Quantitative characterization of the brittleness of deep shales by integrating mineral content,elastic parameters,in situ stress conditions and logging analysis

Deep shale reservoirs(3500–4500 m)exhibit significantly different stress states than moderately deep shale reservoirs(2000–3500 m).As a result,the brittleness response mechanisms of deep shales are also different.It is urgent to investigate methods to evaluate the brittleness of deep shales to meet the increasingly urgent needs of deep shale gas development.In this paper,the quotient of Young’s modulus divided by Poisson’s ratio based on triaxial compression tests under in situ stress conditions is taken as SSBV(Static Standard Brittleness Value).A new and pragmatic technique is developed to determine the static brittleness index that considers elastic parameters,the mineral content,and the in situ stress conditions(BIEMS).The coefficient of determination between BIEMS and SSBV reaches 0.555 for experimental data and 0.805 for field data.This coefficient is higher than that of other brittleness indices when compared to SSBV.BIEMS can offer detailed insights into shale brittleness under various conditions,including different mineral compositions,depths,and stress states.This technique can provide a solid data-based foundation for the selection of‘sweet spots’for single-well engineering and the comparison of the brittleness of shale gas production layers in different areas.

Systematic prediction of the gas content, fractures, and brittleness in fractured shale reservoirs with TTI medium

The main objective is to optimize the development of shale gas-rich areas by predicting seismic sweet spot parameters in shale reservoirs. We systematically assessed the fracture development, fracture gas content, and rock brittleness in fractured gas-bearing shale reservoirs. To better characterize gas-bearing shale reservoirs with tilted fractures, we optimized the petrophysical modeling based on the equivalent medium theory. Based on the advantages of shale petrophysical modeling, we not only considered the brittle mineral fraction but also the combined effect of shale porosity, gas saturation, and total organic carbon(TOC) when optimizing the brittleness index. Due to fractures generally functioning as essential channels for fluid storage and movement, fracture density and fracture fluid identification factors are critical geophysical parameters for fractured reservoir prediction. We defined a new fracture gas indication factor(GFI) to detect fracture-effective gas content. A new linear PP-wave reflection coefficient equation for a tilted transversely isotropic(TTI) medium was rederived, realizing the direct prediction of anisotropic fracture parameters and the isotropic elasticity parameters from offset vector tile(OVT)-domain seismic data. Synthetic seismic data experiments demonstrated that the inversion algorithm based on the L_P quasinorm sparsity constraint and the split-component inversion strategy exhibits high stability and noise resistance. Finally, we applied our new prediction method to evaluate fractured gas-bearing shale reservoirs in the Sichuan Basin of China, demonstrating its effectiveness.

An improved method to calculate the rock brittleness index PEECR based on linear energy storage law

The peak elastic strain energy consumption ratio(PEECR)is a rock brittleness index proposed by Gong and Wang.In the present study,based on the linear energy storage law of rock under triaxial compression,a new method was proposed to calculate the PEECR.The PEECR uses a simplified method to calculate the peak elastic strain energy.To solve this problem accurately,triaxial cyclic loading-unloading compression tests were carried out on shale.Strain energy parameters were calculated from the test curves.The results show that there is a linear relationship between the elastic strain energy and input strain energy,indicating that the linear energy storage law in rock is applicable to triaxial compression state.The universality of the linear energy storage law of rock under triaxial compression is also verified by the data in the published literature.Then,the peak elastic strain energy can be accurately determined using the linear energy storage law,and the PEECR is improved based on this.Finally,the PEECR and the improved PEECR were compared using the triaxial cyclic loading-unloading compression tests on three rocks(shale,red sandstone and granite),and the improved PEECR was compared with 11 existing energy-based brittleness indexes.The results show that the improved PEECR can further reflect the rock brittleness more accurately.

