Elesin, A. V.; Kadyrova, A. Sh. Using the spline function to restore the permeability field under three-phase flow filtration. (English) Zbl 1487.76085 Lobachevskii J. Math. 42, No. 9, 2109-2113 (2021). Summary: The inverse coefficient problem of determining the absolute permeability field in the form of a spline function under a three-phase flow in a porous medium is considered. The problem is reduced to minimization of the residual function which constructed on the known values of the flow rate on the wells. The influence of errors in the flow rate measurements on the calculated fields of the absolute permeability is studied by the example of solving a model problem.© Pleiades Publishing, Ltd. 2021 Cited in 3 Documents MSC: 76S05 Flows in porous media; filtration; seepage 76T30 Three or more component flows 76M21 Inverse problems in fluid mechanics 76M30 Variational methods applied to problems in fluid mechanics 86A05 Hydrology, hydrography, oceanography Keywords:three-phase flow; inverse problem; permeability identification; residual function minimization × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aziz, Kh.; Settari, A., Petroleum Reservoir Simulation (1982), Moscow: Nedra, Moscow [2] Barenblatt, G. I.; Entov, V. M.; Ryzhik, V. M., The Movement of Liquids and Gases in Natural Formations (1984), Moscow: Nedra, Moscow [3] Chen, Z.; Huan, G.; Ma, Y., Computational Methods for Multiphase Flows in Porous Media (2006), Philadelphia: SIAM, Philadelphia · Zbl 1092.76001 · doi:10.1137/1.9780898718942 [4] Romm, E. S., Structural Models of Pore Space in Rocks (1985), Leningrad: Nedra, Leningrad [5] Dakhnov, V. N., Geophysical Methods for Determining Reservoir Properties and Oil and Gas Saturation of Rocks (1985), Moscow: Nedra, Moscow [6] Sun, N.-Z., Inverse Problems in Groundwater Modeling (1994), Norwell, MA: Kluwer, Norwell, MA [7] Oliver, D. S.; Reynolds, A. C.; Liu, N., Inverse Theory for Petroleum Reservoir Characterization and History Matching (2008), New York: Cambridge Univ. Press, New York · doi:10.1017/CBO9780511535642 [8] Yeh, W. W.-G., Review of parameter identification procedures in groundwater hydrology: The inverse problem, Water Resourses Res., 22, 95-108 (1986) · doi:10.1029/WR022i002p00095 [9] Elesin, A. V.; Kadyrova, A. S., The inverse coefficient problem for equations of three-phase flow in porous medium, Lobachevskii J. Math., 40, 724-729 (2019) · Zbl 1419.35242 · doi:10.1134/S1995080219060064 [10] Elesin, A. V.; Kadyrova, A. S., The identification of the relative permeabilities in the class of the piecewise linear functions, Lobachevskii J. Math., 41, 1175-1179 (2020) · Zbl 1454.76090 · doi:10.1134/S1995080220070100 [11] Stone, H. L., Estimation of three-phase relative permeability and residual data, J. Canad. Pet. Technol., 12, 53-61 (1973) [12] V. O. Ashkenazy, Spline Surfaces: Fundamentals of Theory and Computational Algorithms, The School-Book (Tver. Gos. Univ., Tver’, 2003) [in Russian]. [13] Dennis, J. E.; Schanabel, R. B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1987), Philadelphia: SIAM, Philadelphia This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.