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Univers
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Cap
e Tow
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THE RHEOLOGY AND~ BEHAVIOOR OF HIGH
OONCENTRATION MINERAL SWRRIES
by
R. I.G. NEILL
BSc (Civil Engineering)
University of Cape Town
A thesis submitted in partial fulfilment of the requirement for the
degree of Master of Science in the Department of Civil Engineering, I
. University of Cape Town.
September 1988 Civil Engineering Department
University of Cape Town
South Africa
The University of Cape Town has been given the right to reproduce this thesis In whole or in part. Copyright is held by the author.
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The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non-commercial research purposes only.
Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author.
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DEDICATION
To my parents.
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ACKNOlYLEDGEMENTS
The author would like to thank the following people -
Associate Professor J.H. Lazarus for his encouragement and creative input
into this thesis and for sharing his expertise in the field of
hydrotransport.
Miss P. Mc Cabe for her unfailing support.
Mr P.T. Slatter for his introduction to and expertise on rheology •.
Mrs P. Jordaan for typing this thesis.
Associate Professor F.A. Kilner, the staff of the Department of Civil
Engineering and the members of Hydro transport Research for the seminars,
stimulating discussions and advice.
The technical and laborotory staff for their assistance.
Dr. L. Bayvel and Mr. J. Knight for the particle size analyses.
Mr D. Gerneke of the Electron Microscope Unit for the micrographs.
For financial support:
· The Council for Scientific and Industrial Research.
The University of Cape Town.
The Chamber of Mines of South Africa.
Dr. J. von Theurheim of Borneffia.nn Ptunps.
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SYNOPSIS
The rheology and flow behaviour of high concentration backfill tailings are
investigated using a modified Balanc~ Beam Tube Viscometer. The viscometer
is capable of producing reliable data using a computer based data acqui
sition system and three different tube diameters.
The aim of this research is to detennine the rheology of backfill tailings
in order to predict friction head losses.
The backfill tailings were prepared into four different particle size
distributions each with a different maximum particle size. Each particle
size distribution was tested over a range of high concentrations in the
viscometer.
The rheology of the lower concentration backfill tailings was successfully
characterized using the yield-pseudoplastic model.
It has been foui:id that at high concentrations rheological characterization
is impossible because the laminar flow region of the pseudo-shear diagram
varies with tube diameter. This anomalous behaviour in the fonn of diameter
dependence has been recorded in the literature.
The results of high concentration tests on backfill tailings are
investigated using the following theories to establish and accotn'lt for the
cause of the anomalous behaviour:
Effective slip analysis - corrects the measured data for effective slip.
Dense-Phase Model - based oh the sliding friction between solid
Wall Effect
Boundary-Layer E~f ect
particles and the tube wall.
- based on a reduction of in situ concentration
due to a wall effect.
- corrects for the effect of a boundary-layer of
liqtiid at the wall.
Modified Friction Factors - takes into account the hydrodynamic lubrication
between the solid particles and the tube wall.
The existence of a thin layer of liquid at the wall is credible but not yet
proven. The anomalous behaviour is linked to this layer. However a suitable
method for correcting the measured data has not· yet been established.
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TABLE OF CONTENTS
Chapter
1 INTRODUCTION
1.1 The hydraulic transport of solids in pipes
1.2 Rheology
1.3 Viscometers
2 LITERATURE AND THEORY
2.1 Introduction
2.2 Shear stress and shear rate
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
Newtonion rheology
Non-Newtonion rheology
Slurry rheology
Tube flow theory
Friction factors and Reynolds numbers
New method of data reduction
2.8.1 Existing rheological characterization
procedure
2.8,2 New rheological characterization
procedure
Anomalous behaviour at high concentrations
Effective slip
2.10.1 Introduction
2.10.2 Effective slip analysis technique
Dense-pha.Se models
Wall effect (Maude & Whitmore (1955))
Boundary-layer effect
Modified friction factors
Conclusions
1.2
1.2
1.2
2.1
2.1
2.1
2.2
2.3
2.4
2.7
2.9
2.9
2.10
2.10
2.12
2.12
2.13
2.14
2.15
2.16
2.17
2.18
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3 RESEARCH APPARATUS
3.1 Description. of the Balanced Beam Tube Viscometer 3.1
3.2 Measurement techniques 3.2
3.2.1 Flow measurement 3.2
3.2.2 Differential pressure·measurement 3.3
3.2.3 Computer hardware 3.4
3.2.4 Experimental error 3.5
3.3 Operating procedure 3.10
3.3.1 Log on 3.11
3.3.2 Read.channel 3.11
3.3.3 Calibration 3.11
3.3.4 Visco run 3.13
• 3.3.5 Store data 3.16
3.3.6 Utilities 3.16
3.3.7 Operating notes 3.17
3.4 Conclusions 3.17
4 EXPERIMENTAL PROCEDURE
4.1 Preliminary tests 4.1
4.1.1 Comparative tests between full plant
tailings and belt filtered tailings 4.1
4.1.2 Flow at high concentrations 4.1
4.1.3 In situ and delivered concentrations 4.2
4.1.4 Developing flow 4.3
4.2 Experimental procedure 4.3
4.3 Sample preparation 4.5
5 MATERIAL DESCRIPI'ION
5.1 Introduction 5.1
5.2 Particle size distributions 5.1
5.3 Solids relative densities 5.2
5.4 Mixture relative density 5.2
5.5 pH values 5.3
5.6 Temperature 5.3
5.7 Micrographs 5.3
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6 EXPERIMENTAL RESULTS AND ANALYSIS
7
8
6.1
6. 2 .
6.3
Observations during testing
Pseudo-shear diagrams
Friction factor Reynolds number diagrams
ANALYSIS OF EXPERIMENTAL RESULTS
7.1 Introduction
7.2 Tube flow theory
7.3 Anomalous behaviour
7.3.t Effective slip
7.3.2 Dense-phase model
7.3.3 Wall effect
7.3.4 Boundary-layer effect
7.3.5 Modified friction factors
7.4 Conclusions
CONCLUSIONS AND RECXX1MENDATIONS
References
6.1
6.1
6.1
7.1
7.1
7.2
7.3
7.4
7.5
7.6
. 7. 7
7.7
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Figure No.
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
3.1 ..
3.2
3.3
3.4
(viii)
LIST OF FIGURF.8
Description
Shear stress and shear rate in a fluid sheared
between parallel plates.
Rheograms of various rheological models.
A graph of incremental viscosity versus shear rate
for various rheological models.
A typical effect of concentration on rheology
(Slatter (1986).
A typical effect of maximum particle size on
rheology (Slatter (1986).
The effect of zeta potential on rheology
(Horsley and Reizes (1980)).
Tube flow analogy.
Derivation of the shear stress at the wall.
A typical pseudo-shear diagram using three tube
diameters.
Shear stress and shear rate distributions and
the velocity profile for the flow of a yield~
pseudoplastic fluid through a tube.
Friction factor Reynolds number diagram.
A high concentration pseudo-shear diagram
showing anomalous behaviour.
Inward radial migration of solid particles and
the associated reduction in concentration in the
proximity of the tube wall.
Boundary-layer of liquid at the tube wall.
Correction of a pseudo-shear diagram for the
effect of a boundary-layer.
Diagramatic layout of BBTV.
Photograph of BBTV.
Assembly drawing of BBTV.
Photograph of pressure tapping and slurry
isolation pod.
Page No.
2.19
2.10
2.10
2.21
2.22
2.23
2.24
2.24
2.25
2.26
2.27
2.28
2.29
2.29
2.30
3.18
3.18
3.19
3.20
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3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
4.1
4.2
4.3
4.4
5.1
5.2
5.3
5.4
5.5
5.6
(ix)
A run in graphical form (Slatter (1986)).
Load cell (Slatter (1986)).
Photograph of load cell.
Wheatstone bridge circuit.
Load cell response characteristic.
Photograph of high/low pressure selectors.
Diagram of high/low pressure selectors.
Differential pressure transducer (DP cell)
(Gould (1980)).
DP cell circuit d~agram (Slatter (1986)).
DP cell response characteristic.~
Photograph of the computer hardware.
Computer hardware connection diagram.
Software menu tree.
DP cell calibration connections.
Computer printout of a test.
Pseudo-shear diagram of a test.
Appearance of the backfill tailings at various
high mixture relative densities.
The results of a preliminary test to check that
fully developed flow exists between the pressure
3.20
3.21
3.21
3.22
3.22
3.23
3.23
3.24
3.24
3.25
3.25
3.26
3.26
3.27
3.28
3.28
4.6
tappings • 4 ~ 6
Sweco Vibro-Energy Separator used for scalping
(Sweco (1986).
Bornemann EH250 eccentric helical rotor pump used
for scalping (Bornemann (1986)).
Particle size distribution for the -500 µm fraction
of the backfill tailings.
Particle size distribution for the -106 µm fraction
of the backfill tailings.
Particle size distribution for the -62 µm fraction
of the backfill tailings.
Particle size distribution for the -42 µm fraction
of the backfill tailings.
Micrograph of 75 - 100 µm solid particles under a
magnification of lOx.
Micrograph of 20 - 90 µm solid particles under a
magnification of 16x.
4.7
4.7
5.4
5.4
5.5
5.5
5.6
5.6
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5.7
5.8
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.1
7.2
7.3
7.4
(x)
Micrograph of 10 - 20 µm solid particles under a
magnification of 40x.
Micrograph of 2 - 10 µm soli4 particles under a
magnification of 40x.
Pseudo-shear diagrams for all the tests on backfill
· tailings are presented. The results of the tests
done on the -500, -106, -62 and -42 µm fractions are
presented sequentially starting at the highest and
ending with the lowest concentration for each
particle size.
Combined pseudo-shear diagrams for the -500 µm
fraction of the backfill tailings.
Combined pseudo-shear· diagrams for the -106 µn ·
fraction of the backfill tailings.
Combined pseudo-shear diagrams for the -62 µn
fraction of the backfill tailings.
Combined pseudo-shear diagrams for the -42 µn
fraction of the backfill tailings.
Friction factor Reynolds number diagram for the
-500 µm fraction of the backfill tailings.
Friction factor Reynolds number diagram for the
-106 µm fraction of the backfill tailings.
Friction factor Reynolds number diagram for the
-62 µm fraction of the backfill tailings.
Friction factor Reynolds number diagram for the
-42 µm fraction of the backfill tailings,
Rheological characterization of the -500 µm
fraction of the backfill tailings at the lowest
concentration tested.
Rheological characterization of the -106 µn
fraction of the backfill tailings at the lowest
concentration tested.
Rheological characterization of the -62 µn
fraction of the backfill tailings at the lowest
concentration tested.
Rheological characterization of the -42 µm
fraction of the backfill tailings at the lowest
concentration tested.
5.7
5.7
6.2
6.8
6.8
6.9
6.9
6.10
6.10
6.11
6.11
7.8
7.8
7.9
7.9
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7.5
7.6
7.7
7.8
7.9
7 .10
7 .11
7.12
7.13
7.14
7.15
Al
A2
A3
Dl
El
E2
E3
E4
(xi)
Representative sample of high concentration
anomalous behaviour used for analysis.
Effective slip analysis - intermediate graph.
Effective slip analysis - graph used to determine p. Effective slip analysis - variation of slip
velocity with shear stress.
Effective slip analysis - corrected pseudo-shear
diagram.
Dense-phase model - experimental and theoretical
hydraulic gradients.
Dense-phase model - variation of the coefficient
of sliding friction with velocity.
Boundary-layer effect - coincidence of the initial
sections of the pseudo-shear diagrams for a fixed
particle size distribution and tube diameter.
Boundary-layer effect - measured slopes of the
initial sections of the pseudo-shear diagrams
for each tube diameter.
Boundary-layer effect - corrected pseudo-shear
diagram.
Modified friction factors - friction factor
Reynolds number diagram showing experimental
and theoretical curves.
The effect of the Rabinowitch-Mooney relation on a
yield-pseudoplastic rheology.
The effect of the Rabinowitch-Mooney relation on a
Bingham plastic rheology.
The effect of the Rabinowitch-Mooney relation on a
yield-dilatant rheology.
GK2401C Combined electrode.
Particle size distribution comparison between the
-106 µm fraction of FP1' and BFT.
Particle size distribution comparison between the
-62 µm fraction of FP1' and BFT.
Rheological comparison .between the -106 µm fraction
of FP1' and BFT.
Rheological comparison between the -62 µm fraction
of FPI' and BFT.
7 .10
7 .10
7 .11
7 .11
7.12
7.12
7.13
7.13
7.14
7.14
7.15
A6
A6
A7
D4
E4
E4
E5
E5
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•
Table No.
3.1
3.2
3.3
4.1
4.2
5.1
5.2
5.3
7.1
7.2
Dl
El
E2
(xii)
LIST OF TABLES
Description
Maximum error in diameter
Maximum error in velocity
Maximum error in shear stress
Delivered concentrations through different
tube diameters.
Sununa.ry of tests done.
Sununary of d 10 , d 90 and d 90 values.
Solids relative densities
pH Values
Results of the rheological characterization of
low concentration backfill tailings.
Botm.dary-layer thickness in each tube diameter.
Page No.
3.6
3.8
3.10
4.2
4.4
5.1
5.2
5.3
7.2
7.6
Malvern lenses. D3
Sununary of the comparative solids relative densities. E2
Swnmary of the comparative tests. E2
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Symbol
A
c m cvd
cvt
cwd
D
d
F
f
fl
f n
g
i m
i w
K
K
L
Log
ln
.M
m
m
n
n
n'
p
tip
Q
~
(xiii)
NOOENCLA'TIJRE
Description
cross sectional area
maximum packing concentration
delivered volumetric concentration
in situ volumetric concentration
in situ mass concentration
internal tube diameter
particle diameter
force
Fanning friction factor = T /'hpV2
0
friction factor for the liquid phase
function of •••••
gravitational constant = 9.81
hydraulic gradient of mixture in
units of water per length of pipe
hydraulic gradient of water flowing
at velocity V in pipe diameter D m
fluid consistency index
constant defined by the equation in which it is used
tube length
decimal logarithm
natural logarithm
mass flow rate
mass
constant defined by the equation in which it is used
flow behaviour index
number of •••••
apparent flow behaviour index
pressure
pressure drop
volumetric flow rate
volumetric flow rate of mixture
m2
m
µm.
N
m/s 2
m/m
m/m
m
kg/s
kg
Pa
Pa
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R
r
rplug Re
s m
s s s w
t
u
u core u plug u s v
v
v
v v
m x
y
a
(xiv)
radius of tube
radial distance
radius containing plug flow
Newtonian Reynolds number = pVD/µ
relative density of mixture
relative density of solids
relative density of water = 1
time
local velocity
velocity of core
velocity of plug
effective slip velocity
volume
voltage
velocity
mean velocity
mean mixture velocity = Q /A m
direction of uniform flow
direction perpendicular to x
shear stress ratio (~~~0 )
effective slip coefficient
boundary layer thickness
increment
initial pseudo-shear diagram slope
plastic viscosity
a function of concentration defined
by equation 2.37
dynamic viscosity
dynamic viscosity of water = 1,005 x 10- 1
coefficient of sliding friction
3.146
density
density of mixture
density of solids
density of water = 998,2
shear stress
shear'stress at wall
yield stress
m
m
m
s
m/s
m/s
m/s
m/s
v m/s
m/s
m/s
m
Pa s
Pa s
Pa s
Pa s
kg/m•
kg/m•
kg/ma
kg/m3
Pa
Pa
Pa
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(xv)
Subscripts
d delivered
i i-th component
1 liquid phase
m mixture
.0 at the tube wall
s solid phase
t in situ
v volumetric basis
w weight basis _;
w water
calc calculated
obs observed
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INTRODUCTION 1.1
CHAPI'ER 1
INTRODUCTIOO
This dissertation doctunents an investigation into the flow behaviour and
the rheology of high concentration mineral slurries using a novel Balanced
Beam Tube Viscometer (BBTV), The intention of this research is to ~
theoretically model the effect of particle size distribution and concen-
tration on rheology.
[
It has been shown extensively in the literature that high concentration
slurries may exhibit anomalous behaviour. This behaviour is associated
· with a rheology that is pipe diameter dependent. Several theories have
been proposed to explain this behaviour. Extensive tests on backfill
tailings using the Balanced Beam Tube Viscometer are used to evaluate these
theories.
The ob,jectives of this research are as follows:
Investigate the anomalous behaviour that occurrs at high concen
trations in slurries •
. Evaluate theories in the literature that attempt to explain this
anomalous behaviour.
Develop a method for predicting the friction head.losses of these
slurries.
