页岩气滑脱、扩散传输机理耦合新方法

李亚雄; 刘先贵; 胡志明; 高树生; 端祥刚; 常进

doi:10.7498/aps.66.114702

摘要

针对页岩气流动计算中所用耦合机理不同的现状，且为了厘清滑脱和各种扩散之间的关系，首先采用理论分析和数学模型的方法，根据定义和微观运动机制对滑脱和各种扩散进行了分析，然后在考虑吸附层页岩气分子所占空间对气体流动影响的情况下，提出了“壁联扩散”的概念来表征克努森扩散和表面扩散的总效应，并指出壁联扩散和滑脱效应等同，由此提出了壁联扩散和滑脱效应在流动计算中可互换而不重复叠加的耦合新方法.实例验证表明，当毛细管半径从5 nm增大到2000 nm，壁联扩散和滑脱效应的质量通量相对误差较小，在绝大部分范围内都小于10%，且在整个孔径范围内两者平均值相差1.4×10-6kg·m-2·s-1，即平均值的相对误差仅为5.8%，该方法可以满足工程计算的需要.考虑到参数选取、机理数学模型有待完善等方面的影响，新方法的论证存在进一步提升的空间.壁联扩散的提出具有实际开发意义和多重研究意义，耦合新方法的提出阐明了滑脱和各种扩散之间的关系，防止了页岩纳米级孔隙中流动机理的重复叠加，能较好改变页岩气流动计算耦合方法不一致的现状，为页岩气开发定量计算指明新方向.

关键词:

页岩气 /
扩散 /
壁联扩散 /
滑脱

Abstract

In view of the current status that different literature applies different coupling methods to the calculation of shale gas flow, and in order to clarify the relation between slippage and several diffusions, in this paper the slippage effect and various diffusions are analyzed first by theoretical analysis and mathematical models according to the definitions and the mechanisms of microscopic motions. Afterwards, allowing for the spatial effect of the adsorbed molecules on gas flow, the concept “wall-associated diffusion” is proposed for the first time to represent the gross effects of Knudsen diffusion and surface diffusion, and it is pointed out that wall-associated diffusion is equivalent to slippage effect. Therefore a new coupling way where wall-associated diffusion and slippage effect are replaceable and no superposition of them is needed in flow calculation, is proposed. The case study shows that when the capillary radius ranges from 5 nm to 2000 nm, the relative error between wall-associated diffusion and slippage effect mass flux is fairly small, namely less than 10% in the vast majority of the range. The difference between mean values of wall-associated diffusion and slippage effect mass flux in the whole aperture range is 1.4×10- 6 kg·m-2·s-1. That is, the relative error between the mean values is only 5.8%. Therefore, the new method satisfies the requirements for engineering calculations. Taking parameter selection, unfinished improvements in mathematical models of relevant mechanisms and other factors into account, there is some room for further promoting the verification of the proposed method. The development of wall-associated diffusion has practical significance and multiple research significance. And the new coupling way reveals the relation between slippage and diffusions, which prevents reduplicated superposition of shale gas flow mechanisms in nano-scale pores and can well change the status where the current coupling methods for shale gas flow are not consistent, thus specifying a new direction in the quantitative calculations for shale gas development.

Keywords:

作者及机构信息

1.
中国科学院大学, 北京 100049;

2.
中国科学院渗流流体力学研究所, 廊坊 065007;

3.
中国石油勘探开发研究院廊坊分院, 廊坊 065007

通信作者: 李亚雄, 18510284051@163.com

基金项目: 国家重点基础研究发展计划（批准号：2013CB228000）资助的课题.

Authors and contacts

1.
University of Chinese Academy of Sciences, Beijing 100049, China;

2.
Institute of Porous Flow and Fluid Mechanics, Chinese Academy of Sciences, Langfang 065007, China;

3.
Langfang Branch, PetroChina Research Institute of Petroleum Exploration and Development, Langfang 065007, China

Corresponding author: Li Ya-Xiong, 18510284051@163.com

Funds: Project supported by the National Basic Research Program of China (Grant No. 2013CB228000).

