考虑固体变形与表面扩散的页岩气藏数值模拟
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摘要
页岩气在页岩纳米孔隙中的运移对气藏的产能预测具有重要的意义。利用多物理场耦合软件COMSOL研究了单轴应变条件下,同时考虑岩层变形、气体流动及其相互作用时的页岩气运移。基于经典的Biot孔隙弹性理论考虑固体变形,并引入考虑多种流动机制的视渗透率模型修正传统的Darcy渗流模型,重点讨论表面吸附扩散、气藏初始孔隙率和固有渗透率对基质渗透率和流动机制的影响。结果表明:(1)页岩中的表面吸附扩散对页岩视渗透率有着重大的影响,尤其随着压力的降低,该影响更加明显,忽略表面吸附扩散将给出更低的视渗透率;(2)随着页岩气藏初始孔隙率的升高,Knudsen数和视渗透率升高,而随着初始渗透率的升高,Knudsen数和视渗透率降低;(3)Knudsen数、视渗透率和固有渗透率的变化取决于孔隙压力、解吸附、Knudsen扩散和表面吸附扩散等因素相互竞争的结果。
Shale gas migration in the shale nanopores is of great importance to production forecast of gas reservoirs.This work investigates the migration of shale gas under the uni-axial strain condition when considering the coupling effect of shale deformation and gas flow by using the COMSOL software.Based on the classical Biot's theory of poroelasticity to account for solid deformation and introducing the apparent permeability model to modify the traditional Darcy model,the influence of surface sorptive diffusion,the initial porosity and intrinsic permeability of shale on the apparent permeability and flow mechanisms is discussed.Numerical results show that surface sorptive diffusion in the shale has significant impact on the apparent permeability.Such effect becomes more distinct especially when the pressure of the shale gas reservoir falls down.Neglecting the surface sorptive diffusion will give lower apparent permeability.Moreover,both the apparent permeability and Knudsen number increase with the increase of the initial shale porosity while they decrease when increasing the initial intrinsic permeability of shale.Variations of Knudsen number,apparent permeability and intrinsic permeability depend on the competitive consequence of pore pressure,desorption,Knudsen diffusion and surface sorptive diffusion.
Shale gas migration in the shale nanopores is of great importance to production forecast of gas reservoirs.This work investigates the migration of shale gas under the uni-axial strain condition when considering the coupling effect of shale deformation and gas flow by using the COMSOL software.Based on the classical Biot's theory of poroelasticity to account for solid deformation and introducing the apparent permeability model to modify the traditional Darcy model,the influence of surface sorptive diffusion,the initial porosity and intrinsic permeability of shale on the apparent permeability and flow mechanisms is discussed.Numerical results show that surface sorptive diffusion in the shale has significant impact on the apparent permeability.Such effect becomes more distinct especially when the pressure of the shale gas reservoir falls down.Neglecting the surface sorptive diffusion will give lower apparent permeability.Moreover,both the apparent permeability and Knudsen number increase with the increase of the initial shale porosity while they decrease when increasing the initial intrinsic permeability of shale.Variations of Knudsen number,apparent permeability and intrinsic permeability depend on the competitive consequence of pore pressure,desorption,Knudsen diffusion and surface sorptive diffusion.
引文
[1]Javapour F.Nanopores and Apparent Permeability of Gas Flow in Mudrocks(Shale and siltstone)[J].Journal of Canadian Petroleum Technology,2009,48(8):16-21.
[2]CHEN F F,DUAN Y G,WANG K,et al.A novel pressure transient response model considering multiple migration mechanisms in shale gas reservoir[J].Journal of Natural Gas Science and Engineering,2015,22:321-334.
[3]樊冬艳,姚军,孙海,等.考虑多重运移机制耦合页岩气藏压裂水平井数值模拟[J].力学学报,2015,47(6):906-915.
[4]ZHANG H B,LIU J S,Elswortgh D.How sorptioninducedmatrix deformation affects gas flow in coal seams:A new FE model[J].International Journal of Rock Mechanics&Mining Sciences,2008,45:1226-1236.
[5]CAO P,LIU J S,LEONG Y K.Combined impact of flow regimes and effective stress on the evolution of shale apparent permeability[J].Journal of Unconventional Oil&Gas Resources,2016,14:32-43.
[6]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.
[7]Detournay B E,Cheng A H-D.Fundamentals of poroelasticity[C].In:Fairhurst,1993:113-171.
[8]YUAN W N,PAN Z J,LI X,et al.Experimental study and modelling of methane adsorption and diffusion in shale[J].Fuel,2014,117:509-519.
[9]ZHANG H X,LIU W Q,LI Z.Fracture permeability model and experiments of shale gas reservoirs[J].Rock and Soild Mechanics,2015,36(3):719-729.
[2]CHEN F F,DUAN Y G,WANG K,et al.A novel pressure transient response model considering multiple migration mechanisms in shale gas reservoir[J].Journal of Natural Gas Science and Engineering,2015,22:321-334.
[3]樊冬艳,姚军,孙海,等.考虑多重运移机制耦合页岩气藏压裂水平井数值模拟[J].力学学报,2015,47(6):906-915.
[4]ZHANG H B,LIU J S,Elswortgh D.How sorptioninducedmatrix deformation affects gas flow in coal seams:A new FE model[J].International Journal of Rock Mechanics&Mining Sciences,2008,45:1226-1236.
[5]CAO P,LIU J S,LEONG Y K.Combined impact of flow regimes and effective stress on the evolution of shale apparent permeability[J].Journal of Unconventional Oil&Gas Resources,2016,14:32-43.
[6]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.
[7]Detournay B E,Cheng A H-D.Fundamentals of poroelasticity[C].In:Fairhurst,1993:113-171.
[8]YUAN W N,PAN Z J,LI X,et al.Experimental study and modelling of methane adsorption and diffusion in shale[J].Fuel,2014,117:509-519.
[9]ZHANG H X,LIU W Q,LI Z.Fracture permeability model and experiments of shale gas reservoirs[J].Rock and Soild Mechanics,2015,36(3):719-729.