Differential Stress Conditions Research Articles

Rock strength weakening subject to principal stress rotation: Experimental and numerical investigations

During the construction and operation of gas storage reservoirs, changes in the principal stress direction can induce fracture propagation under conditions of lower differential stress, potentially leading to failure in the surrounding rock. However, the weakening of strength due to pure stress rotation has not yet been investigated. Based on fracture mechanics, an enhanced Mohr-Coulomb strength criterion considering stress rotation is proposed and verified with experimental and numerical simulations. The micro-damage state and the evolution of the rock under the pure stress-rotation condition are analyzed. The findings indicate that differential stress exceeding the crack initiation stress is a prerequisite for stress rotation to promote the development of rock damage. As the differential stress increases, stress rotation is more likely to induce rock damage, leading to a transition from brittle to plastic failure, characterized by wider fractures and a more complex fracture network. Overall, a negative exponential relationship exists between the stress rotation angle required for rock failure and the differential stress. The feasibility of applying the enhanced criterion to practical engineering is discussed using monitoring data obtained from a mine-by tunnel. This study introduces new concepts for understanding the damage evolution of the surrounding rock under complex stress paths and offers a new theoretical basis for predicting the damage of gas storage reservoirs.

Analysis of Primary and Secondary Metabolites, Physical Properties, Antioxidant and Antidiabetic Activities, and Chemical Composition of Rosmarinus officinalis Essential Oils under Differential Water Stress Conditions.

This study investigated the effects of varying water stress levels on Rosmarinus officinalis essential oils (EO). Three samples (S1, S2, and S3) were cultivated under different stress levels (40, 60, and 80%). Increased water stress led to changes in primary and secondary metabolites, EO contents, and physical properties. Antioxidant activity varied, with S2 exhibiting the highest IC50 value. In terms of antidiabetic activity, S2 showed robust α-amylase inhibition, while S3 displayed a commendable influence. For α-galactosidase inhibition, S3 had a moderate effect, and S2 stood out with increased efficacy. Gas chromatography-mass spectrometry analysis revealed stress-induced changes in major compounds. The study enhances the understanding of plant responses to water stress, with potential applications in antioxidant therapy and diabetes management. The findings emphasize the importance of sustainable water management for optimizing the EO quality in its various uses.

Anomalous transport and upscaling in critically-connected fracture networks under stress conditions

Anomalous transport in fractured rocks is of high importance for numerous research fields and applications in hydrogeology and has been widely studied in the last decades. This phenomenon is due to the structural heterogeneities of fractured rocks and the high contrast between the fractures and matrix properties. At the same time, the fracture properties in terms of fracture density and geometrical characteristics are related to in-situ stress conditions that impact the connectivity of the system and the distributions of fracture aperture and length, including the creation of new cracks when the differential stress conditions are strong enough. In order to understand how all these features impact the observed anomalous transport, we study the role of in-situ stress in mass transport through a two-dimensional fractured rock. The fracture network is based on a real outcrop with a connectivity state around the percolation threshold, over which we simulate stress-dependent fracture deformation and propagation, and perform hydrodynamic transport through the deformed rock mass. The impact of the changes in aperture and the creation of new cracks on transport behavior is evaluated for various stress scenarios and reproduced with upscaled representations of transport processes. We also consider matrix diffusion as a source of anomalous transport and demonstrate that this process can be incorporated into the proposed upscaled models. Results showed that traditional upscaling methods with space-Lagrangian velocities description capture well the Gaussian-like breakthrough curves (BTCs) under low-stress ratio conditions, but fail under high-stress ratio conditions with multiple-peak early-times BTCs. To characterize the emergence of strong anomalous transport, we extend the Random Walk model Directed by a Markov Process with space-Lagrangian velocity sampling by incorporating multiple transition matrices conditioned by different initial velocity states. This new transport upscaling model shows high accuracy in predicting complex transport behaviors in critically connected fracture networks.