This thesis is a continuation and development of the work presented by
Slatter (1986),
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INTRODUCTION 1.2
1.1 THE HYDRAULIC TRANSPORT OF SOLIDS IN PIPES
The hydraulic transport of solids in pipes is an established and
reliable method of transporting solids. The theory governing the
design and optimization of hydraulic transport systems is still in
i.ts infancy. This is evident in the fact that friction head.loss of
a single phase Newtonian fluid is a function of five variables
whereas the friction head.loss of a two phase slurry is a function of
fourteen variables (Lazarus (1985)).
1 • 2 RHEOLOGY
Rheology ( rheos flow; logos knowledge) describes the
defonnation of a body of fluid under the influence of stress. More specifically rheology means the characterization of the relationship
between shear stress and shear rate in a fluid. The process of
rheological characterization involves the measurement of shear
stress at various shear rates. This data is plotted on a graph
called a rheograrn and characterized using a rheological model.
In the context of this thesis a fluid is defined a material capable
of continuous flow when stressed beyond its yield stress. A slurry
is defined as a mixture of solids and liquids.
1.3 VISCOMETERS
The most common viscometers used in hydrotransport are rotational
and tube viscometers (Barr (1931)), Green (1949), (Scott Blair
(1969)).
The rotational viscometer consists of two coaxial cylinders. The
gap between the cylinders is filled with a sample. One cylinder is
rotated at various speeds and the applied torque measured. From this
the shear rate and the shear stress can be calculated and the
rheology can be det~nnined.
'·
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INTRODUCTION 1.3
The tube viscometer consists of a tube of known lerigth and diameter
through which a sample flows. The , friction head loss across the
tube at various velocities is measured. From this the shear stress
and shear rate at the tube wall can be calculated and the rheology
can be detennined. The viscometer used in this thesis is of a tube
variety and is capable of producing reliable rheological and pipe
line data.
Lazarus and Slatter (1986) showed that rotary viscometers are less ~
suitable than tube viscometers for the rheological characterization
of slurries.
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LITERATURE AND THEORY 2.1
CHAPl'ER 2
LITERA'IURE AND THECEY
2.1 INTRODucTION
This review is based on the literature obtained from journals and
books dating from 1687 to 1987. The main references for this
chapter are Govier and Aziz (1972) and Skelland (1967).
2.2 SHEAR STRESS AND SHEAR RATE
Consider two parallel plates a distance y apart containing a fluid.
One plate is fixed and a force F moves the other at a velocity v
creating a velocity distribution shown in Fig. 2. 1. The shear
stress r is given by
F r = (Pa)
A
The shear rate is given by
dv. dy = ; (!)
(2.1)
(2.2)
A rheogram is defined as a graph of shear stress on the vertical
axis versus shear rate on the horizontal axis shown in Fig. 2.2.
2.3 NEWI'ONIAN R.HE:OLOGY.
In its simplest form hypothesized by Newton in his Principia of
1687, the "resistance arising from the lack of slipperiness in a
fluid'' is defined by one independent variable. Maxwell later named
this variable the coefficient of dynamic viscosity (µ) (Barr
(1931)), Schramm (1981) defined the viscosity as "the resistance of
a fluid against any irreversible positional change of its voltUne
elements". The mathematical fornrulation of this concept is given by
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LITERATURE AND THEORY 2.2
(2.3)
The viscosity (µ) has the lmits (Pa s) and is equal to the slope of
the Newtonion rheological curve shown in Fig. 2.2.
The incremental viscosity ( µ. ) is defined as the tangent to the 1
rheological curve at a fixed shear rate as shown in Fig. 2.3. It
can be likened to the thickness of a fluid at a fixed shear rate.
The incremental viscosity of a Newtonian fluid remains constant with
shear rate as shown in Figs. 2.2 and 2.3. Many coJ1111on fluids such as
water and oil are Newtonian.
2.4 NON-NEWTONIAN RHEOLOGY
The more complex case of non-Newtonian fluids exhibit a variation in
incremental viscosity with shear rate shown in Fig. _ 2. 3. This is
associated with a non-linear rheogram shown in Fig. 2.2. These
fluids may also exhibit a dependence of incremental viscosity on
shear history called time dependence
Shear thinning (pseudoplasticity) occurs when incremental viscosity
decreases with increasing shear rate shown as a flattening rheologi-
cal curve in Fig. 2.2. Shear thickening (dilatency) occurs when
incremental viscosity increases with increasing shear rate shown as
a steepening rheological curve (Fig. 2.2).
Non-Newtonian fluids may also exhibit a yield stress (T ) shown in . y Fig. 2. 2. This occurs in fluids such as toothpaste that only flow
when they are stressed above their yield stress.
In order to acco\Blt for rheogram curvature and yield stress
Herchell-Bulkley proposed the yield-pseudoplastic model. The
mathematical fonnulation of this model is given by
n "t' = 't + K (dydv).
iY (2.4)
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LITERATURE AND THEOOY 2.3
Thisl model and its variations are shown on a rheogram in Fig. 2.2.
The corresponding variations in the incremental viscosity with shear
rate. are shown in Fig. 2.3.
The fluid consistency index (K) corresponds to the steepness of the
rheogram and to the thickness of the fluid. The deviation of the '
flow' behaviour index --( n) from unity corresponds to the amount of
curvature of the rheogram and to the degree of non-Newtonian
be I •
halv1our. I
!
Many industrial fluids such as pa.ints,creams and polymer melts and
most slurries are non-Newtonian.
2.5 SLURRY RHEOlOOY
A slurry is defined as a mixture of solid particles and liquid. For
ana1~ical purposes researchers such as Lazarus ( 1988) , Si ve ( 1988)
and lwasp et al (1979) considered a fictitious fine portion of the I
solids to combine with the free water to f 0I111 the vehicle. The
vehicle is the conveying fluid for the larger particles. The
vehicle is analysed as non-settling and shows virtually no vertical
conqentration gradient. If alt the solid particles foI111 part of the
vehi~cle then the slurry is analysed as a single phase homogeneous
fluid although in a strict sense it is a two phase mixture.
I I
Experience has shown that the vehicle is usually non-Newtonian and
shows minimal time dependence.
The i rheology of fine solid-liquid mixtures is dependent on several
variables listed below.
Slatter (1986) showed that concentration and particle size distri
bution have a significant effect on the rheology shown in Fig. 2.4
and Fig. 2.5.
the surf ace torsley and Reizes ( 1980) showed that a change in
hemical chara.Cteristics such as zeta potential has an effect on the
heology as shown in Fig. 2.6.
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LITERATURE AND THEORY 2.4
I
Davi~ and Shrivastava (1982) showed that an increase in the
t~rature has the effect of reducing the consistency.
The ;slurry rheology is also dependent on other variables such as
partlcle shape and particle roughness (Lazarus (1985)). I I I
Hanks and Ha.Ilks (1982) describe a method of determining the critical
particle size below which all the particles are rheologically active
(vehicle) . By adding successive fractions of coarser particles to
the [finest material the critical particle size is defined as the
s~ze 1 above which any addition of coarser~particles causes no further
ch~e in rheology.
i 2.6 TUBE FLOW THEORY
the evaluation of the The l! fundamental problem in tube flow is
frici ion head loss. Research into this field showed that tube flow
can ~occur in two states namely: laminar and turbulent. In laminar
flow: the friction head loss is mainly proportional to viscous
forces. In turbulent flow the friction head loss is mainly propor
tion~! to the inertial forces. In laminar flow adjacent annuli
shea~ telescopically past each other with axial symmetry as shown I .
in Rig. 2. 7. This shearing action is governed by the rheology of
the 'fluid. For this reason data collected from laminar flow is used
for ;rheology.
The If allowing assumptions are made for the development of tube flow
theory: ~ steady state flow exists ·
-: the fluid is homogeneous
~ no slip occurs at the tube wall
· The ;shear stress at the wall of a tube can be evaluated from a force
balahce on a section of fluid shown in Fig. 2.8 arid is given by
I -r I: D6P ( 2. 5)
0 I ~
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LITERATURE AND THOORY
The continuity equation for tube flow is given by I
I I
Q - nR2V
2.5
(2.6)
The shear rate at the wall (- :)0
cannot be evaluated directly so
a pseudo-shear rate (bulk shear rate) 8V/Dderived from Poiseuille's
equa~ion (eqn. 2.16) is used. I
A t~ical tube flow pseudo-shear diagram obtained from the Balanced
Beam Tube Viscometer is shown in Fig. 2.~.
Rabihowitch and Mooney derived a relation from first principals that
converts the pseudo-shear rate into true shear rate which is given
by
(- t)o =
where n'
(3n 1 +l) 8V 4n' D
= d(ln('t' ))
0
d(ln(~v)
(2.7)
relation effectively converts a pseudo-shear diagram into a
rheogram and a full derivation is given in Appendix A. An analysis
of this relation is shown in Appendix A revealed that the pseudo-
shear diagram resembles a rheogram with a logarithmically compressed
X axis. Slatter ( 1986) showed that the relation cannot be used
beca,use n • is not constant and its value at a particular shear rate
cannbt be accurately detennined.
I A nbw technique for data reduction has been developed and is
described in Section 2.10.
i
A I • 1 tiyp1ca yield-pseudoplastic fluid shown in . Fig. 2.2, has a
veldci ty profile, shear rate distribution and shear stress
distribution shown in Fig. 2.10.
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LITERATURE AND THOORY 2.6
By rearranging equation 2.4 the velocity gradient is given by
- (:) = (l)l/n 1/n
.,..... (T - T ) K y
(2.8)
The plug is defined as an unsheared zone in the center of the tube
in which T < T • - y
The plug is bound by
r· = plug
2 T y
(- ~) and moves at a velocity given by
u plug
~n n n+l
= (- ~) n+l (-co - -cy) n
(2.9)
(2.10)
Integrating equation 2. 8 with respect to r and substituting the
boundary condition u = 0 at r = R yields the velocity profile given
by
(2.11)
The discharge is the S\..UJI. of the flow through the sheared region
(R > r > rplug) and the plug region (r < rplug) g~ven by
R
Q = J 2 n r u dr + n r 1 2 u . pug plug (2.12)
rplug
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LITERATURE AND TIIEORY
Setting T0
= ~and integrating gives
8V D [
('t' - 't' ) 2 0 y
1 + 3n
2.7
2 't' ('t' - T ) 't'2
]
+ Yi ~ 2n y + ~n 2.13
A full derivation of equation 2.13 is given in Appendix B.
By applying various conditions the flow equations for other models
can be derived (detailed derivations are shown in Appendix B).
If n > 1 then the fluid is yield-dilatant and if n < 1 then the
fluid_is yield-pseudoplastic. In both cases equation 2.13 is used.
In the case of a Bingham plastic fluid (n=l) equation 2.13 reduces
to the Buckingham equation given by
8V = D (2.14)
In the case of a power law fluid (i: = 0) equation 2.13 reduces to y
8V D =
4 1/n n 't'
0
Kl/n(l + 3n) (2.15)
In the case of a Newtonian fluid (n = 1 and 't' = 0) equation 2.13 y
• reduces to the Poiseuille equation given by
Q = n R.,. ~p 8 µ L
2.7 FRICTION FACTORS AND REYNOLDS NUMBERS
(2.16)
Tube viscometer data can also be presented on a friction factor
Reynolds number diagram provided that the rheology is known. A
general fonn of the diagram is shown in Fig. 2.11.
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LITERATURE AND THEORY 2.8
Reynolds found that the transition between laminar and turbulent
flow occurred. at a lower bmmd value of 2320 of a dimensionless
group called the Reynolds munber. This is defined as
Re = inertial forces
viscous forces
= B. L2 v2
µ V L
= ~ µ (2.17)
for Newtonian fluids. For non-Newtonian fluids the Reynolds number
contains a more complex version of the viscous tenn.
The Fanning friction factor is defined. as
't'
f = 0 1 . - P v2 2
(2.18)
where 1/2 p V2 is the maximum dynamic pressure that may be obtained. . from a stream velocity V (Lazarus ( 1983)).
In the case of laminar flow of Newtonian fluids the shear stress is
a function of the following variables
't' = fn ( p; V; D; µ) 0
Dimensional analysis gives
't' 0 = fn (p V D)
µ
= fn (Re) (2.19)
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LITERA'l\JRE AND THEORY 2.9
Substituting the equations 2.5, 2.6 and 2.16 into equation 2.18
gives
f = 16 pVD
µ
= 16 Re
(2.20)
In the flow of a solid-liquid mixture the shear stress is a function
of the following variables
T 0 =
The rheology which is a function of Cvt, d and µ is contained
intrinsically in this statement.
Dimensional analysis gives
(2.21)
2.8 NEW METHOD OF DATA REDUCI'ION
A method of data reduction for tube viscometer data yielding the
slurry's rheological parameters is needed.
2.8.1 Existing Rheological Characterization Procedure
The procedure was developed by Slatter ( 1986) to take the
place of the Rabinowitch-Mooney derivation which was found
to be unsuitable. The method is as follows
1. The raw data is plotted on a pseudo-shear diagram.
2. The yield-pseudoplastic equation 2.13 is the used to fit
a curve to the yield stress and the c6ordinates of two
judiciously selected points.
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LITERATURE AND THEORY
3. This is done three times with two different points
each time.
4. The three curves are then plotted back onto the
pseudo-shear diagram with the original data.
2.10
5. The best curve is then selected by eye and its
rheological parameters are used to plot the rheogram.
2.8.2 New Rheological Characterization Procedure
A study revealed that the rheological parameters are highly
sensitive to the selection of points. A program that fitted
the curve with the minimum least-squares error described in
Appendix C was then written and used. The new procedure is
as follows
1. The raw data is plotted on a pseudo-shear diagram.
2. The yield-pseudoplastic equation 2.13 is the used to fit
the best curve to the data.
3. The rheological parameters calculated in step 2 are then
used to plot a rheogram.
2.9 ANa1ALOUS BEHAVIOUR AT HIGH OONCENTRATIONS
At low concentrations it has been shown that the laminar section of
the pseudo-shear diagram coincides for different tube diameters as
shown in Fig. 2, 9. Anomalous behaviour at high concentrations
refers to the mechanism that causes the rheology to be dependent on
tube diameter shown in Fig. 2 .12. The behaviour is anomalous
because rheology ·is a property of the fluid and should not be
dependent on diameter.
This behaviour was first recorded by Green and Bingham in 1919 when
they discovered that the "mobility" of certain paints is higher in
smaller tubes.
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LITERATURE AND THEORY 2.11
Schofield and Scott Blair (1930) doct111ented the anomalous behaviour
at high concentrations naming it the sigma phenomenon. It was :;:::aa r=-=·--====-
though t that a thin layer of liquid at the tube wall , may cause a
reduction in in situ concentration. Tests showed no such reduction
occurred. Mechanical interaction between the solid particles and
the wall does not allow their centers to move closer than one
particle radius to the wall as shown in Fig, 2.13. Solid particles
may be moved towards the pipe axis by Magnus forces which are the
lift force caused by a velocity gradient across a sphere. It was
noted that at high concentrations mechanical interaction was more
l~kely than Magnus forces to create a thin liquid layer at the wall.
The presence of a thin layer of liquid at the wall will reduce the
concentration and therefore the "viscosity" in close proximity to
the wall. The geometry indicates that the increase in the
concentration in the center of the tube is minimal provided the
tube is large in comparison with the solid particles.
Bain and Bonnington ( 1970) doctunent that the flow of fibrous paper
pulp consists of a central plug with a flat velocity distribution
and an annulus of clear water lubricating the plug. This is caused
by the alignment of the fibres at the wall.
The most cormnon method of analysing this anomalous behaviour is
effective slip described in Section 2.10.
It is expected that the effect of mechanical interactions between
the solid particles and the wall for polydisperse systems would be
to change the particle size distribution in close proximity to the
wall.
Several·other researchers namely Barr (1931), Green (1949), Van
Waser (1963), Thomas (1963), Cheng (1975) and Baker et al (1979)
have also documented this phenomenon.
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LITERATURE AND THEORY 2.12
2.10 EFFECTIVE SLIP
2.10.1 Introduction
A prominent rheologist Mooney (1931) introduced the concept
of effective slip with the following description:
In ad.di tion to an lmknown rheology effective slip may also be encountered. This effective slip may in reality be an abnonnally large velocity gradient in a thin layer next to the wall. This is treated maj:.hematically as a discontinuity (slip velocity) at the wall if the thickness of the layer is small in comparison with the viscrn:neter dimensions.
Mooney (1931) developed the analysis technique described in
Section 2.10.2.
