Direct numerical simulation of moderately rarefied gas flow within core samples
Matematičeskoe modelirovanie, Tome 30 (2018) no. 9, pp. 3-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to numerical simulation of isothermal moderately rarefied gas flows within three-dimensional spaces with complex voxel geometry corresponding to core (rock) samples pore space. Classical Maxwell slip boundary conditions are used to take into account slippage effect on the solid boundaries. Simulation results for several core samples under different averaged pressure are presented. The qualitatively right Klinkenberg slippage coefficient dependence on absolute permeability coefficient was obtained.
Mots-clés : quasi-hydrodynamic equations
Keywords: digital rock physics, slippage effect, slip boundary condition, Klinkenberg slippage coefficient, moderately rarefied gas, voxel geometry.
@article{MM_2018_30_9_a0,
     author = {V. A. Balashov},
     title = {Direct numerical simulation of moderately rarefied gas flow within core samples},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {30},
     number = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_9_a0/}
}
TY  - JOUR
AU  - V. A. Balashov
TI  - Direct numerical simulation of moderately rarefied gas flow within core samples
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 3
EP  - 20
VL  - 30
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_9_a0/
LA  - ru
ID  - MM_2018_30_9_a0
ER  - 
%0 Journal Article
%A V. A. Balashov
%T Direct numerical simulation of moderately rarefied gas flow within core samples
%J Matematičeskoe modelirovanie
%D 2018
%P 3-20
%V 30
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_9_a0/
%G ru
%F MM_2018_30_9_a0
V. A. Balashov. Direct numerical simulation of moderately rarefied gas flow within core samples. Matematičeskoe modelirovanie, Tome 30 (2018) no. 9, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2018_30_9_a0/

[1] C. Soulaine, F. Gjetvaj, C. Garing, S. Roman, A. Russian, P. Gouze, H.A. Tchelepi, “The Impact of Sub-Resolution Porosity of X-ray Microtomography Images on the Permeability”, Transport in Porous Media, 113:1 (2016), 227–243

[2] M.J. Blunt, B. Bijeljic, H. Dong, O. Gharbi, S. Iglauer, P. Mostaghimi, A. Paluszny, C. Pentland, “Pore-scale imaging and modelling”, Advances in Water Resources, 51 (2013), 197–216

[3] H. Dong, M.J. Blunt, “Pore-network extraction from micro-computerized-tomography images”, Phys. Rev. E, 80:3 (2009), 036307

[4] P. Ranut, E. Nobile, L. Mancini, “High resolution X-ray microtomography-based CFD simulation for the characterization of flow permeability and effective thermal conductivity of aluminum metal foams”, Experimental Thermal and Fluid Science, 67 (2015), 30–36

[5] J. Escoda, F. Willot, D. Jeulin, J. Sanahuja, C. Toulemonde, “Estimation of local stresses and elastic properties of a mortar sample by FFT computation of fields on a 3D image”, Cement and Concrete Research, 41:5 (2011), 542–556

[6] V.A. Balashov, “Direct numerical simulation of moderately rarefied gas flow within two-dimensional artificial porous media”, Math. Mod. Comp. Simul., 10:4 (2018)

[7] Yu.V. Sheretov, Dinamika sploshnyh sred pri prostranstvenno-vremennom osrednenii, RChD, M.–Izhevsk, 2009, 400 pp.

[8] B.N. Chetverushkin, Kinetic schemes and quasi-gasdynamic system of equations, CIMNE, Barcelona, 2008, 298 pp.

[9] T.G. Elizarova, Quasi-gas dynamic equations, Springer, Berlin–Heidelberg, 2009, 286 pp.

[10] GOST 26450.2-85 Porody gornye. Metody opredeleniia kollektorskikh svoistv. Metod opredeleniia koefficienta absoliutnoi gazopronitsaemosti pri statsionarnoi i nestatsionarnoi filtratsii

[11] L.J. Klinkenberg, “The permeability of porous media to liquids and gases”, Drilling and Production Practice, American Petroleum Institute, 1941, 200–213

[12] M.N. Kogan, Rarefied Gas Dynamics, Springer US, 1969, 515 pp.

[13] D.V. Sivuhin, Obshchii kurs fiziki, v. II, Termodinamika i molekuliarnaia fizika, Fizmatlit, M., 2003, 576 pp.

[14] A.A. Zlotnik, “On conservative spatial discretizations of the barotropic quasigasdynamic system of equations with a potential body force”, Comp. Math. and Math. Phys., 56:2 (2016), 303–319

[15] V.A. Balashov, V.E. Borisov, “Algoritm rascheta trekhmernyh techenii umerenno-razrezhennogo gaza v oblastiakh s vokselnoi geometriei”, Preprint IPM im. M.V. Keldysha, 2017, 099, 24 pp. | DOI

[16] , Imperial College London http://www.imperial.ac.uk/earth-science/research/research-groups/perm/research/pore-scale-modelling/micro-ct-images-and-networks/

[17] K.S. Basniev, N.M. Dmitriev, R.D. Kanevskaya, V.M. Maksimov, Podzemnaia gidromekhanika, Institut Kompiuternykh Issledovanii, M.–Izhevsk, 2006, 488 pp.

[18] D.A. Bikulov, Modelirovanie iavlenii perenosa v poristykh sredakh na gibridnykh superkompiuternykh sistemah, Diss. ... kand. fiz.-mat. nauk, MGU im. M.V. Lomonosova, M., 2015

[19] W. Degruyter, A. Burgisser, O. Bachmann, O. Malaspinas, “Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices”, Geosphere, 6:5 (2010), 470–481

[20] Palabos: Parallel lattice Boltzmann solver, http://www.palabos.org/

[21] F.I. Kotyahov, Fizika neftyanykh i gazovykh kollektorov, Nedra, M., 1977, 287 pp.

[22] D. Tiab, E.C. Donaldson, Petrophysics. Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, Fourth edition, Gulf Professional Publishing, 2015, 918 pp.

[23] G.H. Tang, W.Q. Tang, Y.L. He, “Gas slippage effect on microscale porous flow using the lattice Boltzmann method”, Physical review E, 72:5 (2005), 056301

[24] J. Gao, Q. Yu, X. Lu, “Apparent Permeability and Gas Flow Behavior in Carboniferous Shale from the Qaidam Basin, China: An Experimental Study”, Transp. Porous Med., 116:2 (2017), 585–611

[25] N. Saxena, R. Hofmann, F.O. Alpak, J. Dietderich, S. Hunter, “Effect of image segmentation voxel size on micro-CT computed effective transport elastic properties”, Marne and Petroleum Geology, 86 (2017), 972–990

[26] J.G. Heid, J.J. McMahon, R.F. Nielsen, S.T. Yuster, “Study of the Permeability of Rocks to Homogeneous Fluids”, Drilling and Production Practice, American Petroleum Institute, 1950, 230–244

[27] F.O. Jones, W.W. Owens, “A Laboratory Study of Low-Permeability Gas Sands”, Journal of Petroleum Technology, 32:9 (1980), 1631–1640

[28] W. Tanikawa, T. Shimamoto, “Comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks”, International Journal of Rock Mechanics and Mining Sciences, 46:2 (2009), 229–238