Citation |

- Permanent Link:
- http://ufdc.ufl.edu/UF00091089/00001
## Material Information- Title:
- A laboratory study of mud slurry discharge through pipes
- Series Title:
- UFLCOEL-98013
- Creator:
- Phinai Jinchai, 1968-
University of Florida -- Coastal and Oceanographic Engineering Dept - Place of Publication:
- Gainesville Fla
- Publisher:
- Coastal & Oceanograhic Engineering Dept.
- Publication Date:
- 1998
- Language:
- English
- Physical Description:
- xvii,85 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Drilling muds ( lcsh )
Rheology ( lcsh ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (M.S.)--University of Florida, 1998.
- Bibliography:
- Includes bibliographical references (leaf 58).
- Statement of Responsibility:
- by Phinai Jinchai.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 41608410 ( OCLC )
## UFDC Membership |

Full Text |

UFL/COEL-98/013
A LABORATORY STUDY OF MUD SLURRY DISCHARGE THROUGH PIPES by Phinai Jinchai Thesis 1998 A LABORATORY STUDY OF MUD SLURRY DISCHARGE THROUGH PIPES By PHINAI JINCHAI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 1998 ACKNOWLEDGMENT First of all, I would like to express my gratitude to my advisor and committee chairman, Professor Ashish J. Mehta, for his continuous guidance and encouragement during my years of study in the Coastal and Oceanographic Department at the University of Florida. This study has been a challenging experience in my life. I also would like to express my appreciation to Professor Robert G. Dean and Professor Peter Y. Sheng for serving on my committee, for their advice, comments, and patience in reviewing this thesis. Thanks to Helen T. Twedell and John M. Davis for their help in the Archives, Jim E. Joiner for his assistance with the experiments at the Coastal Engineering Laboratory, and Becky Hudson and Lucy E. Hamm for their kindness which helped directly and indirectly in the completion of this study. Deep appreciation goes to Professor Michel K. Ochi, Professor Robert J. Thieke, and Professor Daniel M. Hanes for the valuable knowledge they provided from their classes. The support of fellow students, Jianhua Jiang, Yeon-sihk Chang, Jun Lee, Chenxia Qiu, Erica Carr,Haifeng Du, Jie Cheng, Kerry Anne Donohue, Ki Jin Park, Craig Conner, Roberto Liotta, Vadim Alymov, and Hugo N. Rodriguez, is also highly appreciated. My final acknowledgment is reserved for my wife, Wararak Jinchai, for her love, support and encouragement throughout the time here, and my parents and my sisters for their support all my life. Support for the experiments conducted was obtained from the U.S.Army Engineer Waterways Experiment Station, Vicksburg, MS, under contract DACW39-96-M-2100. TABLE OF CONTENTS P=g ACKNOWLEDGM[ENT......................................................................1i LIST OF FIGURES......................................................................... vi LIST OF TABLES...........................................................................x LIST OF SYMBOLS .........................................................................xii ABSTRACT ................................................................................. xvi CHAPTERS 1. INTRODUCTION ..................................................................1. 1.1 Need for Investigation ......................................................... 1 1.2 Objective, Tasks and Scope................................................... 3 1.3 Outline of Chapters............................................................ 4 2. SLURRY FLOW IN PIPES ........................................................... 6 2.1 Equations of Motion in Pipes ................................................. 6 2. 1.1 General Problem ...................................................... 6 2.1.2 Poiseuile Flow Problem .............................................. 7 2.2 Viscous Model................................................................ 10 2.2.1 Flow Type ........................................................... 10 2.2.2 Apparent Viscosity .................................................. 10 2.2.3 End and Slip Effects and Corrections............................... 13 2.2.4 Slurry Flow Curve................................................... 17 2.2.5 Three Empirical Non-Newtonian Models ......................... 17 2.3 Poiseuille Flow Velocity Distribution ..................................... 19 2.3.1 Newtonian Fluid..................................................... 19 2.3.2 Bingham Plastic...................................................... 20 2.3.3 Power-Law Fluid.................................................... 22 3. EXPERIMENTAL SETUP, PROCEDURES AM) MATERIALS .............. 24 3.1 Coaxial Cylinder Viscometer ................................................................... 24 3.2 Horizontal Pipe Viscometer .................................................................... 25 3.3 Sediments and Slurries ............................................................................ 26 3.3.1 Sediment and Fluid Properties ..................................................... 26 3.3.2 M ud Slurries ............................................................................... 29 4. EXPERIM ENTAL RESULTS .......................................................................... 34 4.1 Rheometric Results ................................................................................. 34 4.1.1 Power-Law for M ud Flow ........................................................... 34 4.1.2 Power-Law Coeffi cients ............................................................... 36 4.2 End and Slip Effects ............................................................................ 38 4.3 Power-Law Parameters ........................................................................... 40 4.4 Slurry Discharge with Sisko M odel ......................................................... 46 4.5 Calculation of Slurry Discharge ............................................................... 49 4.6 Power-Law Correlations with Slurry CEC ............................................... 52 5. CONCLUDING COM M ENTS ........................................................................... 55 5.1 Conclusions ............................................................................................ 55 5.2 Comments ............................................................................................. 55 5.3 Recommendation for Future Studies ....................................................... 56 BIBLIOGRAPHY ...................................................................................................... 58 APPENDICES A SLURRY VISCO SITY D ATA ...................................................................... 59 B DEPENDENCE OF POWER LAW PARAMETERS ON DENSITY ............. 70 C VELOCITY PROFILES AND CORRESPONDING DISCHARGES ............. 80 BIOGRAPHICAL SKETCH ...................................................................................... 85 LIST OF FIGURES Figure PgW 1.1 Potential for entrainment and spreading of contaminated mud at intake and discharge points during operation..................................... 2 2.1 Pipe flow definition sketch ............................................................... 8 2.2 Typical pressure-drop/flow rate relationship for slurry flow in pipes................. 11 2.3 Plot of In r versus In -r Dashed line is tangent to the curve through a data point ........................................................................ 12 2.4 Equivalent "extra length" due to end effects............................................ 16 2.5 Length and pressure components in two pipes, where and are the fully developed flow sections for longer and shorter pipes, respectively........... 17 2.6 Slurry flow curve for non-Newtonian fluid. Dashed line is tangential extrapolation to obtain the yield stress........................................... 18 2.7 Velocity profile for a generalized Newtonian fluid with Q=0.003 m. and R=O.1I m...................................................... 21 2.8 Schematic of velocity profile for a Bingham plastic .................................... 21 2.9 Velocity profile for a Bingham fluid, with Q=0.003 m3/s, R=O. 1, for slurry density p= 1000, 1, 198 and 1, 314 kg/in3 (from right to left) ............ 22 2.10 Velocity profiles for a power-law fluid, with Q=0.003 m3/s, R0. 1 in., for flow index n=0.5,1.0, 2.0 and 3.0 (from left to right)......................... 23 3.1 Brookfield viscometer with an attached spindle shearing a clay slurry................ 24 3.2 Schematic drawing of a coaxial cylinder viscometer .................................... 25 3.3 Schematic drawing of experimental setup for the horizontal pipe viscometer (HjPV) ................................................................ 26 3.4 Photograph of H PV setup ................................................................................ 27 4.1 Comparison between pseudoplastic (shear-thinning) and Newtonian flow curves. The nature of the shear-thinning curve is such that while at low shear rates its viscosity is higher than the constant value for the Newtonian case (line), with increasing shear rate the pseudoplastic curve becomes asymptotically parallel to the Newtonian line, hence the pseudoplastic viscosity approaches that of the N ew tonian case ..................................................................................... 35 4.2 Data obtained from the end-effect correction experiment ................................. 39 4.3 Plot of(P/4t,) vs. 'c, for slip effect correction ................................................... 39 4.4 Plot of(P/4tw) vs. 1/R for slip effect correction ............................................... 40 4.5 Excess apparent viscosity as a function of shear rate for kaolinite slurry no. 1 ..... 44 4.6 Variation ofil. with density of kaolinite slurries ............................................... 45 4.7 Variation of c with density of kaolinite slurries ................................................. 45 4.8 Variation of n with density of kaolinite slurries .................................................. 45 4.9 Computed velocity profiles and corresponding discharges for slurry no. 1. Line is numerical solution using Sisko model; dots represent analytic N ew tonian solution ............................................................................... 51 4.10 Computed velocity profiles and discharge for slurry no.23 .................................. 51 4.11 Variation of TI with slurry CEC (CECu, ) for all slurries .................................. 53 4.12 Variation of c with slurry CEC (CECj,, ) for all slurries .................. 53 4.13 Variation of n with slurry CEC (CECdUP,) for all slurries ............................... 54 A -i V iscosity data for slurry no. 1 ............................................................................ 59 A -2 V iscosity data for slurry no.2 ............................................................................. 59 A -3 V iscosity data for slurry no.3 ............................................................................. 