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.

Mixed-mode fracture behavior in deep shale reservoirs under different loading rates and temperatures

In the last years,shale gas has gradually substituted oil and coal as the main sources of energy in the world.Compared with shallow shale gas reservoirs,deep shale is characterized by low permeability,low porosity,strong heterogeneity,and strong anisotropy.In the process of multi-cluster fracturing of horizontal wells,the whole deformation process and destruction modes are significantly influenced by loading rates.In this investigation,the servo press was used to carry out semi-circular bend(SCB)mixedmode fracture experiments in deep shales(130,160,190℃)with prefabricated fractures under different loading rates(0.02,0.05,0.1,0.2 mm/min).The fracture propagation process was monitored using acoustic emission.The deformation characteristics,displacementeload curve,and acoustic emission parameters of shale under different loading rates were studied during the mixed-mode fracture propagation.Our results showed that during the deformation and fracture of the specimen,the acoustic emission energy and charge significantly increased near the stress peak,showing at this point the most intense acoustic emission activity.With the increase in loading rate,the fracture peak load of the deep shale specimen also increased.However,the maximum displacement decreased to different extents.With the increase in temperature,the effective fracture toughness of the deep shale gradually decreased.Also,the maximum displacement decreased.Under different loading rates,the deformation of the prefabricated cracks showed a nonlinear slow growthelinear growth trend.The slope of the linear growth stage increased with the increase in loading rate.In addition,as the loading rate increased,an increase in tension failure and a decrease in shear failure were observed.Moreover,the control chart showing the relationship between tension and the shear failure under different temperatures and loading rates was determined.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

Adsorption behaviors of avian immunoglobulins and purification of immunoglobulin Y from chicken serum with mixed-mode resins

The importance of immunoglobulin Y(IgY) as a specific antibody equivalent to mammalian immunoglobulin G(IgG) is well recognized. However, production of highly purified IgY is still difficult due to the lack of specific purification methods. In this study, adsorption behaviors of Ig Y on four mixed-mode resins with functional ligands of 4-mercatoethyl-pyridine(MEP), 2-mercapto-1-methyli-midazole(MMI), 5-aminobenzi-midazole(ABI) and tryptophan-5-aminobenzi-midazole(W-ABI) were evaluated. The results showed that high adsorption ratio were found at p H 6.0–7.0 with little adsorption under acidic conditions. The resin with ABI ligand was then used to separate IgY from immunized chicken serum. An efficient process with Ig Y purity of 95% and recovery of 90% was developed after optimization of loading and elution p H and injection volume. The biological activity of the purified Ig Y was fully maintained. These results indicated that mixed-mode chromatography with specially-designed ligands has great potential for the separation of Ig Y from crude feedstock.

Development of X-FEM methodology and study on mixed-mode crack propagation

The extended finite element method（X-FEM） is a novel numerical methodology with a great potential for using in multi-scale computation and multi-phase coupling problems. The algorithm is discussed and a program is developed based on X-FEM for simulating mixed-mode crack propagation. The maximum circumferential stress criterion and interaction integral are deduced. Some numerical results are compared with the experimental data to prove the capability and efficiency of the algorithm and the program. Numerical analyses of sub-interfacial crack growth in bi-materials give a clear description of the effiect on fracture made by interface and loading condition.

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.

MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation analysis.The domain is divided automatically into sub-domains based on Voronoi cells,which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path.For each increment of the crack extension,the meshless method is applied to carry out a stress analysis of the cracked structure.The J-integral,which can be decomposed into mode Ⅰ and mode Ⅱ for mixed-mode crack,is used for the evaluation of the stress intensity factors(SIFs).The crack-propagation direction,predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method.The meshless results agree well with the experimental ones,which validates the accuracy and efficiency of the method.

A 90° mixed-mode twisted nematic liquid-crystal-on-silicon with an insulating protrusion structure

A 90°mixed-mode twisted nematic liquid-crystal-on-silicon(90°-MTN LCoS) with protrusion located between the adjacent pixels is proposed to reduce the effect of fringing field. The influence of the protrusion with different widths from0.5 μm to 0.9 μm and different heights from 0.3 μm to 0.7 μm is investigated. The results demonstrate that the invalid pixel region width can be reduced by 31.5% via using the protrusion with the suitable width and height compared with no protrusion case, which provides a higher display quality, such as the higher reflectance and contrast ratio.

