Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos
During the last decade, the injection of nanofluids in hydrocarbon fields has been of increasing interest, as an enhanced oil recovery (EOR) technique. Specifically, when applying this technique, search among others, i.) improve the mobility of the hydrocarbon, change the matrix wettability from oil...
- Autores:
-
López Patiño, Eduin Alexander
- Tipo de recurso:
- Work document
- Fecha de publicación:
- 2020
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/78554
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/78554
- Palabra clave:
- 660 - Ingeniería química
Thermal recovery
Multiphysics models
Porous media
Fluid flow
Retention and mobilization of nanoparticles
Modelos multifísicos
Medios porosos
Flujo de fluidos
Retención y movilización de nanopartículas
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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dc.title.spa.fl_str_mv |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
dc.title.alternative.spa.fl_str_mv |
Development of a Probabilistic Model of Flow of Matter and Transport of Scalars in Hydrocarbon Reservoirs Subjected to Nanofluid Injection |
title |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
spellingShingle |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos 660 - Ingeniería química Thermal recovery Multiphysics models Porous media Fluid flow Retention and mobilization of nanoparticles Modelos multifísicos Medios porosos Flujo de fluidos Retención y movilización de nanopartículas |
title_short |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
title_full |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
title_fullStr |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
title_full_unstemmed |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
title_sort |
Desarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidos |
dc.creator.fl_str_mv |
López Patiño, Eduin Alexander |
dc.contributor.advisor.spa.fl_str_mv |
Mejía Cárdenas, Juan Manuel Chejne Janna, Farid |
dc.contributor.author.spa.fl_str_mv |
López Patiño, Eduin Alexander |
dc.contributor.corporatename.spa.fl_str_mv |
Universidad Nacional de Colombia - Sede Medellín |
dc.contributor.researchgroup.spa.fl_str_mv |
Dinámicas de flujo y transporte en medios porosos |
dc.subject.ddc.spa.fl_str_mv |
660 - Ingeniería química |
topic |
660 - Ingeniería química Thermal recovery Multiphysics models Porous media Fluid flow Retention and mobilization of nanoparticles Modelos multifísicos Medios porosos Flujo de fluidos Retención y movilización de nanopartículas |
dc.subject.proposal.eng.fl_str_mv |
Thermal recovery Multiphysics models Porous media Fluid flow Retention and mobilization of nanoparticles |
dc.subject.proposal.spa.fl_str_mv |
Modelos multifísicos Medios porosos Flujo de fluidos Retención y movilización de nanopartículas |
description |
During the last decade, the injection of nanofluids in hydrocarbon fields has been of increasing interest, as an enhanced oil recovery (EOR) technique. Specifically, when applying this technique, search among others, i.) improve the mobility of the hydrocarbon, change the matrix wettability from oil to water, ii.) increase the amount of saturates and aromatics at the expense of the asphaltenes found in the improved hydrocarbon (The -Diasty & Aly, 2015). In general, it has been found that the injection of nanofluids has improved recovery by up to 10%. Therefore, it becomes relevant to generate a phenomenological model that allows the description of the system and the obtaining of relevant information on the process. The novelty of the study of the nanofluid injection problem is that it proposes a deterministic / probabilistic hybrid model, which presents two reference frameworks in its development. First, an Eulerian framework, where the transport of mass of the fluid phases present in the porous medium and energy is considered