Triple Porosity Model For Shale Reservoir And Effective Stress Law For Porous Sorbing Media

As the conventional fuels depletes and carbon emission increases in recent years,the exploit of unconventional energy such as shale gas has become one of the heated topics among world energy research.The study of shale deformation and gas transport mechanism,however,is still immature,and thus largely limiting the development of shale gas extracting techniques.In this study,a general poromechanical model is proposed based on poroelasticity and seepage mechanics,considering desorption and molecular diffusion in kerogen matrix,viscous flow in inorganic matrix and fracture system,and composite deformation of the triple porosity assemblage.The effective stress law for deformation of porous sorbing media is proposed as well.The following conclusions are obtained.(1)A triple poromechanical model for fractured porous shale reservoir is built.According to gas transport and gas storage characteristics in the porosity assemblage,dynamic porosity model and diffusion/permeability model in each system are built.The governing equation of deformation of the triple porosity assemblage,gas diffusion in kerogen matrix,gas flow in inorganic matrix and fracture system are developed.This includes the multiphysics coupling interactions among deformation,diffusion and flow for the triple porosity model.(2)The differences in permeability among the triple porous media lead to more than a single distinct pressure field,which allows a fastest pressure drop in fracture system and slowest pressure drop in kerogen matrix.The results also indicate that the pattern of gas flow is sequential during gas depletion and follows a pattern of series flow– pressure drop in the fracture occurs first,follows the inorganic phase and eventually the kerogen.However,when it comes to a relatively high diffusion coefficient of kerogen matrix,the pressure declines synchronously in kerogen matrix and inorganic matrix,both of which declines slower than pressure drop in fracture system.This leads to a pattern of parallel flow that gas in fracture system comes from both kerogen matrix and inorganic matrix simultaneously.(3)The model is verified by history matching against field data for gas production rate.Sensitivity analyses indicates that permeability of fracture plays a critical role in initial gas production rate,while content of total organic carbon(TOC)and diffusion coefficient of kerogen matrix are key parameters to guarantee long-term shale gas production with an improved rate.(4)By introducing the concept of swelling modulus,an effective stress law accommodating sorption-induced swelling in porous sorbing media is proposed.Through this,the nonlinear problem of deformation in porous sorbing media can be simplified into a linearly elastic problem in nonporous and non-sorbing media.Experiments on coal samples under uniaxial strain conditions and unconstrained condition validate that effective stress coefficient is unified regardless of its boundary condition.(5)Swelling modulus reflects the swelling capacity exposure to sorbing gases.The smaller the swelling modulus,the larger sorption-induced swelling at same pore pressure.The experiments turn out that at low gas pressures(<7 MPa)the swelling modulus is an order of magnitude lower than the bulk modulus of solid grains(Ks).This is consistent with that the dominant influence of sorption-induced swelling at low gas pressures and its important effect on deformation and permeability evolution during gas depletion.