On the b-value dependency of injection-induced seismicity on geomechanical parameters

Variability in the b-value, which describes the frequency distribution of earthquake magnitudes, is usually attributed to variations in differential stress in the setting of natural and laboratory earthquakes. However, differential stress is unlikely to explain b-value variations on the reservoir scale of injection-induced seismicity cases where significant differential stress variability can hardly be expected. We investigate the responsible geomechanical parameters for the b-value reduction observed in injection-induced seismicity at the Basel EGS field in Switzerland, for which a measured in-situ stress model and fault orientations of numerous microseismic events are available. We estimate the shear and normal stresses along faults, differential stress, pore pressure increase at failure, and the Coulomb failure stress, for each event. Event magnitude and shear stress display the most systematic and clear correlation between each other, while other parameters do not show a clear correlation with event magnitude. We further examine the relationship between the b-value and these geomechanical parameters. We discover that the b-value systematically decreases with increasing shear stress. Again, other geomechanical parameters do not show a clear correlation with the b-value. We conclude that b-value variability is explained by variations in shear stress in the injection-induced seismicity setting, where near constant differential stress conditions are expected. Furthermore, we observe that b-value reduction with time also correlates with an increasing number of events along faults having high shear stress, which strongly supports our conclusions. Thus, we discovered a profound physical mechanism behind b-value variation in injection-induced seismicity beyond general understanding of b-value variation.

Permeability enhancement by CO2 injection and chelating agent stimulation for creating geothermal reservoirs in granite

Existing research indicates that to create geothermal reservoirs using CO2 injection, additional stimulation methods are necessary. N, N-bis(carboxymethyl)-L-glutamic acid (GLDA) injection has been predicted to increase the permeability of CO2 injection-induced cloud-fracture networks (CFNs) and could serve as an additional stimulation method. Nevertheless, the influence of differential stress, flow geometry, and scale on the characteristics of permeability enhancement by GLDA injection is yet to be clarified. Accordingly, this study experimentally elucidated the permeability enhancement characteristics of injecting a chelating agent in fractured granite under differential stress conditions as an additional method for creating geothermal reservoirs using CO2 injection. GLDA injection experiments were conducted on fractured-granite samples under conventional- and true-triaxial stress states under varying differential stress and pH conditions. Regardless of the differential stress and pH conditions, rock deformation and acoustic emission (AE) were negligible during the chelating agent flow-through experiments on the fractured samples, whereas similar permeability enhancement factors were achieved within the same duration. Thus, stress did not affect the permeability enhancement by chelating agent injections. The permeability enhancement factors were inferred to be high near the injection borehole because of the high viscosity of the solution. Therefore, reservoir stimulation should be conducted using low-concentration chelating agent solutions at constant injection pressures. The study provides insights into the stimulation strategies for creating geothermal reservoirs using CO2 injection.

Model of shear strength of ultra-deep fractured sandstone considering fracture morphology

Ultra-Deep fractured tight sandstone gas reservoir, the hotpot unconventional petroleum resources, has been the subject of investigation recently. Due to the presence of natural fractures, drilling in ultra-deep fractured tight sandstone may cause complicated wellbore instabilities, which resulted in a substantial challenge to the efficient exploitation and production of tight gas resources. In order to understand the rock mechanical properties of the ultra-deep fractured tight sandstone under shear stress, tight sandstone core samples were artificially shear-fractured, the 3D characteristics of the fractures were reconstructed by CT scanning, and the fracture aperture and roughness characteristics were systematically evaluated. Simultaneously, triaxial shear strength tests were conducted to evaluate the mechanical properties of fractured rock subjected to varying confining pressures. Considering the contact relationship of the fracture surface during shearing, two indexes of average effective shear angle and contact area ratio were proposed to correct the fracture roughness, and a new fracture shear strength model was constructed, which served as the failure criterion for the fractured formation. The results show that the intact rock has a high compressive strength and can only collapse under conditions of substantial differential stress. Consequently, shear failure of fracture ought to be the primary source of wellbore instability. The fracture aperture's spatial distribution is irregular and conforms to a Gaussian distribution. A clear anisotropy in the fracture roughness is present, and there is less roughness along the initial shear failure path and more roughness perpendicularly. With an increase in normal stress, the fracture's peak shear strength rises, while the friction angle steadily falls. The innovative model's accuracy in predicting shear strength is higher than that of the weak-surface model and the JRC-JCS model.