参考文献

[1]	Zhang L H, Guo J J, Tang H M 2014 Development Foundation of Shale Gas Reservoir (1st Ed) (Beijing: Petroleum Industry Press) p1, pp61-63, p84 (in Chinese) [张烈辉, 郭晶晶, 唐洪明 2014 页岩气藏开发基础(第一版)(北京:石油工业出版社) 第1页, 第61-63页, 第84页]
[2]	Deng J, Zhu W Y, Liu J X, Zhang Z, Ma Q, Zhang M, Deng K, Ma L 2013 Nat. Gas Geosci. 24 456 (in Chinese) [邓佳, 朱维耀, 刘锦霞, 张贞, 马千, 张萌, 邓凯, 马丽 2013 天然气地球科学 24 456]
[3]	Yin D Y, Wang D Q, Zhang C L, Duan Y J 2015 Open Pet. Eng. J. 8 203
[4]	Deng J, Zhu W, Ma Q 2014 Fuel 124 232
[5]	Zhu W Y, Qi Q 2016 Sci. Sin. Technol. 46 111 (in Chinese) [朱维耀, 亓倩 2016 中国科学: 技术科学 46 111]
[6]	Lin M, Jiang W B, Li Y, Yi Z X, Zhang Z B 2015 Bull. Mineral. Petrol. Geochem. 34 18 (in Chinese) [林缅, 江文滨, 李勇, 易智星, 张召彬 2015 矿物岩石地球化学通报 34 18]
[7]	Yao T Y, Huang Y Z, Li J S 2012 Chin. J. Theor. Appl. Mech. 44 990 (in Chinese) [姚同玉, 黄延章, 李继山 2012 力学学报 44 990]
[8]	Jiang B Y, Li Z P, Diwu P X, Liu G, Wang J N, Gan H H 2014 Sci. Technol. Eng. 14 58 (in Chinese) [姜宝益, 李治平, 第五鹏祥, 刘刚, 王建宁, 甘火华 2014 科学技术与工程 14 58]
[9]	Swami V, Settari A 2012 SPE Americas Unconventional Resources Conference Pittsburgh, USA, June 5-7, 2012 p1
[10]	Javadpour F, Fisher D, Unsworth M 2007 J. Can. Petrol. Technol. 46 55
[11]	Javadpour F 2009 J. Can. Petrol. Technol. 48 16
[12]	Shabro V, Torres-Verdin C, Sepehrnoori K 2012 SPE Annual Technical Conference and Exhibition San Antonio, USA, October 8-10, 2012 p1
[13]	Wu K, Li X, Wang C C, Chen Z X, Yu W 2015 AlChE J. 61 2079
[14]	Wu K L, Li X F, Chen Z X 2015 Acta Petrol. Sin. 36 837 (in Chinese) [吴克柳, 李相方, 陈掌星 2015 石油学报 36 837]
[15]	Haghshenas B, Clarkson C R, Chen S 2013 SPE Unconventional Resources Conference Calgary, Canada, November 5-7, 2013 p1
[16]	Song H Q, Liu Q P, Yu M X, Wu P, Zhang Y 2014 J. Univ. Sci. Technol. Beijing 36 139 (in Chinese) [宋洪庆, 刘启鹏, 于明旭, 吴鹏, 张雨 2014 北京科技大学学报 36 139]
[17]	Mi L D, Jiang H Q, Li J J 2014 J. Natur. Gas Sci. Eng. 20 74
[18]	Mi L D, Jiang H Q, Li J J, Tian Y 2014 Acta Petrol. Sin. 35 928 (in Chinese) [糜利栋, 姜汉桥, 李俊键, 田野 2014 石油学报 35 928]
[19]	Ai S, Cheng L S, Huang S J, Fu L B, Wang T, Du B J, Zhang J, Liu H J 2014 Nat. Gas Geosci. 25 166 (in Chinese) [艾爽, 程林松, 黄世军, 傅礼兵, 王涛, 杜保健, 张晋, 刘红君 2014 天然气地球科学 25 166]
[20]	Li Y, Li X, Shi J, Wang H, Wu L 2014 SPE Biennial Energy Resources Conf. Port of Spain, Trinidad, June 9-11, 2014 p1
