UFL/COEL98/013
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, Yeonsihk 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 DACW3996M2100.
TABLE OF CONTENTS
page
ACKNOWLEDGMENT.......................................... ...... ........................ ii
LIST OF FIGURES ......................................................................... ...................... vi
L IST O F T A B L E S.................................................................................................... .. xi
LIST OF SYMBOLS....................................................................... .................... xii
ABSTRACT................................ ......... .. ......................... .......................... xvi
CHAPTERS
1. INTRODUCTION ...................................................................... .....................
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 Poiseuille 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 NonNewtonian Models................................. 17
2.3 Poiseuille Flow Velocity Distribution.......................... ................... 19
2.3.1 Newtonian Fluid............................................... .................... 19
2.3.2 Bingham Plastic................................................ ..................... 20
2.3.3 PowerLaw Fluid............................................ ...................... 22
3. EXPERIMENTAL SETUP, PROCEDURES AND MATERIALS..................24
3.1 Coaxial Cylinder Viscometer..............................................................24
3.2 Horizontal Pipe Viscometer...............................................................25
3.3 Sedim ents and Slurries................................................. ...................... 26
3.3.1 Sediment and Fluid Properties.................................................26
3.3.2 M ud Slurries....................................................... ...................... 29
4. EXPERIMENTAL RESULTS.....................................................................34
4.1 R heom etric Results..................... ..................... .. .. ..................... 34
4.1.1 PowerLaw for Mud Flow......................................................34
4.1.2 PowerLaw Coefficients......................................................... 36
4.2 E nd and Slip E ffects................................................... .................... 38
4.3 Pow erLaw Param eters................................................ ...................... 40
4.4 Slurry Discharge with Sisko Model....................................................46
4.5 Calculation of Slurry Discharge..........................................................49
4.6 PowerLaw Correlations with Slurry CEC..........................................52
5. CONCLUDING COMMENTS......................................................................55
5.1 C conclusions ................................................................... ...................... 55
5.2 C om m ents .................................................................... ........... ......... 55
5.3 Recommendation for Future Studies.................................................. 56
B IB L IO G R A PH Y ............................................... .......................... ..................... 58
APPENDICES
A SLURRY VISCOSITY DATA ................................................................. 59
B DEPENDENCE OF POWER LAW PARAMETERS ON DENSITY............. 70
C VELOCITY PROFILES AND CORRESPONDING DISCHARGES .......... 80
BIOGRAPHICAL SKETCH.................................................................................85
LIST OF FIGURES
Figure pAgU
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 pressuredrop/flow rate relationship for slurry flow in pipes ..................... 11
2.3 Plot of In r versus In tc, Dashed line is tangent to the curve through
a data p oint......................................................................... ................... 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 nonNewtonian 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 =0.1 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=0.1, for
slurry density p=1000, 1,198 and 1,314 kg/m3 (from right to left)...............22
2.10 Velocity profiles for a powerlaw fluid, with Q=0.003 m3/s, R=0.1 m., 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
viscom eter (H PV )............................................................. ...................... 26
3.4 Photograph of H PV setup ........................................................... ..................... 27
4.1 Comparison between pseudoplastic (shearthinning) and Newtonian
flow curves. The nature of the shearthinning 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 ewtonian case........................................................................... 35
4.2 Data obtained from the endeffect correction experiment ...................................39
4.3 Plot of (P/4t:) vs. ,, for slip effect correction...................................................39
4.4 Plot of (P/4T,) 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 of i. 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 ewtonian solution...................... ... ....................... 51
4.10 Computed velocity profiles and discharge for slurry no.23 ....................................51
4.11 Variation of i. with slurry CEC (CECdY) for all slurries .................................... 53
4.12 Variation of c with slurry CEC (CEC, ) for all slurries ...................................53
4.13 Variation of n with slurry CEC (CEC& ) for all slurries ..................................54
Ai Viscosity 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
A5 Viscosity data for slurry no.5 ................ .................................... .................... 60
A6 Viscosity data for slurry no.6 ................................................................................ 60
A7 Viscosity data for slurry no.7 ......................................................... .................... 61
A8 Viscosity data for slurry no.8 ........................................................ ..................... 61
A9 Viscosity data for slurry no.9 ........................................................ .................... 61
A10 Viscosity data for slurry no.10 .................................................... ...................... 61
A 11 Viscosity data for slurry no. 11 ..................................................... .......................62
A12 Viscosity data for slurry no. 12 ............................................................................... 62
A13 Viscosity data for slurry no. 13 ....................... ...................... 62
A14 Viscosity data for slurry no.14 ....................................................... ..................... 62
A15 Viscosity data for slurry no. 15 ....................................................... ..................... 63
A16 Viscosity data for slurry no. 16 ....................................................... ..................... 63
A17 Viscosity data for slurry no. 17 ............................................................................... 63
A18 Viscosity data for slurry no. 18 ........................................................ .................... 63
A19 Viscosity data for slurry no.19 ....................................................... ..................... 64
A20 Viscosity data for slurry no.20 ........................ ............................................... 64
A21 Viscosity data for slurry no.21 ......... ..................................................................... 64
A22 Viscosity data for slurry no.22 ............................................................... 64
A23 Viscosity data for slurry no.23 ......................................................... ................... 65
A24 Viscosity data for slurry no.24 .................................................... ........................ 65
A25 Viscosity data for slurry no.25 ...................................................... ...................... 65
A26 Viscosity data for slurry no.26 .......................... ........................ 65
A27 Viscosity data for slurry no.27 ....................................................... ....................66
A28 Viscosity data for slurry no.28 ...................................................... ...................... 66
A29 Viscosity data for slurry no.29 ........................ .... ..................... 66
A30 Viscosity data for slurry no.30 ........................................................ ................... 66
A31 Viscosity data for slurry no.31 ................................. ............................67
A32 Viscosity data for slurry no.32 ....................................................................67
A33 Viscosity data for slurry no.33 ........................................................................... 67
A34 Viscosity data for slurry no.34 ...................................................... ...................... 67
A35 Viscosity data for slurry no.35 .......................... ...................... 68
A36 Viscosity data for slurry no.36 ....................................................... ..................... 68
A37 Viscosity data for slurry no.37 ..................................................... ....................... 68
A38 Viscosity data for slurry no.38 ..................................................................68
A39 Viscosity data for slurry no.39 ....................................................... .................... 69
A40 Viscosity data for slurry no.40 ...................................................... ...................... 69
A41 Viscosity data for slurry no.41 ........................................................ .................... 69
A42 Viscosity data for slurry no.42 ...................................................... ...................... 69
Bi Variation of powerlaw coefficients with density for kaolinite slurries.