Effective slip should not be confused with a slip velocity
defined by SchraJ1111 (1981) as a lack of sufficient adherence
between the wall and the fluid to transmit the applied shear
stress.
Oldroyd (1948) doctUDented that effective slip manifested
itself as a tube diameter dependence on a pseudo-shear
diagram. It was advised that at least two tube diameters be
used for tube rheology. He maintained that a thin layer
with anisotropic rheological properties caused the anomalous
behaviour. The analysis technique described in Section
2.10.2 was presented.
Windhab apd Gleissle (1984) used cone and plate, rotary and
tube viscometers to detennine the rheology of high concen
tration kaolin slurry. The analysis technique described in
Section 2. 10. 2 was presented .and used to correct the tube
viscometer data for effective slip. It was shown that the
modified tube viscometer rheogram corresponded well with the
other .two rheograms. A slip limit was defined as the shear
stress above which slip starts to occur.
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LITERATURE AND THOORY 2.13
Wasp et al (1979) and Skelland (1967) both doctUDent that at
high concentrations solid particles move away from the wall
leaving a layer of liquid. This leads to a reduction in the
"viscosity" of the mixture at the wall, the consequences of
which are analogous to those if slip occurred. Skelland
(1967) presented the analysis technique described in
Section 2.10.2.
Several ·other researchers namely Thomas ( 1962) , Stepanoff
( 1964 ) , Kentchington ( 197 4) , Harris and Quader ( 1971 ) and
Hanks and Hanks ( 1982) have also doctUDented effective slip
and the associated diameter dependence
2.10.2 Effective Slip Analygis Technique
This technique has been described in detail by Mooney
(1931), Oldroyd (1948), Skelland ( 1967)" and Windhab and
Gleissle ( 1984).
_The general equation for tube flow derived in appendix A is
given by:
i: J o 't'z 0
f('t') d 't' (2.22)
Note that this equation is valid for any type of rheological
model.
Mooney (1931) postulates an effective slip velocity at the
wall given by
u ={Ji: s 0 (2.23)
where {J is the effective slip coefficient.
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LITERA'ItJRE AND THEORY 2.14
To account for the thin abnormal layer near the wall a
modified boundary condition is used giving
Q (2.24)
this can be rewritten as.
't'
Q 3L + 1 Jo -r2 f (-r) d T tr R' = R -r -r"' 't'
0 0 0 0
't'
fl. + 1 J 0 -r2 f('.t') d 't' = R i;"' 0 0
(2.25)
Equation 2.25 has the fonn of a straight line where beta is
equivalent to the slope of the graph of Q/rr R1 -r versus l/R 0
at a fixed -r • By calculating values of p over a range of 0
-r values a graph of slip velocity u = -r p versus -r may 0 s 0 0
be plotted.
The equation to correct the collected data is given by
Q corrected for slip = Q measured - p -r0
n R2
't'
: !4 J O -r2 f (-r) d T 0 0
(2.26)
Using this technique the slip function for a fluid tested in
different diameters can be calculated. This is used to
reduce the pseudo-shear diagram for each diameter onto one
curve representing the fluid rheology.
2.11 DENSE-PHASE IDDELS
Dense-phase flow occurs when the subnerged weight of the solid
particles is transferred to the pipe invert by particle-particle
interactions. Typically this type of slurry has a small proportion
of fine particles and a large proportion of coarse particles.
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LITERATURE AND THEORY 2.15
In dense-phase flow the wall friction of the sliding bed is the
largest factor contributing to the overall head loss. A smaller
component of the overall head loss is due to the flow of the vehicle
through the interstitial spaces of the coarse solids.
Streat (1986) developed a equation to predict the hydraulic gradient
of dense-phase flow given by
i = 2 µ (S - S ) Cvt + S i m s s w m w (2.27)
Streat (1986) showed that if the dense-phase flow condition existed
equation 2.27 was applicable.
2. 12 WALL EFFECT (Maude and Whitmore ( 1955))
Maude and Whitmore (1955) hypothesized that the a wall effect occurs
due to the a redistribution of the solid particles at the wall.
This is caused by the mechanical interaction between the solid
particles and the wall as they enter the tube. This causes a
reduction in the in situ concentration (Cvt), Tests were performed
using polystyrene spheres (d90 = 965 j.JID) in a glass tube with a
diameter D = 1.876 DID (ds 0 /D = :t 0.5). The tests showed that the
ln sl tu volumetric concentration (Cvt) maybe as much as 75% lower
than the delivered volumetric concentration (Cvd). It was proposed
that the redistribution of particles away from the wall would have
no effect on the rheological measurements.
It was hypothesized that the reduction in the in situ concentration
and not effective slip was the cause of anomalous behaviour at high
concentrations. This reduction will be more significant in a small
tube therefore the rheology measured in a small tube will appear
less viscous.
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LITERATURE AND THEORY 2.16
2.13 BOUNDARY-LAYER EFFECT
Reiner (1934) and Smoldyrev and Safonov (1979) both doctunent that an
inward radial migration of solid particles near the tube wall
occurred increasing the concentration of the slurry in the core and
leaving a thin boundary layer of lubricating fluid at the wall.
Assume that a layer of thickness a and. viscosity µ exists at the
wall as shown in Fig. 2.14.
A?sume that the velocity distribution~ in the boundary layer is
linear. Using equation 2.3 the rate of shear at the wall for T < T 0 y
is given by
T
= ...Q. + µ
u core 0
and the flow is given by
Q = n (R - 0) 2 u core + n u core
2
assuming that o is infinitesimally small in relation to R
Q = n R2 u core
(2.28)
(2.29)
(2.30)
and substituting equations 2.6 and 2.28 into equation 2.30 gives
(2.31)
For values of T < T the less viscous boundary layer will allow the 0 y .
core to move at a velocity u • This is shown on a pseudo-shear · core diagram in Fig. 2.15. The initial slope of the rheogram is given by
(2.32)
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LITERATURE AND THIDRY 2.17
The thickness of the boundary layer can be solved for by combining
eqn. 2.31 and eqn 2.32 giving
= Y...R 8 E.
(2.33)
The measured data is then corrected as follows
V =V -u actual measured core
where
u core
't' a = _o __ µ (2.35)
Using this technique the thickness of the boundary layer can be
det~rmined from a pseudo-shear diagram. This is then used to
correct the pseudo-shear diagram shown in Fig. 2.15 which can then
be rheologically characterized.
2.14 OODIFIED FRICTION FAC'roRS
Shook ( 1985) hypothesized that the friction ·factor for a solid-.,
liquid mixture was due partly to the liquid friction and partly to
the hydrodynamic lubrication between solid particles and the tube
wall. The final f onn of this equation derived from hydrodynamic
lubrication theory is given as
(2.36)
where A (2.37)
and K and m are dimensionless coefficients, and C is the maximum m pa.eking concentration.
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LITERATURE AND THEORY 2.18
On a log f versus log Re diagram the variation of K and m shift the
curve parallel to its original position. Tiie slope.of this curve is
fixed because the power of the Reynolds m.unber is fixed at -0. 5.
2.15 CX>NCI1JSIONS
Tiie theory of rheology has been presented. Several varying theories
exist for the analysis of anomalous behaviour.
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, LITERATURE AND THOORY
T y
j_
Shear ·Stress 1;
Shear Rate ~~
Area
F I A
v I y
A
Fig. 2.1 Shear stress and shear rate in a fluid sheared
between parallel plates.
2.19
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LITERATURE AND TIIEORY
SHEAR STRESS
YIELD STRESS
't y
SHEAR RATE dv dy
2.20
Yield-Pseudoplastic
Bingham Plastic
Yield Dilatant
Pseudoplastic
Newtonian
Dilatant
Fig. 2.2 Rheograms of various rheological models.
INCREMENT AL VISCOSITY.
~ i Dilatant
----- Pseudoplastic
SHEAR RA TE dv dy
Fig. 2.3 A graph of incremental viscosity versus shear rate
for various rheological models.
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LITERATURE AND WEORY 2.21
VOLUMETRIC CONCENTRATION vs YIELD STRESS ,.... a e; 20.-~~~-+~-t----lf---H-~~---I
r""1 .
°' ..... >-
'-dmax• l OOum
• 10 .,.__ ___ -==-......,,,,,::~-~,-+-------t :dmax•250um
.~ I -
i . 'dmax•2000um
o.ooc----------0----------~------c N ~ "It - Cv %
VOLUMETRIC CONCENTRATION vs FLOW BEHAVIOUR INDEX
c
. 600~--------...._ _____ ---:!!
N Cv % Fig· 2. 4 A typical effect of concentration on rheology
(Slatter (1986).
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•
LITERATURE AND THFXJRY
20
,... 0
Q_
"" (/) (/) OJ 10 L +> Ul
""O ,..... OJ ..... > .
10
2.22
YIELD STRESS vs MAX PART SIZE
\ \ \ \ \ "\
I
\ """'--
100
~1 ~ .... I•"
1~1 1000
I I
KEY + Cv 29% • Cv 23%
10000
Maximum Particle Size (microns)
FLUID CONSISTENCY INDEX vs MAX PART SIZE
~
• 20
. l 8
• 1 6
• 1 4
• 1 2
• 1 0
.o 8
• 06
.o 4
.02
\ \
' \\ \\ \ '· ~' ~~ ~.loo.
"!'lo
I
.... ~ .. I
~ ~
~~
KEY + Cv 29% • Cv 23%
o. "-J ~ 100 1000 1 ] 00
Maximum Particle Size (microns) . FLOW BEHAVIOUR INDEX vs MAX PART SIZE
1. 00
• 90
• BO
• 70
'" ... ~
"~ ", .... ~~
ii...._
• 60
i.. . . .
,,, .. ~
i- >
+
•
KEY Cv 29% Cv 23%
c·SO • 40
.30
.20
.10 , o.·
~u IU uu h AIU
Maximum Particle Size (microns) Fig. 2.5 A typical effect of maximum particle size on
rheology (Slatter (1986).
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I
I I
LITERATURE AND 'I'HroRY
15
10 N 'E z I/) I/) w « .... I/)
«
"" w x I/) s
0 50
,
~ ~«' +
+ .
.. ~·\•
,,o~ ,~,..
r_,((,~ ~o~
Fig. 2.6 The effect of zeta potential on rheology
(Horsley and Reizes (1980)).
2.23
200
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-' '
LITERATURE AND 'l1lIDRY
--J:>---J:>-
p+6p J:>---J:>---}::>-
2.24
Flow Direction
Fig. 2.7 Tube flow analogy.
1 .. L ..1
D t
I I I '--I ~
c:::::::£--
Flow Direction =-p L===> c:::::::£-
c:::::::£--
' 'y; '
Force Balance:
I - D6p GO- 4l
Fig. 2.8 Derivation of the shear stress at the wall.
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I
LITERATURE AND THFXEY 2.25
~ 0: (..:I
< -c
~ L&J %: en
~· L&J en a.
Cl Cl .Jl
.Jl ::J ::J .... ....
E > Cl ::J L&J m .... x L. ,,
a Cl ...J %
• +
Cl .Jl ::J .... --a E
U)
)(
-LL. .., c Cl
.., c Cl
0002[
------ 0000[ c 0 .... ..,
-r--------....--------+-- ::>----t---------..*"""-------1---------f0008
a ~
a an N
a c N
.., c Cl -::J
.Jl L. ::J ....
.Jl L. ::J ....
(Dd) 1 t
a a an a - -1dva SS3~lS ~V3HS
a an
• 0 -LL.
L. a c
Fig. 2.9 A typical pseudo-shear diagram using three tube
diameters.
0001'
0002
D a
-• ..... --c ..... > m
L&J .... < 0:
~ L&J %: en I
a c ~ L&J en a.
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Sh
ear
Sh
ear
Vel
oci
ty
·Str
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.I·
Rat
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rofi
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RI L
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0
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stre
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sh
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dis
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"J:j .....
Ot\ . N . .....
.....
"J:j m~
'1
>
t;· ~ ~
c+ .....
u g
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Univers
ity of
Cap
e Tow
n
I • •
LITERATURE AND TH1IDRY
en z c -I-< a:: I-z IJJ u z c u :c l!) -:c I-< a:: => c -> < :c IJJ m en => c ..J < z 0 z <
% < a:: l!> < -c a:: < L&J :c U1 I c
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QI .a :J .,_
--0 E
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c c (Tl
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(Dd) 1 t I d \J 0 SS3~!S ~V3HS
c c -Fig. 2.12 A high concentration pseudo-shear diagram
showing anomalous behaviour.
2.28
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008 .......
> CD
UJ I-< a:: a::
009 < UJ :c U1 I
0 Cl ::::> UJ U1 a..
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Univers
ity of
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LITERA'IURE AND THroRY
Solid Particle
~ <
Con cen tra ti on
2.29
Zone of .... Reduced
1 Concentration -I>
R Fig. 2.13 Inward radial migration of solid particles and
the associated reduction in concentration in the
proximity of the tube wall.
Velocity Profile for LO <LY
Fictitious Boundary{
1 Layer of Liquid 8 Representing Lr-~~~__..~~~~~-----~~~~~ Concentration l _gill Reduction r~o Tube Wall
Fig. 2.14 Boundary-layer of liquid at the tube wall.
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n
LITERA'IURE AND 'IllOORY
Corrected Curve
Shear Stress
~Measured Curve
Pseudo-Shear Rate
Fig. 2.15 Correction of a pseudo-shear diagram for the
effect of a boundary-layer.
2.30
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I
RESEARCH APPARATUS 3.1
CHAPI'ER 3
RF8EARCH APPARA'IUS
3.1 DF.sCRIPI'ION OF THE BALANCED BEAM TUBE VISCXMETER
The novel Balanced Beam Tube Viscometer, which has been developed at
UC!' is shown in Figs. 3.1 to 3.3. The viscometer consists of two
pressure vessels (1 and 2) mounted on a steel joist and supported at
two points Land F. A load cell is located at point Land point F is
the system fulcrum (supported on a knife edge). Figs. 3.2 and 3.3
show that the pressure vessels are connected by three transparent
PVC tubes with nominal internal diameters of 28 nm, 13 J1BR and 4 nun.
Baker et al ( 1979) r~OllUilends that at least two tube diameters
should be used to ensure time dependance and wall shear anomalies
are detected. The precise internal diameters are 28.38 Diil, 13.37 mm
and 4. 20 nun and were detennined to this precision by weighing
sections of the tubes with and without water. This precision is
required since a rheogram point inherently contains the fourth power
of the diameter.
Each tube has ball valves at either end and only one tube is used at
a time. Each pressure vessel has a nest of stirrers (inside), driven
by motors (on top) connected by shafts through seals in the vessel
cover plate. Air pressure is supplied to either vessel using a 700
KPa air supply, a pressure regulator and a three-way valve. The
necessary driving force to cause the slurry to flow between vessels
is.developed by pressurising one vessel and venting the other to the
atmosphere. Velocities of up to 9 m/s can be achieved in this
manner.
Pressure tappings shown in Fig. 3.4 are fitted to the tubes,
allowing direet measurement of the differential pressure due to
friction head loss. This avoids the inclusion of entrance and exit
losses and hydraulic grade line curvature due to developing flow.
The diameter of the pressure tapping holes is 2 nm. There are four
pressure tappings in each tube, allowing the operator flexibility of
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ity of
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n
RESEARCH APPARATUS 3.2
pressure range. The pressure tappings are water filled and connected.
to the differential pressure transducer (DP cell) via slurry iso
lation pods, and a flushing/bleeding facility shown in Fig, 3. 4.
The pressure tappings are located far enough from the tube entrances
to ensure fully developed flow exists between them. The hydraulic
effective length is thus equal to the physical distance between the
tappings ( L) •
The primary output from the viscometer consists of successive
voltage readings representing load cell input (power supply
voltage), load cell output and DP cell output. These are converted.
into voltlllletric flow rate and differential pressure for analysis.
The operator has the facility to manually reject the _non-steady
state flow readings taken during acceleration. These are distin
guishable as non-linear differential pressures. A sample is taken
for ancillary tests ( S , S , pH and particle size distribution) s m described in Appendix C.
The viscometer is capable of rheologically characterising fluids
such as water and slurries (Slatter 1986), (Lazarus and Sive 1985)).
The viscometer is also a minature pipeline and is capable of
collecting turbulent flow data and indicating the laminar-turbulent
flow transition (Slatter 1986).
3.2 MEASUREMENT TECHNIQUE§
A data acquisition system consisting of a computer, data acquisition
unit and transducers is used to measure flow and differential
pressure.
