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Über dieses Buch

This book covers virtually all of the engineering science and technological aspects of separating water from particulate solids in the mining industry. It starts with an introduction to the field of mineral processing and the importance of water in mineral concentrators. The consumption of water in the various stages of concentration is discussed, as is the necessity of recovering the majority of that water for recycling. The book presents the fundamentals under which processes of solid-liquid separation are studied, approaching mixtures of discrete finely divided solid particles in water as a basis for dealing with sedimentation in particulate systems. Suspensions, treated as continuous media, provide the basis of sedimentation, flows through porous media and filtration. The book also considers particle aggregations, and thickening is analyzed in depth. Lastly, two chapters cover the fundamentals and application of rheology and the transport of suspensions.

This work is suitable for researchers and professionals in laboratories and plants, and can also serve as additional reading for graduate courses on solid liquid separation as well as for advanced undergraduate and graduate level students for courses of fluid mechanics, solid-liquid separation, thickening, filtration and transport of suspensions in tubes and channels.



Chapter 1. Introduction

This chapter introduces the field of Mineral Processing. A mineral processing plant can be divided into four distinct operational units: comminution, concentration, dewatering and pulp transport. Comminution is the process of reducing the particle size of an ore until the free particles of minerals can be separated by available methods. Froth flotation is the most important mineral processing technique to recover sulphide minerals, such as copper, zinc and lead. It uses the differences in physicochemical surface properties of particles of different minerals and gangue to recover a concentrate and leave the gangue as tailing that is discarded. Dewatering is a process of solidliquid separation achieved by thickening and filtration. Thickening uses the force of gravity to separate the particles from the water by sedimentation in large cylindrical tanks called thickeners, while filtration uses pressure forces to pass the slurry through a cloth and separate it into a filter cake on the cloth and clean water called filtrate. Safe and environmentally friendly deposition of mining waste is a major concern in the mining industry worldwide. Almost all the treated minerals in sulphide concentration plants are deposited as tailings since the recovered product represents a very small percentage of the total tonnage. Water has become a major concern in processing raw materials, in terms of water conservation and reuse. The chapter discusses water consumption in the various stages of concentration and the need to recover most of that water by recycling.
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Chapter 2. Theory of Mixtures

This chapter lays out the conceptual basis for the study of processes of solid–liquid separation. For the study of flows in rigid and deformable porous media and of suspension sedimentation and transport, we must consider bodies formed of different materials. The appropriate tool to do this is the Theory of Mixtures. A rigorous but limited account of the Theory of Mixtures of continuum mechanics is given that postulates that each point in space of a body is simultaneously occupied by a finite number of particles, one for each component of the mixture. In this way, the mixture can be represented as a superposition of continuous media, each following its own movement with the restriction imposed by the interaction between components. An introduction discusses the conditions that a multi-component body must fulfill to be considered a continuum. The concepts of body, component, mixture, deformation and rate of deformation are introduced and discussed. Mass and momentum balance equations are formulated for each component of the mixture and the need to establish constitutive equations to complete a dynamic process is discussed.
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Chapter 3. Particulate Systems

Mixtures of finely divided solid particles in water are the subject of this chapter. Here the equations derived in Chap.​ 2 are applied to particulate systems. First, the requisite for considering a particulate system as a continuum is laid out. In such a system the motion of the components of the mixture can be described through local mass and linear momentum balances in all regions where the field variables are continuous. At discontinuities the field equations must be replaced by the corresponding jump conditions. Next, the result is applied to a two-component solid–fluid system. For fluids, constitutive equations are proposed for the stresses, defining pressure and viscous stress. The properties of the solid components in particulate systems depend strongly on their concentration. At concentrations of less than those where particles are in permanent contact with each other, the mixture is called a suspension and all interaction forces are transmitted from particle to particle through the fluid, defining the pore pressure. At greater concentrations the mixture is called a porous medium, a porous bed or sediment, where the stresses are transmitted through the fluid and from particle to particle by direct contact through the effective solid stress. A dynamic process for a solid–liquid system is defined when the set of field variables in regions where the variables are continuous obey the field equations and at discontinuities obey the jump conditions.
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Chapter 4. Sedimentation of Particulate Systems