Top: i.,; middle: c; bottom: n .................................................................. 70
B2 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: ri.; middle: c; bottom: n .................................................................. 71
B3 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: ln.; middle: c; bottom: n .............................................................. 72
B4 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: rl.; middle: c; bottom: n .................................................................. 73
B5 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: 1.; m iddle: c; bottom : n ............................................................... 74
B6 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: Tr.; m iddle: c; bottom : n ......................... .................................... 75
B7 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: "i.; m iddle: c; bottom : n ............................... ................................. 76
B8 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: rl.; m iddle: c; bottom : n .......................... .................................... 77
B9 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: "1.; m iddle: c; bottom : n....................... ...................................... 78
B10 Variation of powerlaw coefficients with density for kaolinite slurries.
Top: r.; m iddle: c; bottom : n ................... .......................................... 79
C1 Velocity profiles and corresponding discharges for slurry no. 1......................... 80
C2 Velocity profiles and corresponding discharges for slurry no.7.........................80
C3 Velocity profiles and corresponding discharges for slurry no. 11....................... 81
C4 Velocity profiles and corresponding discharges for slurry no. 15....................... 81
C5 Velocity profiles and corresponding discharges for slurry no. 19....................... 82
C6 Velocity profiles and corresponding discharges for slurry no.23.......................82
C7 Velocity profiles and corresponding discharges for slurry no.27.......................83
C8 Velocity profiles and corresponding discharges for slurry no.31.......................83
C9 Velocity profiles and corresponding discharges for slurry no.35......................84
C10 Velocity profiles and corresponding discharges for slurry no.39......................84
LIST OF TABLES
Table page
3.1 Chem ical com position of kaolinite................................................. ....................... 27
3.2 Chemical composition of bentonite.......................................................................... 27
3.3 Chemical composition of attapulgite (palygorskite).............................................. 28
3.4 Chem ical com position of w ater....................................................... ...................... 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 m ud slurries tested.............................................................................. 31
4.1 End and slip effects experimental data of 1,236 kg/m3 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
CECAUIapUIj~
CECB.ntomit.
CECK.0Bw
CECSiu,,y
D
DIFF
fAflapugit.
fBcntonite
fKaofinjtc
fwat.r
K
g
9,,9,,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
L, Extra length for end effects
LL Length of longer pipe
LL' Fully developed flow section for longer pipe
Ls Length of shorter pipe
Ls' 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
Ap Pressure loss
APe Pressure loss due to end effects
ApL Pressure loss in the longer pipe
^ps Pressure loss in the shorter pipe
Q Pipe discharge
Qfluid Fluid discharge
Qopug Plug discharge
R Pipe radius
r Radial distance coordinate
ro
Re
Ref
t
u
u
S
V
V
v
V.
V, Vr Vlug
Vi+V
z
a
F
P
no slp
i?
C
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
1T Apparent viscosity
ri. Value of Ti at infinite shear rate
if. Experimental slurry viscosity
6 Cylindrical coordinate, 0
u Plastic viscosity
p Fluid density
T Shear stress
Itj Shear stress tensor
1T: Wall shear stress
ITy Yield shear stress of mud
Tzz, Trr' Too Normal shear stress with contain the elastic effect
trz, tro, tz Shear stresses
'1/2 Shear stress at ir = 0.5 p
0 Pressure 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 nonNewtonian rheology, as
characterized by the threeparameter Sisko powerlaw model for apparent viscosity
variation with shear rate. The overall slurry density range tested was 1,125 kg/m3 to
1,500 kg/m3. Powerlaw 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
pistondiaphragm 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 (CEC,Iuy) is introduced as a cohesion
characterizing parameter dependent on the weight fractions of clays and water in the
slurry. It is shown that the powerlaw parameters correlate reasonable well with CECiy,
which therefore makes it a convenient measure of the rheology of slurries composed of
pure clays and clay mixtures.
The steadystate slurry transport equation for the Sisko powerlaw 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 powerlaw for the slurries,
additional tests were carried out in the HPV at lower pumping pressures than those used
to determine the powerlaw 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 1
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 highpressure water jets in preparation for the suction of the diluted
slurry and its transport to the outtake 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 highpressure pump.
Discharge
Intake /
Entrainment and Spreading
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 knowhow 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 twostep 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 benchtop
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, 6) are as
follows:
Incompressible continuity equation:
1 OrVr IV. 8V
r dr raO 8z
(2.1)
Momentum equations:
rcomponent:
a Vr 8 Vr Vo Vr V2 Vr p 1 arr 1 a .r tOO rz(2.2)
pVp+ +V +g + + 1 +l^ (2.2)
kat r r r 56 r az z ar r ar r 56 r az
0component:
(aV aVo Vo aVo VeVo 8Vy 001.ap 1 ar2 rO 1 ao0 az(
p e +Vr + +V = +pa + + (2.3)
a at ar r 5a r 3z rr 9r r aO az
zcomponent:
8( Vz+'v a, vz o _LVo 8 zap +
"_ V5 =  +pg +_ +, + (2.4)
at zr r V6 z 9z 9z z r ar r a6 az
where z, rr, r TOO are the normal stresses; t1r, T1r, t0o are shear stresses; V z, V, VO are
the velocity components in z, r and 0 directions, g2, 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 nonzero component. These conditions can only be
satisfied if
Vr=Vo=0, Vz *(0) (2.5)
Under the above conditions, the continuity Eq. (2.1) reduces to
oV
z =0 (2.6)
so that Vz >f(z), i.e., V, = V/r) only. The rate of strain tensor therefore becomes
0 dV/dr 0 0 1 0
', = dV/dr 0 0 = j 1 0 0 (2.7)
0 0 0 0 0 0
so that the shear stress tensor has, at most, the following nonzero components
LI rz
0
ar 0
rz
\r 0
Trr 0
0 "oo
Accordingly, the three component momentum equations are simplified as
zcomponent:
az r ar
rcomponent:
Bp 1 8 "C
pgr (r,) TO
9r r ar r
6component:
l ap _9=
r aepg=
L
F>
0L '(
Fig. 2.1 Pipe flow definition sketch.
(2.8)
(2.9)
(2.10)
(2.11)
1 10 1
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
af Lo=04 (2.12)
z ar) ar [z)
In other words, the pressure gradient, (dp/az), is independent of r. Therefore, the pressure
gradient along the pipe can be calculated as ap/az=(pL p)/L, where po 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 (D):
.pgz (rtz) (2.13)
az r ar
Integrating Eq. (2.13) leads to
re C,
rD + (2.14)
"2 r
The integration constant, C,, must be zero, since otherwise an infinite stress would be
predicted at the center (r=0). Considering the stress exerted by the fluid on the pipe wall
7rR20 R
; ..  (2.15)
W 2nR 2
then Eq. (2.14) becomes
reD r
rz 2  (2.16)
10
which is the final form of the equation of motion for Poiseuille flow. It is valid for either
laminar (Newtonian or nonNewtonian) or turbulent flow.
