Analytical modelling of water pipeline start-up processes

Contiene gráficos

Autores:: Patiño Vanegas, Alberto
Payares Guevara, Carlos R.
Pereira Batista, Enrique
Coronado Hernández, Óscar Enrique
Fuertes-Miquel, Vicente S.

Tipo de recurso:

Fecha de publicación:: 2025

Institución:: Universidad Tecnológica de Bolívar

Repositorio:: Repositorio Institucional UTB

Idioma:: eng

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dc.title.eng.fl_str_mv	Analytical modelling of water pipeline start-up processes
title	Analytical modelling of water pipeline start-up processes
spellingShingle	Analytical modelling of water pipeline start-up processes 620 - Ingeniería y operaciones afines::628 - Ingeniería sanitaria Pipeline filling Entrapped air Analytical solution Transient flow Hydraulic engineering Water distribution networks Transient flow (Hydraulics) Fluid mechanics Ingeniería hidráulica - - ) - - - Ecuaciones diferenciales - Interacción aire–agua Redes de distribución de agua Flujo transitorio (Hidráulica Mecánica de fluidos ODS 6: Agua limpia y saneamiento. Garantizar la disponibilidad y la gestión sostenible del agua y el saneamiento para todos ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovación
title_short	Analytical modelling of water pipeline start-up processes
title_full	Analytical modelling of water pipeline start-up processes
title_fullStr	Analytical modelling of water pipeline start-up processes
title_full_unstemmed	Analytical modelling of water pipeline start-up processes
title_sort	Analytical modelling of water pipeline start-up processes
dc.creator.fl_str_mv	Patiño Vanegas, Alberto Payares Guevara, Carlos R. Pereira Batista, Enrique Coronado Hernández, Óscar Enrique Fuertes-Miquel, Vicente S.
dc.contributor.author.none.fl_str_mv	Patiño Vanegas, Alberto Payares Guevara, Carlos R. Pereira Batista, Enrique Coronado Hernández, Óscar Enrique Fuertes-Miquel, Vicente S.
dc.contributor.researcher.none.fl_str_mv	Carlos R. Payares Guevara Enrique Pereira-Batista Oscar E. Coronado-Hernández
dc.contributor.researchgroup.none.fl_str_mv	Grupo de Investigación Física Aplicada y Procesamiento de Imágenes y Señales- FAPIS Grupo de Investigación Gravitación y Matemática Aplicada
dc.contributor.seedbeds.none.fl_str_mv	Semillero de Investigación en Matematica y Estadistica Aplicada
dc.subject.ddc.none.fl_str_mv	620 - Ingeniería y operaciones afines::628 - Ingeniería sanitaria
topic	620 - Ingeniería y operaciones afines::628 - Ingeniería sanitaria Pipeline filling Entrapped air Analytical solution Transient flow Hydraulic engineering Water distribution networks Transient flow (Hydraulics) Fluid mechanics Ingeniería hidráulica - - ) - - - Ecuaciones diferenciales - Interacción aire–agua Redes de distribución de agua Flujo transitorio (Hidráulica Mecánica de fluidos ODS 6: Agua limpia y saneamiento. Garantizar la disponibilidad y la gestión sostenible del agua y el saneamiento para todos ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovación
dc.subject.proposal.eng.fl_str_mv	Pipeline filling Entrapped air Analytical solution Transient flow
dc.subject.lemb.none.fl_str_mv	Hydraulic engineering Water distribution networks Transient flow (Hydraulics) Fluid mechanics Ingeniería hidráulica - - ) - - - Ecuaciones diferenciales - Interacción aire–agua Redes de distribución de agua Flujo transitorio (Hidráulica Mecánica de fluidos
dc.subject.ods.none.fl_str_mv	ODS 6: Agua limpia y saneamiento. Garantizar la disponibilidad y la gestión sostenible del agua y el saneamiento para todos ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovación
description	Contiene gráficos