This chapter deals with sedimentation of particulate systems considered as discrete media. Sedimentation is the settling of a particle or suspension of particles in a fluid due to the effect of an external force such as gravity, centrifugal force or any other body force. Discrete sedimentation has been successful in establishing constitutive equations for continuous sedimentation processes. The foundation of the motion of particles in fluids is discussed in different flow regimes, Euler’s flow, Stokes flow and flows with a boundary layer. Starting from the sedimentation of a sphere in an unbounded fluid, a complete analysis is made of the settling of individual spherical particles and suspensions. The results are extended to isometric particles and to arbitrarily shaped particles. Sphericity as a shape factor is used to describe the form of isometric particles. A hydrodynamic sphericity must be defined for particles with arbitrary shapes by performing sedimentation or fluidization experiments, calculating the drag coefficient for the particles using the volume equivalent diameter and obtaining a sphericity defined for isometric particles that fits experimental values. A modified drag coefficient and sedimentation velocities permits grouping all sedimentation results in one single equation for particles of any shape.
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Chapter 5. Kynch Theory of Sedimentation

This chapter studies sedimentation of suspensions treated as continuous media. Sedimentation processes are studied from two perspectives; a discrete approach and a continuum approach, in which dynamic processes are established. This chapter uses the continuum approach and presents the concept of an ideal suspension and an ideal thickener. Suspensions described by solid concentration, solid component velocity and fluid component velocity constitute the sedimentation process provided they obey the mass conservation equations. Sedimentation can be performed in batches or continuously. Batch sedimentation is studied first and the Modes of batch sedimentation are established. These observations are extended to continuous processes. Finally the capacity of an ideal continuous thickener is derived. Kynch sedimentation theory, besides correctly describing the behavior of incompressible suspensions, forms part of the more general theory of compressible materials. The exercise of constructing solutions to Kynch sedimentation processes allows for a better understanding of the sedimentation of compressible pulps. Anyone wanting to understand the phenomenological theory of sedimentation must first master Kynch sedimentation processes.
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Chapter 6. Flow Through Rigid Porous Media

The best way to analyze the flow through a porous medium is to divide it into two phenomena, depending on whether the porous matrix is compressible or incompressible. In both cases, the result is useful for the process industry. Rigid porous media form the basis for a simplified filtration theory and compressible porous media form part of thickening theory. In this chapter the fundamental equations for the flow through rigid porous media based on the Theory of Mixtures is developed. Consider the flow of a incompressible viscous fluid through a bed of small solid incompressible particles with no mass transfer between the solid and the fluid. Such a mixture of particles is called an incompressible porous medium and can be described with the equations for particulate systems presented in Chap. 3. It is convenient in this case to use porosity as a variable instead of the solid volume fraction. Local balances are laid down for mass and momentum and Darcy’s and Forchheimer’s equations are used as constitutive equations. For a mono-phase flow, permeability is defined and for the case of a two-phase flow, the concepts of relative permeability, saturation and capillary pressure are introduced.
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Chapter 7. Particle Aggregation by Coagulation and Flocculation

This chapter considers particle aggregation. When agglomerated particles in a suspension increase in size they acquire greater sedimentation velocity essential to obtain a good separation by sedimentation. Two methods for increasing the size of solid particles are studied in this chapter, coagulation by reducing inter-particle electrostatic repulsion and flocculation by bridging particles with polymeric agents. Most mineral particles suspended in water in the neutral pH range have negative surface charges. Positive ions in solution are attracted and adsorbed at the negatively charged surface forming the so-called double layer with its Stern plane and the diffuse layer. The Zeta potential measures the difference in the electrical potential of the charged surface and the bulk of the solution in commercial instruments. If particle surfaces come close together, they attract each other by van der Waals force. If there is no counteracting force, the particles will coagulate and settle out of the suspension. The study of orthokinetic coagulation follows. It is generally accepted that polymers used as flocculants in mineral processing plants aggregate fine particle suspensions by bridging mechanisms. Such bridging links the particles into loose flocs and incomplete surface coverage, which ensures that there is sufficient unoccupied surface available on each particle for adsorption during collisions of chain segments attached to the particles. The description of flocs as fractal objects permits a better understanding of their behavior. Flocculation kinetics shows that a short and highly intensive mixing gives the best results for particle aggregation.
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Chapter 8. Thickening

