Gaseous flow through heterogeneous, partially connected networks of pipes
Abstract
Simulations of flow of an ideal gas through heterogeneous simple cubic pipe networks with different pipe radius distributions and variable bond coordination numbers were performed. Networks with monomodal and bimodal radius distributions were constructed. A very wide range of Knudsen numbers was achieved. Flow simulations of purely viscous gases and incompressible liquids were also carried out for comparison. The permeability to gas in the purely viscous regime was larger than the permeability to an incompressible liquid. Based on a variety of computational tests, this result was likely not a numerical artifact. The simulated macroscopic flow behavior differed from the underlying single pipe model, depending on the radius distribution, network connectivity and magnitude of the externally applied pressure gradient, and was compatible with the Klinkenberg analysis only when the maximum Knudsen number used in each simulation was lower than 1. In this condition, the Klinkenberg coefficient was nearly proportional to the inverse of the network hydraulic radius while the effect of the radius distribution was weak and that of the network connectivity essentially negligible. Here, the bimodal simulations displayed a typical percolation behavior, with the Klinkenberg coefficient remaining constant as long as the large pipe population was connected.
- Authors:
-
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Earth, Atmospheric and Planetary Sciences Dept.
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
- OSTI Identifier:
- 1483628
- Grant/Contract Number:
- FG02-97ER14760
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING
Citation Formats
Bernabé, Yves. Gaseous flow through heterogeneous, partially connected networks of pipes. United States: N. p., 2018.
Web. doi:10.1038/s41598-018-33374-2.
Bernabé, Yves. Gaseous flow through heterogeneous, partially connected networks of pipes. United States. https://doi.org/10.1038/s41598-018-33374-2
Bernabé, Yves. Mon .
"Gaseous flow through heterogeneous, partially connected networks of pipes". United States. https://doi.org/10.1038/s41598-018-33374-2. https://www.osti.gov/servlets/purl/1483628.
@article{osti_1483628,
title = {Gaseous flow through heterogeneous, partially connected networks of pipes},
author = {Bernabé, Yves},
abstractNote = {Simulations of flow of an ideal gas through heterogeneous simple cubic pipe networks with different pipe radius distributions and variable bond coordination numbers were performed. Networks with monomodal and bimodal radius distributions were constructed. A very wide range of Knudsen numbers was achieved. Flow simulations of purely viscous gases and incompressible liquids were also carried out for comparison. The permeability to gas in the purely viscous regime was larger than the permeability to an incompressible liquid. Based on a variety of computational tests, this result was likely not a numerical artifact. The simulated macroscopic flow behavior differed from the underlying single pipe model, depending on the radius distribution, network connectivity and magnitude of the externally applied pressure gradient, and was compatible with the Klinkenberg analysis only when the maximum Knudsen number used in each simulation was lower than 1. In this condition, the Klinkenberg coefficient was nearly proportional to the inverse of the network hydraulic radius while the effect of the radius distribution was weak and that of the network connectivity essentially negligible. Here, the bimodal simulations displayed a typical percolation behavior, with the Klinkenberg coefficient remaining constant as long as the large pipe population was connected.},
doi = {10.1038/s41598-018-33374-2},
journal = {Scientific Reports},
number = 1,
volume = 8,
place = {United States},
year = {Mon Oct 08 00:00:00 EDT 2018},
month = {Mon Oct 08 00:00:00 EDT 2018}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Validation of a Second-Order Slip Flow Model in Rectangular Microchannels
journal, April 2004
- Colin, StÉPhane; Lalonde, Pierre; Caen, Robert
- Heat Transfer Engineering, Vol. 25, Issue 3
Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren
journal, January 1909
- Knudsen, Martin
- Annalen der Physik, Vol. 333, Issue 1
Factors Affecting Gas Slippage in Tight Sandstones of Cretaceous Age in the Uinta Basin
journal, November 1982
- Sampath, K.; Keighin, C. William
- Journal of Petroleum Technology, Vol. 34, Issue 11
Pore connectivity, permeability, and electrical formation factor: A new model and comparison to experimental data: CONNECTIVITY, PERMEABILITY
journal, November 2011
- Bernabé, Y.; Zamora, M.; Li, M.
- Journal of Geophysical Research: Solid Earth, Vol. 116, Issue B11
Molecular Simulations of Knudsen Wall-slip: Effect of Wall Morphology
journal, October 2003
- Arya, Gaurav; Chang, Hsueh-Chia; Maginn, Edward J.
- Molecular Simulation, Vol. 29, Issue 10-11
Knudsen’s Permeability Correction for Tight Porous Media
journal, September 2011
- Ziarani, Ali S.; Aguilera, Roberto
- Transport in Porous Media, Vol. 91, Issue 1
The Flow of Gases in Pipes at Low Pressures
journal, October 1946
- Brown, Gordon P.; DiNardo, Albert; Cheng, George K.
- Journal of Applied Physics, Vol. 17, Issue 10
The equivalent channel model for permeability and resistivity in fluid-saturated rock—A re-appraisal
journal, December 1983
- Paterson, M. S.
