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Knudsen number

About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.


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Journal ArticleDOI
TL;DR: In this article, a model is presented for simulating multi-component shale gas transport through nanopores of shale formation, and the effects of multi-particle, slippage flow, and Knudsen diffusion are considered in the model.
Abstract: With the rapid development of shale gas resources, the accurate simulation of shale gas development process is becoming more and more important. Shale gas transport through nanopores of shale formation is the basic of shale gas development simulation. At present, the effect of impurities on methane transport through nanopores is neglected. In this paper, a novel model is presented for simulating multi-component shale gas transport through nanopores of shale formation. The effects of multi-component, slippage flow, and Knudsen diffusion are considered in the model. Results show that when the shale gas in nanopores is very thin, the Knudsen diffusion plays the dominant role over wide range of nanopore radius. While the effect of multi-component on Knudsen number and contribution degree can be neglected, both of the slippage flow rate and the Knudsen diffusion rate increase with increasing of CO2 content. Under medium pressure condition, there exists two turning points where the slippage flow and Knudsen diffusion take turns in charge of the shale gas transmission. Under high pressure condition, the slippage flow is the dominant factor over wide range of nanopore sizes. While the conductivities increase with decreasing methane content, the effect of multi-component on contribution degrees of slippage and Knudsen diffusion can be neglected.

31 citations

Journal ArticleDOI
TL;DR: In this article, the flux equation for the transition region between Knudsen flow and viscous flow with slip was derived for a capillary and transformed for a porous medium using the model of mean transport pore where the slip constant was considered to be an adjustable parameter.

31 citations

Journal ArticleDOI
TL;DR: The results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad's 14-moment expansion are presented in this paper.

30 citations

Journal ArticleDOI
TL;DR: In this paper, a set of linearized 26 moment equations, along with their wall boundary conditions, are derived and used to study low-speed gas flows dominated by Knudsen layers.
Abstract: A set of linearized 26 moment equations, along with their wall boundary conditions, are derived and used to study low-speed gas flows dominated by Knudsen layers. Analytical solutions are obtained for Kramers’ defect velocity and the velocity-slip coefficient. These results are compared to the numerical solution of the BGK kinetic equation. From the analysis, a new effective viscosity model for the Navier–Stokes equations is proposed. In addition, an analytical expression for the velocity field in planar pressure-driven Poiseuille flow is derived. The mass flow rate obtained from integrating the velocity profile shows good agreement with the results from the numerical solution of the linearized Boltzmann equation. These results are good for Knudsen numbers up to 3 and for a wide range of accommodation coefficients. The Knudsen minimum phenomenon is also well captured by the present linearized 26-moment equations.

30 citations

Proceedings ArticleDOI
01 Jan 2001
TL;DR: In this paper, a hybrid EPSM/DSMC was used for the simulation of near-continuous flows, where the gradient of local mean free path has been used to detect those regions where EPSM can be invoked.
Abstract: EPSM is a particle simulation method for the simulation of the Euler equations. EPSM is used here as part of a hybrid EPSM/DSMC method for the simulation of near continuum flows. It is used where the flow gradients are not large and the flow is expected to be in an equilibrium state. The gradient of local mean free path has been used to detect those regions where EPSM can be invoked. Results are presented for the unsteady flow of a gas in a shock tube with Knudsen numbers in the initial state of 0.01 and 0.002 either side of the diaphragm (based on the length of the initial low-pressure region). The results for the hybrid method are very close to those for pure DSMC. The execution speed of the hybrid code is 1.75 times that of standard DSMC.

30 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023112
2022236
2021168
2020163
2019190
2018172