分形理论在天然气水合物研究领域的应用

刘乐乐, 刘昌岭, 孟庆国, 张永超. 分形理论在天然气水合物研究领域的应用[J]. 海洋地质前沿, 2020, 36(9): 11-22. doi: 10.16028/j.1009-2722.2020.064
引用本文: 刘乐乐, 刘昌岭, 孟庆国, 张永超. 分形理论在天然气水合物研究领域的应用[J]. 海洋地质前沿, 2020, 36(9): 11-22. doi: 10.16028/j.1009-2722.2020.064
LIU Lele, LIU Changling, MENG Qingguo, ZHANG Yongchao. APPLICATION OF FRACTAL THEORY TO NATURAL GAS HYDRATE RESEARCHES[J]. Marine Geology Frontiers, 2020, 36(9): 11-22. doi: 10.16028/j.1009-2722.2020.064
Citation: LIU Lele, LIU Changling, MENG Qingguo, ZHANG Yongchao. APPLICATION OF FRACTAL THEORY TO NATURAL GAS HYDRATE RESEARCHES[J]. Marine Geology Frontiers, 2020, 36(9): 11-22. doi: 10.16028/j.1009-2722.2020.064

分形理论在天然气水合物研究领域的应用

  • 基金项目: 国家自然科学基金(41872136,41876051);国家重点研发计划政府间国际科技创新合作重点专项(2018YFE0126400);中国地质调查局项目(DD20190221)
详细信息
    作者简介: 刘乐乐(1986—),男,博士,副研究员,主要从事天然气水合物储层工程地质方面的研究工作. E-mail: lele.liu@qnlm.ac
  • 中图分类号: P744; P618.13

APPLICATION OF FRACTAL THEORY TO NATURAL GAS HYDRATE RESEARCHES

  • 天然气水合物作为一种潜在的替代能源和环境扰动因素,相关研究仍然面临着水合物储层微观结构量化表征不足的问题,而分形理论为此提供了良好的思路与手段。首先介绍分形理论基础,然后对分形理论在水合物研究领域的应用情况进行综述,接着概述含水合物沉积物有效孔隙分形理论,最后对研究进展进行总结并展望未来分形理论在水合物研究领域的可能方向。

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  • 图 1  孔隙-固体分形模型构造图

    Figure 1. 

    图 2  渗透率分形模型与实验数据对比情况(据文献[42]修改)

    Figure 2. 

    图 3  含水合物沉积物水气两相流体相对渗透率曲线(据文献[50]修改)

    Figure 3. 

    图 4  分形孔隙(白色部分)模型示意图(据文献[60]修改)

    Figure 4. 

    图 5  制冷剂水合物生长过程的实验图像与模拟结果(据文献[61]修改)

    Figure 5. 

    图 6  含水合物沉积物的水合物-沉积物-孔隙分形模型(据文献[64]修改)

    Figure 6. 

    图 7  含水合物沉积物分形模型(据文献[64]修改)

    Figure 7. 

  • [1]

    苏丕波,何家雄,梁金强,等. 南海北部陆坡深水区天然气水合物成藏系统及其控制因素[J]. 海洋地质前沿,2017,33(7):1-10.

    [2]

    刘昌岭,李彦龙,孙建业,等. 天然气水合物试采:从实验模拟到场地实施[J]. 海洋地质与第四纪地质,2017,37(5):12-26.

    [3]

    Ruppel C D,Kessler J D. The interaction of climate change and methane hydrates[J]. Reviews of Geophysics,2017,55(1):126-168. doi: 10.1002/2016RG000534

    [4]

    鲁晓兵,张旭辉,王淑云. 天然气水合物开采相关的安全性研究进展[J]. 中国科学(物理学 力学 天文学),2019,49(3):034602.

    [5]

    吴能友,黄 丽,胡高伟,等. 海域天然气水合物开采的地质控制因素和科学挑战[J]. 海洋地质与第四纪地质,2017,37(5):1-11.

    [6]

    刘乐乐,张旭辉,刘昌岭,等. 含水合物沉积物三轴剪切试验与损伤统计分析[J]. 力学学报,2016,48(3):720-729. doi: 10.6052/0459-1879-15-400

    [7]

    Bu Q T ,Hu G W,Ye Y G,et al. The elastic wave velocity response of methane gas hydarte formation in vertical gas migration systems[J]. Journal of Geophysics and Engineering,2017,14(3):555-569. doi: 10.1088/1742-2140/aa6493

    [8]

    Dai S,Seol Y. Water permeability in hydrate-bearing sediments:A pore-scale study[J]. Geophysical Research Letters,2014,41:4176-4184. doi: 10.1002/2014GL060535

    [9]

    Dai S,Santamarina J C,Waite W F,et al. Hydrate morphology:Physical properties of sands with patchy hydrate saturation[J]. Journal of Geophysical Research:Solid Earth,2012,117(B11):B11205.

