A new method for the transport mechanism coupling of shale gas slippage and diffusion

Li Ya-Xiong; Liu Xian-Gui; Hu Zhi-Ming; Gao Shu-Sheng; Duan Xiang-Gang; Chang Jin

doi:10.7498/aps.66.114702

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:

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).

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Cited By

[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

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Vol. 66, Issue 11 - 2017-06-05

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