Geodesic
Numerical simulation of single-phase fluid flow in fractured porous media
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 1, pp. 100-115

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The models of single-phase fluid filtration in the fractured medium have been considered. Fractures have a significant impact on filtration processes, because they act as highly conductive channels. The mathematical model has been described by a parabolic pressure equation. Two approaches to flow approximation in fractures have been discussed: Approach 1 (by defining the nonhomogeneous coefficient for a cell occupied by the fracture); Approach 2 (by using a discrete model of fractures). Both approaches enable the explicit flow simulation in fractures by means of grid methods. Approximation of the problem has been performed using the method of finite differences and the method of finite elements. Numerical comparison of the two methods based on the model two-dimensional problem has been carried out. The results of simulation for the three-dimensional case have been presented.
Keywords: mathematical simulation, single-phase fluid flow, fractured porous media, nonhomogeneous coefficients, discrete model of fractures, method of finite differences, method of finite elements.
Mots-clés : filtration 
@article{UZKU_2017_159_1_a8,
     author = {M. V. Vasilyeva and V. I. Vasilyev and A. A. Krasnikov and D. Ya. Nikiforov},
     title = {Numerical simulation of single-phase fluid flow in fractured porous media},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {100--115},
     publisher = {mathdoc},
     volume = {159},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2017_159_1_a8/}
}
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M. V. Vasilyeva; V. I. Vasilyev; A. A. Krasnikov; D. Ya. Nikiforov. Numerical simulation of single-phase fluid flow in fractured porous media. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 1, pp. 100-115. http://geodesic.mathdoc.fr/item/UZKU_2017_159_1_a8/