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 Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 3, Pages 489–502 (Mi zvmmf11050)

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

Abstract: 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.

Key words: viscous fluids, porous-medium flow, inverse problem, fixed points, Volterra equation.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 075-15-2019-204 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.

DOI: https://doi.org/10.31857/S004446692003014X

English version:
Computational Mathematics and Mathematical Physics, 2020, 60:3, 484–497

Bibliographic databases:

UDC: 517.968
Revised: 05.09.2019
Accepted:18.11.2019

Citation: 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
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