Study on the Phase Transition from Quartz to Coesite under High Temperature and High Pressure

Quartz is an important component of the Earth. In this study, experiments were conducted at temperatures between 600 to 700 °C, confining pressures between 1.5 and 1.8 GPa, and differential stress conditions. It was found that coesite production is closely related to differential stress, reaction time, and reaction temperature, with coesite formation being a multifactorial coupling process.

Velocity Structure and Deep Earthquakes beneath the Kinnaur, NW Himalaya: Constraints from Relocated Seismicity and Moment Tensor Analysis

Abstract The optimum 1D velocity model is calculated for the Kinnaur sector of the NW Himalaya utilizing the arrival time information of the local earthquakes (137 no.) recorded with 12 broadband seismic network within the azimuthal gap of ≤180°. This optimum 1D velocity model is a five-layer model and ranges from the surface to 90 km in the shallow mantle. P velocity varies from 5.5 km/s to 8.6 km/s in the crust and upper mantle, and S-wave velocity varies between 3.2 km/s and 4.9 km/s for the same range. When we relocated the earthquakes with the Joint Hypocenter Determination program incorporating the optimum 1D velocity model, it resulted in a lower RMS residual error of 0.23 s for the hypocenter locations compared to initial hypo71 locations. A total of 1274 P and 1272 S arrival times were utilized to compute station delays. We observed positive variations in P-station delays from -0.19 s below the PULG station to 0.11 s below the SRHN station. Similarly, for S-station delays, we observed negative delays at each individual site from -0.65 s at LOSR station to -0.16 s at the SRHN station. This large variation in P- and S-station delays corresponds to the 3D nature of the subsurface below the Kinnaur Himalaya. The relocated seismicity is clustered along the STD fault at sub-Moho and Moho depths ranging between 40 km and 80 km. The seismicity distribution aligned across the strike of the STD and along the strike of the Kaurik-Chango fault (KCF) can be attributed to the cross-fault interactions of the KCF and the STD fault in the area. We also observed bimodal depth distribution of seismicity in the Higher and Tethys Himalayas. The occurrence of earthquakes down to a depth of ~0-40 km and 50-80 km in the study area can be interpreted in terms of stress contribution from interseismic stress loading associated with the India-Eurasia collision tectonics. The presence of hypocentres in the shallow mantle at 120 km depth highlights the strength of the mantle, which seems to be deforming in a brittle manner below the region. The computed focal mechanisms exhibit generally the flexing of the Indian plate below the Lesser Himalaya with shear parallel to the strike of the MCT and extension orthogonal to it. This study shows deformation over the entire crust and shallow upper mantle levels, with differential stress conditions. Thus, we can consider the crust and the shallow upper mantle down to depths of 120 km to be seismogenic in nature and is capable of producing the microseismicity beneath the Kinnaur Himalaya.

A Griggs apparatus upgrade for stress-controlled testing of geological material at high temperature and pressure

The Griggs apparatus is a triaxial piston-cylinder instrument used in deformation experiments of geological material at temperatures up to 1200 °C and confining pressures up to 3 GPa. Currently, most Griggs apparatuses can carry out deformation experiments only at constant displacement rate. As a result, few experimental studies have explored other geologically-relevant deformation scenarios. We present supplemental instrumentation and software that enables Griggs apparatus users to carry out deformation experiments at controlled differential stress conditions. The add-on instrument includes a feedback loop mechanism that regulates the imposed differential stress on the sample and a data acquisition system that allows for real-time display of mechanical data in units of stress and displacement. We demonstrate the application of this instrument through two deformation experiments at constant differential stress on (1) an aluminum cylinder at room temperature and (2) a quartz aggregate at 850 °C, both at ~1 GPa confining pressure. These experiments show that the instrument can reliably control the imposed differential stress on the sample throughout the deformation. Applications of the instrument can be extended beyond constant differential stress to more sophisticated stress paths (e.g., stress pulse, stress ramp) or to maintain true strain rates by accounting for anticipated geometrical changes in the sample during deformation.

