Placement of Thickened Tailings: Adoption of a Rheology-Oriented Model for Slope Predictions

MASTER'S THESIS

Placement of Thickened Tailings

Adoption of a Rheology-Oriented Model for Slope Predictions

Deniz Dagli

Master of Science (120 credits) Civil Engineering

Luleå University of Technology

Department of Civil, Environmental and Natural Resource Engineering

Placement of Thickened Tailings

Adoption of a Rheology-Oriented Model for Slope Predictions

Deniz Dagli

Lule˚ a University of Technology

Dept. of Civil, Environmental and Natural Resources Engineering Div. of Mining and Geotechnical Engineering

2nd January 2013

A BSTRACT

Thickened tailings or “paste” disposal with deposition slopes varying from 2 to 4% results in steeper slopes compared to those of conventional placement (less than 0.5%). As a consequence, thickened tailings disposal ends up with filling more volume per storage area and thus avoids costly & frequent dam raises. Reported observations describe that the discharged slurry typically flows down the slope or “beach” in a confined, self-formed channel, in a macroscopic equilibrium between erosion and sedimentation, defining an overall slope and then spreads out & deposits on a broader area (Simms, et al., 2011).

The objective of this study is to describe the slope forming elements and adopt the model for beach slope predictions by Fitton (2007) together with a discussion of simulated results and the effects of rheological & hydraulic parameters.

Typical thickened tailings have average particle sizes of 25 to 75 µm with maximum particles of about 0.5 mm. To obtain a conceptually even slope with practically no segregation of particles occurring and no drainage of water taking place, the concentration by volume often needs to exceed 40% (even 45% for some cases). It is reported that these slurries show non-Newtonian behaviour and often found in a supercritical open channel flow state located in the transitional or turbulent zone. When the slurry spreads out, the flow attains a sheet-like, laminar state where particles settle out. The process repeat itself in a cyclic manner and the overall beach profiles are created as a result.

Fitton’s model, based on open channel hydraulics (Darcy-Weisbach friction loss con- cept) and sediment transport approach, considers the self-confined open channel flow to be turbulent, based on field and large scale flume observations. The model relates the deposition velocity to maintain the channelized flow, to a Bingham rheological model parameter.

The model is utilized to simulate the depositional behavior of thickened tailings slurries having a volumetric solids concentration of 46% (71% mass). This value is used to represent homogeneous (non-segregating) conditions for tailings with an average particle size of 50 µm and a solids density of 2900 ^kg / ^m

. Simulation results for slurry flow rates from 25 to 400 ^m

/ h correspond to slopes of about 6 and 2%, respectively, expressing a flow rate dependence at yield stresses and Bingham viscosities of up to 30 Pa and 0.1 Pa.s, respectively. Reynolds numbers were from about 500 to 94500 for which the effect

iii

of channel roughness on predicted slopes was practically negligible within values from 0.3 mm to smooth conditions at 0.05 mm.

Calculated slopes were nearly insensitive to the channel shape as long as the width/depth ratio remained constant about 5.5. A rectangular cross-section was used for the calcula- tions but a parabolic channel shape reflects field observations better.

Equilibrium yield stress requirement for the flow to come to rest and the required shear strength (cohesion) to be developed upon drying for stability of slopes formed by stacked layers of various thicknesses are demonstrated in schematic examples.

iv

P REFACE

This thesis report is submitted as a part of the graduation work for the fulfillment of a MSc. degree at Lule˚ a University of Technology, Dept. of Civil, Environmental and Natural Resources Engineering. After working on the subject of thickened tailings disposal for a considerable amount of time, I would like to use this opportunity to express my gratitudes to the people who have provided invaluable help and support.

First, I wish to thank my thesis supervisor, Professor Emeritus Anders Sellgren, for his patience and guidance. Without the time he has put into this work and the effort to carefully examine the work over and over for constant improvement, I would never be able to overcome this challenge. For that, I will always be grateful.

I wish to express my thanks to Mr. Thord Wennberg at LKAB for the detailed guided tour of the company’s mineral processing plant and the tailings storage facilities.

I also want to thank my examiner, Professor Sven Knutsson, for his support and the encouragement to work on tailings in general.

My special thanks go to Mr. Aziz Kubilay Ovacikli for the help he has provided with the coding of the MATLAB algorithm used throughout this work and also for introducing me to report writing with LATEX.

Above all, I would like to express my deepest gratitudes to my family for the uncondi- tional love and for the moral, motivational & financial support they have provided during my whole life and my stay in Sweden. Without them I could have never achieved any of this and therefore, I dedicate my share of contribution in this work to them.

Deniz Da˘glı

Lule˚ a, December 2012

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C ONTENTS

Chapter 1 – Introduction 1

1.1 Mineral Processing & Tailings . . . . 1

1.2 Tailings Disposal Methods . . . . 2

1.2.1 Conventional Tailings Disposal (Dams/Impoundments) . . . . 2

1.2.2 Thickened Tailings Disposal . . . . 5

1.2.3 Paste Disposal in Underground Mines . . . . 9

1.3 Problem Description . . . . 9

1.4 Objective & Scope . . . . 10

Chapter 2 – Open Channel Flow 11 2.1 Flow Resistance & Friction Losses . . . . 11

2.2 Flow Regime & Reynolds Number . . . . 13

2.3 Friction Factor (f) . . . . 13

2.4 State of Flow . . . . 15

2.5 Conceptual Example 1 . . . . 17

2.6 Non-Newtonian Fluid & Suspension Flow . . . . 19

2.6.1 Models . . . . 19

2.6.2 Non-Newtonian Friction Losses . . . . 23

2.6.3 Conceptual Example 2 . . . . 24

Chapter 3 – Transportation of Tailings Slurries 27 3.1 Solid-Water Mixture Parameters . . . . 27

3.1.1 Solid Content & Density . . . . 27

3.1.2 Particle Size Distribution . . . . 28

3.2 Classification . . . . 28

3.2.1 Settling & Non-Settling Slurries . . . . 28

3.2.2 Deposition Velocity . . . . 31

Chapter 4 – Placement of Tailings Slurries 33 4.1 Slurry Deposition . . . . 34

4.1.1 Geotechnical (Slope Stability/Equilibrium) Approach . . . . 34

4.1.2 Conceptual Example 3 . . . . 37

Chapter 5 – Adoption of the Rheology-Oriented Model by Fitton 39

5.1 Fitton’s Work . . . . 39

5.1.1 Model Development . . . . 39

5.2 Fitton’s Semi-Empirical Beach Slope Model . . . . 41

5.2.1 Segregating vs Non-Segregating Slurries . . . . 42

5.2.2 Minimum Transport Velocity Equations . . . . 43

5.2.3 Flow Resistance Equation . . . . 45

5.2.4 Determination of the Channel Shape for the Open Channel Flow . 46 5.2.5 Running the Model . . . . 47

5.3 Validation with the Field Data . . . . 48

Chapter 6 – Results & Discussion 51 6.1 Model Validation . . . . 51

6.2 Properties of the Tailings Material & Assumptions for the Simulations . . 52

6.3 Results & Discussion . . . . 54

6.3.1 Results . . . . 54

6.3.2 State of Flow . . . . 57

6.3.3 Solid Concentration and Particle Size Distribution . . . . 58

6.3.4 Sediment Transport Approach & Shield’s Diagram . . . . 58

Chapter 7 – Conclusions 61 REFERENCES 62 Appendix A – Parameter Study 67 A.1 Effect of the Yield Stress . . . . 67