publishDate	2025
dc.date.accessioned.none.fl_str_mv	2025-10-20T13:31:22Z
dc.date.issued.none.fl_str_mv	2025-09-12
dc.type.none.fl_str_mv	Artículo de revista
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dc.identifier.citation.none.fl_str_mv	Patiño-Vanegas, A., Payares Guevara, C. R., Pereira-Batista, E., Coronado-Hernández, O. E., & Fuertes-Miquel, V. S. (2025). Analytical modelling of water pipeline start-up processes. Fluids, 10(242). https://doi.org/10.3390/fluids10090242
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/20.500.12585/14216
dc.identifier.doi.none.fl_str_mv	https://doi.org/10.3390/fluids10090242
identifier_str_mv	Patiño-Vanegas, A., Payares Guevara, C. R., Pereira-Batista, E., Coronado-Hernández, O. E., & Fuertes-Miquel, V. S. (2025). Analytical modelling of water pipeline start-up processes. Fluids, 10(242). https://doi.org/10.3390/fluids10090242
url	https://hdl.handle.net/20.500.12585/14216 https://doi.org/10.3390/fluids10090242
dc.language.iso.none.fl_str_mv	eng
language	eng
dc.relation.references.none.fl_str_mv	Martin, C. Entrapped Air in Pipelines. In Proceedings of the Second International Conference on Pressure Surges, London, UK, 22–24 September 1976; pp. 15–28 Liou, C.P.; Hunt, W.A. Filling of pipelines with undulating elevation profiles. J. Hydraul. Eng. 1996, 122, 534–539. Coronado-Hernández, E.; Besharat, M.; Fuertes-Miquel, V.S.; Ramos, H.M. Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: A Numerical and Experimental Analysis. Water 2019, 11, 1814. [ Zhou, L.; Liu, D.; Karney, B. Investigation of hydraulic transients of two entrapped air pockets in a water pipeline. J. Hydraul. Eng. 2013, 139, 949–959. Fuertes-Miquel, V.S.; Coronado-Hernández, O.E.; Mora-Melia, D.; Iglesias-Rey, P.L. Hydraulic modeling during filling and emptying processes in pressurized pipelines: A literature review. Urban Water J. 2019, 16, 299–311. Huang, B.; Fan, M.; Liu, J.; Zhu, D.Z. CFD Simulation of Air–Water Interactions in Rapidly Filling Horizontal Pipe with Entrapped Air. In Proceedings of the World Environmental and Water Resources Congress 2021, Virtually, 7–11 June 2021; pp. 495–507 Aguirre-Mendoza, A.M.; Paternina-Verona, D.A.; Oyuela, S.; Coronado-Hernández, O.E.; Besharat, M.; Fuertes-Miquel, V.S.; Iglesias-Rey, P.L.; Ramos, H.M. Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines. Water 2022, 14, 888 Martins, N.M.C.; Delgado, J.N.; Ramos, H.M.; Covas, D.I.C. Maximum transient pressures in a rapidly filling pipeline with entrapped air using a CFD model. J. Hydraul. Res. 2017, 55, 506–519. Zhou, L.; Liu, D.Y.; Ou, C.-q. Simulation of Flow Transients in a Water Filling Pipe Containing Entrapped Air Pocket with VOF Model. Eng. Appl. Comput. Fluid Mech. 2011, 5, 127–140. Paternina-Verona, D.A.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Saba, M.; Ramos, H.M. Digital Twin Based on CFD Modelling for Analysis of Two-Phase Flows During Pipeline Filling–Emptying Procedures. Appl. Sci. 2025, 15, 2643 Tijsseling, A.S.; Hou, Q.; Bozku¸s, Z.; Laanearu, J. Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines. J. Press. Vessel Technol. 2015, 138, 031301. Paternina-Verona, D.A.; Coronado-Hernández, O.E.; Aguirre-Mendoza, A.M.; Espinoza-Román, H.G.; Fuertes-Miquel, V.S. Three-Dimensional Simulation of Transient Flows during the Emptying of Pipes with Entrapped Air. J. Hydraul. Eng. 2023, 149, 04023007. Zaitsev, V.F.; Polyanin, A.D. Handbook of Exact Solutions for Ordinary Differential Equations; Chapman and Hall/CRC: Boca Raton, FL, USA, 2002. Payares Guevara, C.R.; Patiño-Vanegas, A.; Pereira-Batista, E.