Lattice Boltzmann Method For Microscale Fluid Flow In Tight Gas Reservoirs

Permeability is an important parameter to characterize transport properties of porous media,which is closely related to evaluation and development of oil and gas reservoirs.In the tight gas reservoirs,rock pore structure has following characteristics:micro/nano-meter pores development with complex pore morphology,strong pore anisotropy and pore-distribution heterogeneity.These factors lead significant gas high-Kn effect,traditional analytical/semi-analytical models no longer applicable,and permeability depending on pore structure and fluid pressure.Scholars have done numerous studies on gas high-Kn effect in porous media,but the quantitative characterization of pore anisotropy and pore-distribution heterogeneity,as well as the correlation analysis with permeability are still lacking.Therefore,combining with microscopic experiments,this paper adopts numerical methods to construct two-dimensional(2D)and three-dimensional(3D)porous media.A multi-relaxation-time lattice Boltzmann(MRT-LB)model is applied to simulate fluid migration.The inherent correlations of pore morphology,anisotropy and heterogeneity with permeability and slippage factor are explored.The main works are as follows:(1)The scanning electron microscopy,casting thin sections,mercury injection,nuclear magnetic resonance and CT scanning experiments were conducted on tight sandstone samples to obtain its mineral composition,cementation types,pore types and pore size distribution,etc.In combination with CT images with a resolution of 620nm,3D digital cores of tight sandstones were built.The 3D pore morphology was observed.Meanwhile,pore anisotropy and pore-distribution heterogeneity were quantitatively evaluate based on morphological principle,which lays a foundation for subsequent simulation studies.(2)The quartet structure generation set(QSGS),randomly distributed particles,random fracture generation and improved QSGS algorithms were adopted to construct 2D anisotropy,heterogeneity,different pore shape(circular,intergranular and fracture)and fracture-pore porous media,while four-connected component labelling algorithm was used to remove isolated pores.Combining with bounce-back boundary conditions,fluid migration in 2D porous media was simulated by D2Q9 MRT-LBM.Subsequently,applying the maximum circle method to obtain pore size distribution,the correlations of permeability with anisotropy,heterogeneity and pore morphology in 2D porous media were clarified.The relations of tortuosity with porosity and anisotropy were established.(3)The Bosanquet-type viscosity model was adopted to correct the influence of high-Kn effect on gas viscosity.Combining with diffuse reflection boundary,D2Q9 MRT-LBM was used to simulate gas high-Kn flow in microchannel and 2D porous media.The variations of gas velocity and dimensionless velocity profile in microchannel with Kn were studied,while pore-scale velocity profile,dimensionless velocity frequency distribution and apparent penneability in 2D porous media were discussed.In addition,the flow contribution weights of small pores,large pores and fractures at different Kn were analyzed.(4)Adopting QSGS,randomly distributed particles and random fracture generation methods,3D anisotropy,heterogeneity and different pore morphology porous media were further constructed.The inverse matrix of transformation matrix was solved by gauss principal element elimination method,and fluid migration in 3D porous media was simulated by D3Q19 MRT-LBM.Applying the maximum ball method to obtain pore size distribution,the inherent correlations of permeability in 3D porous media with pore-scale anisotropy,heterogeneity and morphology were illuminated,while the differences of 2D and 3D porous media were analyzed.(5)Based on Navier-Stokes equation and Maxwell first-order slippage boundary condition,gas flow equation in micro-circular tube was derived in the cylindrical coordinate.The influences of viscous flow,gas slippage and Knudsen diffusion were analyzed.Then,the derived apparent permeability model was compared with existing models,and the differences between analytical/semi-analytical models were pointed out.In combination with bosanquet-type viscosity model and diffuse reflection boundary condition,D3Q19 MRT-LBM was used to simulate gas flow in 3D porous media.The correlations of slippage factor with pore anisotropy,heterogeneity,morphology and Kn were further revealed.Through experiments and simulations in this paper,the inherent correlations of pore anisotropy,heterogeneity and morphology with intrinsic permeability,tortuosity and slippage factor of porous media are clarified,which is helpful to further understand the actual fluid migration process and provide more accurate guidance for the development of tight gas reservoirs.