Modelling of Flow and Transport in Fractal Porous Media PDF
Preview Modelling of Flow and Transport in Fractal Porous Media
Modelling of Flow and Transport in Fractal Porous Media Modelling of Flow and Transport in Fractal Porous Media Edited by Jianchao Cai State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing; Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China Liehui Zhang State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China Wei Wei Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates ©2021ElsevierInc.Allrightsreserved. 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Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusing anyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethods theyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhavea professionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,or fromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-817797-6 ForinformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:CandiceJanco AcquisitionsEditor:AmyShapiro EditorialProjectManager:LindsayLawrence ProductionProjectManager:BharatwajVaratharajan CoverDesigner:MilesHitchen TypesetbySPiGlobal,India Contents CONTRIBUTORS.........................................................................................xi ABOUT THE EDITORS...............................................................................xiii PREFACE...................................................................................................xv CHAPTER1 A brief introduction to flow and transportin fractal porousmedia........................................................................1 Jianchao Cai, Liehui Zhang,andWeiWei 1 Introduction................................................................................1 2 Fractalstructuralcharacteristicsofporousmedia..................4 3 Transportmodelbasedonfractalgeometryand othertheories.............................................................................5 4 Modellingoftransportcharacteristicsand itsapplication.............................................................................6 5 Conclusion..................................................................................8 Acknowledgments............................................................................8 References.......................................................................................8 CHAPTER2 Fractal structural parameters from images:Fractal dimension, lacunarity, and succolarity...............................11 YuxuanXia, Jianchao Cai, and WeiWei 1 Introduction..............................................................................11 2 Definitionandphysicalmeaning..............................................12 3 Calculatedmethod...................................................................12 4 Applicationsinfractalporousmedia.......................................15 4.1 Characterizationofcomplexity,heterogeneity, andanisotropy..................................................................15 4.2 Fractalmodelofreservoirpermeability.........................17 4.3 Fracturedistributioncharacterization............................19 4.4 Permeabilityprediction....................................................21 v vi Contents 5 Conclusions..............................................................................22 Acknowledgments..........................................................................23 References.....................................................................................23 CHAPTER3 Tortuosity intwo-dimensional andthree-dimensional fractal porous media: A numerical analysis......................25 WeiWei,Yuxuan Xia,and JianchaoCai 1 Introduction..............................................................................25 2 Therelationbetweentortuosityandfractaldimensions........26 3 Theoreticalcalculationoftortuosityanditsfractal dimension.................................................................................28 4 Numericalsimulationfortortuosity........................................29 5 Comparingthecalculatedresultsfortortuosity.....................32 6 Conclusion................................................................................34 Acknowledgments..........................................................................34 References.....................................................................................34 CHAPTER4 Fractalcharacteristics ofpore structureand its impact on adsorption and flowbehaviors inshale........................37 JunpingZhou, Kang Yang, Xuefu Xian,Shifeng Tian, and Jianchao Cai 1 Introduction..............................................................................37 2 Porestructureinshalecharacterizedbyvariousmethods....39 2.1 SEM..................................................................................39 2.2 Nano-CT...........................................................................42 2.3 MICP.................................................................................43 2.4 CO GAandN GA..............................................................47 2 2 2.5 NMR..................................................................................51 3 InfluencesofCO -water-shaleinteractionsonthepore 2 structureofshale.....................................................................55 3.1 Experimentalsection.......................................................55 3.2 SEManalysis....................................................................56 3.3 N GAanalysis...................................................................56 2 3.4 NMRanalysis...................................................................63 3.5 CombinationofN GAandNMRanalysis.........................66 2 4 Relationshipbetweenfractaldimensionandshalepore structureparameters,adsorption,andseepagecapacity......68 4.1 Relationshipsbetweenfractaldimensionandpore structureparametersofshale........................................68 4.2 Relationshipsbetweenfractaldimensionand adsorptioncapacityofshale............................................68 4.3 Relationshipsbetweenfractaldimensionand gasflowinshale..............................................................71 Contents vii 5 Conclusions..............................................................................72 Acknowledgments..........................................................................73 References.....................................................................................73 CHAPTER5 Modelling flow andtransport in variably saturated porous