LBM simulation of fluid flow in fractured porous media with permeable matrix

To analyze and depict complicated fluid behaviors in fractured porous media with variably permeable matrix,an integrated discrete computational algorithm is proposed based on lattice Boltzmann method（LBM）.This paper combines with the external force model and statistical material physics to effectively describe the feature changes while the fluid passes through the fractures within the permeable matrix.As an application example,a two dimensional rock sample is reconstructed using the digital image and characterized with different feature values at each LBM grid to distinguish pores,impermeable and permeable matrix by stating its local physical property.Compared with the conventional LBM,the results demonstrate the advantages of proposed algorithm in modeling fluid flow phenomenon in fractured porous media with variably permeable matrix.

PENALTY FINITE ELEMENT METHOD FOR NONLINEAR DYNAMIC RESPONSE OF VISCOUS FLUID-SATURATED BIPHASE POROUS MEDIA

The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, trod two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application

For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L 2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy sources.

Determination of Hydrogen Production from Rich Filtration Combustion with Detailed Kinetics Based CFD Method

Computational fluid dynamics （CFD） combined with detailed chemical kinetics was employed to model the filtration combustion of a mixture of methane/air in a packed bed of uniform 3 mm diameter alumina spherical particles. The standard k-ε turbulence model and a methane oxidation mechanism with 23 species and 39 elemental reactions were used. Various equivalence ratios （1.47, 1.88, 2.12 and 2.35） were studied. The numerical results showed good agreement with the experimental data. For ultra-rich mixtures, the combustion temperature exceeds the adiabatic value by hundreds of centigrade degrees. Syngas （hydrogen and carbon monoxide） can be obtained up to a mole fraction of 23%. The numerical results also showed that the combination of CFD with detailed chemical kinetics gives good performance for modeling the pseudo-homogeneous flames of methane in porous media.

Numerical investigation of the effectiveness of radon control measures in cave mines

Ventilation is one of the radon control measures in an underground working environment.However,the dynamics related to the cave mining methods particularly in block/panel cave mines,complicate the design of effective ventilation system,and implementation.Events such as hang ups(in the drawbells),leakage from old workings,and changes in cave porosity lead to differing response of an existing ventilation designs.However,it is difficult to investigate these conditions at the mine or with a laboratory scale study.Therefore,this study develops a discrete model to investigate the impact of different radon control measures in cave mines using computational fluid dynamics techniques.We considered two ventilation conditions for a fully developed cave:with and without the undercut ventilation.For each of the two conditions,we studied four parameters:airflow distribution through the production drifts,radon distribution through the production drifts,the effect of increasing airflow on radon concentration,and the effect of a cave top negative pressure on radon distribution.The results show that:the undercut ventilation significantly increases the radon concentration in the production drift;the growth of radon concentration through the production drift is nonlinear(oscillating pattern);maintaining a negative pressure on top of the cave is more effective at mitigating radon exposure,when the undercut ventilation is active;and increase in air volume flow rate decreases radon concentration in most regions,however,there might be regions with significant radon accumulation due to pressure variation across the drifts.These findings provide vital information for designing an effective ventilation system and for proactive implementation of radon control measures in cave mines.

Prediction of airway resistance in panel cave mines using a discrete and continuum model

The configuration of an airway(or production drift)in panel cave mines is different from the typical(straight)mine airway designs.The drawpoints are connected to the airway(cross-cuts),which allows airflow from the cave into the airway or air loss from the airway into the cave due to the ventilation approach and cave porosity.These affect airflow in the production drifts,but it is difficult to investigate these conditions from field or laboratory scaled studies.Therefore,this study develops discrete and continuum computational fluid dynamics(CFD)models to study the effects of the ventilation approach and cave porosity on the airway resistance.Our findings show that:with active undercut ventilation,a unique resistance model is required for the airway in panel cave mines;and an increase in cave porosity decreases the drift’s resistance.These findings provide essential tools for a panel cave ventilation design.

The numerical simulation and analysis of three-dimensional seawater intrusion and protection projects in porous media

For the three-dimensional seawater intrusion and protection system, the model of dynamics of fluids in porous media and the modified upwind finite difference fractional steps schemes are put forward. Based on the numerical simulation of the practical situation in the Laizhou Bay Area of Shandong Province, predictive numerical simulation and analysis of the consequence of protection projects, underground dams, tidal barrage projects and the applied modular form of project adjustment have been finished. By using the theory and techniques of differential equation prior estimates, the convergence results have been got.