59 A -4 V iscosity data for slurry no.4 .............................................................................. 59 A-5 Viscosity data for slurry no. 5............................................................ 60 A-6 Viscosity data for slurry no.6............................................................ 60 A-7 Viscosity data for slurry no.7............................................................ 61 A-8 Viscosity data for slurry no. 8............................................................ 61 A-9 Viscosity data for slurry no.9 ........................................................... 61 A-10 Viscosity data for slurry no. 10.......................................................... 61 A-l I Viscosity data for slurry no.11I.......................................................... 62 A- 12 Viscosity data for slurry no. 12........................................................... 62 A- 13 Viscosity data for slurry no. 13 .......................................................... 62 A- 14 Viscosity data for slurry no. 14........................................................... 62 A-15 Viscosity data for slurry no. 15........................................................... 63 A- 16 Viscosity data for slurry no. 16........................................................... 63 A- 17 Viscosity data for slurry no. 17........................................................... 63 A- 18 Viscosity data for slurry no. 18........................................................... 63 A- 19 Viscosity data for slurry no. 19........................................................... 64 A-20 Viscosity data for slurry no.20........................................................... 64 A-21 Viscosity data for slurry no.21 1.......................................................... 64 A-22 Viscosity data for slurry no.22........................................................... 64 A-23 Viscosity data for slurry no.23........................................................... 65 A-24 Viscosity data for slurry no.24........................................................... 65 A-25 Viscosity data for slurry no.25........................................................... 65 A-26 Viscosity data for slurry no.26 .......................................................... 65 A-27 Viscosity data for slurry no.27 ............................................................................ 66 A-28 Viscosity data for slurry no.28 ............................................................................ 66 A-29 Viscosity data for slurry no.29 ........................................................................... 66 A-30 Viscosity data for slurry no.30 ............................................................................ 66 A-31 Viscosity data for slurry no.31 ........................................................................... 67 A-32 Viscosity data for slurry no.32 ............................................................................ 67 A-33 Viscosity data for slurry no.33 ............................................................................ 67 A-34 Viscosity data for slurry no.34 ............................................................................ 67 A-35 Viscosity data for slurry no.35 ............................................................................ 68 A-36 Viscosity data for slurry no.36 ............................................................................ 68 A-37 Viscosity data for slurry no.37 ............................................................................ 68 A-38 Viscosity data for slurry no.38 ............................................................................ 68 A-39 Viscosity data for slurry no.39 ............................................................................ 69 A-40 Viscosity data for slurry no.40 ............................................................................ 69 A-41 Viscosity data for slurry no.41 ............................................................................ 69 A-42 Viscosity data for slurry no.42 ............................................................................ 69 B-i Variation of power-law coefficients with density for kaolinite slurries. Top: r-; middle: c; bottom: n ................................................................. 70 B-2 Variation of power-law coefficients with density for kaolinite slurries. Top: r1; middle: c; bottom: n ................................................................. 71 B-3 Variation of power-law coefficients with density for kaolinite slurries. Top: ril; middle: c; bottom: n ............................................................ 72 B-4 Variation of power-law coefficients with density for kaolinite slurries. Top: ril; middle: c; bottom: n ................................................................. 73 B-5 Variation of power-law coefficients with density for kaolinite slurries. Top: rlI; m iddle: c; bottom : n ............................................................ 74 B-6 Variation of power-law coefficients with density for kaolinite slurries. Top: r-; m iddle: c; bottom : n ............................................................ 75 B-7 Variation of power-law coefficients with density for kaolinite slurries. Top: Tl_; m iddle: c; bottom : n ................................................................. 76 B-8 Variation of power-law coefficients with density for kaolinite slurries. Top: r.; m iddle: c; bottom : n .............................................................. 77 B-9 Variation of power-law coefficients with density for kaolinite slurries. Top: r ; m iddle: c; bottom : n ............................................................... 78 B-10 Variation of power-law coefficients with density for kaolinite slurries. Top: r ; m iddle: c; bottom : n .............................................................. 79 C-i Velocity profiles and corresponding discharges for slurry no. 1 ....................... 80 C-2 Velocity profiles and corresponding discharges for slurry no.7 ....................... 80 C-3 Velocity profiles and corresponding discharges for slurry no. 11 ..................... 81 C-4 Velocity profiles and corresponding discharges for slurry no. 15 ..................... 81 C-5 Velocity profiles and corresponding discharges for slurry no. 19 ..................... 82 C-6 Velocity profiles and corresponding discharges for slurry no.23 ..................... 82 C-7 Velocity profiles and corresponding discharges for slurry no.27 ..................... 83 C-8 Velocity profiles and corresponding discharges for slurry no.31 ..................... 83 C-9 Velocity profiles and corresponding discharges for slurry no.35 .................... 84 C-10 Velocity profiles and corresponding discharges for slurry no.39 .................... 84 LIST OF TABLES Table DA" 3.1 Chemical composition of kaolinite ........................................................................ 27 3.2 Chemical composition of bentonite ...................................................................... 27 3.3 Chemical composition of attapulgite (palygorskite) ............................................... 28 3.4 Chemical composition of water ............................................................................. 28 3.5 Size distribution of kaolinite ................................................................................. 29 3.6 Size distribution of bentonite ............................................................................... 30 3.7 Size distribution of attapulgite ............................................................................... 31 3.8 Properties of mud slurries tested ........................................................................... 31 4.1 End and slip effects experimental data of 1,236 kg/r3 slurry of 50%K+50%A ..... 38 4.2 End and slip effects experimental data of 1,125 kg/m3 slurry of 90%K+ 10%B .......... 38 4.3 Pressure drop, discharge, shear rate and wall stress data from HPV tests .............. 42 4.4 Sisko model coefficients and HPV flow Reynolds number ...................................... 47 4.5 Low pressure HPV test parameters for selected slurries ........................................ 50 LIST OF SYMBOLS A B C C; CEC CECAttapulgit CECBentonite CECKaolinitc CEC,1y D DIFF fAttapulgite fBentonite fKaolinite fWater K g gr, g0 Attapulgite Bentonite Consistency Integration constant Cation exchange capacity of clay Cation exchange capacity of Attapulgite Cation exchange capacity of Bentonite Cation exchange capacity of Kaolinite Slurry cation exchange capacity Pipe diameter Viscosity difference between Sisko model and experimental data Weight fraction of Attapulgite Weight fraction of Bentonite Weight fraction of Kaolinite Weight fraction of Water Kaolinite Acceleration due to gravity Gravity acceleration components L Pipe length Le Extra length for end effects LL Length of longer pipe LL' Fully developed flow section for longer pipe Ls Length of shorter pipe s Fully developed flow section for shorter pipe M Number of data point for the method of least squares m Iteration index N Total number of slurry layers in pipe n Flow behavior coefficient p Pressure Po Pressure at the beginning of the pipe PL Pressure at the distance, L Axp Pressure loss APe Pressure loss due to end effects APL Pressure loss in the longer pipe APs Pressure loss in the shorter pipe Q Pipe discharge Qflud Fluid discharge Qolug Plug discharge R Pipe radius r Radial distance coordinate ro Re Ref t U U S V V VV z Pr' 0 Vli+I z F IPDo slip slip YLj Radial distance coordinate for a solid plug Reynolds number Reynolds number of the slurry flow in the pipe Time Flow velocity Slip velocity Velocity Horizontal velocity of the slurry flow in the pipe Mean velocity Plug velocity Velocity components Layer Velocity Cylindrical coordinate, z Empirical constant Slip effect coefficient Flow rate Flow rate with no slip effects Flow rate without slip effects Shear rate Strain tensor Shear rate at the wall Normalized radial distance coordinate Apparent viscosity Value of rj at infinite shear rate rij Experimental slurry viscosity 0 Cylindrical coordinate, 0 Plastic viscosity p Fluid density T Shear stress lTij Shear stress tensor Tw Wall shear stress TY Yield shear stress of mud Tzz' Trr' Too Normal shear stress with contain the elastic effect Trz' Tre' lz Shear stresses T1 1/2 Shear stress at rI = 0.5 [t DPressure gradient in the pipe (DL Pressure gradient in the longer pipe (s Pressure gradient in the shorter pipe Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science A LABORATORY STUDY OF MUD SLURRY DISCHARGE THROUGH PIPES By Phinai Jinchai August 1998 Chairman: Dr. A.J. Mehta Major Department: Coastal and Oceanographic Engineering Given the need to pump comparatively high density mud slurries though dredged material discharge pipes to avoid causing a contamination problem, this study examined the question of whether relevant mud properties can be tested ahead of time in order to predict the rate of slurry flow in pipes. To