2.2 Viscous Model
2.2.1 Flow Type
In terms of flow properties for homogeneous, nonsettling slurries considered here
under steady state in pipes, the flow type, the apparent viscosity and the flow curve (j, versus
*c) must be obtained. The experimental data required include the pressure drop Ap over the
fully developed flow length L and the volumetric flow rate Q (or mean velocity Vm).
From the plot of ln(AplL) versus InQ or InVm shown in Fig. 2.2, where n is called
the powerlaw 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 nonNewtonian 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:
T(o)=_ (2.17)
Y
Now, from Eq. (2.16) it is evident that measurement of the pressure gradient 0 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= f2trVz(r)dr
0
(2.18)
Integrating Eq. (2.18) by parts, with the condition that Vz=0, at r=R, leads to
Q=nrfr 'dVkz=rfr2
0 0
dVz
dr
dr
(2.19)
o Decreasing n value
InQ or InV.
Fig. 2.2 Typical pressuredrop/flow rate relationships for slurry flow
in pipes.
Turbulent
Slope 1.75 to 2
NonNewtonian:
Shear thinning
Newtonian:
Laminar, Slope 1
Inr
Fig. 2.3 Plot of Int, versus InP. 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 T and R) to give
Q= 7R 3'T2d (2.20)
3 f3
w 0
By taking the derivative of Eq. (2.20) with respect to T,, we obtain
d( =^w 42i W (2.21)
where r=4Q/nR3 and yw is the shear rate at the wall. Solving Eq. (2.21) for jw leads to
T dw 3F
" 4 dc (2.22)
13
If we let n '=dn(tc,)/dlnr, Eq. (2.22) can also be written as
JP (2.23)
Based on Eq. (2.23), the apparent viscosity takes the form
T1(() (2.24)
( 3n'+1
From the laboratory data (measurements of discharge and pressure drop), Inrt can be
plotted against InP, as shown in Fig. 2.3. For that purpose, the wall shear stress, t,, 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 ,p is not carried out within the fully developed flow
section, a correction for 4p becomes necessary.
End effects can be corrected for experimentally in various ways. One approach is to
determine an equivalent "extra length" (L,) of the pipe that would have to be added to the
actual length if the total measured ,p 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 L,:
= P= w (2.25)
L+L R
If the pipe is horizontal (g=0) and noting that T,, is a unique function ofF as shown in Eq.
(2.22), Eq. (2.25) can be rearranged to give:
Lr L + L))
Ap= 2t + F( + (2.26)
R R RR
As a result, if several pipes of different L/R ratios are used, and zp 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 ap=O determines L,
(Fig.2.4). The intercept on the ap axis at L/R=O is the pressure drop (Ape) due to the
combined end effects. Since a different value of L, would be obtained for each value of F,
LJR can be empirically correlated with F.
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 =OS=. Then
following relationships are satisfied
PL= Pe +(L Le)D =APe +LL'I (2.27)
^Ps= Pe+(LsLe) APe+Ls' (2.28)
Subtracting Eq. (2.28) from Eq. (2.27), the true pressure gradient in the fully developed
flow section reads
=APLPS (2.29)
L SL
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 (u.) superimposed upon
the fluid in the pipe, and modifying Eq. (2.20), i.e.,
Q=ru f 2 + dR 3 fv dr (2.30)
w 0
l R + f2d (2.31)
W w0
where p=us/tw is a slip coefficient. This coefficient can be evaluated as follows:
1. Using various pipes of the same length but different radii, plot r/4Twversus T
for each pipe. If P=0, these curves should coincide. If not, the curves will be distinct, in
which case one must proceed as follows:
2. At constant Tw, plot r/4,w versus 1/R from the above curves. This plot should
be linear with a slope =p;
3. Repeat step 2 for various values of Tw, and then plot P versus .
The appropriate value of F to use in evaluating w is then a "corrected" value
corresponding to no slip:
=( ) w (2.32)
rnoslip (rslip)measured (2.32)
X *r=const.
L, /R LR
LI
Fig. 2.4 Equivalent "extra length" due to end effects.
Short pipe, radius R
S Ls
P Long pipe, radius R
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 t, and Tr versus Y,, (Fig.
2.6). The yield stress of the mud, T, is obtained by extrapolating the curve of t, versus
' w. Next we will attempt to determine the empirical relationships between t, and Tr
versus jw'
2.2.5 Three Empirical NonNewtonian Models
The most successful attempts at describing the steady rate of shearstress behavior
of nonNewtonian 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 nonNewtonian behavior.
r7 versus Yw
r, versus Yw \
I
Yw
Fig. 2.6 Slurry flow curve for nonNewtonian 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
:= ty+[Y for ty (2.33)
Y=0 for T
This is a twoparameter model, with y as the yield stress and g as the plastic viscosity.
The apparent viscosity function thus becomes, n=,p(ty/Y), for tl>yand r,oo, for r
2.2.5.2 General powerlaw fluid
This is described as
T=cY" (2.35)
This is also a twoparameter model, with n as the flow index, c as the consistency. The
apparent viscosity for this model is 1r==c,".
2.2.5.3 Ellis model
In this model, the apparent viscosity is obtained as
't 1 )(2.36)
The three parameters in Eq. (2.36) are ga, t:12 and a. Here T11/2 is the value of r at which
rl=0.5g, 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, T1.
Given the boundary condition
Vz=O at r=R (2.37)
The solution for the velocity profile is
V R ( 21 (2.38)
The corresponding volumetric flow rate is
Q= 4 (2.39)
41j
and the ratio between Vz and mean velocity V, is
=2Vz r (2.40)
V. R
At steady state Vm 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 ITrZ< Ty, the material will behave like a
rigid solid. Therefore, from the pipe centerline to the point at which rz I= Ty, 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.rR, where ro=(y/w)R:
V [ (r) 21 1R ) (2.41)
z2 2 (R T R
and for rsro:
Vpug 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=0.1 m.
S1
Newtonian fluid with Q=0.003 m3/s and
Fig. 2.8 Schematic of velocity profile for a Bingham plastic.
(2.43)
Examining of above solution indicates that the velocity profile depends on CTy, 71, R and Q.
Sample velocity profiles are shown in Fig. 2.9.
0.5
1/R e 
0.5
0 0.5 1 1.5 2
F/V.
Fig. 2.9 Velocity profile for a Bingham fluid, with Q=O.003m'/s, R=0. m, for slurry density
p=1000, 1099, 1198 and 1314 kg/m3 (from right to left).
