Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Flow simulation considering adsorption boundary layer based on digital rock and finite element method

Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.

Axisymmetric Finite Element Method for Analysis of Plate on Layered Soil

To obtain the fundamental solution of soil has become the key problem for the semi-analytical and semi-numerical (SASN) method in analyzing plate on layered soil. By applying axisymmetric finite element method (FEM),an expression relating the surface settlement and the reaction of the layered soil can be obtained. Such a reaction can be treated as load acting on the applied external load. Having the plate modelled by four-node elements,the governing equation of the plate can be formed and solved. In this case, the fundamental solution can be introduced into the global soil stiffness matrix and five-node or nine-node element soil stiffness matrix.The existing commercial FEM software can be used to solve the fundamental solution of soil, which can bypass the complicated formula derivation and boasts high computational efficiency as well.

FINITE ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL DIFFUSION-REACTION EQUATIONS OF BOUNDARY LAYER TYPE IN POROUS CATALYST PELLET

In this paper,finite element method(FEM)is used to solve two-dimensional diffu-sion-reaction equations of boundary layer type.This kind of equations are usually too complicatedand diffcult to be solved by applying the traditional methods used in chemical engineering becauseof the steep gradients of concentration and temperature.But,these difficulties are easy to be over-comed when the FEM is used.The integraded steps of solving this kind of problems by the FEMare presented in this paper.By applying the FEM to the two actual examples,the conclusion can bereached that the FEM has the advantages of simplicity and good accuracy.

Swelling-induced finite bending of functionally graded pH-responsive hydrogels:a semi-analytical method

Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅰ)——GENERAL THEORY

In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half-space into a scries of layers in the direction of depth, the material junctions in each layer are simulated by exponential functions Consequently, the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used. We have obtained the relationship between the 'layer forces' and 'layer displacements'. This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅱ)——SPECIAL CASES AND NUMERICAL EXAMPLES

In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axisymmetric problems and static problems are discussed, respectively, and this finite layer method is also generalized to the problems in which materials possess viscous properties. Two numerical examples have been presented for the axisymmetric case. From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.

Finite Element Analysis in Combination with Perfectly Matched Layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials

The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the mesh. In fact, these ones do not contribute in practice to the corresponding experimental response. The Perfectly Matched Layer (PML) method, allows to suppress the boundary reflections. In this work, we first demonstrate the basis of PML adapted to FEA formalism. Next, the results of such a method are depicted allowing a discussion on the behavior of finite acoustic resonators.

Finite element analysis on stresses field of normalized layer thickness within ceramic coating on aluminized steel

Multilayer ceramic coatings were fabricated on steel substrate using a combined technique of hot dipping aluminum(HDA) and plasma electrolytic oxidation(PEO). A triangle of normalized layer thickness was created for describing thickness ratios of HDA/PEO coatings. Then, the effect of thickness ratio on stresses field of HDA/PEO coatings subjected to uniform normal contact load was investigated by finite element method. Results show that the surface tensile stress is mainly affected by the thickness ratio of Al layer when the total thickness of coating is unchanged. With the increase of Al layer thickness, the surface tensile stress rises quickly. When Al2O3 layer thickness increases, surface tensile stress is diminished. Meanwhile, the maximum shear stress moves rapidly towards internal part of HDA/PEO coatings. Shear stress at the Al2O3 /Al interface is minimal when Al2O3 layer and Al layer have the same thickness.

Finite Element Modeling of a Fluid Filled Cylindrical Shell with Active Constrained Layer Damping

On the basis of the piezoelectric theory, Mindlin plate theory, viscoelastic theory and ideal fluid equation, the finite element modeling of a fluid-filled cylindrical shell with active constrained layer damping (ACLD) was discussed. Energy methods and Lagrange’s equation were used to obtain dynamic equations of the cylindrical shell with ACLD treatments, which was modeled as well with the finite element method. The GHM (Golla-Hughes-McTavish) method was applied to model the frequency dependent damping of viscoelastic material. Ideal and incompressible fluid was considered to establish the dynamic equations of the fluid-filled cylindrical shell with ACLD treatments, Numerical results obtained from the finite element analysis were compared with those from an experiment. The comparison shows that the proposed modeling method is accurate and reliable.