A.2 Effect of Viscosity . . . . 68

Appendix B – Flow Simulations 71

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List of Figures

1.1 Tailings from the mineral processing of iron ore - Schematic flow chart . . 1

1.2 Conventional tailings disposal system. Slopes for deposited tailings are normally less than 0.5% (Wennberg, 2010) . . . . 2

1.3 Discharging with spigots (Fell, et al., 1992) . . . . 3

1.4 Upstream Method (Fell, et al., 1992) . . . . 5

1.5 Downstream (a) and Centerline (b) construction methods (Fell, et al., 1992) 6 1.6 Schematic representation of the thickening process (Metso Minerals, 2002). The term “pulp” is synonymous to slurry. . . . 6

1.7 Schematic representation of the thickened tailings discharge method (Fell, et al., 2005) . . . . 7

1.8 Thickened discharge method on an inclined ground (Wennberg, et al., 2008) 8 1.9 Tailings disposal system with a thickener located near the deposition zone (Wennberg, 2010) . . . . 8

1.10 Thickener location alternatives for LKAB Svappavaara mine (Wennberg, 2010) . . . . 9

2.1 A uniform open channel flow. The slope is normally less than 5 ^◦ which means that φ = sin φ = tan φ and the depth perpendicular to the bottom is taken as the vertical depth. . . . 12

2.2 Moody chart for pipe flows (After Moody, 1944) . . . . 14

2.3 Transition from sub-critical to supercritical flow . . . . 16

2.4 Transition from supercritical to sub-critical flow . . . . 16

2.5 Undular hydraulic jump taking place at F r < 1.7 . . . . 17

2.6 Open channel equivalent of a pipe flow with 0.15 m diameter and 80 ^m

/ h discharge . . . . 18

2.7 Non-Newtonian fluid models, where ˙γ is the shear rate (Fitton, 2007) . . 19

2.8 Transition point V _T , where flow regime changes from laminar to turbulent in a tailings slurry with Bingham like properties. The arrows indicate various approaches for turbulent friction losses Wennberg (2011) . . . . . 21

2.9 Definition of the apparent viscosity. The subscript 1 relates µ _a to a par- ticular rate of true shear, ^du / dy . Sellgren (1982) . . . . 22

2.10 Representation of the apparent viscosity for non-Newtonian media, Sell-

gren (1982) . . . . 23

3.1 Representative particle size span for tailings (Engman, et al., 2004) . . . 29

3.2 Time history of settling at different concentrations (Andreasson, 1989) . 30 3.3 Classification of slurries based on the particle size and the relative density (Aude, et al., 1971) . . . . 30

3.4 Concentration profiles for different types of slurries. (After Sellgren, 1982) 31 3.5 Graphical solution for the determination of the deposition velocity based on pipe diameter and mean particle size (Thomas, et al., 2011) . . . . 32

4.1 Schematic representation of a slurry flow upon leaving the pipe (After Williams, 2011) . . . . 33

4.2 Angle of repose . . . . 35

4.3 Force equilibrium at angle of repose . . . . 35

4.4 Sheet flow equilibrium (After Robinsky, 1999) . . . . 36

4.5 Depositional behavior of the tailings in the form of a slurry and in desic- cated form . . . . 37

5.1 Schematic representation of the flume that is used in the field experiments for Fitton’s work (Fitton, 2007) . . . . 40

5.2 Graphical representation of the difference between segregating and non- segregating slurries in terms of depositional behavior (After Robinsky, 1999) 43 5.3 Relationship between the flow velocity and Bingham Reynold’s number (equation 5.1) (Fitton, 2007) . . . . 44

5.4 Summary of slope predictions (Seddon & Fitton, 2011) . . . . 49

6.1 Model validation with the experimental data . . . . 52

6.2 Rheological representation of different slurries to be simulated . . . . 53

6.3 Relationship between the yield stress and the deposition slope . . . . 55

6.4 Relationship between the Bingham viscosity and the deposition slope . . 56

6.5 Shield’s diagram to predict sediment motion (Chanson, 2004) . . . . 59

List of Tables

2.1 Material properties of water and a viscous liquid . . . . 17

2.2 Equivalent open channel properties for water and the liquid in table 2.1 . 18 5.1 Excerpt from Fitton’s experimental data . . . . 41

6.1 Summary of simulation results for µ B =0.05 Pa.s . . . . 54

6.2 Summary of simulation results for µ B =0.01 Pa.s . . . . 55

6.3 Summary of simulation results for µ B =0.1 Pa.s . . . . 56

6.4 Summary of simulation results for µ _B =0.05 Pa.s for a parabolic cross-section 57 A.1 Flow simulations with τ y =0Pa . . . . 67

A.2 Flow simulations with τ y =5Pa . . . . 67

A.3 Flow simulations with τ y =10Pa . . . . 68

A.4 Flow simulations with τ _y =20Pa . . . . 68

A.5 Flow simulations with τ y =30Pa . . . . 68

A.6 Flow simulations with µ B =0.01 Pa.s . . . . 69

A.7 Flow simulations with µ B =0.05 Pa.s . . . . 69

A.8 Flow simulations with µ _B =0.1 Pa.s . . . . 69

B.1 Flow simulations with τ y =5 Pa, µ B =0.01 Pa.s . . . . 71

B.2 Flow simulations with τ y =10 Pa, µ B =0.01 Pa.s . . . . 71

B.3 Flow simulations with τ y =20 Pa, µ B =0.01 Pa.s . . . . 72

B.4 Flow simulations with τ _y =30 Pa, µ _B =0.01 Pa.s . . . . 72

B.5 Flow simulations with τ y =5 Pa, µ B =0.05 Pa.s . . . . 72

B.6 Flow simulations with τ y =10 Pa, µ B =0.05 Pa.s . . . . 72

B.7 Flow simulations with τ y =20 Pa, µ B =0.05 Pa.s . . . . 73

B.8 Flow simulations with τ _y =30 Pa, µ _B =0.05 Pa.s . . . . 73

B.9 Flow simulations with τ y =5 Pa, µ B =0.1 Pa.s . . . . 73

B.10 Flow simulations with τ y =10 Pa, µ B =0.1 Pa.s . . . . 73

B.11 Flow simulations with τ y =20 Pa, µ B =0.1 Pa.s . . . . 74

B.12 Flow simulations with τ y =30 Pa, µ B =0.1 Pa.s . . . . 74

List of Notations

A Cross-sectional area (m ² ) B Width of the open channel (m) C Solid concentration (%)

C v Solid concentration by volume (%) C w Solid concentration by weight (%)

d (d ⁵⁰ ) 50th percentile particle diameter (or Average particle diameter) (m) d ⁹⁰ 90th percentile particle diameter (m)

