流体力学格子法的外文文献及翻译资料.doc

2.英文原文SCIENCE CHINAEarth SciencesSeptember 2013 Vol.56 No.9: 15191530doi: 10.1007/s11430-013-4643-0Lattice Boltzmann simulation of fluid flow through coal reservoirs fractal pore structureJIN Yi1,2*, SONG HuiBo1,2, HU Bin1,2, ZHU YiBo1 & ZHENG JunLing11 School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454000, China;2 Key Laboratory of Biogenic Traces & Sedimentary Minerals of Henan Province, Jiaozuo 454000, ChinaReceived November 6, 2012; accepted March 28, 2013; published online June 27, 2013The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by cou-pling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permea-bility of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (j), fractal dimension of pore structure (Db), pore size range (rmin, rmax) and other parameters were systematically analyzed for their influences on the perme-ability (k) of fractal porous medium. The results indicate that: the channels connected by pores with the maximum size (rmax) dominate the permeability k , approximating in the quadratic law; the greater the ratio of rmax and rmin is, the higher k is; the relationship between Db and k follows a negative power law model, and breaks into two segments at the position where Db2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formu-lated as k = Cfrmaxn , where C and n (approximately equal to 2) are constants and f is an expression only containing parametersof fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model k=Crn was verified at Db=2.0.fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM)Citation:Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoirs fractal pore structure. Science China: Earth Sci-ences, 2013, 56: 15191530, doi: 10.1007/s11430-013-4643-0With the rapid development of industrial extraction and commercial exploitation of the CBM in China, more and more attention has been paid to the course of its genesis and migration law in coals.As a dual-porosity medium, coal reservoirs pore spaces which is a kind of matrix porous medium coupled with fractured network, dominates the storage and recoverability of CBM 15. Due to various causes, the microstructures of pores in coal reservoir are always disordered and ex-tremely complicated. There is now considerable evidence at home and abroad showing that coal reservoir is a fractal*Corresponding author (email: )porous medium 1, 611.Since the microstructures of the real porous media in coal are usually disordered and extremely complicated, this makes it very difficult to find the permeability of the media analytically and access the transport property of CBM ac-curately. Over the last several decades, the migration law of CBM in the fractal porous medium in coals has been inves-tigated both experimentally and theoretically by many au-thors 1221. But, experimental study is influenced heavily by many factors, such as experiment condition, scale, and testing environment. At the same time, the underlying con-tinuous media assumption makes the controlling mechanism of fluid flow hard to explore. As to the theoretical analyses Science China Press and Springer-Verlag Berlin Heidelberg 20131520Jin Y, et al.Sci China Earth SciSeptember (2013) Vol.56 No.9based on semi-empirical models, they always fail to predict the macro transport property resulting from the collective chaotic behaviors of fluid particles in such a complicated porous medium in coal 22.Nowadays, much effort has been devoted to numerical simulations. The computational approach can, thus, be use-ful to understand the basic physics of the problem, since one can easily select or neglect any of the relevant effects (such as viscous dissipation or fractal pore structure), and analyze every single fact of the problem 23. At the same time, such approaches are unsubjected to the experimental tech-nique, level, and environment.Based on microscopic models or macroscopic kinetic equations for fluids, the LBM simulates fluid flows by fol-lowing the evolution of a prescribed Boltzmann equation instead of solving the Navier-Stokes equation 24, 25, and has received more and more attention compared to some conventional CFD techniques, such as the finite-difference, finite-volume, and finite-element methods 2635. An im-portant advantage of the LBM is that microscopic physical interaction among fluid particles, such as mass transport, chemical reaction and diagenesis, can be conveniently in-corporated into the model 