A laboratory study of mud slurry discharge through pipes

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

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 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 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 Power-Law for Mud Flow......................................................34
4.1.2 Power-Law Coefficients......................................................... 36
4.2 E nd and Slip E ffects................................................... .................... 38
4.3 Pow er-Law Param eters................................................ ...................... 40
4.4 Slurry Discharge with Sisko Model....................................................46
4.5 Calculation of Slurry Discharge..........................................................49
4.6 Power-Law 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 pressure-drop/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 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 =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 power-law 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 (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 ewtonian case........................................................................... 35

4.2 Data obtained from the end-effect 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

A-i 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

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- 11 Viscosity data for slurry no. 11 ..................................................... .......................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 ......... ..................................................................... 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: i.,; middle: c; bottom: n .................................................................. 70

B-2 Variation of power-law coefficients with density for kaolinite slurries.
Top: ri.; middle: c; bottom: n .................................................................. 71

B-3 Variation of power-law coefficients with density for kaolinite slurries.
Top: ln.; middle: c; bottom: n .............................................................. 72

B-4 Variation of power-law coefficients with density for kaolinite slurries.
Top: rl.; middle: c; bottom: n .................................................................. 73

B-5 Variation of power-law coefficients with density for kaolinite slurries.
Top: 1.; m iddle: c; bottom : n ............................................................... 74

B-6 Variation of power-law coefficients with density for kaolinite slurries.
Top: Tr.; m iddle: c; bottom : n ......................... .................................... 75

B-7 Variation of power-law coefficients with density for kaolinite slurries.
Top: "i.; m iddle: c; bottom : n ............................... ................................. 76

B-8 Variation of power-law coefficients with density for kaolinite slurries.
Top: rl.; m iddle: c; bottom : n .......................... .................................... 77

B-9 Variation of power-law coefficients with density for kaolinite slurries.
Top: "1.; 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-1 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 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 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 (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 power-law 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 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 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 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

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 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, 6) are as

follows:

Incompressible continuity equation:

1 OrVr IV. 8V
r dr raO 8z

(2.1)

Momentum equations:

r-component:

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

0-component:

(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

z-component:

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 non-zero 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 non-zero components

LI rz
0

ar 0
rz

\r 0
Trr 0

0 "oo

Accordingly, the three component momentum equations are simplified as

z-component:

az r ar

r-component:

Bp 1 8 "C
-pgr- (r,) -TO
9r r ar r

6-component:

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=0-4 (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,
r-D + (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 non-Newtonian) or turbulent flow.

2.2 Viscous Model

2.2.1 Flow Type

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

*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 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:

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 pressure-drop/flow rate relationships for slurry flow
in pipes.

Turbulent
Slope 1.75 to 2

Non-Newtonian:
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 d-c (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+(Ls-Le) APe+Ls' (2.28)

Subtracting Eq. (2.28) from Eq. (2.27), the true pressure gradient in the fully developed

flow section reads

=APL-PS (2.29)
L S-L

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)
rno-slip (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 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.

r7 versus Yw

r, versus Yw \
I

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

:= -ty+[Y for -ty (2.33)

Y=0 for T

This is a two-parameter 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 power-law fluid

This is described as

T=cY" (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 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 I|TrZ< 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- 1-R ) (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 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:

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 power-law 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 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 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 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

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 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/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 X-ray 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
5.00-3.20 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 = 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
3.00-2.80 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
(Iun) (%) (%)
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/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 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, %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 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

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 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 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 shear-thinning or shear-

thickening, 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 rT=O, 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 =- VD < 2100 (4.5)

where Vm 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, 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 (fi-rn)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'n-1 (f,-rl- c~-) )} 0 (4.10)
i=l

and

M
E {cn- llog (%i-4T--c"q-l)} =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 low-shear rate non-Newtonian 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 end-effect 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 5E-07 1E-06 1.5E-06 2E-06 2.5E-06
Gamnma4Tau

Fig. 4.3 Plot of ('P/4T,) vs. t, for slip-effect 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 10-8 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 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, 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.

Best-fit 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 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 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
10-2

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 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

=a9v/9r, and the steady-state 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 no-slip 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~i-1 = vi+ A

1- TW

n-i
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 < 10-6 (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 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.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 power-law approximation

of the theological 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 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 Power-Law 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 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 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 inter-particle 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 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:

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 forty-two clay-water 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 power-law 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 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 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, 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

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 (I-k)

10i 10i 10id

Fig. A-2 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. A-3 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. A-4 Viscosity data for slurry no.4.