3.2.1 Flow Measurement
A load cell is located at point L (Fig. 3.1), to determine
the slurry mass distribution between the two vessels. A
typical flow measurement consists of 20 readings- of mass and
time shown in Fig. 3.5. A least squares linear regression on
this data yields the mass flow rate ( dm/dt) • ~ and Vm can
be calculated. from (dm/dt) as follows
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n
RESEARCH APPARATUS 3.3
3.2.2
~ = dm dt (3.1)
Pm
v = ~ - dm m A - dt (3.2)
P, A m
The load cell is designed and constructed at UCT and is
shown in Fig. 3. 6 and Fig. 3. 7. It can operate in both
tension and compression and has a resolution of lN and a
range of ± lOOON ( accuracy of 0.1% ) •
Four strain gauges are bonded in the positions of maximum
strain A, B, C, and D on the load cell (Fig. 3.7). The
strain gauges are cormected in a Wheatstone Bridge shown in
Fig. 3.8.
A HP6214A power supply used for the input voltage and is set
at a nominal lOV. The output voltage of the bridge varies
linearly- with applied force, and is proportional to the
input voltage. The output voltage is divided by the input
voltage, giving a non-dimensional load cell reading ( v /v)
which is independent of input voltage and temperature
fluctuations.
A typical response characteristic is shown in Fig. 3.9.
Differential Pressure Measurement
A differental pressure transducer (DP cell) is used to
measure the differential pressure between two pressure
tappings on a selected tube. The differential pressure is
calculated as the arithmetic mean of 20 differential
pressure measurements shown in Fig. 3. 5. The DP cell is
located next to the viscometer fulchrum and is connected to
the slurry isolation pods with flexible reinforced tubing
with a low strain memory. Because the DP cell carmot read
in reverse, high-low selectors shown in Figs. 3.10 and 3.11
are provided so that the pressure differential can be
reversed.
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RESEARCH APPARATUS 3.4
3.2.3
A Gould PDH 3000 series differential pressure transducer is
used and is shown in Fig. 3.12. The DP cell has an accuracy
of 0.25% and a maximum range of 200 KPa and is connected to
a· 24V power supply as shown in Fig. 3.13. The output is
4-20 IDA in the supply leads which is linear with pressure
differential across the two halves of the cell. The current
output is converted to a 40-200 mV voltage_ output by a 10 a series resistor.
The range and the span are adjustable. A typical response
characteristic is shown in Fig. 3.14.
Computer Hardware
The computer hardware is used for high speed data
acquisition and proeessing.
The computer hardware consists of a HP-87C computer,
. HP82901M double flexible disc drive, HP82905A printer,
HP7470A plotter and a HP3421A data acquisition unit
(analogue to digital converter) shown in Fig. 3.15. These
are located opposite the fulchrum of the viscometer in a
cooled computer box.
The HP-87C is a 128k RAM basic computer with I/O and
Advanced Programming Ra1's and an interface loop (IL}
peripheral.
The data acquisition unit (DAU) equipped with a 10 channel
multiplexer is used as a software controlled digital
voltmeter to read various analogue input channels.
The computer is connected to the data acquisition unit by an
interface loop and to the other three peripheral devices by
an interface bus as shown in Fig. 3.16.
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RESEARCH APPARATUS 3.5
To facilitate operation the following device codes are
listed:
Interface
Interface Loop
Interface Bus
3.2.4 Experimental Error
Peripheral Device
Data Acquisition Unit
Disc Drive 0
Disc Drive 1
Printer
Plotter
Code
901
700
701
701
705
Fluctuations of the analogue outputs of the transducers
occur in any measurement system. The discrete readings of
the _data acquisition unit may be taken at an extreme
analogue value. This can be accounted for using statistical
techniques.
In general if a measured parameter is given by
X = f n ( a , b , c , • • • • • • , n ) (3.3)
then the error in X due to an error in n is given by
(Brinkworth (1968))
(l1X) n
x = (~ An) an X
= (ax n.. An) an X n
and the maximum error is given by
(ax n.. l1n) 2
an X n (3.5)
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) RESEARCH APPARATUS 3.6
Error in Internal Tube Diameter Measurement
The internal tube diameter is ' detennined by measuring the
mass of water that fills a section of tube of length L using
the equation given by
D --
The maximlDD error is given by
(~D) =
(3.6)
( 1 ~ L .6L) 2
-2J~nL (3.7)
and presented in Table 3.1.
Table 3.1 Maximum error in diameter.
Nominal L(m) m Actual Error in Percentage w
Diameter (kg) Diameter Diameter Error (nun) ±0,001 ±0,001 (nun) ( 11111) (%)
28 5 3,163 28.38 ± 0.007 0.0026 13 5 0,702 13.37 ± 0.0022 0.0034 4 5 0,0693 4.20 ± 0.0034 0.0815
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RESEARCH APPARATUS 3.7
Error in Velocity Measurement -----------------------------Velocities between 0.1 and 10 m/s are measured using the
equation
v 4~
= n n2 m
4 M m = n n2 pm
2 F (3.8) = n n2 t p g m
The mass distribution between the two vessels is measured using the
load cell. The load cell is calibrated using the equation given by
F = m (~/v) + c (3.9)
The slope of the calibration curve is determined by a least squares
linear regression shown in Fig. 3.9. The slope is given by
m = L v/v (3.10)
and the maximtun error may be approximated as
(~) = (- (v~v) 2 v/v 6v/v) 2
m v/v + (_1 f. 6F)
2
v/v m F (3.11)
The largest error in the measurement of the dimensionless load cell
output is estimated at O, 5%. The largest error in the measur~t
of applied force 6F/F is 0,06%. Therefore the ma.ximtDD error in
slope f:lm/m is 0,56%.
Univers
ity of
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RESEARCH APPARATUS
The maximum error in F is given by
(m v/v 6v/v)2
F v/v
which is calculated to be 1,06%.
3.8
(3.12)
The maximum error in V calculated using the slope of the graph of · m
mass versus time is approximated by
(v:m) = ( t Pm 2rr Da L ~Fr. g v m
+ ( - 2 F .L 6t)2
t2 pm~ Da g v t m
+ ( - 4 F ~®r \ t pm Tr D1 g V D
m
+ ( - 2 F t p~ rr D2
Pm Pm)2 g vm pm
(3.13)
The largest error in the measurement of force fJ.F/F is 1,06%. The
largest error in the measurement of time fJ.t/t is 0,1%. The largest
error in the measurement of mixture density llp /p is 0,3%. The m m maximum errors in velocity are presented in Table 3.2.
Table 3.2 Maximum error in velocity.
Nominal Diameter
( 11111)
28 13
4
Percentage Error in Velocity
(%)
1.46 1.47 1.62
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ity of
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RESEARCH APPARATUS 3.9
Error in Shear Stress Measurement
Shear stresses between 1 and 600 (Pa) are measured. This
involves the measurement of differential pressure between 1
and 250 (kPa). The calibration curve for the DP cell is
given by
p = m v + C (3.14)
The errors in the measurement of differential pressure are
calculated in the same way as for the load cell. The
accuracy of the DP cell is 0,25%. The largest error in the
measurement of applied pressure is 0,1%. The rnaxirnlDD. error
in the calibration slope &n/m is calculated to be 0, 35%.
The rna.ximlDD. error in the measurement of pressure is
calculated to be 0,6%.
The eqUa.tion used to calculate the shear stress at the wall
is given by
i: 0
_ ·Dflp - 4 L
The rna.xirntDD. error in i: is given by 0
(~:o) =
+
(llp !L ®) 2 + TI:; i: D
0 (D Ap Allp) 2
TI:; :r 2SP 0
(3.15)
(3.16)
The largest error in the measurement of the length between pressure
tappings llL/L is 0. 2%, The ma.ximl.Ull errors in shear stress are
presented in Table 3.3.
Univers
ity of
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RESEARCH APPARATUS 3. 10
Table 3.3 Ma.xi.mum error in shear stress
Percentage Nominal Error in Diameter Shear Stress
(nm) (Pa)
28 0.803 13 0.803
4 0.882
The maximum error in the above experimental measurements is within
acceptable limits.
3.3 OPERATING POOCEDURE
The operating program called "VISOO" ·must be loaded from the
programs disc in drive 0 onto the HP-87 computer and run to start up
the system. The ma.in menu will then display the available software
functions. The menu tree is shown in Fig. 3, 17 to facilitate
operation. The following definitions shall apply:
A READING consists of one transducer output.
A RUN consists of 20 consecutive BBTV transducer outputs (load cell,
DP cell and time) representing one pseudo-shear diagram point.
A TEST consists of up to 100 readings from each tube representing
one pseudo-shear diagram as shown in Fig. 3.19 and 3.20. This may be
rheologically characterised to yield the values for ~ , K and n. y
The load cell is a sensitive device and should be replaced with a
blank when not in use. To install the load cell the BBTV must have
equal amounts of slurry in each vessel so that it balances on its
knife edge.
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RESEARCH APPARATUS 3.11
Details of the fW'lctions are given below.
3.3.l Log On
This function sets the date on the computer clock which is
used at several stages in the program. The computer clock
is zeroed each time the system is switched on, and if it is
not set a date of "00/00/00" will used.
3.3.2 Read.channel
This function reads one of the three input channels namely:
load cell input voltage and load cell output voltage and DP
cell output voltage. It is used to check that the trans
ducers are operating properly.
3.3.3 Calibration
The CALIBRATE LOAD CELL and CALIBRATE DP CELL options are
used to calibrate the load cell and the DP cell respec
tively. The LOAD CELL CALIB PLOT and DP· CELL CALIB PLOT
options are used to plot the respective calibration graphs.
After the calibration the data is stored on the data disc in
drive 1, so that the calibration constants can be recalled
at any time. A calibration of each transducer must be done
before a test.
The following steps are executed for load cell calibration:
1. Standard weights are placed above the centroids of each
vessel (ie. on top of the stirrer motors). A downward
force on the LlI vessel is considered positive and a
downward force on the RH vessel is considered negative.
2. The slurry levels in the vessels must be approximately
the same.
Univers
ity of
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•
RESEARCH APPARATUS 3. 12
3. Select the CALIBRATION function and the CALIBRATE LOAD
CEIL option to start the calibration. The computer will
prompt the operator for the force value in newtons
after which it takes the average of ten load cell input
and output readings.
4. Readings are taken for a range of approximately ten
different load values, noting that a zero load is valid
and desirable for calibration purposes.
5. At the end the computer will do a least squares linear
regression on the data which yields the calibration
constants
m = gradient of the calibration line
c = ordinate- intercept of the calibration line
from the equation
(Applied load) = m x (Transducer output) + c
A typical load cell calibration output is shown in Fig. 3.9.
The following steps are followed for DP cell calibration:
1. Connect the pods to the mercury /water manometer as
shown in Fig. 3.18.
2. Open the manometer relief valve.
3. Bleed the DP cell system and the manometer of all air
and solids by flushing supply water via the bleed valve
through the various components.
4. Close the manometer relief valve •
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ity of
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-
RESEARCH APPARATUS 3. 13
5. Using the manometer relief valve and a low mains flow,
a pressure differential is set up. The pressure
differential can be reduced by releasing some water
with the manometer relief valve. The high-low selectors
must be set to run from LHS to RHS.
6. Select the CALIBRATION function and the CALIBRATE DP
CELL option to start the calibration. The computer will
prompt the operator for the levels of the mercury in
nun, after which it will take the average of ten DP cell
output readings,
7. This is repeated for a range of approximately ten
different differential pressures, noting that a zero
pressure differential is valid and desirable for
calibration pui-poses.
8. At the end the computer will do a least squares linear
regression on the data points which will yield cali
bration constants m and c.
A typical DP cell calibration output is shown in Fig. 3.14.
3.3.4 Visco Run
During a test the data is continously stored in two
workf iles on the programs disc called "WORKFILE" and
"NOPTS". There is also an option of viewing the partially
complete pseudo-shear· diagram after each run, The results
shown in Fig. 3.19 will be printed out if the printer is ON
LINE.
The test data is given a name of the form AABXXDDM-1 where:
M is an identity code
B is the tube size (L, M or S)
XX is the volumetric concentration as a percent
DDMM is the date,
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ity of
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n
RESEARCH APPARATUS 3.14
The following steps are executed to run a test:
1. The power supplies located in the computer hut must be
turned on and allowed to warm up (about 10 minutes).
2. Half fill each vessel throUgh the filling ports, and
replace port lids and insert the load cell.
3. Pump the slurry from one vessel to the other several
times to mix it thoroUghly by using steps 8 to 15
without using the computer. The operator should begin
to get a qualitative "feel" for the slurry rheology.
4. A one litre sample should be taken for record purposes
and ancillary tests ( S , S , pH and particle size m s distribution) described in Appendix C, using a sample
valve.
5. ,Flush any solids from the pods and bleed the pressure
6.
system of air. Connect the pods to the required
tappings and open respective tapping valves.
Insert the load cell. Ensure calibrations of the
transducers are available.
function to start the test.
Select the V!S(X)RUN
7 . The computer will prompt the user for several para
meters and ancillary test results namely: tube
diameter, tapping width, calibration codes, pH,
temperature, solids relative density (S ) , mixture s relative density (S ) and the identity code AA. . m
8. Close the vent valve on the full vessel side and close
the tube valve on that side.
9. Open the vent valve and open the tube valve on the
empty vessel side.
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ity of
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n
• ' •
RESEARCH APPARATUS 3. 15
10. Select the correct direction on the high-low selectors
(see Figs. 3.10 and 3.11).
11. Set the pressure regulator to the desired pressure.
12. Switch the 3-way valve so that the full vessel is
presstirized (see Fig. 3.3).'
13. Open the tube valve on the pressurized side.
14. Press the appropriate time key to specify the time
interval between each of the 20 readings and to start
the data acquisition.
15. At the end of the run close the tube valve slowly to
prevent water hanuner.
16. The accumulated data will be displayed on two graphs,
the upper one a graph of mass versus time and the lower
one a graph of pressure versus time similar to Fig.
3.5. The operator is prompted to select the time span
over which the results are relevant.
discard the data.
Key in 0,0 to
17. Steps 8 to 16 are repeated over a range of pressures.
18, The operator will be prompted to store the data which
transfers the test data from the workfile to the data
disk.
I
The time key selection should be chosen so that at least 15
of the 20 readings are evenly spaced over the flow time.
The stirrer motors should be used when the sl\Jrry particles
have a high settling velocity .
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ity of
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I 4 • I
I I
RESEARCH APPARATUS 3.16
3.3.5 .
Store Data
If a fatal error should occur during the test the
accl.Ullulated data can be recovered by using the STORE DATA
function.
3.3.6 Utilities
This function provides access to several useful programs on
the programs disc. The programs and their functions are
listed below:
Prosram name
GRAPH 1
GRAPH 2
LS SOLVE
FITDRAWU
FILE PRINT
Key label and Description
PLOT ONE P-S GRAPH - plots the results
from one test in the form of a pseudo
shear diagram shown in Fig. 3.20.
PLOT MANY P-S GRAPHS - plots numerous
test results on one pseudo-shear
diagram.
FIT YPP CURVE - fits a yield pseudo
plastic curve a set of test data.
PLOT YPP CURVE & DATA - plots data from
several files and the fitted YPP curve.
FILE PRINT - prints the contents of any
data file on to the screen or the
printer.
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ity of
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RESEARCH APPARATUS 3.17
3.3.7 Operating Notes
The A/G key may be used at any time to view the most
recent graph
The right hand vessel is on a cantilever and may be set
into oscillatory motion when bumped or during a run.
This will show up as an inclined sine wave on the mass
versus time graph and the data should be discarded.
Make sure that no slurry leaks through the tubes that
are not being used.
At the end of a run air may be sucked into the tube.
This should be avoided because it airates the slurry
and sets the viscometer into oscillatory motion.
- Allow a short time for the flow to stabilize before
reading data.
If the slurry isolation pods fill up with slurry they
must be disconnected and flushed.
- At high concentrations the pressure tappings block
causing an error message in the pressure reading.
3.4 CONCLUSIONS
The Balanced Beam Tube Viscometer is a versatile instrument that is
capable of producing reliable rheological and pipeline data.
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RESEARCH APPARATUS
--+_VESSEL PRESSURISED
A [
Fig. 3.1 Diagramatic layout of BBTV.
~ ··.:---; - - . i-.-
~ 1
Fig. 3.2 Photograph of BBTV.
®
3.18
VENT TO
ATM.
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ity of
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e Tow
n
"rj
~·
OCl . w . w ~ [/J
~ ......
'< ~ to'· i 0 H) ~ .
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RESEARCH APPARATUS 3 • 20
Fig. 3.4 Photograph of pressure tapping and slurry
isolation pod.