2.3.3 PowerLaw Fluid
The rheological equation of state for a powerlaw 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:
Q "R'a 4 w TY 41
Q =Qfluid + plug= I  _
V = n 1 .
n+1 J R
=( n * R3
3n+lR1 bm
Ratio between V, and mean velocity V.:
V 3n+11 (I r )
HV i n+1 R
Therefore, when V, 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/V.
Fig. 2.10 Velocity profiles for a powerlaw fluid, with Q=0.003m3/s, R=0. Im, 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 rightcircular 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 laner 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, rI, which is inherently corrected for endeffects 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 workbench, with one end attached to a pistondiaphragm pump and
the other end open, with a bucket receptacle to collect the slurry. The ARO model
6661A3344C nonmetallic doublediaphragm 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 flushdiaphragm gage pressure sensors. The pressure
Hopper
Pump Pipe
SBucket
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 beigecolored powder, was obtained from the EPK
Division of Feldspar Corporation in Edgar, Florida. Its Cation Exchange Capacity (CEC),
as given by the supplier, was 5.26.5 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 greenishwhite 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/m3 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 Na20 0.02
Fe203 0.51 K20 0.40
TiO2 0.36 SO3 0.21
P205 0.19 V20 < 0.001
CaO 0.25
Table 3.2: Chemical composition of bentonite
Chemical % Chemical %
SiO2 63.02 A20z3 21.08
Fe203 3.25 FeO 0.35
MgO 2.67 Na2O & 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
Fe2,O 2.32 FeO 0.19
MgO 8.92 CaO 1.65
H,O 10.03 NH,0 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 double
distilled 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 Xray apparatus were
converted to Stokes equivalent diameters. The median particle sizes of kaolinite, bentonite
and attapulgite were 1.10 pm, 1.01 pm and 0.86 pm, respectively.
Table 3.5: Size distribution of kaolinite
Diameter Frequency distribution Cumulative frequency distribution
(p)m) (%) (%)
5.00< 0.0 0.0
5.003.20 0.0 0.0
3.203.00 2.9 2.9
3.002.80 4.0 6.9
2.802.60 2.6 9.5
2.602.40 4.1 13.6
2.402.20 4.0 17.6
2.202.00 6.0 23.6
2.001.80 5.7 29.3
1.801.60 6.2 35.5
1.601.40 5.5 41.0
1.401.20 6.2 47.2
1.201.00 5.8 53.0
1.000.80 5.0 58.0
0.800.60 10.4 68.4
0.600.40 11.2 79.6
0.400.20 13.6 93.2
0.200.00 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 = fkaoliniteCECkaolinite +attapulgiteCECattapulgitebentoniteCECbentonite (3.1)
where f represents the weight fraction of the subscripted sediment, and subscripted CEC
are the corresponding cation exchange capacities. Note that given father as the weight
fraction of water in the slurry, we have: fkaoliniteattapulgite +fbentonite waterr = 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
(pm) (%) (%)
3.00< 5.9 5.9
3.002.80 1.9 7.8
2.802.60 2.3 10.1
2.602.40 2.5 12.6
2.402.20 3.0 15.6
2.202.00 3.0 18.6
2.001.80 4.9 23.5
1.801.60 5.3 28.8
1.601.40 8.1 36.9
1.401.20 4.5 41.4
1.201.00 9.3 50.7
1.000.80 9.1 59.8
0.800.60 11.4 71.2
0.600.40 11.2 82.4
0.400.20 11.5 93.3
0.200.00 6.1 100.0
Table 3.7: Size distribution of attapulgite
Diameter Frequency distribution Cumulative frequency distribution
(Iun) (%) (%)
2.00< 11.8 11.8
2.001.80 4.1 15.9
1.801.60 4.9 20.8
1.601.40 5.3 26.1
1.401.20 5.6 31.7
1.201.00 5.8 37.5
1.000.80 17.4 54.9
0.800.60 25.5 80.4
0.600.40 12.3 92.7
0.400.20 6.1 98.8
0.200.00 1.2 100.0
Table 3.8: Properties of mud slurries tested
Slurry No. Sediment Density Water Content CECu, ,
(kg/m3) (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%K 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 75%K+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 50%K+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 25%K+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%0/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+10%B 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 40%K+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 15%K+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+10%B 1,175 284 9.29
42 90%A+10%oB 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/m3 to a high 1,500 kg/m3. The water content varied from a high 423% to a low 75%.
Finally, the CECI.,y 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 PowerLaw 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 wellknown
Sisko (1958) powerlaw provides a reasonable fit to the measured decrease in apparent
viscosity, %r, with increasing shear rate, ', a behavior that is consistent with the
pseudoplastic flow curve (Fig. 4.1).
With reference to the Sisko model, it is noted that general powerlaw 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
o (cCi)p (4.1)
where r10 and TI 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 in is the apparent viscosity.
Pseudoplastic shear
thinning flow curve
Newtonian flow curve
Fig. 4.1 Comparison between pseudoplastic (shear
thinning) and Newtonian flow curves. The nature of
the shearthinning 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 rl<< ri, hence the above equation can be simplified as
(cif)P (4.2)
which can be rewritten as
oo
T1 =rT I (4.3)
or
T, = ._ +cn"l
(4.4)
36
Equation (4.4) is the Sisko (1958) model, where ril 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 shearthinning or shear
thickening, that is, when n > 1 the material exhibits shearthickening, and n < 1 denotes a
shearthinning behavior. When n =1 the behavior is Newtonian, with consistency c = 0 and
a constant viscosity equal to rl. Note also that when rT=O, Eq. (4.4) becomes
consistent with the powerlaw 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 wellknown Reynolds number criterion:
Re = VD < 2100 (4.5)
where Vm is the mean velocity in the pipe, and D = 2R is the pipe diameter.
4.1.2 PowerLaw Coefficients
To solve for the three Sisko parameters, ril, 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, 71, as a function of the shear rate, 9, obtained from the measured relationship
between stress (t) 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= Z (firn)2 = minimum (4.6)
i=l
or
M
DIFF= ( .c',1)2 = minimum (4.7)
i=l
where fl, is the slurry viscosity obtained from the experiment, and M is the number of data
points.
Setting
9DIFF =0; 9DIFF =0; 9DIFF 0 (4.8)
arl an ac
from Eq. (4.7 ) it is obtained the following by differentiation:
M
(f ~ c1) =0 (4.9)
i=1
M
{i'n1 (f,rl c~) )} 0 (4.10)
i=l
and
M
E {cn llog (%i4Tc"ql)} =0 (4.11)
i=1
In this way, rTj, 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 lowshear rate nonNewtonian and
high shear rate Newtonian behaviors are identified. In addition, the limitation of rlin this
method is to be greater than water viscosity (0.001 Pa.s).
