Numerical simulation of three-dimensional fracturing fracture propagation in radial wells

A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.

An efficient 3D cell-based discrete fracture-matrix flow model for digitally captured fracture networks

Complex hydraulic fracture networks are critical for enhancing permeability in unconventional reservoirs and mining indus-tries.However,accurately simulating the fluid flow in realistic fracture networks(compared to the statistical fracture net-works)is still challenging due to the fracture complexity and computational burden.This work proposes a simple yet efficient numerical framework for the flow simulation in fractured porous media obtained by 3D high-resolution images,aiming at both computational accuracy and efficiency.The fractured rock with complex fracture geometries is numerically constructed with a cell-based discrete fracture-matrix model(DFM)having implicit fracture apertures.The flow in the complex fractured porous media(including matrix flow,fracture flow,as well as exchange flow)is simulated with a pipe-based cell-centered finite volume method.The performance of this model is validated against analytical/numerical solutions.Then a lab-scale true triaxial hydraulically fractured shale sample is reconstructed,and the fluid flow in this realistic fracture network is simu-lated.Results suggest that the proposed method achieves a good balance between computational efficiency and accuracy.The complex fracture networks control the fluid flow process,and the opened natural fractures behave as primary fuid pathways.Heterogeneous and anisotropic features of fluid flow are well captured with the present model.

A new laboratory method for evaluating formation damage in fractured carbonate reservoirs

Natural carbonate core samples with artificial fractures are often used to evaluate the damage of fractured carbonate formations in the laboratory. It is shown that the most frequent error for evaluation results directly from the random width characterized by the artificial fractures. To solve this problem, a series of simulated fractured core samples made of stainless steel with a given width of fracture were prepared. The relative error for the width of artificial fracture decreased to 1%. The width of natural and artificial fractures in carbonate reservoirs can be estimated by image log data. A series of tests for formation damage were conducted by using the stainless steel simulated core samples flushed with different drilling fluids, such as the sulfonate/polymer drill-in fluid and the solids-flee drill-in fluid with or without ideal packing bridging materials. Based on the experimental results using this kind of simulated cores, a novel approach to the damage control of fractured carbonate reservoirs was presented. The effective temporary plugging ring on the end face of the simulated core sample can be observed clearly. The experimental results also show that the stainless steel simulated cores made it possible to visualize the solids and filtrate invasion.

Experimental research on overlying strata movement and fracture evolution in pillarless stress-relief mining

In multiple seams mining, the seam with relatively low gas content （protective seam） is often extracted prior to mining its overlying and/or underlying seams of high gas content and low permeability to minimize the risk of high gas emission and outbursts of coal and gas. A key to success with this mining sequence is to gain a detailed understanding of the movement and fracture evolution of the overlying and underlying strata after the protective seam in extracted. In Zhuji mine, the No. 11-2 seam is extracted as a protective seam with the pillarless mining method by retaining goal-side roadways prior to its overlying No. 13-1 seam. An investigation has been undertaken in the panel 1111 （1） of Zhuji mine to physically simulate the movement and fracture evolution of the overlying strata alter the No. 1 I-2 seam is extracted. In the physical simulation, the displacement, strain, and deformation and failure process of the model for simulation were acquired with various means such as grating displacement meter, strain gauges, and digital photography. The simulation result shows that： （1） Initial caving interval of the immediate roof was 21.6 m, the first weighting interval was 23.5-37.3 m with the average interval of 33.5 m, and the periodic weighting interval of the main roof was in a range of 8.2-20.55 m and averaged at 15.2 m. （2） The maximum height of the caving zone after the extraction of No. 11-2 seam was 8.0 m, which was 4 times of the seam mining height and the internal strata of the caving zone collapsed irregularly. The mining-induced fractures developed 8-30 m above the mined No. 11-2 seam, which was 7.525 times of the seam mining height, the fracture zone was about 65° upward from the seam open-off cut toward the goaf, the height of longitudinal joint growth was 4-20 times of the mining seam height, and the height of lateral joint growth was 20-25 times of the mining seam height. （3） The ＂arch-in-arch＂ mechanical structure of the internal goaf was bounded by an expansion angle of broken strata in the lateral direction of the retained goaf-side roadway. The spatial and temporal evolution regularities of over- burden＇s displacement field and stress field, dynamic development process and distribution of fracture field were analyzed. Based on the simulation results, it is recommended that several goaf drainage methods, i.e. gas drainage with buried pipes in goaf, surface goaf gas drainage, and cross-measure boreholes, should be implemented to ensure the safe mining of the panel 1111 （1）.