[21]	Jia P, Cheng L S, Huang S J, Xue Y C 2015 SPE Asia Pacific Unconventional Resources Conference and Exhibition Brisbane, Australia, November 9-11 2015 p1
[22]	Zhou X, Zhang S C, Ma X F, Zhang Y 2015 Xinjiang Petrol. Geol. 36 612 (in Chinese) [周祥, 张士诚, 马新仿, 张烨 2015 新疆石油地质 36 612]
[23]	Roy S, Raju R, Chuang H F, Cruden B A, Meyyappan M 2003 J. Appl. Phys. 93 4870
[24]	Huang T, Guo X, Wang K 2015 J. Chem. 2015 1
[25]	Klinkenberg L J 1941 Drilling and Production Practice (New York: American Petroleum Institute) p200
[26]	Li C L 2007 Natur. Gas Ind. 27 85 (in Chinese) [李传亮 2007 天然气工业 27 85]
[27]	Wu Q F, Chen W F, Huang L, Shi Y Z 2004 Rarefied Gas Dynamics (1st Ed.) (Changsha: National University of Defense Technology Press) pp96-97 (in Chinese) [吴其芬, 陈伟芳, 黄琳, 石于中 2004 稀薄气体动力学(第一版) (长沙: 国防科技大学出版社) 第96-97页]
[28]	Zhu G Y, Liu X G, Li S T, Huang Y Z, Hao M Y 2007 Nat. Gas Ind. 27 44 (in Chinese) [朱光亚, 刘先贵, 李树铁, 黄延章, 郝明强 2007 天然气工业 27 44]
[29]	Bear J (translated by Li J S, Chen C X)1983 Dynamics of Fluids in Porous Media (Beijing: China Architecture & Building Press) pp98-99 (in Chinese) [贝尔 J著 (李竞生, 陈崇希译) 1983 多孔介质流体动力学 (北京: 中国建筑工业出版社) 第98-99页]
[30]	Ge H K, Shen Y H, Song Y, Wang X Q, Jiang C F, Shi P, Wang H, Yang L 2014 Nat. Gas Ind. 34 46 (in Chinese) [葛洪魁, 申颍浩, 宋岩, 王小琼, 姜呈馥, 史鹏, 王晖, 杨柳 2014 天然气工业 34 46]
[31]	Chen D X 2002 Chin. J. Theor. Appl. Mech. 34 96 (in Chinese) [陈代珣 2002 力学学报 34 96]
[32]	Brown G P, DiNardo A, Cheng G K, Sherwood T K 1946 J. Appl. Phys. 17 802
[33]	Nie B S, Zhang L, Ma W F 2000 Coal Geol. Explor. 28 20 (in Chinese) [聂百胜, 张力, 马文芳 2000 煤田地质与勘探 28 20]
[34]	Ziarani A S, Aguilera R 2012 Transp. Porous Med. 91 239
[35]	Florence F A, Rushing J A, Newsham K E, Blasingame T A 2007 Rocky Mountain Oil & Gas Technology Symposium (Denver: Society of Petroleum Engineers ) p1
[36]	Tian L, Xiao C, Liu M J, Gu D H 2014 J. Northeast Petrol. Univ. 38 93 (in Chinese) [田冷, 肖聪, 刘明进, 顾岱红 2014 东北石油大学学报 38 93]
[37]	Ren F, Wang X H, Ren K, Li Q Q, Wang S S, Zhang L, Wang Y 2013 Fault-Block Oil Gas Field 20 649 (in Chinese) [任飞, 王新海, 任凯, 李清泉, 王珊珊, 张磊, 王宇 2013 断块油气田 20 649]
[38]	Loucks R G, Reed R M, Ruppel S C, Jarvie D M 2009 J. Sediment. Res. 79 848
