Topic
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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TL;DR: This paper considers the introduction of a body force, in the incompressible limit, into the lattice Boltzmann model and considers a number of methods for application when there is a non-negligible density variation.
Abstract: In this paper we consider the introduction of a body force, in the incompressible limit, into the lattice Boltzmann model. A number of methods are considered and their suitability to our objectives determined. When there is no density variation across the fluid, gravity can be introduced in the form of an altered pressure gradient. This method correctly satisfies the Navier-Stokes equation; however, if there is a non-negligible density variation present (produced by the body force or otherwise) this method becomes less accurate as the density variation increases and the constant density approximation becomes less valid. Three other methods are also considered for application when there is a non-negligible density variation. The equations of motion satisfied by these models are found up to second order in the Knudsen number and it is seen that only one of these methods satisfies the true Navier-Stokes equation. Numerical simulations are performed to compare the different models and to assess the range of application of each.
296 citations
TL;DR: In this article, the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films was proposed, based on numerical calculations based on the linearized Boltzmann equation.
Abstract: We propose the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films. The database is created by numerical calculations based on the linearized Boltzmann equation. The proposed interpolation method is verified to reduce calculation time to several tenths of that required to perform rigorous calculations with the same accuracy
295 citations
TL;DR: In this paper, the dusty-gas model for flow was used to model flow in shale gas systems, which couples diffusion to advective flow and showed that for very small average pore throat diameters, lighter gases preferentially produced at concentrations significantly higher than in situ conditions.
Abstract: Various attempts have been made to model flow in shale gas systems. However, there is currently little consensus regarding the impact of molecular and Knudsen diffusion on flow behavior over time in such systems. Direct measurement or model-based estimation of matrix permeability for these “ultra-tight” reservoirs has proven unreliable. The composition of gas produced from tight gas and shale gas reservoirs varies with time for a variety of reasons. The cause of flowing gas compositional change typically cited is selective desorption of gases from the surface of the kerogen in the case of shale. However, other drivers for gas fractionation are important when pore throat dimensions are small enough. Pore throat diameters on the order of molecular mean free path lengths will create non-Darcy flow conditions, where permeability becomes a strong function of pressure. At the low permeabilities found in shale gas systems, the dusty-gas model for flow should be used, which couples diffusion to advective flow. In this study we implement the dusty-gas model into a fluid flow modeling tool based on the TOUGH+ family of codes. We examine the effects of Knudsen diffusion on gas composition in ultra-tight rock. We show that for very small average pore throat diameters, lighter gases are preferentially produced at concentrations significantly higher than in situ conditions. Furthermore, we illustrate a methodology which uses measurements of gas composition to more uniquely determine the permeability of tight reservoirs. We also describe how gas composition measurement could be used to identify flow boundaries in these reservoir systems. We discuss how new measurement techniques and data collection practices should be implemented in order to take advantage of this method. Our contributions include a new, fit-for-purpose numerical model based on the TOUGH+ code capable of characterizing transport effects including permeability adjustment and diffusion in micro- and nano-scale porous media.
295 citations
TL;DR: In this paper, a gaseous film of small thickness h is presented between fluid and wall and when h is smaller than the mean free path l of the gas, the Navier length b is expected to be independent of h and very large (micrometers).
Abstract: Certain (nonpolymeric) fluids show an anomalously low friction when flowing against well-chosen solid walls. We discuss here one possible explanation, postulating that a gaseous film of small thickness h is present between fluid and wall. When h is smaller than the mean free path l of the gas (Knudsen regime), the Navier length b is expected to be independent of h and very large (micrometers).
288 citations
TL;DR: The UGKS as discussed by the authors is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path.
286 citations