页岩储层纳米孔气体传输耦合模型新研究
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摘要
页岩气在纳米孔隙的传输过程中受多种因素影响,包括孔隙尺寸和压力、孔隙壁面粗糙度、孔隙力学反应、吸附-诱导膨胀反应以及权重因子等。因此需要综合考虑以上因素以及吸附气分子在孔隙中所占空间对气体流动影响的条件下,厘清页岩气的不同运移机制(表面扩散、滑脱流、Knudsen扩散和黏性流动)在不同孔隙尺寸和压力下对纳米孔中总气体流量的贡献率。首先,对页岩气的不同运移方式进行了物理描述及数学表征,然后,在考虑孔隙壁面粗糙度、孔隙力学反应、吸附-诱导膨胀反应和权重因子等因素的条件下,建立页岩气在储层纳米孔中的气体传输耦合数学模型,模型可靠性通过格子Boltzmann方法计算结果验证。研究结果表明,当孔径小于10 nm时,纳米孔的总流量主要由表面扩散流量组成,孔径越小,表面扩散流量越大;当孔径为40～250 nm和低压条件下,滑脱流和Knudsen扩散对气体传输影响较大;当孔径大于10μm时,纳米孔的总流量主要为黏性流量。
Shale gas is affected by many factors during nanopore transport, including pore size and pressure, pore wall surface roughness, pore mechanics reaction, adsorption-induced expansion reaction, and weighting factors. Therefore, the effects that these factors and the space occupied by the adsorbed gas molecules in the pores have on the gas flow must be considered. This is necessary to clarify the contribution to the total gas flow in the nanopores resulting from different migration mechanisms of shale gas(surface diffusion, slip flow, Knudsen diffusion, and viscous flow) based on different pore sizes and pressures.First, physical descriptions and mathematical characterizations of different migration mechanisms of shale gas are provided.A mathematical gas transport coupling model for shale gas is then developed that considers pore wall surface roughness, pore mechanics reaction, adsorption-induced expansion reaction, and weighting factors. The reliability of the model is verified by the lattice Boltzmann method. The results show that when the pore diameter is less than 10 nm, the total flow in the nanopores mainly consists of surface diffusion flux. In addition, the smaller the pore size, the greater is the surface diffusion flux. When the pore diameter is 40～250 nm at low pressure, the slip flow and Knudsen diffusion have a considerable effect on gas transport.When the pore diameter is longer than 10 μm, the total flow in the nanopores is primarily viscous.
Shale gas is affected by many factors during nanopore transport, including pore size and pressure, pore wall surface roughness, pore mechanics reaction, adsorption-induced expansion reaction, and weighting factors. Therefore, the effects that these factors and the space occupied by the adsorbed gas molecules in the pores have on the gas flow must be considered. This is necessary to clarify the contribution to the total gas flow in the nanopores resulting from different migration mechanisms of shale gas(surface diffusion, slip flow, Knudsen diffusion, and viscous flow) based on different pore sizes and pressures.First, physical descriptions and mathematical characterizations of different migration mechanisms of shale gas are provided.A mathematical gas transport coupling model for shale gas is then developed that considers pore wall surface roughness, pore mechanics reaction, adsorption-induced expansion reaction, and weighting factors. The reliability of the model is verified by the lattice Boltzmann method. The results show that when the pore diameter is less than 10 nm, the total flow in the nanopores mainly consists of surface diffusion flux. In addition, the smaller the pore size, the greater is the surface diffusion flux. When the pore diameter is 40～250 nm at low pressure, the slip flow and Knudsen diffusion have a considerable effect on gas transport.When the pore diameter is longer than 10 μm, the total flow in the nanopores is primarily viscous.
引文
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[12] FATHI E, AKKUTLU I Y. Lattice boltzmann method for simulation of shale gas transport in kerogen[C]. SPE146821,2011. doi:10.2118/146821-MS
[13] WANG Junjian,CHEN Li,KANG Qinjun,et al. Apparent permeability prediction of organic shale with generalized lattice Boltzmann model considering surface diffusion effect[J]. Fuel, 2016, 181(1):478-490. doi:10.1016/j.fuel.-2016.05.032
[14]吴克柳,李相方,陈掌星.页岩纳米孔吸附气表面扩散机理和数学模型[J].中国科学:技术科学,2015,45(5):525-540.WU Keliu, LI Xiangfang, CHEN Zhangxing. The mechanism and mathematical model for the adsorbed gas surface diffusion in nanopores of shale gas reservoirs[J]. Science China, 2015, 45(5):525-540.
[15]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.doi:10.3321/j.issn:0438-1157.2008.11.006GUO Liang, PENG Xiaofeng, WU Zhansong. Dynam-ical characterist ics of methane adsorption on monolith nanometer act ivated carbon[J]. Journal of Chemical Industry and Engineering(China), 2008,59(11):2726-2732.doi:10.3321/j.issn:0438-1157.2008.11.006
[16]盛茂,李根生,黄中伟,等.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.doi:10.7623/syxb201402016SHENG Mao, LI Gensheng, HUANG Zhongwei, et al.Shale gas transient flow model with effects of surface diffusion[J]. Acta Petrolei Sinica, 2014, 35(2):347-352. doi:10.7623/syxb201402016
[17]陈代询,王章瑞.致密介质中低速渗流气体的非达西现象[J].重庆大学学报(自然科学版),2000,23(z1):25-27.CHEN Daixun, WANG Zhangrui. Non-Darcy phenomena of gas flow at low velocity in tight porous media[J]. Journal of Chongqing University(Natural Science Edition),2000, 23(zl):25-27.