deterministically and second, a Lagrangian framework, which considers a probability density function that evolves to through the Fokker-Planck equation, giving to the probabilistic component model. Here, the Lagrangian part emerges from the solution of the probability equation obtained by finding the marginal PDFs. For example, if the marginal PDF is found in the position space, the Fokker equation - Planck converts to the probabilistic advection-diffusion equation. Now, to solve this advection-diffusion equation, a Lagrangian method is used. In the particular case of the study the stochastic particle method (SPM) will be used. Some of the results obtained with this work are: first, the extension of the SPM to the description of components such as tracers and nanoparticles is achieved. For this, it is necessary consider non-equilibrium phenomena, such as retention / mobilization. Furthermore, the probabilistic transport model is validated using a commercial simulator and experimental data (Li, et al., 2015). Also, the model is applicable under multiphasic, multidimensional and non-isothermal flow conditions. Among the conclusions obtained from this study are: first, the equivalence between the hybrid and deterministic methods, second, the additional information provided by the hybrid model associated with statistical moments such as standard deviation and the evaluation of PDF's, third, the representation without the use of mesh of the phenomenology associated with the system, e.g, positioning of concentration fronts. All this opens a branch of possibilities to the use of the SPM to the description of other components such as surfactants, polymers or mixtures of these. Finally, the SPM can be expanded to the description of other fields such as temperature, among others. |
publishDate |
2020 |
dc.date.accessioned.spa.fl_str_mv |
2020-10-21T22:10:05Z |
dc.date.available.spa.fl_str_mv |
2020-10-21T22:10:05Z |
dc.date.issued.spa.fl_str_mv |
2020-10-20 |
dc.type.spa.fl_str_mv |
Documento de trabajo |
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info:eu-repo/semantics/workingPaper |
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López, E.A. (2020). Desarrollo de un Modelo Probabilístico de Flujo de Materia y Transporte de Escalares en Yacimientos de Hidrocarburos Sometidos a Inyección de Nanofluidos. Universidad Nacional de Colombia, sede Medellín. Disertación de tesis doctoral. Medellín - Colombia |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/78554 |
identifier_str_mv |
López, E.A. (2020). Desarrollo de un Modelo Probabilístico de Flujo de Materia y Transporte de Escalares en Yacimientos de Hidrocarburos Sometidos a Inyección de Nanofluidos. Universidad Nacional de Colombia, sede Medellín. Disertación de tesis doctoral. Medellín - Colombia |
url |
https://repositorio.unal.edu.co/handle/unal/78554 |
dc.language.iso.spa.fl_str_mv |
spa |
language |
spa |
dc.relation.references.spa.fl_str_mv |
Abdelfatah, E., Pournik, M., Shiau, B. J. Ben, & Harwell, J. (2017). Mathematical modeling and simulation of nanoparticles transport in heterogeneous porous media. Journal of Natural Gas Science and Engineering, 40, 1–16. https://doi.org/10.1016/j.jngse.2017.01.028 Abou-Kassem, J.H., Farouq Ali, S.M. and Islam, M. R. (2006). Petroleum Reservoir Simulations A basic Approach. Gulf Publishing Company. Elsevier Inc. Abou-Kassem, J.H., Farouq Ali, S.M. and Islam, M. R. (2006). Petroleum Reservoir Simulations A basic Approach. Gulf Publishing Company. Elsevier Inc. Bear, J. (2018). Modeling Phenomena of Flow and Transport in Porous Media (First edit). Haifa, Israel: Springer International Publishing Berkowitz, B., Cortis, A., Dentz, M., & Scher, H. (2006). Modeling Non-fickian transport in geological formations as a continuous time random walk. Reviews of Geophysics, 44(2), 1–49. https://doi.org/10.1029/2005RG000178. Berkowitz, B., & Scher, H. (1995). On Characterization of Anomalous Dispersion