Experimental and finite element analysis for fracture of coating layer of galvannealed steel sheet

Mechanical properties of galvannealed (GA) steel sheet used for automotive exposed panel and predicted failure phenomenon of its coating layer were evaluated using finite element method. V-bending test was performed to understand better the fracture of coating layer of GA steel sheet during plastic deformation. Yield strength of the coating layer was calculated by using a relative difference between hardness of coating layer measured from the nano-indentation test and that of substrate. To measure shearing strength at the interface between substrate and coating layer, shearing test with two specimens attached by an adhesive was carried out. Using the mechanical properties measured, a series of finite element analyses coupled with a failure model was performed. Results reveal that the fracture of coating layer occurs in an irregular manner at the region where compressive deformation is dominant. Meanwhile, a series of vertical cracks perpendicular to material surface are observed at the tensile stressed-region. It is found that 0.26-0.28 of local equivalent plastic strain exists at the coating and substrate at the beginning of failure. The fracture of coating layer depends on ductility of the coating layer considerably as well.

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

Influence of gas transport mechanisms on the productivity of multi-stage fractured horizontal wells in shale gas reservoirs

In order to investigate the influence on shale gas well productivity caused by gas transport in nanometer- size pores, a mathematical model of multi-stage fractured horizontal wells in shale gas reservoirs is built, which considers the influence of viscous flow, Knudsen diffusion, surface diffusion, and adsorption layer thickness. A dis- crete-fracture model is used to simplify the fracture mod- cling, and a finite element method is applied to solve the model. The numerical simulation results indicate that with a decrease in the intrinsic matrix permeability, Knudsen diffusion and surface diffusion contributions to production become large and cannot be ignored. The existence of an adsorption layer on the nanopore surfaces reduces the effective pore radius and the effective porosity, resulting in low production from fractured horizontal wells. With a decrease in the pore radius, considering the adsorption layer, the production reduction rate increases. When the pore radius is less than 10 nm, because of the combined impacts of Knudsen diffusion, surface diffusion, and adsorption layers, the production of multi-stage fractured horizontal wells increases with a decrease in the pore pressure. When the pore pressure is lower than 30 MPa, the rate of production increase becomes larger with a decrease in pore pressure.

Quasimolecular Dynamic Simulation for Bending Fracture of Laminar Composite Materials

Recently, quasimolecular dynamics has been successfully used to simulate the deformation characteristics of actual size solid materials. In quasimolecular dynamics, which is an attempt to bridge the gap between atomistic and continuum simulations, molecules are aggregated into large units, called quasimolecules, to evaluate large scale material behavior. In this paper, a 2-dimensional numerical simulation using quasimolecular dynamics was performed to investigate laminar composite material fractures and crack propagation behavior in the uniform bending of laminar composite materials. It was verified that under bending deformation laminar composite materials deform quite differently from homogeneous materials

Design of comprehensive test system for detecting overlying strata mining-induced fractures on surface with radon gas

Based on radon gas properties and its existing projects applications, we firstly attempted to apply geo- physical and chemical properties of radon gas in the field of mining engineering, and imported radioac- tive measurement method to detect the development process of the overlying strata mining-induced fractures and their contained water quality in underground coal mining, which not only innovates a more simple-fast-reliable detection method, but also further expands the applications of radon gas detection technology in mining field. A 3D simulation design of comprehensive testing system for detecting strata mining-induced fractures on surface with radon gas (CTSR) was carried out by using a large-scale 3D solid model design software Pro/Engineer (Pro/E), which overcame three main disadvantages of ''static design thought, 2D planar design and heavy workload for remodification design'' on exiting design for mining engineering test systems. Meanwhile, based on the simulation design results of Pro/E software, the sta- bility of the jack-screw pressure bar for the key component in CTSR was checked with a material mechan- ics theory, which provided a reliable basis for materials selection during the latter machining process.

Bowland Shale well placement strategy-Part 2:Fracture simulations using a 3D geomechanical model and implications for stratigraphic and spatial horizontal well locations

Hydraulic fracture modelling is a key component of a shale reservoir well placement strategy as it provides an indication of the typical lengths and heights of stimulated fractures and of the changes to the stress environment in which these are propagating.However,spatial and stratigraphic variations in the stress and geomechanical properties of shales make accurate modelling a challenging task.For the UK Bowland Shale,stacked horizontal wells targeting multiple stratigraphic intervals could be used to avoid large offset faults in a geologically complex area.However,it is not known how these intervals may respond to hydraulic fracturing and predicting the height and length of hydraulic fractures is necessary in order to assess the likelihood of vertical fracture interference across landing zones or propagation towards major faults.In the case of the former,intervals of high effective stress may be key to containing fractures within their desired target.Using a planar hydraulic fracture simulator,and a 3D geomechanical model incorporating dipping stratigraphy,the issue of predicting hydraulic fracture geometry in the Bowland Shale was assessed through a series of modelling exercises using well Preese Hall-1 and horizontal pseudo-wells.When pre-defined landing zones were targeted,narrow and long transverse fractures around 1 km from the well were simulated.When the simulation design mimicked perforation clusters placed at 12 m intervals along horizontal pseudo-wells,the effects of stress shadowing were acute and resulted in irregular fracture geometries.Furthermore,high effective stress intervals performed efficiently as barriers to vertical hydraulic fracture propagation,reinforcing the feasibility of using stacked production for the Bowland Shale.The modelling results were then used to discuss the possible placement of horizontal wells in a mapped,100 km2 region around well Preese Hall-1,where up to 13 sites could be positioned,with a horizontal well length of around 1.5 km.Finally,by drawing on a wellestablished analogue for the Bowland Shale,it was estimated that up to 195 Bcf of gas could be produced from the 13 locations in the area if three stratigraphic intervals are produced from one location.

