Slurry Transport. Fundamentals, A Historical Overview & The Delft Head Loss & Limit Deposit Velocity Framework. DHLLDV Flow Regime Diagram

Transcription

1 Durand Froude number F L (-) Line speed (m/s) Slurry Transport Fundamentals, A Historical Overview & The Delft Head Loss & Limit Deposit Velocity Framework DHLLDV Flow Regime Diagram Particle diameter (mm) Undefined He-Ho Sliding Flow (SF) 5.0 Homogeneous (Ho) 1.5 Viscous Effects Heterogeneous (He) SB-SF LDV 4.0 SB-He Sliding Bed (SB) FB-SB (LSDV) 0.5 FB-He Fixed/Stationary Bed (FB) 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 Particle diameter d (m) S.A.M. Dp= m, Rsd=1.585, Cvs=0.175, μsf=0.416 By Sape A. Miedema Edited by Robert C. Ramsdell

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3 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. Slurry Transport Fundamentals, A Historical Overview & The Delft Head Loss & Limit Deposit Velocity Framework By Sape A. Miedema Edited by Robert C. Ramsdell Copyright Dr.ir. S.A. Miedema TOC Page i of xx

4 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. Version: Wednesday, March 16, Dr.ir. S.A. Miedema All rights reserved. No part of this book may be reproduced, translated, stored in a database or retrieval system, or published in any form or in any way, electronically, mechanically, by print, photo print, microfilm or any other means without prior written permission of the author, dr.ir. S.A. Miedema. Disclaimer of warranty and exclusion of liabilities: In spite of careful checking text, equations and figures, neither the Delft University of Technology nor the author: Make any warranty or representation whatever, express or implied, (A) with respect of the use of any information, apparatus, method, process or similar item disclosed in this book including merchantability and fitness for practical purpose, or (B) that such use does not infringe or interfere with privately owned rights, including intellectual property, or (C) that this book is suitable to any particular user s circumstances; or Assume responsibility for any damage or other liability whatever (including consequential damage) resulting from the use of any information, apparatus, method, process or similar item disclosed in this book. Design & Production: Dr.ir. S.A. Miedema ISBN Book: ISBN EBook: Page ii of xx TOC Copyright Dr.ir. S.A. Miedema

5 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. This book is dedicated to our wives Thuy K.T. Miedema Nguyen and Jennifer L. Ramsdell Watkins For their loving support and patience Copyright Dr.ir. S.A. Miedema TOC Page iii of xx

6 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. Preface In dredging, trenching, (deep sea) mining, drilling, tunnel boring and many other applications, sand, clay or rock has to be excavated. The productions (and thus the dimensions) of the excavating equipment range from mm 3 /sec - cm 3 /sec to m 3 /sec. After the soil has been excavated it is usually transported hydraulically as a slurry over a short (TSHD s) or a long distance (CSD s). Estimating the pressure losses and determining whether or not a bed will occur in the pipeline is of great importance. Fundamental processes of sedimentation, initiation of motion and erosion of the soil particles determine the transport process and the flow regimes. In all cases we have to deal with soil and high density soil water mixtures and its fundamental behavior. The book covers horizontal transport of settling slurries (Newtonian slurries). Pipelines under an angle with the horizontal and non-settling (non-newtonian) slurries are not covered. Although some basic knowledge about the subject is required and expected, dimensionless numbers, the terminal settling velocity (including hindered settling), the initiation of motion of particles, erosion and the flow of a liquid through pipelines (Darcy Weisbach and the Moody diagram) are summarized. In the theory derived, the Zanke (1977) equation for the settling velocity is used, the Richardson & Zaki (1954) approach for hindered settling is applied and the Swamee Jain (1976) equation for the Darcy-Weisbach friction factor is used, Moody (1944). The models developed are calibrated using these basic equations and experiments. An overview is given of experiments and theories found in literature. The results of experiments are considered to be the physical reality. Semi empirical theories based on these experiments are considered to be an attempt to describe the physical reality in a mathematical way. These semi empirical theories in general match the experiments on which they are based, but are also limited to the range of the different parameters as used for these experiments. Some theories have a more fundamental character and may be more generic as long as the starting points on which they are based apply. Observing the results of many experiments gives the reader the possibility to form his/her own impression of the processes involved in slurry transport. Flow regimes are identified and theoretical models are developed for each main flow regime based on constant volumetric spatial concentration. The 5 main flow regimes are the fixed or stationary bed regime, the sliding bed regime, the heterogeneous regime or the sliding flow regime and the homogeneous regime. It is the opinion of the authors that the basic model should be derived for a situation where the amount of solids in the pipeline is known, the constant volumetric spatial concentration situation. A new model for the Limit Deposit Velocity is derived, consisting of 5 particle size regions and a lower limit. Based on the Limit Deposit Velocity a (semi) fundamental relation is derived for the slip velocity. This slip velocity is required to determine constant volumetric transport concentration relations based on the constant volumetric spatial concentration relations. These relations also enable us to determine the bed height as a function of the line speed. The concentration distribution in the pipe is based on the advection diffusion equation with a diffusivity related to the LDV. Finally a method is given to determine relations for non-uniform sands based on the superposition principle. The last chapter is a manual on how to reproduce the Delft Head Loss & Limit Deposit Velocity model. The DHLLDV Framework is based on numerous experimental data from literature, considered to be the reality. This book is supported by the website containing many additional graphs and tables with experimental data. The website also has spreadsheets and software implementing the model. The name Delft in the title of the DHLLDV Framework is chosen because most of the modelling is carried out at the Delft University of Technology. Another book by the author is: The Delft Sand, Clay & Rock Cutting Model. Published by IOS Press, in Open Access. Modeling is an attempt to approach nature without having the presumption to be nature. Page iv of xx TOC Copyright Dr.ir. S.A. Miedema

