal the mechanism of multifracture synchronous competitive expansion, a multifracture expansion finite element model considering fluid-solid coupling in porous media was established. A wellbore model was built to characterize the fluid pressure drop, incorporating pipe flow and fluid connection elements to emulate fluid flow within the wellbore, and the influence of various factors on the balanced expansion of fractures was investigated. The results show that high porosity, uniform perforation, and high elastic modulus of sweet spots are favorable for the balanced expansion of multiple fractures when using high-volume and low-viscosity fracturing fluids. When the spacing is small and the porosity is low with nonuniform perforation, the threshold generated by perforation friction will dominate the balanced fluid injection and expansion of each fracture. The horizontal well fracturing plan in a certain area of southwest China was optimized using this model. After optimization, when the spacing is less than 15 m, the total number of perforations is 32, and the average injection rate per cluster will be increased by 0.125 m3/min, with a coefficient of variation of 3.9% among clusters. When the perforations are nonuniformly distributed, the average injection rate per cluster will be increased by 0.101 m3/min, the fluid inflow difference coefficient of each cluster is 4.1%, and multiclusters will have a uniformly developed fracture network. This study has certain guiding significance and reference value for the balanced expansion of multifractures in horizontal wells.

A numerical study of complex fractures propagation path in naturally fractured gas shale: Reorientation, deflection and convergence

Shale gas reservoir is characterized as the naturally fractured formation, which is benefit for complex hydraulic fracture network generation. The propagation path is crucial to determine the reservoir stimulation result, and evaluate the quality of complex hydraulic fracture network. To investigate the propagation path of complex hydraulic fracture in gas shale, the hybrid combined discrete fracture network-finite element method (DFN-FEM) model is involved. Combining a linear hardening and a non-linear softening process, a non-linear traction-separation law is proposed to describe the fracture damage evolution. Validated with open-reported laboratory experiments, the hydraulic-natural fracture (HF–NF) interaction criterion is depicted under four geomechanical and injection factors. Based on a field-scale model of Sichuan basin shale gas reservoir, the complex hydraulic fractures propagation process is simulated with rock deformation and stress shadow. Several propagation path indexes are defined with fracture morphology to discuss the effect of representative geomechanical, injection and multi-clustering parameters. The results show that the tension fractures are predominant to hydraulic fractures propagation path and shear the natural fractures, due to the combined influence of natural fractures network and interference between clusters. The horizontal stress contrast and the injection fluid viscosity is governing to the propagation path and morphology, rather than the friction coefficient and injection rate. Multi-clustered hydraulic fractures converge into a dominant fracture due to the attraction with a short clusters-spacing, while the exclusion is observed along the propagation path with the increase of clusters number.

Simulation and optimization of fracture pattern in temporary plugging fracturing of horizontal shale gas wells

Horizontal well-staged fracturing is a key technology for efficient shale gas production. However, stress shadows between clusters make it difficult to synchronize the initiation and expansion of hydraulic fractures in multi-cluster fracturing. Mine practice has shown that the use of temporary plugging fracturing can promote the balanced expansion of the multi-fractures. This study establishes a numerical model for fracture-opening temporary plugging fracturing based on the three-dimensional discrete lattice method. Then, the impacts of perforation cluster spacing, stress difference, temporary plugging timing, amount of temporary plugging balls (TPBs), and temporary plugging times on the expansion pattern of multi-fractures were simulated. Additionally, the effectiveness of temporary plugging was further verified by laboratory experiments and mine site experiments. The result shows that, decreasing the cluster spacing can significantly increase the extension range of hydraulic fractures, but the uneven propagation of fractures is severe. Meanwhile, the fracture volume differentiation coefficient gradually increased with the increase of the stress difference. When the temporary plugging timing is 2/3 of the overall fracturing duration, the fracture clusters expand evenly and the fracture volume differentiation coefficient reaches the minimum value. Moreover, as the quantity of TPBs increases, the fracture volume differentiation coefficient first decreases and then increases. Finally, to increase the effectiveness of temporary plugging fracturing, the times of temporary plugging should be minimized. The results of this research can help optimize temporary plugging fracturing in shale gas reservoirs.

