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Due to the extremely tiny pore size of tight gas and shale gas reservoir, the modified Darcy’s law in which the intrinsic permeability is replaced by the apparent permeability that can be obtained by a function of three transport parameters (intrinsic permeability, porosity and tortuosity), is used to describe the combined mechanisms of viscous flow, Knudsen diffusion, the effect of the adsorbed layer thickness and surface diffusion through the adsorbed layer. A new apparent permeability estimation method based on digital rock was proposed in this paper. The digital rock with nanopores could be constructed by 3D pore structure images obtained from micro/nano CT and FIB-SEM images directly or reconstructed with Markov Chain Monte Carlo (MCMC) method from the 2D SEM images of pore structure; then Lattice Boltzmann method can be applied to calculate the intrinsic permeability, porosity and tortuosity of 3D digital rock. These parameters are used to calculate the apparent permeability under consideration of different combined gas transport mechanisms. This method is applied to samples from the shale gas reservoir in Silurian Longmaxi Formation of Sichuan Basin and from the tight gas reservoir in the Wenchang Formation of Huizhou Sag. The results show that all considered transport mechanisms greatly impact the shale apparent permeability and cannot be ignored in shale samples. In tight gas reservoirs, Knudsen diffusion is an important mechanism at low pressures of less than 1 MPa. However, Knudsen diffusion could be ignored when pressure is greater than 1 MPa due to its smaller impact. [ABSTRACT FROM AUTHOR]

Conventional Darcy law cannot accurately describe the combined gas transport mechanisms in porous media with free gas only (such as tight gas reservoirs) and porous media with both free gas and adsorbed gas (such as shale gas reservoirs). The gas transport mechanisms in tight porous media including viscous flow, Knudsen diffusion, surface diffusion and molecular diffusion are investigated. Both the equivalent hydraulic radius and transport properties including intrinsic permeability, tortuosity and porosity, are used to build the coupled transport models describing the combined mechanisms of gas transport in ultra-tight porous media with free gas only and porous media with both free gas and adsorbed gas respectively. The effect of the pore-volume occupied by the adsorbed layer and surface diffusion through the adsorbed layer is considered in the transport model of porous media with adsorbed gas. The influences of equivalent hydraulic radius and transport properties on the gas transport mode in ultra-tight porous media are analyzed and the gas transport mode criteria in ultra-tight porous media are obtained. The result shows that viscous flow is the dominant mechanism, Knudsen diffusion can be ignored and Darcy law is applicable in porous media with equivalent hydraulic radius more than 100 nm. Surface diffusion can be ignored in the porous media with equivalent hydraulic radius less than 10 nm, while the effect of volume reduction by adsorption of porous media is less than 100 nm. The critical value of the transport function of intrinsic permeability, tortuosity and porosity also is given in this paper. [ABSTRACT FROM AUTHOR]

• Shale permeability upscaling is proposed considering multiple transport mechanisms. • A REV size is determined as 420 μm with experimental data of Sichuan basin. • Bulk gas in inorganic matter contributes roughly 70% to core-scale permeability. • Water film effect can be neglected at mean pore size larger than 40 nm. This paper presents a new upscaling method to derive the core-scale apparent gas permeability from an improved pore-scale permeability model and experimental data, with more rigorous incorporation of varying gas storage/transport mechanisms in nano/micro pores. First, in use of SEM images of a gas-rich shale field example in Sichuan Basin from our lab, pore network models of inorganic-matter (IOM) and organic-matter (OM) are characterized by using a digital-core technique. Next, an improved pore-scale real gas apparent permeability is modeled rigorously for both IOM/OM, respectively, with 1) bulk gas transport, gas adsorption, surface diffusion, pore-size confined phase behavior, and stress-dependent rock properties and 2) an additional reduction in inorganic pore sizes by water film adhered on pore surfaces. Core-scale permeability is then derived by assembling the permeabilities of stochastically distributed IOM/OM patches with different pore network models properties using the Monte Carlo sampling method. The new core-scale permeability model is validated by pulse-decay permeability experiment. Moreover, the representative elementary volume (REV) size is determined by analyzing the relative standard deviation of apparent gas permeability in cases with different sample sizes. The contributions of different gas transport mechanisms are discussed, and the impacts of stress-dependence for several field examples (i.e., Sichuan, Pierre and Barnett Basins) and water film with varying relative humidity (RH) on core-scale apparent permeability are analyzed. This work provides an effective approach to determine the core-scale shale permeability by directly using pore-scale experimental data, which is a common challenge in the unconventional resources. [ABSTRACT FROM AUTHOR]