- Mechanics of Materials, Vol. 2, Issue 4
Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms
journal, October 2010
- Civan, Faruk; Rai, Chandra S.; Sondergeld, Carl H.
- Transport in Porous Media, Vol. 86, Issue 3
Report: a Model for Flows in Channels, Pipes, and Ducts at Micro and nano Scales
journal, February 1999
- Ali Beskok, George Em Karniadakis,
- Microscale Thermophysical Engineering, Vol. 3, Issue 1
Simulation of solute transport through heterogeneous networks: analysis using the method of moments and the statistics of local transport characteristics
journal, February 2018
- Li, Min; Qi, Tao; Bernabé, Yves
- Scientific Reports, Vol. 8, Issue 1
Report: a Model for Flows in Channels, Pipes, and Ducts at Micro and nano Scales
journal, February 1999
- Ali Beskok, George Em Karniadakis,
- Microscale Thermophysical Engineering, Vol. 3, Issue 1
Comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks
journal, February 2009
- Tanikawa, Wataru; Shimamoto, Toshihiko
- International Journal of Rock Mechanics and Mining Sciences, Vol. 46, Issue 2
Gaseous slip flow in long microchannels
journal, June 1997
- Arkilic, E. B.; Schmidt, M. A.; Breuer, K. S.
- Journal of Microelectromechanical Systems, Vol. 6, Issue 2
Determining the intrinsic permeability of tight porous media based on bivelocity hydrodynetics
journal, January 2014
- Lv, Qifeng; Wang, Enzhi; Liu, Xiaoli
- Microfluidics and Nanofluidics, Vol. 16, Issue 5
The impact of gas slippage on permeability effective stress laws: Implications for predicting permeability of fine-grained lithologies
journal, October 2016
- Letham, Eric Aidan; Bustin, Robert Marc
- International Journal of Coal Geology, Vol. 167
A pore network model for simulating non-ideal gas flow in micro- and nano-porous materials
journal, January 2014
- Ma, Jingsheng; Sanchez, Juan Pablo; Wu, Kejian
- Fuel, Vol. 116
Mass flow and tangential momentum accommodation in silicon micromachined channels
journal, June 2001
- Arkilic, Errol B.; Breuer, Kenneth S.; Schmidt, Martin A.
- Journal of Fluid Mechanics, Vol. 437
Mass transfer within the gas-phase of porous media
journal, March 2000
- Kast, W.; Hohenthanner, C. -R.
- International Journal of Heat and Mass Transfer, Vol. 43, Issue 5
A Laboratory Study of Low-Permeability Gas Sands
journal, September 1980
- Jones, F. O.; Owens, W. W.
- Journal of Petroleum Technology, Vol. 32, Issue 09
An Experimental Study on the Slippage Effect of Gas Flow in a Compact Rock
journal, January 2016
- Wang, H. L.; Xu, W. Y.; Cai, M.
- Transport in Porous Media, Vol. 112, Issue 1
The effect of pressure on porosity and the transport properties of rock
journal, January 1984
- Walsh, J. B.; Brace, W. F.
- Journal of Geophysical Research, Vol. 89, Issue B11
Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone)
journal, August 2009
- Javadpour, F.
- Journal of Canadian Petroleum Technology, Vol. 48, Issue 08
Gas and liquid permeability in nano composites gels: Comparison of Knudsen and Klinkenberg correction factors
journal, December 2014
- Anez, Liz; Calas-Etienne, Sylvie; Primera, Juan
- Microporous and Mesoporous Materials, Vol. 200
Klinkenberg gas slippage measurements as a means for shale pore structure characterization
journal, July 2015
- Letham, E. A.; Bustin, R. M.
- Geofluids, Vol. 16, Issue 2
Percolation connectivity, pore size, and gas apparent permeability: Network simulations and comparison to experimental data: Connectivity, Pore Size, and Gas Permeability
journal, July 2017
- Li, M.; Tang, Y. B.; Bernabé, Y.
- Journal of Geophysical Research: Solid Earth, Vol. 122, Issue 7
Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows
journal, June 2013
- Mehmani, Ayaz; Prodanović, Maša; Javadpour, Farzam
- Transport in Porous Media, Vol. 99, Issue 2
An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases
journal, June 1964
- Deissler, R. G.
- International Journal of Heat and Mass Transfer, Vol. 7, Issue 6
An Experimental Study on the Slippage Effect of Gas Flow in a Compact Rock
journal, January 2016
- Wang, H. L.; Xu, W. Y.; Cai, M.
- Transport in Porous Media, Vol. 112, Issue 1
Gas and liquid permeability in nano composites gels: Comparison of Knudsen and Klinkenberg correction factors
journal, December 2014
- Anez, Liz; Calas-Etienne, Sylvie; Primera, Juan
- Microporous and Mesoporous Materials, Vol. 200
Knudsen Diffusion in Silicon Nanochannels
journal, February 2008
- Gruener, Simon; Huber, Patrick
- Physical Review Letters, Vol. 100, Issue 6
Micro/Nano-pore Network Analysis of Gas Flow in Shale Matrix
journal, August 2015
- Zhang, Pengwei; Hu, Liming; Meegoda, Jay N.