D H Hydraulic diameter (m)

f Darcy-Weisbach friction factor

Fr Froude number

g Acceleration due to gravity ( ^m / s

)

h _f Head loss (m)

k _s Surface roughness coefficient (m) L Length of the open channel flow (m)

n Parameter for Power-Law and Herschel-Bulkley models

n Slope of the log-log plot of bottom shear stress versus pseudo shear rate P w Wetted perimeter (m)

Q Discharge rate ( ^m

/ ^h )

Re Reynolds number

Re BP Reynolds number for Bingham plastic model (equation 5.1)

R H Hydraulic Radius (m)

S Slope=sin φ

S s Specific gravity of solids S _c Critical Slope (%)

V Mean flow velocity (m/s)

V c Critical or deposition velocity (m/s)

V _T Transition velocity from laminar to turbulent flow (m/s)

y Flow depth (m)

y c Critical depth (m)

˙γ True shear rate (s ⁻¹ )

µ Newtonian viscosity (P a.s ⁿ ) µ A Apparent viscosity (P a.s ⁿ ) µ B Bingham viscosity (P a.s)

µ H Herschel-Bulkley viscosity (P a.s ⁿ ) µ _P Power-Law viscosity (P a.s ⁿ ) ρ Density of the slurry( ^kg / ^m

) ρ ⁰ Density of water ( ^kg / ^m

) ρ s Density of solids ( ^kg / m

)

σ g Stress due to the effects of gravity (Pa)

σ n Normal component of the gravitational stress (Pa) σ s Shearing component of the gravitational stress (Pa) τ ⁰ Mean boundary shear stress (Pa)

τ _∗ Shield’s parameter (equation 6.1) τ s Shear strength (Pa)

τ w Wall shear stress (Pa)

τ y Yield stress (Pa)

φ Slope angle ( ^◦ )

φ r Angle of repose ( ^◦ )

C HAPTER 1 Introduction

1.1 Mineral Processing & Tailings

Mine tailings can be defined as the by-product of mineral processing operations. During the extraction or separation of the ore in the processing plant, tailings materials are produced. A schematic flow chart of the processing of iron ore is given in figure 1.1.

Figure 1.1: Tailings from the mineral processing of iron ore - Schematic flow chart

Crushed raw ore, having a particle size of about 100 mm, is fed to the processing plant (the plant is sometimes termed also as the concentrator or simply the “mill”) and the size is then reduced to less than about 0.15 mm at the end of the operation by means of milling. The valuable product is successively taken out in various separation steps resulting in an ore concentrate that will be taken for further refinement and processing.

1

Introduction 2

The residual product, “tailings”, together with the water used in mineral processing forms a fine-grained mixture, or tailings “slurry”. The tailings slurry is then transferred to a thickener where water is removed from the mix to be recycled; to be used again in the mineral processing plant.

The slurry is then pumped to the tailings disposal facilities where it will be stored.

At this stage, after in-plant thickening, the solids content in the transported slurry may correspond to 10 to 40% by mass (defined as dry mass of solids over total mass of solids and water). The maximum particle sizes are often 0.5 to 1mm with an average size of 0.025 to 0.075mm depending on the type of ore that has been processed.

1.2 Tailings Disposal Methods

The basic requirement for a tailings disposal method is to store the tailings material in such a way that it remains stable without having a negative impact on the environment.

Some of the most commonly used tailings disposal techniques are going to be discussed in this section. It should be noted that the methods are not limited to ones provided below and there are numerous other available techniques for tailings treatment.

1.2.1 Conventional Tailings Disposal (Dams/Impoundments)

Conventional disposal here is defined as the deposition of the tailings slurries at a solids concentration by mass of about 10 to 40%, which involves a large quantity of water, see figure 1.2.

Figure 1.2: Conventional tailings disposal system. Slopes for deposited tailings are normally less than 0.5% (Wennberg, 2010)

Storing tailings with an impoundment method, generally behind a dam which acts as

a border, is one of the most common methods of tailings disposal. The idea is quite

simple but effective. Once the site to store the tailings material has been decided, a dam

embankment (or several depending on the location where the tailings material is going to

be deposited) is constructed to contain the material. This is generally achieved by making

use of the fine grained material which is engineered to satisfy certain criteria so that the

material stored behind the dam (or embankment) is optimized and the probability of

3 1.2. Tailings Disposal Methods

harming the environment (by means of seepage and/or erosion) is minimized (Fell, et al., 2005), similar to the case of earth-fill dams. The advantage of doing so is generally the fact that the mechanics, general practice and the experience gained from conventional water storage dams are often applicable in this case as well (Fell, et al., 1992).

The area occupied by the deposited tailing is often referred as the “tailings beach” and the general beach slopes for conventional tailings disposal is less than 0.5%

Deposition Methods

The tailings material can be deposited behind the embankment by means of either dis- charging from a single point or from several discharge points (spigotting).

Spigotting makes use of several discharge points placed along the line of deposition as shown in figure 1.3. It also enables uniform spreading of the tailings material behind the embankment. Depending on the need, it is also possible to shift the line of discharge from one point to another on the boundaries of the embankment.

Figure 1.3: Discharging with spigots (Fell, et al., 1992)

Construction Methods

Though it has been stated that the majority of the principles and practices developed in conventional water dam engineering can be applied for tailings dams, it should also be noted that not all the experience and the design philosophy from water retention dams are applicable (Fell, et al., 2005).

As the mining operation will be continuing until the mine reaches the closure state,

there will be a constant production of tailings throughout the life time of the mine. As a

result, there is always a need for more storage space to overcome this problem. This is one

of the major differences between the design philosophies of conventional water storage and

tailings dams. The capacity of a water storage dam is designed for a fixed volume of water

and the excess water can be discharged by means of dam structures (such as spillways)

Introduction 4

embedded to the dam body, when needed. In the case of tailings dams, the amount of tailings to be stored constantly increase; therefore additional storage spaces need to be provided. To address this problem, the tailings dams are designed and constructed in such way that when the capacity of the initial dam has been reached, it is possible to construct a new dam right on top of the previous one to increase the storage capacity in the impoundment.

In the next sections, the construction methods to increase the capacity of a tailings dam are introduced. The descriptions of the techniques were taken from (Vick, 1990) and (ICOLD, 1982).

Upstream Method

As the name suggests, upstream method is a construction technique in which the dam is raised towards the upstream level. The initial dam (sometimes called the starter dam as well) is generally a water retention dam (can be also built from the tailings material directly if the material properties of the tailings permit). At this point, the starter dam acts like a barrier and creates a storage volume and can be considered as a simple em- bankment (Fell, et al., 1992). When the level of stored material reaches to its limiting values, another dam is built on the existing embankment (starter dam) to create an ad- ditional storage volume. The tailings material itself can be used for the construction of the new embankment. This procedure can be repeated when the need arises (i.e. when the capacity of the existing tailings dam has been reached).

One of the greatest advantages of this method is that it requires relatively low amounts of construction material during the raising of the dam (especially when compared to the other two construction methods which will be described in the following sections). How- ever, one important drawback is that since the dam is being raised towards the upstream in stages, each stage of construction results in a decrease in the storage volume compared to the previous stage.

