基于格子玻尔兹曼和有限差分方法的页岩气升尺度渗流模拟
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摘要
格子玻尔兹曼方法(lattice Boltzmann method,LBM)是模拟页岩气微观渗流的一种重要方法,能够在孔隙尺度上比较精确地模拟页岩气的多种渗流机理,但是该方法模拟尺度小,计算量大,限制了其在储层尺度上的渗流模拟和在产能预测中的应用。为了既能保留LBM的模拟精度,又能快速准确地模拟较大尺度渗流,将LBM和有限差分方法相结合形成一种新方法,进行页岩气的升尺度渗流模拟。该新方法同时具有LBM的模拟精度和较快的运算速度,适用于模拟页岩气在宏观尺度的渗流和产能预测。利用新方法进行渗流模拟可得,滑脱效应和气体解吸能提高气体流动速度,补充地层能量,从而提高气井产量。
The lattice Boltzmann method(LBM) is one of the important methods to simulate the micro-percolation of the shale gas, which can precisely simulate the multiple flow mechanisms of the shale gas in the scale of the pore. However the simulated scale of the method is rather smaller, the calculation work is huge, and moreover its applications in the reservoir-scale flow simulation and production prediction are restricted. In order to keep the simulation precision of the LBM and rapidly and accurately simulate the large-scale flow, the LBM was coupled with finite difference method to simulate the upscaling flow of the shale gas. The new method can both has the LBM simulation precision and pretty faster calculation, so this method can be adopted in the simulation of the shale gas flow in the macro-scale and the prediction of the productivity. The flow simulation by this new method shows that the slippage effect and gas desorption can speed up the gas flow and add the formation energy, thus the gas well production can be enhanced finally.
The lattice Boltzmann method(LBM) is one of the important methods to simulate the micro-percolation of the shale gas, which can precisely simulate the multiple flow mechanisms of the shale gas in the scale of the pore. However the simulated scale of the method is rather smaller, the calculation work is huge, and moreover its applications in the reservoir-scale flow simulation and production prediction are restricted. In order to keep the simulation precision of the LBM and rapidly and accurately simulate the large-scale flow, the LBM was coupled with finite difference method to simulate the upscaling flow of the shale gas. The new method can both has the LBM simulation precision and pretty faster calculation, so this method can be adopted in the simulation of the shale gas flow in the macro-scale and the prediction of the productivity. The flow simulation by this new method shows that the slippage effect and gas desorption can speed up the gas flow and add the formation energy, thus the gas well production can be enhanced finally.
引文
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[14]谭苗,张志全,韩鑫,等.低渗透气藏压裂井产能公式推导与分析[J].天然气与石油,2013,31(1):54-56.TAN Miao,ZHANG Zhiquan,HAN Xin,et al.Derivation and analysis on productivity formula in low permeability gas reservoir fracturing well development[J].Natural Gas and Oil,2013,31(1):54-56.
[15]SPAID M A A,PHELAN F R Jr.Modeling void formation dynamics in fibrous porous media with the lattice Boltzmann method [J].Composites Part A:Applied Science & Manufacturing,1998,29(7):749-755.
[16]GUO Zhaoli,ZHAO T S.Lattice Boltzmann model for imcompressible flows through porous media [J].Physical Review E,2002,66:1-9.
[17]吴克柳,李相方,陈掌星,等.页岩气复杂孔裂隙真实气体传输机理和数学模型[J].中国科学:技术科学,2016,46(8):851-863.WU Keliu,LI Xiangfang,CHEN Zhangxing,et al.Real gas transport mechanism and mathematical model through complex nanopores and microfractures in shale gas reservoirs[J].Scientia Sinica(Technologica) ,2016,46(8):851-863.
[2]KLINKENBERG L J.Drilling and production practice[M].New York:American Petroleum Institute,1941:200-213.
[3]YI Jun,YüCEL-AKKUTLU I,?ZGEN-KARACAN C,et al.Gas sorption and transport in coals:A poroelastic medium approach[J].International Journal of Coal Geology,2009,77(1-2):137-144.
