An Initial Analysis of Long-Distance Slurry

Transport in Subarctic Environment

Wilhelm Friberg

Mechanical Engineering, master's level (120 credits)

2021

Luleå University of Technology

Department of Engineering Sciences and Mathematics

Foreword

This report covers the master thesis work conducted for LKAB at Luleå University of

Technology. The thesis is a study of slurry transportation in the subarctic climate in

Norrbotten. Special thanks go to my supervisors Johan Breheim and Anders Sellgren

as well as my examiner Pär Jonsén for their input and support during my thesis.

Thank you to the people at LKAB pilot apatite plant who provided useful data for this

thesis. I also want to send gratitude to my parents, Lars and Helena for their support

during my studies in Luleå.

Abstract

In today’s economy, it is important to have a sustainable business model where as

little as possible goes to waste or finding solutions to create something useful out of

by-products. Therefore, LKAB are looking to make a large investment into creating

an infrastructure of several plants to turn tailings from the production of iron ore into

usable products for several industries which LKAB has designated project ReeMAP

(Rear Earth Elements and MonoAmmonium Phosphate). These products include

phosphorus used in the production of food, gypsum used in the building industry and

fluorine used in the chemical industry.

One of the key ingredients in making these products is apatite, a calcium-phosphate

crystal which is extracted from the tailings. The plant where the apatite is to be

produced will be located close to the mining sites in Kiruna and Malmberget and then

transported to the coast. The transportation can be caried out by rail carts which is

how the iron ore is transported. Depending on the quantity of apatite that will be

transported, a new rail track would need to be built which is a huge investment on top

of the investment for the ReeMAP infrastructure. An alternative transportation

method for the apatite is to use a pipeline that is pressurized by a series of pumps

known as slurry transportation. This method of transporting material has been utilized

in many countries around the world as it has shown to be a cost effective and more

environmentally cautious method of transportation.

Slurry transportation comes with its own unique challenges, the major ones are

making sure the slurry is well mixed and the solid particles do not deposit inside the

pipeline and the other is the risk of freezing during a longer system shutdown. This

has been studied using Computational Fluid Dynamics analysis in the software

ANSYS Fluent. In addition, an overview calculation of the pressure losses to

determine the number of pumps needed for the transportation has been conducted.

The software ANSYS Fluent Multiphase was used to model the interaction of solid

apatite particles with water and determine the volume concentration of apatite inside

the pipeline. For the freezing of water inside the pipeline during a shutdown and

stationary flow, the software ANSYS Fluent Solidification/Melting was used for the

modelling.

The results from the flow model show that the apatite becomes pseudo-homogenous

during the transportation, given that the particle size remains within a certain interval,

which will deposit the correct amount of apatite at the outlet of the pipeline. The

results from the freezing model shows that a shutdown of a few hours is possible

without the risk of the water freezing inside the pipeline. With insulation, this time

may be extended.

Sammanfattning

I dagen samhälle är det viktigt att minska utsläpp och spill i tillverkning av varor. För

LKAB, vid tillverkningen av järnmalm så skapas en stor del avfallsand som resterar.

LKAB har därför valt att utvärdera en stor investering i ett projekt benämnd ReeMAP

(Rear Earth Elements and MonoAmmonium Phosphate) där avfallsanden ska

användas för att skapa bland annat fluor som används inom kemikalier industrin, gips

som används inom byggindustrin och gödsel som används flitigt inom odling.

Ett av huvudämnena vid tillverkning av dessa produkter är apatit, en kalcium-

fosfatkristall som utvinns ur avfallsanden. Verket som utvinner apatiten, apatitverket,

kommer att befinna sig vid gruvorna i Kiruna och Malmberget. Apatiten transporteras

sedan till kusten. Apatiten kan transporteras via järnväg som järnmalmen men det

kommer medföra att ett nytt spår behövs då det är kapacitetsbrist på Malmbanan vid

ett högre tonnage av apatit. Ett alternativ till detta är att apatiten transporteras i en

pipeline med en serie av pumpstationer efter flotationsprocessen i apatitverket.

Slurrytransport är något som används flitigt inom industrin då det har visat sig vara en

mer kostnadseffektiv metod än transport med räls.

Med slurrytransport så tillkommer en del unika utmaningar, bland annat så är det

viktigt att apatiten är väl fördelad i slurryn för att flödet ska vara så jämnt som möjligt

och att slurryn inte fryser när det inte är något flöde och slurryn är stilla i röret. Båda

dessa problem har studerats med Computational Fluid Dynamics analys med

beräkningsprogrammet ANSYS Fluent vilket är ett numeriskt program som har visat

sig kunna modellera slurrytransport med hög precision. En överslagsberäkning har

också utförts för att bedöma tryckfallet i röret och energiförbrukningen av pumparna

för att transportera apatiten. Beräkningsprogrammet ANSYS Fluent Multiphase

används för att modellera apatiten som en kontinuerlig fas av solida partiklar och

volymfördelningen av apatit partiklarna i slurryn bestäms. Beräkningsprogrammet

ANSYS Fluent Solidification/Melting användes för att visa fasövergången mellan

vatten och is i pipelinen och bestämma tiden det tar för att slurryn ska börja frysa och

hur lång tid det tar tills slurryn har fryst.

Resultaten visar att apatiten blir pseudo-homogent under transporten i pipelinen givet

att apatit partiklarna inte är för stora då större partiklar deponeras i botten av röret.

Tryckförlusterna som sker i röret enligt modellen som tagits fram i ANSYS Fluent är

lägre än det tryckfallet som förväntas vilket visar att det finns möjligheter för

förbättringar i modellen. Resultaten visar också att risken för frysning existerar men

att slurryn kan vara stillastående över flera timmars tid innan det börjar frysa och flera

dagar innan slurryn blir helt till is. Isolering kan möjligtvis förlänga isbildnings tiden.

Detta medför att slurrytransport är en möjlighet för LKAB att använda som

transportmedel för apatiten.

Table of Contents

Introduction .................................................................................................................. 1

1.1 Iron Pellets Manufacturing ............................................................................ 1

1.2 Waste Products to Usable Products ............................................................... 2

1.3 Thesis statement & Delimitation ................................................................... 3

1.4 Aims and Objectives ...................................................................................... 5

1.5 Computational Fluid Dynamics ..................................................................... 5

1.6 Pipeline .......................................................................................................... 6

1.7 Earlier work ................................................................................................... 6

Background and Theory.............................................................................................. 8

1.1 Slurry and Slurry pumping............................................................................. 8

1.2 Apatite ............................................................................................................ 8

1.3 ANSYS Fluent Multiphase .......................................................................... 10

1.4 ANSYS Fluent Solidification/Melting ......................................................... 11

Method ........................................................................................................................ 13

1.5 Holistic Perspective ..................................................................................... 13

1.6 Sedimentation Analysis ............................................................................... 14

1.6.1 Physical Test – Sedimentation Analysis ................................................... 14

1.6.2 Simulation – Sedimentation Analysis ....................................................... 15

1.7 Flow Simulation ........................................................................................... 19

1.7.1 Horizontal pipe – Comparision ............................................................... 19

1.7.2 Horizontal pipe – Steady .......................................................................... 20

1.7.3 Horizontal Pipe – Sedimented ................................................................. 22

1.8 Freezing Model ............................................................................................ 23

1.8.1 Freezing Model – ANSYS Fluent Control ................................................ 23

1.8.2 Freezing Model – MATLAB Control........................................................ 25

1.8.3 Freezing Model – Pipeline ....................................................................... 26

Results ......................................................................................................................... 29

1.9 Holistic Perspective ..................................................................................... 29

1.10 Sedimentation Analysis ............................................................................... 29

1.11 Flow Model – Comparison .......................................................................... 32

1.12 Flow Model – Steady ................................................................................... 33

1.13 Flow Model – Transient ............................................................................... 45

1.14 Freezing Model – MATLAB Control .......................................................... 45

1.15 Freezing Model – ANSYS Fluent Control................................................... 46

1.16 Freezing Model – Pipeline ........................................................................... 50

Discussion.................................................................................................................... 52

Conclusion .................................................................................................................. 57

References ................................................................................................................... 59

Appendix 1 – Holistic Perspective ............................................................................ 62

Appendix 2 - Numerical heat flow model in MATLAB.......................................... 66

Appendix 3 – Maximum Packing Limit ................................................................... 68

Appendix 4 – MATLAB script for explicit heat equation ...................................... 69

Appendix 5 – MATLAB script losses approximation ............................................. 71

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1 Introduction

Luossavaara-Kiirunavaara AB (LKAB) is a mining and mineral group that mines and

processes iron ore in the Swedish province of Norrbotten. LKAB was established in

1890 and has stood as a cornerstone for the Swedish export industry ever since,

having supplied iron for steel manufactures in Europe. In 1954, LKAB builds a

pelletization plant to enrich the iron ore further to give added value for their

customers (LKAB Iron, 2017). In 2019, LKAB produced 27.2 million tons of iron ore

which is 80% of the total iron ore produced in Europe, making LKAB the largest iron

ore producer of Europe (LKAB, 2017). As LKAB strives to develop their business

model ever more, the thought of using todays mining waste for the products of the

future is one with many challenges. This is however the ambition of project ReeMAP,

an LKAB Minerals project which involves using as much of the mined material as

possible for the use of green technology and for the production of food.

1.1 Iron Pellets Manufacturing

The waste comes from the production of iron pellets, LKABs main product which is

used as a key ingredient in the production of steel. In order to create the Pellets from

the mined ore, several processes take place which including Sorting, Concentrating

and Pelletizing. The first step of Sorting involves breaking down the mined ore into

smaller pieces and initially sorted from waste rock. This is done using powerful

magnets which attracts the magnetic ore from the waste rock. This increases the iron

content from roughly 45% to 62% (LKAB Sorting, 2017).

When the sorting process is complete, the iron ore is transported to the concentrating

plant. Here the ore is ground to a fine powder and mixed with water to create a slurry.

From there, the slurry is filtered to eliminate waste minerals such as silicon, sodium

and phosphorus. This raises the concentration of iron to 68% (LKAB Conc., 2017).

The concentrating process also includes flotation which involves adding additives to

the slurry to increase the ore concentration further. The additives attract phosphorus

mineral apatite which binds them to form air bubbles and can be removed from the

surface as foam. Once the iron ore has reached the desired concentration it is

transported to the pelletizing plant.

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In the pelletizing plant the concentrated iron ore is mixed with bentonite which is

used as a binder. The concentrate is placed in a large rotating drum which creates

small spheres, 10 mm in diameter, which are known as pellets. The pellets are then

dried and pre-heated to increase the strength of the pellets. After this, the pellets

become sintered to bind the individual iron ore particles together after which they are

cooled and are shipped to the desired destination. The entire pellets production

amounts to 28 million tons of processed iron ore every year, which leaves a lot of

waste materials (LKAB Iron, 2017).

1.2 Waste Products to Usable Products

Many of the waste materials such as phosphorous and fluorine are used in everyday

products for individual consumers such as toothpaste or for the production of food

such as fertilizer. For this to be possible, LKAB is in discussions regarding a large

investment into creating an entire network of plants to manufacture products for the

Swedish and international economy (LKAB Iron, 2017). These products include:

• Fluorine which is heavily used in the medical field and chemicals industry

• Phosphorus used in the production of food

• Gypsum which is used in the construction industry

• Rare Earth Elements (REE) used in green technology such as wind turbines

and electric motors (LKAB Reemap, 2021)

To be able to produce these products, several stages are involved to turn the waste

products to usable products and materials. The first step is the production of pellets

where the waste comes about. This waste or by-product, which from here on is known

as tailing product, is collected and stored in tailing ponds. From there the product is

transported to an apatite plant where the tailing product is upgraded to produce an

apatite concentrate, which contains the necessary minerals to produce the desired

products. The apatite concentrate is then transported to the Hydro where it is mixed

with hydrochloric acid to produce Fluorine, Rare Earth Elements, Gypsum and

Phosphoric acid as shown in figure 1. The Phosphoric acid is then transported to a

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concentration plant where it is mixed with ammonia to produce Mineral fertilizer

(LKAB Reemap, 2021).

Figure 1: Production cycle of materials and plants (Nyhetsbyrån, u.d.)

