# Pipeline Modeling

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Michael V. LurieModeling of Oil Product andGas Pipeline TransportationRelated TitlesOlah, G. A., Goeppert, A., Prakash, G. K. S.Beyond Oil and Gas: The Methanol Economy2006ISBN: 978-3-527-31275-7Olah, G. A., Prakash, G. K. S. (eds.)Carbocation Chemistry2004ISBN: 978-0-471-28490-1Sheldrake, A. L.Handbook of Electrical Engineering For Practitioners in theOil, Gas and Petrochemical Industry2003E-BookISBN: 978-0-470-86478-4Michael V. LurieModeling of Oil Product andGas Pipeline TransportationThe AuthorProf. Dr. Michael V. LurieRussian State Universityof Oil and GasMoscow, Russian FederationTranslationEmmanuil G. SinaiskiLeipzig, GermanyCover PictureTrans-Alaska Pipeline All books published by Wiley-VCH arecarefully produced. Nevertheless, authors,editors, and publisher do not warrant theinformation contained in these books,including this book, to be free of errors.Readers are advised to keep in mind thatstatements, data, illustrations, proceduraldetails or other items may inadvertently beinaccurate.Library of Congress Card No.: applied forBritish Library Cataloguing-in-Publication DataA catalogue record for this book is availablefrom the British Library.Bibliographic information published bythe Deutsche NationalbibliothekDie Deutsche Nationalbibliothek lists thispublication in the Deutsche National-bibliograe; detailed bibliographic data areavailable in the Internet at. 2008 WILEY-VCH Verlag GmbH & Co.KGaA, WeinheimAll rights reserved (including those oftranslation into other languages). No part ofthis book may be reproduced in any form byphotoprinting, microlm, or any othermeans nor transmitted or translated into amachine language without written permissionfrom the publishers. Registered names,trademarks, etc. used in this book, even whennot specically marked as such, are not to beconsidered unprotected by law.Printed in the Federal Republic of GermanyPrinted on acid-free paperComposition Laserwords, ChennaiPrinting Strauss GmbH, M ovlenbachBookbinding Litges & Dopf GmbH,HeppenheimISBN: 978-3-527-40833-7VIn memory of the Teacher academician Leonid I. SedovModeling of Oil Product and Gas Pipeline Transportation. Michael V. LurieCopyright 2008 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40833-7VIIForewordThis book is dedicated rst and foremost to holders of a masters degree andpostgraduate students of oil and gas institutes who have decided to specializein the eld of theoretical problems in the transportation of oil, oil products andgas. It contains methods of mathematical modeling of the processes takingplace in pipelines when transporting these media.By the term mathematical model is understood a system of mathematicalequations in which framework a class of some processes could be studied. Thesolution of these equations provides values of parameters without carrying outmodel and, especially, full scale experiments.Physical laws determining the dynamics of uids and gases in pipes arepresented. It is then shown how these laws are transformed into mathematicalequations that are at the heart of one or another mathematical model. Inthe framework of each model, are formulated problems with the aim ofinvestigating concrete situations. In doing so there are given methods of itssolution.The book is self-sufcient for studying the subject but the text is outlined insuch a way that it impels the reader to address oneself to closer acquaintanceof considered problem containing in special technical literature.Professor Michael V. LurieMoscowModeling of Oil Product and Gas Pipeline Transportation. Michael V. LurieCopyright 2008 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40833-7IXContentsDedication Page VForeword VIIPreface XIIIList of Symbols XV1 Fundamentals of Mathematical Modeling of One-DimensionalFlows of Fluid and Gas in Pipelines 11.1 Mathematical Models and Mathematical Modeling 11.1.1 Governing Factors 31.1.2 Schematization of One-Dimensional Flows of Fluids and Gasesin Pipelines 41.2 Integral Characteristics of Fluid Volume 51.3 The Law of Conservation of Transported Medium Mass.The Continuity Equation 71.4 The Law of Change in Momentum. The Equation of Fluid Motion 91.5 The Equation of Mechanical Energy Balance 111.5.1 Bernoulli Equation 151.5.2 Input of External Energy 161.6 Equation of Change in Internal Motion Kinetic Energy 171.6.1 Hydraulic Losses (of Mechanical Energy) 181.6.2 Formulas for Calculation of the Factor (Re, ) 201.7 Total Energy Balance Equation 221.8 Complete System of Equations for Mathematical Modelingof One-Dimensional Flows in Pipelines 292 Models of Transported Media 312.1 Model of a Fluid 312.2 Models of Ideal and Viscous Fluids 322.3 Model of an Incompressible Fluid 342.4 Model of Elastic (Slightly Compressible) Fluid 34Modeling of Oil Product and Gas Pipeline Transportation. Michael V. LurieCopyright 2008 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40833-7X Contents2.5 Model of a Fluid with Heat Expansion 342.6 Models of Non-Newtonian Fluids 362.7 Models of a Gaseous Continuum 382.7.1 Model of a Perfect Gas 392.7.2 Model of a Real Gas 392.8 Model of an Elastic Deformable Pipeline 423 Structure of Laminar and Turbulent Flows in a Circular Pipe 453.1 Laminar Flow of a Viscous Fluid in a Circular Pipe 453.2 Laminar Flow of a Non-Newtonian Power Fluid in a Circular Pipe 473.3 Laminar Flow of a Viscous-Plastic Fluid in a Circular Pipe 493.4 Transition of Laminar Flow of a Viscous Fluid to Turbulent Flow 513.5 Turbulent Fluid Flow in a Circular Pipe 523.6 A Method to Control Hydraulic Resistance by Injection ofAnti-Turbulent Additive into the Flow 623.7 Gravity Fluid Flow in a Pipe 654 Modeling and Calculation of Stationary Operating Regimes of Oiland Gas Pipelines 734.1 A System of Basic Equations for Stationary Flow of anIncompressible Fluid in a Pipeline 734.2 Boundary Conditions. Modeling of the Operation of Pumps andOil-Pumping Stations 754.2.1 Pumps 754.2.2 Oil-Pumping Station 784.3 Combined Operation of Linear Pipeline Section and PumpingStation 814.4 Calculations on the Operation of a Pipeline with IntermediateOil-Pumping Stations 844.5 Calculations on Pipeline Stationary Operating Regimes inFluid Pumping with Heating 874.6 Modeling of Stationary Operating Regimes of Gas-Pipeline Sections 924.6.1 Distribution of Pressure in Stationary Gas Flow in a Gas-Pipeline 944.6.2 Pressure Distribution in a Gas-Pipeline with Great Differencein Elevations 964.6.3 Calculation of Stationary Operating Regimesof a Gas-Pipeline (General Case) 974.6.4 Investigation of Thermal Regimes of a Gas-Pipeline Section 984.7 Modeling of Blower Operation 1005 Closed Mathematical Models of One-Dimensional Non-StationaryFlows of Fluid and Gas in a Pipeline 1095.1 A Model of Non-Stationary Isothermal Flow of a Slightly CompressibleFluid in a Pipeline 1095.2 A Model of Non-Stationary Gas Flow in a Pipeline 112Contents XI5.3 Non-Stationary Flow of a Slightly Compressible Fluidin a Pipeline 1135.3.1 Wave Equation 1135.3.2 Propagation of Waves in an Innite Pipeline 1155.3.3 Propagation of Waves in a Semi-Innite Pipeline 1175.3.4 Propagation of Waves in a Bounded Pipeline Section 1195.3.5 Method of Characteristics 1215.3.6 Initial, Boundary and Conjugation Conditions 1245.3.7 Hydraulic Shock in Pipes 1275.3.8 Accounting for Virtual Mass 1345.3.9 Hydraulic Shock in an Industrial Pipeline Caused by InstantaneousClosing of the Gate Valve 1355.4 Non-Isothermal Gas Flow in Gas-Pipelines 1385.5 Gas Outow from a Pipeline in the Case of a Complete Breakof the Pipeline 1465.6 Mathematical Model of Non-Stationary Gravity Fluid Flow 1495.7 Non-Stationary Fluid Flow with Flow Discontinuitiesin a Pipeline 1526 Dimensional Theory 1576.1 Dimensional and Dimensionless Quantities 1576.2 Primary (Basic) and Secondary (Derived) Measurement Units 1586.3 Dimensionality of Quantities. Dimensional Formula 1596.4 Proof of Dimensional Formula 1616.5 Central Theorem of Dimensional Theory 1636.6 Dimensionally-Dependent and Dimensionally-IndependentQuantities 1646.7 Buckingham -Theorem 1687 Physical Modeling of Phenomena 1737.1 Similarity of Phenomena and the Principle of Modeling 1737.2 Similarity Criteria 1747.3 Modeling of Viscous Fluid Flow in a Pipe 1757.4 Modeling Gravity Fluid Flow 1767.5 Modeling the Fluid Outow from a Tank 1787.6 Similarity Criteria for the Operation of Centrifugal Pumps 1798 Dimensionality and Similarity in Mathematical Modelingof Processes 1838.1 Origination of Similarity Criteria in the Equations of aMathematical Model 1838.2 One-Dimensional Non-Stationary Flow of a Slightly CompressibleFluid in a Pipeline 1848.3 Gravity Fluid Flow in a Pipeline 1868.4 Pipeline Transportation of Oil Products. Batching 187XII Contents8.4.1 Principle of Oil Product Batching by Direct Contact 1888.4.2 Modeling of Mixture Formation in Oil Product Batching 1898.4.3 Equation of Longitudinal Mixing 1928.4.4 Self-Similar Solutions 194References 199Appendices 201Author Index 205Subject Index 207XIIIPrefaceThis book presents the fundamentals of the mathematical simulation ofprocesses of pipeline transportation of oil, oil products and gas. It is shownhow the basic laws of mechanics and thermodynamics governing the ow ofuids and gases in pipelines are transformed into mathematical equationswhich are the essence of a certain mathematical model and, in the frameworkof a given physical problem, appropriate mathematical problems are formulatedto analyze concrete situations.The book is suitable for graduate and postgraduate students of univers