Downstream Method

One other method for raising the tailings dam is the downstream method. This time, the dam is raised towards the downstream instead of the upstream. The procedure is similar to the one described in the previous section. A starter dam is built first, to act as a barrier for the tailings. When the capacity of this started dam is reached, another em- bankment is placed upon the old one in the downstream direction to provide additional storage space. The procedure can be repeated should the need for more storage volume arise.

One of the biggest problems with this method is that the required amount of construc-

tion materials for each stage increase rapidly, rendering the method not feasible after a

certain height of dam. Its major advantage, however, is the increased storage capacity

5 1.2. Tailings Disposal Methods

Figure 1.4: Upstream Method (Fell, et al., 1992)

for each stage due to the fact that the dam is raised towards the downstream and the ability to construct filter layers to try to reduce the effects of seepage and/or erosion.

Centerline Method

The last method that is used to raise the embankment dams is the centerline method.

The raising of the dam is done along its centerline.

Similar to the downstream method, the centerline method is also costly as it requires more and more amounts of construction material for each stage. It also provides the ability to construct filter and drainage layers to help improving the stability of the dam.

Figure 1.5 illustrates different methods for tailings dam construction.

1.2.2 Thickened Tailings Disposal

In order to avoid the costly dam raises and to limit the operational costs of a tailings storage facility, thickened tailings disposal method can be utilized. With this kind of deposition method, the aim is to end up with a deposition slope value of 2-4% which will result in filling more volume per storage area. As a result, embankment raises will be needed less often which, in turn, will create savings in the construction costs.

For thickened tailings disposal, thickening that results in solids concentration by mass

of 60 to 75%, depending on the ore type and particle size distribution, is required. This

means that an additional thickening is needed besides the in-plant thickening shown in

Introduction 6

Figure 1.5: Downstream (a) and Centerline (b) construction methods (Fell, et al., 1992)

figure 1.1. The working principle of a thickener is schematically shown in figure 1.6.

Figure 1.6: Schematic representation of the thickening process (Metso Minerals, 2002). The term “pulp” is synonymous to slurry.

In order to achieve a discharge (“underflow”) with a solids content up to and over 70%,

the circular tank of the thickener normally has a higher height/diameter ratio than it is

7 1.2. Tailings Disposal Methods

shown in figure 1.6. The effectiveness is related to the extents of the compression zone.

The thickener that generates the high solids content can be located at the concentrator or close to the disposal area depending on local conditions and economics. The underflow thickened slurry can be pumped for placement at the disposal area with various types of pumps based on the pressure requirement.

Provided that the area where the material is being discharged is flat, resulting deposi- tion will be cone shaped. If this area is large enough, then the need to build a dam to confine the tailings material might not be required. However, some kind of a drainage system to collect the run-off water from the boundaries is necessary to prevent the leak- age of the material to the surrounding environment. If a dam is constructed to create a pond to store the water, it might then be possible to use this collected water for recycling purposes to be used again in the processing operation (Fitton, 2007).

Figure 1.7: Schematic representation of the thickened tailings discharge method (Fell, et al., 2005)

If the deposition area for the thickened tailings disposal is rather inclined, the construc- tion of embankments might be required to keep the tailings from spreading. An example of which can be seen in figure 1.8. This kind of thickened tailings deposition is termed as “down-valley discharge” method.

The thickened tailings storage facility given in figure 1.8 is located in Norberg, in central Sweden and is being operated by Harsche AB. The deposition takes place on an inclined ground that is surrounded by tailings dams (or embankments) to contain the material.

The installation has been running since mid-2011.

In cases where the deposition takes place along a hill side or down a valley, it might be

Introduction 8

Figure 1.8: Thickened discharge method on an inclined ground (Wennberg, et al., 2008)

favorable to locate the thickener close to the disposal area (Wennberg, 2010) as shown in figure 1.9.

Figure 1.9: Tailings disposal system with a thickener located near the deposition zone (Wennberg, 2010)

Figure 1.10 provides another tailings storage facility with two alternative locations for the thickener at Svappavaara, northern Sweden. The concept provided in figure 1.9 is marked as 2 in figure 1.10; together with another possibility where the thickener is located at the concentrator (marked as 1). For more information see Wennberg (2010).

Alternative 2 was chosen and the operation will begin in the end of 2012.

9 1.3. Problem Description

Figure 1.10: Thickener location alternatives for LKAB Svappavaara mine (Wennberg, 2010)

1.2.3 Paste Disposal in Underground Mines

Thickened tailings and the term “paste” are often presented in an interchangeable context in the literature. Although it is possible to assume that they loosely refer to the same type of material in many cases, it should also be noted that the true paste is generally thicker than the thickened tailings.

In paste disposal, tailings can be used as a backfill in the underground openings at very high solids concentration by mass (about 75%). Once the underground mining operation is complete, this paste is usually mixed with cement to provide additional strength and pumped back to the openings, in order to help and improve the stability (Fell, et al., 2005). Examples in Sweden are at the Garpenberg and Zinkgruvan mines as described by Lindqvist, et al. (2006) and Tillman (2006), respectively.

1.3 Problem Description

Thickened tailings to be placed in the disposal area must possess properties that give a conceptually even slope of deposited tailings with no segregation of particles and virtually no drainage of water. Compared to an average slope of a maximum of about 0.5% for conventional placement, 2 to 4% are considered for thickened tailings.

Throughout the whole process, starting with thickening & pipeline pumping and ending

up with the placement stage; deposition phase, generally associated with deposition

Introduction 10

slopes, is unpredictable.

It has been observed that discharged slurry, at the disposal area, typically flows down the beach in a confined self-formed channel and then spreads out in a macroscopic equi- librium between erosion and sedimentation. It is indicated that the overall slope of the beach is directly related to the slope of this confined channel.

The free surface open channel flow of tailings slurry forming the beach slope comprises of various flow regimes related to viscous properties and flow behavior. The particle- water mixture may attain Newtonian properties with a high viscosity value (like oil).

When the viscous behavior cannot be described by a fixed viscosity, then the media may be characterized as non-Newtonian (like a tooth paste or ketchup). The corresponding rheological properties are determined through viscometric measurements and analyses.

Jewell (2010) states that despite the recent advances have been made in understanding the mechanisms of slope formations of the deposited tailings; this is still an area where more work is needed to be undertaken. There is at present not a universally accepted method available for the accurate prediction of tailings beach slopes (Jewell 2012) and laboratory flume testing is not a viable method for predicting the beach slopes out on the field.

In the yearly international Paste conferences 2011 and 2012, workshops and special sessions were devoted for slope predictions resulting in new and updated contributions ref.

Depositional behavior of tailings can be considered as an intermediate area shared by several different disciplines, such as mineral processing, geotechnics and fluid mechanics.

Due to this fact, knowledge from these different fields often needs to be combined to get a better understanding of the problem.

1.4 Objective & Scope

The objective is to describe the basic slope forming elements from the open channel flow of thickened tailings slurries which show non-Newtonian behavior. A semi-empirical model for beach slope predictions by Fitton (2007) is adopted and discussed for simulating the placement of thickened tailings.

