Pore to continuum upscaling of permeability in heterogeneous porous media using mortars

International Journal of Oil, Gas and Coal Technology

Volumn 5, Issue 2-3, 2012, Pages 249-266

  Sun, Tie ^a   Mehmani, Yashar ^a   Bhagmane, Jaideep ^a   Balhoff, Matthew Thomas ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Continuum scale; Heterogeneous; Mortar coupling; Multiscale modelling; Network modelling; Pore scale modelling; Porous media; Upscaling

Indexed keywords

DOMAIN DECOMPOSITION METHODS; MORTAR;

CONTINUUM SCALE; HETEROGENEOUS; MORTAR COUPLING; MULTI-SCALE MODELLING; NETWORK MODELLING; PORE-SCALE MODELLING; UPSCALING;

POROUS MATERIALS;

EID: 84859594306     PISSN: 17533309     EISSN: 17533317     Source Type: Journal    
DOI: 10.1504/IJOGCT.2012.046323     Document Type: Article

References (31)

1. Adler, P.M., Jacquin, C.G. and Thovert, J. (1992) 'The formation factor of reconstructed porous media', Water Res., Vol. 28, No. 6, pp.1571-1576.
2. Al-Raoush, R., Thompson, K.E. and Willson, C.S. (2003) 'Comparison of network generation techniques for unconsolidated porous media', Soil Sci. Soc. Am. J., Vol. 67, No. 6, pp.1687-1700. (Pubitemid 37417884)
3. Arbogast, T., Cowsar, L.C., Wheeler, M.F. and Yotov, I. (2000) 'Mixed finite element methods on non-matching multi-block grids', SIAM J. Numerical Analysis, Vol. 37, No. 4, pp.1295-1315.
4. Arbogast, T., Pencheva, G., Wheeler, M.F. and Yotov, I. (2007) 'A multiscale mortar mixed finite element method', Multiscale Model. Simul., Vol. 6, No. 1, pp.319-346. (Pubitemid 351479401)
5. Bakke, S. and Oren, P.E. (1997) '3-D pore-scale modelling of sandstones and flow simulations in the pore networks', SPE Journal, Vol. 2, No. 2, pp.136-149. (Pubitemid 127641413)
6. Balhoff, M.T. and Thompson, K.E. (2004) 'Modeling the steady flow of yield stress fluids in packed beds', AICHE Journal, Vol. 50, No. 12, pp.3034-3048. (Pubitemid 39664635)
7. Balhoff, M.T. and Wheeler, M.F. (2009) 'A predictive pore scale model of non-darcy flow in porous media', SPE J., Vol. 14, No. 4, pp.579-587.
8. Balhoff, M.T., Thomas, S.G. and Wheeler, M.F. (2008) 'Mortar coupling and upscaling of pore-scale models', Computational Geosciences, Vol. 12, No. 1, pp.15-27.
9. Balhoff, M.T., Thompson, K.E. and Hjortso, M. (2007) 'Coupling pore networks to continuum models', Computers and Geosciences, Vol. 33, No. 3, pp.393-410.
10. Bernardi, C., Maday, Y. and Patera, A.T. (1994) 'A new nonconforming approach to domain decomposition: the mortar element method. Non-linear partial differential equations and their applications', CollTege de France Seminar, Pitman Research Notes Mathematics Series, Vol. 299, pp.13-51, Longman Science Technology, Harlow.
11. Bhagmane, J. (2009) 'Using mortars to upscale permeability in heterogeneous porous media from the pore to continuum scale', MS thesis, University of Texas at Austin.
12. Bryant, S.L., Mellor, D.W. and Cade, C.A. (1993) 'Physically representative network models of transport in porous media', AIChE Journal, Vol. 39, No. 3, pp.387-396. (Pubitemid 272271)
13. Chen, J. and Wilkinson, D. (1985) 'Pore-scale viscous fingering in porous media', Phys. Rev. Lett., Vol. 55, No. 18, pp.1892-1895.
14. Chen, S. and Doolen, G. (1998) 'Lattice Boltzman method for fluid flows', Annual Review of Fluid Mechanics, Vol. 30, pp.329-364.