Adaptive Finite Element Method for Steady Convection-Diffusion Equation

This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.

Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.

Initial residual stress experiment and simulation of thin-walled parts for layer removal method

Thin-walled parts have low stiffness characteristic. Initial residual stress of thin-walled blanks is an important influence factor on machining stability. The present work is to verify the feasibility of an initial residual stress measurement of layer removal method. According to initial residual stress experiment for casting ZL205 A aluminum alloy tapered thin-walled blank by a common method,namely hole-drilling method,three finite element models with initial residual stress are established to simulate the layer removal method in ABAQUS and ANSYS software. By analyzing the results of simulation and experiments,the cutting residual stress inlayer removal process has a significant effect on measurement results. Reducing cutting residual stress is helpful to improve accuracy of layer removal method.

Modified Layer-Removal Method for Measurement of Residual Stress in Pre-stretched Aluminium Alloy Plate

Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus,the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieces. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method( FEM). Moreover,the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method,and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.

Numerical Analysis of the Structure of High-Strength Double-Layer Steel Plate Concrete Shaft by Drilling Method of Water-Bearing Weak Rock Formation

In order to ensure the safety of coal mine shaft construction, a double-layer steel plate concrete composite shaft wall structure was proposed. However, fewer studies were conducted on this structure, which made engineers too confused to fully recognize its feasibility of this structure. Hence, based on the previous experimental research on the Taohutu mine construction project in Ordos in Inner Mongolia, this research paper aims to provide a widely deep numerical analysis by the usage of the finite element software, in fact, to establish the corresponding numerical analysis model and make a comparison with the experimental data to get the rationality of the verified model. The influence of the composite characteristics of the steel plate and concrete on the ultimate bearing capacity and stress field of the shaft wall structure is studied here through the method of multi-factor analysis. Also, the optimal design scheme of the double-layer steel plate and concrete composite shaft wall structure is proposed in this research paper.

双参数层状地基中水平动荷载和扭转振动组合作用下受荷桩受力变形分析

为了更准确地分析桩顶在承受水平动荷载H(t)和扭转振动T(t)组合荷载作用下的受力变形特性,基于Pasternak模型,考虑多向荷载间的相互作用,建立层状地基中H(t)-T(t)受荷桩简化分析模型。利用有限杆单元法推导出桩身内力位移数值解,并与已有相关理论解、模型试验和有限元模拟结果进行对比验证。参数分析表明:(1)与Winkler模型计算结果相比,考虑土体剪切效应后,桩顶水平位移和桩身最大弯矩分别减小了11.8%和10.5%。(2)增大外荷载无量纲频率可减小桩身水平位移和弯矩,但同时会减小H(t)-T(t)耦合刚度。(3)在层状地基中,表层土对桩身内力位移的影响最大,且存在临界影响深度,表层硬土的临界影响厚度是表层软土临界影响厚度的3.5~6.5倍。(4)采用杆单元模型可减少单元划分数量和计算时间,有效提高计算效率。

薄橡胶层改善喷丸质量机理研究

目的 为了解决喷丸导致的金属表面粗糙度提升问题,方法 提出在金属表面铺设薄层橡胶层,通过薄橡胶层的变形均匀化丸粒的冲击压力,进而抑制丸粒冲击所造成的粗糙度急剧增加的新工艺。为验证新工艺的可行性并揭示其机理,采用有限元软件Abaqus分别建立传统喷丸、黏结橡胶层喷丸和自由铺设橡胶层喷丸的仿真模型;设定丸粒为半径0.5 mm的球形刚体,丸粒初始速度为50 m/s;工件材料为Q235,采用Johnson-Cook本构模型;薄层橡胶采用双参数Mooney-Rivlin本构模型;仿真模型中不同部件之间的摩擦系数均设定为0.2;所有模型均采用显式求解方法。结果 在传统喷丸、黏结薄橡胶层喷丸和自由铺设橡胶喷丸条件下,工件表面丸粒冲击点的残余压应力分别为96,343,252 MPa,工件表层最大残余压应力分别为391,426,373 MPa,工件表面的残余压应力得到显著提升;3种喷丸工艺下冲击压痕分别为56.2,26.1,35.4μm,表面薄层橡胶有效降低了工件表面粗糙度;工件表层残余应力的分布形式与橡胶层的厚度密切相关,当橡胶厚度分别为0.05,0.20 mm时,所得到的最大残余压应力分别为329,373 MPa,距离工件表面分别为256,141μm。结论 在机理上,橡胶的大变形特征增大了丸粒的冲击作用面积,延长了冲击作用时间,是薄橡胶层能够改善喷丸质量的根本原因。