1.3 Thesis statement & Delimitation

This master thesis work revolves around the transportation of the apatite concentrate.

One option is to transport it as a slurry from the Apatite plant to the Hydro plant using

a pipeline and a series of pumps. Using pipeline transportation would eliminate the

need for additional train transport and potentially reduce the cost. Today, the rail track

is being used to maximum capacity currently and an extra tack would be required to

cover additional transport demands. Since the apatite plant is located at the mines in

Kiruna and Malmberget and the Hydro plant by a site near a harbor, the pipeline

would be roughly 300 km long. Long distance transport of slurry has been used in the

past. Most notably by the OCP Group who utilizes a 235-kilometre pipeline network

in Morocco to transport the slurry from the production plant in Khourigba to the

terminal station in Jorf Lasfar, a schematic of the pipeline is shown in figure 2. This

has helped reduce the water needed by 3 million cubic meters per year and reduce the

CO2 emissions by 930 thousand tons per year (OCP Slurry pipeline, 2015).

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Figure 2: OCP Morocco slurry pipeline network (Aggragate Business, 2014)

There are a number of other examples of utilizing pipelines for slurry transport.

However, using it in the northern most territory of Sweden has its own unique

problems in terms of both terrain and climate. The problem description is defined as:

• What are the opportunities and challenges with long distance slurry transport

in a subarctic environment?

This is a very open description, which leaves a lot of room for identifying and

reasoning of potential problems that can be formulated. This will include:

• Design Computer Aided Design file for geometry for ANSYS Fluent

• Determine ideal geometry for desired slurry velocity and the flow

• Calculation of pressure losses during the transportation

• Map out potential route of pipeline

• CFD analysis for flow in 3D for varying concentration of apatite

• Freezing behavior of slurry in pipeline for different conditions

• Sedimentation of slurry in pipeline

In order to validate the simulation results, physical tests were performed alongside the

simulations. There is a limit to the amount of physical testing that were conducted for

this thesis but will be a part of future work required for a successful system for

LKAB. The physical tests will include:

• Sedimentation of slurry

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Due to the complexity of the models, certain delimitations are stated to reduce the

calculation times. These limitations include:

• Regarding the slurry as incompressible

• No structural mechanics simulations will be performed

• Only a short portion of the pipeline will be analyzed using CFD

• Ambient temperature outside the pipeline will be constant

• No wear is considered on the pipeline

1.4 Aims and Objectives

The main aim of this thesis is to obtain an initial understanding of slurry

transportation with long-distance pipeline systems in a subarctic environment. The

main objective is to develop a model that can predict the flow behavior and the solid

particle distribution in a pipe section. The second objective is to develop a model that

can determine the risk of freezing when there is no flow in the pipeline.

1.5 Computational Fluid Dynamics

The most common method for modelling of fluid flow, is the use of computational

fluid dynamics, (CFD). CFD is a numerical approximation approach to solve partial

differential equations that govern the behavior of the fluid. The governing equations

used in CFD for both 2D and 3D are conservation of momentum, mass, and energy

equations. The nature of these governing equations are non-linear partial differential

equations and an exact solution can only be found in simple cases which rarely exist

in the practice of fluid mechanics (Saqr, 2017). Therefore, equation discretization is

introduced to linearize which creates a set of linear equations. In order to accomplish

this the domain, where the flow problem is to be solved, is discretized into a finite

number of elements and nodes. The solution algorithm solves the set of linear

equations in each of the nodes given the boundary and initial conditions for the flow.

The most common method for discretization of the domain is the Finite Volume

Method (FVM). This method divides the domain into a finite number of elements or

cells where the centroid of the cell is the variable for the linearized equations. The

divided domain is more commonly referred to as the mesh. Interpolation methods are

used to calculate the change of the studied variable in between the centroid nodes

(Saqr, 2017).

6

There are several programs available to perform CFD analysis. The commercial

software ANSYS Fluent was chosen as the preferred tool. ANSYS Fluent has the

capabilities of both calculating turbulent and laminar flow as well as particle

interaction. Fluent also has many pre-described functions such as Multiphase and

Solidification/Melting which can come in handy for slurry transportation and

freezing.

1.6 Pipeline

For this thesis, it is assumed that the apatite pipeline will run as stated from Kiruna

and/or Malmberget to Luleå where the apatite will be used to form the finished

products, which will thereafter be shipped from the Luleå docks. For this thesis, it is

assumed that the pipeline will run parallel to Malmbanan, the train rails that transport

the iron pellets. The rail track is depicted in figure 3.

Figure 3: Rail track map from Luleå to Riksgränsen (järnvägsstyrelsen, 1931)

1.7 Earlier work

There have been several earlier works when it comes to CFD analysis of slurry for

pipeline applications. These include:

• Characteristics of flow

• Influence of particle drag

• Particle size influence on flow

• Concentration and velocity influence on flow

• Temperature drop during flow

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• Freezing risk over longer shutdown time

Some of the previous work that has been done include (Li, et al., 2018) and (Kumar

Gapaliya & Kaushal, 2016) who’s works consists of CFD analysis of slurry flow in

horizontal pipes at a range of velocities, concentrations and particle sizes. Both these

studies have been conducted using ANSYS Fluent and have made comparisons with

experimental data. The results from the data shows that ANSYS Fluent can simulate

the velocity as well as the volume concentration distribution of the sand at a high

precision. From these findings, ANSYS Fluent was chosen as the preferred tool for

simulating the flow of slurry in a pipeline configuration.

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2 Background and Theory

This chapter covers the theories used in the thesis as well as background information

to give a better understanding of slurry pumping.

2.1 Slurry and Slurry pumping

A slurry is defined as a mixture consisting of fluid and solid particle mediums (Metso

Minerals AB, 2012).A slurry can be composed of just a single fluid and solid particles

which is known as a two-phase slurry. Slurry can consist of more fluids, most

commonly water and air together with solid particles which is known as a three-phase

slurry. In most cases, the fluid is simply used to be able to transport the solid particles

using slurry pumping. The fluid used is usually water however other chemical

compound like fluids can be used such as acid and alcohol (Metso Minerals AB,

2012).

Slurry pumping is the method of transporting slurry under pressure via pipelines. The

pressure is supplied from pumps located along the pipeline. The pumps used is

dependent mainly on the type of slurry that is to be pumped as well as the application

for which it is used. The most common pumps used for slurry pumping are centrifugal

pumps and positive displacement pumps. The centrifugal pumps help feed the slurry

to the positive displacement pumps which creates the flow for the slurry. An installed

positive displacement pump along with a schematic of a positive displacement pump

is shown in figure 4.

Figure 4: Positive displacement pump for slurry transportation (Weir, 2015)

2.2 Apatite

The solid particles that make up the slurry along with water is apatite concentrate or

simply apatite. Apatite, in its purest form, is a calcium-phosphate crystal that contain

a variety of minerals. Apatite will be part of the production of the products described

9

in the introduction. The apatite will be produced in a plant consisting of several steps

depicted in figure 5.

Figure 5: Potential apatite plant schematic of the individual processes (Nyhetsbyrån,

u.d.)

The plant consists of several steps that enriches the tailing sand to become apatite

concentrate. The first step involves removing large particles and metals. The metals

will be returned to the pellets plant while the large particles will be transported back

to the tailing ponds. The next step is to remove the absolute smallest particles that can

interfere with the flotation process, these particles are as well transported back to the

tailing ponds. Before the flotation process can begin, a mixing process takes place

where flotation reagents are added to the remaining tailing sand. The flotation process

is where the apatite is extracted from the tailing sand. The reagents react to collector

molecules surrounding the apatite particles. This reaction causes bubbles to form

which raise to the surface with the apatite particles that can then be collected. The

remaining tailing sand is sent back to the tailing ponds. The final step of the process,

as it stands during the writing of this report, is the drying process where the apatite

concentrate is filtered to dewater the apatite and subsequently dried. Since the apatite

is planned to be shipped via trains, it makes logistical sense to ship it dry as it takes up

less space. This process will most likely be changed where a filtration process could

be obsolete. This is due to the apatite needing to be mixed with water for the slurry

transportation. (LKAB apatite, 2020)

For the simulations, it is important to know the density and particle size of the apatite

concentrate. The apatite concentration test lab KA3 were able to produce a sample for

10

this report, specifying the mineral contents of the apatite concentrate, density, and the

particle size. The density of the apatite concentrate is 2970 𝑘𝑔/𝑚3. This value is

taken as the average for the entire test sample of varying particle size.

The particle size was determined using two different methods, sieve analysis and laser

diffraction analysis. Both methods are common practices when looking at particle

distribution to determine particle size. Sieve analysis is a process where sand material

is passed through a series of stacked sieves with varying mesh sizes. The sand is

loaded at the top sieve and a shaker is used to separate the particles. The mass of sand

for each sieve is then measured to produce a particle size distribution spectrum

(Jamal, 2017). Laser diffraction analysis is a method where the diffraction pattern of

laser beams is studied to determine the particle geometry (Malvern Panalytical, 2021).

The reason for using two methods is that sieve analysis cannot be dependable below a

certain diameter, around 45 micrometers. The particle distribution can be seen in

figure 6.

Figure 6: Particle distribution of apatite from apatite pilot plant at the Kiruna mine

The graph shows the cumulative mass of particles up to the given particle size. This

can therefore be used to determine the average particle size, which is around 45

micrometers, which will serve as the base particle size for the simulations. This being

said, there are some industry standard tests, which utilize more than one particle size.

The particle sizes that will be utilized are 50, 100 and 150 micrometers. It will also be

possible to use more than one particle size to obtain a comparative simulation.

2.3 ANSYS Fluent Multiphase

To simulate the slurry, ANSYS Fluent Multiphase solver is used. The Multiphase

solver enables multiple phases to be used within a geometry. A phase can be defined

11

with a set of material properties which interacts with the other phase or phases in

which it presides (ANSYS Multiphase, 2009). The phase interaction can be set as any

combination of gas and liquid together with solid. There are three different types of

multiphase models that can be generated: Volume of Fluid, also known as VOF,

Mixture model and the Eulerian model. The VOF model is strictly a fluid-fluid phase

interaction model, which is not applicable for slurry transport (ANSYS Multiphase,

2009). The difference between the Mixture model and Eulerian model is essentially

that the Mixture model is a simplified multiphase model where a single set of

momentum and continuity equations are solved as a mixture of all the phases

combined. In the Eulerian model however, the turbulence equations can be solved for

each of the different phases, Per Phase model, or together with the Mixture model.

The Mixture model will therefore yield a faster solution however might not give as

correct of a solution. When using Multiphase models in ANSYS, either Mixture or

Eulerian, there is no difference when it comes to the governing equations between

liquid-liquid phases or liquid-solid phases (ANSYS Multiphase, 2009). Instead, the

viscosity of the granular phase is determined by a series of equations that are input

parameters for ANSYS Fluent Multiphase.

2.4 ANSYS Fluent Solidification/Melting

The freezing simulations was performed using ANSYS Fluent using the

Solidification/Melting model. The model allows for simulation of the solidification

and melting process, at a single temperature or over a range of different temperatures

depending on the material used, see (ANSYS Solid, 2009). The model uses an

enthalpy-porosity formulation that, utilizes sink terms that are applied to the

momentum equations to account for pressure drop when the liquid phase becomes

solid (ANSYS Solid, 2009). The porosity will change when the liquid freezes and

becomes solid and the enthalpy-porosity formulation creates a “mushy zone” where

the porosity is taken from the liquid-fraction. The liquid-fraction can be viewed

during post-processing visualization that shows the quantity of solid and liquid

phases.

There are however limitations to the solidification/melting model. The main being

that multiphase modelling cannot be combined with solidification/melting model

(ANSYS Solid, 2009). Therefore, inclusion of water and apatite slurry to the model

was not possible. Because of this, the necessary values needed for the model to be as

12

accurate as possible needs to be derived from the multiphase model. These values

include the viscosity and thermal diffusivity. Another limitation is that it is not

possible to specify different material properties for solid and liquid phase. Since water

expands as it freezes, there could be instances where the simulation shows freezing

where in the real world, it will not be possible and instead the pressure increases.

