## Hydrometallurgical Processing

• Milling
• Leaching Metal (Quantity – % Recovery)
• Removal of Metal from Pulp
• Purification (Quality – g/L and removing other ions)
• Electrowinning or Precipitation Followed by Smelting

## Why Leaching?

• Traditional methods viz – ore sieving, washing, etc. are obsolete and uneconomical.
• Pyro-metallurgy is highly costly and non-viable for low-grade ores.
• Leaching is the only process to extract metallic content from the low-grade ores.
• Among leaching methods – Heap leaching is most economical

### Basics of Dissolution

The choice of leaching method depends on

1. raw material and its impurities
2. chemicals
3. recovery degree and rate
4. environmental aspects
5. money

Dissolution rate can be improved by

1. decreasing the particle size
2. increasing the temperature
3. improving the mass transfer (e.g. stirring)

### Lixiviants

Lixiviant is a liquid medium used to selectively extract a desired metal from a bulk material. It must achieve rapid and complete leaching.

The metal is recovered from the pregnant (or loaded) solution after leaching. The lixiviant in a solution may be acidic or basic in nature.

• H2SO4
• HCl
• HNO3
• HCN >> NaCN/KCN
• NH4OH
• NH4Cl or NH4CO3
• NaOH/KOH

### Heap Leaching

• Heap leaching is a simple, low-cost method of recovering precious metals from low-grade ores.
• Ore is stacked in heaps over an impermeable leaching-pad.
• Leach liquid is irrigated at the top
• Liquid reacts with metal and dissolves it.
• Dissolved metal collected at the bottom in the leaching pad.

### Components of Heap Leach

• Liners
• Crushed metal ore
• Irrigation system
• Pregnant solution pond
• Barren solution pond

### Important Efficiency Factors

1. Retention time-total volume of tanks / slurry volumetric flow
2. Particle Size-high recovery achieved as liberation increases
3. Pulp density-percent solids determines retention time and determines settling rate and viscosity
4. Numbers of tanks
5. Dissolved gases-Gas is injected below the agitator or into the vat bottom to achieve the desired dissolved gas levels. Typically, oxygen or air, or, in some base metal plants, SO2 is used.
6. Reagents-Insufficient reagents reduces metal recovery while Excess reagents increases operating costs and may lead to lower recovery due to dissolution of other metals.

### SX – Solvent Extraction

• Pregnant (or loaded) leach solution is emulsified with a stripped organic liquid and then separated
• Metal is exchanged from pregnant solution to organic
• Resulting streams are loaded organic and raffinate (spent solution)
• Loaded organic is emulsified with a spent electrolyte and then separated
• Metal is exchanged from the organic to the electrolyte
• Resulting streams are stripped organic and rich electrolyte

### Electrowinning and electrorefining

• Electrowinning, electrorefining and electroplating involve the exchange of electrons between a solid electrode and ions or molecules dissolved in solution
• The rate of the reaction involved depends on the
• electrode potential,
• electrode area and
• rate of mass transport of the electroactive species to the electrode surface.
• The main differences are in the construction of t he cells, their geometry, construction materials, and operating practice.