Rheological measurement and evaluation procedures are not discussed in details. Basic

descriptions can be found in Andreasson, (1989), Sundqvist (1994) or in textbooks. No

experimental work has been carried out and details about the thickening and pipeline

pumping in the system leading up to the placement are outside the scope of this study.

C HAPTER 2 Open Channel Flow

An open channel flow can be defined as a channel (of any shape) in which the water flows with a free surface (Chanson, 2004). The channel in which the water flows on can be natural or artificial. Rivers or streams are examples of naturally occurring open channels whereas human built structures such as irrigation channels or flumes are artificial open channels. Man-made channels are often referred as launders in the mining industry.

2.1 Flow Resistance & Friction Losses

Open channel flows can be further classified as uniform (non-varying) or non-uniform (varying) flows. A uniform flow is defined as the type of flow in which the depth and the velocity profile remain unchanged along the direction of flow (i.e. the water depth is constant and the water surface is parallel to the channel bottom), see figure 2.1.

For a fixed discharge, cross-section and slope, the water depth has a unique value at which the gravitational force component is in balance with the resisting shear force.

If the control volume in figure 2.1 with a length of L is considered, the equilibrium between the resistance and the gravitational force component can be stated as

τ P W L = ρgAL sin φ (2.1)

Where, ρgAL (A is the cross-sectional area) is the mass of the water and P W L (P W is the wetted perimeter) is the area on which the resisting shear stress, τ , acts.

Rearranging equation 2.1, and knowing the relationship sin φ= S, where S is the channel slope, yields

S = τ P W

ρgA (2.2)

The ratio of the cross-sectional area to the wetted perimeter is termed as hydraulic radius of the open channel flow.

11

Open Channel Flow 12

Figure 2.1: A uniform open channel flow. The slope is normally less than 5 ^◦ which means that φ = sin φ = tan φ and the depth perpendicular to the bottom is taken as the vertical depth.

R _H = A P W

(2.3) Whether it is an open channel or a pipe flow, the energy of the system decreases continuously along the direction of flow.

For a uniform open channel flow, the head loss occurring over a distance L (denoted as h f in figure 2.1) will give the slope of the channel. In other words, the slope of the free surface (or the slope of the energy grade line) is equal to the slope of the channel bed.

The statement can be formulated as follows S = h f

L (2.4)

This loss of energy (or often termed as the head loss) over a certain distance along the path of a pipe flow can be calculated with the help of Darcy-Weisbach equation.

h f = f L D H

V ²

2g (2.5)

Where, f is the Darcy friction coefficient, D _H is the hydraulic diameter, V is the mean flow velocity and g is the acceleration due to gravity.

The main difference in calculating the head losses for open channels and pipe flows is in the definition of D H (hydraulic diameter). For circular pipes, the hydraulic diameter is simply the diameter of the pipe. For an open channel flow, the hydraulic diameter is given as

D H = 4R H (2.6)

13 2.2. Flow Regime & Reynolds Number

The concept of D H (sometimes noted as “D”) will be used in equations related to circular closed conduits throughout this study.

2.2 Flow Regime & Reynolds Number

Depending on the cross-sectional properties of the open channel, rate of discharge as well as the material properties of the fluid flowing in the channel; the state of the flow can be classified as laminar, turbulent or transitional. The classification is based on the Reynolds number which is given as

Re = ρV 4R H

µ (2.7)

Where, ρ is the density, V is the mean flow velocity, R H is the hydraulic radius and µ is the viscosity of the fluid.

For open channels, the flow regime becomes turbulent for the values of Reynolds number larger than 1000. For values of Reynolds number lower than 500, the flow can be classified as laminar. The flow is in a state of transition for the values of Reynolds number in between. (Fitton, et al., 2006).

2.3 Friction Factor (f)

In section 2.1 it has been stated that the energy of the flow diminishes over the direction of the flow due to the frictional resistance caused by the channel bed.

The frictional resistance of the channel bed is often associated with a friction factor, which is a function of Reynolds number and the channel (or pipe) roughness coefficient.

If the Reynolds number and the channel/pipe roughness properties are known, deter- mination of the friction factor can be carried out with the help of the Moody diagram presented in figure 2.2.

An analytical solution for the Moody chart is also available in the form of equations if the state of the flow can be identified (laminar or turbulent).

For laminar flows,

f = 64

Re (2.8)

For turbulent flows,

√ 1

f = −2 log

 k s

14.8R _H + 2.51 Re √ f



(2.9)

The equation 2.9 is also known as the Colebrook-White equation. Where, k s is the

surface roughness coefficient, R H is the hydraulic radius and Re is the Reynolds number.

Open Channel Flow 14

Figure 2.2: Moody chart for pipe flows (After Moody, 1944)

The resistance (or the boundary shear stress) caused by the channel bed is related to the friction factor in the following way

τ = f ρV ²

8 (2.10)

If the equations 2.4 and 2.6 are substituted into the Darcy-Weisbach equation (equation 2.5), the relationship obtained would be

S = f V ² 8gR H

(2.11) For cross sections where the width of the channel is considerably larger than the water depth (B ≫ y)

R H = By

B + 2y (2.12)

The hydraulic radius approaches to y. Thus, in such cases R H can be takes as the water depth (y) and the equation 2.2 becomes

τ = ρgyS (2.13)

15 2.4. State of Flow

2.4 State of Flow

The flow in closed conduits, flowing full, (e.g. pipe flows) is characterized by the laminar or turbulent regimes.

In open channel flows, the flow is dominated by the effect of gravity. As a result, there are two additional regimes, termed as sub-critical and supercritical. Critical flow conditions occurring at a critical depth, y c , distinguish these two regimes which have completely different physical characterizations. The critical depth corresponds to the maximum possible flow rate for a given amount of energy in the water body. Alternatively, at the critical depth, a given flow rate is discharged at a minimum energy use.

Supercritical flow takes place when the flow depth is less than y c and it is associated with steep slope values and high velocities. Supercritical flows can be observed behaving in a “fast”, “shooting” or “torrential” manner. On the other hand, sub-critical flows have a “slow”, “tranquil” or “fluvial” behavior occurring at mild slope values and low velocities at depths where the flow depth is larger than y _c (Chanson, 2004).

For a rectangular open channel, the critical depth can be calculated according to the formula

y c =  Q ² gB ²



/

(2.14) The slope rate that produces the critical flow depth is defined as the critical slope and is denoted by S c

Critical depth can be observed at locations where there are variations in the channel slope. The transition from sub-critical to supercritical for uniform flow for increasing slopes is shown in figure 2.3.

The classification of the state of flow for open channel flows is often based on the Froude number. The flow takes place under critical conditions when the Froude number is equal to 1. The equation to calculate Froude number for a rectangular cross-section is given as

F r = V

√gy (2.15)

Where V is the mean flow velocity, y is the flow depth in the rectangular channel and g is the acceleration due to gravity.

The calculation of F r and y c for cross-sections of different shape (say, parabolic or elliptic) involves the use of concepts like the hydraulic mean depth (the ratio of area to the surface width - width of the channel section at the free surface). For more details, see the textbooks for open channel flow.