Anomalous yield and intermediate temperature brittleness behaviors of directionally solidified nickel-based superalloy

A nickel-based superalloy with good corrosion resistance was fabricated by directional solidification, and its microstructure and tensile properties at elevated temperatures were investigated. Microstructure observations reveal that the γ＇ precipitates are arrayed in the y matrix regularly with some MC, Ni5Hf and M3B2 particles distributed along the grain boundary. The tensile tests exhibit that the tensile properties depend on temperature significantly and demonstrate obvious anomalous yield and intermediate-temperature brittleness （ITB） behavior. Below 650℃, the yield strength decreases slightly but the ultimate tensile strength almost has no change. When the temperature is between 650 ℃ and 750 ℃, the yield and ultimate tensile strengths rise rapidly, and after then they both decrease gradually with temperature increasing further. The elongation has its minimum value at about 700 ℃. The TEM examination exhibits that sharing of the γ＇ by dislocation is almost the main deformation mechanism at low temperatures, but the γ＇ by-pass dominates the deformation at high temperatures. The transition temperature from shearing to by-pass should be around 800 ℃. The anomalous yield and intermediate-temperature brittleness behaviors should be attributed to the high content of γ＇. In addition, the carbides and eutectic structure also contribute some to the ITB behaviors of the alloy.

Evaluation of Urban Village Renovation System in Xi’an City of China Based on Brittleness Analysis

Renovation system of urban villages in Xi'an City was evaluated. Influence factors of urban village renovation were analyzed on the basis of brittleness theory, and an evaluation index system established through multi-level inconsistency decomposing. By incorporating the catastrophe theory with fuzzy mathematical theory, the mathematic model was created, and catastrophe membership function was obtained as well as evaluation results. Policies for the renovation of urban villages and new direction of the renovation were interpreted. The application case proved that catastrophe progression method was objective and effective and it could provide new concepts for the evaluation and adjustment of urban village renovation. Moreover, application of brittleness theory in the research on urban village renovation is of great instruction and reference value for the present urban construction.

Brittleness index and seismic rock physics model for anisotropic tight-oil sandstone reservoirs

Brittleness analysis becomes important when looking for sweet spots in tightoil sandstone reservoirs. Hence, appropriate indices are required as accurate brittleness evaluation criteria. We construct a seismic rock physics model for tight-oil sandstone reservoirs with vertical fractures. Because of the complexities in lithology and pore structure and the anisotropic characteristics of tight-oil sandstone reservoirs, the proposed model is based on the solid components, pore connectivity, pore type, and fractures to better describe the sandstone reservoir microstructure. Using the model, we analyze the brittleness sensitivity of the elastic parameters in an anisotropic medium and establish a new brittleness index. We show the applicability of the proposed brittleness index for tight-oil sandstone reservoirs by considering the brittleness sensitivity, the rock physics response characteristics, and cross-plots. Compared with conventional brittleness indexes, the new brittleness index has high brittleness sensitivity and it is the highest in oil-bearing brittle zones with relatively high porosity. The results also suggest that the new brittleness index is much more sensitive to elastic properties variations, and thus can presumably better predict the brittleness characteristics of sweet spots in tight-oil sandstone reservoirs.

Construction of a novel brittleness index equation and analysis of anisotropic brittleness characteristics for unconventional shale formations

The brittleness prediction of shale formations is of interest to researchers nowadays.Conventional methods of brittleness prediction are usually based on isotropic models while shale is anisotropic.In order to obtain a better prediction of shale brittleness,our study firstly proposed a novel brittleness index equation based on the Voigt–Reuss–Hill average,which combines two classical isotropic methods.The proposed method introduces upper and lower brittleness bounds,which take the uncertainty of brittleness prediction into consideration.In addition,this method can give us acceptable predictions by using limited input values.Secondly,an anisotropic rock physics model was constructed.Two parameters were introduced into our model,which can be used to simulate the lamination of clay minerals and the dip angle of formation.In addition,rock physics templates have been built to analyze the sensitivity of brittleness parameters.Finally,the effects of kerogen,pore structure,clay lamination and shale formation dip have been investigated in terms of anisotropy.The prediction shows that the vertical/horizontal Young’s modulus is always below one while the vertical/horizontal Poisson’s ratio(PR)can be either greater or less than 1.Our study finds different degrees of shale lamination may be the explanation for the random distribution of Vani(the ratio of vertical PR to horizontal PR).