### Gold Processing

• Gold is usually present as a metal, alloyed with metallic silver and perhaps, copper. The high S.G. (19.3) of gold means that that gold particles, even when of sub-sieve size, settle readily from pulps in which the main gangue mineral is silica.
• Gold is malleable, and during grinding to liberate the gold from associated gangue mineral, the particles of gold become flattened without being reduced in size. This differential grinding effect can assist in the recovery of gold by gravity separation within the grinding circuit itself.
• Against this however, the weight and malleability of gold particles can lead to significant retention in the pump and sump boxes in a closed grinding circuit.
• In addition to “native” gold, the element may occur as inclusions with sulphide minerals such as pyrite, pyrrhotite, stibnite, arsenopyrite, and galena at sizes as small as only 1 micron in diameter.
• Cyanidation for gold recovery is used world-wide for various ore types. The process of Cyanidation proceeds in four stages:
• Preparation of the ore to expose its gold.
• Dissolution of gold using low strength NaCN solutions (0.05%).
• Separation of gold-rich liquid from residual solids.
• Recovery of gold from pregnant solution.
• The gold is recovered from the loaded solution by precipitation with Zn dust in a process known as Merrill-Crowe. This process demands a clarified and de-aerated liquor.
• Today, modern practice utilizes Activated Carbon to strip the gold from solution. This process, known as Carbon-in-Pulp or Carbon-in-Leach can replace the expensive dewatering steps required of conventional methods. Gold is extracted from the carbon using elution with the eluant treated by electrolysis for recovery onto steel-wool cathodes.
• The major advantage of Carbon in Pulp is not the reduction in the use of zinc dust but rather the impact on the dewatering requirements.
• Using carbon allows the gold to be recovered on coarse pellets (16 mesh) of activated carbon. Activated carbon is made from coconut shells or peach pits to ensure the material is hard and doesn’t abrade during contact with the solid particles in the pulp.
• The carbon is first conditioned to remove sharp corners and to remove fines. Then it is used in the process and recycled through an elution stage. The elution stage removes the gold from the carbon and puts it into a very clean electrolyte solution that goes on for gold recovery by electrowinning.
• The carbon can be reused several times without much loss in effectiveness but eventually the pores become blinded with lime deposits and coatings of organic materials (oils, etc.). So a portion of the carbon is bled off the circuit and sent for regeneration which consists of acid- washing and pyrolysis. Some carbon is burned off and lost but the loss is small and there is no gold associated with the regeneration loss.

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## AMIT 145: Lesson 6 Dewatering & Clarification

### Introduction

Dewatering involves a separation between solids and water for one of the following purposes:

• To prepare feed to a downstream process that requires higher solids concentration;
• To reduce the volume of slurry being fed to downstream processes;
• To achieve a product having a moisture content that is equal to or less than a given target value.

Clarification is the process of treating waste slurry to provide water of sufficient quality to be recycled for use in the preparation plant.

### Filtration

Filters are used when it is desired to maximize the recovery of particles having a size less than 325 mesh.

Typical vacuum disk filters are relatively low cost and achieve high particle recovery. However, product moisture values are generally greater than 25%.

To achieve both high particle recovery values and acceptable product moisture values, high pressure filters are used. Two problems:

• High capital cost, i.e., >$500,000 each; • Semi-batch operation and thus two units are required for continuous operation. ### Filter Product Moisture Factors • Cake Thickness • Pressure Drop across cake • Drying Time • Volume of Air pulled through cake • Viscosity of Liquid • Surface Tension of Liquid • Filter Media • Size Distribution of solids • Permeability of Cake • Specific gravity of dry solids • Inherent Moisture of solids • Surface Properties of solids • Type of Filter • Homogeneity of cake formation • Interfacial tension of solids and liquid • Temperature of gas and liquids A good correlation of cake moisture includes the following factors: (cfm/ft2)(P/W)(td) where cfm of air per filter area in ft2, W is the weight of the dry filter cake per filter revolution, P the total pressure drop, and td the filtration time per cycle. As such, production moisture decreases with: • An increase in P and td. • A decrease in the filter cake weight W ### Filter Design The required area and number of filters needed is a direct function of the required product moisture and the required amount of filtrate needed to be separated from the solid. The filtrate, Q, can be assumed using the D’Arcy equation: Q = AΔp/U(Rm+Rc) ΔP = the pressure drop across the cake or driving pressure, U – the filtrate viscocity, A = the filter area, Rm and Rc = membrane and cake resistance ### Clarification (Thickeners) The principle objectives of a thickener are to: • Clarify water for reuse in the plant; • Thickening of the solids. To design a thickener we must know: • Total feed volumetric and mass flow; • Identity of unwanted solids in the overflow stream; • Desired concentration of solids in the underflow stream. The design parameters to be determined include: • Cross-sectional area; • Total depth. There are three modes of sedimentation in a thickener: • Clarification in which solids settle either individually or are collected into separate floccules, each of which then settles at its own characteristic settling rate, closely related to Stoke’s law; • Zone settling in which particles cohere into a structure such that all in a given neighborhood subside at the same rate, but the structure does not lend mechanical support; • Compression in which the structure is capable of mechanical support. ### Particle Growth Particle aggregation is a key component to consider in the design and operation of a thickener. Particle enlargement affects: • Clarity of the overflow stream; • Settling rates (reduces thickener size); • Underflow solids concentration. Particle enlargement typically involves the addition of: • pH modifiers; • Adjusts surface charge • Coagulants; • Neutralizes surface charge. • Flocculants. • Aggregates particles • Cationic = added first to initiate particle aggregation. • Anionic = high molecular weight added last to bridge particles for finalize aggregation. ### Thickener Design ### Clarification Zone Design Clarification zone requirements are commonly expressed in terms of overflow velocity, vo, and, t, retention time. These parameters relate to pool area and depth according to the following expression: vo = Q/A t = V/Q = Ah/Q = h/vO A = settling area of the clarifier in m2, h = depth of the clarification zone in meters, V = clarification zone volume in m3, Q = the volume of the overflow per unit time in m3/h. Residence time should be sufficient to allow the aggregates to settle through the clarification zone. Typical settling rates are 4 to 6 inches/minutes and may go up to 8 to 10 inches/minute for undersized thickeners. ### Thickener Area Design Coe and Clevinger provided an expression that relates the settling rates of the particle aggregates and the required area of the thickener when the medium is water: A = 1.333 (F-D)/V A = the area in ft2/tph of dry solids per 24 hours (unit area), F&D = the liquid-to-solid weight ratio in feed and underflow, respectively, V = aggregate settling velocity in feet/hr. The relationship between area and depth is most important for the following reasons: • Tank volume must provide sufficient residence time considering both operational efficiency and mechanical design; • Thickener efficiency decreases as the ratio between depth and diameter decreases. As such, a number of batch tests are run with vayinf F values and thus different V. A plot of unit area A versus F establishes the maximum value of A which must be used for design purposes. Save Save ## AMIT 145: Lesson 5 Froth Flotation Froth flotation is a physico-chemical separation process. Separation is principally based on differences in surface hydrophobicity. However, particle size and density have a significant