Improved mathematical model of apparent permeability: A focused study on free and multilayer adsorptive phase flow

Li, Wenrui; Wang, Dengke; Wang, Jingguo

doi:10.1016/j.jngse.2022.104508

Cited by 11 publications

(19 citation statements)

References 68 publications

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“…In the present simulations, each computational cell contained at least 20 simulator particles (i.e., PPC = 20), and the time-step size was chosen to be about one-third of the mean collision time and in the order of 10 −12 s [ 3 , 13 ]. Although surface adsorption and diffusion can contribute to gas transport in super nanoporous materials [ 47 , 48 , 49 , 50 ], these aspects are neglected in the present DSMC simulations. All the solid walls were assumed to be fully diffuse, and heat transfer to the solid porous structure was ignored [ 51 , 52 ].…”

Section: Methodsmentioning

confidence: 99%

“…This means that the value of the intrinsic permeability depends solely on the porous structure, regardless of fluid condition. However, the apparent permeability (

) of a porous medium is a measure of gas transport that comprises pressure gradient-driven flow, concentration gradient-driven molecular diffusion, and chemical gradient-driven surface diffusion [ 21 , 50 ].…”

Section: Methodsmentioning

confidence: 99%

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Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

2023

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The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number.

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Section: Methodsmentioning

confidence: 99%

“…This means that the value of the intrinsic permeability depends solely on the porous structure, regardless of fluid condition. However, the apparent permeability (

Section: Methodsmentioning

confidence: 99%

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

2023

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“…Driven by the adsorbed gas concentration gradient and the combination of the diffusivity capacity of the adsorbed gas molecules, the mass flux of the surface diffusion is quantified as follows J ad = prefix− D normals ∇ ( M C a ) where D s is the surface diffusion coefficient (1 × 10 –9 m 2 /s), which was taken with reference to the recommended value in the mathematical model …”

Section: Formulation Of Generic Permeability Modelmentioning

confidence: 99%

“…The Knudsen number (K n ), defined as the ratio of the mean free path of gaseous molecules (λ) to the characteristic spatial length (ω), can classify all flow regimes from Darcy flow to non-Darcy flow. 45 = K n (8) By replacing the characteristic spatial length ω in eq 8 with an equivalent hydraulic diameter (d 0 ) in eq 7, the corrected K n in the bulk shale is obtained as follows…”

Section: Division Of Flow Mechanisms In the Shalementioning

confidence: 99%

Novel Shale Permeability Model Considering the Internal Dependencies of Effective Stress, Gas Sorption, and Flow-Regime Effects

Liu

2023

Energy Fuels

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Traditional theoretical models used to predict shale permeability generally ignore the influence of the effective stress and gas sorption-induced strain on the gas transport process. Consequently, the predicted permeability may deviate from the experimental results, wherein the coupling effect of the fluid and solid is involved. To improve the accuracy of the permeability model for shale stones, a hydraulic diameter-based generic permeability model was proposed that couples the effective stress, gas sorption, and flow-regime effects. Three special degenerate case models, based on the generic model, were validated using three corresponding experimental conditions. Sensitivity studies have demonstrated that the flow-regime effect is sensitive to the size of the equivalent hydraulic diameter, whereas the poroelastic effect is sensitive to the initial porosity and compressibility factor of the shale bulk. The two effects cannot be decoupled from shale permeability during the experimental process. The contribution of the adsorption effects to permeability, as reflected by the Langmuir pressure constant of the matrix, is greater in the high-pressure region, where pore elasticity dominates. The contribution of the adsorption effects to permeability, as reflected by the Knudsen number, is weaker in the low-pressure region, where the flow regime dominates. In addition, the contribution of the adsorption effect varies much more in the poroelasticity deformation than in the fluid dynamics.

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“…Different from coal, shale transports with multiple flow regimes as a result of well-developed nanopores. − The coupling of fluid dynamic effects and poromechanical effects has been discussed, − but the introduction of DSI in poromechanical effects is still new. Importantly, the coupling approach between pore elasticity and flow regimes is not yet uniform.…”

Section: Introductionmentioning

confidence: 99%

Novel Shale Permeability Model Coupling Sorption-Induced Differential Deformation and Multiple Flow Regimes

Zhou

et al. 2022

Energy Fuels

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Under certain stress conditions, tight shale is characterized by the features of gas storage rocks, such as low permeability, low porosity, multiscale pore network, and elastic deformation. Flow-regime-based permeability models can reflect the behavior of non-Darcy gas transport but cannot characterize the elastic performance of tight shale. In this study, we introduce a novel permeability model that couples the sorption-induced differential deformation and multiple flow regimes in shale. The model not only determines flow-regime-based permeability for low pore pressures and micro−nano flow paths but also reflects the differential-swelling-index-based poroelasticity for high pore pressures and macro flow paths. The parameter sensitivity of the proposed model is analyzed. The results show that, with the increase in pore pressure at a constant confining pressure, the model is more sensitive to initial permeability than to initial porosity. The compressibility coefficient, which quantifies shale deformability, significantly affects the permeability evolution predicted by the model. The sorption-capacity-controlled differential deformation does not affect the overall permeability evolution but affects the upper and lower limits of permeability distribution in the intermediate process.

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Improved mathematical model of apparent permeability: A focused study on free and multilayer adsorptive phase flow

Cited by 11 publications

References 68 publications

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

Novel Shale Permeability Model Considering the Internal Dependencies of Effective Stress, Gas Sorption, and Flow-Regime Effects

Novel Shale Permeability Model Coupling Sorption-Induced Differential Deformation and Multiple Flow Regimes

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