Leakage Predictions for Static Gasket Based on the Porous Media Theory

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Pascal Jolly ◽  
Luc Marchand
Keyword(s):  
Porous Media ◽  
Gas Flow ◽  
Molecular Flow ◽  
Intrinsic Permeability ◽  
Slip Boundary Conditions ◽  
Apparent Permeability ◽  
Slip Boundary ◽  
Porous Media Theory ◽  
Porous Media Model ◽  
Different Gases

In the present work, the annular static gaskets are considered as porous media and Darcy’s law is written for a steady radial flow of a compressible gas with a first order slip boundary conditions. From this, a simple equation is obtained that includes Klinkenberg’s intrinsic permeability factor kv of the gasket and the Knudsen number Kn′o defined with a characteristic length ℓ. The parameters kv and ℓ of the porous gasket are calculated from experimental results obtained with a reference gas at several gasket stress levels. Then, with kv and ℓ, the inverse procedure is performed to predict the leakage rate for three different gases. It is shown that the porous media model predicts leak rates with the same accuracy as the laminar-molecular flow (LMF) model of Marchand et al. However, the new model has the advantage of furnishing phenomenological information on the evolution of the intrinsic permeability and the gas flow regimes with the gasket compressive stress. It also enables quick identification of the part of leakage that occurs at the flange-gasket interface at low gasket stresses. At low gas pressure, the behavior of the apparent permeability diverges from that of Klinkenberg’s, indicating that the rarefaction effect becomes preponderant on the leak.

Leakage Predictions for Static Gasket Based on the Porous Media Theory

2006 ◽  
Author(s):  
Pascal Jolly ◽  
Luc Marchand
Keyword(s):  
Porous Media ◽  
Gas Flow ◽  
Molecular Flow ◽  
Intrinsic Permeability ◽  
Slip Boundary Conditions ◽  
Apparent Permeability ◽  
Slip Boundary ◽  
Porous Media Theory ◽  
Porous Media Model ◽  
Different Gases

In the present work, the annular static gaskets are considered as porous media and the Darcy’s law is written for a steady radial flow of a compressible gas with a first order slip boundary conditions. From this, a simple equation is obtained that includes the Klinkenberg’s intrinsic permeability factor kv of the gasket and the Knudsen number Kn′o defined with a characteristic length l. The parameters kv and l of the porous gasket are calculated from experimental results obtained with a reference gas at several gasket stress levels. Then, with kv and l, the inverse procedure is performed to predict the leakage rate for three different gases. It is shown that the porous media model predicts leak rates with the same accuracy as the laminar-molecular flow model (LMF) of Marchand, Derenne and Masi. However, the new model has the advantage of furnishing phenomenological information on the evolution of the intrinsic permeability and the gas flow regimes with the gasket compressive stress. It also enables quick identification of the part of leakage that occurs at the flange-gasket interface at low gasket stresses. At low gas pressure, the behavior of the apparent permeability diverges from that of Klinkenberg’s, indicating that the rarefaction effect becomes preponderant on the leak. Finally, it is demonstrated that the porous media model could be very useful in predicting gasket leakage with liquids.

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

A New Unified Diffusion—Viscous-Flow Model Based on Pore-Level Studies of Tight Gas Formations

SPE Journal ◽  
2012 ◽  
Vol 18 (01) ◽  
pp. 38-49 ◽  
Author(s):  
Mohammad R. Rahmanian ◽  
Roberto Aguilera ◽  
Apostolos Kantzas
Keyword(s):  
Porous Media ◽  
Viscous Flow ◽  
Flow Regime ◽  
Gas Flow ◽  
Flow Model ◽  
Molecular Flow ◽  
Single Element ◽  
Free Molecular Flow ◽  
Flow Through ◽  
Tight Porous Media

Summary In this study, single-phase gas-flow simulation that considers slippage effects through a network of slots and microfractures is presented. The statistical parameters for network construction were extracted from petrographic work in tight porous media of the Nikanassin Group in the Western Canada Sedimentary Basin (WCSB). Furthermore, correlations between Klinkenberg slippage effect and absolute permeability have been developed as well as a new unified flow model in which Knudsen number acts implicitly as a flow-regime indicator. A detailed understanding of fluid flow at microscale levels in tight porous media is essential to establish and develop techniques for economic flow rate and recovery. Choosing an appropriate equation for flow through a single element of the network is crucial; this equation must include geometry and other structural features that affect the flow as well as all variation of fluid properties with pressure. Disregarding these details in a single element of porous media can easily lead to flow misinterpretation at the macroscopic scale. Because of the wide flow-path-size distribution in tight porous media, a variety of flow regimes can exist in the equivalent network. Two distinct flow regimes, viscous flow and free molecular flow, are in either side of this flow-regime spectrum. Because the nature of these two types of flow is categorically different, finding/adjusting a unified flow model is problematic. The complication stems from the fact that the viscosity concept misses its meaning as the flow regime changes from viscous to free molecular flow in which a diffusion-like mechanism dominates. For each specified flow regime, the appropriate equations for different geometries are studied. In addition, different unified flow models available in the literature are critically investigated. Simulation of gas flow through the constructed network at different mean flow pressures leads to investigating the functionality of the Klinkenberg factor with permeability of the porous media and pore-level structure.

scholarly journals Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

2021 ◽  
Vol 3 ◽  
Author(s):  
Francisco J. Valdés-Parada ◽  
Didier Lasseux
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Mass Transport ◽  
Gas Flow ◽  
Macroscopic Model ◽  
Type Model ◽  
Pore Scale ◽  
Advective Transport ◽  
Apparent Permeability ◽  
Slip Effects

In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian and advective transport of a passive solute in rigid and homogeneous porous media is derived. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also in the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The use of the model is restricted by the starting assumptions imposed in the governing equations at the pore scale and by the (spatial and temporal) constraints involved in the upscaling process. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media.

