Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

Hydraulic properties and drought response of a tropical bamboo (Cephalostachyum pergracile)

Bamboo plants are an essential component of tropical ecosystems,yet their vulnerability to climate extremes,such as drought,is poorly understood due to limited knowledge of their hydraulic properties.Cephalostachyum pergracile,a commonly used tropical bamboo species,exhibited a substantially higher mortality rate than other co-occurring bamboos during a severe drought event in 2019,but the underlying mechanisms remain unclear.This study investigated the leaf and stem hydraulic traits related to drought responses,including leaf-stem embolism resistance(P50leaf;P50stem) estimated using optical and X-ray microtomography methods,leaf pressure-volume and water-releasing curves.Additionally,we investigated the seasonal water potentials,native embolism level(PLC) and xylem water source using stable isotope.We found that C.pergracile exhibited strong resistance to embolism,showing low P50leaf,P50stem,and turgor loss point,despite its rapid leaf water loss.Interestingly,its leaves displayed greater resistance to embolism than its stem,suggesting a lack of effective hydraulic vulnerability segmentation(HVS) to protect the stem from excessive xylem tension.During the dry season,approximately 49% of the water was absorbed from the upper 20-cm-deep soil layer.Consequently,significant diurnal variation in leaf water potentials and an increase in midday PLC from 5.87±2.33% in the wet season to 12.87±4.09%in the dry season were observed.In summary,this study demonstrated that the rapid leaf water loss,high reliance on surface water,and a lack of effective HVS in C.pergracile accelerated water depletion and increased xylem embolism even in the typical dry season,which may explain its high mortality rate during extreme drought events in 2019.

Unraveling the hydraulic properties of loess for landslide prediction:A study on variations in loess landslides in Lanzhou,Dingxi,and Tianshui,China

Loess has distinctive characteristics,leading to frequent landslide disasters and posing serious threats to the lives and properties of local re sidents.The involvement of water repre sents a critical factor in inducing loess landslides.This study focuses on three neighboring cities sequentially situated on the Loess Plateau along the direction of aeolian deposition of loess,namely Lanzhou,Dingxi,and Tianshui,which are densely populated and prone to landslide disasters.The variations in hydraulic properties,including water retention capacity and permeability,are investigated through Soil Water Characteristic Curve(SWCC)test and hydraulic conductivity test.The experimental findings revealed that Tianshui loess exhibited the highest water retention capacity,followed by Dingxi loess,while Lanzhou loess demonstrated the lowest water retention capacity.Contrastingly,the results for the saturated permeability coefficient were found to be the opposite:Tianshui loess showed the lowest permeability,whereas Lanzhou loess displayed the highest permeability.These results are supported and analyzed by scanning electron microscopy(SEM)observation.In addition,the water retention capacity is mathematically expressed using the van Genuchten model and extended to predict unsaturated hydraulic properties of loess.The experimental results exhibit a strong accordance with one another and align with the regional distribution patterns of disasters.

Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

A review of reservoir damage during hydraulic fracturing of deep and ultra-deep reservoirs

Deep and ultra-deep reservoirs have gradually become the primary focus of hydrocarbon exploration as a result of a series of significant discoveries in deep hydrocarbon exploration worldwide.These reservoirs present unique challenges due to their deep burial depth(4500-8882 m),low matrix permeability,complex crustal stress conditions,high temperature and pressure(HTHP,150-200℃,105-155 MPa),coupled with high salinity of formation water.Consequently,the costs associated with their exploitation and development are exceptionally high.In deep and ultra-deep reservoirs,hydraulic fracturing is commonly used to achieve high and stable production.During hydraulic fracturing,a substantial volume of fluid is injected into the reservoir.However,statistical analysis reveals that the flowback rate is typically less than 30%,leaving the majority of the fluid trapped within the reservoir.Therefore,hydraulic fracturing in deep reservoirs not only enhances the reservoir permeability by creating artificial fractures but also damages reservoirs due to the fracturing fluids involved.The challenging“three-high”environment of a deep reservoir,characterized by high temperature,high pressure,and high salinity,exacerbates conventional forms of damage,including water sensitivity,retention of fracturing fluids,rock creep,and proppant breakage.In addition,specific damage mechanisms come into play,such as fracturing fluid decomposition at elevated temperatures and proppant diagenetic reactions at HTHP conditions.Presently,the foremost concern in deep oil and gas development lies in effectively assessing the damage inflicted on these reservoirs by hydraulic fracturing,comprehending the underlying mechanisms,and selecting appropriate solutions.It's noteworthy that the majority of existing studies on reservoir damage primarily focus on conventional reservoirs,with limited attention given to deep reservoirs and a lack of systematic summaries.In light of this,our approach entails initially summarizing the current knowledge pertaining to the types of fracturing fluids employed in deep and ultra-deep reservoirs.Subsequently,we delve into a systematic examination of the damage processes and mechanisms caused by fracturing fluids within the context of hydraulic fracturing in deep reservoirs,taking into account the unique reservoir characteristics of high temperature,high pressure,and high in-situ stress.In addition,we provide an overview of research progress related to high-temperature deep reservoir fracturing fluid and the damage of aqueous fracturing fluids to rock matrix,both artificial and natural fractures,and sand-packed fractures.We conclude by offering a summary of current research advancements and future directions,which hold significant potential for facilitating the efficient development of deep oil and gas reservoirs while effectively mitigating reservoir damage.

Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method(LB-DEM).This study starts with a preliminary proppant settling test,from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture.In the established workflow to investigate proppant flowback,a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress.When a pressure gradient is applied to drive the fluid-particle flow,a critical aperture-to-diameter ratio of 4 is observed,above which the proppant pack would collapse.The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture,while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture.The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures,which also supports an optimised proppant size selection for hydraulic fracturing operations.

Extreme massive hydraulic fracturing in deep coalbed methane horizontal wells:A case study of the Linxing Block,eastern Ordos Basin,NW China

Deep coal seams show low permeability,low elastic modulus,high Poisson’s ratio,strong plasticity,high fracture initiation pressure,difficulty in fracture extension,and difficulty in proppants addition.We proposed the concept of large-scale stimulation by fracture network,balanced propagation and effective support of fracture network in fracturing design and developed the extreme massive hydraulic fracturing technique for deep coalbed methane(CBM)horizontal wells.This technique involves massive injection with high pumping rate+high-intensity proppant injection+perforation with equal apertures and limited flow+temporary plugging and diverting fractures+slick water with integrated variable viscosity+graded proppants with multiple sizes.The technique was applied in the pioneering test of a multi-stage fracturing horizontal well in deep CBM of Linxing Block,eastern margin of the Ordos Basin.The injection flow rate is 18 m^(3)/min,proppant intensity is 2.1 m^(3)/m,and fracturing fluid intensity is 16.5 m^(3)/m.After fracturing,a complex fracture network was formed,with an average fracture length of 205 m.The stimulated reservoir volume was 1987×10^(4)m^(3),and the peak gas production rate reached 6.0×10^(4)m^(3)/d,which achieved efficient development of deep CBM.

Hydraulic fracturing behaviors of shale under coupled stress and temperature conditions simulating different burial depths

Fracture propagation in shale under in situ conditions is a critical but poorly understood mechanical process in hydraulic fracturing for deep shale gas reservoirs. To address this, hydraulic fracturing experiments were conducted on hollow double-wing crack specimens of the Longmaxi shale under conditions simulating the ground surface(confining pressure σ_(cp)=0, room temperature(Tr)) and at depths of 1600 m(σ_(cp)=40 MPa, Ti=70 ℃) and 3300 m(σ_(cp)=80 MPa, high temperature Ti=110 ℃) in the study area.High in situ stress was found to significantly increase fracture toughness through constrained microcracking and particle frictional bridging mechanisms. Increasing the temperature enhances rather than weakens the fracture resistance because it increases the grain debonding length, which dissipates more plastic energy and enlarges grains to close microdefects and generate compressive stress to inhibit microcracking. Interestingly, the fracture toughness anisotropy in the shale was found to be nearly constant across burial depths, despite reported variations with increasing confining pressure. Heated water was not found to be as important as the in situ environment in influencing shale fracture. These findings emphasize the need to test the fracture toughness of deep shales under coupled in situ stress and temperature conditions rather than focusing on either in situ stress or temperature alone.

