A fracture model for assessing tensile mode crack growth resistance of rocks

Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering.This investigation developed a brittle fracture model to predict tensile mode(mode I)failure loads of cracked rocks.The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone(FPZ)based on the maximum normal strain(MNSN)ahead of the crack tip,and then use the effective crack to calculate the fracture toughness.We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN.In this way,the FPZ,non-singular terms and the biaxial stress state at the crack tip are simul-taneously considered.The principle of the model is explicit and easy to apply.To verify the proposed model,laboratory experiments were performed on a rock material using six groups of specimens.The model predicted the specimen geometry dependence of the measured fracture toughness well.More-over,the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature.The model was demonstrated su-perior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.

The tectonic fracture modeling of an ultra-low permeability sandstone reservoir based on an outcrop analogy: A case study in the Wangyao Oilfield of Ordos Basin, China

Due to inherent limits of data acquisition and geophysical data resolution, there are large uncertainties in the characterization of subsurface fractures. However, outcrop analogies can provide qualitative and quantitative information on a large number of fractures, based on which the accuracy of subsurface fracture characterization can be improved. Here we take the tectonic fracture modeling of an ultra-low permeability sandstone reservoir based on an outcrop analogy, a case study of the Chang6t~ Formation of the Upper Triassic Yanchang Group of the Wangyao Oilfield in the Ordos Basin of China. An outcrop at the edge of the basin is a suitable analog for the reservoir, but the prerequisite is that they must have equivalent previous stress fields, similar final structural characteristics, relative timing and an identical depositional environment and diagenesis. The relationship among fracture density, rock type and bed thickness based on the outcrop is one of the most important fracture distribution models, and can be used to interpret fracture density in individual wells quantitatively. Fracture orientation, dip, geometry and scale, also should be described and measured in the outcrop, and can be used together with structure restoration and single well fracture density interpretation to guide fracture intensity prediction on bed surfaces and to constrain the construction of the 3D fracture geometry model of the subsurface reservoir. The application of the above principles shows the outcrop-based tectonic fracture models of the target ultra-low permeability sandstone reservoir are consistent with fractures inferred from microseismic interpretation and tracer tests. This illustrated that the fracture modeling based on the outcrop analogy is reliable and can reduce the uncertainty in stochastic fracture modeling.

A Pipeline Fracture Model of Hydrogen-induced Cracking

The relationship between hydrogen concentration and crack tip stress, strain field, hydrogen diffusion and internal pressure respectively in the crack tip process zone was investigated, and the length of the crack tip process zone of hydrogen-induced cracking （HIC） was determined. Based on the mechanism of fracture of micro-crack nucleation, a dislocation model was presented for the fracture criteria of HIC. The influence factors of pipeline tube fracture ductile KISCC in the presence of hydrogen was analyzed, and the critical pressure bearing capability of a pipeline with hydrogeninduced cracking and the critical J-integrity （JISCC） were calculated, which is very important for pipeline safety.

An efficient approach for mesoscale fracture modeling of fully-graded hydraulic concrete

Large coarse aggregates used in fully-graded hydraulic concrete necessitate large specimens for numerical modeling.This leads to a high computational cost for mesoscale modeling and thus slows the development of multiscale modeling of hydraulic mass concrete structures.To overcome this obstacle,an efficient approach for mesoscale fracture modeling of fully-graded hydraulic concrete was developed based on the concept of the governing mesostructure.The mesostructure was characterized by a critical aggregate size.Coarse aggregates smaller than the critical size were homogenized into mortar matrices.Key issues in mesostructure generation of fully-graded hydraulic concrete are discussed,as is the development of mesoscale finite element modeling methodology.The basic concept and implementation procedures of the proposed approach are also described in detail.The numerical results indicated that the proposed approach not only significantly improves the compu-tational efficiency of mesoscale modeling but also captures the dominant fracturing mechanism at the mesoscale and reproduces reasonable fracture properties at the macroscale.Therefore,the proposed approach can serve as a basis for multiscale fracture modeling of hydraulic mass concrete structures.

Performance-based fractal fracture model for complex fracture network simulation

The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models.These methods suffer from drawbacks such as lack of flexibility and of ease of updating.In this study,I combined fracture modeling by elastic gridding which improves flexibility,especially in complex reservoirs.The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production.This is a dubious assumption,especially in reservoirs with a high production rate in the beginning.The proposed elastic fracture modeling considers changes in fracture properties,shape and aperture through the simulation.This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections.Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes,which consequently results in lower production compared with what was previously assumed.It is concluded that an elastic gridded model could better simulate reservoir performance.