Duo to different transport mechanisms and gas storage in organic and inorganic systems, a new triple-continuum model coupling Discrete Fracture Model (DFM) was established to investigate gas flow in shale gas reservoir. Considering the multi-scale and heterogeneity of shale matrix, fractal theory was used to calculate the apparent permeability of organic and inorganic systems while multiple gas transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, gas absorption/desorption effect and real gas effect were incorporated. This coupled mathematical model was solved by Finite Element Method (FEM) and the presented fractal apparent permeability model was validated with the experimental data. The results show that fractal characteristics of shale matrix have great impact on gas reservoir performance. The model without considering the influence of fractal characteristics could lead to underestimate gas production by approximately 17%. Viscous flow is the dominate transport mechanisms of shale gas and Knudsen diffusion has an impact on gas flow when the pressure declines. Surface diffusion should be only considered in organic systems and can be ignored. Then the results of sensitivity analysis show that the characteristic parameters of inorganic matter have a greater impact than those of organic matter and establishing a triple-continuum model with considering comprehensive effect of organic and inorganic matter is necessary. In addition, gas production would decrease as the pore fractal dimension and tortuosity fractal dimension increase, which results from the increasing number of small pores and more tortuous path for gas flow. [ABSTRACT FROM AUTHOR]

Because of the complex pore structure and multiple types of gas storage, the traditional Darcy permeability model is not valid for describing shale gas flow. In this paper, an upscaled transport model is established based on homogenization theory to consider multiple transport mechanisms and the heterogeneity of shale samples. This new transport model is employed to successfully explain pressure decay experimental data. The results show that absorbed gas cannot be ignored in pressure decay experiment and the pressure difference decreases rapidly when the absorbed gas is not considered. Then several critical conclusions have been drawn as follows. The permeability anisotropy for stochastic distribution model can be ignored and the effective permeability will be underestimated by double porosity model if surface diffusion dominates gas flow in shale reservoir. In addition, shale gas transport is dominated by Knudsen diffusion when the pore pressure is below 2 MPa and the contribution of surface diffusion increases as the pore pressure increases. The macroscopic effective permeability of the whole domain is dominated by the permeability of the connected phase; meanwhile, it can be influenced by the permeability of the disconnected phase. When the pore pressure is below 3.52 MPa, the effective permeability increases as the organic matter content (TOC) decreases. However, the effective permeability increases as the TOC increases when the pore pressure is above 3.52 MPa, which is different from traditionally believed when the relationship between the TOC and gas absorption capacity of the shale matrix is not considered. The effective permeability particularly increases at a high pore pressure as the Langmuir volume increases. In addition, the effective permeability increases as the Langmuir pressure decreases; however, this becomes apparent when the pore pressure is smaller. • An upscaled transport model is established based on homogenization theory by considering multiple transport mechanisms and heterogeneity of shale gas reservoir. • This new transport model is employed to successfully explain the pressure decay experiment data successfully and the absorption phenomenon is also considered. • The permeability anisotropy for stochastic distribution model can be ignored and the effective permeability will be underestimated by double porosity model if surface diffusion dominates gas flow in shale reservoir. • The macroscopic effective permeability of whole domain is dominated by the permeability of connected phase meanwhile it can be influenced by the permeability of disconnected phase. [ABSTRACT FROM AUTHOR]