Spatiotemporal variations of sand hydraulic conductivity by microbial application methods

The spatiotemporal distributions of microbes in soil by different methods could affect the efficacy of the microbes to reduce the soil hydraulic conductivity.In this study,the specimens of bio-mediated sands were prepared using three different methods,i.e.injecting,mixing,and pouring a given microbial so-lution onto compacted sand specimens.The hydraulic conductivity was measured by constant-head tests,while any soil microstructural changes due to addition of the microbes were observed by scan-ning electron microscope(SEM)and mercury intrusion porosimetry(MIP)tests.The amount of dextran concentration produced by microbes in each type of specimen was quantified by a refractometer.Results show that dextran production increased exponentially after 5-7 d of microbial settling with the supply of culture medium.The injection and mixing methods resulted in a similar amount and uniform dis-tribution of dextran in the specimens.The pouring method,however,produced a nonuniform distri-bution,with a higher concentration near the specimen surface.As the supply of culture medium discontinued,the dextran content near the surface produced by the pouring method decreased dramatically due to high competition for nutrients with foreign colonies.Average dextran concentration was negatively and correlated with hydraulic conductivity of bio-mediated soils exponentially,due to the clogging of large soil pores by dextran.The hydraulic conductivity of the injection and mixing cases did not change significantly when the supply of culture medium was absent.

Effect mechanism of seepage force on the hydraulic fracture propagation

The flow of fluid through the porous matrix of a reservoir rock applies a seepage force to the solid rock matrix.Although the seepage force exerted by fluid flow through the porous matrix of a reservoir rock has a notable influence on rock deformation and failure,its effect on hydraulic fracture(HF)propagation remains ambiguous.Therefore,in this study,we improved a traditional fluid–solid coupling method by incorporating the role of seepage force during the fracturing fluid seepage,using the discrete element method.First,we validated the simulation results of the improved method by comparing them with an analytical solution of the seepage force and published experimental results.Next,we conducted numerical simulations in both homogeneous and heterogeneous sandstone formations to investigate the influence of seepage force on HF propagation.Our results indicate that fluid viscosity has a greater impact on the magnitude and extent of seepage force compared to injection rate,and that lower viscosity and injection rate correspond to shorter hydraulic fracture lengths.Furthermore,seepage force influences the direction of HF propagation,causing HFs to deflect towards the side of the reservoir with weaker cementation and higher permeability.

Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling(FBCM)of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging.The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis.A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid(i.e.no re-meshing).Further,multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid.The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously:initially without permeating fluids into the rock,to seed fractures uniformly and at high density in the wall rock of the wells;followed by fluid injection to propagate the seeded fracture density hydraulically.FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly.Fractures are modeled as piecewise planar based on intersections with domain elements;fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures;and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock.Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal,shallow-dipping,steeply dipping,or vertical orientation.Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design.The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells:for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures,and in situ vertical compressive stress greater than horizontal.If preexisting fractures are steeply dipping or vertical,and considering the same in situ stress condition,well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

Implications for fault reactivation and seismicity induced by hydraulic fracturing

Evaluating the physical mechanisms that link hydraulic fracturing(HF) operations to induced earthquakes and the anticipated form of the resulting events is significant in informing subsurface fluid injection operations. Current understanding supports the overriding role of the effective stress magnitude in triggering earthquakes, while the impact of change rate of effective stress has not been systematically addressed. In this work, a modified critical stiffness was brought up to investigate the likelihood, impact,and mitigation of induced seismicity during and after hydraulic fracturing by developing a poroelastic model based on rate-and-state fraction law and linear stability analysis. In the new criterion, the change rate of effective stress was considered a key variable to explore the evolution of this criterion and hence the likelihood of instability slip of fault. A coupled fluid flow-deformation model was used to represent the entire hydraulic fracturing process in COMSOL Multiphysics. The possibility of triggering an earthquake throughout the entire hydraulic fracturing process, from fracturing to cessation, was investigated considering different fault locations, orientations, and positions along the fault. The competition between the effects of the magnitude and change rate of effective stress was notable at each fracturing stage. The effective stress magnitude is a significant controlling factor during fracturing events, with the change rate dominating when fracturing is suddenly started or stopped. Instability dominates when the magnitude of the effective stress increases(constant injection at each fracturing stage) and the change rate of effective stress decreases(the injection process is suddenly stopped). Fracturing with a high injection rate, a fault adjacent to the hydraulic fracturing location and the position of the junction between the reservoir and fault are important to reduce the Coulomb failure stress(CFS) and enhance the critical stiffness as the significant disturbance of stresses at these positions in the coupled process. Therefore,notable attention should be given to the injection rate during fracturing, fault position, and position along faults as important considerations to help reduce the potential for induced seismicity. Our model was verified and confirmed using the case of the Longmaxi Formation in the Sichuan Basin, China, in which the reported microseismic data were correlated with high critical stiffness values. This work supplies new thoughts of the seismic risk associated with HF engineering.