20 ,....., m
..x: L-J
(J) (J) 0 ~
0
0 0 0 0 0 0 0 0 t\J .. Ill ID " CII Ol
Ti mg [s)
b o . 0 0 0 0 0 0 0
2000 ,....., 0
0.... L-J
QJ L :J (J) (J) QJ L
0.... 0 11 I I I I I I I I
0 0 0 0 0 0 0 0 0 N ('I) .. Ill ID " CII Ol
Ti mg [s)
0 0
c
0 0
Fig. 3.5 A run in graphical fonn (Slatter (1986)).
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RESEARCH APPARATUS 3 .21
1 38
1 I I
I I I I I
6,3R I'
A B .. ("r) 19 MB @ :-_ J< Jr L • 0 I~ a;
IO
J· " 38 )\
c D -1~ PLAN / I
~ 24, g
FRONT VIEW
Fig. 3.6 Load cell (Slatter (1986)).
~~~· , .
.. -- -.
Fig. 3.7 Photograph of load cell.
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RESEARCH APPARATUS
,.. z ...,, "lJ D 0
..J ... D :J .., u <
STRAIN GAUGE A
STRAIN GAUGE C
400
300
200
100
0
-100
-200
. -300
-400 0 0 0 0
d
OUTPUT VOLTAGE
STRAIN GAUGE B
STRAIN GAUGE D
Fig. 3.8 Wheatstone bridge circuit.
CALIBRATION PLOT of FILE LDAT2002 DATE a 00/00/00
Ill 0 0 0
Load Call Traneducar Output CV/V)
Fig. 3.9 Load cell response characteristic.
3.22
INPUT VOLTAGE
KEY •• -868223.07678 c • . 445.34053161
0 -0 0
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RESEARCH APPARATUS 3.23
·-
Fig. 3.10 Photograph of high/low pressure selectors.
Tube ~
Pressure ~--..---t -----------------------~-~---Tapping
Slurry -Isolation Pod
High/Low Pressure Selectors
Reinforced -Tubing
Flu sh in g Water
DP Cell
Fig. 3.11 Digram of high/low pressure selectors.
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I I
RESEARCH APPARATUS 3. 24
HIGH LOW
Fig. 3.12 Differential pressure transducer (DP cell)
(Gould ( 1980)).
I=4-20mA
D P GROUND CELL
10 OHM
OUTPUT TO DAU C40-200mV>
+
24V SUPPLY
Fig. 3.13 DP cell circuit diagram (Slatter (1986)),
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RESEARCH APPARATUS
" a 11.. 0 Cl L :> • • Cl L
11.. .... a :> ... u <
CALIBRATION PLOT of FILE POAT1013 DATE 1 00/00/00
200
150
100
so
0 ._...__._ ....... __.~.._------~------....... __.---.._....__.__.,~...._...__._ ...... __.,..._.._..._ ....... _. U> N ,· -N ,·
U>
,· ,· U> 0 ,·
Differential Pre&sure Tran&ducer Output CV)
Fig. 3.14 DP cell response characteristic.
;');,:
'~I ,:~ j~.;~
. . . . . . ... ''
Ii -----\ - -._ ... - ---
-0 ,·
Fig. 3.15 Photograph of the computer hardware.
3.25
KEY - -1308185.2089 - -48406.813299
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RESEARCH APPARA'IUS 3.26
I
DP CELL Out.put. I
LOAD CELL Out.put. i---
Irlpw.t. 11 Chat.lllle1 1 234
o,:::::rrA ACQUISITION UNIT
HP-IL
HP-S7C COMPUTER
HP-IB
- DISK DRIVE ...._ PRINTER - PLOTTER
Fig. 3.16 Computer hardware connection diagram.
MENU TREE
MAIN MENU: OPTIONS:
LOGON
READ CHANNEL~ LOAD IN V LOAD OUT V DP OUTPUT MAIN MENU
CALIBRATE ~CALIBRATE LOAD CELL CALIBRATE DP CELL LOAD CELL CALIB PLOT DP CELL CALIB PLOT MAIN MENU
VISCORUN STOREDATA UTILITIES c::-- PLOT ONE P-S GRAPH
DESCRIPTION :
(Sets date on the computer c:loc:K)
(Load c:ell i11put voltage) (Load c:ell output voltage) (DP cell output voltage) (Retur11s to the main menu) (Calibrates the load cell) (Calibrates the DP cell) (Plots the load c:ell c:alibratio11) (Plots the DP c:ell c:alibratio11) (Returns to the mai11 me11u) (Operating program) (Stores data 011 data disc after fatal error) (Plots 011e test 011 a ps;eudo-shear diagram)
PLOT MANY P-S GRAPHS (Plots ma1;y tests on one pseudo-shear diagram) FILE PRINT (Prints a file to the screen or printer)
' FIT YPP CURVE (Fits yield-pseudoplastic: curve to data) PLOT YPP CURVE & DATA (Plots the yield-paeudoplastic: curve and data) MAIN MENU (Returns to the mai11 menu)
Fig. 3.17 Software menu tree.
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'Tj .....
IJO. w .....
co ~ 0 Ct
) I-
' I-
' B
I-' ..... [ .....
§ ~ c-t
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~ .
POD
TRAP
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ATER
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TRAP
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UCKE
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SELE
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SU
PP
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.---
---
BLEE
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~ ! i g w
r-.:>
-l
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RESEARCH APPARATUS
,., 0 e,
...J .. ' a.. <J c
UI UI UJ 0:: .... UI
~ UJ
m
BBTV TEST: FTM400905
DIAM . 01337 TEMP 20 Ss 2.7468 Sm 1.7038 Cv .4029 LOAD CELL CALIBRATION SLOPE -868223.08 CONST 445.34 D P CELL CALI BRATI ON SLOPE -1334155.02 CONST -42569.55 pH 7 . 00 LENGTH BETWEEN TAPPINGS 1.478 m
No v Cm / s ) p CPa> DP / 4L <Pa> ' 8 V/ D (1 / s) 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
.014
.019
. 0 17
.050
. 107
.235
. 480
.860 1. 364 1.902 2.651 3.003 3.750 4 .. 252 4.854 5 .. 285 5.661 6.368 7 . 0 04
11087 17024 22553 29299 36390 44499 52430 60667 68171 75885 88565 94958
100885 107728 114601 121769 127156 135548 1431 32
25. 1 38 .5 51.0 66.3 82. 3
100.6 118.6 137.2 154. 2 171. 6 200 .3 214 .8 228.2 243.6 259.2 275.4 287.6 306.6 323.7
Fig. 3.19 Computer printout of a test.
8.2 11. 4 10.3 29.9 64.0
140.8 287.4 514.6 816.3
11 38.2 1586.4 1796.7 2243 .6 2544.3 2904.0 3162.0 3386 . 7 3809.9 4190 .4
PSUEOO-SHEAR DIAGRAM TEST COOE1 FTM-400905 BACKFILL TAILINGS
350
300
250
200
150
// 100
Ii 50
a J
0 c
~ v
v ,,,..
~
v ..,..
~ -
~
y v
v~
-
§ -PSEUDO-SHEAR RATE 8 V I 0 Cl/S)
· 3 20 Pseudo-shear diagram of a test. Fig. .
3.28
0•13.'4 •• L•l. '478 • T•20.0 C Se•2.7'468 511•1.7038 Cv•-40.29 % pH• 7.0
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EXPERIMENTAL PROCEDURE 4.1
CHAPI'ER 4
EXPERIMENTAL PROCEDURE
4.1 ffiELIMINARY TESTS
The data logging and processing programs were checked by hand and
fotmd to have no significant arithmetical errors.
4.1.1
4.1.2
Comparative Tests between Full Plant Tailings and Belt
Filtered Tailings
Two types of tailings are used for backfilling in the mining
industry namely Full Plant Tailings and Belt Filtered
Tailings. These tailings were obtained from the Ch.amber of
Mines and may vary in origin. Tests detailed in Appendix E
were perf orrned to determine their similarity, These tests
showed that solids relative density and particle size
distribution of the tailings are identical. The -106 J.IIl and
-62 µm fractions of each of the tailings were rheologically
characterized at various concentrations. The pseudo-shear
diagrams of the tailings for each concentration and particle
size distribution are coincident. This indicates that the
variables other than particle size distribution and
concentration affecting the rheology are the same. Due to
their similarity the Full Plant Tailings hereafter referred
to as backfill tailings are taken as being representative of
both tailings.
Flow at High Concentrations
A test was conducted to establish the highest concentration
at which the backfill tailings are fluid. The upper limit
of fluidity is taken when the tailings are able to wet a
smooth · surface completely. Mixtures at various concen
trations were made up and checked for fluidity. The fluidity
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EXPERIMENTAL PROCEDURE 4.2
4.1.3
at each concentration is shown in Fig. 4.1. At S = 2.2 the m
tailings form granules and the fluidity is zero. At S = 2.0 rn
the tailings form a single ball which can be broken up and
show the first signs of fluidity. At this concentration the
consistency is too high for it to be tested in the visco-
meter. At S rn < 1.9 the tailings are flowable and the
rheology can be determined.
In Situ and Delivered Concentrations
A test was conducted to detect differences between in situ
concentration (Cvt) and delivered concentration (Cvd). A
sample of the -42 IJIIl fraction of the ba.ckf ill tailings was
prepared at C = 34. 50% ( S = 1. 62) . The delivered v m
concentration of the sample was measured through four
different tube diameters at a roughly constant shear rate.
The results are presented in Table 4.1.
Table 4.1 Delivered concentrations through different
tube diameters.
Tube Diameter Delivered Diameter Ratio Concentration ( Ill1l) (dso/D) (Cvd) (%)
14 0.0005 34.58 8 0.001 34.44 4 0.002 34.49 2 0.004 34.52
The results suggest that there is no difference between the
in situ concentration and the delivered concentration at
this concentration. Therefore the slurry is homogeneous.
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EXPERIMENTAL PROCEDURE 4.3
4.1.4 Developins Flow
Pseudo-shear diagrams of the -60 µm fraction of the backfill
tailinss at S = 1.7 were obtained from differential m
pressures measured at the initial and final sections of the
28 um diameter tube. The two pseudo-shear diagrams are
superimposed for comparison and shown in Fig. 4.2. Similar
tests were done on the other two tube diameters. The two
curves for each diameter coincide indicatins that the flow
becomes fully developed before the first pressure tappins.
These results also indicate that; the tailinss are not time
dependent.
4.2 EXPERIMENTAL PROCEDURE
In order to evaluate the available methods of analysis, the backfill
tailinss were tested in various size fractions and at various
concentrations. These results will also be used for the prediction
of friction headloss for the design and optimization of backfill
systems usins combinations of backfill material that include the
tailings. A surmnary of the slurries tested is presented in Table
4.2.
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EXPERIMENTAL PRCCEDURE 4.4
Table 4.2 Sumnary of tests done.
Particle Mixture Volumetric Concentration Size Relative Concentration by Weight ( IJlll) Density (S )
m (Cvt) (%) (Cwt) (%)
-500 1.902 51. 71 74.5 1.846 48.50 72.2 1.812 46.58 70.4 1. 754 43.27 ~ 67.4 1.703 40.32 64.7 1.651 37.35 62.0
-106 1.804 46.03 70.08 1.748 42.81 67.23 1.704 40.29 64.95 1.651 37.26 61.99 1.599 34.30 56.72 1.551 31.53 55.85
-62 1.683 38.89 63.69 1.650 36.91 61.68 1.607 34.58 59.30 1.553 31.68 56.22 1.514 29.28 53.29
-42 1.675 38.06 63.02 1.649 36.57 61.53 1.603 34.03 58.86 1.551 31.10 55.59 1.501 28.23 52.15
The -500 µm fraction was tested in nominal internal tube diameters
of 32 and 13f!111· The viscometer was then modified and the remaining
particle sizes were tested in nominal internal tube diameters of 28,
13 and 4nvn as detailed in Chapter 3.
Samples were taken before each test for ancillary tests described in
Appendix D.
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EXPERIMENTAL PROCEDURE 4.5
4.3 SAMPLE PREPARATIOO
A 18" Sweco Vi bro-Energy Separator shown in Fig. 4. 3 was used in
conjunction with a Bornemann EH250 eccentric helical rotor pump
shown in Fig, 4. 4 to scalp the slurry at various particle sizes.
Three sieve sizes were used namely 106 µm ( 150 mesh), 62 µm ( 250
mesh) and 42 µm (325 mesh).
After scalping, the slurry concentration was increased by allowing
it to settle and siphoning off the clear supernatant. The highest
concentration obtained by settling was at all times below the
concentration described in Section 4.1.2 at which the tailings
become fluid. The tailings were tested at this concentration and
then diluted and retested in decrements of S = 0.05. m
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EXPERIMENTAL PRCCEDURE 4, 6
a !!1 ....I
• ...... CL
<J c
UI UI w er: ...... UI
~ w Oi
BACKFILL TAILINGS
Sm=2.2 Sm=2.0 Sm=l.9 Sm=l. 8
Fig. 4.1 Appearance of the backfill tailings at various
high mixture relative densities.
PSElllO-SHEAR DIAGRAM
500
400
300
200
: •
100 " It
It
• ~ 0 c
• • +
i
~
+ • •
+ ....
PSEUDO-SHEAR RATE B V I D Cl/a)
-
§
KEY • Start of Tube + End of Tube
Fig. 4.2 The results of a preliminary test to check that fully
developed flow exists "between the pressure tappings.
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EXPERIMENTAL PR£XE)lJRE
center tie-down assembly
upper frame
undersize discharge
4.7
upper weight
lower frame
motor --r-&=t--+----- angle lead
graduated adjustment
base
Fig. 4.3 Sweco Vibro-Energy Separator used for scalping
(Sweco ( 1986).
Fig. 4.4 Bornemann EH250 eccentric helical rotor plDllP used
for scalping (Bornemann (1986)).
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MATERIAL DESCRIPTION 5.1
CHAPI'ER 5
MATERIAL DESCRIPl'ION
5.1 INTRODUCTION
Backfill refers to hydraulically placed particulate material in
slurry fonn used as an underground support meditun. This technique is
used in the deep gold mines on the Witwatersrand. In order to get
the optimal properties the backfill material is made up of various
combinations of:
Aggregate - coarse crushed rock
Tailings - fine material that is left after the extraction
process
Binder - cementatious material used to add strength
The material tested in this thesis falls under the tailings
category.
5.2 PARTICLE SIZE DISTRIBUTIONS
The four particle size distributions were determined using a Malvern
Particle Sizer described in Appendix D. The particle size
distributions are shown in Figs. 5.1 to 5.4. The d 10 , d 10 , and d, 0
values for each of the slurries are presented in Table 5.1.
Table 5.1 Sunma.ry of d 10 , d10 and d 90 values
Particle d10 dso d,o
Size (µm) (µm) (µm) (µm)
-500 6.0 12.0 20.5 -106 - 10.5 16.0 -62 - 10.0 12.3 -42 - 9.5 11.8
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MATERIAL DESCRIPI'ION 5.2
5.3 SOLIDS RELATIVE DENSITIES
The solids relative densities were detennined using the procedure
outlined in Appendix D. The results of the tests are presented in
Table 5.2.
Table 5.2 Solids relative densities.
Particle Solids Relative Size (µm) Density (S ) s
-500 2.743 -106 2.747 -62 2.757 -42 2.773
5.4 MIXTURE RELATIVE DENSITY
The mixture relative densities were detennined using the procedure
outlined in Appendix D. The results of the tests are presented in
Table 4.1.
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MATERIAL DESCRIPI'ION 5.3
5.5 pH VALUES
The pH of each particle size distribution was measured using the
instrument described in Appendix D. The results are presented in
Table 5.3.
Table 5.3 pH Values
Particle pH Value Size (µm)
-500 7.63 -106 7.67 -62 7.63 -42 7.85
5.6 TEMPERATURE
The temperature of the slurry during testing varied between 15 and
20°C. A minimal increase in temperature due to frictional heating
was measured during testing.
5.7 MICROGRAPHS
Micrographs of the tailings were taken using an optical microscope.
The micrographs are shown in Figs. 5.5 to 5.8. The angularities of a
range of solid particles sizes are clearly visible under different
magnifications.
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MATERIAL DESCRIPI'ION
PARTICLE SIZE DISTRIBUTION BACKFILL TAILINGS <-500) 100
90 D
~ 80 ..... < G:i 70 oc
°" 60 t.:I
~ so (/) (/)
~ 40
~ 30 < 1-rfj 20 u oc ~ 10
0 } 10 100 1000
PARTICLE SIZE IN MICROMETRES
Fig. 5.1 Particle size distribution for the -500 f..Bll fraction
of the backfill tailings.