An experimental investigation on stress-induced cracking mechanisms of a volcanic rock

In underground excavations, different failure features can be induced by complex geological stresses. Therefore, many researchers have investigated rock behaviour and failure mechanisms under high-stress conditions. This study investigated the different failure characteristics to determine the stress-induced cracking mechanisms. Accordingly, a series of tests were performed on a volcanic rock (rhyodacite) under one- to three-dimensional stress states. The results indicated that the samples exhibited different failure characteristics/modes under different stress states. Under 1-D and 2-D compression, the rock exhibited unstable brittle failure induced by tensile cracking (Mode I fracture). Under axisymmetric triaxial stress (σ1 > σ2 = σ3 > 0), the rock exhibited stable failure, and as σ3 increased, the failure mode transitioned from Mode I fracture to Mode II fracture to distributed cataclastic failure. In contrast, under a three-dimensional differential stress state (σ1 > σ2 > σ3 > 0), the risk of unstable failure increased with increasing σ2, and the rock exhibited localized shear failure (Mode II fracture). Based on the acoustic emission (AE)-based cracking classification method, further studies were also conducted on the failure mechanism. Finally, based on the energy release and cracking propagation, the mechanism of the σ2 effect on unstable failure was assessed.

Geomechanical characterization of sedimentary basins using tectonic stress and strain

We examine whether the combination of tectonic stress and strain is useful in characterizing tectonic condition and geomechanics of sedimentary basins. We compile measured stress, pore pressure, and mechanical rock property data from six major sedimentary basins worldwide. We find that the measured horizontal principal stresses are always higher than the theoretically calculated stresses based on a simple uniaxial compaction poroelastic equation, known as Eaton’s model. From this we conclude that there are always external tectonic stresses in seemingly stable basins. We extract these external tectonic stresses by subtracting the theoretically calculated horizontal stresses from the measured horizontal stresses, and relate them to the tectonic strains estimated by the linear elastic constitutive model. Given the external tectonic stresses and associated strains, we interpret the tectonic conditions of individual basins from the tectonic differential stress and strain conditions. The six basins exhibit distinct tectonic stress and strain regimes, which can be related generally to geological processes such as brittle and ductile deformation. The results show that combining tectonic stress and strain is useful in characterizing sedimentary basins.

Variability of orographic architecture of Indo-Burmese Ranges (NE India): constraints from morphotectonic and lineament analysis

Activeness of the tectonic and related sub-surface processes control the surface features that lead to variations in topography and lithostratigraphy. To understand the role of active tectonics in shaping the topography, morphotectonic and lineament studies are important. In this study, geological categorization has helped understand the orogenic evolution of the Indo-Burmese Range (IBR), NE India. This is an arcuate hill range that shows many unique topographic characteristics that incited to categorise the entire IBR into different tectonically active domains: Northern (Changlang district of Arunachal Pradesh); Naga Hills; Cachar and Manipur; and Southern (Mizoram). The Northern and Southern domains are more active than the others. Lineament analysis also indicates the presence of active features in the region with NW–SE, NE–SW, ESE–WNW trends are being common. The Northern and Naga Hills domains have mostly E–W younger lineaments whereas the Cachar and Manipur domains rather show N–S younger trends. The Southern Mizoram domain shows a dominance of older N–S lineaments with younger NW–SE lineaments. These variations result from differential stress conditions, i.e. Indian Plate movement and westward stress from the Burma Plate. This study shows how overall variations in tectonic settings can be related to the orogenic evolution.