Unstable propagation of hydraulic fractures under varying well spacing and initiation sequence of multiple horizontal wells considering shear stress shadows

PurposeMulti-well hydrofracturing is an important technology to create new fractures and expand existing fractures to increase reservoir permeability. The propagation morphology of the fracture network is affected by the disturbance between the fractures initiation sequences and spacings between adjacent wells. However, it remains unclear how well spacing and initiation sequences lead to fracture propagation, deflection and connection.Design/methodology/approachIn this study, the thermal-hydro-mechanical coupling effect in the hydrofracturing process was considered, to establish a finite element-discrete element model of multistage hydrofracturing in a horizontal well. Using typical cases, the unstable propagation of hydraulic fractures in multiple horizontal wells was investigated under varying well spacing and initiation sequences. Combined with the shear stress shadow caused by in situ stress disturbed by fracture tip propagation, the quantitative indexes of fracture propagation such as length, volume, displacement vector, deflection and unstable propagation behavior of the hydrofracturing fracture network were analyzed.FindingsThe results show that the shear stress disturbance caused by multiple hydraulic fractures is a significant factor in multi-well hydrofracturing. Reducing the spacing between multiple wells increases the stress shadow area and aggravates the mutual disturbance and deflection between the fractures. The quantitative analysis results show that a decrease of well spacing reduces the total length of hydraulic fractures but increases the total volume of the fracture; compared with sequential and simultaneous fracturing, alternate fracturing can effectively reduce stress shadow area, alleviate fracture disturbance and generate larger fracture propagation length and volume.Originality/valueThe numerical models and results of the unstable propagation and stress evolution of the hydraulic fracture network under thermal-hydro-mechanical coupling obtained in this study can provide useful guidance for the evaluation and design of rock mass fracture networks in deep unconventional oil and gas reservoirs.

An XFEM-based CZM Numerical Strategy for Modeling Hydraulic Fracture Propagation under Different Fracturing Schemes

Segmented and cluster fracturing can improve the efficiency of volume stimulation in shale reservoirs and reduce construction costs. It is important to clarify the propagation characteristics of hydraulic fractures and stress interference under different fracturing techniques to optimize the process of clustered and staged fracturing. For this purpose, we have developed a 2D XFEM-based CZM hydraulic fracturing model. The capability of this model was validated by analytical solutions and then used to study the propagation paths of hydraulic fractures and the characteristics of stress interference under simultaneous fracturing, sequential fracturing, zipper fracturing and multi-cluster fracturing. The results show that in simultaneous fracturing, the middle cluster is compressed by the external position clusters, and the opening width of hydraulic fractures is reduced. In sequential fracturing, the fracture that first initiates create an additional stress field that inhibits the propagation distance of subsequent fractures and the propagation path of hydraulic fractures is also affected in the stress shadow region. Zipper fracturing can effectively alleviate stress interference between multiple fractures, and internal fractures can also propagate a certain distance. In multi-cluster fracturing, the fluid rate into the internal fractures may be limited, and fracture propagation is also limited by stress interference. Therefore, it is necessary to optimize the parameters of clusters to ensure that all clusters can initiate fractures normally. The research results are important for the parameter optimization of clustered and staged fracturing, especially for well factory fracturing mode.

