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
Autores principales:	Savioli, G.B., Fernández-Berdaguer, E.M.
Formato:	JOUR
Materias:	Conservation law Non-linear equation Parameter estimation Two-phase flow
Acceso en línea:	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

id	todo:paper_03270793_v37_n3_p187_Savioli
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spelling	todo:paper_03270793_v37_n3_p187_Savioli2023-10-03T15:24:39Z The estimation of oil water displacement functions Savioli, G.B. Fernández-Berdaguer, E.M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, G.B. Fernández-Berdaguer, E.M. 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.
format	JOUR
author	Savioli, G.B. Fernández-Berdaguer, E.M.
author_facet	Savioli, G.B. Fernández-Berdaguer, E.M.
author_sort	Savioli, G.B.
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
url	http://hdl.handle.net/20.500.12110/paper_03270793_v37_n3_p187_Savioli
work_keys_str_mv	AT savioligb theestimationofoilwaterdisplacementfunctions AT fernandezberdaguerem theestimationofoilwaterdisplacementfunctions AT savioligb estimationofoilwaterdisplacementfunctions AT fernandezberdaguerem estimationofoilwaterdisplacementfunctions
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The estimation of oil water displacement functions

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