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Tight gas reservoirs are of prominent importance among unconventional petroleum reservoirs. Due to the complicated flow dynamics of gas in tight porous media and compressibility effects, corrections have to be applied to the Darcy equation so that it can properly predict gas flow dynamics. As the mean pore diameter of tight rocks ( e.g . shales) decreases, the ratio of the mean free path to the pore diameter, known as the non-dimensional Knudsen number, rises, the gas rarefaction effects becomes important, and the condition of no-slip on the pore surface is violated. Proper treatments of these complexities have been attempted by using classical continuum fluid mechanics and kinetic theory of gases approaches. The most well-known slip condition correction was presented by Klinkenberg in 1941. Many researchers have tried to correct and extend Klinkenberg's model beyond the slip flow regime. In this research the slip condition of the rarefied gas in low permeability simple porous media is studied by the lattice Boltzmann method and new corrections to Klinkenberg's coefficients are investigated. These corrections allow the extension of Klinkenberg model to higher ranges of Knudsen numbers. All the simulations in this work were performed by codes developed by the authors. [ABSTRACT FROM AUTHOR]

[Display omitted] • Analytical equation predicting mass flow rates for the entire Knudsen ranges. • New equation correlating the flow rate, Knudsen number, and TMAC. • TMAC significantly affected by channel surfaces and gas molecular structures. In this paper, we refer previously reported numerical data to design a new analytic equation for Poiseuille flow in a circular channel. Superposition of the continuum, slip, and free-molecular flow equations provides a versatile solution for the entire Knudsen range; however, it is not accurate in the transition regime. Adding correction factors and modifications to the existing flow-rate model enhances the precision and validity for wide flow ranges. Parameters of each equation are fitted for the collected data with Levenberg–Marquardt algorithm and compared in each regime; subsequently, the equation with the best accuracy and simplicity is selected. The newly suggested formula fits well for the referred data by correlating with the dimensionless flow rate, Knudsen number, and tangential momentum accommodation coefficient (TMAC). Furthermore, we calculate the TMAC using previous experimental data, which reflects the reflective interactions between the channel surfaces and gas molecules. Our newly suggested formula demonstrates effectively that the TMAC is significantly affected not only by the channel surface roughness but also by the molecular structure of gas. [ABSTRACT FROM AUTHOR]

Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates with nonuniform suiface properties in the transverse direction are studied based on kinetic theory. We considered a simplified model in which one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundaty on which the accommodation coefficient varies periodically and smoothly in the transverse direction. The spatially two-dimensional (2D) problem in the cross section is studied numerically based on the linearized Bhatnagar-Gross-Krook-Welander (BGKW) model of the Boltzmann equation. The flow behavior, i.e., the macroscopic flow velocity and the mass flow rate of the gas as well as the velocity distribution function, is studied over a wide range of the mean free path of the gas and the parameters of the distribution of the accommodation coefficient. The mass flow rate of the gas is approximated by a simple formula consisting of the data of the spatially one-dimensional (ID) problems. When the mean free path is large, the distribution function assumes a wavy variation in the molecular velocity space due to the effect of a nonuniform surface property of the plate. [ABSTRACT FROM AUTHOR]

Plane thermal transpiration o f a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas. [ABSTRACT FROM AUTHOR]

Abstract: Continuum hydrodynamics accurately describes the flow of fluids over a wide range of systems. However, continuum models are unable to adequately describe the flow of fluid under extreme confinement. In particular, the no-slip boundary condition invoked in continuum flow calculations is violated for low density gases flowing in microtubes or nanoporous materials. The calculation of gas mass transfer rate in microtubes using experiments and simulation is investigated in the case of small absolute pressures. Specifically, in the present work, Argon gas is considered in a 3D model of two metallic tanks connected through microchannels. The pressure difference between the inlet and the outlet of the structure is monitored as a function of time. Thus the gas transfer rate is evaluated and compared with experimental data, in order to verify the departure from the standard Navier – Stokes equations with the no-slip boundary condition. [Copyright &y& Elsevier]

Abstract: The paper describes the implementation of conservative projection method of solving the Boltzmann equation on GPU. The NVIDIA CUDA technology is used as the computational platform. Methods for optimal implementation of the solver for two-dimensional geometry and methods for setting boundary conditions, implementation of the geometry and storage of integrating grids were developed. The developed methodology was used to perform calculations for the problem of slow gas flow in a rectangular cavity and that of shock wave propagation in a narrow channel. The efficiency of using GPU for analysis of slow and high-speed flows of rarefied gas is demonstrated. [ABSTRACT FROM AUTHOR]