地应力作用下水力裂缝中支撑剂导流能力的数值模拟研究
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摘要
目前,对水力裂缝内支撑剂的运移及其导流能力的研究主要通过实验进行,而完全基于数值模拟的研究不多。基于颗粒离散元对水力裂缝中支撑剂数值模拟的结果,通过数字重构方法,得到了水力裂缝内支撑剂堆积结构的数字模型;在重构的数字模型基础上,采用格子玻尔兹曼方法(LBM),模拟了单相流体在支撑剂孔隙结构内的流动过程,进而得到了不同地应力水平下不同支撑剂的绝对渗透率,且数值计算结果与Kozeny-Carman经验公式吻合。研究结果发现,地应力作用下,裂缝张开度减少,支撑剂颗粒更加密实,可能出现支撑剂嵌入到岩石中的现象;随着地应力的增加,裂缝内支撑剂堆积体的孔隙度减少,比表面积增大,渗透率减少;相同地应力作用下,支撑剂粒径越大,其孔隙度越低,比表面积越小,越易出现支撑剂嵌入现象,渗透率减少越大,但其值一般总大于小粒径支撑剂的渗透率。
The current research on the migration of the proppants in hydraulic fractures and the corresponding flow conductivity are mainly carried out by indoor experiments,though the entirely computer-based research is the tread,yet rare now.In this paper,based on our previous DEM results of proppants in hydraulic fractures,the digital models of the propping agent under different stresses are obtained using digital reconstruction method. Subsequently,based on the digital reconstruction models,the single phase fluid flows through proppants are simulated numerically by utilizing the lattice Boltzmann method,and the absolute permeability values for different proppants and stresses are derived accordingly.Moreover,the numerical permeability coefficients are in good agreement with the empirical Kozeny-Carman formula.The study shows that the higher stresses imply the smaller crack apertures,the tighter proppant packing and the more embedment of proppant.With the increase of stress,the specific surface area increases,and the porosity and per-meability reduce accordingly.Under the same stress level,the larger proppant corresponds to the smaller porosity and specific surface area,the easier to embed,and the larger permeability reduction though generally higher than the smaller proppant size.
The current research on the migration of the proppants in hydraulic fractures and the corresponding flow conductivity are mainly carried out by indoor experiments,though the entirely computer-based research is the tread,yet rare now.In this paper,based on our previous DEM results of proppants in hydraulic fractures,the digital models of the propping agent under different stresses are obtained using digital reconstruction method. Subsequently,based on the digital reconstruction models,the single phase fluid flows through proppants are simulated numerically by utilizing the lattice Boltzmann method,and the absolute permeability values for different proppants and stresses are derived accordingly.Moreover,the numerical permeability coefficients are in good agreement with the empirical Kozeny-Carman formula.The study shows that the higher stresses imply the smaller crack apertures,the tighter proppant packing and the more embedment of proppant.With the increase of stress,the specific surface area increases,and the porosity and per-meability reduce accordingly.Under the same stress level,the larger proppant corresponds to the smaller porosity and specific surface area,the easier to embed,and the larger permeability reduction though generally higher than the smaller proppant size.
引文
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[12]BEAR J.Dynamics of fluids in porous media[M].New York:Dover Publications,INC.,1972.
[2]谭云亮,尹延春,滕桂荣,等.基于Lattice Boltzmann方法的瓦斯渗流模拟研究[J].煤炭学报,2014,39(8):1446-1454.TAN Yunliang,YIN Yanchun,TENG Guirong,et al.Simulation research of gas seepage based on Lattice Boltzmann method[J].Journal of China Coal Society,2014,39(8):1446-1454.
[3]滕桂荣,谭云亮,高明,等.基于LBM方法的裂隙煤体内瓦斯抽放的模拟分析[J].煤炭学报,2008,33(8):914-919.TENG Guirong,TAN Yunliang,GAO Ming,et al.Simulation of gas drainage in fissured coal based on Lattice Boltzmann Method[J].Journal of China Coal Society,2008,33(8):914-919.
[4]温庆志,翟恒立,罗明良,等.页岩气藏压裂支撑剂沉降及运移规律实验研究[J].油气地质与采收率,2012,19(6):104-107.WEN Qingzhi,ZHAI Hengli,LUO Mingliang,et al.Experimental study on sedimentation and migration of proppant in hydraulic fractures of shale gas reservoir[J].Petroleum Geology and Recovery Efficiency,2012,19(6):104-107.
[5]温庆志,张士诚,王雷,等.支撑剂嵌入对裂缝长期导流能力的影响研究[J].天然气工业,2005,25(5):65-68.WEN Qingzhi,ZHANG Shicheng,WANG Lei,et al.Study on the influence of proppant embedment on long term flow conductivity of fractures[J].Natural Gas Industry,2005,25(5):65-68.
[6]MARONGIU-PORCU M,ECONOMIDES M J,HOLDITCH S A.Economic and physical optimization of hydraulic fracturing[J].Journal of Natural Gas Science and Engineering,2013,14(9):91-107.
[7]BORTOLAN NETO L,KOTOUSOV A.On the residual opening of hydraulic fractures[J].International Journal of Fracture,2013,181(1):127-137.
[8]BORTOLAN NETO L,KOTOUSOV A.Residual opening of hydraulically stimulated fractures filled with granular particles[J].Journal of Petroleum Science and Engineering,2012,100:24-29.
[9]DENG S,LI H,MA G,et al.Simulation of shale-proppant interaction in hydraulic fracturing by the discrete element method[J].International Journal of Rock Mechanics and Mining Sciences,2014,70:219-228.
[10]SANEMATSU P,SHEN Y,THOMPSON K,et al.Image-based Stokes flow modeling in bulk proppant packs and propped fractures under high loading stresses[J].Journal of Petroleum Science and Engineering,2015,135:391-402.
[11]孔祥言.高等渗流力学[M].合肥:中国科技大学出版社,2010.
[12]BEAR J.Dynamics of fluids in porous media[M].New York:Dover Publications,INC.,1972.