Displacement of viscous fluids in a set of parallel pipes
G. V. Monakova, S. B. Tikhomirova, A. A. Yakovlevbc
a St. Petersburg State University, St. Petersburg, 199034 Russia
b Gazprom Neft Company, St. Petersburg, 190000 Russia
c Tomsk Polytechnical University, Tomsk, 634050 Russia
The process of pumping water in a formation filled with a more viscous fluid is considered using the simplest model of the interwell space described by a set of parallel pipes. The fluids are assumed to be immiscible with a sharp interface in each pipe. The main task is to recover the parameters of the interwell space from a given displacement characteristic, namely, displacement data for each fluid. An explicit solution of the direct problem is presented for the model under study. It is shown that the problem of medium recovery, which is, in fact, an inverse problem, can be solved up to a one-parameter family. Additionally, a topology is found in which the inverse problem is stable.
viscous fluids, porous-medium flow, inverse problem, fixed points, Volterra equation.
|Ministry of Science and Higher Education of the Russian Federation
|Tikhomirov and Monakov’s research was supported by a grant from the President of the Russian Federation, project no. 075-15-2019-204. Monakov also acknowledges the support from the program of social investments “Hometowns” of the Gazprom Neft Company.
Computational Mathematics and Mathematical Physics, 2020, 60:3, 484–497
G. V. Monakov, S. B. Tikhomirov, A. A. Yakovlev, “Displacement of viscous fluids in a set of parallel pipes”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 489–502; Comput. Math. Math. Phys., 60:3 (2020), 484–497
Citation in format AMSBIB
\by G.~V.~Monakov, S.~B.~Tikhomirov, A.~A.~Yakovlev
\paper Displacement of viscous fluids in a set of parallel pipes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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