A Comprehensive Experimental Study on Immiscible Displacements in Porous Media:Effects of Capillary Forces,Viscous Forces,Wettability and Pore Geometries

Immiscible displacements in porous media are fundamentally significant for many natural processes and industrial applications.Although extensive work has been done in this field,some limitations still exist due to the difficulty to cover the large number of influencing factors.In this paper,we present a systematic study involving the coupled influence of capillary forces,viscous forces,wetting properties and pore geometries.By microfluidic experiments with high resolutions,both residual fluid distributions and dynamical invasion processes were clearly captured and quantitatively characterized.A void-filling behavior was identified for drainage as the capillary number Ca increased.An anomalous void-leaving behavior was found for the case of imbibition with an unfavorable viscosity ratio M,representing many ribbon-like regions invaded at intermediate Ca turned to be not accessible at high Ca.A pore geometry with a large typical pore-throat ratio seemed to enhance the void-leaving behavior.During the dynamical invasion processes,an intermittency behavior was captured in the form of a fluctuation of the increasing rate of the invading saturation with time.The intermittency dynamics were most evident for drainage with an unfavorable M.A pore geometry with high porosity acted to suppress the intermittency behaviors.Our experimental results sketched out a full view of immiscible displacements in porous media under different conditions,and provided a complete dataset which could be used to test the rapid developing pore-scale models.

Simulation of 3D Porous Media Flows with Application to Polymer Electrolyte Fuel Cells

A 3D lattice Boltzmann(LB)model with twenty-seven discrete velocities is presented and used for the simulation of three-dimensional porous media flows.Its accuracy in combination with the half-way bounce back boundary condition is assessed.Characteristic properties of the gas diffusion layers that are used in polymer electrolyte fuel cells can be determined with this model.Simulation in samples that have been obtained via X-ray tomographic microscopy,allows to estimate the values of permeability and relative effective diffusivity.Furthermore,the computational LB results are compared with the results of other numerical tools,as well as with experimental values.

多层非线性渗流耦合系统的特征分数步差分方法

对多层非线性渗流耦合系统提出适合并行计算的特征分数步差分格式,利用变分形式、能量方法、粗细网格配套、分片双二次插值、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,得到收敛性的最佳阶的l^2误差估计.该方法已成功的应用到多层油资源评估的生产实际中.

Effect of Cooling Water Flow Path on the Flow and Heat Transfer in a 660 MW Power Plant Condenser

The effect of the cooling water flow path on the flow and heat transfer in a double tube-pass condenser for a 660 MW power plant unit was numerically investigated based on a porous medium model. The results were used to analyze the streamline, velocity, air mass fraction and heat transfer coefficient distributions. The simulations indicate that the cooling water flow path is important in large condensers. For the original tube arrangement, the heat transfer with the lower-upper cooling water flow path is better than that with the upper-lower cooling water flow path. The reason is that the steam cannot flow into the internal of upper tube bundle and the air fractions are higher in the upper tube bundle with the upper-lower cooling water flow path. An improvement tube arrangement was developed for the upper-lower cooling water flow path which reduced the back pressure by 0.47 kPa compared to the original scheme. Thus, the results show that the tube arrangements should differ for different cooling water flow paths and the condenser heat transfer can be improved for the upper-lower cooling water flow path by modifying the tube arrangement.

Heat Transfer and Hydrodynamics in Annular Chromatography: CFD-Simulation and Experiments

Continuous annular chromatography(CAC) is a separation process for multicomponent liquid mixtures. The performance of the apparatus can be seriously decreased by temperature gradients inside the adsorbent bed. It is shown, that the temperature gradients can be significantly reduced by a pre-heating of the entering liquid in the apparatus itself. Heat transfer and hydrodynamics in the porous media are described by two different modelling approaches. Both are based on a pseudo-homogeneous model for heat transfer with temperature dependent fluid viscosities. The first model considers one-dimensional fluid now and two-dimensional heat transfer. The second, more rigorous one is a three-dimensional model for heat transfer and hydrodynamics. The simulation results obtained with both models are in good agreement with experimental results. The experiments have been performed with glass beads as the stationary phase and water as the liquid phase under different boundary conditions. The temparature profiles inside the packed bed have been measured with thermocouples.

Evaluation of Pressure Boundary Conditions for Permeability Calculations Using the Lattice-Boltzmann Method

Lattice-Boltzmann(LB)simulations are a common tool to numerically estimate the permeability of porous media.For valuable results,the porous structure has to be well resolved resulting in a large computational effort as well as high memory demands.In order to estimate the permeability of realistic samples,it is of importance to not only implement very efficient codes,but also to choose the most appropriate simulation setup to achieve accurate results.With the focus on accuracy and computational effort,we present a comparison between different methods to apply an effective pressure gradient,efficient boundary conditions,as well as two LB implementations based on pore-matrix and pore-list data structures.