Pre-stack basis pursuit seismic inversion for brittleness of shale

Brittleness of rock plays a significant role in exploration and development of shale gas reservoirs. Young＇s modulus and Poisson＇s ratio are the key param- eters for evaluating the rock brittleness in shale gas exploration because their combination relationship can quantitatively characterize the rock brittleness. The high- value anomaly of Young＇s modulus and the low-value anomaly of Poisson＇s ratio represent high brittleness of shale. The technique of pre-stack amplitude variation with angle inversion allows geoscientists to estimate Young＇s modulus and Poisson＇s ratio from seismic data. A model constrained basis pursuit inversion method is proposed for stably estimating Young＇s modulus and Poisson＇s ratio. Test results of synthetic gather data show that Young＇s modulus and Poisson＇s ratio can be estimated reasonably. With the novel method, the inverted Young＇s modulus and Poisson＇s ratio of real field data focus the layer boundaries better, which is helpful for us to evaluate the brittleness of shale gas reservoirs. The results of brittleness evaluation show a good agreement with the results of well interpretation.

Brittleness research on complex system based on brittle link entropy

As the scale of complex system is growing larger and larger, interferences from internal and outer system can result in the collapse of one subsystem in a complex system. They will not only make one subsystem collapse but also influence the other subsystems. Moreover, the whole complex system can collapse consequently. The mechanism of collapse of complex system is clue to the brittleness of complex system that is presented and argued as the basic characteristic in this paper. It is the brittleness link entropy between subsystems that leads to the collapse of whole system. Effective ways that can be adopted to reduce the brittleness entropy can see the successful control of brittleness.

GRAIN BOUNDARY SEGREGATION AND INTERGRANULAR BRITTLENESS IN HIGH STRENGTH ALUMINIUM ALLOY

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Research on basic characteristics of complex system brittleness

The goal of this paper is to research one new characteristic of complex system. Brittleness, which is one new characteritic of complex system, is presented in this paper. The linguistic and qualitative descriptions of complex system are also given in this paper. Otherwise, the qualitative description of complex system is presented at first. On the basis of analyzing the existing brittleness problems, linguistic description and mathematic description of brittleness are given as well. Three kinds of phenomena to judge brittleness of complex system are also given, based on catastrophe theory. Basic characteristics of brittleness are given on the basis of its mathematic description. Two critical point sets are defined by using catastrophe theory. The definition of brittleness and its related theory can serve the control of complex system, and provide theoretical basis for the design and control of complex system.

Rock brittleness indices and their applications to different fields of rock engineering:A review

Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness.As such,it is of high practical value to correctly evaluate rock brittleness.However,the definition and measurement method of rock brittleness have been very diverse and not yet been standardized.In this paper,the definitions of rock brittleness are firstly reviewed,and several representative definitions of rock brittleness are identified and briefly discussed.The development and role of rock brittleness in different fields of rock engineering are also studied.Eighty brittleness indices publicly available in rock mechanics literature are compiled,and the measurement method,applicability and limitations of some indices are discussed.The results show that(1)the large number of brittleness indices and brittleness definitions is attributed to the different foci on the rock behavior when it breaks;(2)indices developed in one field usually are not directly applicable to other fields;and(3)the term“brittleness”is sometimes misused,and many empirically-obtained brittleness indices,which lack theoretical basis,fail to truly reflect rock brittleness.On the basis of this review,three measurement methods are identified,i.e.(1)elastic deformation before fracture,(2)shape of post-peak stressestrain curves,and(3)methods based on fracture mechanics theory,which have the potential to be further refined and unified to become the standard measurement methods of rock brittleness.It is highly beneficial for the rock mechanics community to develop a robust definition of rock brittleness.This study will undoubtedly provide a comprehensive timely reference for selecting an appropriate brittleness index for their applications,and will also pave the way for the development of a standard definition and measurement method of rock brittleness in the long term.

Prediction of brittleness based on anisotropic rock physics model for kerogen-rich shale

The construction of a shale rock physics model and the selection of an appropriate brittleness index （B/） are two significant steps that can influence the accuracy of brittleness prediction. On one hand, the existing models of kerogen-rich shale are controversial, so a reasonable rock physics model needs to be built. On the other hand, several types of equations already exist for predicting the BI whose feasibility needs to be carefully considered. This study constructed a kerogen-rich rock physics model by performing the self- consistent approximation and the differential effective medium theory to model intercoupled clay and kerogen mixtures. The feasibility of our model was confirmed by comparison with classical models, showing better accuracy. Templates were constructed based on our model to link physical properties and the BL Different equations for the BI had different sensitivities, making them suitable for different types of formations. Equations based on Young＇s Modulus were sensitive to variations in lithology, while those using Lame＇s Coefficients were sensitive to porosity and pore fluids. Physical information must be considered to improve brittleness prediction.