Since there are three parameters, ir, c, n, to be determined, least squares analysis was
38
carried out by selecting rTl, 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 kg/m3 slurry of 50%Kaolinite+50%Attapulgite
Pipe no. Pipe Diameter, Pipe Discharge, Q Pressure drop, Ap Wall stress,
D Length, L (m3/s) (Pa) w
(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+10%Bentonite
Pipe no. Pipe Diameter, Pipe Discharge, Q Pressure drop, zap Wall stress, Tw
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
C.
w 80000 
o
40000 
0 
0 100 200 300
L/R
Fig.4.2 Data obtained from the endeffect correction experiments.
From the plot, and referring to Fig. 2.4, 4p,=1,074.3 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 (3) was
determined as follows:
Step 1. Plot(r/4t) vs. ',,
200
150 *
100
1**
50
01 I I
0 5E07 1E06 1.5E06 2E06 2.5E06
Gamnma4Tau
Fig. 4.3 Plot of ('P/4T,) vs. t, for slipeffect correction.
40
The plot indicates that t, is almost constant (167.5 Pa.).
Step 2. Plot(r/4t,) vs. 1/R
0.000003
0.000002 
E
E 0.000001 
0
40 60 80 100 120
1/R
Fig. 4.4 Plot of (r/4t,) vs. 1/R for slip effect correction.
From the plot, the slope of Fig.4.4 is equal to P = 2 x 108 which is close to zero.
Therefore, from Eq.(2.32):
rno sup = (lr.p) 4pTw/R
with P = 0
r...no slip (r.,lip)
which indicates no slip effect.
4.3 PowerLaw 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, 9, and the corresponding shear stress, r, both at the pipe wall, could be
calculated from the following Newtonian flow equations:
8V
Y D (4.12)
D
S DAp (4.13)
w 4L
where Vm is the mean flow velocity in the pipe. Then rl = j For each slurry the measured
pressure drop, Ap, the measured discharge, Q, and the calculated wall stress, T,, 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.
Bestfit coefficients i 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, Ap Discharge, Q Shear rate, Y Wall stress, rT
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 0.00117 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, rl rl, 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 nonturbulent conditions, as required for the rheological analysis. The
powerlaw coefficients show considerable variability with slurry composition and density.
Note that the lowest value of rlwas chosen to be 0.001 Pa, the viscosity of water. In
other words, in the Sisko Model analysis ril was not allowed to have values lower than
the viscosity of water.
102 .
10.3
102
25%K+75%A, density = 1175 kg/m3
.1 0
10"1 100 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, rl_, 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 ral shows an overall increasing trend with increasing density.
In any event, it is logical to expect rl 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<1 throughout, over the entire density range the slurry behavior is seen
to be pseudoplastic.
Eta(inf)=0.23419 Pa.s
c = 3.1439
n = 0.22145
. ..... i . ..
45
Kaolinite
0.8
0.6
0.4
S0.2
0
1200 1250 1300 1350 1400 1450 1500 1550
Density (kg/m^3)
Fig. 4.6 Variation of r,. 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 
c 0.2
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 nonmonotonic 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
=a9v/9r, and the steadystate momentum equation for pipe flow is
1Y = (4.14)
R
where c is the wall shear stress. For expressing the apparent viscosity, 11, in terms of the
shear rate, the Sisko model is given by Eq. (4.4). Next, let
C = 1 (4.15)
R
Eq.4.15 gives a(/ar= 1/R, and av/r can be written as (av/id)(9(/9r). Then, combining Eqs.
(4.4), (4.8) and (4.9) it is obtained
+ + ((1)tK = 0 (4.16)
R R T BC ac
which must satisfy the noslip boundary condition at the wall, i.e., v(71=0) = 0. Next, Eq
(4.10) can be written in the finite difference form as
Table 4.4: Sisko model coefficients and HPV flow Reynolds number
Slurry No.
(Pa.s)
0.1890
0.1403
0.4361
0.5890
0.6626
0.6749
0.3381
0.5465
1.6736
0.9040
0.2382
0.2704
0.2947
0.4527
0.2342
0.3818
0.5597
0.6195
0.1943
0.3046
0.3851
0.5570
0.1887
0.1784
c n Ref
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
0.291
0.223
0.062
0.071
0.174
0.007
0.283
0.221
0.023
0.117
0.247
0.221
0.134
0.126
0.201
0.392
0.073
0.072
0.242
0.161
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
n\
c+ Cv v vi 1 + = 0
R R" A n A r i 2
Based on Eq. (4.17) the following iterative relation was used:
i = A
v~i1 = vi+ A
1 TW
ni
m
11. Vitl i
R R" AC
328
220
428
331
282
113
637
984
568
268
434
502
617
205
401
666
211
64
(4.17)
(4.18)
49
where vi, (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
Vi_+.1 Vi < 106 (4.19)
Finally, the discharge, Q, is obtained from the summation
i=N( V+y \
Q = 2rt I+' rdr (4.20)
i=1 2
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
HPV to obtain the data points for determining the powerlaw relationships. (Compare the
pressure drops in Table 4.5 with the corresponding ones in Table 4.3).
Using the powerlaw 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.1 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. Ap discharge, Q rate, t stress, c, discharge, Q
(Pa) (m3/s) (Hz) (Pa) (m'/s)
1 68,465.5 0.00135 836.6 175.3 0.00131
7 69,969.8 0.00130 807.6 179.2 0.00085
11 82,678.5 0.00136 844.9 211.7 0.00127
15 67,697.0 0.00128 794.5 173.3 0.00108
19 61,719.1 0.00136 842.0 158.0 0.00115
23 71,668.8 0.00133 823.2 183.5 0.00155
27 67,464.2 0.00133 825.4 172.7 0.00101
31 73,927.5 0.00129 800.9 189.3 0.00192
35 78,395.6 0.00132 821.6 200.7 0.00174
39 74,920.0 0.00137 850.0 191.8 0.00134
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 powerlaw approximation
of the theological data, i.e., to the extent to which the powerlaw fits the measured data from
the viscometers. All the computed velocity profiles and corresponding discharges are as
shown in the Appendix C.
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.
I
0.5
Qs;.ko = 0.00155 m8/s
QN.0t.O..n = 0.00155 m3Is
0         
0.5
I
0 2 4 6 8
Velocity (m/s)
Fig. 4.10 Computed velocity profiles and discharges for
slurry no. 23.
52
4.6 PowerLaw Correlations with Slurry CEC
The slurry CEC (CEC.,,), 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 physicochemically related. In Figs. 4.10, 4.12 and 4.13, data from
Table 4.4 have been used to plot the powerlaw coefficients 1T, (logarithm of) c and n
against CECy 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 ir increases with CEC,,i., starting with
0.001 Pa at CECiu, = 0 for water. This trend can be expected since greater cohesion
would imply greater interparticle interaction, hence larger viscosity. Similarly, in Fig. 4.12
the consistency, c, is seen to increase with CEC,,u., 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 CECIu,, approaches zero, log c tends to go to .