impact. Initial flotation patent and application was developed for graphite by the Bessel brothers (1877). Similar to graphite, coal is naturally hydrophobic. ### Conventional Flotation • First developed in 1912. • Employed throughout the 20th century. • Low capital cost. • Due to mixing, several cells are used in series. • Hydraulic entrainment has always caused a battle between grade and recovery. • 10 tph/cell capacity ### Conventional Cell Development Current emphasis is the development and optimization of large cells. Power scale-up and froth recovery are issues. Also, reduced number of units places an emphasis on ensuring high efficiency from each cell. A common cell size in the coal industry is 28 m3. ### Flotation Columns • Initial column was invented in 1907. • Commercial development was minimal until the 1980’s due to sanding of particles in the bottom of the cell. • The ability to use wash water to remove entrainment revived the interest in flotation columns. • L/D ratio is also significant for ultrafine particles. • The coal industry is shifting to larger columns, up to 4.5m diameter and greater. • Types: CoalPro, Microcel, Jameson. ### CoalPro (CPT) Flotation Column • Developed by Cominco Research and owned by Eriez Manufacturing • Coarse Bubble Size Distribution • Good Dispersion w/Sparger Water • High Aeration Rates • Low Energy Input • Typically Use for Deslime Circuit ### CPT Bubble Generation System ### CPT Flotation Column ### Microcel Column Flotation Technology • Developed by Virginia Tech in the late 1980’s. • Licensed by Eriez Manufacturing. • Reduced Bubble Size • Tight Bubble Size Distribution • Increased Capacity • Additional Pump • Higher Energy Input • Typically Use for By- Zero Circuit ### Microcel Bubble Generation ### Installation ### Column Installation ### Jameson Cell • Developed by Dr. Graeme Jameson and owned by MIM Ltd. • Self-aspirating system with froth washing. ### Flotation Recovery Fundamentals A flotation process has two distinctly different phases: 1. Collection Zone 2. Froth Zone Both the collation zone (RC) and froth zone (RF) recoveries determine the overall recovery. Using linear analysis, the overall recovery (R) can be determined: $R&space;=&space;\frac{R_{C}R_{F}}{R_{C}R_{F}&space;+&space;1&space;-&space;R_{C}}$ ### Collection Zone Recovery Parameters ### Collection Zone Recovery, RC The recovery of a given component in the feed is a function of: • Flotation Rate, ki • Particle Residence Time, Tp • Hydrodynamic Conditions Using Levenspiel’s axial mixing equation, collection zone recovery can be determined by $R_{C}&space;=&space;1&space;-&space;\frac{4\mathit{a}&space;exp(0.5&space;Pe)}{(1&space;+&space;a)^{2}&space;exp(0.5&space;\mathit{a}&space;\mathit{Pe})&space;-&space;(1-\mathit{a})^{2}&space;exp(-0.5\mathit{a}&space;\mathit{Pe})}$ $a&space;=&space;\left&space;(&space;1+\frac{4k\tau&space;_{P}}{Pe}&space;\right&space;)^{0.5}$ $Pe=\left&space;(&space;\frac{L}{D}&space;\right&space;)^{0.53}\left&space;(&space;\frac{V_{t}}{\left&space;(&space;1-\varepsilon&space;\right&space;)V_{g}}&space;\right&space;)^{0.35}$ Mankosa et al. (1992) Pe → 0, Perfectly mixed conditions → $R_{c}&space;=&space;\frac{k\tau&space;_{p}}{1+k\tau&space;_{p}}$ Pe → ∞, Plug – flow conditions → $R_{c}&space;=&space;1-exp(-k\tau&space;_{p})$ ### Flotation Rate, ki The flotation rate is a measurement of how fast a particle is recovered in the collection zone. The flotation rate of a given component can be quantified by: $k&space;=&space;\frac{3Vg}{2Db}P&space;=&space;\frac{1}{4}&space;SbP$ P = probability of flotation int he collection zone; Vg = superficial gas velocity; Db = bubble diameter; Sb = superficial bubble surface area rate ### Probability of Flotation The probability of flotation is a stochastic function of three sub-processes that occur in the collection zone: • Probability of Collision, PC • Probability of Attachment, PA • Probability of Detachment, PD P = PCPA(1-PD) For bubble sizes typical in flotation: $PC&space;=&space;(\frac{D}{P})^{2}&space;\left&space;[&space;\frac{3}{2}&space;+&space;\frac{4Re^{0.72}}{15}&space;\right]$ Controls the lower particle size limit associated with the flotation of a given particle type. ### Collection Zone Recovery Parameters ### Flotation Rate Differential Effect $\frac{\partial&space;m}{\partial&space;t}&space;=&space;-&space;kM$ = mass floated per unit of time k = flotation rate (min-1) t = flotation time (min) M = mass flotation cell SpeciesNo CollectorCollector 1k = 1.0R = 68%K = 2.0R = 80% 2k = 0.25R = 33%k = 1.0R = 68% ### Typical Flotation Residence Times MaterialTypical solids concentration for roughing