考虑表面扩散作用的页岩气瞬态流动模型

doi:10.7623/syxb201402016

石油学报 ›› 2014, Vol. 35 ›› Issue (2): 347-352.DOI: 10.7623/syxb201402016

考虑表面扩散作用的页岩气瞬态流动模型

盛茂, 李根生, 黄中伟, 田守嶒

中国石油大学油气资源与探测国家重点实验室北京 102249

收稿日期:2013-09-03 修回日期:2013-12-14 出版日期:2014-03-25 发布日期:2014-04-11
通讯作者: 李根生，男，1961年9月生，1983年毕业于华东石油学院钻井工程专业，1998年获石油大学（北京）油气井工程专业博士学位，现为中国石油大学（北京）教授、博士生导师，主要从事油气井流体力学与工程方面的教学与研究。Email：ligs@cup.edu.cn
作者简介:盛茂，男，1985年9月生，2008年毕业于中国石油大学（北京）石油工程专业，现为中国石油大学（北京）博士研究生，主要从事页岩气压裂增产机理研究工作。Email：bjshm2005@gmail.com
基金资助:
国家自然科学基金重大国际（地区）合作项目（No.51210006）和国家自然科学基金重点项目（No.51234006）资助。

Shale gas transient flow model with effects of surface diffusion

Sheng Mao, Li Gensheng, Huang Zhongwei, Tian Shouceng

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China

Received:2013-09-03 Revised:2013-12-14 Online:2014-03-25 Published:2014-04-11

摘要/Abstract

摘要：

针对甲烷气在页岩孔隙中的流动规律问题，建立了考虑孔内扩散、孔壁表面扩散、黏性滑脱流动和气体解吸附等多种流动机理的瞬态流动毛管束模型，并采用有限差分法的三层隐式差分格式离散控制方程对模型进行了数值求解。该模型考虑了“表面扩散”和吸附层对气体滑脱速度的影响，其预测产气量高于以往模型预测值。实例计算结果表明，孔壁表面扩散是页岩孔隙中不可忽略的传质方式，且表面扩散通量对总流动通量的贡献随孔径减小而增强，孔径小于5 nm孔隙中表面扩散通量占总流动通量百分比可超过50% ；黏性流动通量所占百分比随孔径增大而增加，孔径大于50 nm孔隙中黏性流动通量所占百分比接近100% ；孔内扩散通量相比于表面扩散通量和黏性流动通量可忽略不计。

关键词: 页岩, 毛管束模型, 表面扩散, 数学模型, 有限差分法

Abstract:

This paper proposed a transient flow model for shale-gas in organic-rich shale, which involved the pore molecular diffusion, surface diffusion, slip flow, and gas adsorption and desorption phenomenon during shale-gas production. The three layer discretization format of finite difference method was used to discretize the governing equations. The predicated gas production from the proposed model is larger than that from other published models because of the consideration of surface flux and the effect of adsorption layer on slip flow flux. Numerical results show that the surface diffusion cannot be ignored, whose contribution for total flux is increasing with the pore diameter decreasing. For the given values of model parameters, the surface diffusion flux of Ф 5 nm pore covers over 50% of total flux. The viscous flux is becoming increasing with raising pore diameter; the flux percentage of viscous flux almost reaches 100% if the pore diameter is over 50 nm. However, the pore diffusion flux is extensively less than the surface diffusion flux and viscous slip flux, which can be negligible.

Key words: shale gas, capillary bundle model, surface diffusion, mathematical model, finite difference method

中图分类号:

TE312

盛茂, 李根生, 黄中伟, 田守嶒. 考虑表面扩散作用的页岩气瞬态流动模型[J]. 石油学报, 2014, 35(2): 347-352.

Sheng Mao, Li Gensheng, Huang Zhongwei, Tian Shouceng. Shale gas transient flow model with effects of surface diffusion[J]. ACTA PETROLEI SINICA, 2014, 35(2): 347-352.