Finally, in Fig. 4.13, n is seen to decrease with CEC,SI.,. 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 CEC,I.uy implies increasingly nonNewtonian, shearthinning 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:
rl = 0.0015CECsuy + 0.361
(4.21)
logc = 0.127CEC slu + 0.22
n = 0.033CECSI + 0.278
2.0000
1.5000
j 1.0000
Lu
0.5000
0.0000
0.00
5.00
Slurry CEC
(4.22)
(4.23)
10.00
Fig 4.11 Variation of T. with slurry CEC (CEC,Su,,y) 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,,,,) for all slurries.
0
0
0 0
0 O0 _
00 o
1.000
0.500 
o
0.000 o
0.)0 4.db o o 800 0 1200
0.500
Slurry CEC
Fig 4.13 Variation of n with slurry CEC(CEC.Iuy) 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 fortytwo claywater slurries were pumped through a horizontal pipe
viscometer, CECs can serve as an approximate determinant of slurry discharge in the viscous
flow range. Thus, from the relationship between CECs and the powerlaw coefficients (ri.,
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 powerlaw
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 drawback 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 theological 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, backcalculate 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, powerlaw coefficients, CEC, and discharge
can be determined.
57
For the relationships between density and powerlaw 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 nonNewtonian fluids: a new flow equation for
pseudoplastic systems, Journal of Colloidal Science, 20, 417437.
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 nonsettling slurries, In: Slurry
Handling Design of SolidLiquid Systems, N. P. Brown and N. I. Heywood (eds.),
Elsevier, Amsterdam, 5387.
Jinchai, P., Jiang, J., and Mehta, A.J., 1998. Rheology and rheometry of mud slurry flow in
pipes:a laboratory investigation. Report No. UFL/COEL981001, 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 CPARCHL972, 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, 573589.
Sisko, A. W., 1958. The flow of lubricating greases, Industrial Engineering Chemistry, 50,
17891792.
Thai Pollution Control Department, 1997. Mercury monitoring of coastal environment,
http://www.pcd.go.th/news/hgsea.cfm
Wasp, E. J., Kenny, J. P., and Gandhi, R. L., 1977. SolidLiquid Flow Slurry pipeline
Transportation. Trans Tech Publications, San Francisco.
APPENDIX A
SLURRY VISCOSITY DATA
Ka.linit. d s.Ay = 1250 kgf.
Eta(inf)=0.18902 Pas
c = 2.3515
S n= 0.3002
. ... 0 I .. . . . . .. . . . .
10S 10 10'
Shear rat )
Fig. A Viscosity data for slurry no. 1.
Kalinite, density = 1350 kgfm
10' 10 10r
Sheaf rae (Ik)
10i 10i 10id
Fig. A2 Viscosity data for slurry no.2.
Kainte density = 140D kgfM3
Eta(inf)=0.58895 Pas
1, c = 5.0756
10
i n= 0.29084
loo *
. .. 0 ... . . . . . . . . . .
10S 10 10
Shear re (z)
102 103 10
Fig. A3 Viscosity data for slurry no.3.
Kaiie density = 1300 kfn
1 o3 14
Shear rate ()
Eta(inf)=0.4361 Pas
c = 9.0237
n= 0.19496
Fig. A4 Viscosity data for slurry no.4.
60
Kalinte, density = 1450 kgf
10 10 10
Shew rate(H)
10 10 10
Fig. A5 Viscosity data for slurry no.5.
Kainte density = 1500 kg/
10' 10o 101
Shear re (Hz)
102 10 10
Fig. A6 Viscosity data for slurry no.6.
Eta(inf)=0.66258 Pas
c= 6.9905
n= 0.22284
*<
*ss
Eta(inf)=0.67486 Pas
c= 12.9911
n= 0.062325
10 
102
10
100
10
13
10 
10"
75W1 +25A deity = 1243 IVM3
10' 10 10 101 102 103 1(
Sht at (H")
Fig. A7 Viscosity data for slurry no.7.
75%K+2A. density = 1291 i
10 Eta(inf)=0.54646 Pas
c = 7.6931
n = 0.17393
10
10"
10
0.139
1g
1F
Fig.
75%3K+2SA density = 1330 0'm3
o2 \ Eta(inf)=1.6774 Pas
c= 9.9786
n= 0.0071815
10
1101
10
l0
10 ........ I i . ..... ..... ...
10' 10 100 101 101 103 1C
Shear at )
Fig. A9 Viscosity data for slurry no.9.
10
' 10 10 10' 10' 10 10
Shear rate )
A8 Viscosity data for slurry no.8.
75%K+21A, density = 1387 r'n3
Ea(inf)=0.90398 Pas
c=25.9615
n= 0.28334
........\ .. ...
106 10" 10 10 102 103 10
Sh te r e()
Fig. A10 Viscosity data for slurry no. 10.
50%K+60%A density = 1236 kgVM
10 10' 10 10' 10' 10 10
Shear rae fr)
Fig. A 11 Viscosity data for slurry no. 11.
50WK+WA density = 1306 kgn
lo' Eta(inf)=0.29466 Pas
c = 21.6479
102 n= 0.11719
.1 1
106
10
10' 10' 100 10' 10' 10' 10'
Shear rat (H)
Fig. A13 Viscosity data for slurry no. 13.
50%K4+5%A density = 1263 kr#
+ Eta(inf)=0.27041 Pas
c = 13.206
10 n= 0.022772
jo
104
10
10" . .......  0 ....... . ......I . . ,
10"l' 10 10 10 10' 103 10
Sher rde ()
Fig. A12 Viscosity data for slurry no. 12.
5%K+50%A density = 1329 kWMr
10' 10' 10 10' 10 10 10'
Fig. A14 Viscosity data for slurry no.14.
Fig. A14 Viscosity data for slurry no. 14.
25%K+75%A density = 1175 kgfm
\ Eta(inf)=0.23419 Pas
c=3.1439
n = 0.22145
10' 10 100 10 102 103 104
Fig. A15 Viscosity data for slurry no. 15.
25%K+75%A density = 1225 kW
25%K+75%A, density = 12DD00 kg
10' Eta(inf)=0.38179 Pas
c = 9.3847
n= 0.13384
10
10
10
103... .....
10 10 100 10' 10 103 10
Sher at (O)
Fig. A16 Viscosity data for slurry no. 16.
25%K+75%A, density = 1250 kgi?
10' 10 10o 10' 102 103 10 10' 10 10 10 102 103 10
Shear te ) Shea rte )
Fig. A17 Viscosity data for slurry no.17. Fig. A18 Viscosity data for slurry no.18.