The classification based on Froude’s number yields If F r < 1, the flow is sub-critical,

If F r > 1 then the flow is supercritical.

Open Channel Flow 16

Figure 2.3: Transition from sub-critical to supercritical flow

The transition from supercritical to sub-critical conditions is more dramatic compared to the reversed transition in figure 2.3. The abrupt increase in depth takes place in the form of a hydraulic jump that is characterized by a high turbulence level; eddies rolling on the surface and air entrainment. The concept of hydraulic jump is illustrated in figure 2.4.

Figure 2.4: Transition from supercritical to sub-critical flow

The extent of a hydraulic jump can be expressed by the preceding depth and the

17 2.5. Conceptual Example 1

corresponding Fr. For small jumps, most eddies and air entrainment disappear and the jump is merely an undulation in the liquid surface, see figure 2.5.

Figure 2.5: Undular hydraulic jump taking place at F r < 1.7

At critical flow conditions, relationships between the flow rate, flow depth and the channel slope for typical open channels are such that different flow depths may occur for a constant discharge. In other words, the water depth (y) can vary considerably in the vicinity of y c . Due to this unstable state of flow under critical conditions, the flow is accompanied with undulating surface waves. Therefore in the design of water courses or industrial flumes, critical flow conditions are avoided due to these instabilities.

2.5 Conceptual Example 1

An example will be provided below to further illustrate the concepts introduced in the previous sections.

Consider a flow rate of 80 ^m

/ ^h discharge in a pipe of 0.15m in diameter. The equivalent uniform flow in a rectangular open channel with a water depth, y, of 0.047m and a channel width, B, of 0.378m will have the same cross-sectional area as the pipe and thus the same flow velocity (1.26 m/s) as illustrated in figure 2.6.

The required slopes for uniform flow will be calculated for water and a viscous liquid with the properties given in table 2.1.

Table 2.1: Material properties of water and a viscous liquid Water Viscous Liquid

ρ ( ^kg / ^m

) 1000 1950

µ (Pa.s) 0.001 1.95

The viscosity of the viscous liquid is nearly 2000 times greater than the viscosity of the

Open Channel Flow 18

Figure 2.6: Open channel equivalent of a pipe flow with 0.15 m diameter and 80 ^m

/ h discharge

water. The flow parameters (such as Re, f and S) are calculated with respect to equations 2.7 - 2.11 and are summarized in table 2.2.

Table 2.2: Equivalent open channel properties for water and the liquid in table 2.1 Water Viscous Liquid

Re 188323 188

f 0.025 0.34

S (%) 1.314 18.202

It follows from table 2.2 that the required channel slopes to maintain a uniform flow for the viscous liquid is about 14 times larger than that of water. For the viscous liquid with a viscosity of of 1.95 Pa.s, the corresponding slope is calculated as 18%.

This difference in slopes can be attributed to the constraints (fixed flow rate, flow velocity and the cross-section of the open channel) of the example. Due to these certain limitations, the slope values to maintain a uniform flow under identical (flow depth and flow speed) conditions are different for each sample.

It also follows from table 2.2 that the open channel flow for water takes place under turbulent conditions as the Reynolds number for the flow is greater than 1000. On the other hand, the uniform open channel flow of the viscous liquid takes place under laminar conditions as the Reynolds number is smaller than 500. In addition, the increase in the channel slopes, as the flow shifts from turbulent to laminar is also worth noting.

Furthermore, these laminar and turbulent open channel flows are found to be super-

19 2.6. Non-Newtonian Fluid & Suspension Flow

critical with F r=1.85

F r = V

√gy = 1.26

√ 9.81 × 0.047 ≈ 1.85

The critical depth of the flow in the earlier example becomes (equation 2.14)

y c =  Q ² gB ²



/

=

 0.022 ² 9.81 × 0.38 ²



/

≈ 0.07m

2.6 Non-Newtonian Fluid & Suspension Flow

2.6.1 Models

The non-Newtonian models of particular interest in the context of this work are the Bingham Plastic, Herschel-Bulkley and the Power Law Models. The concepts introduced in the previous sections were valid for Newtonian fluids. A non-Newtonian fluid may exhibit a yield stress which is the amount of stress required in order to get the material moving. Below this yield stress, the material behaves as solid and no flow can be initiated, or a non-linear viscosity characteristic or both (Fitton, 2007).

Figure 2.7 is a graphical representation of the non-Newtonian behavior.

Figure 2.7: Non-Newtonian fluid models, where ˙γ is the shear rate (Fitton, 2007)

Open Channel Flow 20

As figure 2.7 implies, it is possible to further classify the non-Newtonian fluids into sub-classes.

Bingham Plastic Model

Bingham plastic is suitable to model the behavior of fluids with a certain yield stress and a linear viscosity characteristic. Once the yield stress is overcome and the flow is initiated, the shear stress increases linearly with µ _B .

The mathematical model of the Bingham Plastic is given with the following equation (the equation of the line that represents Bingham plastic behavior in figure 2.7)

τ = τ y + µ B ˙γ (2.16)

Where, τ y is the yield stress in Pa and µ B is the plastic viscosity of the fluid in Pa.s.

Power Law Model

Power law model is appropriate to use when the fluid does not have any yield stress but has a non-linear viscosity characteristic. As a result, the rheogram (the graph in which the shear stress of the fluid is plotted against applied shear rate) of a power law fluid intersects the origin and progresses in a non-linear way.

The mathematical equation of the Power law curve is as follows

τ = µ P ˙γ ⁿ (2.17)

µ P is the power law consistency index (P a.s ⁿ ) and n is the fitting parameter.

Herschel-Bulkley Model

Another Non-Newtonian model of interest is the Herschel-Bulkley model. It is suitable for the purpose of modelling the fluids with an initial yield stress as well as a non-linear viscosity characteristic. This can also be treated as the combination of Bingham Plastic model and the Power Law model.

The equation of the curve for Herschel-Bulkley fluid is given as follows

τ = τ y + µ H ˙γ ⁿ (2.18)

Where, τ y is the yield stress in Pa, µ H is the viscosity in P a.s ⁿ and n is the flow index (unit-less) of the fluid.

Generally, the rheological properties are defined in terms of a yield stress and a shear

rate. However, it is also possible to express the rheology of the material in terms of

the operating parameters (such as the wall shear stress, flow velocity and the hydraulic

diameter). The relationship between the bottom shear stress, τ w , of a flow (figure 2.1)

21 2.6. Non-Newtonian Fluid & Suspension Flow

and the ratio 8V/D, which defines the pseudo shear rate, can be taken as a representative of the rheological properties of a fluid. Rabinowitsch (1929) and Mooney (1931) found a technique which relates the pseudo shear rate to the true shear rate, ˙γ

˙γ = (3n + ¹ / ⁴ n ) 8V

D (2.19)

Where n is the slope of the log-log plot of bottom shear stress (τ w ) versus pseudo shear rate (8V/D). True rheogram representations, based on the true shear rate ˙γ, can be transferred into operating parameters in terms of D and V through the pseudo shear rate (8V/D) which serves as a scaling parameter as shown in figure 2.8 by making use of equations 2.16 & 2.19.

