Numerical simulation of non-Archie electrophysical property of saturated rock with lattice Boltzmann method

The electrophysical property of saturated rocks is very important for reservoir identification and evaluation. In this paper, the lattice Boltzmann method （LBM） was used to study the electrophysical property of rock saturated with fluid because of its advantages over conventional numerical approaches in handling complex pore geometry and boundary conditions. The digital core model was constructed through the accumulation of matrix grains based on their radius distribution obtained by the measurements of core samples. The flow of electrical current through the core model saturated with oil and water was simulated on the mesoscopic scale to reveal the non-Archie relationship between resistivity index and water saturation （I-Sw）. The results from LBM simulation and laboratory measurements demonstrated that the I-Sw relation in the range of low water saturation was generally not a straight line in the log-log coordinates as described by the Archie equation. We thus developed a new equation based on numerical simulation and physical experiments. This new equation was used to fit the data from laboratory core measurements and previously published data. Determination of fluid saturation and reservoir evaluation could be significantly improved by using the new equation.

Numerical simulation of dynamic process for liquid film spreading by lattice Boltzmann method and its experimental verification

Combined with the kinetic model of liquid film spreading, a new numerical method of solid-liquid-gas three-phase flow was developed for the moving of contact line, which was a hybrid method of computational fluid dynamics and lattice Boltzmalm method （LBM）. By taking the effect of molecule force in droplet and the wall surface on liquid film into account, the changing law of contact angle with different surface tensions was analyzed on glass and aluminum foil surfaces. Compared with experimental results, the standard deviation by using LBM is less than 0.5°, which validates the feasibility of LBM simulation on the dynamic process of liquid film spreading. In addition, oscillations are discovered both at the initial and end phases. The phenomenon of retraction is also found and the maximum retraction angle is 7.58°. The obtained result shows that the retraction is proved to be correlative with precursor film by tracking the volume change of liquid film contour. Furthermore, non-dimensional coefficient 2 is introduced to measure the liquid film retraction capacity.

Numerical Simulation of Two-Dimensional Flow over Three Cylinders by Lattice Boltzmann Method

The numerical simulation using the multiple relaxation time lattice Boltzmann method （MRT-LBM） is carried out for the purpose of investigating the two-dimensional flow around three circular cylinders. Among these three circular cylinders, one of the three cylinders on which a forced in-line vibrating is used to do this research and attempt to find out the effects of the moving cylinder and the other two rigid cylinders on the wake characteristics and vortex formation. As a benchmark problem to discuss the problem of lift coefficient r.m.s for these cylinders with spacing ratios T/ D between other rigid side-by-side cylinders, and the calculation is carried out with two compared cases at Reynolds number of 100, two of the cylinders are rigid and the other one is an in-line vibrated cylinder lying downstream, in addition, forced vibrating amplitude and frequency are A/D = 0.5 and fv= 0.4 （where A is the forced amplitude, D is the cylinder diameter, and fv stands for the vibrating frequency, respectively）. The calculated results not only indicate that the spacing ratios T/D （T is the center-to-center spacing between the two upstream cylinders） have influence on the wake patterns and the formation of vortex shedding, but also analyze the lift coefficient r.m.s for the three cylinders with the spacing ratios S/D （where S is the center-to-center spacing between the center of upstream two side-by-side cylinders and downstream cylinder）.

Numerical simulation of wind flow fields around buildings using the lattice Boltzmann method

This paper presents the simulation results of the wind environment around a single high-rise building and that around two tall buildings in tandem arrangement by using the lattice Boltzmann method with an aim to understand the ventilation issues around high-rise buildings in an urban environment.We analyzed the velocity distribution around the buildings and performed numericl simulations to reveal the formation and evolution law of the complex vortex system around the high-rise buildings.Numerical simulation results manifest a periodicity phenamenon in the process of the vortex evolution.For the case of two high-rise buildings,wind velocity in the space between the two buildings is very small,which is nearly a silent regime.Wind velocity above the front building is relatively larger and the maximum wind velocity is approximately 2.5 times the incoming wind velocity.The numerical results can be used in layout planning of high-rise residential buildings to create better environment for ventilation purpose in an urban area.

