Reconstruction of 3-D digital cores using a hybrid method

A 3-D digital core describes the pore space microstructure of rocks. An X-ray micro CT scan is the most accurate and direct but costly method to obtain a 3-D digital core. In this study, we propose a hybrid method which combines sedimentation simulation and simulated annealing （SA） method to generate 3-D digital cores based on 2-D images of rocks. The method starts with the sedimentation simulation to build a 3-D digital core, which is the initial configuration for the SA method. We update the initial digital core using the SA method to match the auto-correlation function of the 2-D rock image and eventually build the final 3-D digital core. Compared with the typical SA method, the hybrid method has significantly reduced the computation time. Local porosity theory is applied to quantitatively compare the reconstructed 3-D digital cores with the X-ray micro CT 3-D images. The results indicate that the 3-D digital cores reconstructed by the hybrid method have homogeneity and geometric connectivity similar to those of the X-ray micro CT image. The formation factors and permeabilities of the reconstructed 3-D digital cores are estimated using the finite element method （FEM） and lattice Boltzmann method （LBM）, respectively. The simulated results are in good agreement with the experimental measurements. Comparison of the simulation results suggests that the digital cores reconstructed by the hybrid method more closely reflect the true transport properties than the typical SA method alone.

3-D Geological Modeling-Concept,Methods and Key Techniques

3-D geological modeling plays an increasingly important role in Petroleum Geology, Mining Geology and Engineering Geology. The complexity of geological conditions requires different modeling methods in different situations. This paper summarizes the general concept of geological modeling; compares the characteristics of borehole-based modeling, cross-section based modeling and multi- source interactive modeling; analyses key techniques in 3-D geological modeling; and highlights the main difficulties and directions of future studies.

ANALYSIS OF SLAB EDGING BY A 3-D RIGID VISCO-PLASTIC FINITE ELEMENT METHOD

3-D rigid visco-plastic finite element method (FEM) is used in the analysisof metal forming processes, including strip and plate rolling, shape rolling, slab edging, specialstrip rolling. The shifted incomplete Cholesky decomposition of the stiffness matrix with thesolution of the equations for velocity increment by the conjugate gradient method is combined. Thistechnique, termed the shifted ICCG method, is then employed to solve the slab edging problem. Theperformance of this algorithm in terms of the number of iterations, friction variation, shiftedparameter psi and the results of simulation for processing parameters are analysed. Numerical testsand application of this technique verify the efficiency and stability of the shifted ICCG method inthe analysis of slab edging.

A, ■-Ω METHOD FOR 3-D EDDY CURRENT ANALYSIS

After the field equations and the snonumuoo conditions between the interfaces for 3D eddy current problems Under various gauges were discussed, it was pointed cut in this paper that using the magnetic vector potential A. the electric scalar potential and Coulomb gauge △ .A = 0 in eddy current regions and using the magntetic scalar potential Ω in the non-conducting regions are more suitable. All field equations, the boundary conditions, the interface continuity conditions and the corresponding variational principle of this method are also given

A TENSOR ANALYSIS METHOD FOR ESTIMATING 3-D MOTION PARAMETERS

By using the center projection image sequence to estimate 3-D motion parameters,one needs to know the corresponding relationship between the feature of motion object in spaceand the projection coordinate on image plane.In order to avoid using the relationship of featurecorrespondence,the tensor analysis method in the affine transformation system is presented,andthe simulation data of experimental results are given.

MICRO MECHANICAL ANALYSIS OF 3-D WOVEN COMPOSITES

A micro mechanical model is carried out to predict micro stresses and macro elastic properties of 3-D woven composites. A unit cell is composed of two phases. One is fiber yarn and the other is resin or fiber yarn in transverse. The additional shearing introduced by bending of fiber yarn is considered. The method to determine the microstructure is also discussed. This model is applied to the analysis of a 3-D woven graphite/epoxy composite. Micro stresses of the cell are studied, and then macro modulus is obtained by employing the average method. The predictions agree well with experimental results.