Attapulgit deity = 1125 kgfm3
Eta(inf)=0.19429 Pas
10' c = 1.2258
n = 0.39206
l io*
102
10
10 3 . ....... . ....... . .2.. . . ..... . . .......
10 10 100 101 10 103 10
Sheamre RQ)
Fig. A19 Viscosity data for slurry no. 19.
Attapulgite density = 1175 IVm3
10' 10 10 10' 10 10 10l
Shea rata f r)
Fig. A21 Viscosity data for slurry no.21.
10' 10' 10 10 10 103 10
Shear re )
Fig. A20 Viscosity data for slurry no.20.
Aft giteg deasity = 1200 kIgM
10 "1 . ..... .._. ...... . .... . .. , I
10' 10' 10 10 102 10 10r
Shcosity data for slurry no.22.)
Fig. A22 Viscosity data for slurry no.22.
Eta(inf)=0.38505 Pas
c = 13.2404
n = 0.071769
Eta(inf)=0.55699 Pas
c = 21.3166
n = 0.24189
Attapulgite detsity = 1150 kfm
O3 0K+10%, density = 1200 kgr?
lo' Eta(inf)=0.1887 Pas
Sc = 2.9789
10 n= 0.16114
i100
10
10 4
10 10 100 101 107 10 10
Sheo r rat o)
Fig. A23 Viscosity data for slurry no.23.
10,
10
10
103
I 10'
10'
90%K+10B, density = 1300 kgni/
Eta(inf)=0.25905 Pa,
c = 14.2843
n=0.11646
\ .i .2 3
10' 10' 100 10 10' 103 10'
Shea rate f)
Fig. A25 Viscosity data for slurry no.25.
O %K+10%B density = 1250 kg/rr
lo Eta(inf)=0.17842 Pas
c = 9.2533
10' n=0.13611
10
liod
I100
10
10' 10 10 101 10' 103 10
she rate ()
Fig. A24 Viscosity data for slurry no.24.
10 
10
10
S10' 
10
10'
lO"
itf1
90%K+10%R density = 1350 k#gT
Eta(inf)=0.38044 Pas.
c= 42.8305
n = 0.044113
=4.80
. .., . .. . .. .J . . = . .
10d 10' 10 10 10 103 10
Shr rate or)
Fig. A26 Viscosity data for slurry no.26.

s
WeK+25%A+10%B density = 1225 km3 3
Eta(inf)=0.21778 Pas 10
c = 9.0443
n=0.18173
1100
10
10. d 10o 10' 1l 1e 10' 1o
6%K+25%A+1C B density = 1250 kym3
10 .
102
2
10
2
10 10 10'
Fig. A27 Viscosity data for slurry no.27.
6%K+25%A+10KB, density = 1275 kWWP
10 10' 10 10
Shea rte (z)
..._____.. 10
10' l' 10' 10
Fig. A28 Viscosity data for slurry no.28.
65%K+25%A+10%B density = 1300 kgfm3
SEta(inf)=0.75004 Pas
Sc = 57.8301
n =0.058594
l 0.. . .. . .. .. .. . ... . .
10' 100 10r
Sea ra (z)
10' 10 10'
Fig. A29 Viscosity data for slurry no.29.
10' 10o 10
S rate (Hz)
Eta(inf)=0.27711 Pas
c = 17.4975
n = 0.089808
Fig. A30 Viscosity data for slurry no.30.
4K+50 %A+10 density = 1200kgfm
10 10 10'
Sheaw rate )
10
10'
10'
10"
lleI l
10' 10 10 10
10' 100 10'
Shear te ()
10o 10 10i
Fig. A31 Viscosity data for slurry no.31.
40%K+50%A+10% density = 12Wkgn3
10
o2 + Eta(inf)=0.13784 Pas
c = 10.4596
1o n= 0.14427
WI0 4,
10' 10 10'
Shearate Q)
.10 10 10 1...0. 1
Fig. A32 Viscosity data for slurry no.32.
1 40%K0%A+10%B, density = 12.kWnf .
10' 10 10 10 10 10
S herat k)
Fig. A34 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
*
40%K+50%A+10%B, density = 117Skgf3
. ..... J . ..... . ...... 1 . ...... 1 . ..... d . .....
Fig. A33 Viscosity data for slurry no.33.
15%K+75%A+10%B, density = 1125kIfim
Eta(inf)=0.17731 Pas
10 c = 1.8204
n = 0.20811
lo
b10
10 .
106 10 10 10' 102 10 10
Shear rate )
Fig. A35 Viscosity data for slurry no.35.
15%K+75MA+10%B, density = 1175kgSn
0o2 + Eta(inf)=0.12616 Pas
c= 8.7113
Sn= 0.15601
10
10
10 ........ .. ... ... .. ...i ..., .. ,.
10 10 10o 10' 10 10 10
Shea rate (H)
Fig. A37 Viscosity data for slurry no.37.
10 ...
io'
102 6
,
10
10( ........
0
10 10
Fig. A36
159K+7%A,+10B density = II kW4rm3
Eta(inf)=0.14544 Pas
c = 6.1701
+n = 0.23661
4
o10 lo' 10 10 lO'
Shear rte (Hte)
Viscosity data for slurry no.36.
15%K+75%A+10EB, density = 1200 kgmft
Sh rate ()
Fig. A38 Viscosity data for slurry no.38.
20%A+10%B density= 1125 Ignm
Eta(inf)=0.19921 Pas
10e *' c= 4.1219
n= 0.24578
.10o
102
10 10' 10o 10' 10' l10 10
Shity data for slurry no.39.
Fig. A39 Viscosity data for slurry no.39.
10
lo'
10
16
90%A+10%8 density = 1175 krn3
Eta(inf)=0.37333 Pas
c = 17.3209
n = 0.033589
10
10
10
10
Fi
106
Fig.
10 10 10 10' 10 103 10'
Shity data for slurry no.41.
Fig. A41 Viscosity data for slurry no.41.
10' 100 10' 102 10' 104
Shear ra f)
A40 Viscosity data for slurry no.40.
90%A+10N% density = 1200 Ikrn
10 10' 10o 10' 102 103 10
Shear rat (H)
Fig. A42 Viscosity data for slurry no.42.
90%A+10%8, density= 1150 kIrr?
Eta(inf)=0.10679 Pas
c= 14.8333
Sn= 0.05341
APPENDIX B
DEPENDENCE OF POWER LAW PARAMETERS ON DENSITY
Kaolinite
0.8
0.6 
S0.4
0.2
0
1200 1250 1300 1350 1400 1450 1500 1550
Density (kg/m^3)
Kaolinite
16
12
08 
4
0
1200 1250 1300 1350 1400 1450 1500 1550
Density (kg/m^3)
0.4 Kaolinite
0.4 I
0.3 
c 0.2 
0.1
0 I
1200 1250 1300 1350 1400 1450 1500 1550
Density (kg/m^3)
Fig. B1 Variation of powerlaw coefficients with density for kaolinite slurries. Top: r.;
middle: c; bottom: n.
