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dc.contributor.advisorLópez-Rodríguez, Bibiana
dc.contributor.advisorMejía-Salazar, Carlos Enrique
dc.creatorGonzález-Medina, Wilmar Alberto
dc.date.accessioned2020-05-20T19:18:50Z
dc.date.available2020-05-20T19:18:50Z
dc.date.created2019-12-12
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/77542
dc.descriptionEste trabajo trata aspectos teóricos y computacionales de unas ecuaciones de flujo en medio poroso basadas en Ley de Darcy. Son ecuaciones que incluyen la estructura básica de las que se usan en simulación de yacimientos pero no incluyen varias fases ni varias componentes. La motivación para el trabajo viene de un proyecto de investigación apoyado por COLCIENCIAS del que son responsables varios profesores de la Universidad Nacional de Colombia, tanto de la Facultad de Minas como de la Facultad de Ciencias. El proyecto tiene por objeto el estudio de la estrategia de producción de petróleo denominada Recobro Mejorado de Petróleo (Enhanced Oil Recovery EOR.) Aunque las ecuaciones para modelar procesos de EOR son más complejas, las que presentamos en esta tesis son indispensables para poder enunciar las ecuaciones generales. Los resultados que se obtuvieron en esta tesis están relacionados con el método numérico de discretización por volúmenes finitos y con el procedimiento computacional denominado diferenciación automática. La combinación de estas dos técnicas es de mucho interés en la comunidad dedicada a la simulación de yacimientos. Esta es una tesis en el campo del análisis numérico, contiene resultados teóricos, por ejemplo consistencia de un esquema numérico o existencia y unicidad de una ecuación y también contiene resultados eminentemente computaciones.
dc.description.abstractThis paper deals with theoretical and computational aspects of flow equations in a porous media based on Darcy’s law. These are equations that include the basic structure of those used in reservoir simulation but do not include several phases and several components. The motivation for this thesis comes from a research project supported by COLCIENCIAS which several professors at the Universidad Nacional de Colombia, both the Faculty of Mines and the Faculty of Sciences, are responsible. The project aims to study the oil production strategy called Enhanced Oil Recovery (EOR). Although the equations to shape EOR processes are more complex, those presented in this thesis are indispensable to be able to announce the general equations. The results obtained in this proposal are related to the numerical method of discretization by finite volumes and to the computational procedure called automatic differentiation. The combination of these two techniques is of great interest to the reservoir simulation community. This is a thesis in the field of numerical analysis, it contains theoretical results, for example consistency of a numerical scheme or existence and uniqueness of an equation and also contains eminently computational results.
dc.format.extent70
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/
dc.subjectDarcy
dc.subjectVolúmenes finitos
dc.subjectElementos Finitos
dc.subjectExistencia y unicidad
dc.subjectAnálisis de error
dc.subjectDiferenciación automática
dc.subject.ddc510 - Matemáticas
dc.titleVolúmenes finitos y diferenciación automática en problemas elípticos asociados con simulación de yacimientos de petróleo
dc.title.alternativeFinite volumes and automatic di erentiation on elliptic problems associated with oil reservoir simulation
dc.typeOther
dc.rights.spaAcceso abierto
dc.contributor.institutionUniversidad Nacional de Colombia - Sede Medellín
dc.subject.keywordDarcy
dc.subject.keywordFinite Volumes
dc.subject.keywordFinite Elements
dc.subject.keywordExistence and uniqueness
dc.subject.keywordError analysis
dc.subject.keywordAutomatic differentiation
dc.type.spaOtro
dc.type.hasversionAccepted Version
dc.coverage.programEscuela de matemáticas
dc.coverage.modalityMaestria
dc.rights.accessRightsOpen Access
dc.rights.ccCC0 1.0 Universal
dc.identifier.bibliographicCitation@book{chen2006computational, title={Computational methods for multiphase flows in porous media}, author={Chen, Zhangxin and Huan, Guanren and Ma, Yuanle}, volume={2}, year={2006}, publisher={Siam} }
dc.identifier.bibliographicCitation@techreport{salgado2008finite, title={Finite element discretization of Darcy’s equations with pressure dependent porosity}, author={Salgado, Abner}, year={2008}, institution={Internal Report, Labaratoire Jacques-Louis Lions, Paris} }
dc.identifier.bibliographicCitation@MastersThesis{abadimplementacion, title={Implementaci{\'o}n del m{\'e}todo de elementos finitos para el modelamiento de un proceso de recobro mejorado}, author={Abad L{\'o}pez, Fernando Valentin and others}, school={Universidad Nacional de Colombia-Sede Medell{\'\i}n}, year={2018} }
dc.identifier.bibliographicCitation@article{lieintroduction, title={An Introduction to Reservoir Simulation Using MATLAB: User Guide for the Matlab Reservoir Simulation Toolbox (MRST), SINTEF ICT, Dec. 2015}, author={Lie, Knut-Andreas}, journal={There is no corresponding record for this reference.[Google Scholar]} }
dc.identifier.bibliographicCitation@article{Neidinger_2010, title = {Introduction to automatic differentiation and MATLAB Object-oriented programming}, journal = {SIAM Review}, volume = {52}, author = {Neidinger, R. D.}, year = {2010}, pages = {545--563} }
dc.identifier.bibliographicCitation@MastersThesis{Kjelseth_2014, author = {Kjelseth, V. O. E.}, title = {Efficient calculation of derivatives using automatic differentiation. With applications in optimization and reservoir simulation}, school = {University of Oslo}, address = {Noruega}, year = {2014}, }