Application of computer aided 3D simulation technique for complicated foot and ankle fractures

Objective To investigate the effect of computer aided 3D simulation technique for treating complicated foot and ankle fractures precisely.Methods From November 2007 to August 2009,255 patients with complicated foot and ankle fractures

Microscale crack propagation in shale samples using focused ion beam scanning electron microscopy and three-dimensional numerical modeling

Reliable prediction of the shale fracturing process is a challenging problem in exploiting deep shale oil and gas resources.Complex fracture networks need to be artificially created to employ deep shale oil and gas reserves.Randomly distributed minerals and heterogeneities in shales significantly affect mechanical properties and fracturing behaviors in oil and gas exploitation.Describing the actual microstructure and associated heterogeneities in shales constitutes a significant challenge.The RFPA3D(rock failure process analysis parallel computing program)-based modeling approach is a promising numerical technique due to its unique capability to simulate the fracturing behavior of rocks.To improve traditional numerical technology and study crack propagation in shale on the microscopic scale,a combination of high-precision internal structure detection technology with the RFPA^(3D) numerical simulation method was developed to construct a real mineral structure-based modeling method.First,an improved digital image processing technique was developed to incorporate actual shale microstructures(focused ion beam scanning electron microscopy was used to capture shale microstructure images that reflect the distri-butions of different minerals)into the numerical model.Second,the effect of mineral inhomogeneity was considered by integrating the mineral statistical model obtained from the mineral nanoindentation experiments into the numerical model.By simulating a shale numerical model in which pyrite particles are wrapped by organic matter,the effects of shale microstructure and applied stress state on microcrack behavior and mechanical properties were investigated and analyzed.In this study,the effect of pyrite particles on fracture propagation was systematically analyzed and summarized for the first time.The results indicate that the distribution of minerals and initial defects dominated the fracture evolution and the failure mode.Cracks are generally initiated and propagated along the boundaries of hard mineral particles such as pyrite or in soft minerals such as organic matter.Locations with collections of hard minerals are more likely to produce complex fractures.This study provides a valuable method for un-derstanding the microfracture behavior of shales.

A numerical investigation of hydraulic fracturing on coal seam permeability based on PFC‑COMSOL coupling method

Hydraulic fracturing and permeability enhancement are effective methods to improve low-permeability coal seams.However,few studies focused on methods to increase permeability,and there are no suitable prediction methods for engineering applications.In this work,PFC2D software was used to simulate coal seam hydraulic fracturing.The results were used in a coupled mathematical model of the interaction between coal seam deformation and gas flow.The results show that the displacement and velocity of particles increase in the direction of minimum principal stress,and the cracks propagate in the direction of maximum principal stress.The gas pressure drop rate and permeability increase rate of the fracture model are higher than that of the non-fracture model.Both parameters decrease rapidly with an increase in the drainage time and approach 0.The longer the hydraulic fracturing time,the more complex the fracture network is,and the faster the gas pressure drops.However,the impact of fracturing on the gas drainage effect declines over time.As the fracturing time increases,the difference between the horizontal and vertical permeability increases.However,this difference decreases as the gas drainage time increases.The higher the initial void pressure,the faster the gas pressure drops,and the greater the permeability increase is.However,the influence of the initial void pressure on the permeability declines over time.The research results provide guidance for predicting the anti-reflection effect of hydraulic fracturing in underground coal mines.

Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A tight sandstone multi-physical hydraulic fractures simulator study and its field application

During the past years,the recovery of unconventional gas formation has attracted lots of attention and achieved huge success.To produce gas from the low-permeability unconventional formations,hydraulic fracturing technology is essential and critical.In this paper,we present the development of a three-dimensional thermalhydraulic-mechanical numerical simulator for the simulation of hydraulic fracturing operations in tight sandstone reservoirs.Our simulator is based on integrated finite difference(IFD)method.In this method,the simulation domain is subdivided into sub domains and the governing equations are integrated over a sub domain with flux terms expressed as an integral over the sub domain boundary using the divergence theorem.Our simulator conducts coupled thermal-hydraulic-mechanical simulation of the initiation and extension of hydraulic fractures.It also calculates the mass/heat transport of injected hydraulic fluids as well as proppants.Our simulator is able to handle anisotropic formations with multiple layers.Our simulator has been validated by comparing with an analytical solution as well as Ribeiro and Sharma model.Our model can simulate fracture spacing effect on fracture profile when combining IFD with Discontinuous Displacement Method(DDM).