The chapter analyzes thickening in-depth. In an extensive introduction, the history of thickening is laid out from the Stone Age to the present, emphasizing people and institutions that have been important actors. The chapter then reviews the thickeners used in the mining-mineral industry. During sedimentation, particles settle individually except for collision among them, exerting interaction between them solely through the fluid. At a certain concentration, particles begin to touch each other permanently transforming the suspension into a network of solid particles called sediment. At that point forces among particles are transmitted directly from particle to particle. If settling particles that reach the bottom of the vessel and lie one on top of the other are incompressible, such as glass beads, the whole process ends, but if they are compressible, as in the case of flocculated copper flotation tailings, the weight of the sediment compresses the flocs lying underneath expelling the water from the pores. This phenomenon of extracting water by compression is called consolidation. The theory of sedimentation-consolidation is deduced from the equations for a particulate system and constitutive equations for the solid-fluid interaction force and sediment compressibility are postulated. Batch and continuous sedimentation are analyzed and simulations are compared to data from the literature. Experimental determination of thickening parameters and instruments for their determination are presented. Old and new methods for thickening design are reviewed and software for the design and simulation of batch and continuous thickening are presented. Finally, strategies for the operation and control of industrial thickening are discussed.
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Chapter 9. Filtration

Filtration is the process whereby a solid separates from a fluid by making the suspension pass through a porous bed, known as a filter medium. The bed retains the particles while the fluid passes through the filter medium and becomes a filtrate. To establish a flow of filtrate, it is necessary to apply a pressure difference, called a pressure drop, across the filter medium. There are several ways to do this depending on the driving force, for example: (1) gravity, (2) vacuum, (3) applied pressure, (4) vacuum and pressure combined, (5) centrifugal force, and (6) a saturation gradient. Usually the different driving forces require different filtration equipment called filters. Two main dewatering stages are studied, cake formation and dehumidification, which are studied as mono-phase flow and two-phase flow of a fluid through rigid porous medium, respectively. Field variables and constitutive equations are deduced from the chapter on flow in porous media. Methods of filtration, cake porosity, permeability, capillary curves and relative permeabilities are presented. Finally models of continuous filters are developed.
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Chapter 10. Suspension Rheology

The importance of rheology in the mining industry derives from the fact that all materials being processed are suspensions, that is, mixtures of solid particles and fluids, usually in water. In mineral processing plants, water is mixed with ground ore to form a pulp that constitutes the mill feed. The mill overflow is mixed again with water to adjust the solid content for classification in hydrocyclones. Pulp characteristics are essential in the transport of products to their final destination. A suspension, like all types of materials, must obey the laws of mechanics under the application of forces. The flow patterns of suspensions in tubes depend on their concentrations and transport velocities. In diluted suspensions at low velocities particles will settle. The suspension is termed a settling suspension and the flow regime is considered heterogeneous. At a velocity beyond a value at which all particles are suspended gives a non-settling suspension and the flow regime is homogeneous with Newtonian behavior. Concentrated suspensions are usually homogenous with non-Newtonian behavior. The variables and field equations for all types of fluids are presented and constitutive equations differentiate between Newtonian and non-Newtonian behavior. Empirical models of non-Newtonian behavior are presented, including pseudo-plastic and dilatant behavior with Cross and Carreau and Power-law models, and yield-stress models with Bingham and Hershel-Bulkley models. The study of the operational effect on viscosity includes variable such as solid particle size and concentration, temperature, pressure, time and pH. Rheometry provides experimental methods to determine rheological parameters such as viscosity and yield stress.
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Chapter 11. Transporting Concentrates and Tailings

Ore, water and mineral pulps are transported among the different operational units of a mineral processing plant. Water is pumped through pipelines to the grinding plant to be mixed with the ore to form the pulp that constitutes the mill feed. The mill overflow is again mixed with water to adjust the solid content and is sent through pipes to be classified in hydrocyclones. Cyclone underflow with coarse material is sent back to the mill and the overflow goes to the flotation plant. Transport in the flotation plant and between flotation sections and solid–liquid separation units is through pipelines, and finally flotation tailings are transported to tailing ponds through pipelines or channels. This chapter of the book is related to the transport of pulps in mineral processing plants. Starting from the continuity equation and the equation of motion for a continuous medium, the expression for the pressure drop during fluid flow in a tube is obtained. Newtonian fluid behavior is used to treat cases of laminar and turbulent flows. The concepts of friction factor and Reynolds number are introduced and the distribution of velocity, flow rate and pressure drop in a tube are obtained. The transport of suspensions in pipelines is then treated, defining the different regimes separated by the limiting deposit velocity. First, the flow of heterogeneous suspensions is introduced and the form to calculate head loss is presented. Next, homogeneous suspensions modeled by different rheological approaches are discussed. Finally equations for the transport of suspensions in open channel are dealt with.
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