[4]王敬,罗海山,刘慧卿,等.页岩气吸附解吸效应对基质物性影响特征[J].石油勘探与开发,2016,43(1):145-152.WANG Jing,LUO Haishan,LIU Huiqing,et al.Influences of adsorption/desorption of shale gas on the apparent properties of matrix pores[J].Petroleum Exploration and Development,2016,43(1):145-152.
[5]张磊,姚军,孙海,等.基于数字岩心技术的气体解析/扩散格子Boltzmann模拟[J].石油学报,2015,36(3):361-365.ZHANG Lei,YAO Jun,SUN Hai,et al.Lattice Boltzmann simulation of gas desorption and diffusion based on digital core technology[J].Acta Petrolei Sinica,2015,36(3):361-365.
[6]张磊,姚军,孙海,等.利用格子 Boltzmann 方法计算页岩渗透率[J].中国石油大学学报(自然科学版),2014,38(1):87-91.ZHANG Lei,YAO Jun,SUN Hai,et al.Permeability calculation in shale using lattice Boltzmann method[J].Journal of China University of Petroleum(Edition of Natural Science),2014,38(1):87-91.
[7]王波.基于数字岩心的页岩气微观渗流研究[D].北京:中国石油大学(北京),2013.WANG Bo.The microscopic percolation study of shale gas based on the digital core[D].Beijing:China University of Petroleum,2013.
[8]LI Q,HE Y L,TANG G H,et al.Lattice Boltzmann modeling of microchannel flows in the transition flow regime[J].Microfluid & Nanofluid,2011,10(3):607-618.
[9]赵秀才,姚军,陶军,等.基于模拟退火算法的数字岩心建模方法[J].高校应用数学学报:A辑,2007,22(2):127-133.ZHAO Xiucai,YAO Jun,TAO Jun,et al.A method of constructing digital core by simulated annealing algorithm[J].Applied Mathematics A Journal of Chinese Universities,2007,22(2):127-133.
[10]HU D,Benoit D N,Nguyen P,et al.Quantitative analysis of proppant-formation interactions by digital rock methods[R].SPE 181342-MS,2016.
[11]ALMARZOOQ A,ALGHAMDI T M,KORONFOL S,et al.Shale gas characterization and property determination by digital rock physics[R].SPE 172840-MS,2015.
[12]邓佳,朱维耀,刘锦霞,等.考虑应力敏感性的页岩气产能预测模型[J].天然气地球科学,2013,24(3):456-460.DENG Jia,ZHU Weiyao,LIU Jinxia,et al.Productivity prediction model of shale gas considering stress sensitivity[J].Natural Gas Geoscience,2013,24(3):456-460.
[13]王志平,朱维耀,岳明,等.低、特低渗透油藏压裂水平井产能计算方法[J].北京科技大学学报,2012,34(7):750-754.WANG Zhiping,ZHU Weiyao,YUE Ming,et al.A method to predict the production of fractured horizontal wells in low/ultra-low permeability reservoirs[J].Journal of University of Science and Technology Beijing,2012,34(7):750-754.
[14]谭苗,张志全,韩鑫,等.低渗透气藏压裂井产能公式推导与分析[J].天然气与石油,2013,31(1):54-56.TAN Miao,ZHANG Zhiquan,HAN Xin,et al.Derivation and analysis on productivity formula in low permeability gas reservoir fracturing well development[J].Natural Gas and Oil,2013,31(1):54-56.
[15]SPAID M A A,PHELAN F R Jr.Modeling void formation dynamics in fibrous porous media with the lattice Boltzmann method [J].Composites Part A:Applied Science & Manufacturing,1998,29(7):749-755.
[16]GUO Zhaoli,ZHAO T S.Lattice Boltzmann model for imcompressible flows through porous media [J].Physical Review E,2002,66:1-9.
[17]吴克柳,李相方,陈掌星,等.页岩气复杂孔裂隙真实气体传输机理和数学模型[J].中国科学:技术科学,2016,46(8):851-863.WU Keliu,LI Xiangfang,CHEN Zhangxing,et al.Real gas transport mechanism and mathematical model through complex nanopores and microfractures in shale gas reservoirs[J].Scientia Sinica(Technologica) ,2016,46(8):851-863.