7 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. About the Author Dr.ir. Sape A. Miedema (November 8 th 1955) obtained his M.Sc. degree in Mechanical Engineering with honours at the Delft University of Technology (DUT) in He obtained his Ph.D. degree on research into the basics of soil cutting in relation with ship motions, in From 1987 to 1992 he was Assistant Professor at the chair of Dredging Technology. In 1992 and 1993 he was a member of the management board of Mechanical Engineering & Marine Technology of the DUT. In 1992 he became Associate Professor at the DUT with the chair of Dredging Technology. From 1996 to 2001 he was appointedelft Head of Studies of Mechanical Engineering and Marine Technology at the DUT, but still remaining Associate Professor of Dredging Engineering. In 2005 he was appointed Head of Studies of the MSc program of Offshore & Dredging Engineering and he is also still Associate Professor of Dredging Engineering. In 2013 he was also appointed as Head of Studies of the MSc program Marine Technology of the DUT. Dr.ir. S.A. Miedema teaches (or has taught) courses on soil mechanics and soil cutting, pumps and slurry transport, hopper sedimentation and erosion, mechatronics, applied thermodynamics related to energy, drive system design principles, mooring systems, hydromechanics and mathematics. He is (or has been) also teaching at Hohai University, Changzhou, China, at Cantho University, Cantho Vietnam, at Petrovietnam University, Baria, Vietnam and different dredging companies in the Netherlands and the USA. His research focuses on the mathematical modeling of dredging systems like, cutter suction dredges, hopper dredges, clamshell dredges, backhoe dredges and trenchers. The fundamental part of the research focuses on the cutting processes of sand, clay and rock, sedimentation processes in Trailing Suction Hopper Dredges and the associated erosion processes. Lately the research focuses on hyperbaric rock cutting in relation with deep sea mining and on hydraulic transport of solids/liquid settling slurries. About the Editor Robert Ramsdell (23 rd September 1964) obtained his BA degree in Mathematics at the University of California at Berkeley in Since 1989 he has worked for Great Lakes Dredge & Dock Company. Robert started as Field Engineer, eventually becoming a Project Engineer then Superintendent, working with Trailing Suction, Cutter Suction and Mechanical dredges on a variety of projects in the United States. From 1995 to 1996 Robert was the Project Engineer on the Øresund Link project in DenmarK. In 1996 he joined the Great Lakes Dredge & Dock Production Department as a Production Engineer, becoming Production Engineering Manager in In the department Robert s focus has been on developing methods and software for estimating dredge production, recruiting and training Engineers, and developing methods to analyse and improve dredge operations. A particular focus has been in modeling slurry transport for dredging estimating and production optimization. Copyright Dr.ir. S.A. Miedema TOC Page v of xx

8 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. Acknowledgements The authors want to thank: Ron Derammelaere, Edward Wasp and Ramesh Gandhi, Ausenco PSI, for reviewing the chapter about the Wasp model. Baha E. Abulnaga, director of Splitvane Engineers Inc., for reviewing the chapter about the Wilson 2 layer model, the heterogeneous model and the Wilson & Sellgren 4 component model. Pinchas Doron, CTO Aora Solar, for reviewing the chapter about the Doron & Barnea 2 and 3 layer models. Randy Gillies, Pipe Flow Technology Centre SRC, for reviewing the chapter about the Saskachewan Research Council (SRC) model. Deo Raj Kaushal, Indian Institue of Technologu in Delhi, for reviewing the chapter about the Kaushal & Tomita model. Vaclav Matousek, Czech Technical University in Prague, for reviewing the chapter about the Matousek model. Their contributions have been very valuable for having a correct reproduction of their models. The authors also want to thank all the reviewers of our conference and journal papers for their effort. This has improved the quality of our work. A special thank to the 147 th board of Gezelschap Leeghwater (the student association of Mechanical Engineering of the Delft University of Technology) for letting us use their name for the Double Logarithmic Elephant Leeghwater. Recommendations In this book, the author s intention is to introduce the slurry transport in pipelines to the readers by describing the relevant phenomena both physically and mathematically through underlying theories and governing equations. It is a focused work presented by the author to the upcoming generation of researchers and practitioners, in particular. The special feature of the book is that in a chapter, a specific phenomenon is presented starting with a physical description followed by a derivation and ending with discussion and conclusions. All throughout the book, coherence in presentation is maintained. As a concluding remark, this book can effectively be used as a guide on slurry transport in pipelines. Professor Subhasish Dey, Indian Institute of Technology Kharagpur, India Page vi of xx TOC Copyright Dr.ir. S.A. Miedema

9 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. Table of Contents Chapter 1: Introduction Introduction Flow Regimes Literature The Parable of Blind Men and an Elephant The Delft Head Loss & Limit Deposit Velocity Framework Approach of this book Nomenclature. 6 Chapter 2: Dimensionless Numbers & Other Parameters Dimensionless Numbers The Reynolds Number Re The Froude Number Fr The Archimedes Number Ar The Richarson Number Ri The Thủy Number Th or Collision Intensity Number The Cát Number Ct or Collision Impact Number The Lắng Number La or Sedimentation Capability Number The Shields Parameter θ The Bonneville Parameter D * The Rouse Number P The Stokes Number Stk The Bagnold Number Ba Applications of Dimensionless Numbers The Slurry Flow in the Pipe The Terminal Settling Velocity of a Particle Other Important Parameters The Slip Velocity and the Slip Ratio The Spatial and Delivered Volumetric Concentration Densities The Relative Submerged Density R sd Viscosities The Friction Velocity or Shear Velocity u * The Thickness of the Viscous Sub Layer δ v The Particle Size Distribution (PSD) The Angle of Internal Friction The Angle of External Friction Nomenclature. 21 Chapter 3: Pressure Losses with Homogeneous Liquid Flow Pipe Wall Shear Stress The Darcy-Weisbach Friction Factor. 24 Copyright Dr.ir. S.A. Miedema TOC Page vii of xx