参考文献

[1] Javadpour F, Fisher D, Unsworth M.Nanoscale gas flow in shale gas sediments[J].Journal of Canadian Petroleum Technology, 2007, 46(10):55-61.
[2] Freeman C, Moridis G, Blasingame T.A numerical study of microscale flow behavior in tight gas and shale gas reservoir systems[J].Transport in Porous Media, 2011, 90(1):253-268.
[3] Civan F.Effective correlation of apparent gas permeability in tight porous media[J].Transport in Porous Media, 2010, 82(2):375-384.
[4] Beskok A, Karniadakis G E.Report:a model for flows in channels, pipes, and ducts at micro and nano scales[J].Microscale Thermophysical Engineering, 1999, 3(1):43-77.
[5] Fathi E, Akkutlu I Y.Nonlinear sorption kinetics and surface diffusion effects on gas transport in low-permeability formations[R].SPE 124478, 2009.
[6] Do H, Do D, Prasetyo I.Surface diffusion and adsorption of hydrocarbons in activated carbon[J].AIChE Journal, 2001, 47(11):2515-2525.
[7] Shabro V, Torres-Verdin C, Javadpour F.Numerical simulation of shale-gas production:from pore-scale modeling of slip-flow, Knudsen diffusion, and Langmuir Desorption to reservoir modeling of compressible fluid[R].SPE 144355, 2011.
[8] 李晓强, 周志宇, 冯光, 等.页岩基质扩散流动对页岩气井产能的影响[J].油气藏评价与开发, 2011, 1(5):67-70.
Li Xiaoqiang, Zhou Zhiyu, Feng Guang, et al.The impact of shale matrix diffusion flow on shale gas capacity[J].Reservoir Evaluation and Development, 2011, 1(5):67-70.
[9] 高树生, 于兴河, 刘华勋.滑脱效应对页岩气井产能影响的分析[J].天然气工业, 2011, 31(4):55-58.
Gao Shusheng, Yu Xinghe, Liu Huaxun.Impact of slipage effect on shale gas well productivity[J].Natural Gas Industry, 2011, 31(4):55-58.
[10] 李建秋, 曹建红, 段永刚, 等.页岩气井渗流机理及产能递减分析[J].天然气勘探与开发, 2011, 34(2):34-37.
Li Jianqiu, Cao Jianhong, Duan Yonggang, et al.Seepage mechanism and productivity decline of shale-gas well[J].Natural Gas Exploration & Development, 2011, 34(2):34-37.
[11] 段永刚, 魏明强, 李建秋, 等.页岩气藏渗流机理及压裂井产能评价[J].重庆大学学报:自然科学版, 2011, 34(4):62-66.
Duan Yonggang, Wei Mingqiang, Li Jianqiu, et al.Shale gas seepage mechanism and fractured wells' production evaluation[J].Journal of Chongqing University:Natural Science Edition, 2011, 34(4):62-66.
[12] 关富佳, 吴恩江, 邱争科, 等.页岩气渗流机理对气藏开采的影响[J].大庆石油地质与开发, 2011, 30(2):80-83.
Guan Fujia, Wu Enjiang, Qiu Zhengke, et al.Effect of shale gas flow mechanism of development of gas reservoir[J].Petroleum Geology & Oilfield Development in Daqing, 2011, 30(2):80-83.
[13] 姚同玉, 黄延章, 李继山.页岩气在超低渗介质中的渗流行为[J].力学学报, 2012, 44(6):990-995.
Yao Tongyu, Huang Yanzhang, Li Jishan.Flow regim for shale gas in extra low permeability porous media[J].Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6):990-995.
[14] Bae J S, Do D D.Permeability of subcritical hydrocarbons in activated carbon[J].AIChE Journal, 2005, 51(2):487-501.
[15] Krishna R, Wesselingh J.The Maxwell-Stefan approach to mass transfer[J].Chemical Engineering Science, 1997, 52(6):861-911.
[16] 郭亮, 彭晓峰, 吴占松.甲烷在成型纳米活性炭中的吸附动力学特性[J].化工学报, 2008, 59(11):2726-2732.
