流体力学格子法的外文文献及翻译资料

2.英文原文SCIENCE CHINAEarth SciencesSeptember 2013 Vol.56 No.9: 1519–1530doi: 10.1007/s11430-013-4643-0Lattice Boltzmann simulation of fluid flow through coalreservoir’s 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 (ϕ), fractal dimension of pore structure (D b), pore size range (r min, r max) and other parameters were systematically analyzed for their influences on the perme-ability (κ) of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max) dominate the permeability κ , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher κ is; ③ the relationship between D b and κ follows a negative power law model, and breaks into two segments at the position where D b≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formu-lated as κ =Cfr max n , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model κ=Cr n was verified at D b=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 reservoir’s fractal pore structure. Sci ence China: Earth Sci-ences, 2013, 56: 1519–1530, 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 reservoir’s pore spaces which is a kind of matrix porous medium coupled with fractured network, dominates the storage and recoverability of CBM [1–5]. 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, 6–11].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 [12–21]. 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 Sci September (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 [26–35]. 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, 36–39]. 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 [40–45], 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 coal’s microstructures statistically, and analyzed th e fluid flow’s 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 CBM’s 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-Carman’s.1Materials and methods1.1 Characteristics of coal’s microscopic p ore-struc-ture and its 3D representation rous 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 r l as measurement unit, the media’s pore volume (V m) will result inV = N (r )⨯ r3. (1)m llIncorporating 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)m lDifferentiating eq. (2) with respect to r l results in the volume (d V m) of pores whose sizes are within the infinites-imal range r l to r l+d r l:d V m ∝ r2-D. (3)ld r lEq. (3) indicates that the relationship between volume in-crement (∆V m or d V m/d r) 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: ① 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 N bl smaller cubes; ② repeat step ① 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 [48–50]. After the k th iteration, the side length (r k) of the remaining cubes will be r k=R/m k, but the total number N bk=N b k1 . Based on the construction process of Menger Sponge frac-tals, N bk can be rewritten as⎛R⎫ D b DbCNbk =  ⎪ = R D = = Cr k-D b, (4)D⎝rk ⎭ r k b r k bwhere D b=lg N b1/ lg m, the pore volume fractal dimen- sion. Based on eq. (4), the correlation between pore volume (V k) of coal and the measurement pore size (r k) follows the relationship V k∝ r k3-D b.Differentiating the relationshipwith respect to r k results in the volume (d V k) of pores whose sizes are within the infinitesimal range r k to r k+d r k:d V k ∝r2-D b . (5)kd r kIf the pore size distribution ranged from r min to r max in po- Comparing eq. (3) with eq. (5), D=D b is 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-um’s transport property from fractal’s parameters fully and avoid blink pores, this paper proposes a new Menger Sponge generator to construct fractal porous medium, named “S m V q ” Menger Sponge model (Figure 1). The con -struction process of “S m V q ” Menger Sponges is as follows: ① Divide the initial cube equally with side length R into m 3 smaller cubes with side length R /m , and remove q ×q smaller cubes which are along with the three main axes in the very center of the larger cube; ② Repeat step ① for each of the remaining small cubes, and continue to iterate ad infini-tum . Figure 1 demonstrates the two-dimensional pore struc-ture of S m V q Menger Sponge model, where the white part represents pores and the black denotes solid matrix.In the S m V q Menger Sponge, N b 1 and D b can be written as eqs. (6) and (7), respectively:N b 1 = m 3 - (3mq 2 - 2q 3 ), (6)D = lg N b 1 = lg(m 3 - 3mq 2 + 2q 3) . (7)b lg m lg 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 (ϕ) of a fractal porous medium with pore size within the range from r min to r max can be obtained by eq. (8):⎛ N⎫1+ lg r max -lg r min⎛ r ⎫d -D bb 1 lg mϕ = 1 -⎪= 1 -  min⎪ ,(8)d⎝ m ⎭⎝mrmax ⎭Figure 1 Pore structure diagram of S m V q 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 ϕis determined by and only by D b and log r m max r min . On onehand, as the ratio of r max to r min decreases, its porosity de-creases for porous medium with the same D b . On the otherhand, the porosity increases as D b 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 medium’s 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 Db>2.5 , the negative influence on permeability from Dbis increased significantly.(3) To estimate the permea bility of fractal porous medium, Kozeny-Carman model needs to be modified by a multiplieroperator named as f, where bk d n m q f ）（=. And thus, themodified 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: 1519–1530doi: 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。