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3 Method

This part of the report covers the methods used to get an understanding of the pipeline

pressure loss and energy consumption as well as the setup the models and physical

experimental tests.

3.1 Holistic Perspective

In order to obtain a wider view of the problem at hand, a scenario was created for a

pipeline, which would cover a length equivalent to the length between Kirunavaara

and Luleå. This pipeline however would not undergo the same elevation changes

instead be on a linear decline. The goal of this scenario is to acquire a better

understanding of the pressure losses due to friction on the pipeline wall as well as the

energy consumption required to transport the slurry.

In the scenario, the pipeline has a length of 300 km and an inner diameter of 250 mm.

The elevation difference between the inlet and outlet is 450 meters. This is set using

the elevation difference between the Kiruna and Luleå as shown in figure 3. The

average flow velocity was set using the critical velocity for sedimentation, figure 7.

For example, with a particle size of 150 micrometers and a pipe diameter of 0.25

meters, the critical velocity would be 1.8 m/s. The critical velocity is the limit where

the slurry will undergo deposition if the velocity was any lower. Since deposition of

particles will lead to increased losses and possibly plugging of the pipeline, it is

important to control the maximum particle size that can enter the pipeline system.

Figure 7: Nomogram showing the deposition velocity for solid particles in a fluid

(Metso Minerals AB, 2012)

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Utilizing the methods and equations in Appendix 1, the pressure losses and energy

consumption was determined.

3.2 Sedimentation Analysis

In order to obtain a better understanding of the sedimentation that occurs when the

fluid is stationary, a physical sedimentation analysis was performed using a

measuring cylinder. A sedimentation analysis was also performed in ANSYS Fluent

to validate the model. The data gathered from the physical analysis will also give the

maximum packing limit that is the maximum volume the solid particles in the slurry

as a percentage.

3.2.1 Physical Test – Sedimentation Analysis

The physical test that was performed for this thesis work was the sedimentation

process of tailing sand in a measuring cylinder. The purpose for the test is to be able

to identify the time taken for sedimentation to occur as well as identifying the

maximum packing limit. The maximum packing limit is important to know since it is

an input value used for ANSYS Fluent. The results will also provide with a base

comparison to the simulation results achieved using ANSYS Fluent.

To start of a 250 ml +/- 2 ml measuring cylinder was used as the control volume to

perform the tests. The geometry is very different from the slurry pipeline however, it

will provide a good comparison for a simulation model which will be setup in a

similar manor. In the physical tests, tailing sand sample taken from the tailing ponds

in Kiruna is used due to the lack of plentiful apatite. The tailing sand appeared more

course than the apatite that, one assumes, will not yield an exact packing limit for the

apatite however, it will give a base value to use for the flow simulation.

To begin, a scale was used to measure the weight of the tailings as well as the water.

Using weight instead of volume to measure out the correct volume fraction provided a

more reliable measurement of the different phases. For the experiments 75, 100 and

125 grams of tailing sand and water was measured up using an electronic scale with a

certainty of +/- 1 gram. The tailings and water were then poured into the measuring

cylinder and mixed. The resulting volume was then checked with the theoretical

volume since the density of the phases were both known along with their masses.

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Once a homogenous mixture was achieved, the measuring glass was placed on a table

surface allowing the tailings to sink and sediment completely. Once the mixture has

reached a sufficient sedimentation, the elapsed time will be compared with the

simulation results. In order to determine the maximum packing limit, the volume of

tailings has to be determined. This is calculated using equation 22 while the

maximum packing limit is then determined using equation 23. These equations are

found in appendix 3. The maximum packing limit will be used as an input for ANSYS

Fluent.

The results from this experimental set up will be displayed in tabular form where the

total volume of the slurry is before the experiment, from this the volume of the

tailings can be calculated, the sedimentation volume after one hour and 24 hours

respectfully which are the volumes of the slurry when sedimentation has occurred.

Finally, the maximum packing limit is determined.

3.2.2 Simulation – Sedimentation Analysis

A simulation was created which replicated the scenario with the measuring cylinder.

The purpose of this simulation was to find similarities and differences of the

interaction between the water and tailing sand of the physical experiment vs

numerical models. From the start, there are already differences between the two: In

the model, the tailing sand grains are assumed perfect spheres, which is not the case

with the actual tailing sand. Another difference is the grain size, for the numerical

model a single grain size is used to reduce the computation burden whereas the tailing

sand has varying grain sizes.

To begin the geometry was created using ANSYS DesignModeler. The geometry

replicated the physical experiment where 100 grams of tailing sand was used. In order

to set the geometry, the total volume of the slurry of the measuring cylinder had to be

determined. The total volume of 100 grams of tailing sand mixed with 100 grams of

water was determined to be 138 cubic centimeters. The inner diameter of the

measuring cylinder is 27 mm. With this data, the height of the cylinder was set to 241

mm. The Primitives tool was used to create the geometry setting the radius to 13.5

millimeters and the height along the y-direction to 241 millimeters. The geometry

origin was set to (0,0,0). Once the geometry was set, the cylinder was generated. The

final volume was then verified and compared with the experimental setup.

16

The mesh was then created for the simulation using ANSYS Mesh. The geometry is

simple enough to utilize the Multizone method all Quad elements and Inflation to

refine the mesh around the cylinder wall. Mesh Defeaturing and Use Adaptive Sizing

were both deactivated to improve the mesh quality. Capture Proximity and Capture

Curvature were subsequently activated which minimizes the mesh size. The

remaining settings were left unchanged. The initial element size was set to 0.025

meters, resulting in 450388 elements. For this simulation, there is no inlet or outlet

and all the surfaces are going to be set to Wall boundary condition. Named Select

Faces was used to define the top, bottom and cylinder wall which are to be setup in

Fluent. The final mesh can be seen in figure 8.

Figure 8: Mesh of measuring cylinder model utilizing Multizone and Inflation mesh

method, 450388 elements

Now that the mesh has been defined, the simulation can be setup in Fluent. In the

Fluent Launcher, Double precision is activated which is recommended when using the

Multiphase modeler. When Fluent is opened, a mesh check is performed to see if

there are errors in the mesh or if Fluent has problems reading the mesh. The next step

is to set the simulation as transient and activate gravity setting it to -9.81 m/𝑠2 along

the y-direction. The Model section was then entered too define which models will be

used for the model. The first Model to be selected is Multiphase, which is set to

Eulerian. After the Multiphase Eulerian model is selected, the materials need to be

determined. Since Multiphase Eulerian sees all phases as continuous phases, both the

water and apatite are setup as fluids. Water is added from Fluent Database as water-

liquid with the predetermined material data whereas apatite is defined from air where

17

the density is changed to 2970 kg/𝑚3. The governing equations of the phase

definition will determine the viscosity of the mixture on its own.

When the materials have been defined, the Multiphase model is re-entered. In the

phases tab, the Primary Phase material is set to water-liquid and the Secondary Phase

is set to apatite. The Secondary Phase is also stated to be granular with the diameter

being set to 50 µm. The next step is to define the viscosities so the model can

determine the sheer stress viscosity of the apatite phase. The setting were selected

according to (ANSYS Multiphase, 2009) and (Li, et al., 2018) for modelling solid

particles in Multiphase flow. The sheer stress viscosity consists of the Granular

viscosity, Granular Bulk viscosity and Frictional viscosity. Granular viscosity is set to

Syamlal-Obrien which calculates the granular viscosity according to Symalal and

O’brien’s equation (Syamlal, et al., 1993), The Granular Bulk viscosity is set to Lun-

et-al which calculates the solid particles bulk viscosity according to a formula (Lun, et

al., 1984), and the Frictional viscosity is set to Schaeffer (Scheaffer, 1987). These

settings individually calculate the viscosity based on several parameters including the

volume fraction, density, diameter, collision restitution, granular temperature and the

radial distribution of the solid phase (ANSYS Multiphase, 2009). The Frictional

Pressure is set to Johnson-Jackson, which calculates the pressure gradient of the

granular phase momentum equation (Johnson & Jackson, 1987). The Friction Packing

Limit is left as the default input of 0.61, as is the Angle of Internal Friction of 30

degrees. The Maximum Packing Limit is set based on experimental data collected

from the physical test. Frictional Modulus and Elasticity Modulus are set to derive.

Next, the Phase Interaction is considered. This section dictates how the water interacts

with the apatite and how the apatite interacts with itself. The Drag-Coefficient is set to

Syamlal-Obrien that is best suited for liquid-solid interaction. The Lift Coefficient is

set to none since the inclusion of Lift Coefficient for a solid phase that is closely

packed or consists of small particles has little to no effect (ANSYS Def. EM, 2009).

The Surface Tension coefficient is then specified using the surface tension of water,

setting a constant value of 7.5 N/mm. For the solid-solid phase interaction the

Restitution Coefficient is set to 0.2.

The next step is defining the viscous model. The turbulence model used for this

simulation was k-ϵ, which is recommended for multiphase flow. The Enhanced Wall

Treatment is selected since it is uncertain whether the mesh is fine enough at the walls

18

to use Scalable Wall Function. The k-ϵ model used was Standard which is the default

setting. The Turbulence Multiphase Model was set to Mixture. This model sets that

the phases will share k-ϵ equations which is a simpler model than Per Phase

Turbulence Model which sets individual k-ϵ equations for the phases. Mixture model

was chosen to reduce the computational burden and achieve better convergence.

Next, the Boundary Conditions are considered. For this simulation, no inlet or outlet

exist and instead only wall boundaries are used. Each Wall is set so the Wall Motion

is Stationary Wall and No Slip condition is set for water while Specularity Restitution

slip condition was considered for apatite. The value for Specularity Restitution was

set to 0.45 (Li, et al., 2018). These conditions were set for the all surfaces. Wall

motion is set to Stationary Wall for all surfaces.

In the Solution Methods tab, the Coupling and Discretization equations are set. The

Pressure-Velocity Coupling Scheme is set to Phase Coupled SIMPLE and Solve N-

Phase Volume Fraction Equations activated. The Spatial Discretization Gradient and

Pressure are set to Least Squares Cell Based and Second Order respectfully, which are

the default settings. Momentum, Turbulent Kinetic Energy and Turbulent Dissipation

Rate are all set to Second Order Upwind, which is a more precise method compared

with First Order Upwind. Volume Fraction is set to First Order Upwind which is the

default input. For the Transient Formulation, Second Order Implicit is used to achieve

higher precision of the results.

Now that the Solution Method is set, the initial values are set in Solution

Initialization. Under Solution Initialization, the Initialization Method is set to

Standard Initialization. Compute From is left blank so the initialization occurs from

all surfaces. The Initial Values all remain as default input apart from Turbulent

Kinetic Energy and Turbulent Dissipation Rate for both water and apatite that are set

to 0.001. The Volume Fraction of apatite was set to 0.25 which replicated the physical

experiment. The solution is now initialized.

Final step is to setup Solution Run Calculation. Time Advancement Type is set to

Fixed and Method set to User-Specified. The Parameters are set so the Number of

Time Steps is set to 500 000 and Time Step Size is set to 0.002 s giving the solution a

total time of 16 minutes and 40 seconds. Max Iterations/Time step is set to 250,

Reporting Interval and Profile Update Interval remained as default values of 1.

19

The residual convergence values were changed so that each of the residuals that were

calculated had to achieve 1e-5 for the simulation to be considered converged.

3.3 Flow Simulation

The flow simulations are intended to show the behavior of the flow, distribution of

apatite, pressure losses and how sedimentation affects the flow for a horizontal pipe

section. This simulation will give an initial estimate to the particle distribution and the

pressure gradient. For long distance slurry transport, the velocity of the slurry is most

chosen based on the deposition velocity of the solid particles. The deposition velocity

is chosen based on the particle diameter, particle density and the diameter of the

pipeline. To see if the slurry has been deposited or not during the transportation, the

particle distribution is studied. If the velocity that was chosen for the simulation is

sufficient to avoid deposition, the slurry will be evenly distributed in the pipeline. A

flow, which shows a near homogenous distribution, is referred to as pseudo-

homogenous flow and is distinguished in long distance slurry flow. The diameter of

the pipeline is set to 0.25 meters.