Characteristic Tensor for Evaluation of Singular Stress Field Under Mixed-Mode Loadings

A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius.It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters.Therefore,it can be used to estimate stress intensity factors(SIFs)for cracks of arbitrary shape subjected to multiaxial stress loads.A characteristic tensor can also be used to estimate SIFs for kinked cracks.This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters.Consequently,a single straight crack and a kinked crack of finite length existing in a twodimensional,infinite isotropic elastic body in a plane stress state,were considered to investigate the properties of the characteristic tensor under mixed-mode loadings.To demonstrate the practical utility of the characteristic tensor,the stress distribution obtained through finite element analysis(FEA)was used to estimate mixed-mode SIFs,and the values of estimated SIFs were compared with those obtained using an analytical solution.Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values.This indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips,and can be employed to estimate values of fracture-mechanics parameters,such as SIFs.Owing to its simplicity,the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios.The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.

Autonomous Development Strategies for College English Teachers in a Mixed-mode Learning Community

At present,the improvement of the quality of higher education and the improvement of the professional ability and comprehensive quality of college students all depend on the education level and discipline professional ability of teachers in colleges and universities.In the new era of educational reform and development,university teachers also need to continuously learn and progress in order to adapt to changes in the educational environment and the update of the knowledge system.Nowadays,the construction and development of the mixed-mode learning community environment is becoming one of the effective ways for college teachers to improve their learning.From the perspective of the significance of autonomous development of college English teachers in the context of mixed-mode learning community,the current situation and other issues,this article expounds the strategies that promote the autonomous development of college English teachers in the context of mixed-mode learning community to improve the professional quality of college English teachers.

Experimental Study on Mixed-Mode(Ⅰ–Ⅱ)Fracture Toughness of Freshwater Ice

Ⅰn recent years,the issue of aircraft icing has gained widespread recognition.The breaking and detachment of dynamic ice can pose a threat to flight safety.However,the shedding and fracture mechanisms of dynamic ice are unclear and cannot meet the engineering needs of ice-shedding hazard assessment.Therefore,studying the fracture toughness of ice bodies has extremely important practical significance.To address this issue,this article uses a centrally cracked Brazilian disk(CCBD)specimen to measure the pure mode Ⅰ toughness and pure mode Ⅱ fracture toughness of freshwater ice at different loading rates.The mixed-mode(Ⅰ–Ⅱ)fracture characteristics of ice are discussed,and the experimental results are compared and analyzed with the theoretical values of the generalized maximum tangential stress(GMTS)criterion considering the influence of T-stress.The results indicated that as the loading rate increases,the pure mode Ⅰ toughness and pure mode Ⅱ fracture toughness of freshwater ice decrease,and the fracture toughness of freshwater ice is more sensitive to the loading rate.Ⅰn terms of fracture criteria,the theoretical value of the ratio of pure mode Ⅱ fracture toughness to pure mode Ⅰ fracture toughness based on the GMTS criterion is in good agreement with the experimental value,while the theoretical value based on the maximum tangential stress(MTS)criterion deviates significantly from the experimental value,indicating that the GMTS criterion considering the influence of T-stress can better predict the experimental results.

Comparison of mixed-mode forced-convection solar dryer with and without stainless wire mesh in solar collector

A mixed-mode forced-convection solar dryer(MMFCSD)is a device that utilizes both direct and indirect solar energy.The solar col-lector,which stores thermal energy for indirect solar uses,is an essential component of the dryer.Unfortunately,the thermal effi-ciency of this device is generally low.In this study,a technique was employed to improve the heat transfer of the solar collector in a MMFCSD.The technique involved adjusting the air flow pattern into a swirling flow to disturb the thermal boundary layer on the absorber plate under forced convection by using stainless wire mesh.The experiment was conducted under actual conditions and bananas were used as the drying sample.The experimental results of the thermal efficiency of the solar collector(ƞ_(solar))and the drying efficiency(ƞ_(drying))are presented.The results indicated that the air outlet temperature andƞsolar of the solar collector with stainless wire mesh were higher than the case without stainless wire mesh,reaching a maximum temperature of 46.22°C and 37.97°C,and average ƞ_(solar) of 0.26±0.02 and 0.14±0.01,respectively.The MMFCSD with stainless wire mesh had a higher ƞ_(drying) than the case without stain-less wire mesh,with values of 0.048±0.004 and 0.039±0.003,respectively,resulting in an~23.07%increase.This was attributed to the air swirling flow through the stainless wire mesh and the heat accumulation in the drying chamber,which led to an increase in the drying chamber temperature from 54.03°C to 63.60°C,an increase in the effective moisture diffusivity from 7.28×10^(-7) to 1.19×10^(-6) m^(2)/s and a decrease in the drying time of 5 h 30 min.However,further research is needed to investigate the quality of the dried sam-ples and their economic value.