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S. An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines. Appl. Sci. 2025, 15, 6000. Berglund, E.Z.; Shafiee, M.E.; Xing, L.; Wen, J. Digital Twins for Water Distribution Systems. J. Water Resour. Plan. Manag. 2023, 149, 02523001. Gino Ciliberti, F.; Berardi, L.; Laucelli, D.B.; David Ariza, A.; Vanessa Enriquez, L.; Giustolisi, O. From digital twin paradigm to digital water services. J. Hydroinform. 2023, 25, 2444–2459. Brahmbhatt, P.; Maheshwari, A.; Gudi, R.D. Digital twin assisted decision support system for quality regulation and leak localization task in large-scale water distribution networks. Digit. Chem. Eng. 2023, 9, 100127. Chaudhry, H. Application of lumped and distributed approaches for hydraulic transient analysis. In Proceedings of the International Congress on Cases and Accidents in Fluid Systems, ANAIS, Polytechnic University of Sao Paulo, Sao Paulo, Brazil, 16–17 January 1989 Abreu, J.; Cabrera, E.; Izquierdo, J.; García-Serra, J. Flow modeling in pressurized systems revisited. J. Hydraul. Eng. 1999, 125, 1154–1169. [ Izquierdo, J.; Fuertes, V.S.; Cabrera, E.; Iglesias, P.L.; Garcia-Serra, J. Pipeline start-up with entrapped air. J. Hydraul. Res. 1999, 37, 579–590. [ Laanearu, J.; Annus, I.; Koppel, T.; Bergant, A.; Vuˇckovi´c, S.; Hou, Q.; Van’t Westende, J. Emptying of large-scale pipeline by pressurized air. J. Hydraul. Eng. 2012, 138, 1090–1100. Amer Water Works Assn. Air-Release, Air/Vacuum, and Combination Air Valves: M51; American Water Works Association: Denver, CO, USA, 2001; Volume 51. Bonilla-Correa, D.M.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Application of NewtonRaphson Method for Computing the Final Air-Water Interface Location in a Pipe Water Filling. Water 2023, 15, 1304 Braun, M. Differential Equations and Their Applications; Short version; Springer: Berlin/Heidelberg, Germany, 1978. Apostol, T.M. Calculus. Vol. I: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed.; John Wiley & Sons: New York, NY, USA, 1967; pp. 441–444. Paris, R.B. Incomplete gamma and related functions. In NIST Handbook of Mathematical Functions; U.S. Dept. Commerce: Washington, DC, USA, 2010; pp. 175–192. Boyd, J.P. Chebyshev and Fourier Spectral Methods, 2nd ed.; Dover Publications: New York, NY, USA, 2001. Muzzo, L.E.; Matoba, G.K.; Frölén Ribeiro, L. Uncertainty of pipe flow friction factor equations. Mech. Res. Commun. 2021, 116, 103764. Haaland, S.E. Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow. J. Fluids Eng. 1983, 105, 89–90.
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spelling	Patiño Vanegas, Albertovirtual::6676-1Payares Guevara, Carlos R.Pereira Batista, Enriquevirtual::6677-1Coronado Hernández, Óscar Enriquevirtual::6678-1Fuertes-Miquel, Vicente S.Carlos R. Payares GuevaraEnrique Pereira-BatistaOscar E. Coronado-HernándezGrupo de Investigación Física Aplicada y Procesamiento de Imágenes y Señales- FAPISGrupo de Investigación Gravitación y Matemática AplicadaSemillero de Investigación en Matematica y Estadistica Aplicada2025-10-20T13:31:22Z2025-09-12Patiño-Vanegas, A., Payares Guevara, C. R., Pereira-Batista, E., Coronado-Hernández, O. E., & Fuertes-Miquel, V. S. (2025). Analytical modelling of water pipeline start-up processes. Fluids, 10(242). https://doi.org/10.3390/fluids10090242https://hdl.handle.net/20.500.12585/14216https://doi.org/10.3390/fluids10090242Contiene gráficosThe start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases—water and air—typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system’s transient behaviour.1. Introduction 2. Mathematical Model 