Gas flow through square arrays of circular cylinders with Klinkenberg effect: A lattice Boltzmann study

Communications in Computational Physics

Volumn 8, Issue 5, 2010, Pages 1052-1073

  Chai, Zhenhua ^a   Shi, Baochang ^a   Guo, Zhaoli ^a   Lu, Jianhua ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Klinkenberg effect; Klinkenberg equation; Knudsen number; Multi relaxation time lattice Boltzmann equation

Indexed keywords

EID: 77958546403     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.010809.081209a     Document Type: Article

References (45)

1. A. E. Scheidegger, The Physics of Flow through Porous Media, University of Toronto, Toronto, 1974.
2. L. J. Klinkenberg, The perpeability of porousmedia to liquid and gases, American Petroleum Institute, Drilling and Productions practices, New York, 1941.
3. J. G. Heid, J. J. Mcmahon, R. F. Nielsen and S. T. Yuster, Study of the permeability of rocks to homogeneous fluids, American Petroleum Institute, Drilling and Productions practices, New York, 1950.
4. S. C. Jones, A rapid accurate unsteady-state Klinkenberg permeameter, Soc. Pet. Engr. J., 3535(1972), 383-397.
5. F. O. Jones and W. W. Owen, A laboratory study of low permeability gas sands, J. Pet. Technol., 32(1980), 1631-1640.
6. K. Sampath and C. W. Keighin, Factors affecting gas slippage in tight sandstones, Soc. Pet. Engr. J., 9872(1982), 409-415.
7. S. C. Jones, Using the inertial coefficient, ß, to characterise heterogeneity in reservoir rock, Paper SPE 16949 presented at 62nd. Annual Technical Conference of Society of Petroleum Engineers, New Orleans, 1987.
8. Y. S. Wu, K. Pruess and P. Persoff, Gas flow in porous media with Klinkenberg effects, Transp. Porous Med., 32(1998), 117-137.
9. L. M. de Socio and L. Marino, Gas flow in a permeable medium, J. Fluid Mech., 557(2006), 119-133.
10. F. A. Florece, J. A. Rushing, K. E. Newsham and T. A. Blasingame, Improved permeability prediction relations for low permability sands, Paper SPE 107954 presented at Rocky Mountain Oil & Gas Technology Symposium of Society of Petroleum Engineers, Colorado, 2007.
11. S. Woudberg and J.P. Du Plessis, Predicting the permeability of very low porosity sandstones, Transp. Porous Med., 73(2008), 39-55.
12. W. Tanikawa and T. Shimamoto, Comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks, Int. J. Rock Mech. Min. Sci., 46(2009), 229-238.
13. R. N. Xu and P. X. Jiang, Numerical simulation of fluid flow in microporous media, Int. J. Heat Fluid Flow, 29(2008), 1447-1455.
14. A. Cancelliere, C. Chang, E. Foti, D.H. Rothman and S. Succi, The permeability of a random medium: Comparison of simulation with theory, Phys. Fluids A, 2(1990), 2085-2088.
15. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University press, Oxford, 2001.
16. B. Ferréol and D. H. Rothman, Lattice-Boltzmann simulations of flow through fontainebleau sandstone, Transp. Porous Med., 20(1995), 3-20.
17. A. Koponen, D. Kandhai, E. Hellén, M. Alava, A. Hoekstra, M. Kataja, K. Niskanen, P. Sloot and J. Timonen, Permeability of Three-Dimensional Random Fiber Webs, Phys. Rev. Lett., 80(1998), 716-719.
18. C. Pan, L.-S. Luo and C. T. Miller, An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluids, 35(2006), 898-909.
19. N. Jeong, D. H. Choi and C. L. Lin, Prediction of Darcy-Forchheimer drag for micro-porous structures of complex geometry using the lattice Boltzmann method, J. Micromech. Microeng., 16(2006), 2240-2250.
20. G. H. Tang, W. Q. Tao and Y. L. He, Gas slippage effect on microscale porous flow using the lattice Boltzmann method, Phys. Rev. E, 72(2005), 056301.