10 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. 3.3 The Equivalent Liquid Model Approximation of the Darcy-Weisbach Friction Factor The Friction Velocity or Shear Velocity u * The Thickness of the Viscous Sub Layer δ v The Smallest Eddies The Relative or Apparent Viscosity Nomenclature. 32 Chapter 4: The Terminal Settling Velocity of Particles Introduction The Equilibrium of Forces The Drag Coefficient Terminal Settling Velocity Equations The Shape Factor Hindered Settling Conclusions Nomenclature. 45 Chapter 5: Initiation of Motion and Sediment Transport Initiation of Motion of Particles Introduction Models on Sediment Threshold Hjulström (1935), Sundborg (1956) and Postma (1967) Shortcomings of the existing models Known s and Unknowns Velocity Distributions Scientific Classification Engineering Classification Friction Velocity Turbulent Layer Bed roughness Viscous Sub-Layer The Transition Laminar-Turbulent The Transition Smooth-Rough The Model for Initiation of Motion The Angle of Internal Friction/the Friction Coefficient The Pivot Angle/the Dilatation Angle The Lift Coefficient Turbulence Approach Drag and Lift Induced Sliding Drag and Lift Induced Rolling. 66 Page viii of xx TOC Copyright Dr.ir. S.A. Miedema

11 Slurry Transport: Fundamentals, Historical Overview & DHLLDV Lift Induced Lifting Resulting Graphs Natural Sands and Gravels The Shields-Parker Diagram Conclusions & Discussion Nomenclature Initiation of Motion of Particles Hydraulic Transport of Sand/Shell Mixtures in Relation with the LDV Introduction The Drag Coefficient Non-Uniform Particle Size Distributions Laminar Region Turbulent Region The Exposure Level The Angle of Repose & the Friction Coefficient The Equal Mobility Criterion Shells The Limit Deposit Velocity Conclusions and Discussion Nomenclature Hydraulic Transport of Sand/Shell Mixtures Erosion, Bed Load and Suspended Load Introduction Bed Load Transport in a Sheet Flow Layer Suspended Load Transport in Open Channel Flow Governing Equations A Physical Explanation Law of the Wall Approach (Rouse (1937)) The Constant Diffusivity Approach The Linear Diffusivity Approach The Hunt (1954) Equation Conclusions & Discussion Open Channel Flow Suspended Load in Pipe Flow The Constant Diffusivity Approach, Low Concentrations The Constant Diffusivity Approach, High Concentrations The Constant Diffusivity Approach for a Graded Sand Conclusions & Discussion Pipe Flow Nomenclature Erosion, Bed Load and Suspended Load. 107 Chapter 6: Slurry Transport, a Historical Overview Introduction Early History Blatch (1906) Howard (1938). 113 Copyright Dr.ir. S.A. Miedema TOC Page ix of xx

12 Slurry Transport: Fundamentals, Historical Overview & DHLLDV Siegfried (Durepaire, 1939) O Brien & Folsom (1939) Conclusions & Discussion Early History Empirical and Semi-Emperical Models The Durand & Condolios (1952) School Soleil & Ballade (1952) Durand & Condolios (1952), (1956), Durand (1953) and Gibert (1960) The Limit Deposit Velocity The Worster & Denny (1955) Model The Zandi & Govatos (1967) Model Issues Regarding the Durand & Condolios (1952) and Gibert (1960) Model The Drag Coefficient of Durand & Condolios (1952) vs. the Real Drag Coefficient The Drag Coefficient as Applied by Worster & Denny (1955) The Drag Coefficient of Gibert (1960) The Relative Submerged Density as Part of the Equation The Graph of Zandi & Govatos (1967) The F L Value as Published by Many Authors The Darcy-Weisbach Friction Coefficient λl The Solids Effect Term in the Hydraulic Gradient Equation The Newitt et al. (1955) Model The Heterogeneous Regime The Sliding Bed Regime The Limit Deposit Velocity The Transition Heterogeneous vs. (Pseudo) Homogeneous Transport Regime Diagrams Silin, Kobernik & Asaulenko (1958) & (1962) The Fuhrboter (1961) Model The Jufin & Lopatin (1966) Model Introduction Group A: Fines Group B: Sand The Limit Deposit Velocity Broad Graded Sands or Gravels Group C: Fine Gravel Group D: Coarse Gravel Conclusions & Discussion Charles (1970) and Babcock (1970) Charles (1970) Babcock (1970) Graf et al. (1970) & Robinson (1971) Yagi et al. (1972). 195 Page x of xx TOC Copyright Dr.ir. S.A. Miedema

13 Slurry Transport: Fundamentals, Historical Overview & DHLLDV Introduction Pressure Losses Sand Gravel Limit Deposit Velocity The Slip Velocity A.D. Thomas (1976) & (1979) Head Losses The Limit Deposit Velocity The Turian & Yuan (1977) Fit Model Introduction The Regime Equations Usage of the Equations Analysis of the Turian & Yuan (1977) Equations Transition Equations Conclusions & Discussion Kazanskij (1978) The IHC-MTI (1998) Model for the Limit Deposit Velocity Conclusions & Discussion Empirical and Semi-Empirical Models Introduction The Darcy-Weisbach Friction Factor Heterogeneous Regime Durand & Condolios (1952) Newitt et al. (1955) Fuhrboter (1961) Jufin & Lopatin (1966) Group B Wilson et al. (1992) Heterogeneous DHLLDV Graded, Miedema (2014) Comparison Sliding Bed Regime Homogeneous Regime Nomenclature Early History & Empirical and Semi-Empirical Models Physical Models The Newitt et al. (1955) Model The Wasp et al. (1963) Model The Wilson-GIW (1979) Model The Doron et al. (1987) and Doron & Barnea (1993) Model The SRC Model The Kaushal & Tomita (2002B) Model The Matousek (2009) Model The Talmon (2011) & (2013) Homogeneous Regime Model. 240 Copyright Dr.ir. S.A. Miedema TOC Page xi of xx