[39]	Civan F 2010 Porous Media and Its Applications in Science, Engineering, and Industry: 3rd International Conference (Montecatini: AIP Publishing) p53
[40]	Ren N, Shu L, Hu Y Q, Zhao J Z 2014 J. Southwest Petrol. Univ. (Sci. Technol Ed.) 36 111 (in Chinese) [任岚, 舒亮, 胡永全, 赵金洲 2014 西南石油大学学报(自然科学版) 36 111]
[41]	Song F Q, Zhang X, Huang X H, Long Y Q 2016 Sci. Sin. Technol. 46 120 (in Chinese) [宋付权, 张翔, 黄小荷, 龙运前 2016 中国科学: 技术科学 46 120]
[42]	Li Q Q, Wang X H, Yin H, Ren F, Wang S S, Zhang L 2013 J. Northeast Petrol. Univ. 37 91 (in Chinese) [李清泉, 王新海, 尹虎, 任飞, 王珊珊, 张磊 2013 东北石油大学学报 37 91]
[43]	Chen Q, Kang Y L, You L J, Yu Y F, Liu H L 2013 Nat. Gas Geosci. 24 1298 (in Chinese) [陈强, 康毅力, 游利军, 俞杨烽, 刘洪林 2013 天然气地球科学 24 1298]
[44]	Wu K L, Li X F, Chen Z X 2015 Sci. Sin. Technol. 45 525 (in Chinese) [吴克柳, 李相方, 陈掌星 2015 中国科学:技术科学 45 525]
[45]	Sheng M, Li G S, Huang Z W, Tian S C 2014 Acta Petrol. Sin. 35 347 (in Chinese) [盛茂, 李根生, 黄中伟, 田守嶒 2014 石油学报 35 347]
[46]	Do H D, Do D D, Prasetyo I 2001 AlChE J. 47 2515
[47]	Clarkson C R, Haghshenas B 2013 SPE Unconventional Resources Conference Woodlands, USA, April 10-12, 2013 p1
[48]	Civan F, Rai C S, Sondergeld C H 2011 Transport Porous Med. 86 925
[49]	Wang H Y, Ajao O, Economides M J 2014 J. Nat. Gas Sci. Eng. 21 874
[50]	Guo W, Xiong W, Gao S S, Hu Z M 2013 J. Cent. South Univ. (Sci. Technol.) 44 2836 (in Chinese) [郭为, 熊伟, 高树生, 胡志明 2013 中南大学学报(自然科学版) 44 2836]
[51]	Sladek K J, Gilliland E R, Baddour R F 1974 Ind. Eng. Chem. Fundam. 13 100
[52]	Curtis J B 2002 AAPG Bull. 86 1921
[53]	Kuuskraa V A, Koperna G, Schmoker J W, Quinn J C 1998 Oil Gas J. 96 67
[54]	Wang F P, Reed R M 2009 SPE Annual Technical Conference and Exhibition (New Orleans: Society of Petroleum Engineers) p1
[55]	Arkilic E B 1997 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[56]	Mosher K, He J, Liu Y, Rupp E, Wilcox J 2013 Int. J. Coal Geol. 109 36
[57]	Dubinin M M, Astakhov V A 1971 Russ. Chem. Bull. 20 8
[58]	Zhai Z Q, Wang X Q, Jin X, Sun L, Li J M, Cao D P 2014 Energ. Fuel. 28 7467
[59]	Wang H, Wang X Q, Jin X, Cao D P 2016 J. Phys. Chem. C 120 8986
[60]	Kuila U, Prasad M, Kazemi H 2012 Proceedings of 9th Biennial International Conference and Exposition on Petroleum Geophysics Hyderabad, India, Febrary 16-18, 2012 p182