Direct numerical simulation of particle-fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method

A coupled numerical method for the direct numerical simulation of particle-fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by the time-driven hard-sphere model, while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method （LBM）, Particle-fluid coupling is realized by an immersed boundary method （IBM）, which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid. The proposed scheme is validated in the classical flow-around-cylinder simulations, and preliminary application of this scheme to fluidization is reported, demonstrating it to be a promising computational strategy for better understanding complex behavior in particle-fluid systems.

On the Application of the Lattice Boltzmann Method to Predict Soil Meso Seepage Characteristics

In this study,a two-dimensional approach is elaborated to study with the lattice Boltzmann method(LBM)the seepage of water in the pores of a soil.Firstly,the D2Q9 model is selected to account for the discrete velocity distribution of water flow.In particular,impermeability is considered as macroscopic boundary condition for the left and right domain sides,while the upper and lower boundaries are assumed to behave as pressure boundaries controlled by different densities.The micro-boundary conditions are implemented through the standard rebound strategy and a non-equilibrium extrapolation scheme.Matlab is used for the development of the related algorithm.Finally,the influence of porosity,permeability,osmotic pressure and other factors is assessed with regard to seepage characteristics and the ensuing results are compared with Darcy’s law.The computations show that,for fixed initial conditions,the pore structure has a certain influence on the local velocity of seepage,but the overall state is stable,and the average velocity of each layer is the same.The larger the pore passage is,the faster the flow velocity is,and vice versa.For low permeability,the numerical results are consistent with the Darcy's law.The greater the pressure difference between the inlet and outlet of seepage,the greater the seepage rate.The relationship between them is linear(yet in good agreement with Darcy’s law).

Lattice Boltzmann method and its applications in engineering thermophysics

The lattice Boltzmann method (LBM), a mesoscopic method between the molecular dynamics method and the conventional numerical methods, has been developed into a very efficient numerical alternative in the past two decades. Unlike conventional numerical methods, the kinetic theory based LBM simulates fluid flows by tracking the evolution of the particle distribution function, and then accumulates the distribution to obtain macroscopic averaged properties. In this article we review some work on LBM applications in engineering thermophysics: (1) brief introduction to the development of the LBM; (2) fundamental theory of LBM including the Boltzmann equation, Maxwell distribution function, Boltzmann-BGK equation, and the lattice Boltzmann-BGK equation; (3) lattice Boltzmann models for compressible flows and non-equilibrium gas flows, bounce back-specular-reflection boundary scheme for microscale gaseous flows, the mass modified outlet boundary scheme for fully developed flows, and an implicit-explicit finite-difference-based LBM; and (4) applications of the LBM to oscillating flow, compressible flow, porous media flow, non-equilibrium flow, and gas resonant oscillating flow.

Numerical simulation of immiscible liquid-liquid flow in microchannels using lattice Boltzmann method

Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators.The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet.The five distinct flow regimes of the kerosene-water system,previously identified in the experiments from Zhao et al.,were reproduced.The quantitative and qualitative agreement between the simulations and the experimental data show the effectiveness of the numerical method.The roles of the interfacial tension and contact angle on the flow patterns and shapes of droplets were discussed and highlighted according to the numerical results based on the improved two-phase LB model.This work demonstrated that the developed LBM simulator is a viable tool to study immiscible two-phase flows in microchannels,and such a tool could provide tangible guidance for the design of various microfluidic devices that involve immiscible multi-phase flows.

Numerical simulation of ski-jump jet motion using lattice Boltzmann method

Based on the lattice Boltzmann method,a lattice Boltzmann(LB) model of the ski-jump jet two-phase flow is developed first and the corresponding boundary conditions are studied.A simple case study of a droplet horizontal movement calculation is carried out to test and verify the model,where level set method is used to track and reconstruct the moving droplet free surface. Then,we numerically simulate a two dimensional flow field of the ski-jump jet with the LB model,derive the moving surface and velocity vector field of the jet flow.The simulation results are very consistent with the physical mechanisms.The effectiveness and reliability of the model are demonstrated by the numerical examples.

