NEW MODEL OF GAS FLOW PROBLEM IN MULTI-LAYERED GAS RESERVOIR AND APPLICATION

In this paper,the new model of the real gas filtration problem has been presented multi-layered gas reservoir,when a gas well output and wellbore storage may be variable,and have obtained the exact solutions of pressure distribution for each reservoir bed under three kinds of typical out-boundary conditions.As a special case,according to the new model have also obtained the exact solutions of presssure distribution in homogeneous reservoir and is given important application in gas reservoir development.     

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.     

SIMILARITY SOLUTIONS OF ROUND JETS AND PLUMES

Theκ-εturbulence model,considering the effect of buoyancy on turbulentkinetic energy and its dissipation rate,is adopted to present a mathematical model forround plumes and jets.There are similarity solutions in the uniform environment.Taking into account the conservation of momentum and heat flux.Finite AnalyticMethod is applied to obtain the similarity functions of velocity,temperature andturbulent kinetic energy.The agreement between the calculated and experimental datais good.     

FLUIDIZATION OF FINE POWDERS IN FLUIDIZED BEDS WITH AN UPWARD OR A DOWNWARD AIR JET

The hydrodynamic behavior of fine powders in jet-fluidized beds was studied numerically and experimentally. The starting point of numerical simulation was the generalized Navier-Stokes (N-S) equations for the gas and solids phases. The K-εturbulence model was used for high-speed gas jets in fluidized beds. Computation shows that a suitable turbulence model is necessary to obtain agreement between the simulation and literature experimental data for a high-speed gas jet. The model was applied to simulating the fluidization of fine powders in fluidized beds with an upward or a downward air jet. An empirical cohesion model was obtained by correlating the cohesive force between fine particles using a cohetester. The cohesion model was embedded into the two-fluid model to simulate the fluidization of fine powders in two-dimensional (2-D) beds. To study the fluidization behavior of fine and cohesive powders with a downward jet,experiments were performed in a 2-D bed. Agreement between the computed time-averaged porosity and measured data was obtained. With an upward jet in the bed center, the measured and computed porosities show a dilute centralcore, especially at very high jet velocities. Based on our experiments and computations, a downward jet located inside the bed is recommended to achieve better mixing and contacting of gas and solids.     

Empirical model for estimating vertical concentration profiles of re-suspended,sediment-associated contaminants

Vertical distribution processes of sediment con-taminants in water were studied by flume experiments. Experimental results show that settling velocity of sedi-ment particles and turbulence characteristics are the major hydrodynamic factors impacting distribution of pollutants, especially near the bottom where particle diameter is similar in size to vortex structure.Sediment distribution was uniform along the distance, while contaminant distribution slightly lagged behind the sediment.The smaller the initial sediment concentration was,the more time it took to achieve a uniform concentration distribution for suspended sediment. A con-taminants transportation equation was established depending on mass conservation equations.Two mathematical estima-tion models of pollutant distribution in the overlying water considering adsorption and desorption were devised based on vertical distribution of suspended sediment:equilibrium par-tition model and dynamic micro-diffusion model.The ratio of time scale between the sediment movement and sorption can be used as the index of the models.When this ratio was large,the equilibrium assumption was reasonable,but when it was small,it might require dynamic micro-diffusion model.     

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxelbased simulator V-FLOW VOF3 D, where the vessel geometry is expressed by using volume of fluid(VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model.     

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.     

THE BLOOD FLOW AND THE MOTION OF VESSEL WALL

The correlation problem between the blood fiow and the motion of vessel wall in the mammalian circulatory system is discussed in this paper. Supposing the blood flow is under the stable oscillatory condition, a set of formulas for velocity distribution, pressure distribution, displacement of vessel wall and constraining stress are obtained. Kuchar's formulas are extended from steady flow to unsteady oscillatory flow by means of the formulas obtained in this paper. The problem of elasticity effect of vessel wall is also discussed.     

Drop-weight impact fragmentation of gas-containing coal particles

Research on coal fragmentation can play an important role in understanding coal and gas outbursts.The study discussed in this paper explored the fragmentation of gas-containing coal particles using the drop-weight impact method.The effects of equilibrium gas pressures and type of adsorbate gas on particle size distributions and fragmentation energy were investigated in detail.We found that the Fractal particle size distribution model can most effectively describe the crushed coal particle sizes.The equilibrium pressure and type of gas can influence the Fractal distribution parameter.The crushing energy is composed of energy to create new surfaces and other forms of energy that are dissipated but the equilibrium gas pressure and type of adsorption gas can affect energy consumption and crushing efficiency.This research will be of guiding significance to the intensity evaluation and mechanism understanding of coal and gas outbursts.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

基于REV尺度格子Boltzmann方法的页岩气流动数值模拟

结合页岩扫描电镜图像,提出页岩气藏物理模型,采用表征单元体积(representative elementary volume,REV)尺度格子Boltzmann方法,考虑滑脱效应,模拟页岩气在页岩气藏中的流动.模拟结果表明,页岩气主要沿着天然裂缝窜进,但在有机质和无机质中也存在缓慢的流动,且有机质中的流速要略大于无机质中的流速.通过改变地层压力,研究地层压力对页岩气渗流特性的影响.研究结果表明,整个流场的速度和渗透率均随着地层压力的下降而增加.     