14 Slurry Transport: Fundamentals, Historical Overview & DHLLDV The Wasp et al. (1963) Model Introduction The WASP Method Step 1: Prediction Step Step 2: Correction Steps Different Versions of the WASP Model Abulnaga (2002) Kaushal & Tomita (2002B) Lahiri (2009) The DHLLDV Framework Discussion & Conclusions Nomenclature Wasp Model The Wilson-GIW (1979) Models The Wilson-GIW (1979) Model for Fully Stratified Flow Introduction The Basic Equations for Flow and Geometry The Shear Stresses Involved The Forces Involved Output with the Wilson et al. (1992) Hydrostatic Stress Approach The Fit Functions of Wilson et al. (1992) The Fit Functions of Wilson et al. (1997) The Stratification Ratio Suspension in the Upper Layer Conclusions & Discussion The Wilson-GIW (1992) Model for Heterogeneous Transport The Full Model The Simplified Wilson Model Generic Equation Conclusions & Discussion The 4 Component Model of Wilson & Sellgren (2001) Introduction The Homogeneous or Equivalent Fluid Fraction The Pseudo Homogeneous Fraction The Heterogeneous Fraction The Fully Stratified Fraction The Resulting Equation Modified 4 Component Model Conclusions & Discussion Near Wall Lift. 289 Page xii of xx TOC Copyright Dr.ir. S.A. Miedema

15 Slurry Transport: Fundamentals, Historical Overview & DHLLDV The Demi-McDonald of Wilson (1979) Nomenclature Wilson-GIW Models The Doron et al. (1987) and Doron & Barnea (1993) Model The 2 Layer Model (2LM) The 3 Layer Model (3LM) Conclusions & Discussion Some Issues Modified Doron & Barnea Model Nomenclature Doron & Barnea Models The SRC Model Continuity Equations Concentrations The Mixture Densities Pressure Gradients & Shear Stresses The Sliding Friction The Bed Concentration Discussion & Conclusions Original Model Further Development of the Model Final Conclusions The Limit Deposit Velocity Nomenclature SRC Model The Kaushal & Tomita (2002B) Model Introduction The Hydraulic Gradient The Solids Concentration Distribution Closed Ducts Open Channel Flow Discussion & Conclusions Nomenclature Kaushal & Tomita Models The Matousek (2009) Model Introduction The Iteration Process Conclusions & Discussion Nomenclature Matousek Model Talmon (2011) & (2013) Homogeneous Regime Theory Nomenclature Talmon Model Conclusions & Discussion Physical Models The Newitt et al. (1955) Model The Wasp et al. (1963) Model The Wilson-GIW (1979) Model The Doron et al. (1987) and Doron & Barnea (1993) Model. 361 Copyright Dr.ir. S.A. Miedema TOC Page xiii of xx

16 Slurry Transport: Fundamentals, Historical Overview & DHLLDV The SRC Model The Kaushal & Tomita (2002B) Model The Matousek (2009) Model The Talmon (2011) & (2013) Homogeneous Regime Model The Limit Deposit Velocity (LDV) Introduction Wilson (1942) Durand & Condolios (1952) Newitt et al. (1955) Jufin & Lopatin (1966) Zandi & Govatos (1967) Charles (1970) Graf et al. (1970) & Robinson (1971) Wilson & Judge (1976) Wasp et al. (1977) Thomas (1979) Oroskar & Turian (1980) Parzonka et al. (1981) Turian et al. (1987) Davies (1987) Schiller & Herbich (1991) Gogus & Kokpinar (1993) Gillies (1993) Van den Berg (1998) Kokpinar & Gogus (2001) Shook et al. (2002) Wasp & Slatter (2004) Sanders et al. (2004) Lahiri (2009) Poloski et al. (2010) Souza Pinto et al. (2014) Conclusions & Discussion Nomenclature Limit Deposit Velocity Inclined Pipes Starting Points DHLLDV Framework The Liquid Properties Possible Flow Regimes Flow Regime Behavior The LSDV, LDV and MHGV The Slip Velocity or Slip Ratio The Concentration Distribution The Dimensionless Numbers used. 384 Page xiv of xx TOC Copyright Dr.ir. S.A. Miedema

17 Slurry Transport: Fundamentals, Historical Overview & DHLLDV The Type of Graph used. 384 Chapter 7: The Delft Head Loss & Limit Deposit Velocity Framework Introduction Considerations Energy Dissipation Starting Points Approach Nomenclature Introduction Flow Regimes and Scenario s Introduction Concentration Considerations The 8 Flow Regimes Identified The 6 Scenario s Identified Scenarios L1 & R Scenarios L2 & R Scenarios L3 & R Conclusions & Discussion Verification & Validation L1: Fixed Bed & Heterogeneous, Constant C vs R1: Heterogeneous, Constant C vt L2: Fixed & Sliding Bed & Heterogeneous, Constant C vs R2, R3: Sliding Bed & Sliding Flow, Constant C vt L1, R1, L2, R2:, Homogeneous L3, R3: Sliding Bed & Sliding Flow, Constant C vs Discussion & Conclusions Nomenclature Flow Regimes & Scenario s A Head Loss Model for Fixed Bed Slurry Transport The Basic Equations for Flow and Geometry The Shear Stresses Involved The Forces Involved The Relative Roughness The Darcy-Weisbach friction factor first attempt Conclusion & Discussion The Darcy Weisbach friction factor second attempt Conclusions & Discussion Nomenclature Fixed Bed Regime A Head Loss Model for Sliding Bed Slurry Transport The Friction Force on the Pipe Wall The Active/Passive Soil Failure Approach The Hydrostatic Normal Stress Distribution Approach The Normal Force Carrying The Weight Approach. 447 Copyright Dr.ir. S.A. Miedema TOC Page xv of xx