孔洞形状对层状岩石力学特性影响的FDEM数值模拟研究

为揭示孔洞形状对层状岩石力学性质和破坏模式的影响,采用有限元-离散元耦合数值模拟方法(FDEM)开展系列数值模拟研究。首先,阐述FDEM模拟层状岩石的基本原理,然后,开展不同层理倾角完整试样的单轴压缩模拟,并与试验结果进行对比验证。最后,对含有圆形、椭圆形、三角形、矩形和方形孔洞的层状岩石试样(β为0°、30°、45°、60°和90°)进行单轴压缩模拟研究。研究结果表明:对于不同孔洞形状的试样,抗压强度和试样破坏程度随层理倾角的增大呈V字型变化趋势,且均在层理倾角为0°时抗压强度取得最大值,在90°时破坏程度最为严重;孔洞的存在严重削弱了试样的力学性能,且削弱幅度与孔洞形状密切相关,其中方形和圆形孔洞对抗压强度的削弱能力最弱。将含不同形状孔洞试样的破坏模式随层理倾角的变化主要分为穿层理面拉剪混合破坏(β=0°)、沿层理面与穿层理面混合拉剪破坏(β=30°)、沿层理面剪切破坏(β=45°和60°)和沿层理面拉剪劈裂破坏(β=90°)。

伽马射线探测器冲击减振设计及验证

针对某伽马射线探测器受到振动冲击后敏感器件损坏严重的问题进行减振设计,研究减振器阻尼层尺寸参数对整体固有频率和抗冲击性能的影响,以及薄壁结构基座对抑制振动和冲击传递的影响;进而采取设计减振器、合理选取阻尼层尺寸参数、增加二级阻尼缓冲减振和改进薄壁结构的措施完成减振设计;最后通过仿真和试验验证减振设计的合理性。研究表明:减振器能够降低结构刚度,对冲击产生大幅度衰减作用;阻尼层直径是提高抗冲击性能的主要因素,探测器整体固有频率和冲击响应均随阻尼层直径的增加而减小;薄壁结构基座对激励有放大作用,可以通过调整局部结构降低冲击响应;二级阻尼缓冲减振设计对关键器件有较好的减振功效,尤其是在低频段。该研究可为有结构限制要求的航天器的冲击减振设计提供参考。

电磁波传播测井地层介电常数测量应用分析

受地层水矿化度的影响,复杂油气储层电性特征复杂,采用电阻率测量方法难以对复杂储层流体进行准确评价与识别;但介电常数受地层水矿化度影响小,并且水的介电常数远大于油气介电常数,通过电磁波传播测井仪测量地层介电常数可有效准确区分油气储层与水层,且其地层响应转换图版的精准性对复杂储层流体的准确评价至关重要。本文基于等效磁偶极子模型推导了层状介质中1 GHz电磁波传播计算公式,提出了将测量探头几何工程参数融入有限元的精确仿真方法,采用COMSOL Multiphysics建立1∶1有限元仿真模型,分析了探头几何工程参数对地层转换图版的影响。搭建实验系统验证了理论仿真的准确性,测量结果显示基于精确仿真方法得到介电常数与真实值的相对误差约为1%。研制出电磁波传播测井仪,并在某油田开展了非常规页岩油气测井应用,为油田复杂油气储层的评价提供了一种有效的测量方法。