3.3.1 Horizontal pipe – Comparison

In order to determine how well the model predicts the concentration of apatite as it

flows in the pipeline, a control model was created which replicated the setup in figure

5AI from (Li, et al., 2018). This was to obtain some validation of the model and

determine how well it can perform slurry flow simulations. The model produced by

(Li, et al., 2018) has been validated against empirical data which shows that ANSYS

Fluent Multiphase can produce reliable results for slurry transport.

The geometry for the model was a horizontal pipeline of length L = 6 meters and

diameter D = 103 mm. The mesh method used was Sweep with an element size of

0.015 meters. Mesh Defeaturing was deactivated and Capture proximity was

activated. The mesh size was set to 0.015 meters and resulted in 408033 elements.

When the mesh process was completed, the model setup was started using Fluent. As

with the measuring cylinder simulation, using ANSYS Fluent Launcher double

precision was activated. This simulation was set to steady state. Gravity was enabled,

setting it to -9.81 m/s2 along the y-direction.

20

The Multiphase Model and the Viscous Model were both set up using the same

method as described in section 3.2 in this report. The boundary conditions for the

simulation were then set. For the Inlet, the Velocity magnitude was set to 3 m/s. Since

the flow is internal, the best practice of setting Turbulence is using Specification

Method Intensity and Hydraulic Diameter. The Volume Fraction on the inlet was set

to 0.25 since 25% of the volume will be apatite. The Intensity is set to the default

value of 5% and the Hydraulic Diameter was set to 0.25 meters, the pipeline diameter.

The outlet is set so the gauge-pressure is zero Pa and as with the inlet, Turbulence is

set using Specification Method Intensity and Hydraulic Diameter. The Intensity value

is set as default at 5% and the Hydraulic Diameter is set to 0.25 meter. The sidewall,

pipe wall, is set so the Wall Motion is Stationary Wall and Shear Condition was set to

No slip for both water and apatite.

The Solution Methods used were set to the same settings used for the measuring

cylinder simulation discussed in section 3.2. In the Solution Initialization, Second-

Order Upwind was set for Momentum. Under Solution, Run Calculation was set so

the Number of Iterations were 20000, Reporting Interval set to 1 and Profile Update

Interval set to 1.

3.3.2 Horizontal pipe – Steady

To begin, a simple horizontal pipe was created. The pipe length was set to 2.5 meters,

which was selected to reduce the computation time and 25 meters should the results

necessitate for studying a longer pipeline section. The geometry was created ins

ANSYS DesignModeler since the geometry did not necessitate in any more advanced

CAD software due to its simplicity. A Primitive Cylinder was created and generated.

The mesh was then created using Mesh. The mesh is pre-set to CFD and Fluent mesh

that remained since it is the desired program. Furthermore, the mesh method was

selected. Since the geometry is a simple pipe, Multizone method was used and all

Quads was activated. All Quads attempts to create a mesh of hexahedral shaped

elements, which is desired for CFD meshing. Inflation was also used to refine the

elements close to the pipeline wall. In cases where this is not possible, tetrahedral

elements was used instead. Under Mesh Sizing, Adaptive mesh sizing and Mesh

Defeaturing were deactivated while Capture Proximity and Capture Curvature was

activated. The initial element size was set to 0.02 meters and a mesh convergence

21

study was executed to ensure that the mesh elements were appropriately sized. The

final mesh can be seen in figure 9.

a) b)

Figure 9: Mesh of pipeline utilizing a) Multizone and Inflation mesh method,

510456 elements and b) Sweep mesh method, 470088 elements

Once the mesh was generated, Create Name Selected was used to define the surface to

be used as inlet, outlet and pipeline wall. This is done so that Fluent can recognize the

type of boundary that is necessary for the simulation. Figure 10 shows the inlet, outlet

and pipeline-wall respectfully.

a) b)

c)

Figure 10: Named Select Faces for Inlet, Outlet and Pipe wall used to set boundary

values in ANSYS Fluent

22

When the mesh process was completed, the model setup was started using Fluent. As

with the measuring cylinder simulation, using ANSYS Fluent Launcher double

precision was activated. This simulation is done for both steady-state and transient

flow, to examine the flow pattern when it is stable and determine how the flow

behaves when the slurry has been deposited. This was to gain information on flow

changes over time and when steady state was achieved. Gravity was enabled, setting it

to -9.81 m/s2 along the y-direction.

The Multiphase Model and the Viscous Model were both set up using the same

method as described in section 3.2 in this report. The boundary conditions for the

simulation were then set. Because of the name selection created during the Mesh

process, ANSYS Fluent has set up the faces as the correct boundaries. For the Inlet,

the Velocity magnitude was set to 2 m/s. Since the flow is internal, the best practice

of setting Turbulence is using Specification Method Intensity and Hydraulic

Diameter. The Volume Fraction on the inlet was set to 0.25 since 25% of the volume

will be apatite. The Intensity is set to the default value of 5% and the Hydraulic

Diameter was set to 0.25 meters, the pipeline diameter. The outlet is set so the gauge-

pressure is zero Pa and as with the inlet, Turbulence is set using Specification Method

Intensity and Hydraulic Diameter. The Intensity value is set as default at 5% and the

Hydraulic Diameter is set to 0.25 meter. The sidewall, pipe wall, is set so the Wall

Motion is Stationary Wall and Shear Condition was set to No slip for both water and

apatite.

The Solution Methods used were set to the same settings used for the measuring

cylinder simulation discussed in section 3.2. In the Solution Initialization, Second-

Order Upwind was set for Momentum. Under Solution, Run Calculation was set so

the Number of Iterations were 20000, Reporting Interval set to 1 and Profile Update

Interval set to 1.

3.3.3 Horizontal Pipe – Sedimented

In order to determine the flow behavior if a longer stop has occurred and

sedimentation has happened, a flow analysis was created where the Initial Conditions

were set so the apatite volume fraction was non-homogenous. The geometry and mesh

used for the model were taken from the steady simulation where the pipe length was

23

2.5 meters. The model was now set to transient to calculate the behavior of the flow

reaching a steady state.

The Phase Definition and Interaction were set with the same input as with the steady

flow simulation in section 3.3.1. The boundary conditions used were No-Slip for both

apatite and water to ensure convergence and the Inlet and Outlet conditions were set

the same as in section 3.3.1. In order to set the Initial Condition of the volume

fraction, a Patch is created. The volume that is to be patched is the volume of the

sedimented slurry which is determined from equation 24. Once the patch has been

made, Run Calculation can be setup.

The total number of time steps is set to 20000, the time step size is set to 0.05

seconds, Reporting Interval set to 1 and Profile Update Interval set to 1.

3.4 Freezing Model

The freezing model is created to see the risk of freezing for various stages of the

pipeline. For this thesis work, most of the pipeline is assumed to be dug underground

and surrounded by earth, which will give an extra insulation. However, there could be

certain sections of the pipeline where this is not possible, and the pipeline is exposed

to the very low temperatures experienced of the arctic climate. With these

assumptions in mind, a few different computational setups were created to obtain a

better understanding of the freezing risk for entirety of the pipeline. The freezing

model will be used when the slurry is flowing during normal operation as well as

stationary if there is a stop of flow for maintenance or repairs of the pipe or pumps.

Since the pipeline will, as stated, be placed underground for most of the length,

setting the ambient temperature as the ground temperature is most prevalent. Using

data from Trafikverket, the lowest temperature recorded during the winter of 2020 to

2021 was -4°C at 1 meter below the surface which, is the ideal depth for the pipeline.

3.4.1 Freezing Model – ANSYS Fluent Control

A control model was first developed in order to verify the numerical model results.

The idea was to compare the heat flow simulation with a separately developed

numerical simulation using MATLAB.

Now that the boundary temperature has been established, a model can be created

using ANSYS Fluent. To start a two-dimensional model was created to reduce the

24

calculation time. This model was a simple 1-by-1-meter square which will be used as

a base to compare with a separately developed a numerical solution in MATLAB. For

this simulation, two separate cases were created. One case which utilized the

solidification/melting model and one which did not utilize it. This was done for two

reasons: the case without solidification/melting will be compared with a separately

developed analytical solution done using MATLAB to see its accuracy. The other

reason is to see the effects of having some of the slurry freeze and act as insulation,

which would affect the heat transfer. Figure 11 shows the geometry of the square.

Figure 11: Geometry of 1-by-1-meter square with Sweep mesh method, 10000

elements

The mesh method was set to automatic with all quads selected. Mesh defeaturing was

deselected and Capture proximity was selected. The element size was set to 0.01

meters to obtain the same number of elements as the model developed using

MATLAB.

In ANSYS Fluent Launcher, Double precision was activated to enhance the

calculation. In the General settings of ANSYS Fluent, Time was set too transient. No

gravity is included for this simulation to keep the simulation as similar as possible to

the separate analytical solution created using MATLAB. The 2D Space is set to

Planar.

As stated, this simulation will be run both with and without the Solidification/Melting

model. To begin with, a calculation will be performed without Solidification/Melting

and subsequently only energy model will be used, the turbulence and flow equations

are deactivated. The material water-liquid was then added to the simulation with all

25

values set as default. Water-liquid was then defined as the material for Cell Zone

Condition. The boundary conditions were set as No-Slip for Momentum and -4°C for

Thermal Temperature.

For the simulation, which utilizes Solidification/Melting, the material constants for

water-liquid were changed to piecewise-linear functions for the density, thermal

conductivity, and specific heat capacity. The material data was collected from

(Engineering Toolbox, 2004). The solidus and liquidus temperatures were set to 0°C

and the melting heat set to 334000 j/kg. The boundary conditions were set as No-slip

for momentum and -4°C for Thermal Temperature.

The convergence criteria were set to 1e-4, solution control was set to SIMPLE and

Spatial Discretization for Pressure was set to PRESTO! which is recommended for a

Solidification/Melting model simulation (Ansys Solidification/Melting 2016). The

Solution Control Under-Relaxation Factors were set as default for all except for

Liquid Fraction update which is set to 0.1. The time step size was set to 0.01 seconds

and number of time steps set to 30000.

3.4.2 Freezing Model – MATLAB Control

With the freezing model produced using ANSYS Fluent, a separate model was

produced using MATLAB, which replicated the control scenario. The model created

was an explicit model and utilized the two-dimensional heat equation where the

material data required is the thermal expansion coefficient. This equation does not

consider that the control area freezes at a given temperature which is why a non-

freezing model was created using ANSYS Fluent.

The two-dimensional heat equation can be found in Appendix 2 Numerical heat flow

model in MATLAB along with the MATLAB script in Appendix 4.

An iterative calculation method was produced. First the variables were defined, these

including the lengths in both x and y direction being set to 1, the total calculation time

set to 400 seconds. The total calculation time was set to this initially however was

altered to see the exact time at which the final node reached a temperature of 0°C. The

delta values were also set to 0.01 for Δx and Δy and 0.0002 for Δt. Next, the initial

temperature was set to 4°C and the boundary values were set to -4°C as used for the

model. Figure 12 shows the initial conditions for the explicit simulation.

26

Figure 12: Initial conditions of explicit MATLAB heat-equation solver 1-by-1-meter,

initial temperature 4°C and boundary temperature -4°C

When the initial conditions and boundary values were set, the iteration process was

established. The iterations were created so the temperature is first calculated along the

y-direction, then along the x-direction and finally in time t. Once the calculation

completed all the iterations, a surface plot was produced to determine the temperature

of the surface at the final time. The total calculation time was then altered to meet the

criteria of the final node reaching 0°C. The MATLAB script can be found in

Appendix 3 for further detail regarding the calculation.

3.4.3 Freezing Model – Pipeline

The pipeline section that will be used for the simulations was a 1-meter section of the

pipeline. The Mesh considered was a Multizone mesh with the element size being set

to 0.006 meters resulting in 459000 elements. Figure 13 shows the mesh of the 1-

meter section of pipeline with the pipeline wall.

27

Figure 13: Mesh of 1-meter pipeline for freezing simulation utilizing Multizone and

Inflation mesh method

Double precision is activated in Fluent Launcher. In ANSYS Fluent the simulation is

set to transient since it is desired to determine the volume which has been frozen at a

certain time. Gravity is also activated and set to -9.81 𝑚/𝑠2.

