TY - JOUR

T1 - Displacement of Viscous Fluids in a Set of Parallel Pipes

AU - Monakov, G. V.

AU - Tikhomirov, S. B.

AU - Yakovlev, A. A.

N1 - Funding Information: 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. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - fixed points

KW - inverse problem

KW - porous-medium flow

KW - viscous fluids

KW - Volterra equation

UR - http://www.scopus.com/inward/record.url?scp=85084466287&partnerID=8YFLogxK

U2 - 10.1134/S0965542520030148

DO - 10.1134/S0965542520030148

M3 - Article

AN - SCOPUS:85084466287

VL - 60

SP - 484

EP - 497

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 3

ER -