PARTICLE SIZE DISTRIBUTION BACKFILL TAILINGS <-106) 100
90 D
~ 80 ..... < G:i 70 oc
°" 60 t.:I
~ 50 (/) (/)
~- 40
~ 30 < 1-rfj 20 u oc ~ 10
0 10 100 1000
PARTICLE SIZE IN MICROMETRES
Fig. 5.2 Particle size distribution for the -106 µm fraction
of the backfill tailings.
5.4
10000
10000
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MATERIAL DESCRIPI'ION
PARTICLE SIZE DISTRIBUTION BACKFILL TA IL I NGS C-62) 100
90 CJ
~ 80 -< ~ 70 0::
°" 60 l!l
~ 50 U> U> ~ 40
~ 30 < 1-
d:i 20 u 0:: ~ 10
0 1 10 100 1000
PARTICLE SIZE IN MICROMETRES
5.5
10000
Fig. 5.3 Particle size distribution for the -62 IJlll fraction
of the backfill tailings.
PARTICLE SIZE DISTRIBUTION BACKFILL TAILINGS C-42)
100
90 CJ
~ 80 -< ~ 70 0::
°" 60 l!l
~ 50 U> U> ~ - 40
~ 30 < 1-
d:i 20 u 0:: ~ 10
0 10 100 1000
PARTICLE SIZE IN MICROMETRES
Fig. 5.4 Particle size distribution for the -42 IJlll fraction
of the backfill tailings.
10000
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MATERIAL DESCRIPI'ION 5.6
•
t f
Fig. 5~5 Micrograph of 75 - 100 µm solid particles under a
magnification of lOx.
' -l ~
" - • , •
' . • .. ' ... .
I XII" ' • •
• ' ·fit ....
' ' ' '
Fig. 5.6 Micrograph of 20 - 90 µm solid particles under a
magnification of 16x.
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MATERIAL DESCRIPI'ION 5.7
• • •
'
Fig. 5.7 Micrograph of 10 - 20 µrn solid particles under a
magnification of 40x.
Fig. 5.8 Micrograph of 2 - 10 f..llD solid particles under a
magnification of 40x.
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EXPERIMENTAL RESULTS AND ANALYSIS 6.1
CHAPI'ER 6
EXPERIMENTAL ~TS AND ANALYSIS
6.1 OBSERVATIONS DURING 'I'ESTING
The flow through the clear PVC tubes is clearly visible. Although
the slurry is opaque, the motion of the solid particles near the
tube wall are visible at low velocities. These solid particles were
observed to move along rectilinear paths. The solid particles close
to the tube wall moved slower than the solid particles further from
the tube wall. The existence of a wall layer was not established due
to transparency and optical distortion through the clear PVC. At the
visual onset of turbulence the differential pressure reading
oscillated at a frequency of approximately 2 Hz. Settling of the
solid particles was not observed at any of the concentrations.
6.2 PSEUDO-SHEAR DIAGRAMS
The pseudo-shear diagrams for each of the tests detailed in Table
4.1 are presented in Figs. 6.1. Combined pseudo-shear diagrams for
the laminar flow region of each particle size distributions are
presented in Fig. 6.2 to Fig. 6.5 for comparison.
6.3 FRICTION FACTOR REYNQLDS NUMBER DIAGRAMS
Friction factor Reynolds number diagrams for each of the particle
size distributions are presented in Fig. 6. 6 to Fig 6. 9. The
Reynolds m.unber used is based on the a Reynolds number of water at
the mean mixture velocity.
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EXPERIMENTAL RESULTS AND ANALYSIS
o !!: ..J
' Q.
<J c
o !!: ..J
' Q.
<J c
VJ VJ w ~ VJ
"' < w :z: VJ
6DO
500
4DO
300
2DO
JOO
400
300
200
JOO
PSEUDO-SHEAR DIAGRAM 1 BACKFILL TAILINGS
PSEUDO-SHEAR RATE 8 V I D . CJ I s)
PSEUDO-SHEAR DIAGRAM . 1 BACKFILL TAILINGS
0 0 Ul
PSEUDO-SHEAR RATE 8 V I 0 (J /s)
0 0 N
0 0 a>
KEY
• Lorge Tube
+ Had iuin Tube
Ss-2. 7435 Sm•l. 90J6 Cv•5J. 7JD
Particle Size -500 "'i crons
KEY
• Lor9a Tuba
+ MediUM Tuba
Ss•2. 7435 s .. -i. 8457 Cv•48. 504
Partic l e Size -500 "'icrona
6.2
Fig. 6.1 Pseudo-shear diagrams for all the tests on backfill
tailings are presented. 'Ihe results of the tests
done on the -500, -106, -62 and -42 µm fractions are
presented sequentially starting at the highest and
ending with the lowest concentration for each
particle size.
Univers
ity of
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PS
EU
DO
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EXPERIMENTAL R.EffiJLTS AND ANALYSIS 6.6
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Univers
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EXPERIMENTAL RF.sULTS AND ANALYSIS 6.8
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fraction of the backfill tailings.
PSEUDO-SHEAR DIAGRAM 1 BACKFILL TAILINGS C-106 •icron.>
L M
+ KEY
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fraction of the backfill tailings.
s
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L - LCll"ge Tube M - Medium Tube S - S.oll Tube
the -106 µm
Univers
ity of
Cap
e Tow
n
EXPERIMENTAL RFSULTS AND ANALYSIS 6.9
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fraction of the backfill tailings.
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500 ....-----------.-----------.---------------------------------~ •
L KEY
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M - MadiUll Tuba S - S.all Tuba
Fig. 6.5 Combined pseudo-shear diagrams for the -42 l-111
fraction of the backfill tailings.
Univers
ity of
Cap
e Tow
n
EXPERIMENTAL RESULTS AND ANALYSIS 6.10
~ -1-u -~
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FRICTION FACTOR REYNOUlS NUMBER DIAGRAM 1 BACKFILL TAILINGS C-500 •lcrone>
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LOG CREYNOUlS NUMBER>
L - Larga Tuba M - Madlut1 Tuba
Fig. 6.6 Friction factor Reynolds nunber diagram for the
-500 µm fraction of the backfill tailings.
FRICTION FACTOR REYNOUlS NUMBER DIAGRAM 1 BACKFILL TAILINGS C-106 •icrone>
3 • .. + KEY
I • II x II ,,. • S.•l. BO Cv••6.
II "•x + S.•l. 75 Cv••2. 2 x S••l . 70 Cv••O.
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0
L - Large Tube M - MadlUll Tube
0 S - S.oll Tube
LOG CREYNOUlS NUMBER>
Fig . 6 . 7 Friction factor Reynolds nt.Unber diagram for the
-106 µm fraction of the backfill tailings.
Univers
ity of
Cap
e Tow
n
EXPERIMENTAL RESULTS AND ANALYSIS 6.11
Cl
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•• • S.• l. 68 Cv•3B • + S.•l. 65 Cv•36. IC S.•l. 61 Cv•34. I S.•1.55 Cv•31.7 a S.•l. 51 Cv•29.
L - Lorge Tuba M - Madli.. Tuba S - S•all Tuba
LOG <REYNOUlS NlJCBER>
Fig. 6. 8 Friction factor Reynolds m.Dllber diagram for the
-62 µm fraction of the backfill tailings.
FRICTION FACTOR REYNOUlS NlJIBER DIAGRAM a BACKFILL TAILINGS (-42 •lcrana>
• KEY
• S.-1.67Cv•38.1 2 1-----...---......_ __ ._,,..,... _ _.. ___________ -t-------1 + S.•l. 65 Cv•36.
LOG <REYNOLDS tufflER>
IC S••l.60 Cv•34. I S••l.55Cv•31.1 a S.•l . 50 Cv•28.
L - Lorge Tuba M - Madii.. Tuba S - S•all Tuba
Fig. 6.9 Friction factor Reynolds ntunber diagram for the
-42 µm fraction of the backfill tailings.
Univers
ity of
Cap
e Tow
n
ANALYSIS OF EXPERIMENTAL RESULTS 7.1
CHAPI'ER 7
ANALYSIS OF EXPERIMENTAL RESULTS
7 .1 INTRODUCTION
The author is confident that the measurements taken are an accurate
representation of the intended quantities. It is assumed that the
variations in pH and temperature are not significant enough to
affect the rheology.
The pseudo-shear diagrams presented in Chapter 6 consist of clearly
defined laminar and turbulent flow curves. The transition from
laminar to turbulent flow is distinguishable as a sharp increase in
the slope of the pseudo-shear diagrams. Instability in differential
pressure measurements was recorded at these times.
The low concentration results are discussed in Section 7.2 and the
high concentration results are discussed in Section 7.3.
7.2 TUBE FLOW THEORY
At low concentrations (C < 30%, S < + 1.55) the pseudo-shear v m -
diagrams do not exhibit tube diameter dependence in the laminar flow
region. At these concentrations the slurry behaves as a single phase
fluid and is analysed using tube flow theory. The rheology of the
lowest concentration of each particle size distribution is
characterized using equation 2.13, the procedure described in
Section 2.8.2 and the program described in Appendix C. The results
of this procedure are presented in Table 7.1.
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ANALYSIS OF EXPERIMENTAL RESULTS
Table 7.1 Results of the rheological characterization
of low concentration backfill tailings.
Particle Slurry Yield Fluid Flow Error Size Relative Stress Consistency Behaviour in 8V/D
7.2
Density Index K Index n per point ( µm) (S ) (T )
m y
~
-500 1.651 6 0.09424 0.8309 5.8 -106 1.551 5 0.02687 0.8955 38.7 - 62 1.514 12 0.04179 0.8902 31.3 - 42 1.501 8 0.03708 0.8791 42.8
The fitted curves are plotted with the original data in Fig 7.1 to
Fig. 7. 4. The rheology is characterized using the yield
pseudoplastic model (shear thirming).
These results show that the rheology changes continuously with · an
increase in ma.ximtml particle size. Duckworth et al (1983) found that
rheology changed significantly with the addition of coarser
particles. The hypothesis made by Hanks and Hanks ( 1982 ) that a
rheologically active fraction of the solid particles exists is
contradictory to these findings and therefore unrealistic.
The friction head loss of low concentration backfill tailings in
laminar flow can be predicted using equation 2.13 and the results in
Table 7 .1.
7 • 3. ANCT1ALOUS BEHAVIOUR
At high concentrations (C > 30%, S > + 1.55) the pseudo-shear v m -diagrams exhibit anomalous behaviour in the form of a tube diameter
dependence that becomes more substantial with concentration.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.3
The particle alignment near the tube wall documented by Bain and
Bennington ( 1979) is not the cause of the anomalous behaviour
because the shapes of the solid particles shown in the micrographs
are not elongated.
It has been established that the anomalous behaviour is not caused
by settling of the solid particles, time dependency or undeveloped
flow. Experimental errors are insignificant because the low
concentration results are consistent with the theory.
The -60 µm fraction of backfill tailings at S = 1.68 shown in Fig. m
7. 5 is taken as a representative sample of the high concentration
results. This representative test is evaluated in the fallowing
subsections using the theories outlined in Section 2.10 to 2.14.
7.3.1 Effective slip
The representative test results are analysed using effective
slip theory described in· section 2.9. A verification of the
programs used for this analysis by hand showed no
significant arithmetical errors.
The first step of the procedure is to plot a graph of "t" 0
versus Q/n R1 "t" shown in Fig. 7.6. 0
From this a graph of
Q/n R' i: versus l/R at various fixed values of "t" is 0 0
plotted and shown in Fig. 7.7. The slopes of these lines
which correspond to the effective slip coefficients fJ are
calculated at each value of "t" • At high velocities the slope 0
of the graphs begin to vary and are approximated by straight
lines. A graph of the slip velocity versus shear stress is
then plotted and is shown in Fig. 7.8. Using this graph the
measured data is corrected for effective slip shown in Fig.
7. 9. The results of this analysis for other high
concentration tests yield similar results.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.4
It is evident that the measured data is overcorrected for
slip yielding negative velocities which are clearly
erroneous, A possible cause of this outcome may be that
instead of a reduction in concentration near the wall which
occurs in monodisperse mixtures, a gradual change in
particle size distribution occurs near the wall which is
expected if the mixture is polydisperse.
7.3.2 Dense-phase model
At high concentrations the applicability of rheology is
questionable because at these concentrations the rheology, a
property of the slurry becomes dependent on tube diameter.
It is possible that the backfill tailings flow as a plug
with sliding friction due to the solid particles forming the
largest part of the overall head loss as proposed by Streat
(1986). The representative test results are plotted on a
graph of hydraulic gradient ( i ) versus mean mixture m
velocity (V ) shown in Fig. 7 .10. The equation proposed by m
Streat (1986) is plotted on this graph for comparison using
a random value for the coefficient of sliding friction.
Variation of the coefficient of sliding friction results in
a vertical shift of the theoretical curve.
The predicted hydraulic gradient has a substantially
different shape to the data. This may be due to a
coefficient of sliding friction that is dependent on
velocity. Variations in the coefficient of sliding friction
with mean mixture velocity may be be examined by making it
the subject of equation 2. 27. The test results shown in
Fig. 7.10 are then used to plot a graph of the coefficient
of sliding friction versus mean mixture velocity shown in
Fig. 7.11. It is clear from Fig. 7.11 that the coefficient
of sliding friction is dependent on velocity and is
different for each tube diameter.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.5
A fundamental assunption for dense-phase flow theory is that
the suhnerged weights of the solid particles are transferred
to the tube invert by ?U"ticle-pa.rticle interactions. The
backfill tailings are non-settling therefore assunption is
not correct.
It may be concluded that the flow is not dense-phase and
that the overall head loss is not due to sliding friction
caused by the solid particles.
7.3.3 Wall effect
The pseudo-shear diagrams presented in Section 6 appear less
viscous in the smaller diameter tubes. This may be caused by
a wall effect described in Section 2.12.
A test described in Section 4. 1. 3 was conducted to detect
differences between in situ concentration (Cvt) and
delivered concentration ·(cvd) in different tube diameters.
If a wall effect occurs the difference between the in situ
concentration and the delivered concentration will vary
with tube diameter. The concentration tested was high
enough for the diameter dependence to be significant. No
difference between the in situ concentration and the
delivered concentration was observed.
A reduction in in situ concentration is therefore not
responsible for the anomalous behaviour as recorded by Maude
and Whitmbre (1955). This may be ascribed to the substantial
difference in diameter ratio (d10 /D) between these tests and
the tests conducted by Maude and Whitmore ( 1955) • The
redistribution of solid particles away from the tube wall
will reduce the in sl tu concentration compounded with a
change in the velocity profile which would affect the
measured rheology contrary to the proposed theory.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.6
7.3.4 Botmda.ry-layer effect
The initial sections of the pseudo-shear diagrams for each
diameter and particle size distribution have the same slope
shown in Fig. 7. 12. This is confinnation that a boundary
layer may exist. The representative test results are
analysed using the botmdary-layer theory described in
Section 2.13. The slopes (e.) of the initial sections of the
~eudo-shear diagrams shown in Fig. 7 .13 are measured .. The
viscosity of water is used for the botmdary-layer. The
thicknesses of the boundary-layers in each tube diameter
that would produce these results are calculated using
equation 2.33 and presented in Table 7.2.
Table 7.2 Botmdary-layer thickness in each tube diameter.
Nominal Slope Botmdary-La.yer Tube Diameter ( E.) Thickness (c5)
(nm) (Pa s) ( J.111)
28 8 0.43 13 4 0.42
4 1 0.52
'!be measured velocity is corrected using this data and
plotted on a graph shown in Fig. 7 .14. The corrected data
for this and other high concentration tests exhibit a
substantially higher yield stress and marginally increased
consistency,
The existence of a boundary-layer is credible however it has
not yet been proven. The diameter dependence in the
corrected data is still not accotmted for.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.7
7.3.5 Modified friction factors
The data plotted on log friction factor log Reynolds ntmlber
diagrams in Chapter 6 have a constant slope, The data is
expected to lie on a single curve just as the data for a
Newtonian fluid is expected to lie on the laminar flow curve
f = 16/Re. The spread of data may be due to anomalous
behaviour or the use of an inappropriate Reynolds number.
The use of a viscous term in . the Reynolds m.unber that is
derived from the pseudo-shear diagram such as the apparent
viscosity would result in a graph of the friction factors
versus its inverse. Therefore the Reynolds nlDilber of water
at the mean mixture velocity is used as an approximation.