18 Slurry Transport: Fundamentals, Historical Overview & DHLLDV The Submerged Weight Approach Summary The 3 Layer Model Nomenclature Sliding Bed Regime A Head Loss Model for Heterogeneous Slurry Transport Introduction Physical Energy Considerations Estimating the Slip Velocity Simplified Models Simplified Model for Small Particles, d<0.3 mm Simplified Model for Medium Sized Particles, 0.3 mm d 2 mm Simplified Model for Large Particles, d>2 mm Summary Approximations Comparison with Durand & Condolios (1952) The Slip Velocity Applied to the Fuhrboter Equation Simplified Model for Small Particles, d<0.3 mm Simplified Model for Medium Sized Particles, 0.3 mm d 2 mm Simplified Model for Large Particles, d>2 mm Summary Approximations The Concentration Eccentricity Coefficient Verification & Validation New Dimensionless Numbers Discussion & Conclusions Nomenclature Heterogeneous Regime A Head Loss Model for Homogeneous Slurry Transport Homogeneous Transport The Equivalent Liquid Model (ELM) Approach Method 1: The Talmon (2011) & (2013) Homogeneous Regime Equation Method 2: The Approach using the Nikuradse (1933) Mixing Length Method 3: Adding the von Driest (Schlichting, 1968) Damping to Method Method 4: The Law of the Wall Approach Comparison of the Models Method 5: Applying a Concentration Profile to Method Applicability of the Model Conclusions Nomenclature Homogeneous Regime The Sliding Flow Regime Literature & Theory Verification & Validation Nomenclature Sliding Flow Regime The Limit Deposit Velocity. 519 Page xvi of xx TOC Copyright Dr.ir. S.A. Miedema

19 Slurry Transport: Fundamentals, Historical Overview & DHLLDV Introduction Experimental Data Equations & Models Conclusions Literature Starting Points DHLLDV Framework The Transition Fixed Bed Sliding Bed (LSDV) The Transition Heterogeneous Homogeneous (LDV Very Fine Particles) The Transition Sliding Bed Heterogeneous (LDV Coarse Particles) The Transition Sliding Bed Homogeneous (LSBV) The Limit Deposit Velocity (LDV All Particles) Introduction Very Small Particles, The Lower Limit Smooth Bed Rough Bed The Resulting Limit Deposit Velocity Curves Conclusions & Discussion Nomenclature Limit Deposit Velocity The Slip Velocity Introduction Slip Ratio in the Heterogeneous Regime Comparison with the Yagi et al. (1972) Data Step Derivation of the Slip Ratio at High A b/a p Ratios Comparison with the Yagi et al. (1972) Data Step The Region Around The Limit Deposit Velocity Comparison with the Yagi et al. (1972) Data Step Construction of the Slip Ratio Curve, Step Conclusions & Discussion The Slip Velocity, a Pragmatic Solution Nomenclature Slip Velocity The Concentration Distribution The Advection Diffusion Equation The Diffusivity Based on the LDV Simplification of the Equations Nomenclature Concentration Distribution The Transition Heterogeneous vs. Homogeneous in Detail The Transition Heterogeneous-Homogeneous The Lift Ratio Limit Deposit Velocity & Concentration Distribution Resulting Relative Excess Hydraulic Gradient Curves Conclusions & Discussion Nomenclature The Bed Height. 583 Copyright Dr.ir. S.A. Miedema TOC Page xvii of xx

20 Slurry Transport: Fundamentals, Historical Overview & DHLLDV Concentration Transformation Equations Fixed Bed Sliding Bed Some Results Nomenclature Bed Height Influence of the Particle Size Distribution Introduction The Particle Size Distributions Particle Diameter d 50=0.2 mm Particle Diameter d 50=0.5 mm Particle Diameter d 50= mm Particle Diameter d 50= mm Nomenclature PSD Influence Inclined Pipes Stationary Bed Regime Sliding Bed Regime Heterogeneous Regime Homogeneous Regime Sliding Flow Regime The Limit Deposit Velocity Conclusions & Discussion Nomenclature Inclined Pipes. 610 Chapter 8: Usage of the DHLLDV Framework Introduction Default Equations Used In This Book The Liquid Properties The Fixed or Stationary Bed Regime The Shear Stresses Involved The Forces Involved The Sliding Bed Regime The Heterogeneous Transport Regime The Homogeneous Transport Regime The Sliding Flow Regime The Resulting E rhg Constant Spatial Volumetric Concentration Curve The Transition Heterogeneous Regime - Homogeneous Regime Introduction The Lift Ratio The Heterogeneous Equation The Homogeneous Equation The Resulting Relative Excess Hydraulic Gradient Determining the Limit Deposit Velocity Introduction. 625 Page xviii of xx TOC Copyright Dr.ir. S.A. Miedema