The construction of shale rock physics model and brittleness prediction for high-porosity shale gas-bearing reservoir

Due to the huge differences between the unconventional shale and conventional sand reservoirs in many aspects such as the types and the characteristics of minerals,matrix pores and fluids,the construction of shale rock physics model is significant for the exploration and development of shale reservoirs.To make a better characterization of shale gas-bearing reservoirs,we first propose a new but more suitable rock physics model to characterize the reservoirs.We then use a well A to demonstrate the feasibility and reliability of the proposed rock physics model of shale gas-bearing reservoirs.Moreover,we propose a new brittleness indicator for the high-porosity and organic-rich shale gas-bearing reservoirs.Based on the parameter analysis using the constructed rock physics model,we finally compare the new brittleness indicator with the commonly used Young’s modulus in the content of quartz and organic matter,the matrix porosity,and the types of filled fluids.We also propose a new shale brittleness index by integrating the proposed new brittleness indicator and the Poisson’s ratio.Tests on real data sets demonstrate that the new brittleness indicator and index are more sensitive than the commonly used Young’s modulus and brittleness index for the high-porosity and high-brittleness shale gas-bearing reservoirs.

Brittleness characteristics of tight oil siltstones

Rock brittleness directly affects reservoir fracturing and its evaluation is essential for establishing fracturing conditions prior to reservoir reforming. Dynamic and static brittleness data were collected from siltstones of the Qingshankou Formation in Songliao Basin. The brittle-plastic transition was investigated based on the stress-strain relation. The results suggest that the brittleness indices calculated by static elastic parameters are negatively correlated with the stress drop coefficient and the brittleness index B2, defined as the average of the normalized Young＇s modulus and Poisson＇s ratio, is strongly correlated with the stress drop. The brittleness index B2, Young＇s modulus, and Poisson＇s ratio correlate with the brittle minerals content; that is, quartz, carbonates, and pyrite. We also investigated the correlation between pore fluid and porosity and dynamic brittle characteristic based on index B2. Pore fluid increases the plasticity of rock and reduces brittleness; moreover, with increasing porosity, rock brittleness decreases. The gas-saturated siltstone brittleness index is higher than that in oil- or water-saturated siltstone; the difference in the brittleness indices of oil- and water-saturated siltstone is very small. By comparing the rock mechanics and ultrasonic experiments, we find that the brittleness index obtained from the rock mechanics experiments is smaller than that obtained from the ultrasonic experiments; nevertheless, both decrease with increasing porosity as well as their differences. Ultrasonic waves propagate through the rock specimens without affecting them, whereas rock mechanics experiments are destructive and induce microcracking and porosity increases; consequently, the brittleness of low-porosity rocks is affected by the formation of internal microcrack systems.

Influence of brittleness and confining stress on rock cuttability based on rock indentation tests

In order to understand the influence of brittleness and confining stress on rock cuttability,the indentation tests were carried out by a conical pick on the four types of rocks.Then,the experimental results were utilized to take regression analysis.The eight sets of normalized regression models were established for reflecting the relationships of peak indentation force(PIF)and specific energy(SE)with brittleness index and uniaxial confining stress.The regression analyses present that these regression models have good prediction performance.The regressive results indicate that brittleness indices and uniaxial confining stress conditions have non-linear effects on the rock cuttability that is determined by PIF and SE.Finally,the multilayer perceptual neural network was used to measure the importance weights of brittleness index and uniaxial confining stress upon the influence for rock cuttability.The results indicate that the uniaxial confining stress is more significant than brittleness index for influencing the rock cuttability.