in Porous and Fractured Media. Water Resources Research, 31(6), 1461–1466. https://doi.org/10.1029/95WR00483 Cardona Rojas, L. (2017). Efecto de nanopartículas en procesos con inyección de vapor a diferentes calidades. Universidad Nacional de Colombia - Sede Medellín. Retrieved from http://bdigital.unal.edu.co/62562/1/1152199431.2018.pdf Chen, Y., Zhou, C., & Jing, L. (2009). Modeling coupled THM processes of geological porous media with multiphase flow: Theory and validation against laboratory and field scale experiments. Computers and Geotechnics, 36(8), 1308–1329. https://doi.org/10.1016/j.compgeo.2009.06.001 Curl, R. L. (1963). Dispersed phase mixing: I. Theory and effects in simple reactors. AIChE Journal, 9(2), 175–181. https://doi.org/10.1002/aic.690090207 Dentz, M., Cortis, A., Scher, H., & Berkowitz, B. (2004). Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport. Advances in Water Resources, 27(2), 155–173. https://doi.org/10.1016/j.advwatres.2003.11.002 El-Diasty, A. I., & Aly, A. M. (2015). Understanding the mechanism of nanoparticles applications in enhanced oil recovery. Society of Petroleum Engineers - SPE North Africa Technical Conference and Exhibition 2015, NATC 2015, 000, 944–962. https://doi.org/10.2118/175806-ms Janicka, J., Kolbe, K., & Kollmann, W. (1977). Closure of the transport equation for the probability density function of turbulent scalar fields. Journal of Non-Equilibrium Thermodynamics., 4, 47–66 Li, S., & Torsæter, O. (2015). Experimental Investigation of the influence of nanoparticles adsorption and transport on wettability alteration for oil wet Berea sandstone. SPE Middle East Oil and Gas Show and Conference, MEOS, Proceedings, 229–244. Liu, M., Meakin, P., & Huang, H. (2007). Dissipative particle dynamics simulation of pore-scale multiphase fluid flow. Water Resources Research, 43(August 2006), 1–14. https://doi.org/10.1029/2006WR004856 Meyer, D. W., Jenny, P., & Tchelepi, H. a. (2010). A joint velocity-concentration PDF method for tracer flow in heterogeneous porous media. Water Resources Research, 46(12), 1–17. https://doi.org/10.1029/2010WR009450 Morales, O. A. (2019). Simulación del mejoramiento in-situ en yacimientos de crudo pesado con el uso de nanocatalizadores en procesos de inyección de vapor. Universidad Nacional de Colombia - Sede Medellín. Sahimi, M. (2012). Dispersion in porous media, continuous-time random walks, and percolation. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 85(1). https://doi.org/10.1103/PhysRevE.85.016316 Tartakovsky, D. M., & Dentz, M. (2019). Diffusion in Porous Media : Phenomena and Mechanisms. Transport in Porous Media, 130(1), 105–127. https://doi.org/10.1007/s11242-019-01262-6 Tyagi, M. (2010). Probability Density Function Approach for Modeling Multi-Phase Flow in Porous Media Tyagi, Manav, Jenny, P., Lunati, I., & Tchelepi, H. A. (2008). A Lagrangian, stochastic modeling framework for multi-phase flow in porous media. Journal of Computational Physics, 227, 6696–6714. https://doi.org/10.1016/j.jcp.2008.03.030 Whitson, C. H., & Brulé, M. R. (2000). Phase Behavior. Monograph 20, Society of Petroleum Engineers Inc. (Vol. 20) Zhang, K., Li, Y., Hong, A., Wu, K., Jing, G., Torsæter, O., … Chen, Z. (2015). Nanofluid alternating gas for tight oil exploitation. Society of Petroleum Engineers - SPE/IATMI Asia Pacific Oil and Gas Conference and Exhibition, APOGCE 2015, 1–17. https://doi.org/10.2118/176241-ms Zhang, T. (2012). Modeling of Nanoparticle Transport in Porous Media. Transport in Porous Media. University of Austin Texas |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de ColombiaAcceso abiertohttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Mejía Cárdenas, Juan Manuelb4e18ab6-066b-4890-a2fd-7c244d070797-1Chejne Janna, Farid401f8232cbbed073cf4612ce7bc3b54b-1López Patiño, Eduin Alexander13f16d0e-4875-478d-a5b7-7ab94f071768Universidad Nacional de Colombia - Sede MedellínDinámicas de flujo y