Geodesic
Numerical simulation of one-phase flow to multi-stage hydraulically fractured horizontal well
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 2, pp. 287-301

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This paper presents a method of numerical simulation of one-phase flow near multi-stage fractured horizontal well in oil reservoir. Differential models for flows within reservoir and within fractures are formulated separately on the basis of Darcy's law. Numerical approximations of these models are performed using the finite volume method. The resulting systems of linear equations are then assembled into the single system to avoid an iterative coupling of numerical solutions for problems in the reservoir and fractures. Different solution methods for coupled ill-conditioned systems of linear equations are examined.
Keywords: horizontal well, multi-stage hydraulic fracturing, algebraic multigrid method, preconditioner.
Mots-clés : one-phase filtration 
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     author = {M. R. Khamidullin},
     title = {Numerical simulation of one-phase flow to multi-stage hydraulically fractured~horizontal well},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {287--301},
     publisher = {mathdoc},
     volume = {158},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_2_a10/}
}
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M. R. Khamidullin. Numerical simulation of one-phase flow to multi-stage hydraulically fractured horizontal well. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 2, pp. 287-301. http://geodesic.mathdoc.fr/item/UZKU_2016_158_2_a10/