施引文献

[1]	Zhang L H, Guo J J, Tang H M 2014 Development Foundation of Shale Gas Reservoir (1st Ed) (Beijing: Petroleum Industry Press) p1, pp61-63, p84 (in Chinese) [张烈辉, 郭晶晶, 唐洪明 2014 页岩气藏开发基础(第一版)(北京:石油工业出版社) 第1页, 第61-63页, 第84页]
[2]	Deng J, Zhu W Y, Liu J X, Zhang Z, Ma Q, Zhang M, Deng K, Ma L 2013 Nat. Gas Geosci. 24 456 (in Chinese) [邓佳, 朱维耀, 刘锦霞, 张贞, 马千, 张萌, 邓凯, 马丽 2013 天然气地球科学 24 456]
[3]	Yin D Y, Wang D Q, Zhang C L, Duan Y J 2015 Open Pet. Eng. J. 8 203
[4]	Deng J, Zhu W, Ma Q 2014 Fuel 124 232
[5]	Zhu W Y, Qi Q 2016 Sci. Sin. Technol. 46 111 (in Chinese) [朱维耀, 亓倩 2016 中国科学: 技术科学 46 111]
[6]	Lin M, Jiang W B, Li Y, Yi Z X, Zhang Z B 2015 Bull. Mineral. Petrol. Geochem. 34 18 (in Chinese) [林缅, 江文滨, 李勇, 易智星, 张召彬 2015 矿物岩石地球化学通报 34 18]
[7]	Yao T Y, Huang Y Z, Li J S 2012 Chin. J. Theor. Appl. Mech. 44 990 (in Chinese) [姚同玉, 黄延章, 李继山 2012 力学学报 44 990]
[8]	Jiang B Y, Li Z P, Diwu P X, Liu G, Wang J N, Gan H H 2014 Sci. Technol. Eng. 14 58 (in Chinese) [姜宝益, 李治平, 第五鹏祥, 刘刚, 王建宁, 甘火华 2014 科学技术与工程 14 58]
[9]	Swami V, Settari A 2012 SPE Americas Unconventional Resources Conference Pittsburgh, USA, June 5-7, 2012 p1
[10]	Javadpour F, Fisher D, Unsworth M 2007 J. Can. Petrol. Technol. 46 55
[11]	Javadpour F 2009 J. Can. Petrol. Technol. 48 16
[12]	Shabro V, Torres-Verdin C, Sepehrnoori K 2012 SPE Annual Technical Conference and Exhibition San Antonio, USA, October 8-10, 2012 p1
[13]	Wu K, Li X, Wang C C, Chen Z X, Yu W 2015 AlChE J. 61 2079
[14]	Wu K L, Li X F, Chen Z X 2015 Acta Petrol. Sin. 36 837 (in Chinese) [吴克柳, 李相方, 陈掌星 2015 石油学报 36 837]
[15]	Haghshenas B, Clarkson C R, Chen S 2013 SPE Unconventional Resources Conference Calgary, Canada, November 5-7, 2013 p1
[16]	Song H Q, Liu Q P, Yu M X, Wu P, Zhang Y 2014 J. Univ. Sci. Technol. Beijing 36 139 (in Chinese) [宋洪庆, 刘启鹏, 于明旭, 吴鹏, 张雨 2014 北京科技大学学报 36 139]
[17]	Mi L D, Jiang H Q, Li J J 2014 J. Natur. Gas Sci. Eng. 20 74
[18]	Mi L D, Jiang H Q, Li J J, Tian Y 2014 Acta Petrol. Sin. 35 928 (in Chinese) [糜利栋, 姜汉桥, 李俊键, 田野 2014 石油学报 35 928]
[19]	Ai S, Cheng L S, Huang S J, Fu L B, Wang T, Du B J, Zhang J, Liu H J 2014 Nat. Gas Geosci. 25 166 (in Chinese) [艾爽, 程林松, 黄世军, 傅礼兵, 王涛, 杜保健, 张晋, 刘红君 2014 天然气地球科学 25 166]
[20]	Li Y, Li X, Shi J, Wang H, Wu L 2014 SPE Biennial Energy Resources Conf. Port of Spain, Trinidad, June 9-11, 2014 p1