that end, laboratory rheometric experiments were conducted to assess the dependence of slurry flow rate on mud composition and density. Muds consisted of clays and clay mixtures of varying density. The selected clays included a kaolinite, an attapulgite and a bentonite. The choice of these clays was based on the need to vary mud properties widely in terms of their non-Newtonian rheology, as characterized by the three-parameter Sisko power-law model for apparent viscosity variation with shear rate. The overall slurry density range tested was 1,125 kg/m3 to 1,500 kg/m3. Power-law parameters (characterizing ultimate viscosity, consistency and pseudoplasticity) as functions of mud composition and density were obtained by testing the slurries in two type of rheometers. For low shear rate, a coaxial cylinder viscometer (CCV) of the Brookfield type generating annular couette flows was used. For comparatively high shear rates, a specially designed horizontal pipe viscometer (HPV) generating Poiseuille flow was used. The latter apparatus consisted of a 2.54 cm i.d. and 3.1 m long, horizontally positioned, PVC pipe through which slurry flow was driven by a piston-diaphragm pump. Rheometric results obtained by combining the CCV an HPV data confirmed the pseudoplastic (shear thinning) behavior of all slurries. For slurry of given composition, the ultimate viscosity, consistency and the degree of pseudoplasticity generally increased with density. A slurry cation exchange capacity (CECjy) is introduced as a cohesion characterizing parameter dependent on the weight fractions of clays and water in the slurry. It is shown that the power-law parameters correlate reasonable well with CEC.j,,y, which therefore makes it a convenient measure of the rheology of slurries composed of pure clays and clay mixtures. The steady-state slurry transport equation for the Sisko power-law fluid is solved numerically to yield the velocity distribution in the pipe and the corresponding discharge. To test the model, including the applicability of the derived power-law for the slurries, additional tests were carried out in the HPV at lower pumping pressures than those used to determine the power-law coefficients. It is shown that for most slurries tested the calculated discharge agrees reasonably with that measured. The approach developed in this study leads itself to further exploration as a method designed to test the bottom mud to be dredged for its pumping requirements. CHAPTER I INTRODUCTION 1. 1 Need for Investigation Internationally, there is a growing concern over the water contamination. For example, like many countries, Thailand has its Pollution Control Department for monitoring and reporting coastal water quality on yearly basis. In the past few years, the water quality in the Gulf of Thailand and the Chao Praya River (the main Thai navigation channel) has been tested. The results have indicated that this area has had a growing rate of water contamination so that, for instance, the mercury levels in the proximity of the area are now higher than at other estuaries and pristine seawater resources (Thai Pollution Control Department, 1997). The major causes of the water contamination are industrial activities and the effects of dredging of contaminated fine sediments. Minimization of the contamination of the ambient waters while dredging of bottom mud is in progress is an important consideration because this sort of contamination is the major negative environmental effect of dredging. As coastal navigation channels are deepened by dredging due to requirements for greater draft vessels calling at ports, the need to maintain these channels against sedimentation has also risen. Disposal of dredged material has become problematic in many urbanized estuaries (Marine Board, 1985). Added to this is the problem of contaminated bottom sediments, which can pose a threat 2 to habitats both at the intake point and at the discharge point, as a result of the potential for the dispersal of sediment and associated pore fluid into the ambient waters. Referring to Fig. 1. 1, it is a common practice to cut and loosen bottom mud at the intake point mechanically or by high-pressure water jets in preparation for the suction of the diluted slurry and its transport to the out-take point. In this process the water content of mud may increase from, say, 20% for a compacted bed to as much as 400% in a diluted slurry (Parchure and Sturdivant, 1997). It is therefore evident that this procedure can cause contaminant dispersal at both ends, especially where strong currents or waves are present. The question therefore arises as to whether it is possible to transport the slurry at in situ bottom density, as this would be a "cleaner" operation and therefore would be highly desirable for areas where sediment at toxic "hot spots" needs to be removed and transported as safely as possible. Although this seems like an obvious solution, the reason for diluting the mud at the intake point in the first place is that it is often difficult to transport undiluted, relatively dense bottom mud without a very high-pressure pump. Discharge Fig. 1. 1 Potential for entrainment and spreading of contaminated mud at intake and discharge points during dredging operation. 3 In general, because bottom mud composition and density can vary widely, the pumping requirements can also vary accordingly. It is therefore a matter of considerable engineering interest to have the know-how to determine, ahead of time, what the pumping requirements will be in a given situation, in order to design the dredging operation and its execution. Since the transport of a slurry of given composition and density depends on the rheological behavior of the slurry (Heywood, 1991; Wasp et al., 1977), by determining this behavior of mud to be dredged in a rheometer should make it possible to ascertain: 1) if the bottom mud can or cannot be transported without dilution, and 2) what the rate of transport will be. This laboratory study was therefore concerned with a two-step procedure, namely: 1) relating slurry discharge in a pipe to mud rheology, and 2) relating mud rheology characterizing coefficients to mud composition and density. Accordingly, the study objective, tasks and scope were as follows. 1.2 Objective. Tasks and Scope The objective of this study was to correlate mud slurry discharge in a pipe with mud composition and density through mud rheology, as a basis for developing a predictive tool for assessing pumping requirements for transportation of relatively dense dredged bottom mud. The associated tasks were as follows: 1. To select muds of widely varying composition. 2. For mud of given composition and density, to determine its rheological behavior. 3. To pump each mud of given composition and density through a horizontal pipe, and measure the discharge and pressure loss. 4 4. For mud of given composition, to determine the relationship between discharge, density and rheology characterizing parameters. 5. To explore the possibility of using the above relationship as a predictive tool for assessing the transportability of a given bottom mud. The experimental scope of the work was defined by the choice of muds selected and the facility used for experiments. Since this work was of an exploratory nature, it was decided to select pure clays and their mixtures in water at different densities as mud slurries. The rheological behavior of each slurry was determined by combining the data from two types of rheometers: a coaxial cylinder viscometer (CCV) and a horizontal pipe viscometer (HPV). A Brookfield (model LVT) viscometer was used as CCV for testing the slurries at low shear rates. For relatively high shear rates, an HPV was designed specially. This particular type of viscometer was chosen because it also served as the arrangement used to measure slurry discharge at different pump pressures. The bench-top apparatus consisted of a 2.54 cm i.d. and 3.1 long PVC pipe through which mud was made to flow due to pressure applied by a diaphragm pump. The objectives of the study were met entirely by data obtained using these two types of viscometers, as described in the subsequent chapters. 1.3 Outline of Chapters In Chapter 2, the slurry transport problem is formulated in terms of Poiseuille flow in horizontal pipes. Also, in this chapter, rheological models for slurry flow, and analytical solutions for slurry discharge are given. The experimental setup, materials used and test 5 procedures are described in Chapter 3. Results of rheometry along with the flow simulations with reference to the overall objective of the study are in Chapter 4. Study conclusion and comments are given in Chapter 5. Finally, relevant references are given in Chapter 6. CHAPTER 2 SLURRY FLOW IN PIPES 2.1 Equations of Motion in Pipes 2.1.1 General Problem The general equations of motion in a pipe in cylindrical coordinates (z, r, 0) are as follows: Incompressible continuity equation: 1 arV + avo +V r ar r aO 8z (2.1) Momentum equations: r-component: a Vr a Vr Vo Vr V Vr) p +pg+ I arr aro + (2.2) p +V + +V = +pg +--+ + (2) at ar r ao r vz 8z-r rr r r 86 r az 0-component: SaV Vo Vo V V Vo VrVo 8 Vo, iap 1 2 2 z (2.3) at a r r O6 r z rr r a0 dz z-component: aV aVz Vo a V aV -p 1 Iarrz 1 aToz azz a V a + +V z +pg -+ + (2.4) zva +V zI _____ ___ ___at ,r r z z r ar r ae az where -zz T, tOO are the normal stresses; z, zrO, Oz are shear stresses; Vz, Vr, V are the velocity components in z, r and 0 directions, gz, gr, go are the corresponding gravity acceleration components; t is the time; p is the pressure and p is the density of mixture of water and sediment. 2.1.2 Poiseuille Flow Problem In this section, the steady, isothermal, axial and laminar flow of an incompressible fluid in a pipe (Fig. 2.1), known as Poiseuille flow, will be described. For further details see (Jinchai et al., 1998). It is assumed that the flow is symmetric and that the axial (z) velocity component is the only non-zero component. These conditions can only be satisfied if V=V=O0, Vz f(O) (2.5) Under the above conditions, the continuity Eq. (2.1) reduces to dV -0 (2.6) so that V -f(z), i.e., V, = V(r) only. The rate of strain tensor therefore becomes 0 dV/dr 0 0 1 0 y = dVz/dr 0 0 = 1 0 0 (2.7) 0 0 0 0 0 0 so that the shear stress tensor has, at most, the following non-zero components t zz = rz 0 t 0 rz t 0 rr 0 'Coo Accordingly, the three component momentum equations are simplified as z-component: -Pg'- (rrz) 8z r ar r-component: ap _1 ar8 Tcoo r rr r r 0-component: 1 p r ap -pg,=0 r 86 IL I .