21 Slurry Transport: Fundamentals, Historical Overview & DHLLDV Very Small & Small Particles Large & Very Large Particles The Resulting Upper Limit Froude Number The Lower Limit The Resulting Froude Number Constructing the Transport Concentration Curves The Bed Height The Concentration Distribution Graded Sands & Gravels A Set of Resulting Graphs Conclusions & Discussion Nomenclature DHLLDV Framework. 645 Chapter 9: Comparison of the DHLLDV Framework with Other Models Introduction The Transition Velocity Heterogeneous-Homogeneous Considerations The DHLLDV Framework Durand & Condolios (1952) & Gibert (1960) Newitt et al. (1955) Fuhrboter (1961) Jufin & Lopatin (1966) Zandi & Govatos (1967) Turian & Yuan (1977) 1: Saltation Regime Turian & Yuan (1977) 2: Heterogeneous Regime Wilson et al. (1992) (Power, Non-Uniform Particles) Wilson et al. (1992) (Power 1.7, Uniform Particles) Wilson & Sellgren (2012) Near Wall Lift Model The Saskachewan Research Council Model Examples Heterogeneous versus Homogeneous The Influence of the Particle Diameter & Terminal Settling Velocity The Influence of the Pipe Diameter The Influence of the Concentration The Influence of the Sliding Friction Coefficient The Influence of the Relative Submerged Density The Influence of the Line Speed Summary A 254 m Diameter Pipe (1 inch) A 508 m Diameter Pipe (2 inch) A m Diameter Pipe (4 inch) A m Diameter Pipe (8 inch) A m Diameter Pipe (16 inch). 665 Copyright Dr.ir. S.A. Miedema TOC Page xix of xx

22 Slurry Transport: Fundamentals, Historical Overview & DHLLDV A m Diameter Pipe (30 inch) A 1.2 m Diameter Pipe Conclusions & Discussion Heterogeneous-Homogeneous Transition The Limit Deposit Velocity Analysis Conclusions Limit Deposit Velocity Graphs Nomenclature Comparisons. 677 Chapter 10: Application of the Theory on a Cutter Suction Dredge Head Loss Equation The Limit Deposit Velocity The Resulting Head Loss versus Mixture Flow Graph The Relative Excess Hydraulic Gradient of Pump and Pipeline. 682 Chapter 11: Publications. 683 Chapter 12: Bibliography. 685 Chapter 13: List of Figures. 697 Chapter 14: List of Tables. 709 Chapter 15: Appendices Appendix A: List of Solids Densities Appendix B: List of Liquid Densities Appendix C: List of Mesh Sizes Appendix D: Flow Regime Diagrams. 721 Page xx of xx TOC Copyright Dr.ir. S.A. Miedema

23 Introduction. Chapter 1: Introduction. 1.1 Introduction. In dredging, the hydraulic transport of solids is one of the most important processes. Since the 50 s many researchers have tried to create a physical mathematical model in order to predict the head losses in slurry transport. One can think of the models of Durand & Condolios (1952) & Durand (1953), Worster & Denny (1955), Newitt et al. (1955), Gibert (1960), Fuhrboter (1961), Jufin & Lopatin (1966), Zandi & Govatos (1967) & Zandi (1971), Turian & Yuan (1977), Doron et al. (1987) & Doron & Barnea (1993), Wilson et al. (1992) and Matousek (1997). Some models are based on phenomenological relations and thus result in semi empirical relations, other tried to create models based on physics, like the two and three layer models. It is however the question whether slurry transport can be modeled this way at all. Observations in our laboratory show a process which is often nonstationary with respect to time and space. Different physics occur depending on the line speed, particle diameter, concentration and pipe diameter. These physics are often named flow regimes; fixed bed, shearing bed, sliding bed, heterogeneous transport and (pseudo) homogeneous transport. It is also possible that more regimes occur at the same time, like, a fixed bed in the bottom layer with heterogeneous transport in the top layer. It is the observation of the author that researchers often focus on a detail and sub-optimize their model, which results in a model that can only be applied for the parameters used for their experiments. 1.2 Flow Regimes Literature. Based on the specific gravity of particles with a magnitude of 2.65, Durand (1953) proposed to divide the flows of non-settling slurries in horizontal pipes into four flow regimes based on average particle size as follows: 1. Homogeneous suspensions for particles smaller than 40 μm (mesh 325) 2. Suspensions maintained by turbulence for particle sizes from 40 μm (mesh 325) to 0.15 mm (mesh 100) 3. Suspension with saltation for particle sizes between 0.15 mm (mesh 100) and 1.5 mm (mesh 11) 4. Saltation for particles greater than 1.5 mm (mesh 11) Due to the interrelation between particle sizes and terminal and deposition velocities, the original classification proposed by Durand has been modified to four flow regimes based on the actual flow of particles and their size (Abulnaga, 2002). 1. Flow with a stationary bed 2. Flow with a moving bed and saltation (with or without suspension) 3. Heterogeneous Heterogeneous mixture with saltation and rolling Heterogeneous mixture with all solids in suspension 4. Pseudo homogeneous and/or homogeneous mixtures with all solids in suspension The four regimes of flow described can be represented by a plot of the hydraulic gradient versus the average speed of the mixture as in Figure The 4 transitional velocities are defined as: V1: velocity at or above which the bed in the lower half of the pipe is stationary. In the upper half of the pipe, some solids may move by saltation or suspension. Below V1 there are no particles above the bed. V2: velocity at or above which the mixture flows as an asymmetric mixture with the coarser particles forming a moving/saltating bed. V3: velocity at or above which all particles move as an asymmetric suspension and below which the solids start to settle and form a moving bed. V4: velocity at or above which all solids move as an almost symmetric suspension. Wilson (1992) developed a model, which will be discussed in detail later, for the incipient motion of granular solids at V2, the transition between a stationary bed and a sliding bed. He assumed a hydrostatic pressure exerted by the solids on the wall. Wilson also developed a model for heterogeneous transport with a V50, where 50% of the solids are in a (moving/saltating) bed and 50% in suspension. This percentage is named the stratification ratio. The transitional velocity V3 is extremely important because it is the speed at which the hydraulic gradient is at a minimum. Although there is evidence that solids start to settle at lower line speeds in complex mixtures, operators and engineers often refer to this transitional velocity as the speed of deposition or critical velocity. Figure shows the 4 regimes and the velocity and concentration profiles. At very high line speeds the pressure drop will reach an equivalent liquid curve asymptotically. Whether or not this occurs at practical line speeds depends on the particle diameter, pipe diameter and the concentration. For large particle diameters and concentrations it may seem like the pressure drop reaches the water curve asymptotically, but at higher line speeds the pressure drop will increase again up to an equivalent liquid model. Whether or not this equivalent liquid model contains the mixture density instead of the water density, or some value in between is still the question. Copyright Dr.ir. S.A. Miedema TOC Page 1 of 738