Study of the Impact of Hard Rock Pillar Behavior on the Raise Caving Mining System

Raise caving is a novel mining method with an active stress control approach, which is suitable for deep mining environments. The application of raise caving is investigated for LKAB’s Kiruna mine. This mining method consists of two different phases. In the de-stressing phase, inclined de-stressing slots are created with a minimum amount of infrastructure and long-raise bore holes. The de-stressing slots provide stress shadows for subsequent large scale mining activities. These slots are separated by massive pillars, with width to height ratios of up to 10 and a length of several hundreds of meters, which are required to control stresses and seismicity and prevent hangingwall caving. Due to the stress redistribution in the mine, pillars and abutment areas become highly stressed. In the so-called “production phase”, which follows the de-stressing phase, large scale mineral extraction is conducted. As pillars are highly stressed after the de-stressing phase, it is important to de-stress them in the production phase to be able to extract them in a safe manner. Overall, pillars play a decisive role for the success of the raise caving mining method. Hence, studies on pillars and their impact on the raise caving mining method are of great importance. The first part of the contribution outlines the importance of pillars in the raise caving mining method on a conceptual basis. Numerical simulations for different mine layouts and different pillar behavior are then conducted to study the impact of pillar behavior on the system. The stress redistribution in the mining system and the infrastructure stability, with the help of the RCF-value, are analyzed. For this purpose, simulations with a linear elastic material behavior are a well-suited method. Consequently, the de-stressing of the pillar due to crushing cannot be analyzed with a linear elastic model. To do so, a method for de-stressing the pillar has to be implemented into the simulation. The behavior for pillars with a different width to height ratio is implemented with the help of pre-calculated stress-strain curves from available knowledge on pillar strength and behavior. Since mining is a progressive process, the sequence of mining plays an important role for the stress development in pillars and abutment areas and is also included in the simulations. Different ways for pillar de-stressing are outlined and discussed. Furthermore, the influence of stoping in the production phase is discussed in this contribution.

Evidence for a prehistoric multifault rupture along the southern Calico fault system, Eastern California Shear Zone, USA

Abstract Geomorphic mapping and paleoseismologic data reveal evidence for a late Holocene multifault surface rupture along the Calico-Hidalgo fault system of the southern Eastern California Shear Zone (ECSZ). We have identified ~18 km of continuous surface rupture along the combined Calico and Hidalgo faults in the vicinity of Hidalgo Mountain in the southern Mojave Desert. Based on the freshness of geomorphic fault features and continuity of surface expression, we interpret this feature to reflect a simultaneous paleorupture of both faults. Displacement along the paleorupture is defined by 39 field measurements to be generally pure right-slip with a mean offset of 2.3 m. Scaling relationships for this offset amount imply that the original surface rupture length may have been ~82 km (corresponding to a M7.4 earthquake) and that much of the rupture trace was erased by subsequent erosion of sandy and unconsolidated valley alluvium. Eight luminescence ages from a paleoseismic trench across the paleorupture on the Hidalgo fault bracket the timing of the most recent rupture to 0.9–1.7 ka and a possible penultimate event at 5.5–6.6 ka. This timing is generally consistent with the known earthquake clusters in the southern ECSZ based on previous paleoseismic investigations. The ages of these earthquakes also overlap with the age brackets of the most recent events on the Calico fault 42 km to the north and the Mesquite Lake fault 40 km to the south from earlier work. Based on these age constraints and the expected surface rupture length, we propose that the Calico fault system experienced a major, multifault rupture that spanned the entire length of the fault system between the historical Landers and Hector Mine ruptures but preceded these events by ~1–2 k.y. Coulomb stress change modeling shows that the Calico paleorupture may have delayed the occurrence of the Landers-Hector Mine cluster by placing their respective faults in stress shadows and may have also prevented a triggered event from occurring on the Calico fault following the historic events. This work implies that closely spaced ruptures in complex shear zones may repel each other and thereby stretch out the duration of major earthquake clusters. These results also suggest that complex multifault ruptures in the ECSZ may not follow simple, repeatable patterns.