    [10]

    陈国旗,李承峰,刘昌岭,等. 多孔介质中甲烷水合物的微观分布对电阻率的影响[J]. 新能源进展,2019,7(6):493-499.

    [11]

    Mahabadi N,Dai S,Seol Y,et al. The water retention curve and relative permeability for gas production from hydrate-bearing sediments:pore-network model simulation[J]. Geochemistry,Geophysics,Geosystems,2016,17(8):3099-3110. doi: 10.1002/2016GC006372

    [12]

    胡高伟,李承峰,业渝光,等. 沉积物孔隙空间天然气水合物微观分布观测[J]. 地球物理学报,2014,57(5):1675-1682. doi: 10.6038/cjg20140530

    [13]

    Chaouachi M,Falenty A,Sell K,et al. Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographic microscopy[J]. Geochemistry,Geophysics,Geosystems,2015,16(6):1711-1722.

    [14]

    Ta X H,Yun T S,Muhunthan B,et al. Observations of pore-scale growth patterns of carbon dioxide hydrate using X-ray computed microtomography[J]. Geochemistry,Geophysics,Geosystems,2015,16(3):912-924.

    [15]

    Delli M L,Grozic J L H. Experimental determination of permeability of porous media in the presence of gas hydrates[J]. Journal of Petroleum Science and Engineering,2014,120:1-9. doi: 10.1016/j.petrol.2014.05.011

    [16]

    Carman P C. Permeability of saturated sands,soils and clays[J]. The Journal of Agricultural Science,1939,29(2):262-273. doi: 10.1017/S0021859600051789

    [17]

    Wang J Q,Zhao J F,Yang M J,et al. Permeability of laboratory-formed porous media containing methane hydrate:Observations using X-ray computed tomography and simulations with pore network models[J]. Fuel,2015,145:170-179. doi: 10.1016/j.fuel.2014.12.079

    [18]

    Wang D G,Wang C C,Li C F,et al. Effect of gas hydrate formation and decomposition on flow properties of fine-grained quartz sand sediments using X-ray CT based pore network model simulation[J]. Fuel,2018,226:516-526. doi: 10.1016/j.fuel.2018.04.042

    [19]

    Wang D G,Li Y,Liu C L,et al. Study of hydrate occupancy,morphology and microstructure evolution with hydrate dissociation in sediment matrices using X-ray micro-CT[J]. Marine and Petroleum Geology,2020,113:104138. doi: 10.1016/j.marpetgeo.2019.104138

    [20]

    Mandelbrot B B. How long is the coast of Britain? Statistical self-similarity and fractional dimension[J]. Science,1967,156(3775):636-638. doi: 10.1126/science.156.3775.636

    [21]

    Mandelbrot B B. Fractals: Form, Chance and Dimension[M]. New York: W. H. Freeman and Company, 1977.

    [22]

    Mandelbrot B B. The fractal geometry of nature[M]. New York: W. H. Freeman and Company, 1982: 1-468.

    [23]

    蔡建超, 胡祥云. 多孔介质分形理论与应用[M]. 北京: 科学出版社, 2015: 1-208.

    [24]

    张济忠. 分形[M]. 北京: 清华大学出版社, 2011: 1-310.

    [25]

    Falconer K. Fractal Geometry: Mathematical Foundations and Applications[M]. New Jersey: Wiley, 2005:1-398.

    [26]

    郁伯铭. 多孔介质输运性质的分形分析研究进展[J]. 力学进展,2003,33(3):333-346. doi: 10.3321/j.issn:1000-0992.2003.03.005

    [27]

    Cai J C,Luo L,Ye R,et al. Recent advances on fractal modeling of permeability for fibrous porous media[J]. Fractals,2015,23(1):1540006. doi: 10.1142/S0218348X1540006X

    [28]

    Yu B. Analysis of Flow in Fractal Porous Media[J]. Applied Mechanics Reviews,2008,61(5):050801. doi: 10.1115/1.2955849

    [29]

    张佳瑞,王金满,祝宇成,等. 分形理论在土壤学应用中的研究进展[J]. 土壤通报,2017,48(1):221-228.

    [30]

    詹卫华,黄冠华. 土壤水力特性分形特征的研究进展[J]. 水科学进展,2000,11(4):457-462. doi: 10.3321/j.issn:1001-6791.2000.04.019

    [31]

    官 庆,李 允. 具有分形特性的油藏渗流理论进展概述[J]. 西南石油大学学报,2007,29(2):106-190.