Study on a Dual Embedded Discrete Fracture Model for Fluid Flow in Fractured Porous Media

Simulation of fluid flow in the fractured porous media is very important and challenging.Researchers have developed some models for fractured porous media.With the development of related research in recent years,the prospect of embedded discrete fracture model(EDFM)is more and more bright.However,since the size of the fractures in the actual reservoir varies greatly,a very fine grid should be used which leads to a huge burden to the computing resources.To address this challenge,in the present paper,an upscaling based model is proposed.In this model,the flow in large-scale fractures is directly described by the EDFM while that in the small-scale fractures is upscaled through local simulation by EDFM.The EDFM is used to simulate the large-and small-scale fractures independently two times,so the new model is called dual embedded discrete fracture model(D-EDFM).In this paper,the detailed implementation process of D-EDFM is introduced and,through test cases,it is found the proposed model is a feasible method to simulate the flow in fractured porous media.

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and. nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.

Finite Element Convergence for State-Based Peridynamic Fracture Models

We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to both the strain between two points and the change in volume inside the domain of the nonlocal interaction.The pairwise interactions between points are mediated by a bond potential of multi-well type while multi-point interactions are associated with the volume change mediated by a hydrostatic strain potential.The hydrostatic potential can either be a quadratic function,delivering a linear force–strain relation,or a multi-well type that can be associated with the material degradation and cavitation.We first show the well-posedness of the peridynamic formulation and that peridynamic evolutions exist in the Sobolev space H2.We show that the finite element approximations converge to the H2 solutions uniformly as measured in the mean square norm.For linear continuous fi nite elements,the convergence rate is shown to be Ct Δt+Csh2/ε2,where𝜖is the size of the horizon,his the mesh size,and Δt is the size of the time step.The constants Ct and Cs are independent of Δt and h and may depend on ε through the norm of the exact solution.We demonstrate the stability of the semi-discrete approximation.The stability of the fully discrete approximation is shown for the linearized peridynamic force.We present numerical simulations with the dynamic crack propagation that support the theoretical convergence rate.

Effect of proppant sizes and injection modes on proppant transportation and distribution in the tortuous fracture model

Particle-fluid transport and placement mechanism in tortuous fracture played a crucial role in uncon-ventional reservoirs.Currently,most studies focused on mono-size proppant with fluid transport pro-cesses in tortuous fractures.However,the mixture-size proppant with fluid movement mechanism in tortuous fracture was still uncommon.Therefore,this study designed and applied a series of experiments with a physical analog model of a tortuous fracture with 120°and 90°-angled bends and combined high-speed camera-based equipment.This experimental system was used to track different-mixture-sized proppant particle motion trajectories for a series of proppant injection schemes;The following conclu-sions were drawn from this study:1.The pile-up processes mechanism in all investigated schemes were similar and could be reduced to four main stages.2.The packing structure at both sides of the fracture wall had different variation rates,which were controlled by the mix ratio(change from 1∶1-1∶5)of proppant size.3.Some new packing patterns,such as Zebra Stripe,had occurred,controlled by the different proppant injection sequences.4.Small-sized mono-proppant(30/50 mesh)had the highest transport efficiency in the tortuous fracture,followed by the mixed-sized multi-proppant(10/20 mesh:30/50 mesh),large-sized proppant(10/20 mesh)was the worst.5.An optimized alternating in-jection mode was recommended as injecting small-sized proppant first(30/50 mesh)and followed by mixed-sized multi-proppant(10/20 mesh:30/50 mesh),which could contribute to obtaining the optimal both proppant packing height and travel distance in tortuous fracture.6.Two correlations were devel-oped for predicting the proppant packing height and transportation distance.