The representative test results are plotted on a friction
factor Reynolds ntmlber diagram shown in Fig. 7 .15, The
equation proposed by Shook ( 1985) and the effect of the
dimensionless coefficients K and m are shown for comparison
in Fig. 7 .15. The slope of the data is significantly
different from the slope of the equation proposed by Shook
( 1985) . The turbulent flow data appear to lie on a
distinctive line.
The slurry's behaviour is therefore not governed by partial
hydrodynamic lubrication if it occurs at all. The equation
proposed by Shook (1986) does however theoretically accolll'lt
for some form of diameter dependence.
7.4 CONCLUSIONS
The theories presented in the literature and theory chapter have
been evaluated using extensive test results on backfill tailings
obtained in the Balanced Beam Tube Viscometer.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.8
PSUEDO-SHEAR DIAGRAM 1 -500 •icron Cv•:37. 3 S.-1. 65
KEY Ty • 6 K • • 0942396 n • .B308BB
a 151--~~~~~--4~~~~~~-t-~~~~~~+-~~~~~_,
e. ..J
.... ' <I Cl
"a &
..J
.... ' Q.
<I Cl
UI UI I.I.I a:: ..... UI
~
*
150
125
100
75
so
25
PSEUDO-SHEAR RATE 8 V I D Cl/S)
Fig. 7.1 Rheological ch~terization of the -500 I-Ill
fraction of the backfill tailings at the lowest
concentration tested.
PSUEDO-SHEAR DIAGRAM 1 -106 •icron Cv•31.5 S.-1.55
~v ~
II
../. l«
~ r? "
l
~ x
~
KEY Ty • 5 K • .0268656 n • • 895539
D Cl 8 -
PSEUDO-SHEAR RATE 8 V I D Cl/S)
Fig. 7.2 Rheological characterization of the -106 I-Ill
fraction of the backfill tailings at the lowest
concentration tested.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.9
c
Ill Ill UI ar:: Ill)
PSUEOO-SH£AR DIAGRAM 1 -62 •lcran Cv•29.3 S.•l.51
200.---------,.---------.---------....-------........ --------~------~
o._ ______ _.. ________ ......_ ________ L---------L---------'-------__J 0 § -
PSEUDO-SHEAR RATE 8 V I D Cl/5)
KEY Ty • 12 K • • 0417944 n • .890197
Fig. 7.3 Rheological characterization of the -62 j.111
fraction of the backfill tailings at the lowest
concentration tested.
PSUEOD-SHEAR DIAGRAM 1 -42 ·•tcran Cv•28. 3 S.-1. 50
KEY Ty • 8 K • • 037on1s n • • 879065
a lSOt----------+----------+-----------i.-----------+-----------' !!J
.J
• '
PSEOOO-SHEAR RA TE 8 V I D Cl /5)
Fig. 7.4 Rheological characterization of the -42 j.111
fraction of the backfill tailings at the lowest
concentration tested.
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I
ANALYSIS OF EXPERIMENTAL RFSULTS
'a ei ...J
• ' Q.
<I c
~ e: U)
i
PSEUDO-SHEAR DIAGRAM 1 BACKFILL TAILINGS
•
--- •
400
300
200
JOO
PSEUDO-SHEAR RATE B V I 0 Cl/a)
Fig. 7.5 Representative sample of high concentration
anomalous behaviour used for analysis.
EFFECTIVE SLIP ANALYSIS 1 BACKFILL TAILINGS C-62 •icr-ona)
.. L
7.10
KEY • Large Tube + MediLW Tube x S•all Tube
Sa•2. 7566 S••l.6831 Cv•3B.BB6
Particle Size -62 •icr-on•
KEY
'a + S.•l. 68 Cv•38. 9 ei 400 ~------!------+-~-----+-------+-----~
...J
• M ' a.. <l 300 1--------t-7"-----+-..,...."""-----+-------+--------i c
.. .. 0 i..... _____ .._ _____ ..._ _____ ..._ _____ ...._ _____ ....
CD 0 0
d N
Q I "'t'o 'If R 3 Cl/Paa>
Fig. 7.6 Effective slip analysis - intermediate graph.
L - Large Tube M - Madiu• Tuba S - S•all Tube
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ANALYSIS OF EXPERIMENTAL RESULTS 7 .11
• ' •
~
~ .... u c crl > 2; oj
EFFECTIVE SLIP ANALYSIS 1 BACl<FIU TAILINGS (-62 alcrane> SHEAR STRESS
275
150 .3t-~~~-t~~"7"""~"'7"'~""7''-----lt>-'~~7"""'"1""~~~..._-r-~~~--1
125 100-25
Fig. 7.7 Effective slip an'alysis - graph used to detennine p.
SLIP VELOCITY VERSUS SHEAR STRESS 1 BACKFILL TAILINGS <-62 alcrane>
1. a
I
I I
/ ~
v
.8
.6
...
.2
a.a c 8 -
SHEAR STRESS D A P I -4 L < Pa >
Fig. 7.8 Effective slip analysis - variation of slip
velocity with shear stress.
KEY
• S.•1.68 Cv•3B.9
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ANALYSIS OF EXPERIMENTAL RESULTS 7.12
'a e, _J
• ' a..
<I c
~ w ~ Ill
~ w Oi
PSEUDO-SHEAR DIAGRAM 1 BACKFILL TAILINGS
* * KEY
400 • Large Tube + Mediu• Tube
* x S•all Tube
s.-2.7566
300 S••l.6831 Cv•38.886
Particle SiZe -62 •icron•
200
100
PSEUDO-SHEAR RATE 8 V I D <ll•>
Fig. 7.9 Effective slip analysis - corrected pseudo-shear
diagram.
DENS£ PHASE MODEL <Coe+'f'icl.rt af' Sliding Friction • 3)
30
.J
I J T
25
20
15 )
l
-----f~ _. _ _.,.-----
* & & &
& * ~
10
5
~
0 a N LI)
MEAN MIXTURE VELOCITY V• C.t•l
• + x
--
--
1(£Y Lar99 Tube Medium Tub. S.all Tub•
Large Tube Medium Tub. S.all Tub.
Fig. 7.10 Dense-phase model - experimental and theoretical
hydraulic gradients.
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ANALYSIS OF EXPERIMENTAL RESULTS 7 .13
a..
~ ! -1-u -e:
DENSE-PHASE MODEL
u 101.+-----1-----___,f---------1------+-------1 ~ s of ~ 1-
ffi -u -~
o------.__ ___ __...._ ___ __.~----..1----~ Cl N
MEAN MIXTURE VELOCITY V• [•/el
KEY
• Large Tuts. + Medii.. Tube x S.all Tube
Fig. 7.11 Dense-phase model - variation of the coefficient
of sliding friction with velocity.
PSEUDO-SHEAR DIAGRAM 1 BACKFILL TAILINGS C-62 •icrane)
• KEY
• • S••l.68 Cv•39.9 + S.-1.65 Cv•36.9
150 1-----+-----+---..:::;_----+----------J'"--------1 x S.-1. 61 Cv•34. 6
Kl 8 -PSEUDO-SHEAR RATE 8 V I 0 Cl/e)
I S••l.55 Cv•31.7 o S••l.51 Cv•Z9.3
Large Tube Only
Fig. 7.12 Boundary-layer effect - coincidence of the initial
sections of the pseudo-shear diagrams for a fixed
particle size distribution and tube diameter.
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ANALYSIS OF EXPERIMENTAL RESULTS 7.14
...J
.... ' ci.
<l c
...J
.... '
PSEUDO-SHEAR DIAGRAM a BACKFILL TAILINGS
PSEUDO-SHEAR RATE B V I 0 Cl/e)
Fig. 7.13 Botmda.ry-layer eff~t - measured slopes of the
initial sections of the pseudo-shear diagrams
for each tube diameter.
PSEUDO-SHEAR DIAGRAM a BACKFILL TAILINGS
KEY
• Large Tuba + MediUll Tube x S.all Tube
Se•2.7566 s.-1. 6831 Cv•38.BB6
Particle Size -62 •icrane
KEY
• Large Tuba + Medium Tube
300 f---li----------+-----------ll---::::::oo ...... -=-----1x S.al 1 Tube
x
Se•2.7566 S.•1.6831 Cv•3B.BB6
<l 200 f---li---....,...::.....--,,,.....:::;_-+-.......,,,......c:;;;:__ ___ -"-il----------1 Particle Size c
~ ... Ill
x x
-62 •icrone
O L---loL..-------,...----~o ... '-----------o'-----------o 0 iii ii!
PSEl.llO-SHEAR RATE B V I D Cl/e)
Fig. 7.14 Boundary-layer effect - corrected pseudo-shear
diagram.
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ANALYSIS 'OF EXPERIMENTAL RESULTS 7.15
~ .... u < I&.
~ -.... u a: \!;
9
2
a
-1
FRICTION FACTOR REYNOLDS NUMBER DIAGRAM 1 BACKFILL TAILINGS <-106 •1cron•>
l(EY
+ S..-1.68 Cv•38.9
L - Large Tuba M - Medium Tuba S - Sniall Tuba
- Theoretical Modal
} K•IDD m• O
' -3 L-------'N------~J......-----~L'..:......-----=~~___:::::::.;_......:::::........JmJ- K• l m•O
LOG <REYNOLDS tl.JM9ER>
Fig. 7.15 Modified friction factors - friction factor
Reynolds ntunber diagram showing experimental
and theoretical curves.
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<X>NCLUSIONS AND RECCM1ENDATIONS 8.1
CHAPrER 8
OONCUJSIOOS AND RECX.tflENDATIOOS
1. The Balanced Beam Tube Viscometer is an instrument capable of
collecting reliable laminar and turbulent flow data as well as the
laminar-turbulent transition. The errors in the measurements taken
are within acceptable limits.
2. The backfill tailings were tested in the viscometer and exhibited
two distinctive types of behaviour depending on concentration.
3. At low concentrations (Cv < 30%, Sm < ± 1.55) the backfill tailings
behave as a single phase fluid. At these concentrations the rheology
was successfully characterized using the yield-pseudoplastic model
and a new curve fitting program.
4. At high concentrations (Cv > 30%, Sm > ± 1.55) the backfill tailings
exhibited anomalous behaviour in the form of a marked tube diameter
dependence.
5. The anomalous behaviour is not due to incorrect measurements, time
dependency, settling of the solid particles or undeveloped flow.
6. Effective slip analysis accounts for diameter dependence but yields
negative velocities. If effective slip occurs it can therefore not
be corrected for using this technique.
7. The flow is not dense-phase and the overall head loss is not due to
sliding fiction caused by the solid particles.
8. · The diameter dependence observed is not due to a reduction in in
situ concentration caused by a wall effect.
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CONCLUSIONS AND RECCM1ENDATIONS 8.2
9. The existence of a boundary-layer of liquid is credible however it
has not yet been proven. Correction for a boundary-layer does not
account for the anomalous behaviour.
10. The diameter dependence is theoretically accmmted for using a
modified friction factor that takes the hydrodynamic lubrication
between solid particles and tube wall into account. A comparison
between theoretical and predicted hydraulic gradients show that the
hydrodynamic lubrication as formulated does not take place.
11. It is recommended that the velocity profile is experimentally
determined using wall and traversing velocity probes. The
experimental and theoretical (based on the rheology) velocity
profiles may be compared thus verifying the rheology. The velocity
profile will also enable the existence of a liquid layer near the
wall to be investigated.
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Biorheology 1.
"The Wall Effect in Capillary Instruments".
VAN WAZER, J.R., LYONS, J.W., KIM, K.Y. and COLWELL, R.E. (1963) "Viscosity
and Flow Measurement - A Laboratory Handbook of Rheology". John Wiley and
Sons, Inc. New York.
WASP, E.J., KENNY, J.P. and GRANDI, R.L. (1979) "Solid-Liquid Flow Slurry
Pipeline Transportation". Gulf Publishing Co. Houston.
WINDHAB, E. and GLEISSLE, W ( 1984) " The Flow Behaviour of Highly
Concentrated Suspensions Determined with a New Shear- and Slip Flow
Separating Method". Proc. 9th Int. Cog. on Rheology.
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Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
OONTENTS OF APPENDICES
The Rabinowitsch-Mooney Relation Derivation and Analysis
Tube Flow Derivations
Yield-Pseudoplastic Curve Fitting Program Description
Ancilliary Tests
Comparative Tests Between Full Plant Tailings (FPT) and Belt
Filtered Tailings (BFT)
Examinations Written by Author in Completion of the MSc
Degree Requirements
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-APPENDIX A A.1
APPENDIX A
'lllE RABINCMITSCH-t-IXNEY RELATIOO DERIVATIOO AND ANALYSIS
A.1. INTRODUCTION
The Rabinowitsch-Mooney relation (as applied to tube flow) relates
the pseudo-shear rate to the true shear rate at the tube wall. This
is useful in tube viscometry in reducing bulk flow parameters to a
rheogram.
i.e. [- ~L = 8V [3n• + D 4n' 11 (Al)
d (en ( r ) ) where n' 0
= d (en (~v))
(A2)
A.2. DERIVATION (Slatter (1986))
We start with the completely general constitutive equation for
circular tube flow:-
du f (r) dr = (A3)
A force balance on a cylindrical element of radius r and length dL
yields
and
n r 2 dp = 2n r r dL
QJ2 _ ~ dL - r
d 2 T QE. - __ o dL - R
r = RT T
0
rZ and dr = !L dr T
0
(A4)
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APPENDIX A
also T 0
Dl1p = 4L
A.2
The flow rate can be obtained by integrating the velocity profile:
Q = 2 " ( u.r.dr
Integrating by parts:
Assuming that u = 0 (no slip at the tube wall) 0
T
du dr dr
(A5)
(AG)
I o R2r2
= 1l' 2 • T
!L T
0
• dT (substituting A4)
=
0 0
T
J 0
r 2 • f (r) . dr
0
Substituting R = D/2
T
~. = ~v = ; , J 0
r z • f ( r ) • dr 0 0
.. 8V D
4 = -;:> 0
T
J 0 r 2 • f(r) • dr
0
Now, differentiating with respect to T (product rule) 0
-d(~v) = d T
0
- 12 --;:r-0
T J 0 r 2
• f(r) • dr + ~. 0 0
T ] ddT [ I 0 T2 , f ( T) , dT
0 0
(A7)
(AB)
(A9)
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APPENDIX A A.3
The first tenn on the R.H.S
- 12 fro r2 • f(r) • dr = =-1 [;. Ir 0 r2 • f ( r) • dr] r"' r 0 0 0 0 0
- 3 8V (substituting A8) = r D 0
The second tenn on the RRS is treated with the Liebniz fonnula
[The Liebniz fonnula states:-
g_ J u 1 (a) da F ( x, a) dx =
du f ( ) d U1 F( ) 0
U1,a da - uo' a da u (a)
0
Now, let a
I ui (a) aF(x,a)
+ • dx u (a) aa.
0
= r ; u (a) = O; 0 0
x = r;
and F(x,a) = F(r,r0
) = r 2 f(r) (i.e. F(r) only)]
_g_ T
• dr] r
Then (Joo r2 • f(r) = r2 • f(r ) 1 - 0 + J 0 0 • dr dr .
0 0 0 0
d (~v) d T
0
f(r ) 0 =
-3 ·(~v) + 4 = T T
0
= r2 • f(r ) 0 0
T2 • f(r ) J • 0 0
0
a(~v) To dr
0 ]
(AlO)
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APPENDIX A
Examining the last term:-
(eonsider
x ~ = y • dx
x l ~ l'y'dx
Now d( in x) dx
= 1 d d(in y) = 1 x an dy Y
x ~ y • dx
dx = d(en x) ·
= d( en y) d(in x)
d( en y) dy
Similarly
(§:!_\ ( 8V \ = in..J_ [ d en (D~l]
4 3 + d (in (T )) 0
Let n'
Then
A.3 DISCUSSION
d (in ( T ) ) 0
= 8V D [3n I + l]
4n'
~ dx
]
A.4
(All)
(A2)
(Al) q.e.d.
Since no asstunptions are made concerning the nature of the fluid,
the result is perfectly general, and can be applied to any fluid,
provided that there is no slip at the tube wall.
The relation is a unique mapping from a pseudo-shear diagram to a
rheogram.
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APPENDIX A A.5
The effect of this relation for yield-pseudoplastic, bingham plastic
and yield-dilatant rheologies is shown in Fig. Al, Fig. A2 and
Fig. A3 respectively. The relation logarithmically stretches the x
axis of the pseudo-shear diagram yielding a rheogram. It is there
fore possible using a pseudo-shear diagram to speculate on the shape
of the rheogram. This is the basis for the use of the pseudo-shear
rate.
