An Initial Analysis of Slurry Transportation in Subarctic Environment

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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

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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.

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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.

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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.

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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

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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.

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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).

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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

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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

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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

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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

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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.

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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

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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

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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.

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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.

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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

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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

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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

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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

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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

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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.

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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.

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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

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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.

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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 𝑒_𝑛 = 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.

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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

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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.

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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 𝐶_𝑎𝑓 = 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.

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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.

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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 𝐶_𝑎𝑓 = 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)

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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 𝐶_𝑎𝑓 = 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

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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.

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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 𝐶_𝑎𝑓 = 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

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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.

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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 𝐶_𝑎𝑓 = 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

An Initial Analysis of Slurry Transportation in Subarctic Environment

An Initial Analysis of Long-Distance Slurry Transport in Subarctic Environment

Wilhelm Friberg

Foreword

Abstract

Sammanfattning

Table of Contents

1 Introduction

2 Background and Theory

3 Method

4 Results