The non-plane initiation and propagation mechanism of multiple hydraulic fractures in tight reservoirs considering stress shadow effects

Multi-cluster fracturing in horizontal wells is an important stimulation technology for unconventional tight reservoirs. The interference among multiple simultaneously growing hydraulic fractures results in a non-uniform fluid distribution into fractures and non-planar fracture geometries. In this paper, the competition mechanism between perforations under the stress shadow, the formation mechanism of complex non-plane fractures near the wellbore, and the initiation and propagation mechanism of multiple hydraulic fractures are investigated by using the 3D lattice method. Also, the effects of fracture geometry, fracture spacing and rock mechanics parameters on the stress interaction among fractures are analyzed by the dislocation theory. The results showed the complexity of fracture initiation near the wellbore and the low efficiency of the perforation initiation in the case of spiral perforation, due to a strong interaction between perforations. However, these initial micro-cracks will eventually coalesce to be a macroscopical fracture which perpendicular to the direction of minimum principal stress. The study indicated that stress interaction and fracture propagation is significantly affected by inclined well orientation. The hydraulic fracture is more likely to deflect and propagate non-uniformly with the increasing width of hydraulic fracture, the decreasing spacing between perforation clusters and the increasing rock modulus. When the horizontal principal stress difference is small, it is obvious to cause a large deflection angle and sometimes furcation of fractures. This study can provide a theoretical basis and technical guidance for hydraulic fracturing design in tight reservoirs.

Numerical analysis of unstable propagation of three-dimensional parallel hydraulic fractures induced by interferences of adjacent perforation clusters and thermal diffusion

PurposeThe purpose of this study is to investigate the unstable propagation of parallel hydraulic fractures induced by interferences of adjacent perforation clusters and thermal diffusion. Fracture propagation in the process of multistage fracturing of a rock mass is deflected owing to various factors. Hydrofracturing of rock masses in deep tight reservoirs involves thermal diffusion, fluid flow and deformation of rock between the rock matrix and fluid in pores and fractures.Design/methodology/approachTo study the unstable propagation behaviours of three-dimensional (3D) parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion, a 3D engineering-scale numerical model is established under different fracturing scenarios (sequential, simultaneous and alternate fracturing) and different perforation cluster spacings while considering the thermal-hydro-mechanical coupling effect. Stress disturbance region caused by fracture propagation in a deep tight rock mass is superimposed and overlaid with multiple fractures, resulting in a stress shadow effect and fracture deflection.FindingsThe results show that the size of the stress shadow areas and the interaction between fractures increase with decreasing multiple perforation cluster spacing in horizontal wells. Alternate fracturing can produce more fracture areas and improve the fracturing effect compared with those of sequential and simultaneous fracturing. The larger the temperature gradient between the fracturing fluid and rock matrix, the stronger the thermal diffusion effect, and the effect of thermal diffusion on the fracture propagation is significant.Originality/valueThis study focuses on the behaviours of the unstable dynamic propagation of 3D parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion. Further, the temperature field affects the fracture deflection requires could be investigated from the mechanisms; this paper is to study the unstable propagation of fractures in single horizontal well, which can provide a basis for fracture propagation and stress field disturbance in multiple horizontal wells.

A wellbore-fracture coupled fracturing model to simulate non-uniform fracture propagation under multiple clusters of fracturing

Multiple clusters of fracturing within one stage have been widely used in the unconventional reservoir production. However, the non-uniform fracture propagation under multiple clusters of fracturing has not yet fully been understood, due to the fluid flow in the wellbore being neglected in the fracturing model. In view of this, a wellbore-fracture coupled fracturing model was established to simulate fracture non-uniform propagation under multiple clusters of fracturing. In this model, the governing equation was firstly given based on the pressure continuity and flow conservation, to obtain the flow distribution in each fracture. Then, equations of fracture propagation, fracture height growth and stress shadow were combined to determine the fracture geometric parameters. Substituting fracture geometric parameters into the governing equation, the wellbore-fracture coupled fracturing model was finally solved. The proposed model was validated by a ABAQUS cohesive elements numerical by comparing the fracture parameters, respectively considering conditions of wellbore-fracture coupling and non-wellbore-fracture coupling, within a maximum deviation that did not exceed 6.14%. Using the proposed model, the parametric analyses were performed, including energy-related parameters and wellbore-related parameters. For energy-related parameters, with the increase of surface energy density of rock and the minimum principal stress, the fracture length and height decreased, while the fracture width increased to some extent. In addition, with the increase of pumping rate of fracturing fluid, the fracture length, height and width increased significantly. For wellbore-related parameters, with the decrease of diameter of perforation and perforation number as well as the increase of wellbore roughness coefficient and viscosity of fracturing fluid and cluster distance, the flow distribution in each fracture and the injection pressure became more uniform and the non-uniform propagation of each fracture was reduced, but fracture dimensions were simultaneously decreased.