[18] JAVADPOUR F. Nanopores and apparent permeability of gas flow in mudrocks(shales and siltstone)[J]. Journal of Canadian Petroleum Technology, 2009,48(8):16-21. doi:10.2118/09-08-16-DA
[19] BROWN G P, DINARDO A, CHENG G K, et al. The flow of gases in pipes at low pressures[J]. Journal of Applied Physics, 1946, 17(10):802-813. doi:10.1063/1.1707647
[20] JAVADPOUR F,FISHER D,UNSWORTH M. Nanoscale gas flow in shale gas sediments[J]. Journal of Canadian Petroleum Technology, 2007, 45(10):55-56. doi:10.2118/07-10-06
[21] SWAMI V, SETTARI A, JAVADPOUR F. A numerical model for multi-mechanism flow in shale gas reservoirs with application to laboratory scale testing[C]. SPE164840-MS, 2013. doi:10.2118/164840-MS
[22] TINNI A, FATHI E, AGARWAL R, et al. Shale permeability measurements on plugs and crushed samples[C]. SPE162235-MS, 2012. doi:10.2118/162235-MS
[23] WANG S,ELSWORTH D,LIU J. A mechanistic model for permeability evolution in fractured sorbing media[J].Journal of Geophysical Research Solid Earth, 2012,117(B6):6205-6215. doi:10.1029/2011JB008855
[24] BIOT M A,WILLIS D G. The elastic coefficients of the theory of consolidation[J]. J. Appl. Mech, 1957, 24(2):594-601.
[25] ALNOAIMI K R, KOVSCEK A R. Experimental and nu-merical analysis of gas transport in shale including the role of sorption[C]. SPE 166375-MS, 2013. doi:10.2118/-166375-MS
[26] THOMPSON S L, OWENS W R. A survey of flow at low pressures[J]. Vacuum, 1975,25(4):151-156. doi:10.-1016/0042-207X(75)91404-9
[2]陆程,刘雄,程敏华,等.页岩气体积压裂水平井产能影响因素研究[J].特种油气藏,2014, 21(4):108-112.doi:10.3969/j.issn.1006-6535.2014.04.026LU Cheng, LIU Xiong, CHENG Minhua, et al. Research on factors influencing shale gas productivity of volumetric fractured horizontal wells[J]. Special Oil and Gas Reservoirs, 2014, 21(4):108-112. doi:10.3969/j.issn.-1006-6535.2014.04.026
[3]邹才能,朱如凯,吴松涛,等.常规与非常规油气聚集类型、特征、机理及展望一以中国致密油和致密气为例[J].石油学报,2012, 33(2):173-187.ZOU Caineng,ZHU Rukai,WU Songtao,et al. Types,characteristics, genesis and prospects of conventional and unconventional hydrocarbon accumulations:Taking tigh oil and tight gas in China as an instance[J]. Acta Petrolei Sinica, 2012, 33(2):173-187.
[4]朱如凯,白斌,崔景伟,等.非常规油气致密储集层微观结构研究进展[J].古地理学报,2013, 15(5):615-623.doi:10.7605/gdlxb.2013.05.049ZHU Rukai,BAI Bin, CUI Jingwei,et al. Research advances of micro structure in unconventional tight oil and gas reservoirs[J]. Journal of Palaeogeography, 2013,15(5):615-623. doi:10.7605/gdlxb.2013.05.049
[5] CURTIS M E,AMBROSE R J,SONDERGELD C H.Structural characterization of gas shales on the micro and nanoscales[C]. SPE 137693-MS, 2010. doi:10.2118/-137693-MS
[6]胡琳,朱炎铭,陈尚斌,等.蜀南双河龙马溪组页岩孔隙结构的分形特征[J].新疆石油地质,2013, 24(1):79-82.HU Lin, ZHU Yanming, CHEN Shangbin, et al. Fractal characteristics of shale pore structure of Longmaxi Formation in Shuanghe Area in Southern Sichuan[J]. Xinjiang Petroleum Geology, 2013,24(1):79-82.
[7]魏明强,段永刚,方全堂,等.页岩气藏孔渗结构特征和渗流机理研究现状[J].油气藏评价与开发,2011,1(4):73-77. doi:10.3969/j.issn.2095-1426.2011.04.015WEI Mingqiang, DU AN Yonggang, FANG Quantang, et al. Current research situation of porosity&permeability characteristics and seepage mechanism of shale gas reservo ir[J]. Reservoir Evaluation and Development, 2011,1(4):73-77. doi:10.3969/j.issn.2095-1426.2011.04.015
[8] SIGAL R F. The effects of gas adsorption on storge and transport of methane in organicshales[C]. New Orleans:SPWLA 54th Annual Logging Symposium, 2013.