transporte en medios porosos2020-10-21T22:10:05Z2020-10-21T22:10:05Z2020-10-20López, E.A. (2020). Desarrollo de un Modelo Probabilístico de Flujo de Materia y Transporte de Escalares en Yacimientos de Hidrocarburos Sometidos a Inyección de Nanofluidos. Universidad Nacional de Colombia, sede Medellín. Disertación de tesis doctoral. Medellín - Colombiahttps://repositorio.unal.edu.co/handle/unal/78554During the last decade, the injection of nanofluids in hydrocarbon fields has been of increasing interest, as an enhanced oil recovery (EOR) technique. Specifically, when applying this technique, search among others, i.) improve the mobility of the hydrocarbon, change the matrix wettability from oil to water, ii.) increase the amount of saturates and aromatics at the expense of the asphaltenes found in the improved hydrocarbon (The -Diasty & Aly, 2015). In general, it has been found that the injection of nanofluids has improved recovery by up to 10%. Therefore, it becomes relevant to generate a phenomenological model that allows the description of the system and the obtaining of relevant information on the process. The novelty of the study of the nanofluid injection problem is that it proposes a deterministic / probabilistic hybrid model, which presents two reference frameworks in its development. First, an Eulerian framework, where the transport of mass of the fluid phases present in the porous medium and energy is considered deterministically and second, a Lagrangian framework, which considers a probability density function that evolves to through the Fokker-Planck equation, giving to the probabilistic component model. Here, the Lagrangian part emerges from the solution of the probability equation obtained by finding the marginal PDFs. For example, if the marginal PDF is found in the position space, the Fokker equation - Planck converts to the probabilistic advection-diffusion equation. Now, to solve this advection-diffusion equation, a Lagrangian method is used. In the particular case of the study the stochastic particle method (SPM) will be used. Some of the results obtained with this work are: first, the extension of the SPM to the description of components such as tracers and nanoparticles is achieved. For this, it is necessary consider non-equilibrium phenomena, such as retention / mobilization. Furthermore, the probabilistic transport model is validated using a commercial simulator and experimental data (Li, et al., 2015). Also, the model is applicable under multiphasic, multidimensional and non-isothermal flow conditions. Among the conclusions obtained from this study are: first, the equivalence between the hybrid and deterministic methods, second, the additional information provided by the hybrid model associated with statistical moments such as standard deviation and the evaluation of PDF's, third, the representation without the use of mesh of the phenomenology associated with the system, e.g, positioning of concentration fronts. All this opens a branch of possibilities to the use of the SPM to the description of other components such as surfactants, polymers or mixtures of these. Finally, the SPM can be expanded to the description of other fields such as temperature, among others.Durante la última década, la inyección de nanofluidos en yacimientos de hidrocarburos como técnica de recobro mejorado de petróleo (EOR) ha tenido un interés creciente. Específicamente, al aplicar esta técnica, se busca entre otras, mejorar la movilidad del hidrocarburo, cambiar la humectabilidad de la matriz de aceite a agua, incrementar la cantidad de saturados y aromáticos a expensas de los asfáltenos que se encuentren en el hidrocarburo mejorado (El-Diasty & Aly, 2015). En general, se ha encontrado que la inyección de nanofluidos ha mejorado el recobro hasta en valores 10%. Por tanto, se hace relevante generar un modelo fenomenológico que permita la descripción del sistema y la obtención de información