The relationship between the pseudo shear rate and the rheological properties for a Bingham plastic can be expressed as follows (Shook and Roco 1991).

8V D = τ w

µ p

"

1 − 4τ y

3τ w

+ 1 3

 τ _y τ w

 ⁴ #

(2.20)

Figure 2.8: Transition point V T , where flow regime changes from laminar to turbulent in a tail- ings slurry with Bingham like properties. The arrows indicate various approaches for turbulent friction losses Wennberg (2011)

The following relationship relates V T to the material properties, Wilson et al. (2006).

V T ≈ 22.5 p

τ

/ ^ρ (2.21)

Open Channel Flow 22

Where τ y is yield stress and ρ the slurry density.

Neglecting the higher order term in equation 2.20, the relationship for laminar flows can be explained as follows

τ _w = 4

3 τ _y + µ _B 8V

D (2.22)

Where 8V/D = 2V/R _H is the pseudo shear rate and thus equation 2.22 becomes τ w = 4

3 τ y + µ B

2V R H

(2.23) This relationship will be used to approximate a true Bingham fluid, i.e. the yield stress is defined by a straight line back to the vertical axis, see the dashed line in figure 2.8.

Apparent Viscosity

As defined in section 2.6, a non-Newtonian fluid exhibits either yield strength or a non- linear viscosity characteristic or both.

At any given instant and for a given shear rate, the apparent viscosity is defined as the slope of the line from the origin to a point on the rheogram, see figure 2.9.

Figure 2.9: Definition of the apparent viscosity. The subscript 1 relates µ _a to a particular rate of true shear, ^du / dy . Sellgren (1982)

It can be concluded from figure 2.9 that the apparent viscosity has a constant value,

independent of the shear rate, for Newtonian media only. For non-Newtonian media, a

constant value can only be related to a particular rate of shear. The apparent viscosity

for very large shear rates can be represented by an asymptotic constant value, µ R , for

non-Newtonian fluids, see figure 2.10.

23 2.6. Non-Newtonian Fluid & Suspension Flow

Figure 2.10: Representation of the apparent viscosity for non-Newtonian media, Sellgren (1982)

The apparent viscosity is defined as the viscosity of a non-Newtonian fluid at a given shear rate and can be defined as the slope of the line from the origin to the representation in figure 2.9 for a given value of a pseudo shear rate. The statement can be formulated as follows

µ A = τ 2V R H

(2.24)

Where, ^{2 V} / ^R

is the pseudo shear rate (8V/D). The yield stress of a Herschel-Bulkley fluid is given as (equation 2.18)

Substituting equation 2.18 into equation 2.24 yields

µ A = τ 2V R H

= τ y + µ ˙γ ⁿ 2V R H

=

τ y + µ  2V R H

 n

2V R H

(2.25)

If the equation 2.25 is substituted into equation 2.7 (to take the shear rate dependent viscosity characteristic of a non-Newtonian fluid into account), the modified version of the Reynolds number expression becomes

Re = 8ρV ² τ y + µ  2V

R H

 n (2.26)

Friction factor calculations of the non-Newtonian open channel flows should then be carried out with the modified version of the Reynolds number provided in equation 2.26.

2.6.2 Non-Newtonian Friction Losses

Reynolds number of a Newtonian fluid can be expressed as (equation 2.7)

Open Channel Flow 24

Re = ρV 4R H

µ

Due to the significant differences in the viscosity property between a Newtonian and a non-Newtonian fluid (viscosity of the Newtonian fluid is independent of applied shear rate whereas the viscosity of a non-Newtonian fluid is shear rate dependent), the above formula needs to be modified (see equation 2.26) in order to take the rheology of the non-Newtonian fluids into account.

2.6.3 Conceptual Example 2

The following example is aimed to provide more insight on the concepts like the yield stress and the modified Reynolds number.

The liquid in the example of the previous section will now be treated as a non- Newtonian fluid (as Bingham plastic with a Bingham plasticity of 0.01Pa.s) and the required yield stress of these fluid will be determined to obtain the same slopes as in the case of conceptual example 1 (Newtonian open channel flow). In order to do that, the Reynolds number expressions (Newtonian & non-Newtonian) will be equated to each other and will be solved for the yield stress, τ _y .

Recall that the Darcy-Weisbach equation is applicable for non-Newtonian fluids for the determination of head losses of a uniform open channel flow. The re-arranged version of Darcy-Weisbach equation to obtain the channel slope was as follows (equation 2.11)

S = f V ² 8gR H

In conceptual example 1, there were constraints on parameters such as the discharge and the cross-section of the channel (in order to have an open channel equivalent of a pipe flow, see section 2.5 for more details). As a result, the only parameter that is going to be affecting the channel slope is the friction factor.

Knowing that the friction factor is a function of Reynolds number, in order to end up with the same slope value, one needs to equate the friction factors (or the Reynolds numbers for the flow). Equating Reynolds numbers for Newtonian and non-Newtonian versions of the viscous liquid (ρ=1950 ^kg / ^m

, µ=1.95 Pa.s) yields

Re = 8ρV ² τ y + µ  2V

R H

 n = 4ρV R H

µ

8 × 1950 × 1.255 ² τ y + 0.01  2 × 1.255

0.038

 =

4 × 1950 × 1.255 × 0.038 1.95

τ y = 128.14P a

25 2.6. Non-Newtonian Fluid & Suspension Flow

The calculations demonstrate that with the material properties τ y =128.14 Pa and

µ _B =0.01 Pa.s, the flow of the viscous liquid is going to have the same properties sum-

marized in table 2.2. Therefore, for non-Newtonian fluids, it is possible to conclude that

high slope rates for open channel flows can be associated with high yield stresses. The

slope of the flow for the viscous liquid (with a yield stress 128.14 Pa) was found to be

around around 18%.

C HAPTER 3

Transportation of Tailings Slurries

Tailings material contains solid particles in the liquid mixture. Therefore, the transporta- tion and flow characteristics of the slurry are controlled not only by the liquid portion, but also by the solid particles present in the mix. In the coming sections of this chapter, the properties of solid-water mixtures of key interest are going to be presented.

3.1 Solid-Water Mixture Parameters

3.1.1 Solid Content & Density

Solid content is often defined in terms of percentage and can be expressed as either concentration by weight (C w ) or concentration by volume C v . It is possible to convert the concentration by weight to concentration by volume (and vice versa) provided that the relative density of the solids in the mix is known. Concentration by weight is given as

C w = M s

M _w + M _s (3.1)

Where C w is the solid concentration by weight, M s is the mass of solids and M w is the mass of water (or the mass of the liquid in the slurry mixture).

In soil mechanics the water content is defined as w = M w

M s

(3.2) Substituting equation 3.2 in equation 3.1 yields

C w = 1

1 + w (3.3)

27

Transportation of Tailings Slurries 28

The formula to convert the concentration by weight to concentration by volume is presented below

C v = C w

S s − C w (S s − 1) (3.4)

Where C v is the solid concentration by volume, S s is the relative density of solid particles and C w is the solid concentration by weight.