Guo Liang, Peng Xiaofeng, Wu Zhansong.Dynamical characteristics of methane adsorption on monlith nanometer activated carbon[J].Journal of Chemical Industry and Engineering (China), 2008, 59(11):2726-2732.
[17] Popielawski J, Baranowski B.Statistical mechanics of transport processes in adsorbed gases[J].Molecular Physics, 1965, 9(1):59-66.
[18] 杨胜来, 魏俊之.油层物理学[M].北京:石油工业出版社, 2004:155-156.
Yang Shenglai, Wei Junzhi.Petrophysics[M].Beijing:Petroleum Industry Press, 2004:155-156.
[19] 王瑞, 张宁生, 刘晓娟, 等.页岩气扩散系数和视渗透率的计算与分析[J].西北大学学报:自然科学版, 2013, 43(1):75-80.
Wang Rui, Zhang Ningsheng, Liu Xiaojuan, et al.The calculation and analysis of diffusion coefficient and apparent permeability of shale gas[J].Journal of Northwest University:Natural Science Edition, 2013, 43(1):75-80.
[20] Kaviany M.Principles of heat transfer in porous media[M].New York:Springer-Verlag, 1991:26-28.
[21] Eu B C, Khayat R E, Billing G D, et al.Nonlinear transport coefficients and plane Couette flow of a viscous, heat-conducting gas between two plates at different temperatures[J].Canadian Journal of Physics, 1987, 65(9):1090-1103.
[22] Myong R.Gaseous slip models based on the Langmuir adsorption isotherm[J].Physics of Fluids, 2004, 16(1):104-117.
[23] Fathi E, Akkutlu I Y.Lattice boltzmann method for simulation of shale gas transport in Kerogen[R].SPE 146821, 2011.
[24] Dubinin M.The potential theory of adsorption of gases and vapors for adsorbents with energetically nonuniform surfaces[J].Chemical Reviews, 1960, 60(2):235-241.
[25] Langmuir I.The constitution and fundamental properties of solids and liquids.Part I.solids[J].Journal of the American Chemical Society, 1916, 38(11):2221-2295.
[26] Ambrose R J, Hartman R, Diaz-Campos M, et al.Shale Gas-in-Place calculations part I:New Pore-Scale considerations[J].SPE Journal, 2012, 17(1):219-229.
[27] Hartman R C, Ambrose R, Akkutlu I Y, et al.Shale gas-in-place calculations Part Ⅱ-Multicomponent gas adsorption effects[R].SPE 144097, 2011.
[28] 张文生.科学计算中的偏微分方程有限差分法[M].北京:高等教育出版社, 2006:246-249.
Zhang Wensheng.Finite difference methods for partial differential equations in science computation[M].Beijing:Higher Education Press, 2006:246-249.
[29] Curtis J B.Fractured shale-gas systems[J].AAPG Bulletin, 2002, 86(11):1921-1938.
[30] Kuuskraa V A, Koperna G, Schmoker J W, et al.Barnett Shale rising star in Fort Worth Basin[J].Oil and Gas Journal, 1998, 96(1):67-76.
[31] Wang F P, Reed R M.Pore networks and fluid flow in gas shales[R].SPE 124253, 2009.
[32] 崔景伟, 邹才能, 朱如凯, 等.页岩孔隙研究新进展[J].地球科学进展, 2012, 27(12):1319-1325.
Cui Jingwei, Zou Caineng, Zhu Rukai, et al.New advances in shale porosity research[J].Advances in Earth Science, 2012, 27(12):1319-1325.
[33] 叶振华.化工吸附分离过程[M].北京:中国石化出版社, 1992:58-60.
Ye Zhenhua.Chemical engineering adsorption separation process[M].Beijing:China Petrochemical Press, 1992:58-60.
[34] 崔永君, 张庆玲, 杨锡禄.不同煤的吸附性能及等量吸附热的变化规律[J].天然气工业, 2003, 23(4):130-131.
Cui Yongjun, Zhang Qingling, Yang Xilu.Adsorption capacity and isosteric heat of methane adsorption for various types of coal[J].Natural Gas Industry, 2003, 23(4):130-131.

