Three-dimensional Finite Element Algorithm Research Articles

Analysis of the Influence of Different Fracture Network Structures on the Production of Shale Gas Reservoirs

Volume fracturing is a key technology in developing unconventional gas reservoirs that contain nano/micron pores. Different fracture structures exert significantly different effects on shale gas production, and a fracture structure can be learned only in a later part of detection. On the basis of a multiscale gas seepage model considering diffusion, slippage, and desorption effects, a three-dimensional finite element algorithm is developed. Two finite element models for different fracture structures for a shale gas reservoir in the Sichuan Basin are established and studied under the condition of equal fracture volumes. One is a tree-like fracture, and the other is a lattice-like fracture. Their effects on the production of a fracture network structure are studied. Numerical results show that under the same condition of equal volumes, the production of the tree-like fracture is higher than that of the lattice-like fracture in the early development period because the angle between fracture branches and the flow direction plays an important role in the seepage of shale gas. In the middle and later periods, owing to a low flow rate, the production of the two structures is nearly similar. Finally, the lattice-like fracture model is regarded as an example to analyze the factors of shale properties that influence shale gas production. The analysis shows that gas production increases along with the diffusion coefficient and matrix permeability. The increase in permeability leads to a larger increase in production, but the decrease in permeability leads to a smaller decrease in production, indicating that the contribution of shale gas production is mainly fracture. The findings of this study can help better understand the influence of different shapes of fractures on the production in a shale gas reservoir.

Quasi 3D Finite Element Algorithm for Rotating Mixing Flows

The present research article presents numerical simulations of rotating of Newtonian fluid mixing flows in a cylindrical container through single rotating stirrer with agitator, where stirrer is located on the lid of container in concentric position. For this purpose a Quasi 3D (Three-Dimensional) FEA (Finite Element Algorithm) has been developed. The numerical algorithm is based on fractional stages semiimplicit Taylor-Galerkin/Pressure-Correction scheme. The simulation has been carried out to analyze the effects of agitator on mixing behavior. The numerical results show that Quasi 3D FEA is an accurate mathematical tool and able to achieve good results for flow structure in laminar regime.

Application of Linear Viscoelastic Properties in Semianalytical Finite Element Method with Recursive Time Integration to Analyze Asphalt Pavement Structure

Traditionally, asphalt pavements are considered as linear elastic materials in finite element (FE) method to save computational time for engineering design. However, asphalt mixture exhibits linear viscoelasticity at small strain and low temperature. Therefore, the results derived from the elastic analysis will inevitably lead to discrepancies from reality. Currently, several FE programs have already adopted viscoelasticity, but the high hardware demands and long execution times render them suitable primarily for research purposes. Semianalytical finite element method (SAFEM) was proposed to solve the abovementioned problem. The SAFEM is a three‐dimensional FE algorithm that only requires a two‐dimensional mesh by incorporating the Fourier series in the third dimension, which can significantly reduce the computational time. This paper describes the development of SAFEM to capture the viscoelastic property of asphalt pavements by using a recursive formulation. The formulation is verified by comparison with the commercial FE software ABAQUS. An application example is presented for simulations of creep deformation of the asphalt pavement. The investigation shows that the SAFEM is an efficient tool for pavement engineers to fast and reliably predict asphalt pavement responses; furthermore, the SAFEM provides a flexible, robust platform for the future development in the numerical simulation of asphalt pavements.

SAFEM – Software With Graphical User Interface for Fast and Accurate Finite Element Analysis of Asphalt Pavements

Abstract To effectively investigate the mechanical performance of asphalt pavements, software named SAFEM with a user friendly graphical user interface (GUI) was developed. It is based on the semi-analytical finite element (FE) method, which is a three-dimensional FE algorithm that only requires a two-dimensional mesh by incorporating the Fourier series in the third dimension. SAFEM is able to analyze static and dynamic responses of asphalt pavements under stationary or moving loads. Besides linear elasticity, a viscoelastic material model for asphalt layers has also been integrated. Verification was carried out to test and explore the functionality of the software package. We showed that SAFEM is an accurate tool for the fast prediction of asphalt pavement responses, such as the surface deflection and the strain/stress at response points. Furthermore, SAFEM provided a flexible, robust platform for the future development in the numerical simulation of asphalt pavements.

Thermal-stress analysis and calculation of single and dual chip set double-sided circuit board based on three-dimensional finite element algorithm

Purpose – The purpose of this paper is to analyze and figure out the temperature field and thermal stress field with the calculation model of thermal insulation material and composite material. Design/methodology/approach – The paper adopted the three-dimensional finite element algorithm. Findings – The simulated results showed great shearing strength between the chipset and the printed circuit board. The position of chip exerts great influence on the distribution of temperature field and thermal stress field of circuit board. The reasonable distribution of chip will effectively reduce the temperature extremum and stress extremum of circuit board. Originality/value – The paper analyzes and presents a discussion of the problems relating to the density of electronic packaging. The analysis process and the method of the paper provide essential help in resolving electronic device heat problems.

Three-dimensional simulation of heat and mass transport phenomena in planar SOFCs

High temperature Solid Oxide Fuel Cells (SOFCs) represent a promising and efficient technology for electrochemical conversion of chemical energy of a fuel into electrical energy. The future development of such technology depends on the availability of detailed and efficient multi-dimensional modeling tools. In this paper, a new three-dimensional finite element algorithm, based on a detailed mathematical model for fuel cells and on the fully explicit Artificial Compressibility (AC) Characteristic Based Split (CBS) scheme, is employed for the effective and efficient modeling of heat and mass transport phenomena coupled with electrochemical reactions in SOFC. The thermal field in the fuel cell is analyzed and the influence of the operating temperature on the fuel cell overall performance is investigated. The three-dimensional results obtained in this work are also compared to the results carried out by employing the two-dimensional version of the present scheme. The results are validated against experimental data available in the literature.