Effect of rock anisotropy on wellbore stresses and hydraulic fracture propagation

Using a newly developed 2D numerical model based on the displacement discontinuity method (DDM) and the fictitious stress method (FSM), hydraulic fracture propagation near and away from a horizontal wellbore in anisotropic mudstones is studied. In addition to elastic anisotropy, the effect of fracture toughness anisotropy on hydraulic fracture propagation is included and fluid flow in fractures is fully coupled with rock deformation. Simulations show wellbore failure pressure, fracture trajectory, and near wellbore fracture apertures are significantly affected by elastic and fracture toughness anisotropy. A simple plane strain analytical solution might indicate that near wellbore fracture opening is enhanced in vertically transversely isotropic (VTI) rock. However, near wellbore fracture turning in a rock with high fracture toughness anisotropy results in severe constriction of fracture apertures. This effect becomes more severe with increase in fracture toughness anisotropy and perforation misalignment angle. Simulations of multiple hydraulic fractures from horizontal wellbores suggest that fracture lengths and apertures are affected by their orientation with respect to the directions of elastic symmetry. The spatial extent of the induced normal stresses perpendicular to the fracture surface increases when the fracture is aligned with the direction of least Young's modulus. The larger spatial extent of induced stresses in anisotropic rock leads to early termination of the fractures emanating from the inner perforation clusters, resulting in fracture networks with dominant outer fractures. In the presence of fracture toughness anisotropy, the fractures deviate towards the plane of least fracture toughness under low differential stress conditions.

Dilatancy as a measure of fracturing development in the process of rock damage

Abstract Dilatancy understood as inelastic volume changes of rock under conditions of differential stress not only foreshadows brittle rock failure [1, 2, 3], preceding such phenomena as earthquakes or mining-induced rockbursts, but also defines the kinematics of rock deformation [4, 5]. This article shows that there is a quantitative relationship between the dilatancy occurring at different levels of rock load and the development of fracturing that accompanies the process of rock degradation. Based on the mechanical laboratory test results of Wustenzelleer fine-grained sandstone, the article presents analyses of plastic volume changes in rock samples and a certain measure of fracture development accompanying the process of their degradation. Thanks to the characteristics obtained through mechanical tests with unloading, the inelastic volumetric strain of the samples was established, and the scalar damage variable (CDM - continuum damage mechanics approach) was determined at various load levels. These results demonstrated the relationship between dilatancy and rock stiffness changes describing the development of fracturing. Three load intervals were determined, in which the nature of the analysed phenomena, i.e. dilatancy and damage describing the development of cracks, undergoes significant changes. The highest intensity of both phenomena was obtained in the post-critical load range, between the ultimate strength limit and the residual strength of the samples, in which rock samples undergo the process of degradation the most. Obtained dependencies allow the correlation to be taken into account in damage mechanics models describing the variable stiffness of rocks in the loading process.

Analysis of injection-induced shear slip and fracture propagation in geothermal reservoir stimulation

Permeability enhancement via shear slip is commonly accepted as the main stimulation mechanism. However, the mechanism of permeability increase appears to have been understood to be limited to shear dilation and perceived to exclude the propagation in tensile and shear mode of the natural fractures that experience slip. This has led to the claims of the discovery of a new stimulation mechanism, namely, stimulation via wing crack propagation. The root cause of the misconceptions is likely the inability to model natural fracture propagation and coalescence. However, natural fracture propagation in general and wing cracks in particular are to be viewed as an integral part of the shear slip stimulation mechanism because shear slip increases the stress-intensity at the fracture tips, potentially leading to fracture propagation. In an effort to better illustrate the underlying mechanisms in the geothermal reservoir stimulation process, a displacement discontinuity (DD) model is developed and used to simulate secondary crack propagation associated with natural fracture slip. The model uses Mohr-Coulomb joint (contact) elements and rigorously accounts for fracture propagation. The model is applied to explore the conditions conducive to shear and tensile mode fracture propagation. When natural fractures undergo shear slip due to direct and indirect water injection, out-of-plane wing (tensile) cracks form and propagate at injection pressures below the minimum in-situ stress level and turn toward the maximum in-situ stress direction as they grow longer. It was found in our results that the injection pressure is stabilized at approximately the minimum in-situ stress level. The secondary cracks form as wing cracks and/or shear cracks. The predominance of wing cracks and their lengths and propagation paths were found to be controlled by the relative value of differential and mean stresses, natural fracture length, as well as rock and natural fracture frictional properties. In deeper geothermal reservoir with relatively low differential stress conditions and/or high mean stress levels, the shear crack propagation could play a major role in fracture network formation and permeability enhancement.