Propagation of multiple hydraulic fractures in a transversely isotropic shale formation

Shale anisotropy can lead to deviated patterns of hydraulic fractures in multi-stage hydraulic fracturing (MSHF) operations, significantly hindering hydrocarbon production. Such deviation usually occurs in formations where the induced fractures interfere with natural bedding planes or where the stress shadow is created. In this work, the elastic behavior of a transversely isotropic shale rock during MSHF is investigated using the extended finite element method (XFEM) in conjunction with the cohesive zone model (CZM) in ABAQUS. In comparison to the linear elastic fracture mechanics approach, the CZM considers the plasticity and softening effects at the fracture tip, and therefore, leads to a more accurate prediction of fracture geometry. The XFEM model is capable of simulating fractures with an arbitrary path without requiring re-meshing. The 2D numerical model is first verified against the Kristianovich-Geertsma-de Klerk (KGD) analytical solutions. Five injection clusters in a single fracturing stage are simulated to analyze the effects of the material isotropy, the dip angle of shale bedding, and the fracture spacing on the geometry of multiple hydraulic fractures. The transversely isotropic poroelasticity model predicts narrower and longer hydraulic fractures than the isotropic poroelasticity model. The bedding dip angle plays a crucial role in the deviation and the shape of multiple hydraulic fractures. Increasing the dip angle from zero to 90° results in an increase in the average fracture width and an increase-peak-decrease trend in the fracture length. A strong correlation is observed between the fracture spacing and the fracture geometry, and a spacing of 75 m is considered optimal because it results in no discernible stress shadow at all dip angle cases.

Induced hydraulic fractures in underground block caving mines using an extended finite element method

Block caving has become an attractive underground rock mining method that requires effective preconditioning of the orebody to initiate the progressive rock collapse by its weight. Hydraulic fracturing is commonly used in cave mining as a preconditioning method to induce artificial fractures in the orebody rock mass. This paper presents the numerical model of hydraulic fracture propagation in underground caving mines. An extended finite element method based on phantom nodes is adopted to simulate the propagation of multiple fractures along arbitrary paths. A poroelastic constitutive model governs the behavior of orebody rock mass, while a cohesive zone model controls the hydraulic fracture propagation. The adopted method is validated against analytical solutions for penny-shaped hydraulic fracture. The stress shadowing effect on hydraulic fracturing is investigated using representative rock properties from the “El Teniente mine”, obtained by calibrating a hydraulic fracturing field test. Several analyses of multiple hydraulic fractures considering a sequential fracturing scheme are simulated to investigate the influence of in-situ stresses, fracture spacing, injection flow rate, and Young's modulus and permeability of the matrix. The numerical results show that small fracture spacing, in-situ stress, and rock permeability locally change the principal stress magnitude, resulting in a more extensive fracture propagation. Also, the injection of new fractures induces stress shadows that reinitiate the propagation of the previous ones. This behavior is reduced by increasing the fracture spacing and rock permeability. Finally, this paper provides insights into the main parameters that affect fracture extension, which can be used to optimize the preconditioning process of underground block caving mines.