Multistage hydraulic fracturing of a horizontal well for hard roof related coal burst control:Insights from numerical modelling to field application

Multistage hydraulic fracturing of horizontal wells(MFHW)is a promising technology for controlling coal burst caused by thick and hard roofs in China.However,challenges remain regarding the MFHW control mechanism of coal burst and assessment of the associated fracturing effects.In this study,these challenges were investigated through numerical modelling and field applications,based on the actual operating parameters of MFHW for hard roofs in a Chinese coal mine.A damage parameter(D)is proposed to assess the degree of hydraulic fracturing in the roof.The mechanisms and effects of MFHW for controlling coal burst are analyzed using microseismic(MS)data and front-abutment stress distribution.Results show that the degree of fracturing can be categorized into lightly-fractured(D≤0.3),moderately fractured(0.3<D≤0.6),well-fractured(0.6<D≤0.9),and over-fractured(0.9<D≤0.95).A response stage in the fracturing process,characterized by a slowdown in crack development,indicates the transition to a wellfractured condition.After MFHW,the zone range and peak value of the front-abutment stress decrease.Additionally,MS events shift from near the coal seam to the fractured roof layers,with the number of MS events increases while the average MS energy decreases.The MFHW control mechanisms of coal bursts involve mitigating mining-induced stress and reducing seismic activity during longwall retreat,ensuring stresses remain below the ultimate stress level.These findings provide a reference for evaluating MFHW fracturing effects and controlling coal burst disasters in engineering.

Estimation of the anisotropy of hydraulic conductivity through 3D fracture networks using the directional geological entropy

With an extension of the geological entropy concept in porous media,the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks.A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions.Compared with the traditional connectivity indexes based on the statistics of fracture geometry,the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks.According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks,the hydraulic conductivities and entropic scales in different directions both increase with spatial order(i.e.,trace length decreasing and spacing increasing)and are independent of the dip angle.As a result,the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function,which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors.

Experimental Investigation on Vertical Hydraulic Transport of Ores in Deepsea Mining

Deepsea mining has been proposed since the 1960s to alleviate the lack of resources on land.Vertical hydraulic transport of collected ores from the seabed to the sea surface is considered the most promising method for industrial applications.In the present study,an indoor model test of the vertical hydraulic transport of particles was conducted.A noncontact optical method has been proposed to measure the local characteristics of the particles inside a vertical pipe,including the local concentration and particle velocity.The hydraulic gradient of ore transport was evaluated with various particle size distributions,particle densities,feeding concentrations and mixture flow velocities.During transport,the local concentration is larger than the feeding concentration,whereas the particle velocity is less than the mixture velocity.The qualitative effects of the local concentration and local fluid velocity on the particle velocity and slip velocity were investigated.The local fluid velocity contributes significantly to particle velocity and slip velocity,whereas the effect of the local concentration is marginal.A higher feeding concentration and mixture flow velocity result in an increased hydraulic gradient.The effect of the particle size gradation is slight,whereas the particle density plays a crucial role in the transport.

Physical and numerical investigations of target stratum selection for ground hydraulic fracturing of multiple hard roofs

Ground hydraulic fracturing plays a crucial role in controlling the far-field hard roof,making it imperative to identify the most suitable target stratum for effective control.Physical experiments are conducted based on engineering properties to simulate the gradual collapse of the roof during longwall top coal caving(LTCC).A numerical model is established using the material point method(MPM)and the strain-softening damage constitutive model according to the structure of the physical model.Numerical simulations are conducted to analyze the LTCC process under different hard roofs for ground hydraulic fracturing.The results show that ground hydraulic fracturing releases the energy and stress of the target stratum,resulting in a substantial lag in the fracturing of the overburden before collapse occurs in the hydraulic fracturing stratum.Ground hydraulic fracturing of a low hard roof reduces the lag effect of hydraulic fractures,dissipates the energy consumed by the fracture of the hard roof,and reduces the abutment stress.Therefore,it is advisable to prioritize the selection of the lower hard roof as the target stratum.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Numerical analysis of hydraulic fracture propagation in deep shale reservoir with different injection strategies