2.1 Physical Considerations of the System 2.2 Transient Model of Pipe Filling with Trapped Air 2.3 Initial and Boundary Conditions 2.4 Description of the Oscillatory Dynamics 3. Analytical Solution 3.1 Reduction of the System to a Second-Order ODE 3.2 Solution of the Autonomous Equation 3.3 Determination of Key Variables 4. Verification of the Analytical Model 4.1 Comparison Between the Integral-Form Analytical Solution and the Numerical Model 4.2 Convergence of the Series-Based Analytical Solution 4.3 Comparison with Existing Experimental Measurements 5. Conclusions 6. Acknowledgments 7. Conflicts of Interest 8. Abbreviations Appendix A. Expression of Hn in Terms of the Normalised Lower Incomplete Gamma Function γ∗ Appendix B. Expression of Kn in Terms of the Normalised Lower Incomplete Gamma Function γ∗ ReferencesSistemas dinámicosHidráulica urbana y costeraMecánica de fluidos20 páginasapplication/pdfengFluidsCopyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessAtribución 4.0 Internacional (CC BY 4.0)http://purl.org/coar/access_right/c_abf2620 - Ingeniería y operaciones afines::628 - Ingeniería sanitariaPipeline fillingEntrapped airAnalytical solutionTransient flowHydraulic engineeringWater distribution networksTransient flow (Hydraulics)Fluid mechanicsIngeniería hidráulica - - ) - - - Ecuaciones diferenciales - Interacción aire–aguaRedes de distribución de aguaFlujo transitorio (HidráulicaMecánica de fluidosODS 6: Agua limpia y saneamiento. Garantizar la disponibilidad y la gestión sostenible del agua y el saneamiento para todosODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovaciónAnalytical modelling of water pipeline start-up processesArtículo de revistainfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/redcol/resource_type/ARTTextinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Martin, C. Entrapped Air in Pipelines. In Proceedings of the Second International Conference on Pressure Surges, London, UK, 22–24 September 1976; pp. 15–28Liou, C.P.; Hunt, W.A. Filling of pipelines with undulating elevation profiles. J. Hydraul. Eng. 1996, 122, 534–539.Coronado-Hernández, E.; Besharat, M.; Fuertes-Miquel, V.S.; Ramos, H.M. Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: A Numerical and Experimental Analysis. Water 2019, 11, 1814. [Zhou, L.; Liu, D.; Karney, B. Investigation of hydraulic transients of two entrapped air pockets in a water pipeline. J. Hydraul. Eng. 2013, 139, 949–959.Fuertes-Miquel, V.S.; Coronado-Hernández, O.E.; Mora-Melia, D.; Iglesias-Rey, P.L. Hydraulic modeling during filling and emptying processes in pressurized pipelines: A literature review. Urban Water J. 2019, 16, 299–311.Huang, B.; Fan, M.; Liu, J.; Zhu, D.Z. CFD Simulation of Air–Water Interactions in Rapidly Filling Horizontal Pipe with Entrapped Air. In Proceedings of the World Environmental and Water Resources Congress 2021, Virtually, 7–11 June 2021; pp. 495–507Aguirre-Mendoza, A.M.; Paternina-Verona, D.A.; Oyuela, S.; Coronado-Hernández, O.E.; Besharat, M.; Fuertes-Miquel, V.S.; Iglesias-Rey, P.L.; Ramos, H.M. Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines. Water 2022, 14, 888Martins, N.M.C.; Delgado, J.N.; Ramos, H.M.; Covas, D.I.C. Maximum transient pressures in a rapidly filling pipeline with entrapped air using a CFD model. J. Hydraul. Res. 2017, 55, 506–519.Zhou, L.; Liu, D.Y.; Ou, C.-q. Simulation of Flow Transients in a Water Filling Pipe Containing Entrapped Air Pocket with VOF Model. Eng. Appl. Comput. Fluid Mech. 2011, 5, 127–140.Paternina-Verona, D.A.