Application of Dimensional Analysis to Project Laboratory Scale Numerical Modelling Prescribed Hydraulic Fracturing Results to Field Scales

Hydraulic fracturing has been applied in the cave mining industry with the purpose of re-creating an orebody rock mass condition that is suitable for caving. Prescribed hydraulic fracturing was proposed in a previous study as a supplement to the conventional hydraulic fracturing strategy. In this paper; dimensional analysis is used to project laboratory scale numerical modelling results to field scales in order to study the applicability of creating prescribed hydraulic fractures (PHFs) under field conditions. The results indicate that field scale PHFs are feasible if the stress shadows of the pre-located fractures are properly utilized. Water can be used to create the pre-located fractures that induce the local stress change in a low differential stress state; and the use of more proppants and a shorter pre-located fracture spacing lead to PHFs propagating more quickly towards the pre-located fractures. For field condition having high differential stresses, more viscous fluid must be used to create the pre-located fractures in order to enhance the stress shadows. In this case, a shorter pre-located fracture spacing does not necessarily result in the re-orientation of PHFs towards the pre-located fractures and may even lead to unsatisfactory pre-conditioning. A sufficiently high pre-located fracture net pressure to the differential stress ratio (close to 0.5) is the prerequisite for creating PHFs.

Ca-rich garnets and associated symplectites in mafic peraluminous granulites from the Gföhl Nappe System, Austria

Abstract. Mafic peraluminous granulites associated with the mantle-derived peridotites of the Dunkelsteiner Wald provide evidence of the tectono-metamorphic evolution of the Gföhl Nappe System, Austria. They contain the primary assemblage garnet + Al-rich clinopyroxene + kyanite. Large Ca- and Mg-rich garnets are embedded in a granoblastic matrix of Al-rich clinopyroxene, Ca-rich plagioclase and minor hornblende. They were partially replaced by different generations of symplectites: (a) corundum + sapphirine + spinel + plagioclase formed around kyanite inclusions, (b) orthopyroxene + spinel + plagioclase ± hornblende formed at their rims and (c) clinopyroxene + orthopyroxene + spinel + plagioclase ± hornblende formed within cracks. Large garnets show complex compositional structure comprising several repeatedly occurring garnet types, which are characterized by specific compositions. The areal extent and the cross-cutting relations observed in element distribution maps allowed for the derivation of the relative timing of the formation of the different garnet types. The compositional features of the garnets indicate post-formational modification by intra-crystalline diffusion and metasomatic agents. The garnet composition isopleths in equilibrium assemblage diagrams are in line with compositions modification as indicated by the element distribution maps. They confirm the deviation of composition from equilibrium for all garnet types. Furthermore, at least the youngest garnet types show evidence of metasomatic (Fe + Mg) loss affecting their Ca content. Pressure–temperature (P–T) estimates are based on equilibrium assemblage diagrams that reproduce satisfactorily the observed mineral assemblages and measured mineral compositions. Criteria for checking the existence of preserved equilibrium compositions are suggested. The results call into question the invariability of the assumption that the Ca content and/or zoning in garnet preserves primary P–T information from garnet growth in every case. Recrystallization and compositional readjustment of the reactive garnet volume during symplectite formation led to the development of pronounced, secondary diffusion-induced zoning profiles overprinting the different garnet types and post-dating the complex garnet compositional structure. The primary assemblage is stable between 760 and 880 °C and pressures > 11 kbar. The bulk composition of the crack symplectites is almost isochemical to the oldest, broken-down garnet type. These symplectites were formed above 730 °C and pressures between 5 and 7.5 kbar. The rocks studied underwent more or less isothermal decompression from pressures above 11 to ∼ 6 kbar at temperatures of about 800 °C. Crack and rim symplectites were formed after decompression during the early stage of approximately isobaric cooling under conditions of low differential stress. Due to limited availability of fluids promoting symplectite formation, the timescale of symplectite formation calculated from secondary diffusion profiles associated with crack symplectites is shown to be geologically very short (< 0.5 ka).