Solidification/Melting model is then activated, and mushy zone coefficient is set to

default value of 10000. Water-Liquid is then added to the materials list from the

Fluent Database. The solidus and liquidus temperatures are set to 0°C which sets the

temperature at which the phase transition will occur. The Pure Solvent Melting Heat

is set to 334000 J/kg which is the heat required to melt or freeze water. Density,

Thermal Conductivity and Specific heat capacity are all defined as linear-piecewise

functions with data for both water and ice, this data is collected from Engineering

Toolbox (Engineering Toolbox, 2004). By setting these values, the model will

consider that 0°C is ice and anything above this value is water.

The Boundary Conditions are initially set so the inlet and outlet are regarded as walls.

This will replicate the scenario without flow. Setting the inlet and outlet as walls

instead of setting the velocity as 0 m/s was done to simplify the calculation. No Slip

conditions were set for all walls while a temperature of -20°C was set for the pipe

wall and the inlet and outlet temperatures were set to 1°C. A wall was also added to

the pipeline wall with a thickness set to 0.015 mm and material stated as steel.

The Solution Method Scheme was set to SIMPLE and Spatial Discretization for

Pressure was set to “PRESTO!” which is recommended for a Solidification/Melting

model simulation. The Solution Control Under-Relaxation Factors were set as default

28

for all except for Liquid Fraction update which is set to 0.1. The Solution Equations

are set so the Flow equations are deactivated for the simulation. This is done to reduce

the computational burden for the simulation.

The Solution Initialization is set so the temperature is 4°C and all other variables are

set as default.

29

4 Results

In this section, the results from the experiments and simulations are presented.

4.1 Holistic Perspective

The main parameters found from the holistic perspective analysis in Appendix 1 are

displayed in table 1.

Table 1: Results from holistic perspective analysis where velocity is 2 m/s, pipe

diameter 250 mm, pipe length 300 km, inlet outlet height difference of 450 meters,

solid particle diameter 𝑑50 = 50 𝜇𝑚, pump efficiency 𝑒𝑛 = 0.9, mass fraction 50%

apatite and particle density 2970 kg/𝑚3

Parameter Value

Total Flow rate 0.0981 𝑚3/𝑠

Slurry density 1490 kg/𝑚3

Apatite mass flow rate 73.3 𝑘𝑔/𝑠

Apatite annual mass flow rate 2.31 Mtons/year

Head requirement in meters slurry 5912 m

Total Pressure requirement 86.8 MPa

Power Consumption 9450 kW

Energy requirement 35.8 kWh per ton of apatite

The results from the holistic perspective analysis shows that the total pressure loss is

~87 MPa. This pressure loss would require 3-4 separate pump stations to deliver

apatite at a rate of 73 kg/s.

4.2 Sedimentation Analysis

The results from the sedimentation analysis yields the maximum packing limit for the

solid particles in the slurry and are recorded in table 2. The packing limit is derived by

dividing the volume of solid particles by the volume of the settled slurry.

30

Table 2: Results from sedimentation experiments using measuring cylinder with

varying mass of tailing sand and water

The average Maximum packing limit is determined as 39.14% which is the value that

will be entered into ANSYS Fluent for the Multiphase model.

a) b)

Figure 14: Volume fraction of apatite in sedimentation simulation for measuring

cylinder with 100 grams of apatite and 100 grams of water at time a) t = 0 seconds

and b) t = 245 seconds

Figure 14.a) shows the homogenous slurry at the start of the simulation, no deposition

of solid particles has occurred. Figure 14.b) shows that the settled slurry volume is

~90 ml at time t = 245 seconds.

Mass [g] Total Volume

[𝑐𝑚3]

Sedimentation

Volume after 1

hour [𝑐𝑚3]

Sedimentation

Volume after 24

hours [𝑐𝑚3]

Maximum

packing limit [%]

75 106 78 76 39.57

100 138 100 98 38.21

125 174 124 122 39.65

31

a) b) c)

Figure 15: Sedimentation experimental test with 100 grams of tailing sand and 100

grams of water in measuring cylinder at time a) t = 0 seconds, b) t = 245 seconds and

c) t = 40 minutes

Figure 15 shows the experimental sedimentation analysis. Figure 15.a) depicts the

tailing sand homogenously distributed in the water at the start of the analysis, time t =

0 seconds. Figure 15.b) shows that some deposition has occurred at time t = 245

seconds, the deposited slurry has a volume of ~130 ml. Figure 15.c) shows the

deposited tailing sand at time t = 40 minutes, with a volume of ~98 ml.

32

4.3 Flow Model – Comparison

The control model for flow was set according to figure 5AI from (Li, et al., 2018)

which geometry and input data was used to verify the model developed for this thesis.

I) II)

III) IV)

Figure 16: Solid particle concentration for flow in a pipeline with pipe diameter D =

103 mm, particle diameter d = 90 μm, particle density ρ=2520 kg/𝑚3, solid particle

concentration 𝐶𝑎𝑓 = 19% and velocity v = 3 m/s utilizing Sweep mesh method and

1e-3 convergence criteria

Figure 16.I) shows the contour of the volume fraction of solid particles at L = 5

meters. The volume fraction of solid particles is the percentage of volume taken up by

the solid particles. Figure 16.II) shows the volume faction on a rake from the top of

the pipe to the bottom at the center of the pipe at L = 5 meters with the red line

replicating the volume fraction from (Li, et al., 2018). The value along the x-axis in

figure 16.II) is volume fraction ratio where the volume fraction is divided by 19%.

Figure 16.III) and 16.IV) are taken from (Li, et al., 2018). Figure 16.III) shows the

volume fraction for cross-section at length L = 5 meters. Figure 16.IV) shows the

volume fraction ratio of the volume fraction divided by 19% along the x-axis. The

dimensionless height of the pipeline is set along the y-axis.

33

4.4 Flow Model – Steady

Below are the results from the steady flow simulations. The results are depicted for a

variety of velocities and apatite particle sizes. Each model was created with two

different mesh methods and had two different convergence criteria: one where the

mesh method was set to Multizone and Inflation and the convergence criteria was set

to 1e-3. The other where the mesh method was set to Sweep, and the convergence

criteria was set to 1e-5. The mesh sizes were similar, number of elements being

~500000. The first results depict the apatite concentration in a cross-section of the

pipeline for a range of velocities. The concentration of apatite contour, rake and

velocity profiles were all measured at L = 21 meters.

34

a.I.) a.II.)

b.I) b.II)

c.I) c.II)

Figure 17: Apatite concentration contour and graph for flow in a pipeline with

diameter D = 250 mm, particle diameter d=50μm, particle density ρ=2970 kg/𝑚3,

apatite concentration 𝐶𝑎𝑓 = 25%, a) v=2 m/s, b) v=2.5 m/s and c) v=3 m/s utilizing

Multizone and Inflation mesh method and 1e-5 convergence criteria

Figures 17 a.I), 17 b.I) and 17 c.I) shows the volume fraction of apatite on a pipeline

cross-section measured at L = 21 meters with an inlet velocity of 2 m/s, 2.5 m/s and 3

m/s respectfully. The figures depict the results from simulations with the model

utilizing Multizone and Inflation mesh method. The color scale shows the different

volume fraction of apatite on the cross-section. Figures 17 a.II), 17 b.II) and 17 c.II)

35

shows the volume fraction ratio as a rake from the top of the pipeline to the bottom at

L = 21 meters for 2 m/s, 2.5 m/s and 3 m/s respectfully. The volume fraction ratio is

the volume fraction at a certain point divided by 25%. The volume fraction ratio is set

along the x-axis and the height of the pipeline is set along the y-axis in the figures.

a.I) a.II)

b.I) b.II)

c.I) c.II)

Figure 18: Apatite concentration contour and graph for flow in a pipeline with

diameter D = 250 mm, particle diameter d=50μm, particle density ρ=2970 kg/𝑚3,

apatite concentration 𝐶𝑎𝑓 = 25%, a) v=2 m/s, b) v=2.5 m/s and c) v=3 m/s utilizing

Sweep mesh method and 1e-3 convergence criteria

36

Figures 18 a.I), 18 b.I) and 18 c.I) shows the volume fraction of apatite on a pipeline

cross-section at length L = 21 meters for 2 m/s, 2.5 m/s and 3 m/s respectfully.

Figures 18 a.I), 18 b.I) and 18 c.I) are the results from simulations where the model

utilized Sweep mesh method and 1e-3 convergence criteria. A color scale is used to

show the volume fraction of apatite on the cross-section. Figures 18 a.II), 18 b.II) and

18 c.II) depict the volume fraction ratio of apatite at a rake from the bottom of the

pipeline to the top at length L = 21 meters for 2 m/s, 2.5 m/s and 3 m/s slurry velocity

respectfully. The volume fraction ratio is set along the x-axis and the vertical position

in the pipe along the y-axis. The volume fraction ratio of apatite is the volume

fraction at a set point divided by 25%. Figures 18 a.I) and 18 a.II) shows that the

slurry is pseudo-homogenous and deposition of solid particles has not occurred.

Figures 18 b.I) and 18 b.II) shows that the slurry is more pseudo-homogenous. Figure

18 c.I) and 18 c.II) shows that the slurry is even pseudo-homogenous.

The second analysis was a change of particle diameter, setting it to 50, 100 and 150

μm respectfully. Two models were analyzed: one that utilized Multizone and Inflation

mesh method, and one that utilized Sweep mesh method.

37

a.I) a.II)

b.I) b.II)

c.I) c.II)

Figure 19: Apatite concentration contour and graph for flow in a pipeline with

diameter D = 250 mm, velocity v = 2 m/s, particle density ρ=2970 kg/𝑚3, apatite

concentration 𝐶𝑎𝑓 = 25%, particle diameter a) d = 50 µm, b) d =100 µm and c)

d=150 µm, utilizing Multizone and Inflation mesh method

Figures 19 a.I), 19 b.I) and 19 c.I) shows the volume fraction of apatite on a pipeline

cross-section at length L = 21 meters for apatite particle diameters of 50, 100 and 150

micrometers respectfully. A color range is used represent the various volume fractions

of apatite on the cross-section. Figures 19 a.II), 19 b.II) and 19 c.II) depicts the

volume fraction ratio of apatite along a vertical rake from the top to the bottom of the

pipeline at length L = 21 meters. The volume fraction ratio of apatite is set along the

38

x-axis and the vertical placement in the pipeline along the y-axis. The volume fraction

ratio is the volume fraction divided by 25%, the inlet volume fraction. Figures 19 a.I)

and 19 a.II) shows that the slurry is pseudo-homogenous and deposition of solid

particles has not occurred. Figures 19 b.I) and 19 b.II) shows that the slurry is more

heterogeneous however no deposition of solid particles has occurred. Figure 19 c.I)

and 19 c.II) shows that the slurry is not pseudo-homogenous and that deposition of

solid particles has occurred.

39

a.I) a.II)

b.I) b.II)

c.I) c.II)

Figure 20: Apatite concentration contour and graph for flow in a pipeline with

diameter D = 250 mm, velocity v = 2 m/s, particle density ρ=2970 kg/𝑚3, apatite

concentration 𝐶𝑎𝑓 = 25%, particle diameter a) d = 50 µm, b) d =100 µm and c)

d=150 µm, utilizing Sweep mesh method

Figures 20 a.I), 20 b.I) and 20 c.I) shows the volume fraction of apatite on a pipeline

cross-section at length L = 21 meters for apatite particle diameters of 50, 100 and 150

micrometers respectfully. A color range is used represent the various volume fractions

of apatite on the cross-section. Figures 20 a.II), 20 b.II) and 20 c.II) depicts the

volume fraction ratio of apatite along a vertical rake from the top to the bottom of the

pipeline at length L = 21 meters. The volume fraction ratio of apatite is set along the

40

x-axis and the vertical placement in the pipeline along the y-axis. The volume fraction

ratio is the volume fraction divided by 25%, the inlet volume fraction. Figures 20 a.I)

and 20 a.II) shows that the slurry is pseudo-homogenous and deposition of solid

particles has not occurred. Figures 20 b.I) and 20 b.II) shows that the slurry is more

heterogeneous however no deposition of solid particles has occurred. Figure 20 c.I)

and 20 c.II) shows that the slurry is not pseudo-homogenous and that deposition of

solid particles has occurred.