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Saba, M.; Ramos, H.M. Digital Twin Based on CFD Modelling for Analysis of Two-Phase Flows During Pipeline Filling–Emptying Procedures. Appl. Sci. 2025, 15, 2643Tijsseling, A.S.; Hou, Q.; Bozku¸s, Z.; Laanearu, J. Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines. J. Press. Vessel Technol. 2015, 138, 031301.Paternina-Verona, D.A.; Coronado-Hernández, O.E.; Aguirre-Mendoza, A.M.; Espinoza-Román, H.G.; Fuertes-Miquel, V.S. Three-Dimensional Simulation of Transient Flows during the Emptying of Pipes with Entrapped Air. J. Hydraul. Eng. 2023, 149, 04023007.Zaitsev, V.F.; Polyanin, A.D. Handbook of Exact Solutions for Ordinary Differential Equations; Chapman and Hall/CRC: Boca Raton, FL, USA, 2002.Payares Guevara, C.R.; Patiño-Vanegas, A.; Pereira-Batista, E.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S. An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines. Appl. Sci. 2025, 15, 6000.Berglund, E.Z.; Shafiee, M.E.; Xing, L.; Wen, J. Digital Twins for Water Distribution Systems. J. Water Resour. Plan. Manag. 2023, 149, 02523001.Gino Ciliberti, F.; Berardi, L.; Laucelli, D.B.; David Ariza, A.; Vanessa Enriquez, L.; Giustolisi, O. From digital twin paradigm to digital water services. J. Hydroinform. 2023, 25, 2444–2459.Brahmbhatt, P.; Maheshwari, A.; Gudi, R.D. Digital twin assisted decision support system for quality regulation and leak localization task in large-scale water distribution networks. Digit. Chem. Eng. 2023, 9, 100127.Chaudhry, H. Application of lumped and distributed approaches for hydraulic transient analysis. In Proceedings of the International Congress on Cases and Accidents in Fluid Systems, ANAIS, Polytechnic University of Sao Paulo, Sao Paulo, Brazil, 16–17 January 1989Abreu, J.; Cabrera, E.; Izquierdo, J.; García-Serra, J. Flow modeling in pressurized systems revisited. J. Hydraul. Eng. 1999, 125, 1154–1169. [Izquierdo, J.; Fuertes, V.S.; Cabrera, E.; Iglesias, P.L.; Garcia-Serra, J. Pipeline start-up with entrapped air. J. Hydraul. Res. 1999, 37, 579–590. [Laanearu, J.; Annus, I.; Koppel, T.; Bergant, A.; Vuˇckovi´c, S.; Hou, Q.; Van’t Westende, J. Emptying of large-scale pipeline by pressurized air. J. Hydraul. Eng. 2012, 138, 1090–1100.Amer Water Works Assn. Air-Release, Air/Vacuum, and Combination Air Valves: M51; American Water Works Association: Denver, CO, USA, 2001; Volume 51.Bonilla-Correa, D.M.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Application of NewtonRaphson Method for Computing the Final Air-Water Interface Location in a Pipe Water Filling. Water 2023, 15, 1304Braun, M. Differential Equations and Their Applications; Short version; Springer: Berlin/Heidelberg, Germany, 1978.Apostol, T.M. Calculus. Vol. I: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed.; John Wiley & Sons: New York, NY, USA, 1967; pp. 441–444.Paris, R.B. Incomplete gamma and related functions. In NIST Handbook of Mathematical Functions; U.S. Dept. Commerce: Washington, DC, USA, 2010; pp. 175–192.Boyd, J.P. Chebyshev and Fourier Spectral Methods, 2nd ed.; Dover Publications: New York, NY, USA, 2001.Muzzo, L.E.; Matoba, G.K.; Frölén Ribeiro, L. Uncertainty of pipe flow friction factor equations. Mech. Res. Commun. 2021, 116, 103764.Haaland, S.E. Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow. J. 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Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).open.accesshttps://repositorio.utb.edu.coRepositorio Digital Universidad Tecnológica de 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

Analytical modelling of water pipeline start-up processes

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