Seismic potential in the southeastern margin of Bayanhar block after 2017 Jiuzhaigou earthquake, China – insight from stress evolution and earthquake probability estimation

The southeastern margin of the Bayanhar block (BHB) is located at the junction of the Bayanhar block and the southern China block (SCB). Strong earthquakes occurred frequently in this region because of the intensive tectonic movement. The stress changes caused by strong earthquakes and the observed background seismicity can be used to forecast strong earthquake probability in this region. Therefore, we construct a 3D (three Dimension) viscoelastic finite element model that includes the complex fault system, inhomogeneous medium, tectonic stress, and gravity to simulate the evolutionary stress field when using the observed Global Positioning System (GPS) vectors as the boundary conditions. In addition, we calculate the strong earthquake probability based on the calculated stress and a Poisson probability distribution. The stress evolution result shows the Xianshuihe fault (XSHF), the Huya fault (HYF) and the southern segment except for the Yaan County of Longmenshan fault (LMSF) are located in the stress enhancement area indicating high seismic potential. However, the Minjiang fault (MJF) is located in the stress shadow area. After the Lushan and Jiuzhaigou earthquakes, there is still a high possibility of strong earthquakes in the MJF, HYF, and LMSF zone, according to the strong earthquake probability result.

A criterion for a hydraulic fracture crossing a natural fracture in toughness dominant regime and viscosity dominant regime

Hydraulic fracturing is an efficient stimulation technology in the process of unconventional reservoir development, and the hydraulic fracture morphology directly affected oil and gas recovery. In this paper, we proposed a new criterion based on linear elastic fracture mechanics (LEFM) to predict the intersection behavior of hydraulic fracture (HF) and natural fracture (NF) with non-orthogonal angle. The new criterion considered the coupling effects of the fluid flow, stress shadow, and poroelastic response, and was validated with published analytical criteria and laboratory tests. Sensitivity analysis results indicated that an HF tends to cross NF under conditions of short HF half-length, high friction coefficient, high fracturing fluid viscosity and high fracture toughness. In addition, high principal stress difference inhibited the crossing behavior when the intersection angle was less than the transition angle, the HF would be arrested or divert along NF.

The Impact of Formation Anisotropy and Stresses on Fractural Geometry—A Case Study in Jafurah’s Tuwaiq Mountain Formation (TMF), Saudi Arabia

Multi-stage hydraulic fracturing (MsHF) is the main technology to improve hydrocarbon recovery from shale plays. Associated with their rich organic contents and laminated depositional environments, shales exhibit transverse isotropic (TI) characteristics. In several cases, the lamination planes are horizontal in shale formations with a symmetric axis that are vertical to the bedding plane; hence, shale formations are known as transverse isotropic vertical (TIV) rocks. Ignoring the TIV nature of shale formations leads to erroneous estimates of in situ stresses and consequently to inefficient designs of fractural geometry, which negatively affects the ultimate recovery. The goal of this study is to investigate the effects of TIV medium characteristics on fractural geometry, spacing, and stress shadow development in the Jurassic Tuwaiq Mountain formation (TMF) in the Jafurah basin, which is a potential unconventional world-class play. This formation is the main source for prolific Jurassic oil reservoirs in Saudi Arabia. On the basis of a petrophysical evaluation in the Jafurah basin, TMF exhibited exceptional unconventional gas characteristics, such as high total organic content (TOC) and low clay content, and it was in the proper maturity window for oil and gas generation. The unconventional Jafurah field covers a large area that is comparable to the size of the Eagle Ford shale play in South Texas, and it is planned for development through multi-stage hydraulic fracturing technology. In this study, analytical modeling was performed to estimate the fractural geometry and in situ stresses in the anisotropic medium. The results show that the Young’s modulus anisotropy had a noticeable impact on fractural width, whereas the impact of Poisson’s ratio was minimal. Moreover, we investigated the impact of stress anisotropy and other rock properties on the stress shadow, and found that a large stress anisotropy could result in fractures being positioned close to one another or theoretically without minimal fractural spacing concerns. Additionally, we estimated the fractural aspect ratio in different propagation regimes and observed that the highest aspect ratio had occurred in the fractural toughness-dominated regime. This study also compares the elastic properties and confirms that TMF exhibited greater anisotropic properties than those of Eagle Ford. These findings have practical implications for field operations, particularly with regard to the fractural geometry and proppant placement.