The velocity profile was also studied for various particle sizes and depicted in figures

21 and 22. As with the concentration of apatite analysis, both Multizone and Inflation

mesh method and Sweep mesh method were analyzed.

41

a)

b)

c)

Figure 21: Velocity profiles of water in slurry flowing in pipeline with pipe diameter

D=250 mm, velocity v=2 m/s, apatite volume concentration 𝐶𝑎𝑓 = 25%, apatite

particle diameter a) d=50 µm, b) d=100 µm and c) d=150 μm utilizing Multizone and

Inflation mesh method and convergence criteria 1e-5

Figures 21 a), 21 b) and 21 c) shows the velocity profile of the water phase inside the

pipeline measured from the bottom to the top of the pipeline at L = 21 meters for

particle diameters of 50, 100 and 150 micrometers respectfully. The velocity

magnitude is set along the x-axis and vertical position in the pipeline is set along the

y-axis. Figure 21 a) shows an even, well-formed velocity profile. Figure 21 b) shows

42

an even velocity profile. Figure 21 c) shows an uneven velocity profile where the

velocity is 1.5 m/s near the bottom of the pipeline and deposition of solid particles has

occurred.

a)

b)

c)

Figure 22: Velocity profiles of water in slurry flowing in pipeline with pipe diameter

D=250 mm, velocity v=2 m/s, apatite volume concentration 𝐶𝑎𝑓 = 25%, apatite

particle diameter a) d=50 µm, b) d=100 µm and c) d=150 μm utilizing Sweep mesh

method and convergence criteria 1e-3

Figures 22 a), 22 b) and 22 c) shows the velocity profile of the water phase inside the

pipeline measured from the bottom to the top of the pipeline at L = 21 meters. The

velocity magnitude is set along the x-axis and vertical position in the pipeline is set

43

along the y-axis. Figure 22 a) shows an even, well-formed velocity profile. Figure 22

b) shows an even velocity profile. Figure 22 c) shows an uneven velocity profile

where the velocity is 1.5 m/s near the bottom of the pipeline and deposition of solid

particles has occurred.

The pressure gradients were studied, and the results are displayed in figures 23 a), 23

b) and 23 c). The pressure gradient as the derivative of pressure with respect to z,

which is the direction of the pipeline and is set along the y-axis. The position along

the pipeline in the flow direction is set along the x-axis. The pressure gradient depicts

the decrease in pressure per meter of pipeline. The pressure gradient stabilizes after

certain length of pipeline. The pressure gradient for slurry with solid particles

diameter of 50 micrometers, figure 23 a), is ~85 Pa/m. With solid particles diameter

of 100 micrometers, figure 23 b), the pressure gradient is ~90 Pa/m. With solid

particles diameter of 150 micrometers, figure 23 c) the pressure gradient is ~140

Pa/m.

44

a)

b)

c)

Figure 23: Pressure gradient in pipeline with pipe diameter D=250 mm, velocity v=2

m/s, apatite volume concentration 𝐶𝑎𝑓 = 25%, apatite particle diameter a) d=50 µm,

b) d=100 µm and c) d=150 μm utilizing Sweep mesh method and convergence

criteria 1e-3

45

4.5 Flow Model – Transient

The transient simulation shows how the flow behaves after a shutdown where the

solid apatite particles have deposited at the bottom of the pipeline. The volume

fraction for the deposited apatite particles is taken from the sedimentation analysis

performed with the measuring cylinders.

a)

b)

Figure 24: Flow in 2.5-meter pipeline with deposited particles at the bottom of the

pipeline where the pipeline diameter D = 250 mm, apatite particle diameter d =

50μm, velocity v = 2 m/s, apatite concentration 𝐶𝑎𝑓 = 25% at time a) t = 0 seconds

and b) t = 5 seconds with Sweep mesh method and convergence criteria 1e-3

Figure 24 a) shows the volume fraction of the deposited apatite inside the pipeline of

length L = 2.5 meters. This volume fraction is set to 39.14% for the deposited apatite

particles and the remaining volume is pure water, volume fraction of 0% apatite. This

is to represent the distribution of apatite if flow is stopped over a longer time. Figure

24 b) shows the volume fraction of apatite when a constant flow is run for 5 seconds.

The slurry becomes pseudo-homogenous after 5 seconds of flow.

4.6 Freezing Model – MATLAB Control

The MATLAB control model shows that at time 282 seconds for all of the nodes too

reached a temperature of 0°C.

46

Figure 25: Temperature plot of 1-by-1-meter square with initial temperature of 4°C

and boundary temperature of -4°C at time t=282 seconds

Figure 25 shows the 1-by-1-meter plate where x-axis shows the length of the plate

and the y-axis shows the other length of the plate. The z-direction shows the

temperature in Celsius. The temperature for the node located at (0.5,0.5) is the last

node to reach 0°C at time t = 282 seconds.

4.7 Freezing Model – ANSYS Fluent Control

The freezing model control developed in ANSYS Fluent was simulated to determine

the time at which the temperature reached 0°C and compare the results with the

simulation results from the MATLAB developed model. The model was developed

with and without Solidification/Melting model.

a) b)

Figure 26: Temperature of 1-by-1-meter square in ANSYS Fluent with initial

temperature T = 4°C and boundary temperature T = -4°C without

Solidification/Melting model at time a) t = 0 sec and b) t = 30 sec

47

Figure 26 a) shows the temperature at the start of the simulation where the 1-by-1-

meter plate is 4°C except for the boundaries, which are set at -4°C. Figure 26 b)

shows the temperature of the at time t = 30 seconds where the 1-by-1-meter plate is -

1.5°C except for the boundaries where the temperature is -4°C.

Figure 27: Temperature plot over time for point located at (0.5,0.5) on 1-by-1-meter

square from ANSYS Fluent developed model without solidification/melting model with

initial temperature 4°C and boundary temperature -4°C

Figure 27 shows a time plot of the temperature of the node located at (0.5,0.5) on the

1-by-1-meter plates. The times is set along the x-axis and the temperature in Celsius is

set along the y-axis. Figure 27 shows that the node at (0.5,0.5) reaches 0°C after 20

seconds without solidification/melting model.

a) b)

Figure 28: Temperature of 1-by-1-meter square in ANSYS Fluent with initial

temperature T = 4°C and boundary temperature T = -4°C with Solidification/Melting

model at time a) t = 0 sec and b) t = 20 sec

48

a) b)

Figure 29: Liquid fraction of 1-by-1-meter square in ANSYS Fluent with initial

temperature T = 4°C and boundary temperature T = -4°C with Solidification/Melting

model at time a) t = 0 sec and b) t = 65 sec

Figure 30: Temperature of point located at (0.5,0.5) on 1-by-1-meter square over

time in ANSYS Fluent with initial temperature T = 4°C and boundary temperature T

= -4°C with Solidification/Melting model

49

Figure 31: Liquid fraction of point located at (0.5,0.5) on 1-by-1-meter square over

time in ANSYS Fluent with initial temperature T = 4°C and boundary temperature T

= -4°C with Solidification/Melting model

Figure 28 a) shows the temperature at the start of the simulation where the 1-by-1-

meter plate is 4°C except for the boundaries, which are set at -4°C. Figure 28 b)

shows the temperature of the at time t = 20 seconds where the 1-by-1-meter plate is

0°C except for the boundaries where the temperature is -4°C. Figure 29 a) shows the

liquid fraction, the fraction of water which is liquid at the start of the simulation, time

t = 0 seconds. Figure 29 b) shows the liquid fraction of the water at time t = 65

seconds. At time t = 65 seconds, figure 29 b) shows that the plate has completely

frozen and become ice. Figure 30 shows the temperature of the node located at

(0.5,0.5) over time. Flow time is set along the x-axis and temperature in Celsius is set

along the y-axis. Figure 30 shows that the node located at (0.5,0.5) reaches 0°C at

time t = 20 seconds. Figure 31 shows the liquid fraction of the node located at

(0.5,0.5) over time. The flow time is set along the x-axis and the temperature is set

along the y-axis. Figure 31 shows that the freezing process for the node located at

(0.5,0.5) starts at time t = 20 seconds. Figure 31 also shows that the node located at

(0.5,0.5) freezes completely at time t = 65 seconds. During the freezing process,

figure 30 shows that the temperature at the node located at (0.5,0.5) decreases from

0°C at time t = 20 seconds to -3.1°C at time t = 65 seconds.

50

4.8 Freezing Model – Pipeline

The freezing simulation for the pipeline model shows how the temperature and liquid

fraction changes over time. The measurement was taken at half the length of the

pipeline, L = 0.5 meters.

Figure 32: Temperature plot of 1 meter section of pipeline with water with initial

temperature 4°C and boundary temperature -4°C at time t=2634 seconds

Figure 33: Heat flux from the inner pipeline wall over time for stationary flow and

pipeline diameter D = 250 mm, boundary temperature T = -4°C and initial

temperature T = 4°C

Figure 32 shows the temperature of a cross-section of the 1-meter pipeline set at L =

0.5 meters at time t = 2634 seconds, roughly 44 minutes. The temperature of the solid

51

pipeline wall is -4°C and the temperature of the water is 2.97°C. Figure 33 shows the

heat-flux out of the inner wall of the pipeline, the wall between the pipeline and

water, over time. The flow time is set along the x-axis and the heat-flux, measured in

Watts, is set along the y-axis. At the start of the simulation, the heat-flux is 0 Watts.

During the first stage of the simulation the heat-flux has a minimum value at time t =

25 seconds where it reaches -500 W. As the simulation progresses, the heat-flux starts

to increase and stabilize. At time t = 1400 seconds, the heat flux is -54 W.

52

5 Discussion

The methods used for this thesis were a holistic perspective and the software ANSYS

Fluent to conduct an initial analysis of slurry transportation in a sub-arctic

environment. The idea behind the holistic perspective was to obtain a better

understanding of the pressure losses and the power consumption required to run the

pumps. The pipeline location used for this thesis should not be viewed as the final

rendition but as a guideline for future work that will give good input for further

development. A comprehensive script was developed which can be further developed

and used to obtain more assessments that are accurate if an exact placement of the

pipeline is made in the future.

The flow models were created in ANSYS Fluent which has been proven to be able to

calculate the solid particle concentration and velocity profile with to a high degree of

accuracy. For this thesis however, there were certain simplifications made which were

necessary due to the ANSYS License being limited and the computers, which were

unable to compute for elements ranging in the millions. This effected the Turbulence

model which could be used, necessitating in a simple Mixture Turbulence model

instead of the preferred Per phase Turbulence model due to the simulation not

yielding a converged result. Since this was discovered during the thesis work, in

retrospect it could have been beneficial to use a different program to solve the flow

problem. Initially, LS-Dyna was a potential other computational tool that could have

been used. LS-Dyna has capabilities of computing flow and multi-physics problems

with the ICFD keyword, see (Larsson, et al., 2020), (Larsson, et al., 2021) and

(Jonsén, et al., 2019). This was later abandoned due to a lack of time to develop

separate models for each program and a lack of experience with this tool but can be a

potential software for future work in this area.

Another aspect, which effects the results in the ANSYS Fluent models, is the

Multiphase model setup. There are a number of different setting which can be used

for defining the phases in Multiphase model. The setting chosen for this thesis work

may not be the most appropriate since the selection was made via recommendations

from ANSYS Study Guide along with (Li, et al., 2018) choice of phase definition for

the solid particles. Further analysis would be required to determine which settings are

most appropriate for the apatite phase.

53

The freezing models developed were limited due to the Multiphase model not being

applicable with Solidification/Melting model. This setback lead to the freezing model

only being developed with water as the fluid in the domain. The freezing process will

therefore be different from reality since the heat capacity is most likely different for

apatite than for water. An opportunity does arise when only water is used for the

simulation which is the freezing can be roughly calculated by hand. If it is assumed

the specific heat capacity is constant when the water is fluid and the heat flux from

the pipeline-wall is known along with the mass of water, the time for the water to

reach 0°C from the initial temperature 4°C can be calculated. From there the time it

takes for the water to freeze can be calculated. The latent heat capacity during the

phase change from water to ice is known and the heat flux from the pipeline-wall is

known. The two durations can then be added to give the total duration for water to go

from 4°C water to 0°C ice. This can serve as a control test to see if the simulation

yields a reasonable result. The idea of creating the control models was however, in

retrospect, of little relevance for freezing in the pipeline. It does however depict how

the Solidification/Melting model functions and how it effects the heat transfer.