24 Particle Diameter d (mm) Flow with a Stationary Bed D p = 1 inch D p = 6 inch Hydraulic gradient i m (m water/m pipe) Stationary Bed Without Suspension Stationary Bed With Suspension Moving Bed/Saltating Bed Heterogeneous Transport Pseudo Homogeneous Transport Homogeneous Transport Slurry Transport: Fundamentals, Historical Overview & DHLLDV. Hydraulic gradient i m versus Line speed v ls V Water V2 V3 V4 Slurry V1: Start Fixed Bed With Suspension V2: Start Moving Bed/Saltating Bed V3: Start Heterogeneous Transport V4: Start (Pseudo) Homogeneous Transport Line speed v ls (m/sec) S.A.M. Figure 1.2-1: The 4 regimes and transitional velocities (Abulnaga, 2002), Dp=0.15 m, d50=2 mm, Cvt=0.2. Figure gives the impression that the 4 flow regimes will always occur sequentially. Starting from a line speed zero and increasing the line speed, first the fixed or stationary bed will occur without suspension, at a line speed V1 part of the bed starts to erode and particles will be in suspension, at a line speed V2 the remaining bed will start to slide while the erosion increases with the line speed, at a line speed V3 the whole bed is eroded and the heterogeneous regime starts and finally at a line speed V4 the heterogeneous regime transits to the (pseudo) homogeneous regime. In reality not all the regimes have to occur, depending on the particle size, the pipe diameter and other governing parameters Flow Regimes according to Newitt et al. (1955) & Durand & Condolios (1952) Flow with a Moving Bed D p =1 inch Limit of Stationary Bed Dp=1 inch 100 Limit of Stationary Bed Dp=6 inch D p =6 inch 00 Flow as a Heterogeneous Suspension Limit of Moving Bed, All Dp Flow as a Homogeneous Suspension Heterogeneous vs Homogeneous Dp=1 inch 10 Heterogeneous vs Homogeneous Dp=6 inch Line Speed v ls (m/sec) S.A.M. Figure 1.2-2: Flow regimes according to Newitt et al. (1955). Page 2 of 738 TOC Copyright Dr.ir. S.A. Miedema

25 Introduction. Figure shows the regimes according to Newitt et al. (1955). From this figure it is clear that not all regimes have to occur and that the transition velocities depend on the particle and the pipe diameter. The influence of the volumetric concentration is not present in this graph. Figure shows the flow regimes as used by Matousek (2004) also showing velocity and concentration distributions. Figure 1.2-3: Different mixture transport regimes. 1.3 The Parable of Blind Men and an Elephant. Wilson et al. (1992), (1997) and (2006) refer to the old parable of 6 blind men, who always wanted to know what an elephant looks like. Each man could touch a different part of the elephant, but only one part. So one man touched the tusk, others the legs, the belly, the tail, the ear and the trunk. The blind man who feels a leg says the elephant is like a pillar; the one who feels the tail says the elephant is like a rope; the one who feels the trunk says the elephant is like a tree branch; the one who feels the ear says the elephant is like a hand fan; the one who feels the belly says the elephant is like a wall; and the one who feels the tusk says the elephant is like a solid pipe. They then compare notes and learn they are in complete disagreement about what the elephant looks like. When a sighted man walks by and sees the entire elephant all at once, they also learn they are blind. The sighted man explains to them: All of you are right. The reason every one of you is telling a different story is because each one of you touched a different part of the elephant. So actually the elephant has all the features you mentioned. The story of the blind men and an elephant originated in the Indian subcontinent from where it has widely diffused. It has been used to illustrate a range of truths and fallacies; broadly, the parable implies that one's subjective experience can be true, but that such experience is inherently limited by its failure to account for other truths or a totality of truth. At various times the parable has provided insight into the relativism, opaqueness or inexpressible Copyright Dr.ir. S.A. Miedema TOC Page 3 of 738

26 Slurry Transport: Fundamentals, Historical Overview & DHLLDV. nature of truth, the behavior of experts in fields where there is a deficit or inaccessibility of information, the need for communication, and respect for different perspectives (source Wikipedia). Figure 1.3-1: Flow regimes and the Double Logarithmic Elephant Leeghwater. Figure shows a comparison between the parable of the elephant and slurry flow. Slurry transport also has many truths, points of view. Experiments can be carried out with small versus large pipes, small versus large particles, low versus high concentrations, low versus high line speeds, low versus high particle diameter versus pipe diameter ratios, laminar versus turbulent flow, Newtonian versus non Newtonian liquids, low versus high solid densities, etc. Depending on the parameters used, experiments are carried out in different flow regimes, or maybe at the interface between flow regimes, resulting in different conclusions. Wilson et al. (1992), (1997) and (2006) show with this parable that the research of slurry flow often focusses on different parts or aspects of the process, but not many times it will give an overview of the whole process. The starting point is that every researcher tells the truth, based on his/her observations. Combining these truths gives an impression of the aggregated truth, which is still not the whole truth. The 6 men for example cannot look inside the elephant, only touch the outside. The internal structure of slurry flow may however be very important to understand the slurry flow behavior. The 6 men cannot access the memory of the elephant, which is supposed to be very good. In long pipelines the overall behavior of the slurry flow does depend on the history, so the memory function is also important. The Double Logarithmic Elephant is named after the student association of Mechanical Engineering of the Delft University of Technology, Leeghwater, using the elephant as their symbol. Leeghwater stands for strength, precision and of course hydraulic transport through the proboscis. 1.4 The Delft Head Loss & Limit Deposit Velocity Framework. In the following chapters the different models from literature will be analyzed, leading to a new integrated model based on a new classification of the flow regimes. This new model is named the Dredging Head Loss & Limit Deposit Velocity Framework (DHLLDV Framework). The Framework is integrated in a way that all flow regimes are described in a consistent way showing the transition velocities. The model is validated by many experiments from literature and experiments carried out in the Delft University Dredging Engineering Laboratory for particles ranging from 5 to 45 mm, pipe diameters ranging from 254 to 0.9 m and relative submerged densities ranging from 0.24 to 4 ton/m 3. The model does not just give hydraulic gradient relations, but also Limit Deposit Velocity relations, slip ratio relations (the relation between the volumetric spatial concentration and the volumetric delivered concentration), bed height relations and a concentration distribution model. The Framework also gives a tool to determine the influence of the grading of the sand or gravel. The starting point of the model is a uniform sand or gravel and a constant volumetric spatial concentration. Based on the hydraulic gradient and slip ratio relations, the volumetric delivered concentration hydraulic gradient relations are derived. The latter is very important for practical applications. Page 4 of 738 TOC Copyright Dr.ir. S.A. Miedema