Simulation of 3D fracture propagation under I-II-III mixed-mode loading

Fracture propagation under mixed-mode loading conditions prevails in many natural geological processes and deep engineering projects,while the corresponding numerical simulation is very challenging in rock mechanics,especially in 3D cases.In most previous studies,the complexity of 3D fracture geometry was over-simplified,and model III loading was often not considered.In this study,we propose to use an efficient stress-based Sch€ollmann criterion combined with Displacement Discontinuity Method(DDM)to model 3D fracture propagation under arbitrary I+II+III mixed-mode loading conditions.A novel curve-smoothing algorithm is developed to smoothen the fracture front during propagation,which significantly enhances the model's ability in dealing with complex 3D fracture geometry.In particular,we adopt two different solution schemes,namely staggered and monolithic,to simulate mode I fracture propagation in the case of hydraulic fracturing.The accuracy,efficiency and convergency of the two solution schemes are compared in detail.Our research findings suggest that the degree of coupling between fracture aperture and fluid pressure in hydraulic fracturing lies somewhere between one-way and two-way,which favors the staggered solution scheme.To further test our new model,we provide three additional numerical examples associated with 3D fracture propagation under various mixed-mode loading conditions.Our model shows excellent performance in efficiently locating the new fracture front and reliably capturing the complex 3D fracture geometry.This study provides a generic algorithm to model high-fidelity 3D fracture propagation without simplifying fracture geometry or loading conditions,making it widely applicable to fracture-propagation-related problems.

Preparation of copolymer-grafted mixed-mode resins for immunoglobulin G adsorption

The mixed-mode resins for protein adsorption have been prepared by a novel strategy, copolymer grafting. Specially, the copolymer-grafted resins CG-MA with two functional groups, 5-amino-benzimidazole (ABI) and methacryloxyethyltrimethyl ammonium chloride (METAC), have been prepared through surfaceinitiated activator generated by electron transfer for atom transfer radical polymerization of METAC and glycidyl methacrylate (GMA), followed by a ring-open reaction to introduce ABI. The charge and hydrophobicity of CG-MA resins could be controlled by manipulating the addition of METAC and GMA/ABI. Besides, METAC and ABI provided positive effects together in both protein adsorption and elution: dynamic binding capacity of human Immunoglobulin G (hlgG) onto CG-M-A resin with the highest ligand ratio of METAC to ABI is 46.8 mg-g 1 at pH 9 and the elution recovery of hlgG is 97.0% at pH 5. The separation experiment showed that purity and recovery of monoclonal antibody from cell culture supernatant are 96.0% and 86.5%, respectively, indicating that copolymer-grafted mixed-mode resins could be used for antibody purification.

A reversed phase/hydrophilic interaction/ion exchange mixed-mode stationary phase for liquid chromatography

A reversed phase (RP)/hydrophilic interaction (HILIC)/ion exchange (IEX) mixed tri-mode stationary phase (TMSP) has been prepared via a divergent synthesis scheme starting from propylamine on silica then by amine-epoxy reactions with 1,4-butanedioldiglycidyl ether and tertiary amines (N,Ndimethyldecylamine, DMDA). Its retention mechanism was found to follow RP/HILIC/IEX mixed-mode.The stop-flow test revealed that TMSP had good compatibility with 100% aqueous mobile phase. It demonstrated effective separation towards several kinds of compounds or drug molecules and their counterions within a single run.

Formation mechanism of partial stacking faults by incompletemixed-mode phase transformation: A case study of Fe-Ga alloys

Partial stacking faults(PSFs) formed by incomplete mixed-mode phase transformation have been found to exhibit unfixed slip distance of closely-packed planes unlike those of the deformation-induced stacking faults(SFs) with fixed distance. Though engineering PSFs can yield appealing properties, such as the enhanced damping capacity, understanding of the interaction between lattice distortion and atomic diffusion and their influences on forming PSFs is still far from being clear. Herein we performed a case study on aged Fe-Ga alloy that undergoes a mixed-mode phase transformation from body-centered cubic(BCC)to ordered face-centered cubic(FCC). The TEM investigations showed that the faulted {111}-FCC distance of the PSFs is shorter than a/6<112> of the typical {111}-<112> SFs in deformed FCC materials and the PSFs have disordered Fe and Ga arrangements. Further studies revealed that such PSFs will not be completely dissociated at FCC twin boundaries(TBs) even after long term isothermal aging. Consequently,the formation of PSFs can be ascribed to the transformation-dependent atomic ordering and lattice shear strain of the parent BCC lattice, where the diffusion-controlled glides of the PSFs-associated dislocations will accelerate atomic diffusions due to the dislocation-pipe effect along <112>-FCC direction, but may hinder the atomic diffusions across the {111}-FCC TBs due to the retarding effect. This study may add important insight into the defects process during mixed-mode phase transformation and broaden the knowledge of the interaction between concurrently-happened lattice distortion and atomic diffusion.