Experimental Investigation of Formation Rock Drillability under Complex Bottom Hole Stress Conditions

The rock drillability measurements are usually conducted at atmospheric pressure, the results deviate heavily from the real Rock Drillability under complex bottom hole stress conditions. In this paper, a newly devised rock drillability testing apparatus with a cone bit is utilized to investigate the rock drillability under various bottom hole differential pressures and different effective stress conditions. The experimental results showed that both bottom hole differential pressure and effective stress have great impact on rock drillability: the smaller the bottom hole differential pressure, the smaller the formation rock drillability index and thus the easier to break the rock; the greater the effective stress, the larger the formation rock drillability index and thus the harder to crush the rock. Mathematical statistics methods have been applied to analyze the correlation between rock drillability index and bottom hole differential pressure, effective stress as well as the rock drillability index at atmospheric pressure. This model provided an important approach to forecast rock drillability under various bottom hole differential pressure conditions based on rock drillability measured at atmospheric pressure. Compared to directly testing under bottom hole stresses, this method is easier to conduct and cost saving.

Transpressional folding and associated cross-fold jointing controlling the geometry of post-orogenic vein-type W-Sn mineralization: examples from Minas da Panasqueira, Portugal

The world-class W-Sn Panasqueira deposit consists of an extensive, subhorizontal vein swarm, peripheral to a late-orogenic greisen cupola. The vein swarm consists of hundreds of co-planar quartz veins that are overlapping and connected laterally over large distances. Various segmentation structures, a local zigzag geometry, and the occurrence of straight propagation paths indicate that they exploited a regional joint system. A detailed orientation analysis of the systematic joints reveals a geometrical relationship with the subvertical F2 fold generation, reflecting late-Variscan transpression. The joints are consistently orthogonal to the steeply plunging S0–S2 intersection lineation, both on the regional and the outcrop scale, and are thus defined as cross-fold or ac-joints. The joint system developed during the waning stages of the Variscan orogeny, when already uplifted to an upper-crustal level. Veining reactivated these cross-fold joints under the conditions of hydraulic overpressures and low differential stress. The consistent subperpendicular orientation of the veins relative to the non-cylindrical F2 hinge lines, also when having an inclined attitude, demonstrates that veining did not occur during far-field horizontal compression. Vein orientation is determined by local stress states variable on a meter-scale but with the minimum principal stress consistently subparallel to fold hinge lines. The conspicuous subhorizontal attitude of the Panasqueira vein swarm is thus dictated by the geometry of late-orogenic folds, which developed synchronous with oroclinal buckling of the Ibero-Armorican arc.

Dynamic conductivity of proppant-filled fractures

A common challenge in matching the production from hydraulically fractured wells is related to changes in conductivity of propped fractures due to changes in the stress configuration. In this paper, we investigate the dynamic nature of fracture conductivity, by evaluating the permeability and width of a propped fracture segment at variable differential stress conditions. We combine the Discrete Element Method (DEM) and the Lattice Boltzmann Model (LBM) to simulate the evolution of a fracture segment filled with proppant and to evaluate the related fracture conductivity at various stress states. An ensemble of spherical proppant particles is generated and compacted under a specified confining stress via DEM to generate an initial propped fracture segment. A representative elementary volume (REV) of the proppant pack is then extracted from the DEM representation and used for fluid flow simulations. LBM is used to calculate the detailed single-phase flow field, at the pore-scale, and allows for calculation of permeability. In-situ conditions are then simulated by applying confining and differential stress on the REV via DEM. The differential stress is gradually increased on the REV, to simulate a reduction in the pore pressure due to production, until the formation of shear band(s) is observed and fracture failure begins. Permeability of the proppant pack, from LBM simulations, combined with the fracture aperture, from DEM simulations at different differential stress levels, allow us to determine the dynamic conductivity of the propped fracture segment. From a range of proppant-size distributions, we demonstrate that a well-graded proppant pack outperforms a poorly graded pack in maintaining the fracture conductivity over a broader range of differential stress conditions. Furthermore, we demonstrate that a well-graded proppant pack keeps the fracture segment open over a larger range of differential stress states.