A study on 3-D velocity structure of crust and upper mantle in Sichuan -Yunnan region, China

Based on the first arrival P and S data of 4 625 regional earthquakes recorded at 174 stations dispersed in the Yunnan and Sichuan Provinces, the 3-D velocity structure of crust and upper mantle in the region is determined, incorporating with previous deep geophysical data. In the upper crust, a positive anomaly velocity zone exists in the Sichuan basin, whereas a negative anomaly velocity zone exists in the western Sichuan plateau. The boundary between the positive and negative anomaly zones is the Longmenshan fault zone. The images of lower crust and upper mantle in the Longmenshan fault, Xianshuihe fault, Honghe fault and others show the characteristic of tectonic boundary, indicating that the faults likely penetrate the Moho discontinuity. The negative velocity anomalies at the depth of 50 km in the Tengchong volcanic area and the Panxi tectonic zone appear to be associated with the temperature and composition variations in the upper mantle. The overall features of the crustal and the upper mantle structures in the SichuanYunnan region are the lower average velocity in both crust and uppermost mantle, the large crustal thickness variations, and the existence of high conductivity layer in the crust or/and upper mantle, and higher geothermal value. All these features are closely related to the collision between the India and the Asia plates. The crustal velocity in the SichuanYunnan rhombic block generally shows normal value or positive anomaly, while the negative anomaly exists in the area along the large strike-slip faults as the block boundary. It is conducive to the crustal block side-pressing out along the faults. In the major seismic zones, the seismicity is relative to the negative anomaly velocity. Most strong earthquakes occurred in the upper-mid crust with positive anomaly or normal velocity, where the negative anomaly zone generally exists below.

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.

Thre-dimensional topographic responses in MT using finite diference method

In this paper, the magnetotelluric response to 3-D earth topography was studied using the finite difference method for rectangular cells. Three numerical modeling calculations were carried out; the results indicate that the finite difference method is applicable to the magnetotelluric problem in estimating the 3-D topographic responses.

A SELF-SIMILAR CRACK EXPANSION METHOD FOR THREE-DIMENSIONAL CRACKS IN AN INFINITE OR SEMI-INFINITE MEDIUM

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples shaw that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks ate in good agreement with other analytical solutions.

Improved treatments for evaluating horizontal magnetic components through the 3-D FDM in E-polarization induction problems

To improve the accuracy of the numerical evaluation through the 3-D finite difference method, the surface boundary conditions are added to modify the old program. The author has tested the new program by making calculations for the model constructed by Wanamaker, et al (1984). The comparison between the numerical results obtained from this paper and those by Wannamaker, et al (1984) indicates that a pronounced improvement is realized in the evaluation of the horizontal magnetic components. Moreover, better calculations for the vertical magnetic components are also obtainable by using the new program.

Reconstruction of Temperature Field in 3-D, Absorbing, Emitting, and Anisotropically Scattering Medium

The soft measurement technology of flame temperature field is an efficient method to learn the combustion status in furnace. Generally, it reconstructs the temperature field in furnace through the image of flame, which is a process to solve radiative inverse problem. In this paper, the flame of pulverized coal is considered as 3-D, absorbing, emitting, and anisotropically scattering non-gray medium. Through the study on inverse problem of radiative heat transfer, the temperature field in this kind of medium has been reconstructed. The mechanism of 3-D radiative heat transfer in a rectangular media, which is 2 m×3 m× 5 m and full of CO2, N2 and carbon particles, is studied with Monte Carlo method. The 3-D temperature field in this rectangular space is reconstructed and the influence of particles density profile is discussed.

