Displacement of Viscous Fluids in a Set of Parallel Pipes

G. V. Monakov, S. B. Tikhomirov, A. A. Yakovlev

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)484-497
Number of pages14
JournalComputational Mathematics and Mathematical Physics
Issue number3
Publication statusPublished - 1 Mar 2020


  • fixed points
  • inverse problem
  • porous-medium flow
  • viscous fluids
  • Volterra equation

ASJC Scopus subject areas

  • Computational Mathematics

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