The results from the flow simulation shows the particle distribution inside a pipeline

of 250 mm diameter for various velocities and particle sizes. The methods used for

the models were simplified in terms of both mesh and Turbulence model used. The

mesh generated was not fine enough to utilize Per phase Turbulence model. Looking

at (Li, et al., 2018) and (Kumar Gapaliya & Kaushal, 2016) models, the mesh

included around 10 million elements, which was not able to be replicated for this

thesis work. The reason for this is that the ANSYS Academic license does not allow

for more than ~500 thousand elements. When using Per phase turbulence with only

500 thousand elements, the solution did not give a converged result. This necessitated

in the use of Mixture Turbulence model that is more suited when the different phases

have a similar density i.e. a density ratio close to 1. In this case, the density ratio is ~3

which indicates that Per phase Turbulence model will yield better results.

The holistic perspective calculations show that the total flow of apatite is 2.31 million

tons per year. The pressure loss for this flow is roughly calculated to ~87 MPa which

would require 3-4 pump stations along the pipeline and a total energy requirement of

35.8 kWh/tons dry apatite. For these calculations, the losses that occur inside the

pump stations for instance are not accounted for, as they are considered minor losses.

54

The sedimentation simulation, figure 14, shows that the sedimented slurry at time t =

245 seconds is very different from the sedimented slurry volume at the same time for

the experimental setup. This difference is due to the particle sizes not being the same

and the shape of each particle in the model are perfect spheres while the tailing sand

in the experimental setup have more odd shape.

The control simulation results which replicated one of (Li, et al., 2018) models, but

utilized Mixture Turbulence model instead of Per phase Turbulence, shows that the

model can describe the concentration of apatite during flow in a pipeline. The contour

plane, figure 16, shows that there is a higher percentage of apatite at the bottom of the

pipeline than at the upper part, which is consistent with the simulation results

achieved by (Li, et al., 2018). The simulation results show 0.3% higher concentration

of solid particles when compared with (Li, et al., 2018) results shown in figure 16.III).

The model used for this verification has a more simplified mesh in comparison to the

other models. A simple sweep mesh is used without inflation and the convergence

criteria is set to 1e-3. This resulted in performing simulations with a Sweep mesh

method and convergence criteria set to 1e-3 for all other flow models.

The results from figure 17 shows that an increase in velocity decreases the spread of

the concentration of apatite in the pipeline. With higher velocity, the slurry becomes

more pseudo-homogenous. This is consistent with the findings of both (Li, et al.,

2018) and (Kumar Gapaliya & Kaushal, 2016). The increase in velocity will yield a

higher flow so more apatite can be transported over the same length of time. This

does however also affect the pressure losses. With a higher velocity comes a higher

pressure-loss and would require more powerful or even a larger number of pumps to

transport. Figure 18 shows the same behavior however for each velocity the slurry is

more homogenous, but the effect of the slurry becoming more homogenous with

increased velocity remains but to a lesser degree.

Figure 19 shows that as the particles in the slurry increase in diameter, the slurry

becomes less homogenous. With a particle diameter of 50 and 100 micrometers, the

slurry is still pseudo-homogenous but with a particle diameter of 150 micrometers, the

slurry has become a sedimented bed at the bottom of the pipeline. This behavior will

cause the pipeline to wear unevenly. This could over a longer period cause issues

which would require the pipeline to be changed. This behavior is apparent in both the

55

mesh method where Multizone and Inflation is utilized as well as Sweep method

depicted in figure 20.

The velocity profiles depicted in figure 21 for Multizone and Inflation mesh as well as

figure 22 for Sweep mesh both show that transporting slurry with an apatite particle

size of 50 and 100 micrometers will transport all the apatite particles at an even flow.

However, with a particle size of 150 micrometers, particles will not be transported as

desired due to the velocity being reduced near the bottom of the pipeline. The slurry

will not contain the desired amount of apatite at the outlet.

The pressure gradients, shown in figure 23, indicate that with larger particles, the

pressure gradient increases i.e. the pressure loss per meter pipeline is greater. This is

consistent with the findings of Kumar & Kaushal’s report (Kumar Gapaliya &

Kaushal, 2016). The pressure gradient is somewhat lower than the pressure gradient

for the holistic perspective where the pressure drop per meter of pipeline is 275 Pa/m

and the pressure drop from the simulation utilizing 150 micrometers stabilizes at ~130

Pa/m. It should be observed that the pressure gradients achieved is lower than the

pressure gradient for pure water in the holistic perspective. This indicates that the

pressure gradient derived from the models is not reliable. The actual apatite slurry has

an average particle size of about 50µm which in the horizontal pipeline in Figure 23

a) would require a pressure gradient of about 85 Pa/m However, the corresponding

gradient for water flow only at the same velocity (2 m/s) would be about 115 Pa/m.

The pressure requirement simulations are here uncertain for the slurry with a solids-

to-water density ratio of nearly 3 and a distribution of particle sizes. A finer mesh and

additional numerical capabilities may be required, which in turn would require a more

comprehensive tool license. The pressure requirement is discussed further in

Appendix 1.

The transient flow model in figure 24 shows how the solid particles would settle in

the pipeline if flow were to stop for a longer period. When the flow is initiated, the

particles start to flow with the slurry and again becomes pseudo-homogenous after ~5

seconds.

The freezing model results depicted in figure 25 shows that the temperature will reach

below 0°C for all nodes after 282 seconds. This model is very simple by design and

does not accurately depict reality but instead serves to compare with the model.

56

Figure 25 shows that the temperature reaches 0°C for all nodes well before 282

seconds, roughly 20 seconds. This disparity in results could be a result of an ill-

developed model in MATLAB which is an explicit model and could use improvement

to give more reliable results. An interesting result from the freezing simulation results

with Solidification/Melting model, figure 29 and 30, shows that the temperature is not

constant during the freezing process. This could be due to the solidus and liquidus

temperature set to the same temperature which

The results from the freezing simulation in the pipeline shows that the water inside

the pipeline can withstand freezing for ~44 minutes at least, since the temperature has

only decreased by 1°C from the initial temperature. The heat flow out of the pipeline

wall averages at ~76 Watts after over 20 minutes, which indicates that the water will

start to freeze after approximately 3 hours if the specific heat capacity is considered as

constant. The heat flow out of the pipeline wall does however decrease over time so

the time will be extended slightly. If a longer stop is required, insulation will be

needed around the pipeline to reduce the risk of freezing.

57

6 Conclusion and Future Work

The conclusions that can be made with confidence for the CFD models developed in

this thesis work to simulate the flow and freezing process as well as the holistic

perspective are as follows. The flow of apatite gives a pseudo-homogenous flow

pattern, which is desired for slurry transportation. Furthermore, the model can to some

degree simulate slurry transportation despite being simplified. It is uncertain how well

the model can describe slurry flow due to a lack of experimental data. A well-

instrumented experimental setup can be used to evaluate how well the model

describes the concentration of apatite particles as well as the shape of the velocity

profile. The developed CFD model has been a limiting factor for the results of this

thesis work as only a student license is available. By utilizing a full license and more

processing power, the steady and sedimented flow models could both be set to give

improved accuracy; Per Phase turbulence model and finer mesh are the recommended

changes.

The freezing model developed is limited due to the phase being modelled is water and

not slurry. However, it could be concluded that the fluid will not freeze for many

hours, if not longer with insulation surrounding the pipeline.

The holistic perspective calculations show that it would be possible to transport a

large quantity of slurry over a long distance. A pipeline is an environmentally friendly

solution with small maintenance and installation cost compared to railway. LKAB has

a good foundation to make further analysis to see if slurry transportation should be

considered as an alternative transportation method.

The future work that would be recommended is to continue to develop the models and

utilize a more complete license. This would open the possibilities of creating a finer

mesh and utilize Per Phase turbulence model which is highly recommended for

phases where the density ratio is larger than 1 (ANSYS Multiphase, 2009). Applying

this to the model, a more accurate pressure gradient could be determined, which is

important when designing the pipeline system. It would also be possible to model

more than one particle size of apatite in the same model. This would allow for

simulations of slurry flow where the particles are more representative of the particle

distribution curve in figure 6. Another possible future work is to model some more

complex geometries. This could be beneficial to determine the flow during elevation

changes or curvature over the terrain. The freezing model could also be further

58

developed. A more representative material could be used instead of pure water where

the slurry is modelled instead. This would give a more accurate simulation of the

freezing process.

59

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[Accessed 22 May 2021].

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port/processing/sorting/

[Accessed 20 May 2021].

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[Accessed 20 May 2021].

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Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General

Flow Field.. Journal of Fluid Mechanics, Volume 140, pp. 223-256.

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scattering/laser-diffraction

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the ASME.

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incompressible granular flow. Journal of Differential Equations, 66(1), pp. 19-50.

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61

pd-pump-range/26348-781545.html

[Accessed 09 June 2021].

62

8 Appendix 1 – Holistic Perspective

Equations used for holistic perspective for pseudo-homogenous long-distance

slurry transport. After Sellgren (1986).

A pseudo-homogenous slurry flow is characterized by the particle distribution being

nearly uniformly distributed along the cross-section of the pipeline. It is important

that the velocity is sufficiently high so the solid particles do not deposit along the

bottom of the pipeline. With an average particle size of 50 μm, the slurry may exhibit

viscous non-Newtonian behavior. Therefore, the frictional resistance is impacted by

both the viscous flow of the fluid and the mechanical behavior of solid particles.

For simplicity, the total frictional effects of the pseudo-homogenous slurry will be

calculated as water friction losses multiplied by a factor to account for the solid

particles’ mechanical losses. The velocity is set as the velocity in which deposition

does not occur.

The cross-section area A of the pipeline,

𝐴 =

𝜋𝐷2

4 Eq. 1

where D is the inner diameter of the pipeline.

The total flow Q in the pipeline,

𝑄 = 𝐴 ∙ 𝑣 Eq. 2

where v is the velocity of the slurry.

The solids density ratio ss,

where 𝜌𝑎 is the compact solid density of the apatite and 𝜌𝑣 is the density of water.