The density of the solid particles in a tailings mix is generally around 2700-3000 ^kg / ^m

depending on the ore type. The density of the slurry, ρ, is related to the volumetric solids concentration in the following way

ρ = ρ 0 [1 + C _v (S _s − 1)] (3.5)

Where, ρ ⁰ is the density of water, C v is the solid concentration by volume and S s is the relative density (or the specific gravity) of solid particles. The density of the slurry with properties of C v =48.5% and S s =2.85, can be calculated as 1900 ^kg / ^m

with respect to equation 3.5.

3.1.2 Particle Size Distribution

The particle size distribution of the solids in the tailings slurry is of key interest. The particle size distribution curve is a simple semi-logarithmic graph where the percentage by mass which smaller than a certain size is plotted against that particular particle size (see figure 3.1). The size at which %50 of the particles are finer is denoted as d ⁵⁰ . Similarly, the size that the 90% of the particles are finer is denoted as d ⁹⁰ . For the discussions which will be introduced in the following chapters, d ⁵⁰ and d ⁹⁰ are of major importance. The size d ⁵⁰ is sometimes referred as the characteristic, the average or the median particle size as well.

3.2 Classification

3.2.1 Settling & Non-Settling Slurries

A classification based on the particle size distribution and the amount of solid particles present in the mix is significant as the presence of solid particles and their concentration play a vital role in many aspects of the slurry behavior. The rheology of the slurry, as well as the flow properties and the deposition velocity (the velocity at which the solid particles start to settle down in the channel bed instead moving along the path of flow) are highly dependent on the solids concentration.

It has been stated that the solid concentration has a significant effect on whether the

slurry is going to be behaving as settling or non-settling. To further demonstrate the ef-

fect of the solid concentration, consider a mixture in a transparent column that is stirred

29 3.2. Classification

Figure 3.1: Representative particle size span for tailings (Engman, et al., 2004)

to homogeneity and thereafter left to settle. The progress of the clear water interface is then recorded in time. The time history results for a tailings slurry in figure 3.2 demon- strates the strong effect of solid concentration on the homogeneity of a tailings slurry. At volumetric concentration values below about 10%, the interface quickly progresses down.

The water only appears at the upper portions with relatively small layer thickness after several hours when the solid concentration approaches to 40% (Andreasson, 1989).

Figure 3.3 provides regions (or intervals) for settling (heterogeneous) and non-settling (homogeneous) pipeline pumping characteristics based on the particle size distribution and the relative density of the solids in the mix (Aude, et al., 1971).

Generally speaking, slurries dominated by particles larger than 40µm with maximum particles from a few hundred µm to very large sizes can be defined as settling, where large particles may slide along the bottom of the pipe (Sellgren, 2010).

Truly non-settling slurries can be treated as homogeneous fluids for clay-sized particles, i.e. less than a few microns in diameter. The suspension may have Newtonian viscous properties or non-Newtonian rheological properties along with a yield stress, especially at relatively high solids concentrations (Sellgren, 2010).

In most industrial applications it should be noted that it is difficult to classify the slurry as non-settling or settling. The fine particle fraction (less than about 40µm) and the liquid may form a nearly homogeneous “carrier fluid” slurry with non-settling behavior (Sellgren, 2010).

Slurries in mineral processing typically have average particles sizes of 20 to 100µm with

Transportation of Tailings Slurries 30

Figure 3.2: Time history of settling at different concentrations (Andreasson, 1989)

Figure 3.3: Classification of slurries based on the particle size and the relative density (Aude, et al., 1971)

maximum sizes of up to 500 to 1000µm. Coarser tailings products may have average sizes

of 50 to 100µm. With volumetric concentrations varying from a few per cent up to and

over 40%, the task of classifying the slurry becomes rather difficult. Therefore, slurries

having such configurations are generally termed as complex slurries because of the fact

that they cover an intermediate area between homogeneous and heterogeneous (“non-

settling” and “settling”, respectively) type of behavior (Sellgren, 2010).

31 3.2. Classification

In conventional tailings disposal, the solid concentration of the slurry generally ranges between 5-20%. This results in a heterogeneous (or settling) behavior of the tailings slurry if all the particles are not very fine, say less than 20µm.

In order to obtain pseudo-homogeneous or homogeneous (non-settling) behavior for placement without segregation, the volumetric solid concentration should exceed 40%

(often 45%) for the type of tailings considered in this work.

Finally, figure 3.4 further illustrates the concept of homogeneous and heterogeneous slurries (non-settling and settling) in terms of distribution of particles and the concen- tration profile.

Figure 3.4: Concentration profiles for different types of slurries. (After Sellgren, 1982)

3.2.2 Deposition Velocity

From a sediment transport point of view (which can be applied to the case of tailings slurries), deposition velocity is defined as the minimum velocity in pipe or open channel flows at which the solid particles start to settle in the pipe or channel bed. At velocities larger than this deposition velocity, the particles will keep moving along the direction of flow without any deposition/sedimentation occurring. Deposition velocity is also referred as the minimum transport velocity or the critical velocity in the literature.

Figure 3.5 is suitable for the determination of the deposition velocity provided that the particle size and the pipe diameter values are known.

There are a variety of equations available to calculate the deposition velocity for pipe

flows in literature. The equation presented by (Wasp, et al., 1979) was found to be

suitable for the open channel flow of tailings flows (Fitton, 2007) as will be discussed in

the following chapters.

Transportation of Tailings Slurries 32

Figure 3.5: Graphical solution for the determination of the deposition velocity based on pipe diameter and mean particle size (Thomas, et al., 2011)

V c = 3.8C _v

^/

 d D



/

 2gD (ρ s − ρ ⁰ ) ρ 0



/

(3.6) Where, C v is the solid concentration (% by volume), d is the mean particle size diameter (d 50 ), D is the pipe diameter, g is the gravitational acceleration, ρ _s is the density of solid particles, ρ ⁰ is the density of the carrier fluid.

It should be noted that the equation 3.6 is valid for pipe flows. However, with the substitution D=4R H (R H is the hydraulic radius for an open channel) the equation can easily be converted to be applied for open channel flows.

The deposition velocities for a tailings slurry with d=0.05 mm, C v = 20% and ρ s =2800

kg / m

corresponds to 1.34 and 2.14 ^m / s for D=0.1 and 0.4 m, respectively.

Corresponding values at C v =45% are, 2.61 and 1.65 ^m / ^s , respectively.

The calculations demonstrate that the effect of the hydraulic diameter and the vol-

umetric concentration on deposition velocity is not strong. Even though the hydraulic

diameter is reduced by 75% (from 0.4 to 0.1) the change in the deposition velocity is

around 37%. Similarly, doubling the volumetric concentration does also not cause any

significant differences.

C HAPTER 4 Placement of Tailings Slurries

Upon discharging from a pipe or launder, the tailings slurry will be undergoing an open channel flow through cross-sections which the material forms by itself by eroding the base material of the storage area. Immediately after leaving the pool, the state of flow is normally supercritical, see figure 4.1.

Figure 4.1: Schematic representation of a slurry flow upon leaving the pipe (After Williams, 2011)

As the material progresses through the naturally occurring channels, the flow undergoes hydraulic jumps and the state of the flow shifts to sub-critical. In the last phases of the

33