Slatter ( 1986) showed that the errors involved in the use of the
relation were too large for it to be of practical use.
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I
I I
APPENDIX A A.6
KEY - PSEl.00 SHEAR
RATE
-TRt£ SHEAR RATE
~ 100,-~~~~-t'7"~~~--;;.f£-~~~~-+~~~.,.c:::::,,.i...:~~~~-J
' a. <l 0
" l. v
..I .. ' a. <l c
oa~· -----'-------::~----'-----~:--~~~~L...-----L------...l...-------'-----__J ~ § § §
150
100
50
8 v I D and d v I d r < 1 I e' > -Fig. Al The effect of the Rabinowitch-Mooney relation on a
yield-pseudoplastic rheology.
PSlEXHil£AR DIACRAM Atll TRl£-51£AR DIAGRAM <RHEOCRAM>
KEY
- PSELDO-SHEAR RATE
- TRl£-Sl£AR RATE
oo~~~~i~~~§~--'-------L§~-'-~L----~----J~
8v/D and dv/dr (1/e)
Fig. A2 The effect of the Rabinowitch-Mooney relation on a
bingham plastic rheology.
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•
•
I I
APPENDIX A A.7
PSlEXHit£AR DIAGRAM 00 TRlE-5t£AR DIAGRAM <RHEDCIWO
KEY - PSElD> !HAR
RATE
lSDt--~~~~-t-~~~~-+~~~~--lh.4.,..:_~~~+-~~~~....J- -TRUE !HAR RATE
~ IDDr-~~~~-+~~~--.:;,,C-t""'~~~~-+~~--:..,,...,e.:::,_~~~~~-1 .. ' ~ <1 Q
Bv/D and dv/dr <lie>
Fig. A3 The effect of the Rabinowitch-Mooney relation on a
yield-dilatant rheology.
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..
APPENDIX B B.1
APPENDIX B
TUBE FLOW DERIVATIONS
B.1 INTRODUCl'ION
This derivation is based on the yield-pseud.oplastic model. By
applying various conditions the flow equations for other rheological
models are determined.
B.2 YIELD-PSEUDOPLASTIC DERIVATION
The general flow equation A7 from Appendix A given by
"C" 0
n RJ J Q = ~ 0
'"C" 2 f(-r) d 1:"
0
Applying the continuity equation Q = nR 2V gives
8V D
In the plug
-o $ r $
0 $ 1:" $ 1:"
and f(-r) =
1:" 0
0
1:" 2 f(-r) d 1:"
region:
rplug
y
0
(Bl)
(B2)
(B3)
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APPENDIX B
In the sheared region:
rplug ~ r ~ R
't' ~ 't' ~ 't' y 0
and f(i:) = (kf/n ( ) 1/n 't' - 't' y
For fluids with a yield stress equation B2 becomes
av D
4 = i:'
0
't' 't'
[ { -r' f(T) d T + [ -r'_ f(T) d T ]
y
Applying the conditions B3 and B4 gives
8V D
4 = 1:'1 0
set x
then dx
and 't'
=
=
=
1/n (i: - 't' ) d 't' y
T - 't' y
d 't'
x + 't' y
B.2
(B4)
(B5)
(B6)
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APPENDIX B B.3
Equation B6 becomes
i;
(k) 1/n 0
8V 4 J
Ta (x - T ) 2 xl/n d x = TJ D y 0
T y
T 2n+l n+l 1
(k//n
0
4 J
I n + 2-r n ~ ~) dx = ~ \x x + -r; x 0
y 't
y
3n+l 2n+l
::: ] T
0
4n (k) 1/n [ x 3n~l n
+ 2-r x + 1:2 x = Tl 2n+1 0
y y n n T
y
3n+l 2n+l n+ 1 i: -- 0
(k)l/n r. ( i:-i: Y) n ( 1:-1:' ) n
(i:-i:Y) n ] 4n + 2r y + r2 = 't"3 3n+l 2n+l n+l
0 L y y
1: y
3n+l 2n+l n+l
(k)l/n f (i: -i: ) n ( T -1:' )
n (i: -i: ) n ] 4n 0 y + 2i: 0 y + 1:2
0 y = TJ 3n+l y 2n+1 y n+l
0
n+l
4n (i) 1/n ( 1: - )-~f" -· )' ( 1: -1:' ) "' j 1: 0 y + 2i: 0 y + n~l = TJ 0 Y 3n+l 2n+l 0
y
(B7)
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APPENDIX B
B.3 BINGHAM PLASTIC (n = 1)
Applying the condition n = 1 to equation B7 gives
8V D
4 (i; - i; )2 = K't'> o y
y t(T -T ) 2
0 y 4
t ;o' + 4 (T - T ) 2
= Ki:~ o y y
= ~ [1 - t (::) • t (::r] T
+ 2T O y + y (T -T ) T2
]
y 3 z-
B.4
Setting a = Y , q = K and making T the subject of the equation i;o p o
yields the Buckingham equation given by
1
(1 - 4/3a + a~/3)
B. 4 roWER LAW ( -r = 0) y
Applying the condition of T = 0 to equation (B7) gives 0
(k)l/n
n+l TJ -8V 4n n _o_
= ~ T D 0 1+3n
0
4 1/n IlT
0 =
Kl/n ( 1+3n)
(B8)
(B9)
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APPENDIX B B.5
B.5 NEWIPNIAN (i; = O, n = 1) y
Applying the conditions of i; = 0 and n = 1 to equation (B7) gives y
8V D
i;
= _Q K
Setting µ = K and making i; the subject of the equation gives 0
8V i; = µ -
o D (BlO)
Substituting in the continuity equation yields the Hagen-Poiseuille
equation given by
n R:a Q = --i; 4 µ 0
(Bll)
B.6 CONCLUSIONS
These equations are all identical to the equations presented in
Skelland (1967), Govier and Aziz (1972) and Wasp (1979).
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APPENDIX C
APPENDIX C
YIELD-PSEUOOPLASTIC CURVE FITTING PROORAM DF.sCRIPl'ION
C.1 INTRODUCTION
This program fits the yield-pseudoplastic equation given by
8V D =
n+l 4n (-r _ -r ) n
Kl/n-rJ y
y + y y
t(-r--r ) 2 2-r (-r--r )
-3-n-+~l-- Zn+l
to a set of data on pseudo-shear diagram.
C.2 DESCRIPI'ION
C.1
(Cl)
The value of the yield stress ( -r ) is read off the pseudo-shear y
diagram directly. Using this value the program selects the values
of K and n that give the minimum error in 8V/D on a graph of 8V/D
versus -r • The error for fixed value of -r , K and n is given by 0 y
Error = n 8V.
2 ((~)obs (8V.) ) 2
D1
calc I n-1
i=l
n
( (:v i)obs
n+
2 ( 4n ( "t'. -r ) n = - Kl/n -r~ 1 y
i=l 1
[<-r.--r )2 2-r (-r. --r ) -c; l)) 2
1 y + y 1 y + I n-1 (C2)
L 3 n+1 2n+l n+I J II
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APPENDIX C C.2
At a fixed value of n the mininrum value for K is obtained by setting
d.Error/dK = O. This gives
n
2 2 (v i/n)
1/ t T' r K. i=l (C3) = IDJ.n n ((Ti-Ty)' 2T (T.-T ) nL 3n+l +
y ]. y + y ) I T1
2n+1 n+l Y i=l
The program calculates the error over a range of n values at the
miniml.DD K value. By zooming in on the value of n with the lowest
error the best fit values of K and n are obtained. The error in the
fit is calculated as error in 8V/D per point using equation C2.
C.3 OONCLUSION
The program is capable of efficiently selecting the values of K and
n associated with the minimlDll error.
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APPENDIX D D. l
APPENDIX D
ANCILLARY TESTS
D.l SOLIDS RELATIVE DENSITY DETERMINATIONS
Aim To determine the solids relative density.
Method : Find the mass of a clean dry density bottle of known
volume. Fill the bottle with the mixture to the etched level remove
any air bubbles with a vacuum pump and weigh. Empty the bottle into
a weighed evaporation dish using water to rinse off all the solid
particles. Dry the dish at 102°C and weigh. The relative density is
determined twice using the calculation procedure. The average of the
two re la ti ve densities is calculated if their difference is less
than 0.01.
Readings . Volume of bottle = v ml
Mass of dry bottle = ml g
Mass of bottle + mixture = m2 g
Mass of dry evaporation dish = m3 g
Mass of evaporation dish + dried mixture = m4 g
Calculations
Mass of mixture = m2 ml g
Mass of solids = m4 m3 g
Mass of liquid = m2 ml - m4 + m3 g
Volume of liquid = (m2 - ml m4 + m3)/0.9982 ml
Volume of solids = v - ( (m2 ml m4 + m3)/0.9982) ml
Density of solids (ps) m4 m3 = (v - ((m2 - ml - m4 + m3)/0.9982)) g/ml
Relative density of solids (S ) s = 0.9982
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APPENDIX D D.2
Masses were determined using a Mettler scale accurate to ± 0.01 mg.
The accuracy of this determination is approximately 0.3%.
D.2 MIXTURE RELATIVE DENSITY DETERMINATIONS
Aim To determine the mixture relative density.
Method : Find the mass of a clean dry density bottle of known
vollilDe. Fill the bottle with the mixture until it is almost full and
weigh. Fill the bottle with water to the etched level and remove any
air bubbles with a vacuum pump and weigh again. Empty the the bottle
and rinse with water. Refill the bottle with water to the etched
mark and weigh again.
Readings . Mass of dry bottle = ml g
Mass of bottle + mixture = m2 g
Mass of bottle + mixture + water = m3 g
Mass of bottle + water = m4 g
Calculations . Mass of mixture = m2 ml
Mass of added water = m3 m2
VollilDe of added water = (m3 - m2)/0.9982
Mass of water = m4 - ml
Volume of water = (m4 ml)/0.9982
VollilDe of mixture = (m4 ml - m3 + m2)/0.9982
Density of mixture (p )= m2 - ml m (m4 - ml - m3 + m2)/0.9982
Relative density of mixture (S ) m = 0.9982
g
g
ml
g
ml
ml
g/ml
Masses were determined using a Mettler scale accurate to ± 0.01 mg.
The accuracy of this determination is 0.3%.
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APPENDIX D D.3
D.3 pH DETERMINATION
pH determinations are made using a Radiometer model pHM 80 pH meter
and a GK 2401C glass electrode calibrated using Radiometer buffer
(Disodium hydrogen phosphate I potassium dihydroge!l phosphate) of pH
= 7. 02 CtO. 001) at 20°C, calibrated at the measuring temperature
shown in Fig. Dl.
D.4 PARTICLE SIZE DISTRIBlJI'ION DETERMINATIONS
The particle size distributions were determined using a Malvern
2600/3600 Particle Sizer VF. 6. The instnunent is calibrated using
particles of a known diameter. Three lenses (63 DID, 100 nun and
300 mm) may be used. The particle ranges of each lense are shown in
Table Dl. The 300mm lens is used because it has the most appropriate
particle sizes range.
Table Dl Malvern lenses
Lens Size Range (mm) ( µm)
63 1.2 - 118.4 100 1.9 - 188.0 300 5.8 - 564.0
D.5 MICROGRAPHS
The micrographs were taken using an optical microscope. The micro
scope is equipped with 10 rrm, 16 mm and 40 nun dry lenses and side
and bottom lighting.
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APPENDIX D
KCI filling hole
Saturated KCI solution
Red reference stems (Ag/AgCI)
Reference part
Porous pin
KCI crystals
Glass membrane
r
..
..
,- .· I
..
~ .
~1
..,
E E (") 0 T"""
9.5mm
il~ -
RADIOMETERP'dn COPENHAGEN~ Analytcal hstn.rnents DrvisOl
Fig. Dl GK2401C Combined electrode.
D.4
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APPENDIX E E.1
APPENDIX E
CU1PARATIVE TESTS BETWEEN FULL PLANT TAILINGS (FPr) AND
BELT FILTERED TAILINGS (BFT)
E. 1 INTRODUCTION
The similarity between two types of backfill tailings is investi
gated in this appendix. 'lbe two tailings are the result of the same
process but may differ in geographic origin.
E.2 CU1PARATIVE TESTS
'lbe two tailings were scalped
Separator at 106 µm and 62 j.111•
using a 18" Sweco Vibro-Energy
'lbe -106 j.111 and the -62 j.111
fractions of each of the tailings are compared.
E.2.1
E.2.2
Particle Size Distribution
'lbe particle size distributions of the two slurries were
determined using the Malvern Particle Sizer described in
Appendix D. 'lbe results are shown together in Fig. El and
Fig. E2.
Solids Relative Density
'lbe solids relative density of each of the two tailings was
determined using the procedure outlined in Appendix D. 'lbe
results of the tests are presented in Table El.
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APPENDIX E E. 2
Table El Surmnary of the comparative solids relative densities
Tailings Particle Solids Relative Size (µm) Density (S )
s
FPI' -106 2.747 BFT -106 2.745 FPI' - 62 2.754 BFT - 62 2.749
E.2.3 Rheology
The two tailings were tested in the Balanced Beam Tube
Viscometer. A surmnary of the tests done is presented in
Table E2.
Table E2 Sununary of the comparative tests.
Tailings Particle Mixture Relative Vohunetric Size Densities Concentration
( µm) ( s ) m
(C ) v
FPI' -106 1.704 40.30 % BFT -106 1.701 40.17 % FPI' - 62 1.605 34.50 % BFT - 62 1.607 33.47 %
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APPENDIX E E.3
The pseudo-shear diagrams at each concentration and particle
size for each of the tailings are plotted together for
comparison and shown in Fig. E3 to Fig. E4.
E.3 CONCLUSIONS
The differences in the above tests are considered to be
insignificant with reference to the rheology, The differences in the
rheograms are ascribed to small variations in the mixture relative
densities shown in Table E2 and experimental error. Asstuning that
no variables have been over looked the tests show that all the
variables that affect rheology for each of the tailings are for all
intents and purposes the same.
cohesive analysis to be made.
This conclusion enables a more
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APPENDIX E
PARTICLE SIZE DISTRIBUTION -106 MICRON COMPARISON 100
90
80
l.!) 70 z ...... ~ 60 < Q..
LU 50 l.!)
~ 40 z LU
~ 30 LU Q..
20
10
0 10 100
PARTICLE SIZE IN MICROMETRES
Fig. El Particle size distribution comparison between the
-106 µm fraction of FPI' and BFT.
PARTICLE SIZE DISTRIBUTION -62 MICRON COMPARISON 100
90
80
l.!) 70 z ...... (./) 60 (./)
< Q..
LU 50
l.!)
< 40 I-z LU u 30 IX: LU Q..
20
10
0 10 100 1000
PARTICLE SIZE IN MICROMETRES
Fig. E2 Particle size distribution comparison between the
-62 µrn fraction of FPI' and BFT.
E.4
10000
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"
APPENDIX E E.5
" D e, ....I .. ' a.. <l c
....I .. ' a..
PSEUDO-SHEAR DIAGRAM 1 S.•1. 70 -106 MICRON COMPARISON
200
100
0"-~~~~--'~~~~~.......1.~~~~~...i....~~~~~-L-~~~~__J c § -
8 v I D <1/a)
KEY • Large Tuba
+ Madii.. Tuba
X Large Tuba
I Madiu. Tuba
Fig . E3 Rheological comparison between the -106 µm fraction
of FPI' and BFT.
PSEUDO-SHEAR DIAGRAM 1 S.•1. BO -62 MICRON COMPARISON
KEY • Larga Tuba
+ Madii.. Tuba
X Large Tuba
I MadiUll Tuba
<l 1001--~F--,..a:::....~~~~~4-~~~~~~~~-+-~~~~~~~~--I
c
O'L-~~~~~~~~---'~~~~~~~~~...i....~~~~~~~~__..J c § -
B V I D Cl/a)
Fig. E4 Rheological comparison between the -62 j.111 fraction
of FPI' and BFT.
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~ 6 JUN '
EXAMINATIONS WRITTEN BY AUTHOR
IN CCMPLETION OF MSc REQUIREMENTS
APPENDIX F
EXAMINATIONS WRITI'EN BY AtJIHCE IN cnfPLETION
OF THE MSc DEGREE R1RJIRFl1ENTS
Examination Credit Rating
CIV 516F
CIV 525S
CIV 526F
CIV 5242
END 5072
Coastal Hydraulics
Contract Law
Properties of Concrete
Irrigation Systems
Management for Engineers
Thesis "The Rheology and Flow Behaviour
of High Concentration Mineral Slurries"
TOTAL
Credit requirements for degree = 40
5
3
4
3
5
20
40
F.1