    [32]

    Wei W,Xia Y X. Geometrical,fractal and hydraulic properties of fractured reservoirs:A mini-review[J]. Advances in Geo-Energy Research,2017,1(1):31-38. doi: 10.26804/ager.2017.01.03

    [33]

    Majumdar A,Bhushan B. Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces[J]. Journal of Tribology,1990,112(2):205-216. doi: 10.1115/1.2920243

    [34]

    Yu B M,Li J H. Some fractal characters of porous media[J]. Fractals,2001,9(3):365-372. doi: 10.1142/S0218348X01000804

    [35]

    Xu P,Qiu S X,Yu B M,et al. Prediction of relative permeability in unsaturated porous media with a fractal approach[J]. International Journal of Heat and Mass Transfer,2013,64:829-837. doi: 10.1016/j.ijheatmasstransfer.2013.05.003

    [36]

    Yu B M,Cheng P. A fractal permeability model for bi-dispersed porous media[J]. International Journal of Heat and Mass Transfer,2002,45(14):2983-2993. doi: 10.1016/S0017-9310(02)00014-5

    [37]

    Xia Y X,Cai J C,Wei W,et al. A new method for calculating fractal dimensions of porous media based on pore size distribution[J]. Fractals,2018,26(1):1850006. doi: 10.1142/S0218348X18500068

    [38]

    Costa A. Permeability-porosity relationship:A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption[J]. Geophysical Research Letters,2006,33:L02318. doi: 10.1029/2005GL025134

    [39]

    Zhao Y X,Zhu G P,Dong Y H,et al. Comparison of low-field NMR and microfocus X-ray computed tomography in fractal characterization of pores in artificial cores[J]. Fuel,2017,210:217-226. doi: 10.1016/j.fuel.2017.08.068

    [40]

    Zhang Z,Li C F,Ning F L,et al. Pore fractal characteristics of hydrate-bearing sands and implications to the saturated water permeability[J]. Journal of Geophysical Research:Solid Earth,2020,125:e2019JB018721. doi: 10.1029/2019JB018721

    [41]

    Perrier E,Bird N,Rieu M. Generalizing the fractal model of soil structure:the pore–solid fractal approach[J]. Geoderma,1999,88(3):137-164.

    [42]

    Daigle H. Relative permeability to water or gas in the presence of hydrates in porous media from critical path analysis[J]. Journal of Petroleum Science and Engineering,2016,146:526-535. doi: 10.1016/j.petrol.2016.07.011

    [43]

    Kleinberg R L,Flaum C,Griffin D D,et al. Deep sea NMR:Methane hydrate growth habit in porous media and its relationship to hydraulic permeability,deposit accumulation,and submarine slope stability[J]. Journal of Geophysical Research:Solid Earth,2003,108(B10):2508.

    [44]

    Katagiri J,Konno Y,Yoneda J,et al. Pore-scale modeling of flow in particle packs containing grain-coating and pore-filling hydrates:Verification of a Kozeny-Carman-based permeability reduction model[J]. Journal of Natural Gas Science and Engineering,2017,45:537-551. doi: 10.1016/j.jngse.2017.06.019

    [45]

    Singh H,Mahabadi N,Myshakin E M,et al. A mechanistic model for relative permeability of gas and water flow in hydrate-bearing porous media with capillarity[J]. Water Resource Research,2019,55(4):3414-3432. doi: 10.1029/2018WR024278

    [46]

    Chen X Y,Espinoza D N. Ostwald ripening changes the pore habit and spatial variability of clathrate hydrate[J]. Fuel,2018,214:614-622. doi: 10.1016/j.fuel.2017.11.065

    [47]

    Li C F,Liu C L,Hu G W,et al. Investigation on the multiparameter of hydrate-bearing sands using Nano-Focus X-Ray computed tomography[J]. Journal of Geophysical Research:Solid Earth,2019,124(3):2286-2296. doi: 10.1029/2018JB015849

    [48]

    Li C F,Hu G W,Zhang W,et al. Influence of foraminifera on formation and occurrence characteristics of natural gas hydrates in fine-grained sediments from Shenhu area,South China Sea[J]. Science China Earth Sciences,2016,59(11):2223-2230. doi: 10.1007/s11430-016-5005-3

    [49]

    Ning F L, Li C F, Cai J C, et al. Study on the relative permeability of hydrate-bearing sediments by a fractal parallel capillary model[C] //9th International Conference on Gas Hydrates, Denver, Colorado, USA 2017.

    [50]

    Liu L L,Dai S,Ning F L,et al. Fractal characteristics of unsaturated sands−implications to relative permeability in hydrate-bearing sediments[J]. Journal of Natural Gas Science and Engineering,2019,66:11-17. doi: 10.1016/j.jngse.2019.03.019

    [51]

    Mahabadi N,Jang J. Relative water and gas permeability for gas production from hydrate-bearing sediments[J]. Geochemistry,Geophysics,Geosystems,2014,15(6):2346-2353.