applications, percentTypical residence times for roughing applications, minutesTypical laboratory flotation times, minutes Copper32-4213-166-8 Lead25-356-83-5 Molybdenum35-4514-206-7 Nickel28-3210-146-7 Tungsten25-328-125-6 Zinc25-328-125-6 Barite30-408-104-5 Coal4-83-52-3 Feldspar25-358-103-4 Flourspar25-358-104-5 Phosphate30-354-62-3 Potash25-354-62-3 Sand (Impurity Float)30-407-93-4 Silica (Iron Ore)40-508-103-5 Silica (Phosphate)30-354-62-3 EffluentsAs received7-124-5 OilAs received4-62-3 ### Froth Recovery, RF Recovery through the froth phase can be achieved as a result of one of the following: • Bubble-Particle Attachment • Particle Entrapment • Hydraulic Entrainment ### Flotation Carrying Capacity  Feed Size (Micron) Target Capacity (tph/m2) Minus 600 Minus 150 Minus 45 150 x 45 1.8-2.6 1.0-1.4 0.6-0.9 1.8-2.2 Example: 3m diameter column CC = 1.2 tph/m2 Froth = 1.2 x Area = 1.2 x 7.065 m2 = 8,5 tph ### Froth Washing Fundamentals Selectivity in a flotation process is typically achieved on the basis of differences in surface hydrophobicity. However, selectivity is based on all recovery mechanisms as well as hydrodynamic conditions. Selectivity can be enhanced by: • Maximizing flotation rate differences. • Eliminating or Minimizing Entrainment. • Selective Detachment. • High length-to-diameter ratios. ### Hydraulic Entrainment ### Froth Washing; The Original Flotation Column Benefit ### Pan-Type Froth Wash Water System ### Wash Water Ring System ### Entrainment Effect on Separation Performance ### Typical Flotation Cell Dimensions Trade NameLength (m) Width (m) Depth (m) Pulp Volume (m3) Denver 1001.521.521.222.8 Denver 2001.831.831.595.7 Denver 3002.102.101.898.5 Denver 4002.302.302.1211.3 Denver5002.702.701.9814.2 Wemco 441.121.120.510.57 Wemco 661.521.680.691.7 Wemco 841.602.131.354.2 Wemco 1202.293.051.358.5 Wemco 1442.743.661.6014.2 Wemco 1643.024.172.3628.3 ### Wemco Convention & Outotec Tank Cells ### Outotec Tank Cells ModelCell Volume (m3)Diameter (m)Lip Length (m)Froth Area (2)Air Flow (m3)Motor (kW) TankCell-552.04.73.02.811 TankCell-10102.56.34.74.318.5 TankCell-20203.17.97.16.737 TankCell-30303.69.49.79.045 TankCell-40403.810.010.610.055 TankCell-50504.712.716.515.0110 TankCell-70705.314.121.319.0110 TankCell-1001003.016.327.525.0132 TankCell-1301306.417.631.028.0160 TankCell-1601606.819.035.232.0185 TankCell-2002007.220.140.036.0250 TankCell-3003008.022.049.045.0300 ### Flotation Circuits Flotation circuits are typically comprised of rougher, scavenger and cleaner flotation banks. Rougher and scavenger banks are focused on recovery and thus provide maximum residence time. Rougher banks can be large with the number of cells being 5 or greater. Scavenger cells are the last line of defense for avoiding losses. Therefore, they are generally larger in size and numbers. Cleaner banks are focused on product grade and thus provide low residence time. As such, the number of cells are lower and the cells smaller. Column flotation is sometimes used as cleaners. ### Rougher-Scavenger-Cleaner Effect ### Cadia Processing Facility ### Cadia Metallurgical Balance Sheet StreamCuAu Head Grade (%, g/t)0.190.77 Concentrate Grade (%, g/t)26.381.0 Overall Recovery (%)77.971.2 Dorè Recovery (%)---11.3 ### Gold Flotation Circuit ## AMIT 145: Lesson 4 Gravity Separation ## Reading ### Gravity Concentration Ratio (CC) CC = SG of heavy mineral – SG of fluid/SG of light material – SG of fluid Concentration CriteriaSuitability for Gravity Separation CC > 2.5Easy down to 75 microns 1.75 < CC < 2.5Possible down to 150 microns 1.5 < CC < 1.75Possible down to 1.7mm 1.25 < CC < 1.5Possible down to 6.35mm CC < 1.25Impossible at any size • Reflects the difficulty in separating particles of near density and ultra-fine particles. • New technologies have enabled density-based separations at finer particle sizes. ### Concentration Ratio Examples CC = SG of heavy mineral – SG of fluid/SG of light material – SG of fluid MineralFluidCC GoldWater10.3 GoldAir6.8 CassiteriteWater3.5 CoalWater3.4 HematiteWater2.5 *Gangue material SG = 2.65 ### Separation by Differential Setting Velocity Note that the low CC value results in a narrow particle size range in which density separation can be achieved in H2O. ### Daniels Dense Separators CC = SG of heavy mineral – SG of fluid/SG of light material – SG of fluid ### Viscosity Limits on Medium Type ### Heavy Medium Separation Mineral Applications Operator/Plant LocationMineral ProcessedSize RangePlant Feed tphHMS UnitsSink/Float RatioSeparation Density Aluminum Co. od Canada, Ltd. St. Lawrence, Newfoundland Flourspar Barites -3/4" + 20M802-15"40/602.72 Barton Mines North Creek, NY