[21]	Jia P, Cheng L S, Huang S J, Xue Y C 2015 SPE Asia Pacific Unconventional Resources Conference and Exhibition Brisbane, Australia, November 9-11 2015 p1
[22]	Zhou X, Zhang S C, Ma X F, Zhang Y 2015 Xinjiang Petrol. Geol. 36 612 (in Chinese) [周祥, 张士诚, 马新仿, 张烨 2015 新疆石油地质 36 612]
[23]	Roy S, Raju R, Chuang H F, Cruden B A, Meyyappan M 2003 J. Appl. Phys. 93 4870
[24]	Huang T, Guo X, Wang K 2015 J. Chem. 2015 1
[25]	Klinkenberg L J 1941 Drilling and Production Practice (New York: American Petroleum Institute) p200
[26]	Li C L 2007 Natur. Gas Ind. 27 85 (in Chinese) [李传亮 2007 天然气工业 27 85]
[27]	Wu Q F, Chen W F, Huang L, Shi Y Z 2004 Rarefied Gas Dynamics (1st Ed.) (Changsha: National University of Defense Technology Press) pp96-97 (in Chinese) [吴其芬, 陈伟芳, 黄琳, 石于中 2004 稀薄气体动力学(第一版) (长沙: 国防科技大学出版社) 第96-97页]
[28]	Zhu G Y, Liu X G, Li S T, Huang Y Z, Hao M Y 2007 Nat. Gas Ind. 27 44 (in Chinese) [朱光亚, 刘先贵, 李树铁, 黄延章, 郝明强 2007 天然气工业 27 44]
[29]	Bear J (translated by Li J S, Chen C X)1983 Dynamics of Fluids in Porous Media (Beijing: China Architecture & Building Press) pp98-99 (in Chinese) [贝尔 J著 (李竞生, 陈崇希译) 1983 多孔介质流体动力学 (北京: 中国建筑工业出版社) 第98-99页]
[30]	Ge H K, Shen Y H, Song Y, Wang X Q, Jiang C F, Shi P, Wang H, Yang L 2014 Nat. Gas Ind. 34 46 (in Chinese) [葛洪魁, 申颍浩, 宋岩, 王小琼, 姜呈馥, 史鹏, 王晖, 杨柳 2014 天然气工业 34 46]
[31]	Chen D X 2002 Chin. J. Theor. Appl. Mech. 34 96 (in Chinese) [陈代珣 2002 力学学报 34 96]
[32]	Brown G P, DiNardo A, Cheng G K, Sherwood T K 1946 J. Appl. Phys. 17 802
[33]	Nie B S, Zhang L, Ma W F 2000 Coal Geol. Explor. 28 20 (in Chinese) [聂百胜, 张力, 马文芳 2000 煤田地质与勘探 28 20]
[34]	Ziarani A S, Aguilera R 2012 Transp. Porous Med. 91 239
[35]	Florence F A, Rushing J A, Newsham K E, Blasingame T A 2007 Rocky Mountain Oil & Gas Technology Symposium (Denver: Society of Petroleum Engineers ) p1
[36]	Tian L, Xiao C, Liu M J, Gu D H 2014 J. Northeast Petrol. Univ. 38 93 (in Chinese) [田冷, 肖聪, 刘明进, 顾岱红 2014 东北石油大学学报 38 93]
[37]	Ren F, Wang X H, Ren K, Li Q Q, Wang S S, Zhang L, Wang Y 2013 Fault-Block Oil Gas Field 20 649 (in Chinese) [任飞, 王新海, 任凯, 李清泉, 王珊珊, 张磊, 王宇 2013 断块油气田 20 649]
[38]	Loucks R G, Reed R M, Ruppel S C, Jarvie D M 2009 J. Sediment. Res. 79 848