    [52]

    刘乐乐,张 准,宁伏龙,等. 含水合物沉积物渗透率分形模型[J]. 中国科学:物理学力学天文学,2019,49(3):034614.

    [53]

    Liu L L,Zhang Z,Li C F,et al. Hydrate growth in quartzitic sands and implication of pore fractal characteristics to hydraulic,mechanical,and electrical properties of hydrate-bearing sediments[J]. Journal of Natural Gas Science and Engineering,2020,75:103-109. doi: 10.1016/j.jngse.2019.103109

    [54]

    Jiang S F , Kang Y H, Sun Z Q. A digital image method for analysis of soil pores[C] //Proceedings of the IFIP International Federation for Information Processing, Boston, Massachusetts, USA: Springer US, 2009.

    [55]

    Silin D,Patzek T. Pore space morphology analysis using maximal inscribed spheres[J]. Physica A:Statistical Mechanics and its Applications,2006,371(2):336-360. doi: 10.1016/j.physa.2006.04.048

    [56]

    Breyiannis G,Varoutis S,Valougeorgis D. Rarefied gas flow in concentric annular tube:Estimation of the Poiseuille number and the exact hydraulic diameter[J]. European Journal of Mechanics - B/Fluids,2008,27(5):609-622. doi: 10.1016/j.euromechflu.2007.10.002

    [57]

    Liu L,Wu N,Liu C,et al. Maximum sizes of fluids occupied pores within hydrate-bearing porous media composed of different host particles[J]. Geofluids,2020. doi: 10.1155/2020/8880286

    [58]

    Cai J C, Xia Y X,Lu C,et al. Creeping microstructure and fractal permeability model of natural gas hydrate reservoir[J]. Marine and Petroleum Geology,2020,115:104282. doi: 10.1016/j.marpetgeo.2020.104282

    [59]

    Li D L,Du J W,He S,et al. Measurement and modeling of the effective thermal conductivity for porous methane hydrate samples[J]. Science China Chemistry,2012,55(3):373-379. doi: 10.1007/s11426-011-4459-8

    [60]

    陈玉凤,吴能友,梁德青,等. 基于分形孔隙模型的含天然气水合物沉积物电阻率数值模拟[J]. 天然气工业,2018,38(11):128-134. doi: 10.3787/j.issn.1000-0976.2018.11.017

    [61]

    Zhao Y L,Guo K H,Liang D,et al. Formation process and fractal growth model of HCFC-141b refrigerant gas hydrate[J]. Science in China Series B:Chemistry,2002,45(2):216-224. doi: 10.1360/02yb9029

    [62]

    杨海健,李小森,陈朝阳,等. 多孔介质中气体水合物降压分解的分形理论研究[J]. 化学学报,2009,67(8):808-812. doi: 10.3321/j.issn:0567-7351.2009.08.016

    [63]

    Li S L,Ma Q L,Sun C Y,et al. A fractal approach on modeling gas hydrate phase equilibria in porous media[J]. Fluid Phase Equilibria,2013,356:277-283. doi: 10.1016/j.fluid.2013.07.047

    [64]

    Zhang H T,Luo X Q,Bi J F,et al. Multi-component fractal representation of multi-scale structure of natural gas hydrate-bearing sediments[J]. Journal of Natural Gas Science and Engineering,2018,60:144-152. doi: 10.1016/j.jngse.2018.10.015

    [65]

    沈建东,王胜杰,何晓霞,等. 分形扩散对海下沉积层中水合物生成过程的影响[J]. 天然气工业,2004,24:24-26,126. doi: 10.3321/j.issn:1000-0976.2004.05.008

    [66]

    姚衍桃,詹文欢. 分形在南海北部陆坡断裂与天然气水合物关系研究中的应用[J]. 中山大学学报(自然科学版),2009,48(5):131-136. doi: 10.3321/j.issn:0529-6579.2009.05.026

    [67]

    韩 博,李承中,范 勇,等. 水合物钻井液微观结构热传导分形模型研究[J]. 地质与勘探,2012,48(4):829-834.

    [68]

    Jang J B,Cao S C,Stern L A,et al. Impact of pore-fluid chemistry on fine-grained sediment fabric and compressibility[J]. Journal of Geophysical Research:Solid Earth,2018,123:5495-5514. doi: 10.1029/2018JB015872

    [69]

    Santamarina J, Klein K, Palomino A, et al. Micro-scale aspects of chemical-mechanical coupling: Interparticle forces and fabric[C] //Dimaio C. Chemo-mechanical Coupling in Clays: From Nano-scale to Engineering Applications. Maratea, Italia, 2001.

    [70]

    钱学森. 论技术科学[J]. 科学通报,1957,8(3):97-104.

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收稿日期:  2020-05-30
刊出日期:  2020-09-28

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