750/K + 25/A
Vol"
i
0
1
30
20
10
0
1:
0.2
0
 1
0.2
0.4
200
1250 1300
Density (kg/m^3)
1350
1400
75/JK + 25/A
.00
200
1250
1300
Density (kg/m^3)
1350
1400
75/K +2501A
Density (kg/m^3)
Fig. B2 Variation of powerlaw coefficients with density for 75% kaolinite+25% attapulgite
slurries. Top: rl.; middle: c; bottom: n.
^
f
4
500%K + 50o/A
1240 1260 1280 1300
Density (kg/m^3)
1320 1340
500/O + 500/A
220 1240 1260 1280 1300 1320 13
Density (kg/m^3)
50/K + 50/A
Density (kg/m^3)
Fig. B3 Variation of powerlaw coefficients with density for 50% kaolinite+50% attapulgite
slurries. Top: il; middle: c; bottom: n.
0.6 
S0.4 
i 0.2 
0
1220
120
80
( 40
0
1:
40
0.3
0.15
0.
0.15
12
i
1240 1260 1280 1320
w
250/K + 7501A
1180 1200 1220
Density (kg/mA3)
25/K + 75/A
1180 1200 1220
Density (kg/mA3)
1240 1260
0.3
0.15
C 0
11
0.15
0.3
250/K + 75/A
Density (kg/mA3)
Fig. B4 Variation of powerlaw coefficients with density for 25% kaolinite+75% attapulgite
slurries. Top: iL; middle: c; bottom: n.
0.8
0.6
S0.4
0.2
0 
1160
1240
1260
40
30
u 20 
10 
0
1160
30 1180 1200 122 1240 1:
0.6 
1 0.4 
S0.2 .
0
1120
24 
16 
0
1120
1120
Attapulgite
1140 1160 1180
Density (kg/m^3)
1200 1220
1200 1220
Attapulgite
A
V
11
J0t3
"I,/.^ 
Density (kg/m^3)
Fig. B5 Variation of powerlaw coefficients with density for attapulgite slurries. Top: rl.;
middle: c; bottom: n.
1140 1160 1180
Density (kg/m^3)
1 1
1140 1160
*
00
0.6
S0.4 
, 0.2 
0
1150
ou
40
20
0
1
0.2
0.1
c 0
1
0.1
0.2
90W + 10%B
1200 1250 1300
Density (kg/m^3)
1350
1400
90%K + 100/1B
150
1200
1250 1300
Density (kg/m^3)
1350
90% K + 10% B
150 1200 1250 1300 130 14
1400
Density (kg/mA3)
Fig. B6 Variation of powerlaw coefficients with density for 90% kaolinite+10% bentonite
slurries. Top: r1.; middle: c; bottom: n.
i ,
650/cK+250/A+100/
1240 1260 1280
0.8 
0.6
0.4
0.2
0
122
20
1240 1260 1280
Density (kg/m^3)
1300 1320
1300 1320
650/K+250/A+100/1B
Density (kg/m^3)
Fig. B7 Variation of powerlaw coefficients with density for 65% kaolinite+25% attapulgite+
10% bentonite slurries. Top: ir; middle: c; bottom: n.
1240 1260 1280
Density (kg/m^3)
650/K+250/A+100/B
80
60
u 40
20
0
12
0.2
0.1
0
1
0.1
i j,:
20 1240 1260 1280 13
!0

;
40%/K+500/A+ 100/cB
1200 1220
Density (kg/m^3)
400/%K+500/A*+100/B
160
1180 1200 1220
Density (kg/m^3)
400/AK+500 A+100/B
1240 1260
Density (kg/m^3)
Fig. B8 Variation of powerlaw coefficients with density for 40% kaolinite+50% attapulgite+
10% bentonite slurries. Top: ri.; middle: c; bottom: n.
0.4
0.3
0.2
0.1 .
0
116
1180
1240
1260
40
30
u 20
10
0
11
0.2
0.1
0
1
0.1
130 1180 1200 1220 1240 12
 
30
1 50/K+705%A+1 oVB
1140 1160 1180
Density (kg/m^3)
15% K+75% A+10% B
e* It
0.3 
0.2 
0.1
0
1120
1140 1160 1180
Density (kg/m^3)
150/JK+75%A+10 B
1140 1160 1180
Density (kg/m^3)
Fig. B9 Variation of powerlaw coefficients with density for
10% bentonite slurries. Top: rl; middle: c; bottom: n.
1200 1220
1200 1220
15%kaolinite+75% attapulgite+
0.4
S0.3
0.2 
0.1 
0
1120
1200
1220
10
0
1
120
90/A+ 100%B
1.2
C 0.8
a 0.4
0
11
90%/A+ 10/8
1140 1160 1180
Density (kg/m^3)
90%A+10%B
1140 1160 118
1200 1220
1200 1220
Density (kg/mA3)
Fig. B10 Variation of powerlaw coefficients with density for 90% attapulgite +10%
bentonite slurries. Top: rL; middle: c; bottom: n.
1140 1160 1180
Density (kg/m^3)
1200
1220
120 
80
40
1120
0.4 
0.2 
S 0 
1120
0.2 
0.4 

20
APPENDIX C
VELOCITY PROFILES AND CORRESPONDING DISCHARGES
.QN.w.onn = 0.00134 m'Is
0.5
QSsko = 0.00131 mIs 3/
0.5
1
0 1 2 3 4 5 6
Velocity (m/s)
Fig. C1 Computed velocity profiles and corresponding
discharges for slurry no. 1.
0.5
0.5
1
0 1 2 3 4
Velocity (m/s)
Fig. C2 Computed velocity profiles and corresponding
discharges for slurry no. 7.
Qsiko = 0.00085 m 3/s
QN.wtonlan = 0.00085 m /s
0 1 2 3 4 5 6
Velocity (m/s)
Fig. C3 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. C4 Computed velocity profiles and corresponding
discharges for slurry no. 15.
QN.wtonl.an = 0.00118 m'/Is
0.5
Qskko = 0.00115 m' 3/s
0.5
0 0.8 1.6 2.4 3.2 4.0
Velocity (m/s)
Fig. C5 Computed velocity profiles and corresponding
discharges for slurry no. 19.
4.
0.5
0
0.5
I 
0 2 4 6 8
Velocity (m/s)
Fig. C6 Computed velocity profiles and corresponding
discharges for slurry no. 23.
Qsi,,,, = 0.00155 m3/s
QN11t,111, = 0.00155 M 3/S
 