dc.identifier.bibliographicCitation@article{wengert1964simple, title={A simple automatic derivative evaluation program}, author={Wengert, Robert Edwin}, journal={Communications of the ACM}, volume={7}, number={8}, pages={463--464}, year={1964}, publisher={ACM} }
dc.identifier.bibliographicCitation@book{bucker2006automatic, title={Automatic differentiation: applications, theory, and implementations}, author={B{\"u}cker, H Martin and Corliss, George and Hovland, Paul and Naumann, Uwe and Norris, Boyana}, volume={50}, year={2006}, publisher={Springer Science \& Business Media} }
dc.identifier.bibliographicCitation@misc{miller2014think, title={How to Think Like a Computer Scientist: Interactive Edition}, author={Miller, Brad and Ranum, David and Elkner, J and Wentworth, P and Downey, AB and Meyers, C and Mitchell, D}, howpublished={\url{https://runestone.academy/runestone/books/published/thinkcspy/index.html}}, note={Consultado en 2019-09-08} }
dc.identifier.bibliographicCitation@article{girault2010finite, title={Finite element discretization of Darcy's equations with pressure dependent porosity}, author={Girault, Vivette and Murat, Fran{\c{c}}ois and Salgado, Abner}, journal={ESAIM: Mathematical Modelling and Numerical Analysis}, volume={44}, number={6}, pages={1155--1191}, year={2010}, publisher={EDP Sciences} }
dc.identifier.bibliographicCitation@article{ubale2012numerical, title={NUMERICAL SOLUTION OF BOOLE’S RULE IN NUMERICAL INTEGRATION BY USING GENERAL QUADRATURE FORMULA}, author={Ubale, PV}, journal={Bulletin of Society for mathematical services \& standards (B SO MA SS)}, volume={1}, number={2}, pages={1--5}, year={2012} }
dc.identifier.bibliographicCitation@article{martinez2000practical, title={Practical quasi-Newton methods for solving nonlinear systems}, author={Mart{\'i}nez, Jos{\'e} Mario}, journal={Journal of Computational and Applied Mathematics}, volume={124}, number={1-2}, pages={97--121}, year={2000}, publisher={Elsevier} }
dc.identifier.bibliographicCitation@article{burden1997numerical, title={Numerical Analysis}, author={Burden, Richard L and Faires, J Douglas}, journal={Brooks-Cole}, year={1997} }
dc.identifier.bibliographicCitation@article{galantai2000theory, title={The theory of Newton's method}, author={Gal{\'a}ntai, Aurel}, journal={Journal of Computational and Applied Mathematics}, volume={124}, number={1-2}, pages={25--44}, year={2000}, publisher={Elsevier} }
dc.identifier.bibliographicCitation@article{rajagopal2007hierarchy, title={On a hierarchy of approximate models for flows of incompressible fluids through porous solids}, author={Rajagopal, KR}, journal={Mathematical Models and Methods in Applied Sciences}, volume={17}, number={02}, pages={215--252}, year={2007}, publisher={World Scientific} }
dc.identifier.bibliographicCitation@inproceedings{Eymard_2000, title = {Finite volume methods}, booktitle = {Handbook of Numerical Analysis VII}, author = {Eymard, R., Gallouet, T. and Herbin, R.}, editor = {Ciarlet, P. G. and Lions, J. L.}, publisher = {North-Holland, Amsterdam}, year = {2000}, pages = {713--1020}, }
dc.identifier.bibliographicCitation@article{moukalled2016finite, title={The finite volume method in computational fluid dynamics}, author={Moukalled, F and Mangani, L and Darwish, M and others}, journal={An Advanced Introduction with OpenFOAM and Matlab}, pages={3--8}, year={2016}, publisher={Springer} }
dc.identifier.bibliographicCitation@book{anderson1995computational, title={Computational Fluid Dynamics}, author={Anderson, J.}, isbn={9780070016859}, lccn={94021237}, series={Computational Fluid Dynamics: The Basics with Applications}, url={https://books.google.com.co/books?id=dJceAQAAIAAJ}, year={1995}, publisher={McGraw-Hill Education} }
dc.identifier.bibliographicCitation@phdthesis{jasak1996error, title={Error analysis and estimation for the finite volume method with applications to fluid flows.}, author={Jasak, Hrvoje}, year={1996}, school={Imperial College London (University of London)} }
dc.identifier.bibliographicCitation@book{brezis2010functional, title={Functional analysis, Sobolev spaces and partial differential equations}, author={Brezis, Haim}, year={2010}, publisher={Springer Science \& Business Media} }
dc.identifier.bibliographicCitation@article{gatica2014simple, title={A simple introduction to the mixed finite element method}, author={Gatica, Gabriel N}, journal={Springer Briefs in Mathematics. Springer, London}, year={2014}, publisher={Springer} }
dc.identifier.bibliographicCitation@book{gatica2014introduccion, title={Introducci{\'o}n al an{\'a}lisis funcional: teor{\'\i}a y aplicaciones}, author={Gatica, Gabriel N}, year={2014}, publisher={Revert{\'e}} }
dc.identifier.bibliographicCitation@article{achdou2003priori, title={A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations}, author={Achdou, Yves and Bernardi, Christine and Coquel, Fr{\'e}d{\'e}ric}, journal={Numerische Mathematik}, volume={96}, number={1}, pages={17--42}, year={2003}, publisher={Springer} }
dc.identifier.bibliographicCitation@article{azaiez2010spectral, title={Spectral discretization of Darcy’s equations with pressure dependent porosity}, author={Aza{\"\i}ez, Mejdi and Belgacem, Faker Ben and Bernardi, Christine and Chorfi, Nejmeddine}, journal={Applied Mathematics and Computation}, volume={217}, number={5}, pages={1838--1856}, year={2010}, publisher={Elsevier} }
dc.contributor.generoMasculino
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemática Aplicada


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