[9] HAMED D,ETTEHAD A,JAVADPOUR F,et al. Gas flow in ultra-tight shale strata[J]. Journal of Fluid Mechanics, 2012, 710(12):641-658. doi:10.1017/jfm.2012.424
[10]吴克柳,李相方,陈掌星.页岩气纳米孔气体传输模型[J].石油学报,2015, 36(7):837-848, 889. doi:10.-7623/syxb201507008WU Keliu,LI Xiangfang,CHEN Zhangxing. A model for gas transport throughnanopores of shale gas reservoirs[J].Acta Petrolei Sinica, 2015, 36(7):837-848, 889. doi:10.-7623/syxb201507008
[11]宋洪庆,刘启鹏,于明旭,等.页岩气渗流特征及压裂井产能[J].北京科技大学学报,2014, 36(2):139-144.doi:10.13374/j.issn1001-053x.2014.02.001SONG Hongqing, LIU Qipeng, YU Mingxu, et al. Characteristics of gas flow and productivity of fractured wells in shale gas sediments[J]. Journal of University of Science and Technology Beijing,2014, 36(2):139-144. doi:10.-13374/j.issn1001-053x.2014.02.001
[12] FATHI E, AKKUTLU I Y. Lattice boltzmann method for simulation of shale gas transport in kerogen[C]. SPE146821,2011. doi:10.2118/146821-MS
[13] WANG Junjian,CHEN Li,KANG Qinjun,et al. Apparent permeability prediction of organic shale with generalized lattice Boltzmann model considering surface diffusion effect[J]. Fuel, 2016, 181(1):478-490. doi:10.1016/j.fuel.-2016.05.032
[14]吴克柳,李相方,陈掌星.页岩纳米孔吸附气表面扩散机理和数学模型[J].中国科学:技术科学,2015,45(5):525-540.WU Keliu, LI Xiangfang, CHEN Zhangxing. The mechanism and mathematical model for the adsorbed gas surface diffusion in nanopores of shale gas reservoirs[J]. Science China, 2015, 45(5):525-540.
[15]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.doi:10.3321/j.issn:0438-1157.2008.11.006GUO Liang, PENG Xiaofeng, WU Zhansong. Dynam-ical characterist ics of methane adsorption on monolith nanometer act ivated carbon[J]. Journal of Chemical Industry and Engineering(China), 2008,59(11):2726-2732.doi:10.3321/j.issn:0438-1157.2008.11.006
[16]盛茂,李根生,黄中伟,等.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.doi:10.7623/syxb201402016SHENG Mao, LI Gensheng, HUANG Zhongwei, et al.Shale gas transient flow model with effects of surface diffusion[J]. Acta Petrolei Sinica, 2014, 35(2):347-352. doi:10.7623/syxb201402016
[17]陈代询,王章瑞.致密介质中低速渗流气体的非达西现象[J].重庆大学学报(自然科学版),2000,23(z1):25-27.CHEN Daixun, WANG Zhangrui. Non-Darcy phenomena of gas flow at low velocity in tight porous media[J]. Journal of Chongqing University(Natural Science Edition),2000, 23(zl):25-27.
[18] JAVADPOUR F. Nanopores and apparent permeability of gas flow in mudrocks(shales and siltstone)[J]. Journal of Canadian Petroleum Technology, 2009,48(8):16-21. doi:10.2118/09-08-16-DA
[19] BROWN G P, DINARDO A, CHENG G K, et al. The flow of gases in pipes at low pressures[J]. Journal of Applied Physics, 1946, 17(10):802-813. doi:10.1063/1.1707647
[20] JAVADPOUR F,FISHER D,UNSWORTH M. Nanoscale gas flow in shale gas sediments[J]. Journal of Canadian Petroleum Technology, 2007, 45(10):55-56. doi:10.2118/07-10-06
[21] SWAMI V, SETTARI A, JAVADPOUR F. A numerical model for multi-mechanism flow in shale gas reservoirs with application to laboratory scale testing[C]. SPE164840-MS, 2013. doi:10.2118/164840-MS
[22] TINNI A, FATHI E, AGARWAL R, et al. Shale permeability measurements on plugs and crushed samples[C]. SPE162235-MS, 2012. doi:10.2118/162235-MS
[23] WANG S,ELSWORTH D,LIU J. A mechanistic model for permeability evolution in fractured sorbing media[J].Journal of Geophysical Research Solid Earth, 2012,117(B6):6205-6215. doi:10.1029/2011JB008855
[24] BIOT M A,WILLIS D G. The elastic coefficients of the theory of consolidation[J]. J. Appl. Mech, 1957, 24(2):594-601.
[25] ALNOAIMI K R, KOVSCEK A R. Experimental and nu-merical analysis of gas transport in shale including the role of sorption[C]. SPE 166375-MS, 2013. doi:10.2118/-166375-MS
[26] THOMPSON S L, OWENS W R. A survey of flow at low pressures[J]. Vacuum, 1975,25(4):151-156. doi:10.-1016/0042-207X(75)91404-9