Scattering of seismic waves by three-dimensional large-scale hill topography simulated by a fast parallel IBEM

To solve seismic wave scattering by a large-scale three-dimensional(3-D) hill topography, a fast parallel indirect boundary element method(IBEM) is developed by proposing a new construction method for the wave field, modifying the generalized minimum residual(GMRES) algorithm and constructing an Open MP plus MPI parallel model. The validations of accuracy and efficiency show that this method can solve 3-D seismic response of a large-scale hill topography for broadband waves, and overcome the weakness of large storage and low efficiency of the traditional IBEM. Based on this new algorithm architecture, taking the broadband scattering of plane SV waves by a large-scale Gaussian-shaped hill of thousands-meters height as an example, the influence of several important parameters is investigated, including the incident frequency, the incident angle and the height-width and length-width ratio of the hill. The numerical results illustrate that the amplification effect on the ground motion by a near-hemispherical hill is more significant than the narrow hill. For low-frequency waves, the scattering effect of the higher hill is more pronounced, and there is only a single peak near the top of the hill. However, for high-frequency waves, rapid spatial variation of displacement amplitude appears on the hill surface.

Detection technology and application of electromagnetic method for hidden danger of water gushing at coal face

The principles, methods, technologies and application effects of several electromagnetic methods for the detection of the hidden danger of water gushing at the coal face were introduced. Also, emphasis was laid on expounding the methods, principles and effects of down-hole detections by electric transmission tomography and transient electromagnetic method. The potential of point power supplied in the underground homogeneous semi-space, as well as the response to a low-resistivity abnormal body in the homogeneous semi-space, was simulated by adopting 3-D finite element method to interpret the basic theory of the electric transmission tomography. The results of actual measurement show that the mine electromagnetic method is sensitive to water-bearing low-resistivity bodies and can play a unique role in detecting the hidden danger of water gushing at the coal face.

A Lifting Line Theory for a Three-dimensional Hydrofoil

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.

Numerical simulation of 3-D water collapse with an obstacle by FEM-level set method

An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method （FEM）： （1） solving a two-fluid Navier-Stokes （N-S） equations over the whole domain, （2） transporting the level set function with the obtained velocity field, （3） the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface. In this paper, the 3-D water colunm collapse with an obstacle is simulated, which yielded good agreement with the experimental data.

Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media

In this paper,we establish the exponential convergence theory for the multipole and local expansions,shifting and translation operators for the Green's function of 3-dimensional Laplace equation in layered media.An immediate application of the theory is to ensure the exponential convergence of the FMM which has been shown by the numerical results reported in[27].As the Green's function in layered media consists of free space and reaction field components and the theory for the free space components is well known,this paper will focus on the analysis for the reaction components.We first prove that the density functions in the integral representations of the reaction components are analytic and bounded in the right half complex wave number plane.Then,by using the Cagniard-de Hoop transform and contour deformations,estimates for the remainder terms of the truncated expansions are given,and,as a result,the exponential convergence for the expansions and translation operators is proven.

Analysis of 3-D Frictional Contact Mechanics Problems by a Boundary Element Method

The development of two boundary element algorithms for solving 3-D, frictional, and linear elastostatic contact problems is reported in this paper. The algorithms employ nonconforming discreti- zations for solving 3-D boundary element models, which provide much needed flexibility in the bound- ary element modeling for 3-D contact problems. These algorithms are implemented in a new 3-D boundary element code and verified using several examples. For the numerical examples studied, the results using the new boundary element algorithms match very well with the results using a commercial finite element code, and clearly demonstrate the feasibility of the new boundary element approach for 3-D contact analysis.

A Two-Streamfunction-Coordinate Method for the Numerical Solution of 3-D Aero-Thermodynamics Direct and Inverse Problems

This paper describes a new method which has been developed for the solution of direct and inverse problems of 3-D compressible flows in turbomachinery.Two types of streamfunctions are proposed in the paper and the streamfunction-coordinate system is applied in numerical computations.The algorithm is applied to stator blades and the results are compared with experimental data,It is shown that the comparisons are very satis- factory.