-. V(r) I Fig. 2.1 Pipe flow definition sketch. (2.8) (2.9) (2.10) (2.11) 9 Considering that the velocity varies only in the r direction, all internal stresses which depend on flow deformation must also be functions only of r. Using this condition, differentiating Eq. (2.10) with respect to z leads to IP = 0= (2.12) az ar) ar az) In other words, the pressure gradient, (ap/az), is independent of r. Therefore, the pressure gradient along the pipe can be calculated as ap/az=(pL-pO)/L, where p0 is the pressure at the beginning of the pipe and pLis its value at a distance L. Considering Eq. (2.9), the left hand side is independent of r, whereas the right side is a function only of r. This can be true only if both are equal to a constant ((I): 1 Pgz-- (r,) (2.13) ap~z r ar Integrating Eq. (2.13) leads to r= D+ Ci (2.14) r2 r The integration constant, C,, must be zero, since otherwise an infinite stress would be predicted at the center (r=O). Considering the stress exerted by the fluid on the pipe wall UR 20 R . .R (2.15) w 27uR 2 then Eq. (2.14) becomes rD r Z 2 R W (2.16) 10 which is the final form of the equation of motion for Poiseujille flow. It is valid for either laminar (Newtonian or non-Newtonian) or turbulent flow. 2.2 Viscous Model 2.2.1 Flow ype In terms of flow properties for homogeneous, non-settling slurries considered here under steady state in pipes, the flow type, the apparent viscosity and the flow curve (j' versus -r) must be obtained. The experimental data required include the pressure drop .6p over the fully developed flow length L and the volumetric flow rate Q (or mean velocity Vm). From the plot of ln(.6p/L) versus lnQ or lnVm shown in Fig. 2.2, where n is called the power-law index, the flow type can be determined. The flow can be laminar or turbulent, and Newtonian or Non- Newtonian. 2.2.2 Apparent Viscosity For a non-Newtonian fluid, the ratio of shear stress and shear rate is not constant, i.e., doubling the shear stress will not result in twice the shear rate, or vice versa. Thus the viscosity is not independent of the shear rate. Therefore, a function called the apparent viscosity is defined as: ri~y)=i(2.17) Now, from Eq. (2.16) it is evident that measurement of the pressure gradient cD provides a direct means of determination of the shear stress at any point in the pipe. The calculation of the apparent viscosity of the fluid also requires the determination of the shear rate at some 11 point in the pipe. An expression for this shear rate can be obtained by considering the following relation for the volumetric flow rate, Q: Q=f2TrrVz(r)dr 0 (2.18) Integrating Eq. (2.18) by parts, with the condition that Vz=0, at r=R, leads to R R dV Q= Ifr 2dV=-tfr2 dr S0 dr (2.19) Turbulent Slope 1.75 to 2 Non-Newtonian: S Shear thinning Newtonian: a "ngLaminar, Slope 1 Decreasing n value InQ or InV., Fig. 2.2 Typical pressure-drop/flow rate relationships for slurry flow in pipes. InI Fig. 2.3 Plot of Int, versus lnP. Dashed line is tangent to the curve through a point. Equation (2.19) can now be used to change the variables from r to t (for a given wall shear stress cand R) to give Q= ruR 3 z T 2 'dt (2.20) w 0 By taking the derivative of Eq. (2.20) with respect to w,, we obtain d(PT,3) =4z2Y w (2.21) dTw where P=4Qh/tRR3 and is the shear rate at the wall. Solving Eq. (2.21) for ?' leads to Tw( dP 3P Y w-=- -- (2.22) 4 dt wW 13 If we let n/=dln(,)/dlnP, Eq. (2.22) can also be written as 3n+1 r (2.23) Based on Eq. (2.23), the apparent viscosity takes the form z z( 4n / ( M (2.24) Yw ,, 3n'+1 From the laboratory data (measurements of discharge and pressure drop), Intr can be plotted against ln1P, as shown in Fig. 2.3. For that purpose, the wall shear stress, -w, is calculated from Eq. (2.15). Values of the coefficient, n,' are obtained manually from tangents drawn to the curve, as shown by the example in Fig.2.3. Where necessary, end and slip corrections must be applied to correct for the measured values of the pressure drop, Ap. These corrections are described next. 2.2.3 End and Slip Effects and Corrections 2.2.3.1 End effects A major error which may arise in pipe flow measurements is due to end effects. Near the entrance and exit regions of the pipe, the velocity profile is not constant along the pipe but is in a state of transition between the flow configurations outside and inside the pipe, and the pressure gradient is not constant over these regions. Therefore, if the measurement of pressure drop Ap is not carried out within the fully developed flow section, a correction for .p becomes necessary. End effects can be corrected for experimentally in various ways. One approach is to determine an equivalent "extra length" (Le) of the pipe that would have to be added to the actual length if the total measured 6p were that for an entirely fully developed flow region. This can be done as follows. Consider the total pressure gradient due to friction in fully developed flow in the pipe (of length L), plus an extra pressure drop due to end effects that would be equivalent to friction in fully developed flow over an additional length Le: P Pg= 2(2.25) L+L R If the pipe is horizontal (g--O) and noting that Tw is a unique function ofF as shown in Eq. (2.22), Eq. (2.25) can be rearranged to give: Ap =-2t4 L) =f(F)( L+-=S) (2.26) As a result, if several pipes of different L/R ratios are used, and Ap is plotted against L/R for the same value of F in each pipe, the plot should be linear if the flow becomes fully developed within each pipe, and the intercept at A6p=O determines L, (Fig.2.4). The intercept on the .p axis at L/R=O is the pressure drop (*pe) due to the combined end effects. Since a different value of Le would be obtained for each value ofF, L}R can be empirically correlated with r. An alternate procedure involves the use of two pipes of the same diameter, operating at the same flow rate (Q or F). Using subscript S for the shorter pipe and L for the longer, the various lengths and pressure components are defined in Fig. 2.5. Care must 15 be taken in choosing the pipe lengths so that errors in pressure measurement are not unduly compounded by taking differences of large numbers. Assume the pressure gradient in the fully developed flow sections of the longer and shorter pipes are identical, i.e., (DL='Ds=cD. Then following relationships are satisfied LPL = Lp +(LL -L)1 =Ape +LL'4( (2.27) APs= A/P+(Ls-L)D =Ap +L'4 (2.28) Subtracting Eq. (2.28) from Eq. (2.27), the true pressure gradient in the fully developed flow section reads DPLLPS (2.29) LL -LS 2.2.3.2 Slip effect An error in the measurement of Q can arise from an apparent slip between the fluid and the solid wall. This effect is actually due to the general inhomogeneity of the fluid near the wall. However, the extent of the region affected is often very small, so that the effect may be accounted for by assuming an effective slip velocity (us) superimposed upon the fluid in the pipe, and modifying Eq. (2.20), i.e., O=TuR2+ rTR 3f2tdr (2.30) w 0 rt R + fr29dv (2.31) 4T R w 0 where 13P=us/w is a slip coefficient. This coefficient can be evaluated as follows: 1. Using various pipes of the same length but different radii, plot P/4twversus I, for each pipe. If 3=0, these curves should coincide. If not, the curves will be distinct, in which case one must proceed as follows: 2. At constant t, plot P/4tw versus 1/R from the above curves. This plot should be linear with a slope =3; 3. Repeat step 2 for various values of u, and then plot P3 versus T. The appropriate value of F to use in evaluating ,w is then a "corrected" value corresponding to no slip: 4[=30 )(2.32) rno-slip (slip)measured R(2.32) R Ap* r=const. L, /R LIR Fig. 2.4 Equivalent "extra length" due to end effects. Short pipe, radius R xps I A Long pipe, radius R PLL IL, LL' Fig. 2.5 Length and pressure components in two pipes, where LL' andLs' are the fully developed flow sections for longer and shorter pipes, respectively. 2.2.4 Slurry Flow Curve After completing the above calculations, the slurry flow curves characterizing the theological behavior of the slurry can be drawn, i.e., plots of c,, and 11 versus j'w (Fig. 2.6). The yield stress of the mud, zy is obtained by extrapolating the curve of -c versus Y w. Next we will attempt to determine the empirical relationships between cz, and Tj versus 2.2.5 Three Empirical Non-Newtonian Models The most successful attempts at describing the steady rate of shear-stress behavior of non-Newtonian fluids have been largely empirical. The following represents three of the more common empirical models which have been used to represent the various classes of experimentally observed non-Newtonian behavior. r77 77 versus y r, versus y Yw Fig. 2.6 Slurry flow curve for non-Newtonian fluids. Dashed line is tangential extrapolation to obtain the yield stress. 2.2.5.1 Bingham plastic Given T and both positive, this model is t=-ty+t for cty (2.33) =O for 2.2.5.2 General power-law fluid This is described as r =c (2.35) This is also a two-parameter model, with n as the flow index, c as the consistency. The apparent viscosity for this model is Tl =cy2.2.5.3 Ellis model In this model, the apparent viscosity is obtained as 1 = 'r =1 +( / ) -1 (2.36) The three parameters in Eq. (2.36) are pt, -:1/2 and a. Here cl/2 is the value of t at which rj=0.5[., and a is an empirical constant. 2.3 Poiseuille Flow Velocity Distribution 2.3.1 Newtonian Fluid We will obtain the velocity distribution for a Newtonian fluid of viscosity, 1. Given the boundary condition Vz=O at r=R (2.37) The solution for the velocity profile is 2 R ] The corresponding volumetric flow rate is Q_ 4w (2.39) and the ratio between V and mean velocity V,, is Vz 2 [ -( (2.40) At steady state V. is constant, and the velocity profile only depends on R. A sample of velocity profile in the pipe is shown in Fig. 2.7. 2.3.2 Bingham Plastic For a material that conforms to the Bingham plastic model, the rheological formulas are given in Eqs. (2.33) and (2.34). If Irz,< ty, the material will behave like a rigid solid. Therefore, from the pipe centerline to the point at which Itrz I= y, the material moves as a" solid plug", as shown in Fig.2.8. Solving Eqs. (2.21), (2.33) and (2.34) leads to: for ro r-R, where ro=(ty/T)R: V R 1-- (2.41) z21j R 11 R and for rsro: plug 2I 1- (2.42) The corresponding volumetric flow rate is: 0 0.5 1 1.5 2 V/V. Fig. 2.7 Velocity profile for a R=O.1 m. U ", Newtonian fluid with Q=0.003 m3/s and Fig. 2.8 Schematic of velocity profile for a Bingham plastic. Q Qf ,dRQp g 1 4 + 1 41 4 Q =Qfluid plug I 3 - (2.43) Examining of above solution indicates that the velocity profile depends on Ty, rn, R and Q. Sample velocity profiles are shown in Fig. 2.9. 0.5 0.5 0 0.5 1 1.5 2 V/V. Fig. 2.9 Velocity profile for a Bingham fluid, with Q=O.003m3/s, R=0. I m, for slurry density p=1000, 1099, 1198 and 1314 kg/m3 (from right to left). 2.3.3 Power-Law Fluid The rheological equation of state for a power-law fluid takes the form (2.35). Combining Eqs. (2.16) and (2.35) leads to the following solutions: Velocity profile: (2.44) Volumetric flow rate: V= n nw 1- r. z n+I1 p R Q ( n ( R) 3 Ratio between V, and mean velocity V : Vj 3n+l[1 (-] 311J +I Therefore, when Vm is constant, the velocity profile only depends on n and R. Examples of velocity profiles are shown in Fig. 2.10. 