pertinente sobre el proceso. Lo novedoso del estudio del problema de inyección de nanofluidos, es que propone un modelo hibrido determinista / probabilista, el cual presenta en su desarrollo dos marcos de referencia. De un lado, un marco Euleriano, donde se considera el transporte de masa de las fases fluidas presentes en el medio poroso y la energía de forma determinista y de otro lado, un marco Lagrangiano, que inicialmente considera una función de densidad de probabilidad que evoluciona a través de la ecuación de Fokker-Planck, otorgándole al modelo de la componente probabilista. Aquí, la parte Lagrangiana emerge de la solución de la ecuación de probabilista que se obtenga al encontrar las PDF marginales. Por ejemplo, si se encuentra la marginal en el espacio de la posición, se obtiene la ecuación de Fokker – Planck se convierte en la ecuación de advección-difusión probabilística. Ahora para dar solución a esta ecuación de advección-difusión, se utiliza un método Lagrangiano. En el caso particular del estudio se utilizó el método de partículas estocásticas SPM. Algunos de los resultados obtenidos con este trabajo son: primero, se logra la extensión del SPM a la descripción de componentes como trazadores y nanopartículas, dotándolo de modelos que consideran fenómenos de no equilibrio como retención / movilización. Además se valida el modelo de transporte probabilista usando un simulador comercial y datos experimentales. Adicionalmente, el modelo es aplicable bajo condiciones de flujo multifásico, multidimensional y no-isotérmico. Dentro de las conclusiones obtenidas de este estudio se encuentran: primero, la equivalencia entre los métodos hibrido y determinista, segundo, la información adicional que brinda el modelo hibrido asociado a momentos estadísticos como la desviación estándar y la evolución de las PDF’s, tercero, la representación sin el uso de malla de la fenomenología asociada al sistema representado por ejemplo en el posicionamiento de frentes de concentración. Todo esto abre una rama de posibilidades al uso del SPM a la descripción de otros componentes como surfactantes, polímeros o mezclas de estos componentes. Finalmente, el SPM puede expandirse a la descripción de otros campos que afectan el medio poroso como temperatura, entre otrosColciencias y ANHCOLCIENCIAS y ANH por el soporte dado en el contrato 272-2017Doctorado156application/pdfspa660 - Ingeniería químicaThermal recoveryMultiphysics modelsPorous mediaFluid flowRetention and mobilization of nanoparticlesModelos multifísicosMedios porososFlujo de fluidosRetención y movilización de nanopartículasDesarrollo de un modelo probabilístico de flujo de materia y transporte de escalares en yacimientos de hidrocarburos sometidos a inyección de nanofluidosDevelopment of a Probabilistic Model of Flow of Matter and Transport of Scalars in Hydrocarbon Reservoirs Subjected to Nanofluid InjectionDocumento de trabajoinfo:eu-repo/semantics/workingPaperinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_8042http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/WPMedellín - Minas - Doctorado en Ingeniería - Sistemas EnergéticosDepartamento de Procesos y EnergíaUniversidad Nacional de Colombia - Sede MedellínAbdelfatah, E., Pournik, M., Shiau, B. J. Ben, & Harwell, J. (2017). Mathematical modeling and simulation of nanoparticles transport in heterogeneous porous media. Journal of Natural Gas Science and Engineering, 40, 1–16. https://doi.org/10.1016/j.jngse.2017.01.028Abou-Kassem, J.H., Farouq Ali, S.M. and Islam, M. R. (2006). Petroleum Reservoir Simulations A basic Approach. Gulf Publishing Company. Elsevier Inc.Abou-Kassem, J.H., Farouq Ali, S.M. and Islam, M. R. (2006). Petroleum Reservoir Simulations A basic Approach. Gulf Publishing Company. Elsevier Inc.Bear, J. (2018). Modeling Phenomena of Flow and Transport in Porous Media (First edit). Haifa, Israel: Springer International PublishingBerkowitz, B., Cortis, A., Dentz, M., & Scher, H. (2006). Modeling