The solids concentration by volume, C, is determined by the volume of solids divided

by the volume of solids and water. Utilizing mass equals volume times density, then

the dry solids mass flow per hour, Ms in kg/s, is determined from the total flow 𝑄

multiplied by the density of water which yields

𝑠𝑠 = 𝜌𝑎

𝜌𝑣

Eq. 3

𝑀𝑠 = 𝑄 ∙ 𝜌𝑎 ∙ 𝐶 Eq. 4

63

The dry solids particle mass flow per year is given as,

The friction losses for liquids are determined using the Darcy-Weisbach friction

equation to determine the head loss during flow in a pipe. The Darcy-Weisbach

equation is stated as ΔHf given in meters head loss of the flowing medium,

𝛥𝐻𝑓 = 𝑓𝑑 ∙

𝐿

𝐷∙

𝑣2

2 ∙ 𝑔 Eq. 6

The friction coefficient is approximated using the Moody diagram which is dependent

on the surface roughness coefficient of the pipe, ϵ, and Reynolds number, Re,

𝑅𝑒 =

𝜌𝑣 ∙ 𝑣 ∙ 𝐷

𝜇𝑣

Eq. 7

Where 𝜇𝑣 and 𝜌𝑣 is the viscosity and density of water respectively. The Moody

Diagram considers Reynolds number where the medium is turbulent i.e. Re > about

4000. From this the friction coefficient can be determined from the Moody diagram

(Moody, 1944) or it can be calculated directly using the following relationship

presented by (Swamee & Jain, 1976) which gives values within 1% of the Moody

diagram ,

𝑓𝑑 = 1.325(𝑙𝑛 (

𝜀

𝐷∙3.7+

5.7

𝑅𝑒0.9))2.⁄

Eq. 8

The best practice in engineering terms for a flowing medium is to refer to the

mechanical energy balance as “head” in meters which is a measure of the mechanical

energy of the flowing medium per unit mass. The total required pumping “head” for a

pseudo-homogenous slurry is given as

𝛥𝐻 = 𝛥𝐻𝑓 + 𝛥𝐻𝑚 − 𝐻, Eq. 9

Where H is the total elevation difference between the inlet and outlet. The minor head

loss in the pipeline, Δ𝐻𝑚, are calculated as

𝑀𝑠,𝑦𝑒𝑎𝑟 = 𝑀𝑠 ∙ 3600 ∙ 24 ∙ 365.25 Eq. 5

64

𝛥𝐻𝑚 = ∑ 𝐾𝑖

𝑖

∙𝑣2

2 ∙ 𝑔 Eq. 10

Where Ki are coefficients connected to the physical obstacles that the slurry

must overcome i.e. inlet, bends and outlet. The minor losses for this initial

calculation of long-distance slurry transport are neglected so the total head is

given as

𝛥𝐻 = 𝛥𝐻𝑓 − 𝐻. Eq. 11

This equation holds for an arbitrary pipeline length L provided that the pressure is not

lower than ambient pressure at any stage of the pipeline. The losses in equation 11 are

regarded in terms of meters head loss of the flowing medium, the total pressure

required to transport the slurry with regards to the mechanical energy is determined as

𝛥𝑝 = 𝛥𝐻 ∙ 𝜌𝑡𝑜𝑡 ∙ 𝑔, Eq. 12

Where 𝜌𝑡𝑜𝑡 is the density of the slurry,

𝜌𝑡𝑜𝑡 = 𝜌𝑣(1 + 𝐶(𝑆𝑆 − 1)). Eq. 13

The total power output of the pumps 𝑃,

𝑃 = 𝛥𝑝 ∙

𝑄

𝑒𝑛

Eq. 14

Where 𝑒𝑛 is the efficiency of the pumps. The energy consumption can also be

expressed as kWh/ton dry apatite by dividing P by the mass flow of apatite per hour.

By studying available information along with experience from supervisors, the

friction coefficient determined from equation 8 should be multiplied by 1.8 to achieve

a more realistic approximation of the head losses.

These equations, are applied to the case presented in section 3.3 in this report utilizing

the particle distribution presented in figure 6, surface roughness inside the pipeline set

65

to ϵ = 0.025 mm, an inner pipe diameter of 250 mm giving a fd = 0.0145 (eq.8) for

water and 0.0145.1.8=0.026 for slurry. The velocity is set to 2 m/s based on the

deposition velocity at 1.5 m/s which is increased to get a margin of safety to avoid

deposition of solid particles at the bottom of the pipe. A total pipeline length of 300

km applied to (eq. 6) gives Hf = 6360 m. Applying an elevation difference between

inlet and outlet of 450 m, (eq.11) yields H = 5912 m. The friction loss and velocity

values should be regarded as preliminary and seen as estimates.

The slurry density is obtained from eq.13 for the solid particle density of 2970 𝑘𝑔/𝑚3

and a concentration by volume of 25%. The apatite mass flow is obtained from eq.4

utilizing the flow determined from eq. 2 and the cross-sectional area of the pipe

utilizing eq.1. With a pipeline diameter of 0.25 m, an operating velocity of 2 m/s and

the apatite density of 2970 kg/𝑚3, the apatite mass flow is 73.3 kg/s (eq. 4). Utilizing

eq. 5, the apatite mass flow per year is determined to be 2.31 Mtons/year. The total

pressure loss is determined from the total head loss in meters, 5628 m, together with

the slurry density as well as the gravitational constant. The total pressure loss from

Eq. 12 yields 82.6 MPa. The power consumption in W is determined from eq. 14.

Utilizing a total flow of 0.0981𝑚3/𝑠, total pressure loss of 82.6 MPa and a pump

efficiency of 90% then the power consumption is 9450 kW. With eq. 5, total mass

flow rate of apatite is 2.3 Mtons per year, the energy requirement is 35.8 kWh per ton

dry apatite can be calculated.

66

9 Appendix 2 - Numerical heat flow model in MATLAB.

The premise equation is the two-dimensional heat flow equation,

𝑑𝑇𝑑𝑡

= 𝛼 (𝑑

2𝑇

𝑑𝑥2

+𝑑

2𝑇

𝑑𝑦2

) Eq. 14

Where 𝑇 is the temperature, 𝑑𝑇

𝑑𝑡 is the differentiation of temperature over time,

𝑑2𝑇

𝑑𝑥2 is

the second order differentiation of temperature over x and 𝑑2𝑇

𝑑𝑦2 is the second order

differentiation of temperature over y. The constant 𝛼 is the thermal diffusivity given

in 𝑚2

𝑠.

The temperature 𝑇 is denoted as

𝑇 = 𝑇𝑛,𝑚𝑝

= 𝑇(𝑥𝑛, 𝑦𝑚 , 𝑡𝑝) Eq. 15

The variables are defined as

𝑥𝑛 = 𝑛 ∙ 𝛥𝑥, 𝑛 ∈ [1, 𝑁],

𝑦𝑚 = 𝑚 ∙ 𝛥𝑦, 𝑚 ∈ [1, 𝑀],

𝑡𝑝 = 𝑝 ∙ 𝛥𝑡, 𝑝 ∈ [1, 𝑃].

Push forward method of differentiation of temperature T with respect to time t yields

𝑑𝑇𝑑𝑡

=𝑇𝑛,𝑚

𝑝+1 − 𝑇𝑛,𝑚𝑝

𝛥𝑡. Eq. 16

Second order differentiation of temperature T with respect to x,

𝑑2𝑇

𝑑𝑥2=

𝑇𝑛+1,𝑚𝑝

− 2𝑇𝑛,𝑚𝑝 + 𝑇𝑛−1,𝑚

𝑝

𝛥𝑥2. Eq. 17

67

Second order differentiation of temperature T with respect to y,

𝑑2𝑇

𝑑𝑦2=

𝑇𝑛,𝑚+1𝑝

− 2𝑇𝑛,𝑚𝑝 + 𝑇𝑛,𝑚−1

𝑝

𝛥𝑦2. Eq. 18

Applying equations 16, 17 and 18 into equation 14 yields

𝑇𝑛,𝑚𝑝+1

− 𝑇𝑛,𝑚𝑝

𝛥𝑡= 𝛼(

𝑇𝑛+1,𝑚𝑝

− 2𝑇𝑛,𝑚𝑝

+ 𝑇𝑛−1,𝑚𝑝

𝛥𝑥2+

𝑇𝑛,𝑚+1𝑝

− 2𝑇𝑛,𝑚𝑝

+ 𝑇𝑛,𝑚−1𝑝

𝛥𝑦2). Eq. 19

By stating that 𝛥y2 = 𝛥x2, equation 18 can be rearranged to give

𝑇𝑛,𝑚𝑝+1

= 𝐾(𝑇𝑛+1,𝑚𝑝

+ 𝑇𝑛−1,𝑚𝑝

+ 𝑇𝑛,𝑚+1𝑝

+ 𝑇𝑛,𝑚−1𝑝

) + 𝑇𝑛,𝑚𝑝 (1 − 4𝐾), Eq. 20

Where K is defined as

𝐾 = 𝛼𝛥𝑡

𝛥𝑥2, Eq. 21

68

10 Appendix 3 – Maximum Packing Limit

The volume of apatite in the measuring cylinder is approximated to be

𝑉𝑎 = 𝑉𝑡𝑜𝑡,𝑚𝑐 −𝑀𝑤

𝜌𝑤, Eq. 22

Where 𝑉𝑡𝑜𝑡,𝑚𝑐 is the total volume of slurry inside the measuring cylinder, 𝑀𝑤 is the

mass of water and 𝜌𝑤 is the density of water.

The Maximum Packing Limit is determined by

𝑣𝑚𝑝𝑙% = 𝑉𝑎

𝑉𝑠𝑒𝑑× 100, Eq. 23

Where Va is the volume of apatite and Vsed is the total volume of the sedimented

slurry.

The volume which is patched for the sedimentation analysis is defined as

𝑉𝑠𝑒𝑑,𝑝𝑖𝑝𝑒 = 𝑉𝑡𝑜𝑡 ∙0.25

𝑣𝑚𝑝𝑙%, Eq. 24

Where 𝑉𝑡𝑜𝑡 is the total volume of the pipe.

69

11 Appendix 4 – MATLAB script for explicit heat equation

Defining variables

nx = 100; %Discrete steps in x-

direction

ny = 100; %Discrete steps in y-

direction

x = linspace(0,1,nx); %Vector in x-direction from 0 to

1 meter y = linspace(0,1,ny); %Vector in y-direction

from 0 to 1 meter

dx = 1/(nx-1); %Step size in x-direction

dy = 1/(ny-1); %Step size in y-direction

[X,Y] = meshgrid(x,y); %Mesh of surface

t = 282.2; %Total calculation time

nt = 16000; %Number of discrete time

steps

dt = t/nt; %Step size for time

T = 4*ones(nx,ny,nt); %Initial temperature for

surface alpha = 210e-6; %Thermal expansion

coefficient

K = (alpha*dt)/(dx^2); %Coefficient

Boundary conditions

for p = 1:nt+1

T(1,:,p) = -4; T(end,:,p) = -4; T(:,1,p) = -4;

T(:,end,p) = -4;

end

Inital temperature

initialT = T(:,:,1);

Loop

for l = 1:nt

for i = 2:nx-1

for j = 2:ny-1

T(i,j,l+1) = K*(T(i+1,j,l)-(2*T(i,j,l))+T(i-1,j,l))...

+ K*(T(i,j+1,l)-(2*T(i,j,l))+T(i,j-1,l))+T(i,j,l);

70

end

end

end

Plot FinalTmiddle = T(nx/2,ny/2,nt);%Temp. in middle of mesh FinalT = T(:,:,nt); %Temp. at final time step

%figure(2)

%surf(X,Y,initialT) %Figure of initial temp.

%figure(1)

%surf(X,Y,FinalT); %Figure of final temp.

71

12 Appendix 5 – MATLAB script losses approximation

Mf = 2.284893099676012e+06; %Apatite flow tons per year

Mfkg = Mf.*1e3; %Apatite flow kg per year

L = 300e3; %Total Length of pipeline

g = 9.82; %Gravitational acceleration

phi = 0.25; %Volume fraction

rhof = 2950; %Density of Apatite

rhov = 998.2; %Density of Water

ss = rhof/rhov; %Density ratio

muv = 0.001; %Viscosity of water

Mfs = Mfkg./(365.25*24*60*60); %Apatite flow kg per second

Mvs = Mfs; %Water flow kg per second

Mtot = Mfs+Mvs; %Total flow kg per second

Qf = Mfs./rhof; %Apatite flow m3 per second

Qv = Mvs./rhov; %Water flow m3 per second

Qtot = Qf+Qv; %Total flow m3 per second

C = Qf./Qtot; %Volume fraction of apatite

Qtottimme = Qtot*60*60; %Total flow m3 per hour

rhotot = Mtot./Qtot; %Density of slurry

D = 0.25; %Pipe inner diameter

A = pi*(D^2)/4; %Cross-section area of pipe

Vtot = Qtot./A; %Velocity of slurry

Re = rhov*(Vtot.*D)./mu; %Reynolds Number

epsD = 0.05/250; %Approx. of surface roughness ratio

fd = 1.325./((log((epsD./3.7)+(5.74./(Re.^0.9)))).^2); %Friction loss coefficient

fd = fd*1.8; %Friction loss coefficient slurry

deltah = (fd.*(L/D).*(Vtot.^2))/(2*g); %Head loss from major losses

deltah = deltah-440; %Total head loss with elevation

deltapminor = 3000*(Vtot^2)/(2*g); %Head loss from minor losses

72

deltap = deltah.*(rhotot.*g) + deltapminor; %Total pressure loss in Pa

deltapmpa = deltap./1e6; %Total pressure loss in MPa

deltapmeter = deltap/L; %Pressure loss gradient

en = 0.9; %Pump efficiency

Effekt = deltap.*Qtot./en; %Power consumption

e = 1e-6.*(1/en).*deltap./(C.*ss.*3.6); %Energy usage