[39]	Civan F 2010 Porous Media and Its Applications in Science, Engineering, and Industry: 3rd International Conference (Montecatini: AIP Publishing) p53
[40]	Ren N, Shu L, Hu Y Q, Zhao J Z 2014 J. Southwest Petrol. Univ. (Sci. Technol Ed.) 36 111 (in Chinese) [任岚, 舒亮, 胡永全, 赵金洲 2014 西南石油大学学报(自然科学版) 36 111]
[41]	Song F Q, Zhang X, Huang X H, Long Y Q 2016 Sci. Sin. Technol. 46 120 (in Chinese) [宋付权, 张翔, 黄小荷, 龙运前 2016 中国科学: 技术科学 46 120]
[42]	Li Q Q, Wang X H, Yin H, Ren F, Wang S S, Zhang L 2013 J. Northeast Petrol. Univ. 37 91 (in Chinese) [李清泉, 王新海, 尹虎, 任飞, 王珊珊, 张磊 2013 东北石油大学学报 37 91]
[43]	Chen Q, Kang Y L, You L J, Yu Y F, Liu H L 2013 Nat. Gas Geosci. 24 1298 (in Chinese) [陈强, 康毅力, 游利军, 俞杨烽, 刘洪林 2013 天然气地球科学 24 1298]
[44]	Wu K L, Li X F, Chen Z X 2015 Sci. Sin. Technol. 45 525 (in Chinese) [吴克柳, 李相方, 陈掌星 2015 中国科学:技术科学 45 525]
[45]	Sheng M, Li G S, Huang Z W, Tian S C 2014 Acta Petrol. Sin. 35 347 (in Chinese) [盛茂, 李根生, 黄中伟, 田守嶒 2014 石油学报 35 347]
[46]	Do H D, Do D D, Prasetyo I 2001 AlChE J. 47 2515
[47]	Clarkson C R, Haghshenas B 2013 SPE Unconventional Resources Conference Woodlands, USA, April 10-12, 2013 p1
[48]	Civan F, Rai C S, Sondergeld C H 2011 Transport Porous Med. 86 925
[49]	Wang H Y, Ajao O, Economides M J 2014 J. Nat. Gas Sci. Eng. 21 874
[50]	Guo W, Xiong W, Gao S S, Hu Z M 2013 J. Cent. South Univ. (Sci. Technol.) 44 2836 (in Chinese) [郭为, 熊伟, 高树生, 胡志明 2013 中南大学学报(自然科学版) 44 2836]
[51]	Sladek K J, Gilliland E R, Baddour R F 1974 Ind. Eng. Chem. Fundam. 13 100
[52]	Curtis J B 2002 AAPG Bull. 86 1921
[53]	Kuuskraa V A, Koperna G, Schmoker J W, Quinn J C 1998 Oil Gas J. 96 67
[54]	Wang F P, Reed R M 2009 SPE Annual Technical Conference and Exhibition (New Orleans: Society of Petroleum Engineers) p1
[55]	Arkilic E B 1997 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[56]	Mosher K, He J, Liu Y, Rupp E, Wilcox J 2013 Int. J. Coal Geol. 109 36
[57]	Dubinin M M, Astakhov V A 1971 Russ. Chem. Bull. 20 8
[58]	Zhai Z Q, Wang X Q, Jin X, Sun L, Li J M, Cao D P 2014 Energ. Fuel. 28 7467
[59]	Wang H, Wang X Q, Jin X, Cao D P 2016 J. Phys. Chem. C 120 8986
[60]	Kuila U, Prasad M, Kazemi H 2012 Proceedings of 9th Biennial International Conference and Exposition on Petroleum Geophysics Hyderabad, India, Febrary 16-18, 2012 p182