0 0.5 1 1.5 2 2.5 V/Vm Fig. 2.10 Velocity profiles for a power-law fluid, with Q=O.003m3/s, R=O. lm, for flow index n=0.5, 1.0, 2.0 and 3.0 (from left to right). (2.45) (2.46) CHAPTER 3 EXPERIMENTAL SETUP, PROCEDURES AND MATERIALS 3.1 Coaxial Cylinder Viscometer The coaxial cylinder viscometer (CCV) (Fig. 3.2) used was of the Brookfield (model LVT) type (Fig. 3.1). The general procedure for using the CCV involves rotating a metallic bob (i.e., a right-circular cylinder) or a spindle at a selected rate in a beaker containing mud slurry of known density. In the present case the spindle could rotate at fixed speeds, giving a shear rate range of 0.063 to 20.4 Hz. The torque generated by the rotation of the spindle was recorded from a readout meter. The shear stress, which is proportional to the torque, was calculated directly from the torque using a formula supplied by the maker (Brookfield Dial Viscometer, 1981). Fig. 3.1 Brookfield (model LVT)viscometer with an attached spindle shearing a clay slurry. 24 25 Outer Torque Inner Cylinder Cylinder (Bob Fig. 3.2 Schematic drawing of a coaxial cylinder viscometer. The Brookfield viscometer is actually equipped with a series of spindles. The spindle required to shear a particular slurry depends on the density and viscosity of the slurry. Use of these spindles along with the charts provided yield values of the apparent viscosity, il, which is inherently corrected for end-effects in this viscometer (Brookfield Dial Viscometer, 1981). 3.2 Horizontal Pipe Viscometer The horizontal pipe viscometer (HPV) constructed in the Coastal Engineering Laboratory of the University of Florida is shown schematically in Fig. 3.3, and a photographic view is given in Fig. 3.4. The 3.1 m long, 2.54 cm i.d. PVC pipe was clamped on to the a work-bench, with one end attached to a piston-diaphragm pump and the other end open, with a bucket receptacle to collect the slurry. The ARO model 6661A3-344-C non-metallic double-diaphragm pump was operated at a nominal pressure of 40 psi (276 kPa). Pressurized air required at the pump inlet was supplied by a compressed air line observed in Fig. 3.4. Over the central 2.46 m length of the pipe the pressure dropwas measured by two flush-diaphragm gage pressure sensors. The pressure Hopper Pump Pipe AB Bucket Pressure Drop Fig. 3.3 Schematic drawing of experimental setup for the horizontal pipe viscometer (HPV). readings at A and B were recorded by a PC using Global Lab software. Mud slurry could be fed through a hopper above the pump and connected to it. 3.3 Sediments and Slurries 3.3.1 Sediment and Fluid Properties Three types of commercially available clays: a kaolinite, a bentonite, and an attapulgite, which together cover a wide range of cohesive soil properties, were selected. Kaolinite (pulverized kaolin), a light beige-colored powder, was obtained from the EPK Division of Feldspar Corporation in Edgar, Florida. Its Cation Exchange Capacity (CEC), as given by the supplier, was 5.2-6.5 milliequivalents per 100 grams. Its granular density was 2,630 kg/m3. Bentonite was obtained from the American Colloid Company in Arlington Heights, Illinois. It was a sodium montmorillonite (commercial name Volclay) of a light gray color. Its CEC was 105 milliequivalents per 100 grams, and its granular density was 2,760 kg/m 3. Attapulgite, of greenish-white color, was obtained from Floridin Company in Quincy, Florida. Also called palygorskite, its CEC was 28 milliequivalents per 100 grams, and its granular density was 2,300 kg/m 3. Tables 3.1 through 3.3 respectively give the chemical compositions of the three clays (provided by the suppliers). Fig. 3.4 Photograph of HPV setup. Table 3.1: Chemical composition of kaolinite Chemical % Chemical % SiO2 46.5 MgO 0.16 Al203 37.62 Na2O 0.02 Fe203 0.51 K20 0.40 TiO2 0.36 SO3 0.21 P20 0.19 V205 < 0.001 CaO 0.25 Table 3.2: Chemical composition of bentonite Chemical % Chemical % SiO2 63.02 A1201 21.08 Fe203 3.25 FeO 0.35 MgO 2.67 Na20 & K20 2.57 CaO 0.65 H20 5.64 Trace Elements 0.72 Table 3.3: Chemical composition of attapulgite (palygorskite) Chemical % Chemical % SiO2 55.2 A1203 9.67 Na2O 0.10 K20 0.10 Fe203 2.32 FeO 0.19 MgO 8.92 CaO 1.65 HO 10.03 NHO 9.48 Table 3.4 gives the results of chemical analysis of the tap water used to prepare mud, whose pH value was 8 and the conductivity was 0.284 millimhos. This analysis was conducted at the Material Science Department of the University of Florida (Feng, 1992). The procedure was as follows: firstly, an element survey of both the tap water and doubledistilled water was performed, which determined the ions in tap water. Secondly, standard solutions of these ions contained in the tap water were made, and the tap water was analyzed against the standard solutions to determine the concentrations of the ions by an emission spectrometer (Plasma II). Table 3.4: Chemical composition of water Chemical Concentration (ppm) Si 11.4 Al 1.2 Fe 0.2 Ca 24.4 Mg 16.2 Na 9.6 Total Salts 278 The particle size distributions of kaolinite, bentonite and attapulgite are given in Tables 3.5, 3.6 and 3.7, respectively. The procedure for determination was: firstly, a particular suspension was prepared at about 0.5% by weight concentration, and run for at least 15 29 minutes in a sonic dismembrater (Fisher, model 300) to breakdown any agglomerates. Secondly, the suspension was analyzed in a particle size distribution analyzer (Horiba, model CAPA 700), and allowed to gradually settle down to the bottom. Particle concentration and fall velocities determined with an X-ray apparatus were converted to Stokes equivalent diameters. The median particle sizes of kaolinite, bentonite and attapulgite were 1.10 p m, 1.01 g m and 0.86 g m, respectively. Table 3.5: Size distribution of kaolinite Diameter Frequency distribution Cumulative frequency distribution (lm) (%) (%) 5.00< 0.0 0.0 5.00-3.20 0.0 0.0 3.20-3.00 2.9 2.9 3.00-2.80 4.0 6.9 2.80-2.60 2.6 9.5 2.60-2.40 4.1 13.6 2.40-2.20 4.0 17.6 2.20-2.00 6.0 23.6 2.00-1.80 5.7 29.3 1.80-1.60 6.2 35.5 1.60-1.40 5.5 41.0 1.40-1.20 6.2 47.2 1.20-1.00 5.8 53.0 1.00-0.80 5.0 58.0 0.80-0.60 10.4 68.4 0.60-0.40 11.2 79.6 0.40-0.20 13.6 93.2 0.20-0.00 6.8 100.0 3.3.2 Mud Slurries Mud slurries of different densities were prepared by thoroughly mixing the selected dry clays and clay mixtures with tap water at the ambient temperature, allowing these 30 mixtures to stand for a minimum of 24 hours before testing them in the CCV and the HPV. Mud composition, density and water content are given in Table 3.8. Also given in the last column is the CEC of the slurry, which was calculated as follows: CECsluny =kaoliniteCECkaolinite +fattapulgiteCECattapulgite +fbentoniteCECbentonite (3.1) where f represents the weight fraction of the subscripted sediment, and subscripted CEC are the corresponding cation exchange capacities. Note that given fwater as the weight fraction of water in the slurry, we have: fkaolinite +attapulgite+fbentonite+f water = 1. The CEC values (in milliequivalents per 100 g) were selected to be: 6 (nominal) for kaolinite, 28 for attapulgite and 105 for bentonite. The weight fractions depend on the composition of each slurry given in Table 3.8. Table 3.6: Size distribution of bentonite Diameter Frequency distribution Cumulative frequency distribution (tm) (%) (%) 3.00< 5.9 5.9 3.00-2.80 1.9 7.8 2.80-2.60 2.3 10.1 2.60-2.40 2.5 12.6 2.40-2.20 3.0 15.6 2.20-2.00 3.0 18.6 2.00-1.80 4.9 23.5 1.80-1.60 5.3 28.8 1.60-1.40 8.1 36.9 1.40-1.20 4.5 41.4 1.20-1.00 9.3 50.7 1.00-0.80 9.1 59.8 0.80-0.60 11.4 71.2 0.60-0.40 11.2 82.4 0.40-0.20 11.5 93.3 0.20-0.00 6.1 100.0 Table 3.7:Size distribution of attapulgite Diameter Frequency distribution Cumulative frequency distribution (Im) (%) (%) 2.00< 11.8 11.8 2.00-1.80 4.1 15.9 1.80-1.60 4.9 20.8 1.60-1.40 5.3 26.1 1.40-1.20 5.6 31.7 1.20-1.00 5.8 37.5 1.00-0.80 17.4 54.9 0.80-0.60 25.5 80.4 0.60-0.40 12.3 92.7 0.40-0.20 6.1 98.8 0.20-0.00 1.2 100.0 Table 3.8: Properties of mud slurries tested Slurry No. Sediment Density Water Content CECU,, (kg/inm) (meq/100 g) 1 100%K 1,250 210 1.94 2 100%K 1,300 167 2.25 3 100%K 1,350 139 2.51 4 100%/oK 1,400 117 2.84 5 100%K 1,450 100 3.00 6 100%K 1,500 86 3.23 7 75%K+25%A 1,243 210 3.71 8 750/oK+25%A 1,291 169 4.28 9 75%K+25%A 1,339 139 4.80 10 75%K+25%A 1,387 117 5.29 11 50%K+50%A 1,236 210 5.48 12 500/oK+50%A 1,283 169 6.33 13 50%K+50%A 1,306 153 6.72 14 50%K+50%A 1,329 139 7.10 15 25%K+75%A 1,175 289 5.79 16 25%K+75%A 1,200 253 6.38 17 250/oK+75%A 1,225 215 7.14 18 25%K+75%A 1,250 189 7.77 19 100%A 1,125 409 5.50 20 100%A 1,150 333 6.46 21 100%A 1,175 280 7.38 22 100%A 1,200 239 8.26 23 90 /K + 10%B 1,200 273 4.26 24 90%K+10%B 1,250 211 5.12 25 90%K+10%B 1,300 169 5.90 26 90%K+10%/B 1,350 140 6.63 27 65%K+25%A+100oB 1,225 231 6.47 28 65%K+25%A+10%B 1,250 204 7.04 29 65%K+25%A+10%B 1,275 182 7.59 30 65%K+25%A+10%B 1,300 163 8.12 31 40%K+50%A+10%B 1,175 299 6.74 32 40%K+50%A+10%B 1,200 257 7.54 33 400/oK+50%A+10%B 1,225 224 8.31 34 40%K+50%A+10%B 1,250 197 9.05 35 15%K+75%A+10%B 1,125 423 6.20 36 15%K+75%A+10%B 1,150 345 7.28 37 150/oK+75%A+10%B 1,175 290 8.31 38 15%K+75%A+10%B 1,200 248 9.30 39 90%A+10%B 1,125 415 6.93 40 90%A+10%B 1,150 339 8.13 41 90%A+100/oB 1,175 284 9.29 42 90%A+10%B 1,200 244 10.39 33 From Table 3.3 it is noted that the density range covered was from a low 1,125 kg/m' to a high 1,500 kg/m3. The water content varied from a high 423% to a low 75%. Finally, the CECS,, values ranged from 1.94 meq/100g for a kaolinite slurry (no. 1) to 10.39 meq/100g for a slurry (no. 42) composed of attapulgite and bentonite. CHAPTER 4 EXPERIMENTAL RESULTS 4.1 Rheometric Results 4.1.1 Power-Law for Mud Flow Previous work on flocculated bottom muds in the coastal environment has established their pseudoplastic (shear thinning) flow behavior (e.g., Parker and Kirby, 1982). Subsequent work by, among others, Feng (1992) has revealed that the well-known Sisko (1958) power-law provides a reasonable fit to the measured decrease in apparent viscosity, ri, with increasing shear rate, j, a behavior that is consistent with the pseudoplastic flow curve (Fig. 4.1). With reference to the Sisko model, it is noted that general power-law equations that predict the shape of the curves representing the variation of viscosity with shear rate typically need at least four parameters. One such relation is the Cross (1965) equation given by T (Cl ) (4.1) ri rlwhere r0 and ri= refer to the asymptotic values of the viscosity at very low and very high shear rates, respectively, c, is a constant parameter having dimensions of time, p is a dimensionless constant, and ri is the apparent viscosity. Fig. 4.1 Comparison between pseudoplastic (shearthinning) and Newtonian flow curves. The nature of the shear-thinning curve is such that while at low shear rates the viscosity is higher than the constant value for the Newtonian case (straight line), with increasing shear rate the pseudoplastic curve becomes asymptotically parallel to the Newtonian line, hence the pseudoplastic viscosity approaches that of the Newtonian case. It is generally found that "<< ro, hence the above equation can be simplified as 0 (c1t)P (4.2) which can be rewritten as 11 + (4.3) (CI Wj)P or , =11_ +cYn-I (4.4) 36 Equation (4.4) is the Sisko (1958) model, where il_ is the constant ultimate viscosity at the limit of high (theoretically infinite) shear rate, c is a measure of the consistency of the material, and n is a parameter which indicates whether the material is shear-thinning or shearthickening, that is, when n > 1 the material exhibits shear-thickening, and n < 1 denotes a shear-thinning behavior. When n =1 the behavior is Newtonian, with consistency c = 0 and a constant viscosity equal to rl. Note also that when rl=0, Eq. (4.4) becomes consistent with the power-law given by Eq. (2.35). It is important to recognize that the coefficients of Eq. (4.4) must be derived from measurements conducted under a laminar flow. The laminar limit for Newtonian slurries is given by the well-known Reynolds number criterion: Re = pVD < 2100 (4.5) where V is the mean velocity in the pipe, and D = 2R is the pipe diameter. 