Numerical evaluation of the effect of fracture network connectivity in naturally fractured shale based on FSD model

In this paper, the effect of pre-existing discrete fracture network(DFN) connectivity on hydraulic fracturing is numerically investigated in a rock mass subjected to in-situ stress. The simulation results show that DFN connectivity has a significant influence on the hydraulic fracture(HF) & DFN interaction and hydraulic fracturing effectiveness, which can be characterized by the total interaction area, stimulated DFN length, stimulated HF length, leak-off ratio, and stimulated total length. In addition, even at the same fluid injection rate, simulation models exhibit different responses that are strongly affected by the DFN connectivity. At a low injection rate, total interaction area decreases with increasing DFN connectivity; at a high injection rate, total interaction area increases with the increase of DFN connectivity. However, for any injection rate, the stimulated DFN length increases and stimulated HF length decreases with the increase of connectivity. Generally, this work shows that the DFN connectivity plays a crucial role in the interaction between hydraulic fractures, the pre-existing natural fractures and hydraulic fracturing effectiveness; in return, these three factors affect treating pressure, created microseismicity and corresponding stimulated volume. This work strongly relates to the production technology and the evaluation of hydraulic fracturing effectiveness. It is helpful for the optimization of hydraulic fracturing simulations in naturally fractured formations.

Stable and realistic crack pattern generation using a cracking node method

This paper presents a method for simulating surface crack patterns appearing in ceramic glaze, glass, wood and mud. It uses a physically and heuristically combined method to model this type of crack pattern. A stress field is defined heuristically over the triangle mesh of an object. Then, a first-order quasi-static cracking node method （CNM） is used to model deformation. A novel combined stress and energy combined crack criterion is employed to address crack initiation and propagation separately according to physics. Meanwhile, a highest-stress-first rule is applied in crack initiation, and a breadth-first rule is applied in crack propagation. Finally, a local stress relaxation step is employed to evolve the stress field and avoid shattering artifacts. Other related issues are also discussed, such as the elimination of quadra- ture sub-cells, the prevention of parallel cracks and spurious crack procession. Using this method, a variety of crack patterns observed in the real world can be reproduced by changing a set of parameters. Consequently, our method is robust because the computational mesh is independent of dynamic cracks and has no sliver elements. We evaluate the realism of our results by comparing them with photographs of realworld examples. Further, we demonstrate the controllability of our method by varying different parameters.

Triangular element partition method with consideration of crack tip

In fracture simulation,how to model the pre-existing cracks and simulate their propagation without remeshing is an important topic.The newly developed triangular element partition method(TEPM)provides an efficient approach to this problem.It firstly meshes the cracked body regardless of the geometry integrity of the interesting object with triangular elements.After the meshing procedure is completed,some elements are intersected by cracks.For the element intersected by a crack,the TEPM takes the element partition technique to incorporate the discontinuity into the numerical model without any interpolation enrichment.By this approach,the TEPM can simulate fracture without mesh modification.In the TEPM,all the cracked elements are treated as the usual partitioned elements in which the crack runs through.The virtual node pairs(the intersection points of crack faces and elements)at the opposite faces of the crack move independently.Their displacements are respectively determined by their neighbor real nodes(nodes formatted in the original mesh scheme)at the same side of the crack.However,among these cracked elements,the element containing a crack tip,referred to as the crack tip element thereafter,behaves differently from those cut through by the crack.Its influence on the singular field at the vicinity of the fracture tip becomes increasingly significant with the element size increasing.In the crack tip element,the virtual node pair at the crack tip move consistently before fracture occurs while the virtual node pair separate and each virtual node moves independently after the fracture propagates.Accordingly,the crack tip element is automatically transformed into the usual partitioned element.In the present paper,the crack tip element is introduced into the TEPM to account for the effect of the crack tip.Validation examples indicate that the present method is almost free from the element size effect.It can reach the same precision as the conventional finite element method under the same meshing scheme.But the TEPM is much more efficient and convenient than the conventional finite element method because the TEPM avoids the troubles that the conventional finite element method suffers,e.g.,the meshing problem of cracked body,modification of mesh scheme,etc.Though the extended finite element method can also avoid these troubles,it introduces extra degrees of freedom due to node interpolation enrichment.Due to the simplicity of the present TEPM,it is believed that its perspective should be highly inspiring.