The estimation of oil water displacement functions

We introduce an algorithm to solve an inverse problem for a non-linear hyperbolic partial differential equation. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The direct model is non-linear: the sought for parameter is a function of the solution of t...

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Detalles Bibliográficos
Autor principal: Savioli, Gabriela Beatriz
Publicado: 2007
Materias:
Conservation law
Non-linear equation
Parameter estimation
Two-phase flow
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03270793_v37_n3_p187_Savioli
http://hdl.handle.net/20.500.12110/paper_03270793_v37_n3_p187_Savioli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_03270793_v37_n3_p187_Savioli2023-06-08T15:33:11Z The estimation of oil water displacement functions Savioli, Gabriela Beatriz Conservation law Non-linear equation Parameter estimation Two-phase flow We introduce an algorithm to solve an inverse problem for a non-linear hyperbolic partial differential equation. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The direct model is non-linear: the sought for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the election of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The parameter is inferred from measurements of saturation at different spatial points as a function of time. The estimation procedure is carried out linearizing the solution of the direct model with respect to the parameter and then computing the least-squares solution in functional spaces. The sensitivity equations are derived. We test the algorithm with several numerical experiments. Fil:Savioli, G.B. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03270793_v37_n3_p187_Savioli http://hdl.handle.net/20.500.12110/paper_03270793_v37_n3_p187_Savioli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Conservation law
Non-linear equation
Parameter estimation
Two-phase flow
spellingShingle Conservation law
Non-linear equation
Parameter estimation
Two-phase flow
Savioli, Gabriela Beatriz
The estimation of oil water displacement functions
topic_facet Conservation law
Non-linear equation
Parameter estimation
Two-phase flow
description We introduce an algorithm to solve an inverse problem for a non-linear hyperbolic partial differential equation. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The direct model is non-linear: the sought for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the election of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The parameter is inferred from measurements of saturation at different spatial points as a function of time. The estimation procedure is carried out linearizing the solution of the direct model with respect to the parameter and then computing the least-squares solution in functional spaces. The sensitivity equations are derived. We test the algorithm with several numerical experiments.
author Savioli, Gabriela Beatriz
author_facet Savioli, Gabriela Beatriz
author_sort Savioli, Gabriela Beatriz
title The estimation of oil water displacement functions
title_short The estimation of oil water displacement functions
title_full The estimation of oil water displacement functions
title_fullStr The estimation of oil water displacement functions
title_full_unstemmed The estimation of oil water displacement functions
title_sort estimation of oil water displacement functions
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03270793_v37_n3_p187_Savioli
http://hdl.handle.net/20.500.12110/paper_03270793_v37_n3_p187_Savioli
work_keys_str_mv AT savioligabrielabeatriz theestimationofoilwaterdisplacementfunctions
AT savioligabrielabeatriz estimationofoilwaterdisplacementfunctions
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