A multi-mechanism numerical simulation model for CO_(2)-EOR and storage in fractured shale oil reservoirs

Under the policy background and advocacy of carbon capture,utilization,and storage(CCUS),CO_(2)-EOR has become a promising direction in the shale oil reservoir industry.The multi-scale pore structure distribution and fracture structure lead to complex multiphase flow,comprehensively considering multiple mechanisms is crucial for development and CO_(2) storage in fractured shale reservoirs.In this paper,a multi-mechanism coupled model is developed by MATLAB.Compared to the traditional Eclipse300 and MATLAB Reservoir Simulation Toolbox(MRST),this model considers the impact of pore structure on fluid phase behavior by the modified Peng—Robinson equation of state(PR-EOS),and the effect simultaneously radiate to Maxwell—Stefan(M—S)diffusion,stress sensitivity,the nano-confinement(NC)effect.Moreover,a modified embedded discrete fracture model(EDFM)is used to model the complex fractures,which optimizes connection types and half-transmissibility calculation approaches between non-neighboring connections(NNCs).The full implicit equation adopts the finite volume method(FVM)and Newton—Raphson iteration for discretization and solution.The model verification with the Eclipse300 and MRST is satisfactory.The results show that the interaction between the mechanisms significantly affects the production performance and storage characteristics.The effect of molecular diffusion may be overestimated in oil-dominated(liquid-dominated)shale reservoirs.The well spacing and injection gas rate are the most crucial factors affecting the production by sensitivity analysis.Moreover,the potential gas invasion risk is mentioned.This model provides a reliable theoretical basis for CO_(2)-EOR and sequestration in shale oil reservoirs.

Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network(DFN)flow model poses challenges when dealing with complex fracture networks.This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures.Notably,this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry.All geometric analyses,such as identifying connected fractures,dividing the two-dimensional domain into closed loops,triangulating arbitrary loops,and refining triangular elements,are fully automated.The analysis processes are comprehensively introduced,and core algorithms,along with their pseudo-codes,are outlined and explained to assist readers in their programming endeavors.The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures.In practical application,the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project.The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures.Furthermore,following extensive modification and optimization,the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

Fracture model for the prediction of the electrical percolation threshold in CNTs/Polymer composites

In this paper, we propose a 3D stochastic model to predict the percolation threshold and the effective electric conductivity of CNTs/Polymer composites. We consider the tunneling effect in our model so that the unrealistic interpenetration can be avoided in the identification of the conductive paths between the CNTs inside the polymer. The results are shown to be in good agreement with reported experimental data.

A smart productivity evaluation method for shale gas wells based on 3D fractal fracture network model

The generation method of three-dimensional fractal discrete fracture network(FDFN)based on multiplicative cascade process was developed.The complex multi-scale fracture system in shale after fracturing was characterized by coupling the artificial fracture model and the natural fracture model.Based on an assisted history matching(AHM)using multiple-proxy-based Markov chain Monte Carlo algorithm(MCMC),an embedded discrete fracture modeling(EDFM)incorporated with reservoir simulator was used to predict productivity of shale gas well.When using the natural fracture generation method,the distribution of natural fracture network can be controlled by fractal parameters,and the natural fracture network generated coupling with artificial fractures can characterize the complex system of different-scale fractures in shale after fracturing.The EDFM,with fewer grids and less computation time consumption,can characterize the attributes of natural fractures and artificial fractures flexibly,and simulate the details of mass transfer between matrix cells and fractures while reducing computation significantly.The combination of AMH and EDFM can lower the uncertainty of reservoir and fracture parameters,and realize effective inversion of key reservoir and fracture parameters and the productivity forecast of shale gas wells.Application demonstrates the results from the proposed productivity prediction model integrating FDFN,EDFM and AHM have high credibility.

Well interference evaluation considering complex fracture networks through pressure and rate transient analysis in unconventional reservoirs

Severe well interference through complex fracture networks(CFNs)can be observed among multi-well pads in low permeability reservoirs.The well interference analysis between multi-fractured horizontal wells(MFHWs)is vitally important for reservoir effective development.Well interference has been historically investigated by pressure transient analysis,while it has shown that rate transient analysis has great potential in well interference diagnosis.However,the impact of complex fracture networks(CFNs)on rate transient behavior of parent well and child well in unconventional reservoirs is still not clear.To further investigate,this paper develops an integrated approach combining pressure and rate transient analysis for well interference diagnosis considering CFNs.To perform multi-well simulation considering CFNs,non-intrusive embedded discrete fracture model approach was applied for coupling fracture with reservoir models.The impact of CFN including natural fractures and frac-hits on pressure and rate transient behavior in multi-well system was investigated.On a logelog plot,interference flow and compound linear flow are two new flow regimes caused by nearby producers.When both NFs and frac-hits are present in the reservoir,frac-hits have a greater impact on well#1 which contains frac-hits,and NFs have greater impact on well#3 which does not have frac-hits.For all well producing circumstances,it might be challenging to see divergence during pseudosteady state flow brought on by frac-hits on the logelog plot.Besides,when NFs occur,reservoir depletion becomes noticeable in comparison to frac-hits in pressure distribution.Application of this integrated approach demonstrates that it works well to characterize the well interference among different multi-fractured horizontal wells in a well pad.Better reservoir evaluation can be acquired based on the new features observed in the novel model,demonstrating the practicability of the proposed approach.The findings of this study can help for better evaluating well interference degree in multi-well systems combing PTA and RTA,which can reduce the uncertainty and improve the accuracy of the well interference analysis based on both field pressure and rate data.