[1]	邓永和, 张宇文, 谭恒博, 文大东, 高明, 吴安如. NiCu双金属纳米粒子的表面偏析、结构特征与扩散. , 2021, 70(17): 177601. doi: 10.7498/aps.70.20210336
[2]	成潇潇, 刘建国, 徐亮, 徐寒杨, 金岭, 束胜全, 薛明. 基于页岩气返排液中污染气体浓度及扩散模型研究. , 2021, 70(13): 130202. doi: 10.7498/aps.70.20210017
[3]	刘心卓, 王华光. 椭球胶体在圆球胶体体系中扩散行为的实验研究. , 2020, 69(23): 238201. doi: 10.7498/aps.69.20201301
[4]	廖晶晶, 蔺福军. 混合手征活性粒子在时间延迟反馈下的扩散和分离. , 2020, 69(22): 220501. doi: 10.7498/aps.69.20200505
[5]	张恒, 黄燕, 石旺舟, 周孝好, 陈效双. Al原子在Si表面扩散动力学的第一性原理研究. , 2019, 68(20): 207302. doi: 10.7498/aps.68.20190783
[6]	刘汝霖, 方粮, 郝跃, 池雅庆. 金红石TiO2中本征缺陷扩散性质的第一性原理计算. , 2018, 67(17): 176101. doi: 10.7498/aps.67.20180818
[7]	王超, 陈英才, 周艳丽, 罗孟波. 两嵌段高分子链在周期管道内扩散的Monte Carlo模拟. , 2017, 66(1): 018201. doi: 10.7498/aps.66.018201
[8]	高雪云, 王海燕, 李春龙, 任慧平, 李德超, 刘宗昌. 稀土La对bcc-Fe中Cu扩散行为影响的第一性原理研究. , 2014, 63(24): 248101. doi: 10.7498/aps.63.248101
[9]	向辉, 刘大欢, 阳庆元, 密建国, 仲崇立. 骨架柔性对短链烷烃分子在金属-有机骨架材料中扩散的影响. , 2011, 60(9): 093602. doi: 10.7498/aps.60.093602
[10]	陆裕东, 何小琦, 恩云飞, 王歆, 庄志强. 倒装芯片上金属布线/凸点互连结构中原子的定向扩散. , 2010, 59(5): 3438-3444. doi: 10.7498/aps.59.3438
[11]	陈德彝, 王忠龙. 白交叉关联色噪声驱动的线性振子的扩散. , 2010, 59(1): 111-115. doi: 10.7498/aps.59.111
[12]	杨春, 冯玉芳, 余毅. 动力学研究AlN/α-Al2Ｏ3（0001）薄膜生长初期的吸附与扩散. , 2009, 58(5): 3553-3559. doi: 10.7498/aps.58.3553
[13]	张传瑜, 高涛, 张云光, 周晶晶, 朱正和, 陈波. 氦对LaNi5晶体结构的影响及其扩散特性研究. , 2008, 57(7): 4379-4385. doi: 10.7498/aps.57.4379
[14]	王永亮, 张超, 唐鑫, 张庆瑜. 表面Cu原子间相互作用对Cu(001)表面跳跃扩散行为的影响. , 2006, 55(8): 4214-4220. doi: 10.7498/aps.55.4214
[15]	曹博, 包良满, 李公平, 何山虎. Cu/SiO2/Si(111)体系中Cu和Si的扩散及界面反应. , 2006, 55(12): 6550-6555. doi: 10.7498/aps.55.6550
[16]	杨春, 余毅, 李言荣, 刘永华. 温度对ZnO/Al2O3(0001)界面的吸附、扩散及生长初期模式的影响. , 2005, 54(12): 5907-5913. doi: 10.7498/aps.54.5907
[17]	常福宣, 陈　进, 黄　薇. 反常扩散与分数阶对流-扩散方程. , 2005, 54(3): 1113-1117. doi: 10.7498/aps.54.1113
[18]	王秀英, 高明, 孙力玲, 刘日平, 张君, 王文魁. 注入Mo 在Zr57Nb5Cu15.4Ni12.6Al10非晶合金中的扩散. , 2004, 53(1): 200-203. doi: 10.7498/aps.53.200
[19]	胡晓君, 戴永兵, 何贤昶, 沈荷生, 李荣斌. 空位在金刚石近(001)表面扩散的分子动力学模拟. , 2002, 51(6): 1388-1392. doi: 10.7498/aps.51.1388
[20]	张海燕. 多分量胶体悬浮系统转动扩散张量的反射理论. , 2002, 51(2): 449-455. doi: 10.7498/aps.51.449

计量

文章访问数: 6415
PDF下载量: 247
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板