On the Use of Gas Flow Models to Predict Leak Rates Through Sheet Gasket Materials

2017 ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Ali Salah Omar Aweimer
Keyword(s):  
Flow Regime ◽  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Rise ◽  
Second Order ◽  
Leak Rate ◽  
Molecular Flow ◽  
Flow Models ◽  
Micro Channels ◽  
Different Gases

The prediction of leak rate through porous gaskets for different gases based on test conducted on a reference gas can prevent bolted joint leakage failure and save the industry a lot of money. This work gives a basic comparison between different gas flow models that can be used to predict leak rates through porous gasket materials. The ability of a model to predict the leak rate at the micro and nano levels in tight gaskets relies on its capacity to incorporate different flow regimes that can be present under the different working conditions. Four models based on Navier-Stokes equations and incorporate the boundary conditions of the appropriate flow regime considered. The first and second order slip, diffusivity and molecular flow models are used to predict and correlate leak rates of gases namely helium, nitrogen, SF6, methane, argon and air passing through three frequently used nanoporous gasket materials which are flexible graphite, PTFE and compressed fiber. The methodology is based on the determination experimentally of the porosity parameter (N and R) of the micro channels assumed to simulate the leak paths present in the gasket using helium as the reference gas. The predicted leak rates of different gases at the different stresses and pressure levels are confronted to the results obtained experimentally by measurements of leak rates using pressure rise and mass spectrometry techniques. The results show that the predictions depend on the type of flow regime that predominates. Nevertheless the second order slip model is the one that gives better agreements with the measured leaks in all cases.

On the Use of Gas Flow Models to Predict Leak Rates Through Sheet Gasket Materials

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Ali Salah Omar Aweimer
Keyword(s):  
Flow Regime ◽  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Rise ◽  
Second Order ◽  
Leak Rate ◽  
Molecular Flow ◽  
Specific Flow ◽  
Flow Models ◽  
Different Gases

The prediction of leak rate through porous gaskets for different gases based on test conducted on a reference gas can prevent bolted joint leakage failure and save the industry lots of money. This work gives a basic comparison between different gas flow models that can be used to predict leak rates through porous gasket materials. The ability of a model to predict the leak rate at the micro- and nanolevels in tight gaskets relies on its capacity to incorporate different flow regimes that can be present under different working conditions. Four models based on Navier–Stokes equations that incorporate different boundary conditions and characterize specific flow regime are considered. The first- and second-order slip, diffusivity, and molecular flow models are used to predict and correlate leak rates of gases namely helium, nitrogen, SF6, methane, argon, and air passing through three frequently used porous gasket materials which are flexible graphite, polytetrafluoroethylene (PTFE), and compressed fiber. The methodology is based on the determination experimentally of the porosity parameter (N and R) of the microchannels assumed to simulate the leak paths present in the gasket using helium as the reference gas. The predicted leak rates of different gases at different stresses and pressure levels are confronted to the results obtained experimentally by measurements of leak rates using pressure rise and mass spectrometry techniques. The results show that the predictions depend on the type of flow regime that predominates. Nevertheless, the second-order slip model is the one that gives better agreements with the measured leaks in all cases.

scholarly journals Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media

1998 ◽  
Vol 09 (08) ◽  
pp. 1479-1490 ◽  
Author(s):  
P. V. Coveney ◽  
J.-B. Maillet ◽  
J. L. Wilson ◽  
P. W. Fowler ◽  
O. Al-Mushadani ◽  
...  
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Single Phase ◽  
Lattice Gas ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Dimensional Lattice ◽  
Slip Boundary ◽  
Saturated Rock

We develop our existing two-dimensional lattice-gas model to simulate the flow of single phase, binary immiscible and ternary amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of "no-slip" boundary conditions. Here we report on preliminary applications of this model to the flow of such fluids within model porous media. We also construct fluid invasion boundary conditions, and the effects of invading aqueous solutions of surfactant on oil-saturated rock during imbibition and drainage are described.

Gas flow in ultra-tight shale strata

2012 ◽  
Vol 710 ◽  
pp. 641-658 ◽  
Author(s):  
Hamed Darabi ◽  
A. Ettehad ◽  
F. Javadpour ◽  
K. Sepehrnoori
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Gas Flow ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Initial Pressure ◽  
Flow In Porous Media ◽  
Upper And Lower Bounds ◽  
Apparent Permeability ◽  
Permeability Function

AbstractWe study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.

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