SIMULATION OF THE TWO PHASE FLOW OF DROPLET IMPINGEMENT ON LIQUID FILM BY THE LATTICE BOLTZMANN METHOD

A Lattice Boltzmann Method （LBM） with two-distribution functions is employed for simulating the two-phase flow induced by a liquid droplet impinging onto the film of the same liquid on solid surface.The model is suitable for solution of twophase flow problem at high density and viscosity ratios of liquid to vapor and phase transition between liquid and its vapor.The roles of the vapor flow,the density ratio of liquid to vapor and the surface tension of the droplet in the splashing formation are discussed.It is concluded that the vapour flow induced by the droplet fall and splash in the whole impinging process may affect remarkably the splash behaviour.For the case of large density ratio of liquid to vapor a crown may engender after the droplet collides with the film.However,for the case of small density ratio of liquid to vapor a ＂bell＂ like splash may be observed.

Aerodynamic simulation of high-speed trains based on the Lattice Boltzmann Method (LBM)

Aerodynamic simulation of high-speed trains has been carried out by using Lattice Boltzmann Method (LBM). Non-simplified train model was used and the number of space grids reached tens of millions. All results under different working conditions reflected the actual situation.

Lattice Boltzmann method for simulating particle-fluid interactions

The lattice Boltzmann method （LBM） has gained increasing popularity in the last two decades as an alternative numerical approach for solving fluid flow problems. One of the most active research areas in the LBM is its application in particle-fluid systems, where the advantage of the LBM in efficiency and parallel scalability has made it superior to many other direct numerical simulation （DNS） techniques. This article intends to provide a brief review of the application of the LBM in particle-fluid systems. The numerical techniques in the LBM pertaining to simulations of particles are discussed, with emphasis on the advanced treatment for boundary conditions on the particle-fluid interface. Other numerical issues, such as the effect of the internal fluid, are also briefly described. Additionally, recent efforts in using the LBM to obtain closures for particle-fluid drag force are also reviewed.

Simulation of Droplet Impact onto Horizontal and Inclined Solid Surfaces with Lattice-Boltzmann Method

In this paper, the lattice-Bohzmann method is used to investigate the droplet dynamics after impact on horizontal and inclined solid surface. The two-phase interparticle potential model is employed. The model is found to possess a linear relation between the macroscopic properties （ surface tension σ and contact angle α） and microscopic parameters （ G, G, ）. The flow state of the droplet on the surface is analyzed in detail, and the effects of surface characteristic, impact velocity, impact angle, the viscosity and surface tension of the liquid are investigated, respectively. It is shown that the lattice-Bohzmann method can not only track exactly and automatically the interface, but also the simulation results have a good qualitative agreement with ones of the previous experimental and numerical studies.

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions （BCs） play an essential role in lattice Boltzmann （LB） simulations. This paper investigates several most commonly applied BCs by evaluating the relative L2-norm errors of the LB simulations for two-dimensional （2-D） Poiseuille flow. It is found that the relative L2-norm error resulting from FHML＇s BC is smaller than that from other BCs as a whole. Then, based on the FHML＇s BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations,

基于格子Boltzmann方法的液滴在圆柱壁面上运动过程研究

采用真实流体状态方程的伪势格子Boltzmann方法大密度比多相流模型,模拟了重力作用下的单液滴在圆柱壁面上的运动过程。计算结果表明,随着圆柱壁面疏水性沿重力方向逐渐增强,液滴运动过程可分为铺展和滑落两个阶段。壁面浸润性分布及其变化率均会影响液滴运动过程,当液滴运动至圆柱下半部分时,其平均速度、最大速度、附着长度和液滴高度等参数随时间变化开始发生分化。此外,当液滴开始及完全运动至圆柱下半部分时,其所受附着力的水平及垂直分量分别达到最大。这些发现为深入理解液滴在圆柱壁面上的运动特性提供了重要的理论支持。