Non-fickian transport in geological formations as a continuous time random walk. Reviews of Geophysics, 44(2), 1–49. https://doi.org/10.1029/2005RG000178.Berkowitz, B., & Scher, H. (1995). On Characterization of Anomalous Dispersion in Porous and Fractured Media. Water Resources Research, 31(6), 1461–1466. https://doi.org/10.1029/95WR00483Cardona Rojas, L. (2017). Efecto de nanopartículas en procesos con inyección de vapor a diferentes calidades. Universidad Nacional de Colombia - Sede Medellín. Retrieved from http://bdigital.unal.edu.co/62562/1/1152199431.2018.pdfChen, Y., Zhou, C., & Jing, L. (2009). Modeling coupled THM processes of geological porous media with multiphase flow: Theory and validation against laboratory and field scale experiments. Computers and Geotechnics, 36(8), 1308–1329. https://doi.org/10.1016/j.compgeo.2009.06.001Curl, R. L. (1963). Dispersed phase mixing: I. Theory and effects in simple reactors. AIChE Journal, 9(2), 175–181. https://doi.org/10.1002/aic.690090207Dentz, M., Cortis, A., Scher, H., & Berkowitz, B. (2004). Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport. Advances in Water Resources, 27(2), 155–173. https://doi.org/10.1016/j.advwatres.2003.11.002El-Diasty, A. I., & Aly, A. M. (2015). Understanding the mechanism of nanoparticles applications in enhanced oil recovery. Society of Petroleum Engineers - SPE North Africa Technical Conference and Exhibition 2015, NATC 2015, 000, 944–962. https://doi.org/10.2118/175806-msJanicka, J., Kolbe, K., & Kollmann, W. (1977). Closure of the transport equation for the probability density function of turbulent scalar fields. Journal of Non-Equilibrium Thermodynamics., 4, 47–66Li, S., & Torsæter, O. (2015). Experimental Investigation of the influence of nanoparticles adsorption and transport on wettability alteration for oil wet Berea sandstone. SPE Middle East Oil and Gas Show and Conference, MEOS, Proceedings, 229–244.Liu, M., Meakin, P., & Huang, H. (2007). Dissipative particle dynamics simulation of pore-scale multiphase fluid flow. Water Resources Research, 43(August 2006), 1–14. https://doi.org/10.1029/2006WR004856Meyer, D. W., Jenny, P., & Tchelepi, H. a. (2010). A joint velocity-concentration PDF method for tracer flow in heterogeneous porous media. Water Resources Research, 46(12), 1–17. https://doi.org/10.1029/2010WR009450Morales, O. A. (2019). Simulación del mejoramiento in-situ en yacimientos de crudo pesado con el uso de nanocatalizadores en procesos de inyección de vapor. Universidad Nacional de Colombia - Sede Medellín.Sahimi, M. (2012). Dispersion in porous media, continuous-time random walks, and percolation. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 85(1). https://doi.org/10.1103/PhysRevE.85.016316Tartakovsky, D. M., & Dentz, M. (2019). Diffusion in Porous Media : Phenomena and Mechanisms. Transport in Porous Media, 130(1), 105–127. https://doi.org/10.1007/s11242-019-01262-6Tyagi, M. (2010). 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University of Austin TexasORIGINAL75050786.2020.pdf75050786.2020.pdfTesis de Doctorado en Ingeniería - Sistemas Energéticosapplication/pdf4446354https://repositorio.unal.edu.co/bitstream/unal/78554/4/75050786.2020.pdf6972f79af9e7838c6ae5a2c948da79dfMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-83895https://repositorio.unal.edu.co/bitstream/unal/78554/5/license.txte2f63a891b6ceb28c3078128251851bfMD55CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.unal.edu.co/bitstream/unal/78554/6/license_rdf42fd4ad1e89814f5e4a476b409eb708cMD56THUMBNAIL75050786.2020.pdf.jpg75050786.2020.pdf.jpgGenerated Thumbnailimage/jpeg5877https://repositorio.unal.edu.co/bitstream/unal/78554/7/75050786.2020.pdf.jpg9bcebb313b46691a9b753538c647f9d5MD57unal/78554oai:repositorio.unal.edu.co:unal/785542023-10-13 11:54:04.537Repositorio Institucional Universidad Nacional de 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