27 Introduction. 1.5 Approach of this book. The book covers horizontal transport of settling slurries (Newtonian slurries). Pipelines under an angle with the horizontal and non-settling (non-newtonian) slurries are not covered. The book has the following approach: 1. Chapter 1 explains the context of slurry flow, based on flow regimes as indentified in literature. 2. Chapter 2 gives definitions of the dimensionless numbers and other important parameters as used in the book. Definitions are the language of engineers and scientists and are thus essential for the understanding. 3. Chapter 3 deals with homogeneous Newtonian liquid flow through horizontal circular pipes. Equations and graphs are given to determine the Darcy Weisbach friction factor. The Swamee Jain (1976) equation for the Darcy Weisbach (Moody (1944)) friction factor is used in this book. Also the influence of the concentration of very fine particles on the liquid properties is discussed. 4. Chapter 4 explains the terminal settling velocity of particles, including hindered settling. In the theory derived, the Zanke (1977) equation for the settling velocity is used and the Richardson & Zaki (1954) approach for hindered settling is applied. 5. Chapter 5 shows the basics of the initiation of motion of particles and shells, which is important to understand the behavior of the interface between a bed and the liquid flow above the bed, especially for the stationary and sliding bed regimes. Initiation of motion is the start of sediment motion, but at higher flow velocities also erosion and/or sediment transport will occur. The basics of sediment transport as bed load and suspended load are discussed for open channel flow and pipe flow. 6. Chapter 6 gives an overview of the historical developments of models to predict head losses in slurry flow. The overview starts with the early history, followed by empirical and semi empirical models. The models are given, analysed and discussed and issues of the models are addressed. The models for the Limit Deposit Velocity (LDV) are discussed, analysed and compared. Conclusions are drawn regarding the behavior of the LDV related to the solids, liquid and flow parameters. A number of 2 layer models (2LM) and 3 layer models (3LM) based on physics are given and analysed, as well as other physical models. 7. Chapter 7 describes the new Delft Head Loss & Limit Deposit Velocity (DHLLDV) Framework. The DHLLDV Framework is based on uniform sands or gravels and constant spatial volumetric concentration. This chapter starts with an overview of 8 flow regimes and 6 scenarios. The new models for the main flow regimes, the stationary bed regime without sheet flow and with sheet flow, the sliding bed regime, the heterogeneous regime, the homogeneous regime and the sliding flow regime, are derived and discussed. A new model for the Limit Deposit Velocity is derived, consisting of 5 particle size regions and a lower limit. Based on the LDV a method is shown to construct slip velocity or slip ratio curves from zero line speed to the LDV and above. Based on the slip ratio, the constant delivered volumetric concentration curves can be constructed. Knowing the slip ratio, the bed height for line speeds below the LDV can be determined. New equations are derived for this. The transition from the heterogeneous regime to the homogeneous regime requires special attention. First of all, this transition line speed gives a good indication of the operational line speed and allows to compare the DHLLDV Framework with many models from literature. Secondly the transition is not sharp, but depends on 3 velocities. The line speed where a particle still fits in the viscous sub layer, the transition line speed heterogeneous-homogeneous and the line speed where the lift force on a particle equals the submerged weight of the particle. Finally the grading of the Particle Size Distribution (PSD) is discussed. A method is given to construct resulting head loss, slip velocity and bed height curves for graded sands and gravels. 8. Chapter 8 summarises the DHLLDV Framework. The essential equations are given, with reference to the original equations, to reproduce the DHLLDV Framework, accompanied with flow charts. 9. In chapter 9 the DHLLDV Framework is compared with other models from literature. 10. Chapter 10 shows how to apply the DHLLDV Framework on the hydraulic transport of a cutter suction dredge. 11. Chapter 11 gives the journal and conference publications of the authors on which this book is based. The DHLLDV Framework models have been verified and validated with numerous experimental data. The results of experiments and calculations are shown in standard graphs showing Hydraulic Gradient versus Line Speed i(vls), the Relative Excess Hydraulic Gradient versus the Line Speed Erhg(vls) and the Relative Excess Hydraulic Gradient versus the Liquid Hydraulic Gradient (the clean water resistance) Erhg(il). The advantage of the Erhg(il) graph is that this type of graph is almost independent of the values of the spatial concentration Cvs and relative submerged density Rsd. The advantage of the im(vls) graph is that is clearly shows head losses versus flow and thus gives an indication of the required power and specific energy, combined with pump graphs. Most experimental data is shown in the Relative Excess Hydraulic Gradient versus the Liquid Hydraulic Gradient graph, Erhg(il). Copyright Dr.ir. S.A. Miedema TOC Page 5 of 738