填埋气体迁移气-热-力耦合动力学模型的研究

基于连续介质力学—势弹性力学原理，运用多场耦合理论建立了填理场中可压缩垃圾气体迁移耦合的动力学模型，并采用摄动法及积分变换法对该强非线性数学模型进行拟解析求解。通过算例对比分析，探讨了耦侵动力场中气压、温度和应力变化对可压缩气体迁移的影响，得出了垃圾气体迁移过程中的孔隙压力分布规律。结果表明，三场耦合作用与非耦合作用相对差别较大，耦合效应不能忽略。这为定量化研究垃圾气体在填埋场中的扩散状况以及污染气体的排放和收集、防止二次污染提供了可靠的理论依据。     

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir including the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The non-linear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.     

FLUID-SOLID COUPLING MATHEMATICAL MODEL OF CONTAMINANT TRANSPORT IN UNSATURATED ZONE AND ITS ASYMPTOTICAL SOLUTION

IntroductionThetransportofcontaminantsinunsaturatedzonehascausedmuchattention .Inearly1960s,contaminationproblemsofsoilandgroundwaterhadbeenstudiedathomeandabroad[1].Andinrecentyears ,thetransformationandtransportationofcontaminantshavebeendeeplystudiedinthefieldsofhydrogeology ,petroleumengineering ,environmentalengineeringandsoon[2 ,3].Somecontaminanttransportmodelshavebeenpresentedsofar.Forexample ,Paker[4 ]etal.presentedaconstitutivemodelgoverningparametersofwater,gasandcontaminantswhenth…     

球形容器内气体的泄爆过程

为了得到球形容器内可燃气体的泄爆强度产生机理以及燃烧火焰与压力传播的基本规律，从流体力学和化学反应动力学守恒出发，采用-湍流模型和EBU-Arrhenius燃烧模型，利用SIMPLE算法对带泄爆导管的球形容器二维空间内甲烷-空气预混气体的泄爆过程内外场进行了数值计算，获得了气体燃烧过程中火焰和压力传播特性以及气体流动特性，能够比较清晰地反映泄爆的整个过程。研究表明，燃烧火焰在泄爆过程中发生湍流，传播得到了极大的加速，泄爆导管对于容器内的高压气体泄放有很大的约束作用。     

GAS-WATER TWO-PHASE DIFFUSION MODEL FOR UNSATURATED LAYERED COVER SYSTEMS

为了研究垃圾填埋场内部生物降解产生的气体(以甲烷为主) 和氧气等在非饱和覆盖层中的运移规律,建立了气体在成层非饱和覆盖层中的一维扩散模型. 该模型考虑了覆盖层含水量瞬态变化和气体扩散的耦合作用. 采用有限元多物理场耦合分析软件COMSOL Multiphysics 4.3进行求解. 其计算结果与前人实验结果能符合得很好. 研究结果表明,对典型垃圾填埋场中厚度为1m的非饱和黏土覆盖层,含水量变化对覆盖层中气体污染物的扩散运移有显著影响. 与含水量稳态变化情况相比,20 d到100 d的运移时间内同一覆盖层深度处耦合含水量作用下,气体相对浓度可以相差接近8倍. 含水量是气体在非饱和覆盖层中不稳定运移的重要影响因素.     

虚拟质量力对酸性气体-钻井液两相流波速的影响

基于两流体模型、酸性气体和钻井液状态方程,考虑酸性气体与钻井液相间虚拟质量力、粘性剪切力、相间动量交换及狭义相间阻力等条件,建立酸性气体与钻井液两相中压力波传播速度的数学模型,依据小扰动原理,对波速模型求解,得到关于波数K的波速方程。结果表明,在一定范围内,随空隙率、频率的增大,虚拟质量力对波速的影响显著增强;在高空隙率下,压强增大,虚拟质量力对波速的影响减弱;增大流体的密度或不可压缩性,均可使两相压力波速增大;延长气液交换时间或减小波动频率使相间有足够时间进行动量交换,两相压力波波速随之减小。     

Relative Permeability of Gas for Unconventional Reservoirs

Relative permeability of gas gains great significance in exploring unconventional gas. This paper developed a universal relative permeability model of gas, which is applicable for unconventional gas reservoirs such as coal, tight sandstone and shale. The model consists of the absolute relative permeability of gas and the gas slippage permeability. In the proposed model, the effects of water saturation and mean pore pressure on gas slippage permeability are taken into account. Subsequently, the evaluation of the model with existing model is done and then the validation of the model is made with data of tight sandstones, coals and shales from published literatures. The modeling results illustrate that a strong power-law relationship between relative permeability of gas and water saturation and the contribution of gas slippage permeability to relative permeability is determined by water saturation and mean pore pressure simultaneously. Furthermore, a sensitivity analysis of the impact of the parameters in the model is conducted and their effects are discussed.