- Scientific Reports, Vol. 5, Issue 1
A new electrical formation factor model for bimodal carbonates: numerical studies using dual-pore percolation network
journal, April 2015
- Tang, Y. B.; Li, M.; Bernabé, Y.
- Geophysical Journal International, Vol. 201, Issue 3
Determining the intrinsic permeability of tight porous media based on bivelocity hydrodynetics
journal, January 2014
- Lv, Qifeng; Wang, Enzhi; Liu, Xiaoli
- Microfluidics and Nanofluidics, Vol. 16, Issue 5
Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity
journal, January 2015
- Chen, Li; Zhang, Lei; Kang, Qinjun
- Scientific Reports, Vol. 5, Issue 1
Steady-State Permeability Measurements on Intact Shale Samples at Reservoir Conditions - Effect of Stress, Temperature, Pressure, and Type of Gas
conference, March 2013
- Sinha, S.; Braun, E. M.; Determan, M. D.
- SPE Middle East Oil and Gas Show and Conference
Effective Correlation of Apparent Gas Permeability in Tight Porous Media
journal, July 2009
- Civan, Faruk
- Transport in Porous Media, Vol. 82, Issue 2
Second-order slip laws in microchannels for helium and nitrogen
journal, August 2003
- Maurer, Jean; Tabeling, Patrick; Joseph, Pierre
- Physics of Fluids, Vol. 15, Issue 9
Second-order slip laws in microchannels for helium and nitrogen
journal, August 2003
- Maurer, Jean; Tabeling, Patrick; Joseph, Pierre
- Physics of Fluids, Vol. 15, Issue 9
Flow and Diffusion of Gases in Porous Media
journal, April 1967
- Mason, E. A.; Malinauskas, A. P.; Evans, R. B.
- The Journal of Chemical Physics, Vol. 46, Issue 8
Analytical solution of gaseous slip flow in long microchannels
journal, August 2007
- Dongari, Nishanth; Agrawal, Abhishek; Agrawal, Amit
- International Journal of Heat and Mass Transfer, Vol. 50, Issue 17-18
A pore network model for simulating non-ideal gas flow in micro- and nano-porous materials
journal, January 2014
- Ma, Jingsheng; Sanchez, Juan Pablo; Wu, Kejian
- Fuel, Vol. 116
Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation
journal, November 1990
- Loyalka, S. K.; Hamoodi, S. A.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 11
Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms
journal, October 2010
- Civan, Faruk; Rai, Chandra S.; Sondergeld, Carl H.
- Transport in Porous Media, Vol. 86, Issue 3
Effective Correlation of Apparent Gas Permeability in Tight Porous Media
journal, July 2009
- Civan, Faruk
- Transport in Porous Media, Vol. 82, Issue 2
The Flow of Gases in Pipes at Low Pressures
journal, October 1946
- Brown, Gordon P.; DiNardo, Albert; Cheng, George K.
- Journal of Applied Physics, Vol. 17, Issue 10
Gaseous slip flow in long microchannels
journal, June 1997
- Arkilic, E. B.; Schmidt, M. A.; Breuer, K. S.
- Journal of Microelectromechanical Systems, Vol. 6, Issue 2
Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation
journal, November 1990
- Loyalka, S. K.; Hamoodi, S. A.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 11
Experimental study of gas and liquid permeability of a mortar
journal, September 2002
- Loosveldt, Hélène; Lafhaj, Zoubeir; Skoczylas, Frédéric
- Cement and Concrete Research, Vol. 32, Issue 9
Klinkenberg gas slippage measurements as a means for shale pore structure characterization
journal, July 2015
- Letham, E. A.; Bustin, R. M.
- Geofluids, Vol. 16, Issue 2
Permeability and storativity of binary mixtures of high- and low-permeability materials
journal, January 2004
- Bernabé, Y.
- Journal of Geophysical Research, Vol. 109, Issue B12
A new electrical formation factor model for bimodal carbonates: numerical studies using dual-pore percolation network
journal, April 2015
- Tang, Y. B.; Li, M.; Bernabé, Y.
- Geophysical Journal International, Vol. 201, Issue 3
Comparisons of water and argon permeability in natural clay-bearing fault gouge under high pressure at 20°C
journal, July 2000
- Faulkner, D. R.; Rutter, E. H.
- Journal of Geophysical Research: Solid Earth, Vol. 105, Issue B7
Works referencing / citing this record:
Klinkenberg Effect and Effective Pressure for Gas Permeability of Tight Sandstones
journal, February 2019
- Xiao, Wenlian; Bernabé, Yves; Evans, Brian
- Journal of Geophysical Research: Solid Earth, Vol. 124, Issue 2