4.1.2 Power-Law Coefficients To solve for the three Sisko parameters, r1, c and n, the method of least squares was used for fitting the curves obtained from Eq. (4.4) to the experimental data on the apparent viscosity, ri, as a function of the shear rate, j', obtained from the measured relationship between stress (,u) versus j, such as shown qualitatively in Fig. 4.1. For this method it is required that the viscosity difference between the model [Eq. (4.4)] and data, DIFF, be minimized, that is, M DIFF= E (f'i-1l)2 = minimum (4.6) I=l or M DIFF= j (f-ri-c'n-1)2 = minimum (4.7) /=1 where l, is the slurry viscosity obtained from the experiment, and Mis the number of data points. Setting 8DIFF 8aDIFF 8DIFF0 (4.8) =0; =0; (4.8) 8rL an ac from Eq. (4.7) it is obtained the following by differentiation: M S(fl- .-c'"-) =0 (4.9) i=1 M {" '(-l (,-B cyt -1)} =0 (4.10) i=1 and M {cf n-' logy(fqly- Cf n-l)} =:0 (4.11) i=1 In this way, ril, c and n can be determined by solving Eqs. (4.9), (4.10) and (4.11). A requirement for the determination of these coefficients is that each slurry be tested over a comparatively wide range of the shear rate ?, so that the low-shear rate non-Newtonian and high shear rate Newtonian behaviors are identified. In addition, the limitation of in this method is to be greater than water viscosity (0.001 Pa.s). Since there are three parameters, rl, c, n, to be determined, least squares analysis was 38 carried out by selecting rl_, then calculating c and n. This procedure was repeated until the optimal values of the three coefficients were obtained. 4.2 End and Slip Effects As mentioned in Chapter 2, end and slip effects are errors which may arise in pipe flow measurements. Therefore, their investigation and corresponding corrections must be provided. The investigation was carried out by testing two sediments, one with 1,236 kg/m3 density and consisting of 50%Kaolinite+50%Attapulgite, and another with 1,125 kg/m3 density and consisting of 90%Kaolinite+10%Bentonite, and also using four different pipes with different ratios of L/R. The data obtained are given in table 4.1 and table 4.2. Table 4.1:1,236 kmg/i3 slurry of 50%Kaolinite+50%Attapulgite Pipe no. Pipe Diameter, Pipe Discharge, Q Pressure drop, .Ap Wall stress, D Length, L (m3/s) (Pa) (m.) (m.) (Pa) 1 0.0191 1.8 0.00120 61,783.9 163.47 2 0.0254 1.8 0.00135 46,034.6 162.44 3 0.0254 3.1 0.00137 79,804.3 163.47 4 0.0381 1.8 0.00122 32,521.4 172.09 Table 4.2: 1,125 kg/m3 slurry of 90%Kaolinite+O%Bentonite Pipe no. Pipe Diameter, Pipe Discharge, Q Pressure drop, .Ap Wall stress, T, D Length, L (m3/s) (Pa) (Pa) (m.) (m.) 1 0.0191 1.8 0.00121 60,275.9 159.48 2 0.0254 1.8 0.00138 48,231.5 170.15 3 0.0254 3.1 0.00136 82,918.9 169.85 4 0.0381 1.8 0.00074 32,097.6 169.85 39 For the correction of the end effects, the result (Fig. 4.2) indicates that the plots of both sediments are linear. Accordingly, the correction can be determined as the value of Le as follows: 120000 CL a. W W 80000 0 _o 40000 Cn 0 100 200 300 L/R Fig.4.2 Data obtained from the end-effect correction experiments. From the plot, and referring to Fig. 2.4, pe=l,074.3 Pa, and L=/R -0.68. As a result, the effective length of the 0.0254 m diameter pipe = 2.46+0.02 = 2.48 m. In order to obtain the correction for the slip effect, the slip coefficient (13) was determined as follows: Step 1. Plot(F/4tr) vs. 200 150 . 100 50 0 I I 0 5E-07 1 E-06 1.5E-06 2E-06 2.5E-06 Gama4Tau Fig. 4.3 Plot of(F/4t%) vs. T, for slip-effect correction. 40 The plot indicates that r, is almost constant (167.5 Pa.). Step 2. Plot(F/4t) vs. 1/R 0.000003 cc - 0.000002 E E 0.000001 C9 0 40 60 80 100 120 1/R Fig. 4.4 Plot of(P/4t,) vs. 1/R for slip effect correction. From the plot, the slope of Fig.4.4 is equal to 3 = 2 x 10- which is close to zero. Therefore, from Eq.(2.32): sno sip = (,lip) 4PTw/R with 3 = 0 rno slip ( slip) which indicates no slip effect. 4.3 Power-Law Parameters All 42 slurries noted in Table 3.8 were tested in the CCV and the HPV; the CCV for data at low shear rates, and the HPV for high shear rates. The overall rage of shear rates covered in the CCV was 0.063 Hz to 20.4 Hz, whereas the in the HPV they were considerably higher, in the range of 150.7 to 1,094.5 Hz. Note that in the CCV the shear rate 41 is an independent parameter which is inputted, whereas in the HPV it depends on the pipe diameter, length, pressure drop and slurry rheology. As discussed further in Section 4.4, at the high shear rates in the HPV the behavior of the slurry was close to Newtonian, hence the shear rate, ', and the corresponding shear stress, T.,, both at the pipe wall, could be calculated from the following Newtonian flow equations: 8V,- (4.12) D SDAp (4.13) S 4L where V,. is the mean flow velocity in the pipe. Then rI = -j For each slurry the measured pressure drop, Ap, the measured discharge, Q, and the calculated wall stress, ", are given in Table 4.3. Note that while in the CCV each sample was tested only once after the correct spindle was selected, in the HPV each sample was tested three times. For each slurry, the reported pressure reading and the discharge (obtained by timing the rate of flow of the slurry out of the pipe, weighing the mass accumulated in the bucket placed to receive the slurry, converting this weight to volume knowing the density and dividing the volume by the measured time) are means of the three measurements. An example of the Sisko relationship [Eq. (4.4)] based on the combined CCV and HPV data is shown in Fig. 4.5, in which the eight points within the lower shear rate range were obtained by the CCV, and the single value at the higher shear rate from the HPV. Best-fit coefficients r, c and n for all the slurries obtained in the same way are listed in Table 4.4, which also gives the characteristic HPV flow Reynolds number, Ref, calculated Table 4.3: Pressure drop, discharge, shear rate and wall stress data from HPV tests Slurry Pressure drop, zip Discharge, Q Shear rate, j' Wall stress, T,. no. (Pa) (ms/s) (Hz) (Pa) 1 76,065.9 0.00150 931.8 194.8 2 54,452.4 0.00140 869.7 139.4 3 150,503.0 0.00136 844.9 385.4 4 192,067.5 0.00130 807.6 491.8 5 205,348.3 0.00124 770.3 525.8 6 144,997.7 0.00086 534.3 371.3 7 119,050.5 0.00144 898.7 304.8 8 177,736.9 0.00129 803.4 455.1 9 312,957.7 0.00076 472.1 801.3 10 54,381.6 0.00024 150.7 139.2 11 93,544.0 0.00149 927.7 239.5 12 85,376.3 0.00123 766.2 218.6 13 78,436.3 0.00104 647.1 200.8 14 73,784.9 0.00064 399.7 188.9 15 95,384.3 0.00158 980.9 244.2 16 137,272.7 0.00141 874.8 351.5 17 168,589.8 0.00121 754.2 431.7 18 179,701.1 0.001 17 728.2 460.1 19 75,907.4 0.00156 907.0 194.4 20 106,010.3 0.00141 873.2 271.4 21 128,008.6 0.00130 809.2 327.8 22 167,889.2 0.00123 764.1 429.9 23 81,047.4 0.00176 1094.5 207.5 24 73,888.0 0.00153 953.5 189.2 25 95,130.6 0.00141 872.9 243.6 26 126,692.1 0.00130 810.1 324.4 27 95,659.2 0.00166 1030.1 244.9 28 113,064.7 0.00157 974.4 289.5 29 115,010.4 0.00145 898.7 294.5 30 249,492.7 0.00134 829.6 638.8 31 58,314.3 0.00161 1002.2 149.3 32 33,372.3 0.00150 931.8 85.4 33 55,968.5 0.00146 907.9 143.3 34 96,128.4 0.00130 809.2 246.1 35 71,254.7 0.00157 976.1 182.4 36 57,862.2 0.00144 895.5 148.2 37 54,352.8 0.00153 952.2 139.2 38 121,193.6 0.00131 811.6 310.3 39 82,942.3 0.00156 968.8 212.4 40 45,127.2 0.00147 911.3 115.5 41 134,873.8 0.00141 878.0 345.3 42 160,813.2 0.00084 520.6 411.8 according to Eq. (4.5). All plots of excess apparent viscosity, rj_-Tl, as a function of shear rate are given in Appendix A. As seen in Table 4.4 from the range of Reynolds numbers experienced, all tests were carried under non-turbulent conditions, as required for the rheological analysis. The power-law coefficients show considerable variability with slurry composition and density. Note that the lowest value of r9_was chosen to be 0.00 1 Pa, the viscosity of water. In other words, in the Sisko Model analysis il_ was not allowed to have values lower than the viscosity of water. 102 25%K+75%A, density = 1175 kg/m3 Eta(inf)=0.23419 Pa.s c = 3.1439 n = 0.22145 .2 .1 0 10.2 10"1 10o 10' Shear rate (Hz) 102 103 104 Fig. 4.5 Excess viscosity as a function of shear rate or kaolinite slurry no. 15. In Figs. 4.6, 4.7, 4.8, rTl, c and n are plotted as functions of kaolinite slurry density (for slurry nos. 1 through 6). Analogous data for all ten mud types tested are given in Appendix B. Observe that rl shows an overall increasing trend with increasing density. In any event, it is logical to expect r_ to increase with density. The consistency, c, is also seen to increase linearly with density. This trend can also be expected as it implies that for a given shear rate (and holding n invariant), slurry viscosity increases with density. Finally, n seems at first to be independent of density, then decreases with further increase in density. Since n 45 Kaolinite 0.8 0.6 S0.4 , 0.2 0 I 1200 1250 1300 1350 1400 1450 1500 1550 Density (kg/m^3) Fig. 4.6 Variation of T with density of kaolinite slurries. Kaolinite 16 12 08 4 0 1200 1250 1300 1350 1400 1450 1500 1550 Density (kg/m ^ 3) Fig. 4.7 Variation of c with density of kaolinite slurries. 0.4 Kaolinite 0.3 S0.2 0.1 0 1200 1250 1300 1350 1400 1450 1500 1550 Density (kg/m^3) Fig. 4.8 Variation of n with density of kaolinite slurries. 46 Reviewing the data for the other nine slurry types in Appendix B it is noted that the trends are qualitatively akin to those for kaolinite, especially with regard to consistent pseudoplastic behavior. The non-monotonic effects of density on the coefficients observed in some cases may reflect the complex physical and physicochemical interactions between the particles and the pore fluid at different shear rates. 4.4 Slurry Discharge with Sisko Model From section 2.1.2, given horizontal velocity of the slurry v(r), the shear rate is ?=av/8r, and the steady-state momentum equation for pipe flow is r BY = --r (4.14) R where t, is the wall shear stress. For expressing the apparent viscosity, r1, in terms of the shear rate, the Sisko model is given by Eq. (4.4). Next, let r ( = 1 - (4.15) R Eq.4.15 gives 8(/8r= 1/R, and 8v/8rcan be written as (8v/8()(C(/8r). Then, combining Eqs. (4.4), (4.8) and (4.9) it is obtained [r c'v By + 1 a + ((-1)r = 0 (4.16) R R" SC 5 c which must satisfy the no-slip boundary condition at the wall, i.e., v(7=0) = 0. Next, Eq (4.10) can be written in the finite difference form as Table 4A4 Sisko model coefficients and HPV flow Reynolds number Slurry No. 110 (Pa. s) 0. 