33. The LBM has been applied successfully to a lot of fluid dynamics, including fluid flows in porous medium, thermal two-phase flow, diffusion in the multi-component fluids, heat conduction problem and mul-ti-scale flow 22, 3639. And now, the LBM has proven to be a powerful tool to investigate the controlling mechanism behind the complex flow problems.In recent years, some Chinese scholars have analyzed the migration law of the CBM focused on different aspects 4045, but all these investigations are carried out on mesoscopic scale under the continuous media assumption, few on pore scale. Recently, Jin et al. 46 modified the QSGS algorithm to generate fractal porous medium to mimic coals microstructures statistically, and analyzed the fluid flows spatial-temporal evolution pattern in such me-dia based on Lattice Boltzmann simulations. But, the report is few on the systematic analysis of the influences of fractal pore structure parameters on its transport property.So, to fully understand the response mechanism of fluid flow in fractal porous medium, different types of fractals were generated to represent coal media and the controlling influences on CBMs migration were investigated in detail by coupling theoretical models and Lattice Boltzmann sim-ulations. Based on the results above, the permeability model of fractal porous medium was proposed, and the equivalence was verified between new model and Kozeny-Carmans.1Materials and methods1.1 Characteristics of coals microscopic pore-struc-ture and its 3D representationrous medium exhibits fractal characteristics, such medium is called fractal porous medium. For such medium, the cumu-lative size-distribution of pores (N(r), whose sizes are equal to or greater than the size r , should follow the fractal scaling law as N(r)r-D, where represents proportionality and D is the pore volume fractal dimension. Taking a cube with side length rl as measurement unit, the medias pore volume (Vm) will result inV= N (r ) r3 .(1)mllIncorporating the fractal scaling law “N(r)r-D” of pore size distribution into eq. (1), the pore volume can be expressed asV r3- D .(2)mlDifferentiating eq. (2) with respect to rl results in the volume (dVm) of pores whose sizes are within the infinites-imal range rl to rl+drl:dVm r2- D .(3)ldrlEq. (3) indicates that the relationship between volume in-crement (DVm or dVm/dr) and pore size also follows the fractal scaling law 47.In practice, Menger sponge fractals are always taken to mimic the microstructures of coal medium 11. The con-struction process of Menger Sponge fractal is as follows: divide equally the initial cube with side length R into m3 smaller cubes with side length R/m, and remove a part of such smaller cubes according to a certain rule, leaving Nbl smaller cubes; repeat step for each of the remaining small cubes, and continue to iterate ad infinitum. With the continuous iteration, the size of remaining cubes reduces continuously and their number increases on and on 4850. After the kth iteration, the side length (rk) of the remaining cubes will be rk=R/mk, but the total number Nbk = Nbk1 . Based on the construction process of Menger Sponge frac-tals, Nbk can be rewritten asRDbDbCN bk= =RD= Crk- Db ,(4)D rk rk brk bwhere Db = lg N b1 / lg m,the pore volume fractal dimen-sion. Based on eq. (4), the correlation between pore volume (Vk) of coal and the measurement pore size (rk) follows therelationshipVk rk3- Db .Differentiating the relationshipwith respect to rk results in the volume (dVk) of pores whose sizes are within the infinitesimal range rk to rk+drk:dVk r2- Db .(5)kdrkIf the pore size distribution ranged from rmin to rmax in po-Comparing eq. (3) with eq. (5), D=Dbis concluded.Jin Y, et al. Sci China Earth Sci September (2013) Vol.56 No.91521Based on the conclusion above, Menger sponge fractal can be employed to model the homogeneous coal media fully 51.To explore the control influences on the porous medi-ums transport property from fractals parameters fully and avoid blink pores, this paper proposes a new Menger Sponge generator to construct fractal porous medium, named “SmVq” Menger Sponge model (Figure 1). The con-struction process of “SmVq” Menger Sponges is as follows: Divide the initial cube equally with side length R into m3 smaller cubes with side length R/m, and remove qq smaller cubes which are along with the three main axes in the very center of the larger cube; Repeat step for each of the remaining small cubes, and continue to iterate ad infini-tum. Figure 1 demonstrates the two-dimensional pore struc-ture of SmVq Menger Sponge model, where the white part represents pores and the black denotes solid matrix.In the SmVq Menger Sponge, Nb1 and Db can be written as eqs. (6) and (7), respectively:Nb1= m3- (3mq2 - 2q3 ),(6)D =lg Nb1=lg(m3 - 3mq2 + 2q3 ).