Analysis of fracture propagation and shale gas production by intensive volume fracturing

This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.

Horizontal Well Interference Performance and Water Injection Huff and Puff Effect on Well Groups with Complex Fracture Networks:A Numerical Study

Well interference has become a common phenomenon with the increasing scale of horizontal well fracturing.Recent studies on well interference in horizontal wells do not properly reflect the physical model of the postfracturing well groups and the realistic fracturing process of infill wells.Establishing the correspondence between well interference causative factors and manifestations is of great significance for infill well deployment and secondary oil recovery.In this work,we develop a numerical model that considers low velocity non-Darcy seepage inshale reservoirs to study the inter-well interferencephenomenon that occurs in theSantanghufield,andconstruct an explicit hydraulic fracture and complex natural fracture network model with an embedded discrete fracture model,focusing on the effect of fracture network morphology on well interactions.The model also considers a multi-segment wellbore model to accommodate the effect of inter-well crossflow on wellbore tubular flow.The changes in formation pressure and water saturation during fracturing are performed by controlling the injection pressure and water injection rate.The result shows that the shape of the fracture network generated by the infill well with the old well determines the subsequent fluid and oil-increasing performance of the disturbed well.The synergistic production or competitive relationship formed by fractures with different connectivity between the two wells determines the positive and negative effects of the interference.The paper also investigates the adaptation study of water injection huff and puff schemes for well groups with different connectivity,and demonstrated a potential yield increase of up to 10.85%under adaptation injection.This method of identifying well interference based on the production dynamics of affected wells and the subsequent corresponding water injection method provides valuable references for the selection of secondary oil recovery measures.

Fracture mechanics model of fully mechanized top coal caving of shallow coal seams and its application

Based on break characteristics of roofs in fully mechanized top-coal mining of thick shallow coal seams, a fracture mechanics model was built, and the criterion of crack propagation in the main roof was derived using the fracture mechanics theory. The relationships between the fracture length of the roof and the working resistance of the supports were discovered, and the correlations between the load on the overlying strata and the ratio of the crack's length to the thickness of the roof were obtained. Using a working face of Jindi Coal Mine, Xing county Shanxi province as an example, the relationships between the fracture length of the roof and the working resistance of the supports were analysed in detail. The results give a design basis in hydraulic top coal caving supports, which could provide useful references in the practical application. On-site experiment proves that the periodic weighting step interval of the caving face is 15–16 m, which is basically consistent with the theoretical analysis results, and indicates that the mechanized caving hydraulic support is capable of meeting the support requirements in the mining of a super-thick but shallowly buried coal seam.

Application of Pore Evolution and Fracture Development Coupled Models in the Prediction of Reservoir "Sweet Spots" in Tight Sandstones

The Chang-63 reservoir in the Huaqing area has widely developed tight sandstone ＂thick sand layers, but not reservoirs characterized by rich in oil＂, and it is thus necessary to further study its oil and gas enrichment law. This study builds porosity and fracture development and evolution models in different deposition environments, through core observation, casting thin section, SEM, porosity and permeability analysis, burial history analysis, and ＂four-property-relationships＂ analysis.

Review of permeability evolution model for fractured porous media

The ability to capture permeability of fractured porous media plays a significant role in several engineering applications, including reservoir, mining, petroleum and geotechnical engineering. In order to solve fluid flow and coupled flow-deformation problems encountered in these engineering applications,both empirical and theoretical models had been proposed in the past few decades. Some of them are simple but still work in certain circumstances; others are complex but also need some modifications to be applicable. Thus, the understanding of state-of-the-art permeability evolution model would help researchers and engineers solve engineering problems through an appropriate approach. This paper summarizes permeability evolution models proposed by earlier and recent researchers with emphasis on their characteristics and limitations.