60

Kalinte, density = 1450 kgf

10 10 10
Shew rate(H)

10 10 10

Fig. A-5 Viscosity data for slurry no.5.

Kainte density = 1500 kg/

10' 10o 101
Shear re (Hz)

102 10 10

Fig. A-6 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
1-3

10 -
10"

75W1 +25A deity = 1243 IVM3

10' 10 10 101 102 103 1(
Sht at (H")

Fig. A-7 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
l-0

10 ........ I i . ..... ..... ...
10' 10 100 101 101 103 1C
Shear at )

Fig. A-9 Viscosity data for slurry no.9.

10

' 10 10 10' 10' 10 10
Shear rate -)

A-8 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. A-10 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. A-13 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. A-12 Viscosity data for slurry no. 12.

5%K+50%A density = 1329 kWMr

10' 10' 10 10' 10 10 10'
Fig. A-14 Viscosity data for slurry no.14.

Fig. A-14 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. A-15 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. A-16 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. A-17 Viscosity data for slurry no.17. Fig. A-18 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. A-19 Viscosity data for slurry no. 19.

Attapulgite density = 1175 IVm3

10' 10 10 10' 10 10 10l
Shea rata f r)

Fig. A-21 Viscosity data for slurry no.21.

10' 10' 10 10 10 103 10
Shear re -)

Fig. A-20 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. A-22 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. A-23 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. A-25 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. A-24 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. A-26 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. A-27 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. A-28 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. A-29 Viscosity data for slurry no.29.

10' 10o 10
S rate (Hz)

Eta(inf)=0.27711 Pas
c = 17.4975
n = 0.089808

Fig. A-30 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. A-31 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. A-32 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. 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

*

40%K+50%A+10%B, density = 117Skgf3

. ..... J . ..... . ...... 1 . ...... 1 . ..... d . .....

Fig. A-33 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. A-35 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. A-37 Viscosity data for slurry no.37.

10 ...

io'

102 6

,
10

10( ........
-0
10- 10-

Fig. A-36

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. A-38 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. A-39 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

F-i
106

Fig.

10 10 10 10' 10 103 10'
Shity data for slurry no.41.

Fig. A-41 Viscosity data for slurry no.41.

10' 100 10' 102 10' 104
Shear ra f)

A-40 Viscosity data for slurry no.40.

90%A+10N% density = 1200 Ikrn

10 10-' 10o 10' 102 103 10
Shear rat (H)

Fig. A-42 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. B-1 Variation of power-law 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. B-2 Variation of power-law 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. B-3 Variation of power-law 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. B-4 Variation of power-law 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. B-5 Variation of power-law 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. B-6 Variation of power-law 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. B-7 Variation of power-law 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. B-8 Variation of power-law 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. B-9 Variation of power-law 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. B-10 Variation of power-law 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. C-1 Computed velocity profiles and corresponding
discharges for slurry no. 1.

0.5

-0.5

-1

0 1 2 3 4
Velocity (m/s)
Fig. C-2 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. 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.

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. C-5 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. C-6 Computed velocity profiles and corresponding
discharges for slurry no. 23.

Qsi,,,, = 0.00155 m3/s

QN11t,111, = 0.00155 M 3/S
--------------- ----

MILLISECOND	CLASS.METHOD	MESSAGE
0	sobekcm_page_globals.constructor
0	sobekcm_page_globals.constructor	Application State validated or built
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.constructor	Navigation Object created from URI query string
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.display_item	Retrieving item or group information
0	sobekcm_page_globals.get_entire_collection_hierarchy	Retrieving hierarchy information
0	sobekcm_assistant.get_entire_collection_hierarchy
0	cached_data_manager.retrieve_item_aggregation
0	cached_data_manager.retrieve_item_aggregation	Found item aggregation on local cache
0	item_aggregation_builder.get_item_aggregation	Found 'all' item aggregation in cache
0	system.web.ui.page.page_load (ufdc.page_load)
0	sobekcm_page_globals.constructor.on_page_load
0	html_echo_mainwriter.add_style_references	Adding style references to HTML
0	html_echo_mainwriter.add_text_to_page	Reading the text from the file and echoing back to the output stream
117	html_echo_mainwriter.add_text_to_page	Finished reading and writing the file