media: Applications from percolation theory and effective-medium approximation........................................79 Behzad Ghanbarian and Allen G.Hunt 1 Introduction..............................................................................79 1.1 Percolationtheory...........................................................80 1.2 Effective-mediumapproximation....................................87 2 Combininguniversalscalinglawsfrompercolation theoryandtheeffective-mediumapproximation....................90 3 Diffusion....................................................................................92 4 Electricalconductivity..............................................................93 5 Permeability.............................................................................96 5.1 Single-phasepermeability...............................................97 5.2 Waterrelativepermeability...........................................102 6 Conclusion..............................................................................111 Acknowledgment..........................................................................112 References...................................................................................112 CHAPTER6 Fractal analysison conductive heat transfer inporous media................................................................119 Xuan Qin, Jianchao Cai, and Peng Xu 1 Introduction............................................................................119 2 Exactlyself-similarfractalmodel.........................................121 3 Statisticallyself-similarfractalmodel..................................125 4 Statisticallyself-similarfractalmodelwiththeeffect ofroughsurfaces...................................................................131 5 Conclusions............................................................................136 Acknowledgment..........................................................................136 References...................................................................................136 CHAPTER7 Transport property andapplication oftree-shaped network..............................................................................141 Peng Xu, Boming Yu,Arun S. Mujumdar,and Jianchao Cai 1 Introductionandbackground.................................................141 2 Applicationoftree-shapednetwork......................................143 3 Optimizationprinciplefortree-shapednetwork...................144 3.1 TheoriginofMurray’slaw.............................................144 3.2 Optimizationoftree-shapedstructure..........................147 3.3 Fractaltree-shapednetwork.........................................150 viii Contents 4 Fluidflowintree-shapednetwork........................................153 4.1 Single-phaseflow..........................................................153 4.2 Flowinporousmedia....................................................154 5 Conclusions............................................................................157 Acknowledgments........................................................................158 References...................................................................................158 CHAPTER8 Fractalcharacterization offracture networks and production prediction formultiple fracturedhorizontal wells in unconventional gas reservoirs............................165 Qi Zhangand Guanglong Sheng 1 Introduction............................................................................165 2 Fractalfracturepropertydistribution....................................167 2.1 Fractaldimensionsofinducedfractures......................167 2.2 Fractalfractureporosity,permeability, andcompressibilitydistribution....................................168 2.3 Resultsanddiscussion..................................................170 3 DMFDEconstruction..............................................................174 3.1 Diffusivityequationsofdual-mediasystems................174 3.2 Modelvalidationandapplication...................................182 4 Conclusions............................................................................189 Acknowledgments........................................................................189 References...................................................................................189 CHAPTER9 Application offractal theory intransient pressure properties ofhydrocarbon reservoir................................193 LiehuiZhang 1 Introduction............................................................................195 2 Fractalwelltestingmodelforaverticalwellina homogeneousoilandgasreservoir......................................196 2.1 Physicalmodeldescription............................................197 2.2 Mathematicalmodelanditssolution............................197 2.3 Pressureresponseanalysis..........................................201 3 Fractalnonlinearseepageflowmodelfordeformable dualmediareservoir..............................................................204 3.1 Background....................................................................204 3.2 Problemsstatement......................................................206 3.3 Solutionanalysis............................................................211 3.4 Applicationtopressureanalysis...................................220 4 Transientpressurefractalanalysisofaverticalwellin acompositereservoir............................................................221 4.1 Physicalmodel...............................................................221 4.2 Mathematicalmodel......................................................222 Contents ix 4.3 Solutiontothemodel....................................................224 4.4 Resultsanalysis.............................................................227 5 Fractaltheoryinshalegasreservoir....................................233 5.1 Background....................................................................233 5.2 Fractalmodelforshale.................................................233 5.3 Multilayerfractaladsorptionmodel..............................236 5.4 Experimentalresultsanddiscussion............................239 6 Conclusions............................................................................246 References...................................................................................246 INDEX...................................................................................................................251
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