1890 0. 1403 0.436 1 0.5890 0.6626 0.6749 0.338 1 0.5465 1.6736 0.9040 0.2382 0.2704 0.2947 0.4527 0.2342 0.38 18 0.5597 0.6 195 0. 1943 0.3046 0.3 85 1 0.5570 0. 1887 0. 1784 C nlRe 2.35 3.43 9.02 5.08 6.99 12.99 1.44 7.69 9.98 25.96 4.30 13.21 21.65 76.08 3.14 9.38 22.05 34.08 1.23 3.37 13.24 21.32 2.98 9.25 0.300 0.320 0.195 0.29 1 0.223 0.062 -0.07 1 0.174 -0.007 -0.283 0.22 1 -0.023 -0.117 -0.247 0.22 1 0.134 -0.126 -0.20 1 0.392 0.073 0.072 -0.242 -0.16 1 0.136 450 569 202 150 132 93 266 148 30 18 358 278 220 91 373 211 130 116 440 260 189 131 559 484 0.2591 0.3804 0.2178 0.2771 0.3077 0.7500 0.1290 0.0717 0.1378 0.2842 0.1773 0.1454 0.1262 0.3624 0.1992 0.1068 0.3733 0.7709 14.28 42.83 9.04 17.50 21.05 57.83 7.82 12.17 10.46 36.00 1.82 6.17 8.71 22.13 4.12 14.83 17.32 89.59 0.116 -0.044 0.182 0.090 0.056 -0.059 0.182 0.154 0.144 -0.019 0.208 0.237 0.156 0.025 0.246 0.053 0.034 -0.198 328 220 428 331 282 113 637 984 568 268 434 502 617 205 401 666 211 64 (4.17) c vi'l-vi v +,-v i +( i 1 = 0 B s on E ( 2 Based on Eq. (4.17) the following iterative relation was used: M+l v i+1 =vi + AC 2 g n-I TL+C Vi)I , R R"n AC (4.18) 49 where v,,,, (i = 1,2. ..N) is the layer velocity, N is the total number of layers into which the distance from the wall to the centerline is divided, and m is the iteration index. Equation (4.18) was solved with the initial condition v, =0 at the wall. The chosen criterion for convergence was i+n i+M+ _V MI< 10-6 (4.19) Finally, the discharge, Q, is obtained from the summation Q = 27rE rIdr (4.20) 4.5 Calculation of Slurry Discharge In order to test the applicability of the Eq. (4.20) for numerical determination of the discharge, Q, several slurries were pumped again through the HPV. The data are given in Table 4.5. These tests were deliberately carried out at pressures lower than those used in the HIPV to obtain the data points for determining the power-law relationships. (Compare the pressure drops in Table 4.5 with the corresponding ones in Table 4.3). Using the power-law coefficients for these slurries form Table 4.4, Eqs. (4.18) and (4.20) were solved along with the convergence criterion of Eq. (4.19). The number of layers, N, into which the pipe radius was divided was 20. As an example, the calculated result for slurry no. 1 is shown in Fig. 4.9, which plots the computed velocity profile and gives the corresponding discharge. Observe that this discharge agrees well with that measured in Table 4.5. Also plotted is the velocity profile assuming the slurry to be Newtonian [Eq. (2.37)], and 50 the corresponding discharge is calculated from Eq. (2.38). It is seen that the Newtonian assumption is reasonable at the high shear rate (836.6 Hz) for slurry no.1I at which the data were obtained. Another illustrative plot (for slurry no. 23) is given in Fig. 4. 10. Table 4.5: Low pressure HPV test parameters for selected slurries Slurry Pressure drop, Measured Shear Wall shear Computed no. zip discharge, Q rate, stress, -r, discharge,Q (Pa) (m3Is) (Hz) (Pa) (m3Is) 68,465.5 69,969.8 82,678.5 67,697.0 61,719.1 71,668.8 67,464.2 73,927.5 78,395.6 74,920.0 0.00 135 0.00130 0.00 136 0.00 128 0.00 136 0.00 133 0.00 133 0.00129 0.00 132 0.00 137 836.6 807.6 844.9 794.5 842.0 823.2 825.4 800.9 821.6 850.0 175.3 179.2 211.7 173.3 158.0 183.5 172.7 189.3 200.7 191.8 0.00131 0.00085 0.00127 0.00108 0.00115 0.00 155 0.00 101 0.00192 0.00174 0.00 134 Measured and computed discharges for all slurries tested are given in Table 4.5. The degree of agreement varies, and can be shown to be sensitive to the power-law approximation of the rheological data, i.e., to the extent to which the power-law fits the measured data from the viscometers. All the computed velocity profiles and corresponding discharges are as shown in the Appendix C. 0.5 I 0 1 2 3 4 5 6 Velocity (m/s) Fig. 4.9 Computed velocity profiles and corresponding discharges for slurry no. 1. Line is numerical solution using Sisko model; dots represent analytic Newtonian solution. Ie 0.5 QSk =0.00155 m31s QN..tO.I.. = 0.00 155 m3/s -0.5 .1I 0 2 4 4 8 Velocity (m/s) Fig. 4.10 Computed velocity profiles and discharges for slurry no. 23. 52 4.6 Power-Law Correlations with Slurry CEC The slurry CEC (CEC,1 ), as defined by Eq. (3.1), potentially lends itself as a measure of slurry cohesion, hence its rheology, at least to the extent to which cohesion and rheology are likely to be physico-chemically related. In Figs. 4.10, 4.12 and 4.13, data from Table 4.4 have been used to plot the power-law coefficients 9_ (logarithm of) c and n against CECU. given in Table 3.8. Observe that while there is considerable data scatter, not all of which is likely to be "random", correlations indeed seem to exist in the mean (lines). It is observed in Fig. 4. 11 that in the mean il_ increases with CECIUy, starting with 0.001 Pa at CECSI,,y = 0 for water. This trend can be expected since greater cohesion would imply greater inter-particle interaction, hence larger viscosity. Similarly, in Fig. 4.12 the consistency, c, is seen to increase with CECI,y, which is in agreement with the trend in Fig. 4.11, given that consistency can be expected to vary directly with viscosity. It is noted that because c = 0 for water, as CECUy approaches zero, log c tends to go to --. Finally, in Fig. 4.13, n is seen to decrease with CECIU. Note that since n = 1 would mean a Newtonian fluid, and for a shear thinning material n < 1, the observed trend of variation of n with CECIUIV implies increasingly non-Newtonian, shear-thinning behavior of the slurries with increasing cohesion. The mean trend lines in Figs. 4.11, 4.12 and 4.13 respectively correspond to the following relations: il_ = 0.0015CECQI, + 0.361 (4.21) logc = 0.127CECsiu + 0.22 n = -0.033CECsly + 0.278 2.0000 1.5000 1.0000 0.5000 0.0000 0.00 5.00 Slurry CEC (4.22) (4.23) 10.00 Fig 4.11 Variation of r1. with slurry CEC (CEC,,,) for all slurries. 0.00 2.00 4.00 6.00 8.00 10.00 12.00 Slurry CEC Fig 4.12 Variation of log c with slurry CEC (CEC,,y) for all slurries. 0 0 0 0 0 00o o,: 0 00lo0-; 1.000 0.500 0 0 0 o 0. )0 4.db o o800 0 1200 -0.500 Slurry CEC Fig 4.13 Variation ofn with slurry CEC(CECI,,) for all slurries. CHAPTER 5 CONCLUDING COMMENTS 5.1 Conclusion The dependence of the discharge of clayey mud slurries in pipes on cohesion and water content was examined in terms of a slurry cation exchange capacity, CECS. Based on tests in which forty-two clay-water slurries were pumped through a horizontal pipe viscometer, CEC, can serve as an approximate determinant of slurry discharge in the viscous flow range. Thus, from the relationship between CECs and the power-law coefficients (1. c, and n) as determined from Eqs. 4.21, 4.22, and 4.23, the values of these coefficients can be predicted from the known CECs value. Then, for a given pipe with the power-law coefficients known, the discharge can be calculated for a measured pressure loss from Eq. 4.14 to Eq. 4.20. The results shown in Appendix C indicate that the calculated discharges are close to the measured values. 5.2 Comments The experiments and analyses presented in the previous chapters essentially highlight a method which may be explored further in future for assessing pumping requirements. A draw-back is that without knowing the rheology of a given mud its transportation characteristics cannot be determined. Secondly, the use of CEC as a measure 56 of rheological behavior of a slurry cannot be extended to sediments that are not clayey. Given these two limitations, it will be necessary to: 1) examine a wide range of natural muds for their rheological behavior, and 2) develop correlations between rheology characterizing parameters and readily determinable parameters including, but not limited to, CEC. Finally, it should be added that slurries of densities higher than those tested must be studied, using pumps which can supply higher pressures, in order to fulfill the need to quantify the understanding of the transportability of high density muds at in situ densities. In any event, the following procedure, developed as part of this study, can serve as a guide for future efforts in this regard. 1. For the site to be dredged determine the required pipe discharge. 2. Collect the bottom mud sample to be discharged. 3. With mud rheology known, back-calculate the pressure drop required to achieve the discharge for a pipe of known dimensions. This can be done by matching the required discharge with that calculated from Eqs. (4.19) and (4.21), for a given (calibrated) value of Ap. 4. This value of Ap should be considered to be the minimum pressure drop required for the pump to be selected. 5.3 Recommendation for future studies As mentioned earlier, higher density sediments need to be tested, so that more accurate relationships between the pressure drop, power-law coefficients, CEC, and discharge can be determined. 57 For the relationships between density and power-law coefficients as plotted in Appendix B, future experiments might lead to better predictions for slurry flow in pipes, provided more sediments can be tested along with a wider range of slurry densities. BIBLIOGRAPHY Brookfield Dial Viscometer, 1981. Operating Manual, Brookfield Engineering Laboratories, Stoughton, MA. Cross, M. M., 1965. Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems, Journal of Colloidal Science, 20, 417-437. Feng, J., 1992. Laboratory experiments on cohesive soil bed fluidization by water waves, M S. Thesis, University of Florida, Gainesville, FL. Heywood, N. I., 1991. Rheological characterization of non-settling slurries, In: Slurry Handling Design of Solid-Liquid Systems, N. P. Brown and N. I. Heywood (eds.), Elsevier, Amsterdam, 53-87. Jinchai, P., Jiang, J., and Mehta, A.J., 1998. Rheology and rheometry of mud slurry flow in pipes:a laboratory investigation. Report No. UFL/COEL-981001, Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL. Marine Board, 1985. Dredging Coastal Ports: An Assessment of the Issues, National Research Council, Washington, DC. Parchure, T. M., and Sturdivant, C. N., 1997. Development of a portable innovative contaminated sediment dredge. Final Report CPAR-CHL-97-2, Construction Productivity Research Program, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Parker, W. R., and Kirby, W. R., 1982. Time dependent properties of cohesive sediment relevant to sedimentation management European experience, In: Estuarine Comparisons, V. S. Kennedy (ed.), Academic Press, New York, 573-589. Sisko, A. W., 1958. The flow of lubricating greases, Industrial Engineering Chemistry, 50, 1789-1792. Thai Pollution Control Department, 1997. Mercury monitoring of coastal environment, http://www.pcd.go.th/news/hg-sea.cfm Wasp, E. J., Kenny, J. P., and Gandhi, R. L., 1977. Solid-Liquid Flow Slurry pipeline Transportation. Trans Tech Publications, San Francisco. APPENDIX A SLURRY VISCOSITY DATA Kainit, densky = 1250 kgf Eta(inf)=0.18902 Pas c = 2.3515 n= 0.3002 10 10 10 Fig. A- 1 Viscosity data for slurry no.1. Kaolinite, densitAy = 1350 kgfn3 16 1 10' Shear rte (Ft) id id id Fig. A-3 Viscosity data for slurry no.3. Fig. A-2 Viscosity data for slurry no.2. Kairwe, demsity = 1400 kgIm3 Eta(inf)=0.58895 Pas c = 5.0756 n= 0.29084 10lI 16 10' 10o 10 id 10 10 Shear rate (H) Fig. A-4 Viscosity data for slurry no.4. 