Adaptive finite element–discrete element analysis for stratal movement and microseismic behaviours induced by multistage propagation of three-dimensional multiple hydraulic fractures

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Three Dimensional ◽  
Fracture Propagation ◽  
Discrete Element ◽  
Hydraulic Fractures ◽  
Adaptive Finite Element ◽  
Fracture Networks ◽  
Content Type ◽  
Microseismic Events

Purpose Optimized three-dimensional (3D) fracture networks are crucial for multistage hydrofracturing. To better understand the mechanisms controlling potential disasters as well as to predict them in 3D multistage hydrofracturing, some governing factors, such as fluid injection-induced stratal movement, compression between multiple hydraulic fractures, fracturing fluid flow, fracturing-induced microseismic damaged and contact slip events, must be properly simulated via numerical models. This study aims to analyze the stratal movement and microseismic behaviours induced by multistage propagation of 3D multiple hydraulic fractures. Design/methodology/approach Adaptive finite element–discrete element method was used to overcome the limitations of conventional finite element methods in simulating 3D fracture propagation. This new approach uses a local remeshing and coarsening strategy to ensure the accuracy of solutions, reliability of fracture propagation path and computational efficiency. Engineering-scale numerical models were proposed that account for the hydro-mechanical coupling and fracturing fluid leak-off, to simulate multistage propagation of 3D multiple hydraulic fractures, by which the evolution of the displacement, porosity and fracture fields, as well as the fracturing-induced microseismic events were computed. Findings Stratal movement and compression between 3D multiple hydraulic fractures intensify with increasing proximity to the propagating fractures. When the perforation cluster spaces are very narrow, alternate fracturing can improve fracturing effects over those achieved via sequential or simultaneous fracturing. Furthermore, the number and magnitude of microseismic events are directly proportional to the stratal movement and compression induced by multistage propagation of fracturing fracture networks. Originality/value Microseismic events induced by multistage propagation of 3D multiple hydraulic fractures and perforation cluster spaces and fracturing scenarios that impact the deformation and compression among fractures in porous rock matrices are well predicted and analyzed.

scholarly journals Adaptive Finite Element-Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre-Existing Fractures

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yongliang Wang ◽  
Yang Ju ◽  
Yongming Yang
Keyword(s):  
Finite Element ◽  
Hydraulic Fracture ◽  
Horizontal Well ◽  
Numerical Models ◽  
Fracture Propagation ◽  
Discrete Element ◽  
Hydraulic Fractures ◽  
Adaptive Finite Element ◽  
Naturally Fractured ◽  
Hydraulic Fracture Propagation

Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre-existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element-discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre-existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre-existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B-values, Hudson source type plots, and focal spheres.

Three Dimensional Dynamic Analyses on Stroller Wheel with Shock Absorber

2013 ◽  
Vol 387 ◽  
pp. 159-163
Author(s):  
Yi Chern Hsieh ◽  
Minh Hai Doan ◽  
Chen Tai Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
The Road ◽  
Dimensional Finite Element ◽  
On The Road ◽  
Three Dimensional Finite Element ◽  
Element Method

We present the analyses of dynamics behaviors on a stroller wheel by three dimensional finite element method. The vibration of the wheel system causes by two different type barriers on the road as an experiment design to mimic the real road conditions. In addition to experiment analysis, we use two different packages to numerically simulate the wheel system dynamics activities. Some of the simulation results have good agreement with the experimental data in this research. Other interesting data will be measured and analyzed by us for future study and we will investigate them by using adaptive finite element method for increasing the precision of the computation results.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Haohan Sun ◽  
Si Yuan
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Mesh Refinement ◽  
Error Tolerance ◽  
Maximum Norm ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Local Mesh Refinement ◽  
Elastic Membranes ◽  
Element Energy Projection

Purpose A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique. Design/methodology/approach By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems. Findings Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm. Originality/value By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.

A MSFEM to simulate the eddy current problem in laminated iron cores in 3D

2019 ◽  
Vol 38 (5) ◽  
pp. 1667-1682 ◽  
Author(s):  
Karl Hollaus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eddy Current ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Three Dimensions ◽  
Magnetic Vector Potential ◽  
Content Type ◽  
Element Method

Purpose The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty. Design/methodology/approach A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied. Findings Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM. Originality/value The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

scholarly journals 3D harmonic modeling of eddy currents in segmented conducting structures

2019 ◽  
Vol 38 (1) ◽  
pp. 2-23 ◽  
Author(s):  
C.H.H.M. Custers ◽  
J.W. Jansen ◽  
M.C. van Beurden ◽  
E.A. Lomonova
Keyword(s):  
Finite Element ◽  
Eddy Current ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Spatial Period ◽  
Content Type ◽  
Current Distributions ◽  
Wide Range ◽  
Conductivity Function ◽  
Electromagnetic Quantities

PurposeThe purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed.Design/methodology/approachIn conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results.FindingsThe method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed.Research limitations/implicationsBecause of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large.Practical implicationsBecause of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained.Originality/valueWith the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.

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