Geodesic
Using relative permeabilities dependent on capillary number in hydrodynamic models of oil and gas fields
Matematičeskoe modelirovanie, Tome 17 (2005) no. 2, pp. 92-102.

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We propose numerical method for including the capillary number in the oil relative permeability functions. This method allows hydrodynamic model to be done more accurately and gives more realistic prediction. In this paper, results of reservoir simulation with relative permeability dependent on flow velocity and without it are reviewed. This method allows to form hydrodynamic grid varying in time that will decrease time of calculation. 
@article{MM_2005_17_2_a8,
     author = {V. I. Popkov and S. V. Zatsepina and V. P. Shakshin},
     title = {Using relative permeabilities dependent on capillary number in hydrodynamic models of oil and gas fields},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {92--102},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_2_a8/}
}
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V. I. Popkov; S. V. Zatsepina; V. P. Shakshin. Using relative permeabilities dependent on capillary number in hydrodynamic models of oil and gas fields. Matematičeskoe modelirovanie, Tome 17 (2005) no. 2, pp. 92-102. http://geodesic.mathdoc.fr/item/MM_2005_17_2_a8/