考虑表面扩散作用的页岩气瞬态流动模型

Shale gas transient flow model with effects of surface diffusion

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	付锁堂, 金之钧, 付金华, 李士祥, 杨伟伟. 鄂尔多斯盆地延长组7段从致密油到页岩油认识的转变及勘探开发意义[J]. 石油学报, 2021, 42(5): 561-569.
[2]	糜利栋. 基于产气剖面的页岩气离散裂缝网络反演方法[J]. 石油学报, 2021, 42(4): 481-491.
[3]	张建国, 姜在兴, 刘立安, 袁方, 冯路尧, 李长昇. 渤海湾盆地沾化凹陷沙河街组三段下亚段细粒沉积岩岩相特征与沉积演化[J]. 石油学报, 2021, 42(3): 293-306.
[4]	赵贤正, 蒲秀刚, 周立宏, 金凤鸣, 韩国猛, 时战楠, 韩文中, 丁娱娇, 张伟, 王国娜, 刘学伟, 汪虎. 深盆湖相区页岩油富集理论、勘探技术及前景——以渤海湾盆地黄骅坳陷古近系为例[J]. 石油学报, 2021, 42(2): 143-162.
[5]	游利军, 康毅力, 周洋, 陈强, 程秋洋, 徐洁明, 陈杨. 油气储层氧敏性概念、机理与意义[J]. 石油学报, 2021, 42(2): 186-197.
[6]	何骁, 吴建发, 雍锐, 赵圣贤, 周小金, 张洞君, 张德良, 钟成旭. 四川盆地长宁—威远区块海相页岩气田成藏条件及勘探开发关键技术[J]. 石油学报, 2021, 42(2): 259-272.
[7]	匡立春, 侯连华, 杨智, 吴松涛. 陆相页岩油储层评价关键参数及方法[J]. 石油学报, 2021, 42(1): 1-14.
[8]	梁兴, 徐政语, 张介辉, 张朝, 李兆丰, 蒋佩, 蒋立伟, 朱斗星, 刘臣. 浅层页岩气高效勘探开发关键技术——以昭通国家级页岩气示范区太阳背斜区为例[J]. 石油学报, 2020, 41(9): 1033-1048.
[9]	陈浩, 周涛, 樊怀才, 张鉴, 杨胜来. 页岩储层人工裂缝岩样制备方法及应力敏感性[J]. 石油学报, 2020, 41(9): 1117-1126.
[10]	周立宏, 韩国猛, 马建英, 陈长伟, 杨飞, 张莉华, 周可佳, 陈双清, 杨帆, 董越崎, 周静. 歧口凹陷西南缘沙河街组一段下亚段古环境特征与沉积模式[J]. 石油学报, 2020, 41(8): 903-917.
[11]	李俊乾, 卢双舫, 张鹏飞, 李文镖, 荆铁亚, 冯文俊. 页岩基质孔隙水定量表征及微观赋存机制[J]. 石油学报, 2020, 41(8): 979-990.
[12]	付锁堂, 付金华, 牛小兵, 李士祥, 吴志宇, 周新平, 刘江艳. 庆城油田成藏条件及勘探开发关键技术[J]. 石油学报, 2020, 41(7): 777-795.
[13]	赵贤正, 周立宏, 蒲秀刚, 时战楠, 韩国猛, 吴佳朋, 韩文中, 张伟, 高欢欢, 马建英, 汪虎. 歧口凹陷歧北次凹沙河街组三段页岩油地质特征与勘探突破[J]. 石油学报, 2020, 41(6): 643-657.
[14]	罗文彬, 马中良, 郑伦举, 谭静强, 王张虎, 宁传祥. 海相页岩成岩-成烃过程中孔隙结构的演变——来自热模拟实验的启示[J]. 石油学报, 2020, 41(5): 540-552.
[15]	毕海滨, 孟昊, 高日丽, 郑婧, 徐小林, 鞠秀娟, 牛伟, 张劲, 周明庆, 赵丽华. 页岩气未开发区单井可采储量评估方法[J]. 石油学报, 2020, 41(5): 565-573.