First-principles and experimental investigations on ductility/brittleness of intermetallic compounds and joint properties in steel/aluminum laser welding

Morphology,distribution,composition,forming ability,structural stability and intrinsic mechanical properties of the intermetallic compounds(IMCs)formed in steel/aluminum laser welding were determined through scanning electron microscope,energy dispersive spectrometer,X-ray diffractometer and first-principles calculation.It was found that the mechanical properties of the joint are limited by the Fe−Al IMCs,whose brittleness is attributed to the orbital hybridization between Al(s),Al(p)and Fe(d).However,the joint properties are improved by adding interlayer,which is ascribed to some changes of electronic structure of the generated IMCs.The transition mechanism of IMCs changing from brittle to ductile is mainly due to the weak ability of interlayer elements to attract electrons.The mechanical properties of the joint are closely related to the ductility or brittleness of the IMCs.Moreover,the addition of Ti foil interlayer effectively improves the mechanical properties of the joints,which means that the experimental verification is in good agreement with the theoretical calculation predictions.

Characterization and evaluation of brittleness of deep bedded sandstone from the perspective of the whole life-cycle evolution process

The quantitative determination and evaluation of rock brittleness are crucial for the estimation of excavation efficiency and the improvement of hydraulic fracturing efficiency.Therefore,a“three-stage”triaxial loading and unloading stress path is designed and proposed.Subsequently,six brittleness indices are selected.In addition,the evolution characteristics of the six brittleness indices selected are characterized based on the bedding effect and the effect of confining pressure.Then,the entropy weight method(EWM)is introduced to assign weight to the six brittleness indices,and the comprehensive brittleness index Bcis defined and evaluated.Next,the new brittleness classification standard is determined,and the brittleness differences between the two stress paths are quantified.Finally,compared with the previous evaluation methods,the rationality of the proposed comprehensive brittleness index Bcis also verified.These results indicate that the proposed brittleness index Bccan reflect the brittle characteristics of deep bedded sandstone from the perspective of the whole life-cycle evolution process.Accordingly,the method proposed seems to offer reliable evaluations of the brittleness of deep bedded sandstone in deep engineering practices,although further validation is necessary.

Cascading failure prevention of complex systems based on brittleness entropy game

A non-cooperative game model based on brittleness entropy is formulated for preventing cascading failure of complex systems.Subsystems of a complex system are mapped to the players of the game.The influence of collapsed subsystems to other subsystems is also taken into account in the definition of payoff function except for their own entropy increase.This influence is named brittleness entropy.Each player has two optional strategies;rational for negative entropy and irrational for negative entropy.The model is designed to identify the players who select an irrational strategy for negative entropy.The players who select the irrational strategy for negative entropy continue to compete for negative entropy after the recovery of ordered state and make other subsystems can' t get enough negative entropy to reduce entropy increase.It leads to cascading failure of the complex system in the end.Genetic algorithm is used to seek the solution of game model,and the simulation result verifies the effectiveness of the proposed model.The model provides a new way to prevent cascading failure of complex systems.

Study on brittleness templates for shale gas reservoirs——A case study of Longmaxi shale in Sichuan Basin,southern China

Differentiating brittle zones from ductile zones in low permeability shale formations is imperative for efficient hydraulic fracturing stimulation.The brittleness index(BI) is used to describe the rock resistance to hydraulic fracture initiation and propagation and measures the ease at which complex fracture networks can be created.In this study,we constructed brittleness templates through the correlation of fundamental rock properties and geomechanical characterization.We then employed the templates to distinguish the brittle,ductile,and brittle-ductile transition zones in the Longmaxi shale gas reservoir,Sichuan Basin of southern China.The approach works in two steps.First,we suggest a new expression for the mineralogical BI by their respective weights based on the analysis of correlation coefficients between mechanical testing and XRD results.Second,we correlate TOC,porosity,pore fluid,natural fractures,and improved BI model with multiple elastic properties to define the brittle,ductile,and transitional zones in the Longmaxi shale gas reservoir of China.Compared with the traditional mineralogy-based BI definition,the improved BI model differentiates the brittle and ductile zones and provides a better sense of the most suitable fracturing regions.Our results show that the brittleness templates,which combine fundamental rock properties,improved BI model,and geomechanical characterization led to identifying favorable zones for hydraulic fracturing and enhanced shale characterization.The proposed brittleness templates’ effectiveness was verified using data from horizontal wells,offset wells,shale gas wells from different origins,laboratory core testing,and seismic inversion of BI across the studied wells.