{"title":"Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well","authors":"M. Kh. Khairullin, E. R. Badertdinova","doi":"10.1134/s1995080224602224","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Unsteady filtration of a Bingham non-Newtonian fluid to a horizontal well is considered. The experimental results show that when such liquids flow in porous media at low pressure gradients, deviations from the linear Darcy law appear. A feature of the movement of Bingham non-Newtonian fluids in a porous medium is the fact that filtration becomes noticeable only after the pressure gradient reaches a certain critical value—the limiting pressure gradient. The formulation of the inverse coefficient problem for determining filtration parameters during the flow of Bingham non-Newtonian fluid to a horizontal well is given. Pressure change curves measured at the well are used as initial information. To numerically solve the inverse coefficient problem, a computational algorithm based on regularization methods is proposed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602224","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Unsteady filtration of a Bingham non-Newtonian fluid to a horizontal well is considered. The experimental results show that when such liquids flow in porous media at low pressure gradients, deviations from the linear Darcy law appear. A feature of the movement of Bingham non-Newtonian fluids in a porous medium is the fact that filtration becomes noticeable only after the pressure gradient reaches a certain critical value—the limiting pressure gradient. The formulation of the inverse coefficient problem for determining filtration parameters during the flow of Bingham non-Newtonian fluid to a horizontal well is given. Pressure change curves measured at the well are used as initial information. To numerically solve the inverse coefficient problem, a computational algorithm based on regularization methods is proposed.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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