21. G. H. Tang, W. Q. Tao and Y. L. He, Three-dimensional lattice Boltzmann model for gaseous flow in rectangular microducts and microscale porous media, J. Appl. Phys., 97(2005), 104918.
22. X. Nie, G. D. Doolen and S. Chen, Lattice-Boltzmann simulations of fluid flows in MEMS, J. Stat. Phys., 107(2002), 279-289.
23. S. Succi, Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis, Phys. Rev. Lett., 89(2002), 064502.
24. M. Sbragaglia and S. Succi, Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions, Phys. Fluids, 17(2005), 093602.
25. L. Szalmás, Knudsen layer theory for high-order lattice Boltzmann models, Europhys. Lett., 80(2007), 24003.
26. S. Ansumali and I. V. Karlin, Kinetic boundary conditions in the lattice Boltzmann method, Phys. Rev. E, 66(2002), 026311.
27. S. Ansumali, I. V. Karlin, S. Arcidiacono, A. Abbas and N. Prasianakis, Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy, Phys. Rev. Lett., 98(2007), 124502.
28. Z. L. Guo, T. S. Zhao and Y. Shi, Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows, J. Appl. Phys., 99(2006), 074903.
29. Z. L. Guo and C. G. Zheng, Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation time, Boundary condiction, and Knudsen layer, Int. J. Comput. Fluid Dyn., 22(2008), 465-473.
30. Z.H. Chai, Z. L. Guo, L. Zheng and B. C. Shi, Lattice Boltzmann simulation of surface roughness effect on gaseous flow in a microchannel, J. Appl. Phys., 104(2008), 014902.
31. F. Verhaeghe, L.-S. Luo and B. Blanpain, Lattice Boltzmann modeling of microchannel flow in slip flow regime, J. Comput. Phys., 228(2009), 147-157.
32. Y. H. Qian, D. d'Humires and P. Lallemand, Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17(1992), 478-484.
33. I. Ginzburg and D. d'Humières, Multireflection boundary conditions for lattice Boltzmann models, Phys. Rev. E, 68(2003), 066614.
34. F. Higuera, S. Succi and R. Benzi, Lattice gas-dynamics with enhanced collisions, Europhys. Lett. 9(1989), 345-349.
35. D. d'Humières, in Rarefied Gas Dynamics: Theory and Simulations, Progress in Astronautics and Aeronautics, edited by Shizgal B D and PWeaver D, AIAA Press,Washington, DC, 159(1992), 450-458.
36. P. Lallemand and L.-S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invarioance and stability, Phys. Rev. E, 61(2000), 6546-6562.
37. I. Ginzburg, F. Verhaeghe and D. d'Humières, Two-relaxation-time lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions, Commun. Comput. Phys., 3 (2008), pp. 427-478.
38. X. He, Q. Zou, L.-S. Luo and M. Dembo, Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model, J. Stat. Phys., 87(1997), 115-136.
39. I. Ginzbourg and P. M. Adler, Boundary flow condition analysis for the three-dimensional lattice Boltzmann model, J. Phys. II, 4(1994), 191-214.
40. N. G. Hadjiconstantinou, Comment on Cercignani's second-order slip coefficient, Phys. Fluids, 15(2003), 2352-2354.
41. Z. L. Guo, C. G. Zheng and B. C. Shi, Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chin. Phys., 11(2002), 366-374.
42. A. A. Kirsch and N. A. Fuchs, Studies on fibrous aerosol filters-II Pressure drops in systems of parallel cylinders, Ann. Occup Hyg., 10(1967), 23-30.
43. T. A. K. Sadiq, S. G. Advani and R. S. Parnas, Experimental investigation of transverse flow through aligned cylinders, Int. J. Multiphase flow, 21(1995), 755-774.
44. A. S. Sangani and A. Acrivos, Slow flow past periodic arrays of cylinders with application to heat transfer, Int. J. Multiphase flow, 8(1982), 193-206.
45. M. V. Bruschke and S. G. Advani, Flow of generalized Newtonian fluids across a periodic array of cylinders, J. Rheol., 37(1993), 479-497.