Three-dimensional finite element simulation of large-scale nonlinear contact friction problems in deformable rocks

A three-dimensional finite element method is proposed and used to deal with large-scale nonlinear contact friction problems in deformable rocks. Together with the use of the node-to-point contact element strategy, the corresponding three-dimensional finite element algorithm is presented to simulate the nonlinear contact friction behaviour between deformable rock blocks. In order to ensure the correctness and accuracy of the resulting numerical solutions, the proposed finite element formulation for a three-dimensional nonlinear contact friction problem is verified using a benchmark problem, for which the analytical solution is available. As an application example, the proposed three-dimensional finite element method is used to investigate the plate behaviour of a subduction fault model, which simulates a region around Northeast Japan. Due to the general nature of the methodology, the proposed three-dimensional finite element algorithm can be also used to simulate many nonlinear contact friction problems associated with the slope instability process and the sliding failure mechanism between a gravity dam and its foundation in the engineering field.

Finite element resistivity modelling for three-dimensional structures with arbitrary anisotropy

We present a three-dimensional finite element algorithm for direct current resistivity modelling. The standard Fortran code allows for nearly arbitrary conductivity structures including general anisotropy. The problem is formulated in terms of secondary potentials where mixed boundary conditions are incorporated. Also in case of anisotropy, this type of boundary condition is superior to the Dirichlet type. We have verified the finite element method using an anisotropic two-layered earth, whose analytical solutions are available. For this simple model, the algorithm achieves high accuracy. The relative deviation between numerical and analytical solution is less than 1.2%. Due to the lack of further analytical references, the responses of three representative model types serve as a cross-check for plausibility and prove the operativeness of the code.

A three-dimensional abrasion algorithm for projectile mass loss during penetration

A three-dimensional finite-element algorithm is presented for the computation of projectile mass loss due to abrasion at a projectile/target interface. The algorithm is an extension of the algorithm previously presented by the authors for axisymmetric computations. A description of the algorithm emphasizes the additional complexities introduced by three dimensions. The most significant complexity is the adjustment of the Lagrangian projectile mesh to avoid the convergence of nodes at the tip of the projectile nose as mass is removed from the nose. This adjustment is achieved in three dimensions by combining periodic calls to a rezoning algorithm (that redistributes the interior nodes of the mesh without changing connectivities) with an incremental adjustment of the surface nodes (that is applied tangent to the surface each timestep.) Numerical examples include comparisons to test data and demonstrations of the effects of non-axisymmetric impact.

An adaptive three-dimensional finite element algorithm for the orthogonal cutting of composite materials

In order to analyze the mechanism of cutting a fiber-reinforced composite using the finite element method (FEM) an appropriate meshing for the matrix, the fibers and their interfaces is essential. In a two-dimensional FEM analysis, the uniform increase of elements remains an attractive way with reasonable cost. However, this is not true in three-dimensional cases as the degrees of freedom rise dramatically. This paper aims at an efficient way to achieve smooth material removal in three-dimensional cuttings of fiber-reinforced composites. An adaptive algorithm was developed to control the solution steps and input data and to handle the remeshing of the selected elements using the criterion of the maximum shear stress. Different sets of three-dimensional elements were used to account for the fiber and matrix materials. At each solution step, the algorithm examined all sets of elements, determined those with the maximum shear stress and replaced them with refined meshes such that interconnectivity of the new elements satisfies the compatibility conditions. The solution of the previous time step was then mapped to the new mesh as the initial conditions. The chip formation was realized by the technique of element death. It was found that although the use of an algorithm increases the computational time, it offers a more cost-effective finite element mesh than the conventional method of refinement. In addition, the algorithm can accommodate the behavior of a fiber-reinforced composite under general cutting conditions. The numerical result shows a close agreement with the relevant experimental results.

Numerical and experimental investigation of the laser forming process

In this paper numerical and experimental results from an investigation on the laser forming process of metallic plates are discussed. The laser forming process has been simulated numerically, a three-dimensional finite-element algorithm having been developed. The algorithm includes a non-linear transient coupled thermal–structural analysis; the temperature dependency of the thermal and mechanical properties of the material being accounted for. The proposed algorithm is capable of calculating the time-dependent temperatures, stresses and strains during the process as well as of predicting the final shape of steel-plates and sheets. Numerical simulation has been carried out for bending as well as for the forming of sine-shaped plates. Validation of the numerical simulation was made experimentally. An experimental parametric study was performed on one-edge-clamped plates irradiated by a CO2 laser. Good correlation between the numerical simulation and the experimental results was demonstrated.

Numerical Simulation Of The Laser Forming ProcessIn Metallic Plates

This paper presents results from an on - going study on the numerical simulation of the laser forming process in metallic plates. To this scope a three-dimensional finite element algorithm is developed, by means of the ANSYS' code: the algorithm is capable of simulating the laser forming process. A transient Thermal - Structural analysis has been carried out for the calculation of the time dependency of temperatures, stresses and strains during the process such that the prediction of the final shape of steel-plates can be achieved. During the transient analysis, the dependency of thermal and mechanical properties of the material on the temperature has been taken into account. The algorithm has been applied for simulating the bending process of a plate. For assessing the accuracy of the numerical forming process simulation a series of experiments have been performed on steel plates, by using different laser parameters. The experiments have been carried out on one-edge-clamped plates irradiated by a CO 2 laser in an one-line pass parallel to the clamp. A device comprising LVD Transducers has been used allowing to monitor the distortion of the plate. Numerical simulation and experimental results fit well.