15. Christie, M. (1996) 'Upscaling for reservoir simulation', Journal of Petroleum Technology, Vol. 48, No. 11, pp.1004-1010. (Pubitemid 126608272)
16. Durlofsky, L. (1998) 'Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to existing upscaling techniques', Computational Geosciences, Vol. 2, No. 2, pp.73-92.
17. Fatt, I. (1956) 'The network model of porous media, I, Capillary pressure characteristics', Pet. Trans. AIME, Vol. 207, pp.144-159.
18. Koplik, J., Lasseter, T.J. (1985) 'Two-phase flow in random network models of porous media', SPE Journal, Vol. 25, No. 1, pp.89-100. (Pubitemid 15474885)
19. Liang, Z., Ioannidis, A. and Chatzis, I. (2000) 'Permeability and electrical conductivity of porous media from 3D replicas of the microstructure', Chem. Eng. Sci., Vol. 55, No. 22, pp.5247-5262. (Pubitemid 32258615)
20. Lindquist, W.B., Lee, S., Coker, D.A., Jones, K.W. and Spanne, P. (1996) 'Medial axis analysis of void structure in three-dimensional tomographic images of porous media', J. Geophys. Res., Vol. 101, No. B4, pp.8297-8310.
21. Lindquist, W.B., Venkatarangan, A., Dunsmuir, J. and Wong, T. (2000) 'Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones', J. Geophys. Res., Vol. 105, No. B9, pp.21509-21528.
22. Lopez, X., Valvatne, P. and Blunt, M. (2003) 'Predictive network modeling of single-phase non-Newtonian flow in porous media', Journal of Colloid and Interface Science, Vol. 264, No. 1, pp.256-265. (Pubitemid 36918391)
23. Payatakes, A.C., Ng, K.M. and Flumerfelt, R.W. (1980) 'Oil ganglion dynamics during immiscible displacement: model formulation', AIChE Journal, Vol. 26, No. 3, pp.430-443.
24. Peszynska, M., Wheeler, M. and Yotov, I. (2002) 'Mortar upscaling for multiphase flow in porous media', Computational Geosciences, Vol. 6, No. 1, pp.73-100. (Pubitemid 34990061)
25. Prodanovic, M. and Bryant, S.L. (2006) 'A level set method for determining critical curvatures for drainage and imbibitions', Journal of Colloid and Interface Science, Vol. 304, No. 2, pp.442-458. (Pubitemid 44781219)
26. Sok, R.M., Knackstedt, M.A., Sheppard, A.P., Pinczewski, W.V., Lindquist, W.B., Venkatarangan, A. and Paterson, L. (2002) 'Direct and stochastic generation of network models from tomographic images. Effect of topology on residual saturations', TIPM, Vol. 46, Nos. 2-3, pp.345-371.
27. Tartakovsky, A. and Meakin, P. (2005) 'Simulation of unsaturated flow in complex fractures using smoothed particle hydrodynamics', Vadose Zone Journal, Vol. 4, No. 3, pp.848-855.
28. Valvatne, P. and Blunt, M. (2004) 'Predictive pore-scale modeling of two-phase flow in mixed wet media', Water Resources Research, Vol. 40, pp.1-21.
29. Venkatarangan, A.B. (2000) 'Geometric and statistical analysis of porous media', Thesis, State University of New-York at Stony Brook.
30. Wen, X.H., Durlofsky, L.J. and Edwards, M.G. (2003) 'Use of border regions for improved permeability upscaling', Mathematical Geology, Vol. 35, No. 5, pp.521-547. (Pubitemid 38149251)
31. Willson, C.S. and Al-Raoush, R.I. (2005) 'Extraction of physically realistic pore network properties from three-dimensional synchrotron Xray microtomography images of unconsolidated porous media systems', J. Hydrol., Vol. 300, No. 1, pp.44-64. (Pubitemid 39588504)