(7)blg mlg mHowever, the pore size distribution can only be within a certain range for real coal media in nature. Based on the fractal character of porous medium 52 and eq. (7), the porosity (j) of a fractal porous medium with pore size within the range from rmin to rmax can be obtained by eq. (8):N1+lg rmax -lg rminrd - Dbb1lg mj = 1- = 1 - min,(8)dm mrmax Figure 1Pore structure diagram of SmVq model.where d is the Euclidean dimension, and d=2 and 3 in the two- and three-dimensional spaces, respectively.Eq. (8) implies that if the pore size distribution of a po-rous medium follows the fractal scaling law, its porosity jis determined by and only by Db and logrmmax rmin . On onehand, as the ratio of rmax to rmin decreases, its porosity de-creases for porous medium with the same Db. On the otherhand, the porosity increases as Db decreases for those with the same pore size range and m 52, 53. Conclusions(1) Transport property of coal porous media with fractal pore structures is controlled by the maximum pores, the pore size distribution, and the fractal dimension number of pore structure. The channels connected by the maximum aperture dominate the permeability of fractal porous medium. The permeability increases as the size ratio of Rmax and Rmin increases, and the fractal dimension, Db influences the permeability negatively following a power law model. Although a positive correlation exists between porosity and permeability, porosity is the result of pore size range, fractal dimension of pore structure, so we do not take porosity as he basic control factor of porous mediums transport property of porous media.(2) In fractal porous medium, the relationship between fractal dimension and permeability will be divided into two parts at point near Db=2.5 . When Db2.5 , the negative influence on permeability from Dbis increased significantly.(3) To estimate the permeability of fractal porous medium, Kozeny-Carman model needs to be modified by a multiplier operator named as f, where . And thus, the modified model can unify permeability prediction model or porous medium, which are fractals or not.2.中文翻译中国科学地球科学研究论文 September 2013 Vol.56 No.9: 15191530doi: 10.1007/s11430-013-4643-0煤储层流体流动的格子-气模拟分形孔隙结构作者：晋毅*，宋会波,2，胡斌,2，朱一波 郑君玲单位：1河南理工大学资源与环境学院，焦作454000； 2河南省生物沉积矿产资源与沉积矿产重点实验室，焦作454000时间：2012年11月6日2013年6月27日收到；接受2013年3月28日出版【引 言】 ：通过耦合理论模型和数值计算方法，详细分析了煤储层中的分形孔隙结构对煤层气（CBM）运移的影响。基于标准Menger海绵模型的三维非线性煤孔隙结构建立了不同类型的分形。然后采用并行和串行模式，格子法（LBM）验证推导得到分形多孔介质的渗透性及其孔隙分布特征之间的相关模型。基于耦合方法，孔隙度（），孔隙结构的分形维数（DB），孔径范围（RminRmax）等参数系统的分析了分形多孔介质对渗透率（K）的影响。结果表明：管道在具有最大孔径（Rmax）时的渗透率（K），满足二次法近似最大孔径（Rmax）和Rmin之比越大，k越高；DB和k之间满足负幂律函数关系，在Db2.5处分为两段。在上述研究的基础上，提出了一种分形多孔介质渗透率的预测模型，公式为，其中C和N（约等于2）是常数，f是一个只含有参数的分形孔隙结构表达式。此外，由多孔介质新模型和Kozeny-Carman模型的等价性可以验证出DB = 2。【关键词】 ：分形孔隙结构，多孔介质，格子模型、煤层气（CBM）引用：晋毅，宋会波,胡斌,等。煤储层分形孔隙结构中流体流动的格子-气模拟。科学中国：地球科学，2013、56：15191530，DOI: 10.1007/s11430-013-4643-0 随着我国煤层气工业的快速发展，对煤层气的开发利用，煤的成因和运移规律越来越受到重视。煤储层的孔隙空间是一种具有多孔介质耦合矩阵与裂隙网络的双重孔隙介质，占具存储和回收煤层气的主导地位。由于各种原因，煤储层孔隙的微观结构往往是无序的、极其复杂的。目前国内外都有大量的证据表明，煤储层是一种分形多孔介质。由于实际上多孔介质的微观结构通常是无序的、极其复杂的，因此很难发现介质的渗透率分析和煤层气的输运性质。在过去的几十年中，许多作者对煤层气在煤的分形多孔介质中的迁移规律进行了实验和理论上的研究。但实验研究受多种因素的影响，如实验条件、规模、测试环境等。同时，底层连续介质的假设使得流体流动的控制原理难以探索。在半经验模型的理论分析基础上，它们始终不能预测煤中流体颗粒在这样一种复杂多孔介质中的宏观输运性质。如今，人们致力于数值模拟研究。因为这样的计算方法对于了解基本物理问题是有效果的。这样，人们可以很容易地选择或忽略任何相关的影响（如粘性耗散或分形孔隙结构），并分析了单个问题的本质。同时，这样的方法经受住了实验的技术、水准、和环境的考验。基于微观模型和宏观动力学方程的流体，格子法（LBM）模拟流体流动可以演变为特定的玻尔兹曼方程，来代替斯托克斯方程的求解方法，相比如同有限差分法，有限体积和有限元方法之类的一些传统的CFD技术，越来越受到人们的重视。格子法（LBM）的一个重要优势是研究流体颗粒间微观的相互作用时，如物质运输，化学反应和岩化作用都可以很方便地纳入模型。格子法（LBM）已成功地应用于许多流体动力学中，包括多孔介质中的流体流动、热两相流，在多组分流体的扩散、热传导问题和多尺度流动。现在，它已被证明是一个用来探讨复杂流动问题背后的控制机制的强大工具。近年来，一些中国学者对煤层气的迁移规律进行了不同的分析，但在连续介质假设下，所有这些研究都是在介观尺度上进行的，很少在孔隙尺度上进行。最近，金等人，修改了通过生成分形多孔介质来统计模拟煤层微观结构的QSGS算法，又在基于格子模拟法的媒体上分析了流体流动的时空演化规律。但是，在该报告中对分形孔隙结构参数对其输运性质影响的系统性的分析较少。因此，充分了解流体分形多孔介质中的反应机理，不同类型的分形生成代表着对煤介质和煤层气运移的控制因素研究的详细耦合理论模型和格子模拟。基于以上结果，提出了分形多孔介质的渗透率模型，并验证了新模型和康采尼-卡曼模型之间的等价性1材料与方法1.1煤的微观孔隙结构特征及其三维表示如果孔径分布范围从最小孔径（Rmin）到最大孔径（Rmax）具有多孔介质的分形特征值，这种介质就称为分形多孔介质。对于这样的媒体，气孔的累积尺寸分布（N（R）其大小大于或等于R，应遵循分形规律，其中Db是孔隙体积分形维数。以一个为边长的立方体为单位元，媒体的孔隙体积（Vm）结果是 （1）结合分形标度律“”孔径分布为式（1），孔体积可表示为 （2）微分方程（ 2）相