Friction Factor Correlations for Gas Flow in Slip Flow Regime

2007 ◽  
Vol 129 (10) ◽  
pp. 1268-1276 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Stephen E. Turner ◽  
Mohammad Faghri
Keyword(s):  
Friction Factor ◽  
Flow Regime ◽  
Gas Flow ◽  
Slip Flow ◽  
Channel Height ◽  
Inlet Temperature ◽  
Arbitrary Lagrangian Eulerian ◽  
Knudsen Numbers ◽  
Wide Range ◽  
Slip Flow Regime

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

Estimation of Leak Flow Rates Through Narrow Cracks

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Jae-Heon Lee
Keyword(s):  
Friction Factor ◽  
Gas Flow ◽  
Slip Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Opening Displacement ◽  
Flow Rates ◽  
Choked Flow ◽  
Runge Kutta Method ◽  
Wide Range ◽  
Leak Before Break

The estimation of the gaseous leak flow rates through a narrow crack is important for a leak-before-break analysis as a method of nondestructive testing. Therefore, the methodology to estimate the gaseous leak flow rates in a narrow crack for a wide range of flow conditions, from no-slip to slip flow and from unchoked to choked flow, by using f⋅Re (the product of friction factor and Reynolds number) correlations obtained for a microchannel, was developed and presented. The correlations applied here were proposed by the previous study (Hong, et al., 2007, “Friction Factor Correlations for Gas Flow in Slip Flow Regime,” ASME J. Fluids Eng., 129, pp. 1268–1276). The detail of the calculation procedure was appropriately documented. The fourth-order Runge–Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure, and the regular-Falsi method was employed to find the inlet Mach number. An idealized crack, whose opening displacement ranges from 2 μm to 50 μm, with the crack aspect ratio of 200, 1000, and 2000, was chosen for sample estimation. The present results were compared with both numerical simulations and available experimental measurements. The results were in excellent agreement. Therefore, the gaseous leak flow rates can be correctly predicted by using the proposed methodology.

Analytical and Experimental Investigations of Gas-Flow Regimes in Shales Considering the Influence of Mean Effective Stress

SPE Journal ◽  
2016 ◽  
Vol 21 (02) ◽  
pp. 557-572 ◽  
Author(s):  
Alireza A. Moghadam ◽  
Rick Chalaturnyk
Keyword(s):  
Flow Regime ◽  
Effective Stress ◽  
Gas Flow ◽  
Gas Permeability ◽  
Slip Flow ◽  
Flow Regimes ◽  
Absolute Permeability ◽  
Apparent Permeability ◽  
Reservoir Conditions ◽  
Slip Flow Regime

Summary Flow conditions determine the flow regimes governing gas flow in porous media. Slip-flow regime commonly occurs in laboratory gas-permeability measurements, and one must consider the physics of that when finding the absolute permeability of a sample. Accurate permeability estimates are paramount for production forecasts, financial planning, and recovery estimation. Slip flow is present in low-permeability rocks, both in the laboratory environment and at reservoir conditions. Gas flow through the matrix lies under the slip-flow regime for the majority of low-permeability-reservoir production scenarios, and accurate prediction of pressure and production rate requires a good understanding of the flow regime. In this paper, an analytical study is conducted on the dominant flow regimes under typical shale-gas reservoir conditions. A flow-regime map is produced with respect to gas pressure and matrix permeability. Steady-state gas-permeability experiments are conducted on three shale samples. An analytical model is used to match the experimental results that could explain the order-of-magnitude difference between the permeabilities of gas and liquid in shales. Experimental results are combined with further tests available in the literature to inform a discussion of the model's parameters. The results improve the accuracy of gas-flow modeling and of absolute-permeability estimates from laboratory tests. Similar tests performed at various mean effective stresses investigate the influence of mean effective stress on flow regime and apparent permeability. The results indicate that flow regime is a function of mean effective stress, and that the apparent permeability of shale rocks is a function of both flow regime and mean effective stress.

Friction Factor Correlations of Slip Flow in Micro-Tubes

2007 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Mohammad Faghri
Keyword(s):  
Mach Number ◽  
Friction Factor ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Arbitrary Lagrangian Eulerian ◽  
Constant Wall Temperature ◽  
Wide Range ◽  
Exit Mach Number ◽  
Poiseuille Number ◽  
Energy Equations

Poiseuille number, the product of friction factor and Reynolds number (f·Re) for quasi-fully developed flow in a micro-tube was obtained in slip flow regime. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers with two thermal boundary conditions: CWT (constant wall temperature) and CHF (constant heat flux), respectively. The tube diameter ranges from 3 to 10μm and the tube aspect ratio is 200. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at the atmospheric pressure. In slip flow, Mach and Knudsen numbers are systematically varied to determine their effects on f·Re. The correlation for f·Re is obtained from numerical results. It was found that f·Re is mainly a function of Mach number and Knudsen number and is different from the values obtained by 64/(1+8Kn) for slow flow. The obtained f·Re correlations are applicable to both no-slip and slip flow regimes.

Behaviour of rarefied gas flow near the junction of a suddenly expanding tube

2013 ◽  
Vol 739 ◽  
pp. 363-391 ◽  
Author(s):  
Vijay Varade ◽  
Amit Agrawal ◽  
A. M. Pradeep
Keyword(s):  
Flow Regime ◽  
Mass Flow ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Sudden Expansion ◽  
Momentum Balance ◽  
Straight Tube ◽  
Rarefied Gas Flow ◽  
Slip Flow Regime

AbstractThis paper presents an experimental study of isothermal rarefied gas flow through a tube with sudden expansion in the slip flow regime. The measurements reported here are for nitrogen flowing at low pressures in conventional tubes with sudden expansion area ratios of 1.48, 3.74, 12.43 and 64. The flow is dynamically similar to gas flow in a microchannel as the Knudsen number $(0. 0001\lt \mathit{Kn}\lt 0. 075)$ falls in the slip flow regime; the Reynolds number in the smaller section (${\mathit{Re}}_{s} $) ranges between 0.2 and 837. The static pressure along the wall is measured for different mass flow rates controlled by a mass flow controller and analysed to understand the flow behaviour. The velocity profiles are obtained through a momentum balance and using the pressure measurements. A discontinuity in the slope of pressure at the sudden expansion junction is noted and given special attention. The absence of flow separation is another key feature observed from the measurements. The streamlines are found to be concave near the junction. It is demonstrated that the flow ‘senses’ the oncoming sudden expansion junction and starts adjusting itself much before reaching the junction; this interesting behaviour is attributed to an increased axial momentum diffusion and wall slip. The additional acceleration of the central core of the gas flow causes an increase in the wall shear stress and a larger pressure drop as compared with a straight tube. These results are not previously available and should help in improving understanding of gaseous slip flows.

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