Two-dimensional MOF Cu-BDC nanosheets/ILs@silica core-shell composites as mixed-mode stationary phase for high performance liquid chromatography

Here,silica microspheres were decorated with two-dimensional metal-organic frameworks(2 D MOFs)nanosheets and ionic liquids,and evaluated as the mixed-mode stationary phase for chromatographic separation.The ionic liquids were used to assist the synthesis of 2 D MOFs nanosheets,and also acted as adhesives among the nanosheets and silica.In contrast with the 2 D MOFs-based column without ionic liquids and commercial columns,the prepared column exhibited enhanced chromatographic separation performance for partially hydrophilic compounds such as alkaloids,sulfonamides and antibiotics,etc.In addition to excellent chromatographic repeatability and stability,it has also been verified that the composites could be easily and repeatedly prepared.The relative standard deviation of the retention time of the same type of analyte between the three batches of materials was ranging from 0.21%to 1.7%.In short,these results indicated that the synthesized composites were promising separation material for liquid chromatography,which made it possible to broaden the application of 2 D MOFs in the field of chromatography.

Compliance-based testing method for fatigue crack propagation rates of mixed-modeⅠ-Ⅱcracks

Mixed-mode I-II crack-based fatigue crack propagation(FCPⅠ-Ⅱ)usually occurs in engineering structures;however,no theoretical formula or effective compliance test methods have been established for FCPI-IIto date.For mixed-mode I-II flawed components,based on the principle of mean-value energy equivalence,we propose a theoretical method to describe the relationship between material elastic parameters,geometrical dimensions,load(or displacement),and energy.Based on the maximum circumferential stress criterion,we propose a uniform compliance model for compact tensile shear(CTS)specimens with horizontal cracks deflecting and propagating(flat-folding propagation)under different loading angles,geometries,and materials.Along with an innovative design of the fixture of CTS specimens used for FCPI-IItests,we develop a new compliancebased testing method for FCPⅠ-Ⅱ.For the 30Cr2Ni4MoV rotor steel,the FCP rates of modeⅠ,modeⅡ,and mixed-modeⅠ-Ⅱcracks were obtained via FCP tests using compact tension,Arcan,and CTS specimens,respectively.The obtained da/d N versusΔJ curves of the FCP rates are close.The loading angleαand dimensionless initial crack length a0/W demonstrated negligible effects on the FCP rates.Hence,the FCP rates of mode I crack can be used to predict the residual life of structural crack propagation.

Facile Fabrication of Polymeric Ionic Liquid Grafted Porous Polymer Monolith for Mixed-Mode High Performance Liquid Chromatography

A novel polymeric ionic liquid grafted porous polymer monolith has been facilely fabricated for mixed-mode chromatography.The column is prepared from poly(glycidyl methacrylate-co-ethylene dimethacrylate)monolith through hydrolyzation of the epoxy moieties into hydroxyl groups,followed by“grafting from”polymerization of ionic liquid of 1-vinyl-3-butylimidazolium chloride.Successful modification is characterized by scanning electron microscope,infrared spectroscopy,elemental analysis and mercury intrusion porosimetry.The HPLC performance of developed column is evaluated by separating acidic vitamin B analytes,neutral steroids and basic aromatic amines in mixed-mode chromatography on a single column,respectively.The ionic liquid affords the monolith with both enhanced separation ability and improved column efficiency.

Low-power SiPM readout BETA ASIC for space applications

The BETA application-specific integrated circuit(ASIC)is a fully programmable chip designed to amplify,shape and digitize the signal of up to 64 Silicon photomultiplier(SiPM)channels,with a power consumption of approximately~1 mW/channel.Owing to its dual-path gain,the BETA chip is capable of resolving single photoelectrons(phes)with a signal-to-noise ratio(SNR)>5 while simultaneously achieving a dynamic range of~4000 phes.Thus,BETA can provide a cost-effective solution for the readout of SiPMs in space missions and other applications with a maximum rate below 10 kHz.In this study,we describe the key characteristics of the BETA ASIC and present an evaluation of the performance of its 16-channel version,which is implemented using 130 nm technology.The ASIC also contains two discriminators that can provide trigger signals with a time jitter down to 400 ps FWHM for 10 phes.The linearity error of the charge gain measurement was less than 2%for a dynamic range as large as 15 bits.