0 1 10 10i 10o' Shear rate R) Shear rte k) Eta(inf)=0.4361 Pas c = 9.0237 n= 0.19496 . . ..... I . ...... . ...... . ...... . ....... . ... Kalinie, demAy = 1300 kmg 60 Kainite, dMsiy = 1450 kWm3 10 10 10, Sha rate (Ft) 102 103 1 10, 10 10 Fig. A-5 Viscosity data for slurry no.5. Kadite, desity = 15 kgfm d10 10 10 Sha rae) 102 103 104 10, 10 10 Fig. A-6 Viscosity data for slurry no.6. Eta(inf)=-0.66258 Pas c = 6.9905 n = 0.22284 Eta(inf)=0.67486 Pas c= 12.9911 n = 0.062325 10 10 loo 10 10 10 10 75%K+2WA density = 1243 knM3 10 10 10 10 10 10 I( Fig. A-7 Viscosity data for slurry no.7. 75%K+25%A demaity = 1291 kgm3 102 Eta(inf)=0.54646 Pas c = 7.6931 n= 0.17393 10 10 1o '10 lid, 162. 10 1 Fig. 75%K+25%A density = 1339 kgm3 lo2 Eta(inf)=1.6774 Pas c = 9.9786 n =-0.0071815 10 l*d, 101'$ Ib 162 10 10 .. . 102 i' 10 0 10' 10 103 1 Shetw rate r s Fig. A-9 Viscosity data for slurry no.9. 10 o2 Io o0 Io o2 3o 4o 1d 10 10 10 10 10 she rae -) A-8 Viscosity data for slurry no.8. 75%K+25%A, density = 1387 kgm3 Ea(inf)=0.90398 Pas c = 25.9615 n -0.28334 ........ Ets.i.0. 9 8 P o1 o lo 10 10 d 1o' Fig. A-10 Viscosity data for slurry no.10. 50%K+50%~A density = 1236 km3 d10 d10 10 10 10 10 10 Shuear rae (") Fig. A- I Viscosity data for slurry no.11. 50K+W0%A dway = 1306 kgfwM 1 0 10 Eta(inf)=0.29466 Pas c = 21.6479 10 n= -0.11719 . 10" 10o; 10~ 102 10 10 10 100 10 10 10 10 Fig. A-13 Viscosity data for slurry no.13. Fig. A- 13 Viscosity data for slurry no. 13. 50%KA denty = 1283 kgfr3 10' + Eta(inf)=0.27041 Pas c = 13.206 11 n = -0.022772 10 lo 110 10 lid, 10 10 10 10 10 10 10 10 She rate () Fig. A-12 Viscosity data for slurry no.12. 5K+50KA density = 1329 IkM3 2o I- 0o Io 2o 3o 4o 10 10 10 0 10 n 1 10 Sg rA s d l) Fig. A- 14 Viscosity data for slurry no. 14. 2K75%A desitry = 1175 kgWm3 25%+75%A, density = 120 kVrm3 102 10 10 10 b 1 0 102 103 104 10 10 -1 1 o 1 10 10 10 sher n (H) 12 3 4 10 10 10 Fig. A- 15 Viscosity data for slurry no.15. 29%K+75%A, density = 1225 kgm3 10 10- 10o 101 Shere H) 102 103 10 Fig. A- 17 Viscosity data for slurry no.17. Fig. A-16 Viscosity data for slurry no.16. 25%K+75A desity = 1250 kgtm 102 10 10 10 102 10 10 Shear date ()f Fig. A- 18 Viscosity data for slurry no. 18. Eta(inf)=0.23419 Pas c = 3.1439 n = 0.22145 10 10 10 Shear rte(H) Eta(inf)=0.38179 Pas c = 9.3847 n=0.13384 Eta(inf)=0.55966 Pas c= 22.0489 n = -0.12579 .10 106 10 10 -6 102 Aftqxd deity= 1125 kg/3 10 . . ., 102 10 10 10 10 10 10 Sho m e-") Fig. A-19 Viscosity data for slurry no.19. 3i AttaAgitA demity = 1175 kg/m3 10 . 10 10 10 10, 10, 10 10 she rate r) Fig. A-21 Viscosity data for slurry no.21. Attqxdgg dewsty = 1150 kgm3 102 10 100 10 10 103 10 Fig. A-20 Viscosity data for slurry no.20.) Fig. A-20 Viscosity data for slurry no.20. Attqgxtd derty = 1200 kgm3 10 1 . ., 10 10- 10 10 102 103 10 Fig. A-22 Viscosity data for slurry no.22.) Fig. A-22 Viscosity data for slurry no.22. Eta(inf)=0.19429 Pas c = 1.2258 n= 0.39206 Eta(inf)=0.38505 Pas c = 13.2404 n = 0.071769 Eta(inf)=0.55699 Pas c = 21.3166 n= -0.24189 103 %K+10%, density = 1200 kgm3 lo'1 Eta(inf)=0.1887 Pas *c = 2.9789 o10 n= -0.16114 l6"o 10' I 10'2 10, 10 10 10 1 10 10o' 10 o1 Sh rte ) Fig. A-23 Viscosity data for slurry no.23. 10 10 10 10 10 10 " 9%K+10%B, density = 1300 kg/Im3 Eta(inf)=0.25905 Pas c = 14.2843 n= 0.11646 t. 10 917K+10%B, density= 1250 kgn? 10 10' Eta(inf)=0.17842 Pas c = 9.2533 o n= 0.13611 10 1103 10 10 10 10 1 10 1 10 1 10lliod,' id l' o Fig. A-24 Viscosity data for slurry no.24. 90%K+10%B, dmsity = 1350 kg/i 10 2d 6 1 0 1 2d 36 4 10 10' 10 10 10 10 10 Fig. A-25 Viscosity data for slurry no.25. Fig. A-25 Viscosity data for slurry no.25. 10' 10 10 100 102 10 10 - I' 10' 10 10 10 10 10 Shea rte r) Fig. A-26 Viscosity data for slurry no.26. Eta(inf)=0.38044 Pas c = 42.8305 n=-0.044113 65K+25%A+10b density = 1225 kg/m3 103 10 10 lo 102 10 102 66%K+25%A+10% density = 1250 kg/m3 102 103 10 10 1 1 10 10 10 She rae (t) 102 103 10 Fig. A-27 Viscosity data for slurry no.27. 665%K+25%A+10%, density = 1275 kg/In3 16 10 10 10 Shear ne() 10 103 10 10 Fig. A-28 Viscosity data for slurry no.28. 66WK+25%A+10%B, density = 1300 kg/n3 *Eta(inf)=0.75004 Pas c= 57.8301 n= -0.058594 0559 10 100 10 Shear nte (Hk) 10 103 10 Fig. A-29 Viscosity data for slurry no.29. 10 100 10 Shear rate (H) Eta(inf)=0.21778 Pas c = 9.0443 n=0.18173 Eta(inf)=0.27711 Pas c = 17.4975 n = 0.089808 Fig. A-30 Viscosity data for slurry no.30. 40%K+50%A+10B, density = 1175kgftr? 10 10 10 Shear r te S 10I 10 10 10 10 2 10 10 10 She re th-) 102 13 4 10, 10 10 Fig. A-31 Viscosity data for slurry no.31. 40%K+50 A+10B, density = 122kgm3 10 100 101 Sheark ) I 10L 10 10 10 10 Fig. A-32 Viscosity data for slurry no.32. 4WK+SA+10B, deity = 120fm 3 10 S10 10 10 Sheer rate -k) 102 103 4 10? 10 10 Fig. A-34 Viscosity data for slurry no.34. Eta(inf)=0.12899 Pas c = 7.8202 n= 0.18243 Eta(inf)-=0.071703 Pas c = 12.1661 n=0.1543 Eta(inf)=0.28417 Pas c = 36.0003 n = -0.018832 . ...... I . ..... d . ...... I . ...... I . ...... I . ..... 40%K+5%A+10%B, densy = 1200kgfrn3 Fig. A-33 Viscosity data for slurry no.33. 15%K+75%A+10%1 density = 1125kgrr 3 Eta(inf)=0.17731 Pas c = 1.8204 S n= 0.20811 0 1 10 10 i shear a (z) 15%K+75%A+10%R desty = 110kgfm3 10 10 10 Shear ne ) 10 10 i Fig. A-35 Viscosity data for slurry no.35. Fig. A-36 Viscosity data for slurry no.36. 15%K+75%A+10B, density = 1175kg/rn3m 15%K+75%A+10%RB, density = 1200 kgM3 Shewrnae- k) Shea rte rk) Fig. A-37 Viscosity data for slurry no.37. Eta(inf)=0.14544 Pas c = 6.1701 n= 0.23661 21 13o I 10 10 10 10 . ....... . ....... . ....... . ...... I . ...... I . .... Fig. A-38 Viscosity data for slurry no.38. 96 A+10%, density = 1150 ivn 10 101 10 ,IoI i10 10 10 10j .10 lid1 10 10 10 10 10' 103 10' 10 10' 100 10 shea rate r) 10 lo lo4 10 10 1 0 Fig. A-39 Viscosity data for slurry no.39. 96A+10%B, densiAty = 1175 kgm3 Fig. A-40 Viscosity data for slurry no.40. A+10m, dernty = 120 kM3 1061 10o 10 Shear rate ) 1 10" 10 1od0L 10d 10) 10 10 10 10 She rate -k) Fig. A-42 Viscosity data for slurry no.42. Eta(inf)=0.19921 Pas c=4.1219 n = 0.24578 . .. .., . .. id.. .. . 0 I I1 10 10 10 ) she ) Eta(inf)=0.10679 Pas c = 14.8333 n = 0.05341 Eta(inf)=0.37333 Pas c = 17.3209 n= 0.033589 . ...... I . ..... I . ..... I . ...... I . ...... i . ..... %A+104B, density = 1125 14,3 Fig. A-41 Viscosity data for slurry no.41. APPENDIX B DEPENDENCE OF POWER LAW PARAMETERS ON DENSITY 0.8 0.6 0.4 0.2 0 1200 1250 0 1200 Kaolinite 1300 1350 1400 1450 Density (kg/m^3) Kaolinite 1250 1300 1350 1400 1450 Density (kg/m^3) 1500 1550 50 1500 15 0.4 0.3 c 0.2 0.1 Kaolinite 0 i I I I II 1200 1250 1300 1350 1400 1450 1500 1550 Density (kg/m^3) Fig. B-I Variation of power-law coefficients with density for kaolinite slurries. Top: r; middle: c; bottom: n. 0 1200 750/%K + 250/A Vo* 1250 1300 Density (kg/m^3) 1350 1400 750/JK + 2501A 30 2010 0 120 0.2 0 S 1e -0.2 -0.4 )0 00 1250 1300 Density (kg/m^3) 1350 1400 75%0K +25%A Density (kg/m^3) Fig. B-2 Variation of power-law coefficients with density for 75% kaolinite+25% attapulgite slurries. Top: rl; middle: c; bottom: n. 0.6 C 0.4 u 0.2 0 1220 120- OU 40 0 1 -40 50%K + 500/A 1240 1260 1280 1300 Density (kg/mA3) 1320 1340 500/X + 5001A 2 20 1240 1260 1280 1300 1320 13 Density (kg/mA3) 500/K( + 500A Density (kg/mA3) Fig. B-3 Variation of power-law coefficients with density for 50% kaolinite+50% attapulgite slurries. Top: r4; middle: c; bottom: n. w m 250/J( + 750/A 1180 1200 1220 Density (kgIm^3) 250/A + 7501A 1180 1200 1220 Density (kg/m^3) 1240 1260 0.3 0.15 S 0 11 -0.15 -0.3 250/%K + 750A Density (kg/m^3) Fig. B-4 Variation of power-law coefficients with density for 25% kaolinite+75% attapulgite slurries. Top: rj; middle: c; bottom: n. 0.8 0.6 S0.4 0.2 0 - 1160 1240 1260 40 30a 20 10 0 1160 30 1180 1200 122 1240 1: 120 Attapulgite 0.6 C 0.4 M 0.2 0 11 Attapulgite 1140 1160 1180 Density (kg/m^3) 1200 1220 1200 1220 Attapulgite 0 n 11 03 " Density (kg/m^3) Fig. B-5 Variation of power-law coefficients with density for attapulgite slurries. Top: ij; middle: c; bottom: n. 1160 1180 Density (kg/mA3) v20 20 1140 1140 24 16 8- 0 1120 1140 1160 1140 1160 00 * - 900/JK + 10%B 1200 1250 1300 Density (kg/m^3) 1350 1400 0.6 S0.4 S cc L 0.2 0 1150 60 40 20 0 1150 0.2 0.1 0 1150 -0.1 -0.2 - 1200 1250 1300 Density (kg/m^3) 1350 90%K+10%B 1400 Density (kg/m^3) Fig. B-6 Variation of power-law coefficients with density for 90% kaolinite+10% bentonite slurries. Top: 7; middle: c; bottom: n. 90%K + 10%B v* * 1300 &10 1A . 12o0 1250 65%K+250/A+10/8 1240 1260 1280 Density (kg/m^3) 1300 1320 650/%K+250/A+100/B 1240 1260 1280 Density (kg/m^3) 1300 1320 650/K+25/,+ 10/B Density (kg/m^3) Fig. B-7 Variation of power-law coefficients with density for 65% kaolinite+25% attapulgite+ 10% bentonite slurries. Top: r1; middle: c; bottom: n. 20 0.8 0.6 0.4 U 0.2 0 12z 80 60 c40 20 0 12 0.2 0.1 0 1 -0.1 20 20 1'0 , 20 1240 1260 1280 13 - 2 400/K+50 OA+100/B 1200 1220 Density (kg/m^3) 400/K+500/A+ 10OI * 2 1180 1200 1220 Density (kg/m^3) 400WK+500/A+ 100B 1240 1260 Density (kg/m^3) Fig. B-8 Variation of power-law coefficients with density for 40% kaolinite+50% attapulgite+ 10% bentonite slurries. Top: 71-; middle: c; bottom: n. 0.4 0.3 0.2 0.1 0 116 1180 1180 1240 1240 1260 60 40 30 S20 10 0 11 0.2 0.1 0 1 -0.1 150 1180 1200 1220 1240 12 -- 0 1 5/J(+75/A+1 0/B 1140 1160 1180 Density (kg/m^3) 15% K+75% A+I 0% B 1140 1160 1180 Density (kg/m^3) 1 50/cK+75%A+10V0B 1140 1160 1180 Density (kg/m^3) Fig. B-9 Variation of power-law coefficients with density for 10% bentonite slurries. Top: 71; middle: c; bottom: n. 1200 1220 1200 1220 15%kaolinite+75% attapulgite+ 0.4 0.3 0.2 0.1 0 112 1200 1200 1220 10 0 1 120 0.3 0.2 0.1 0 1120 0 900/A + 10/0 1.2 C 0.8 u 0.4 0 11 90/ + I100B 1140 1160 1180 Density (kg/m^3) 90% A + 10%B 1140 1160 11 1200 1220 100 1220 Density (kg/m^3) Fig. B-10 Variation of power-law coefficients with density for 90% attapulgite +10% bentonite slurries. Top: i; middle: c; bottom: n. 1160 1180 Density (kg/m^3) 1140 1200 1220 120 80 40 1120 0.4 0.2 0 S 1120 -0.2 -0.4 - - 20 APPENDIX C VELOCITY PROFILES AND CORRESPONDING DISCHARGES 0 1 2 3 4 5 6 Velocity (m/s) Fig. C-I Computed velocity profiles and corresponding discharges for slurry no. 1. 5 QSMk = 0.00085 m 3/S QNWt,,I.. = 0.00085 m 3/S 5 0 1 2 3 4 Velocity (m/s) Fig. C-2 Computed velocity profiles and corresponding discharges for slurry no. 7. 0 1 2 3 4 5 6 Velocity (m/s) Fig. C-3 Computed velocity profiles and corresponding discharges for slurry no. 11. 0 0.8 1.6 2.4 3.2 4.0 Velocity (m/s) Fig. C-4 Computed velocity profiles and corresponding discharges for slurry no. 15. I QNewtonian = 0.00118 m3Is 0.5 QSisk0 = 0.00115 m3Is 0.5 0 0.8 1.6 2.4 3.2 4.0 Velocity (m/s) Fig. C-5 Computed velocity profiles and corresponding discharges for slurry no. 19. -0.5 I 0 2 4 6 8 Velocity (m/s) Fig. C-6 Computed velocity profiles and corresponding discharges for slurry no. 23. QSisko = 0.00155 M 3IS QN.wteenan = 0.00155 m'Is |