基于lattice Boltzmann方法对裂隙煤体中瓦斯运移规律的模拟研究

基于lattice Boltzmann方法建立一个新的模拟裂隙煤体内瓦斯渗流的动力学模型,并利用该模型模拟二维裂隙煤体内瓦斯流动。模拟结果表明,采动压力差对瓦斯流动速度、孔隙瓦斯压力及瓦斯压力梯度都有很大的影响。在采动压力条件下,瓦斯在裂隙煤体中的流动压力具有波动性,波动幅度的大小与流场两端的压力差有关。在瓦斯压力达到峰值前的瞬时,孔隙瓦斯压力梯度很大。随着采动压力差的增大,瓦斯流动由层流过渡到紊流,同时孔隙压力出现发散,压力变化出现明显的非线性特征。基于lattice Boltzmann方法的模拟结果与用其他方法得到的瓦斯渗流规律比较吻合,表明lattice Boltzmann方法可有效模拟瓦斯在裂隙煤体中的运移规律,这为进一步探讨煤与瓦斯两相耦合机制、煤与瓦斯突出机制及瓦斯抽放方案的设计提供新的思路。

LATTICE-BOLTZMANN方法及其在顶盖驱动流数值模拟中的应用

Ｌａｔｔｉｃｅ－Ｂｏｌｔｚｍａｎｎ方法（以下简称ＬＢ方法），作为一种新的数值计算方法，在近十年得到迅速发展。本文对ＬＢ方法的基本思想及实施方法进行了概括介绍，并将该方法运用到顶盖驱动流的计算中，所得结果与基准解吻合良好。

Phase field lattice Boltzmann model for non-dendritic structure formation in aluminum alloy from LSPSF machine

The formation of non-dendritic structures in the primary phase of an aluminum alloy solidified using low superheat pouring with a shearing field(LSPSF) machine was investigated by numerical simulation.The growth and motion of a dendrite during solidification was simulated by a combination of the lattice Boltzmann method and the phase field method.The simulation results indicated that enough shear flow helped homogenize the concentration fields,rotate crystals and altere microstructures from dendritic to non-dendritic.The interaction of grains was also discussed.A fragmentation criterion was established based on partial remelting of dendrite arms;fragmentation was enhanced by a strong shear flow and larger inclined angles.The simulation results were verified experimentally.

Recent Development in Numerical Simulation of Enhanced Geothermal Reservoirs

This paper briefly introduces the current state in computer modelling of geothermal reservoir system and then focuses on our research efforts in high performance simulation of enhanced geothermal reservoir system. A novel supercomputer simulation tool has been developing towards simulating the highly non-linear coupled geomechanical-fiuid flow-thermal systems involving heterogeneously fractured geomaterials at different spatial and temporal scales. It is applied here to simulate and visualise the enhanced geothermal system （EGS）, such as （1） visualisation of the microseismic events to monitor and determine where/how the underground rupture proceeds during a hydraulic stimulation, to generate the mesh using the recorded data for determining the domain of the ruptured zone and to evaluate the material parameters （i.e., the permeability） for the further numerical analysis and evaluation of the enhanced geothermal reservoir; （2） converting the avail- able fractured rock image/fracture data as well as the reservoir geological geometry to suitable meshes/grids and further simulating the fluid flow in the complicated fractures involving the detailed description of fracture dimension and geometry by the lattice Boltzmann method and/or finite element method; （3） interacting fault system simulation to determine the relevant complicated rup- ture process for evaluating the geological setting and the in-situ reservoir properties; （4） coupled thermo-fluid flow analysis of a geothermal reservoir system for an optimised geothermal reservoir design and management. A few of application examples are presented to show its usefulness in simulating the enhanced geothermal reservoir system.

Lattice Boltzmann方法不同边界条件的混用

在Lattice Boltzmann方法数值模拟中,比较重要的一个环节就是边界条件的确定.通过对不同边界条件混用情况的研究,发现不同的边界条件确定方法可以相互混用,说明了Lattice Bolt-zmann方法对于边界的处理是比较灵活的.