Deep shale reservoirs are characterized by elevated breakdown pressures,diminished fracture complexity,and reduced modified volumes compared to medium and shallow reservoirs.Therefore,it is urgent to investigate particular injection strategies that can optimize breakdown pressure and fracturing efficiency to address the increasing demands for deep shale reservoir stimulation.In this study,the efficiency of various stimulation strategies,including multi-cluster simultaneous fracturing,modified alternating fracturing,alternating shut-in fracturing,and cyclic alternating fracturing,was evaluated.Subsequently,the sensitivity of factors such as the cycle index,shut-in time,cluster spacing,and horizontal permeability was investigated.Additionally,the flow distribution effect within the wellbore was discussed.The results indicate that relative to multi-cluster simultaneous fracturing,modified alternating fracturing exhibits reduced susceptibility to the stress shadow effect,which results in earlier breakdown,extended hydraulic fracture lengths,and more consistent propagation despite an increase in breakdown pressure.The alternating shut-in fracturing benefits the increase of fracture length,which is closely related to the shut-in time.Furthermore,cyclic alternating fracturing markedly lowers breakdown pressure and contributes to uniform fracture propagation,in which the cycle count plays an important role.Modified alternating fracturing demonstrates insensitivity to variations in cluster spacing,whereas horizontal permeability is a critical factor affecting fracture length.The wellbore effect restrains the accumulation of pressure and flow near the perforation,delaying the initiation of hydraulic fractures.The simulation results can provide valuable numerical insights for optimizing injection strategies for deep shale hydraulic fracturing.

Numerical Analysis of Perforation during Hydraulic Fracture Initiation Based on Continuous-Discontinuous Element Method

Perforation is a pivotal technique employed to establish main flow channels within the reservoir formation at the outset of hydraulic fracturing operations.Optimizing perforation designs is critical for augmenting the efficacy of hydraulic fracturing and boosting oil or gas production.In this study,we employ a hybrid finite-discrete element method,known as the continuous–discontinuous element method(CDEM),to simulate the initiation of post-perforation hydraulic fractures and to derive enhanced design parameters.The model incorporates the four most prevalent perforation geometries,as delineated in an engineering technical report.Real-world perforations deviate from the ideal cylindrical shape,exhibiting variable cross-sectional profiles that typically manifest as an initial constriction followed by an expansion,a feature consistent across all four perforation types.Our simulations take into account variations in perforation hole geometries,cross-sectional diameters,and perforation lengths.The findings show that perforations generated by the 39g DP3 HMX perforating bullet yield the lowest breakdown pressure,which inversely correlates with increases in sectional diameter and perforation length.Moreover,this study reveals the relationship between breakdown pressure and fracture degree,providing valuable insights for engineers and designers to refine perforation strategies.

Stomatal dynamics are regulated by leaf hydraulic traits and guard cell anatomy in nine true mangrove species

Stomatal regulation is critical for mangroves to survive in the hyper-saline intertidal zone where water stress is severe and water availability is highly fluctuant.However,very little is known about the stomatal sensitivity to vapour pressure deficit(VPD)in mangroves,and its co-ordination with stomatal morphology and leaf hydraulic traits.We measured the stomatal response to a step increase in VPD in situ,stomatal anatomy,leaf hydraulic vulnerability and pressure-volume traits in nine true mangrove species of five families and collected the data of genome size.We aimed to answer two questions:(1)Does stomatal morphology influence stomatal dynamics in response to a high VPD in mangroves?with a consideration of possible influence of genome size on stomatal morphology;and(2)do leaf hydraulic traits influence stomatal sensitivity to VPD in mangroves?We found that the stomata of mangrove plants were highly sensitive to a step rise in VPD and the stomatal responses were directly affected by stomatal anatomy and hydraulic traits.Smaller,denser stomata was correlated with faster stomatal closure at high VPD across the species of Rhizophoraceae,and stomata size negatively and vein density positively correlated with genome size.Less negative leaf osmotic pressure at the full turgor(πo)was related to higher operating steady-state stomatal conductance(gs);and a higher leaf capacitance(Cleaf)and more embolism resistant leaf xylem were associated with slower stomatal responses to an increase in VPD.In addition,stomatal responsiveness to VPD was indirectly affected by leaf morphological traits,which were affected by site salinity and consequently leaf water status.Our results demonstrate that mangroves display a unique relationship between genome size,stomatal size and vein packing,and that stomatal responsiveness to VPD is regulated by leaf hydraulic traits and stomatal morphology.Our work provides a quantitative framework to better understand of stomatal regulation in mangroves in an environment with high salinity and dynamic water availability.