An unequal fracturing stage spacing optimization model for hydraulic fracturing that considers cementing interface integrity

Determining reasonable fracturing stage spacing is the key to horizontal well fracturing. Different from traditional stage spacing optimization methods based on the principle of maximum stimulated reservoir volume, in this paper, by considering the integrity of the wellbore interface, a fracture propagation model was established based on displacement discontinuity method and the competition mechanism of multifracture joint expansion, leading to the proposal of an unequal stage spacing optimization model. The results show that in the first stage, the interfacial fractures spread symmetrically along the axis of the central point during that stage, while in the second and subsequent stages, the interfacial fractures of each cluster extend asymmetrically along the left and right sides. There are two kinds of interface connectivity behaviour: in one, the existing fractures first extend and connect within the stage, and in the other, the fractures first extend in the direction close to the previous stage, with the specific behaviour depending on the combined effect of stress shadow and flow competition during hydraulic fracture expansion. The stage spacing is positively correlated with the number of fractures and Young’s modulus of the cement and formation and is negatively correlated with the cluster spacing and horizontal principal stress difference. The sensitivity is the strongest when the Young’s modulus of the cement sheath is 10–20 GPa, and the sensitivity of the horizontal principal stress difference is the weakest.

Numerical Study on Simultaneous Propagation of Multiple Fractures: A Method to Design Nonuniform Perforation and In-Stage Diversion

Summary The uneven propagation of multifractures is a key factor restricting production growth due to stress shadow and heterogeneity. To date, limited-entry fracturing techniques, nonuniform perforation, and in-stage diversion have been commonly used to promote even multifracture growth. In this study, a fully coupled multiple pseudo-3D (P3D) fracture simulator has been developed to examine the competitive propagation of multifractures during multicluster fracturing in a horizontal well. The present model considers stress interaction among multiple fractures, perforation erosion, fluid distribution among clusters, and in-stage diversion. The results of the model are validated against the reference data. Using the model, a series of numerical simulations are performed to investigate multifracture propagation with nonuniform perforation and in-stage diversion fracturing. We estimate the value of stress interaction for different fractures and time based on the approximate solution of Perkins-Kern-Nordgren (PKN) fracture in the viscosity-dominated regime and improve the dimensionless parameter that characterizes the competition between stress interaction and perforation friction. The fluid distributes evenly when the dimensionless parameter is less than unity (perforation friction is larger than stress interference). Based on this dimensionless parameter, a method to design nonuniform perforation and in-stage diversion is proposed. Results show that in the case of homogeneous in-stage stress, the perforation parameters should be selected under the condition that the dimensionless parameter is less than unity. In the case of heterogeneous in-stage stress and based on the perforation parameters selected under homogeneous stress conditions, the perforation holes in the high-stress cluster should be increased, making the reduction of perforation friction equal to the value of the in-stage stress heterogeneity. The stress heterogeneity can be balanced by decreasing the perforation friction of the high-stress clusters. In this way, nonuniform perforation under heterogeneous in-stage stress conditions can be designed quantitatively without numerical simulation. For in-stage diversion treatment, a method to design the number of ball sealers is proposed based on the results of nonuniform perforation, and only several or even zero groups of simulation are necessary to find the optimal number of ball sealers. A series of numerical simulations shows that the proposed design method is reliable and achieves a satisfactory result in an actual field case. The results can be helpful for nonuniform perforation and in-stage diversion design for multicluster fracturing in a horizontal well.