Garnets-1/4" + 45M601-12" &1-9" 60/403.2 Basics Inc. Gabbs, NV Magnesite-3/8" + 20M301-9"75/252.9 Bethlehem Steel Corp. Icomi Mine, Amapa, Brazil Manganese-1/4" + 20M1302-15"80/202.9 Cia. Minera de Autlan S.A. Autlan, Mine Manganese-20mm +1mm 901-18"70/302.95 Universe Tankships Inc. Para, Brazil (Jari, Project) Bauxite-3/8"181-9"95/52.3 Companhia Mineira do Lobito Jamba Mine, Angola, Africa Iron-1/4" + 20M4006-15"80/202.7 Dresser Minerals Ryder Point Plant Flourspar Barites -25mm +1mm 802-15"50/502.75 Fundy Gypsum Co. Ltd Windsor, Nova Scotia Gypsum Rock -3/4" + 20M802-15"30/702.5 International Mining Co. Enramada Mine, Bolivia Tin/Tungsten-1" + 20M301-12"25/752.95 Lithium Corp. of America Bessemer City, NC Lithium-1/4" + 65M651-15"30/702.8 NL Industries Inc Guatemala Scheelite-1/2" + 14M101-9"60/402.7 Renison Ltd. Zeehan, Tasmania Tin-1/2" + 28M802-15"80/203.0 Southern Peru Copper Corp. Ilo, Peru Coquina Shells -1/4" + 30M501-15"50/502.7 Turk Maadin Sirketi Beyoglu, Turkey Chrome-1/4" + 20M101-9"60/402.9 ### Emeralds Processing by Heavy Medium ### Jigging Principles Jigging uses a pulsation of a fluid at a given frequency and amplitude to induce a separation based on differential acceleration, hindered settling and consolidated trickling. For small particles, short pulsations are preferred to emphasize separation based on differential acceleration. 1. Particles in a mixed pile before laying 2. Rising water level lifts the bed layer 3. Particle sedimentation stratification in the water 4. The water level drops, the bed layer is dense, and the heavy mineral settles at the bottom ### Jig Types ### Industrial Jig ### Teeter Bed Separators Utilizes an upward current of water that has a velocity equal to the high-ash content particles thereby creating a fluidized particle bed. The bed level is monitored and control by measuring the bed pressure and manipulating the underflow discharge valve. To report to the underflow stream, the particles must have a density or total mass that can overcome the hindered settling conditions in the fluidized particle bed. As such, Teeter-Bed units are commonly referred to as autogenous dense-medium devices. 3:1 particle size range. • Typical throughput capacity of around 1.0 – 2.0 tons/hr/ft2. • Previous studies have indicated the ability to achieve efficient density-based separations over a range of medium densities. • Concern is the bypass of coarse, light particles to the underflow. • Benefits include a large feed capacity which would eliminate distribution needs. • Commercial units: • Stokes Hydrosizer • Crossflow Separator • Reflux Classifier • Floatex Classifier ### Iron Ore Processing Circuit ### Iron Ore Processing Using Teeter-beds First Stage SeparationSecond Stage SeparationThird Stage Separation Capacity (t/h)Nom. 216 Max. 246 Min. 186 ~132~52 Degree of Enrichment≥64.5% Fe≥68% Fe Or 68% in total over the two stages ≤0.15% P ≤1.0% SiO2 Iron Recovery (Each stage) ≥81%≥80%≥61% Iron Recovery (Compared to incoming Fe-content) ≥83% Solids concentration in underflow (% by weight)≥79Average ≥76 ### Spiral Concentrators (Flowing Film) • Separation by density occurs as a result of primary flow and circulating secondary flow patterns that are created as the feed slurry travels along an elongated helical trough surface that spirals downward around a central axis. • The primary flow is responsible for carrying the particles in the downward direction toward the discharge point. • The secondary flow caused by retardation of the fluid flow near the trough surface provides the density separation by carrying light particles to the outer trough. ### Iron Ore Gravity Circuit ### Chromite Processing ### Centrifugal Force, Fc When the particle size falls below 1 mm, the rate of separation significantly impacts efficiency. To allow density‐based separations, a centrifugal field is applied by either a mechanical action or by accelerating the particles around a rotational axis. Particle acceleration is given by: ac = rw2 r = radial distance from center of rotation ω = angular velocity, (rad/s) The centrifugal force, Fc , is given by: Fc= mac= mrw2 The angular velocity ω can be expressed as a function of the tangential velocity of the particle (νT) and the radial distance (r): w = νr/r The centrifugal force, Fc is given by: Fc = mr(νr/r)2 = w = mνT2/r The angular velocity (ω) is often expressed in terms of the rotational speed, N w = 2πN/60 where w = 60νr/2πr The centrifugal force, Fc, is given by: Fc = mf(2πN/60)2 = 0.01097 mrN2 Centrifugal force is often expressed in the magnitude of the force with respect to the gravitation force (g’s): Fc/Fg = mrw2/mg = r/g(2πN/60)2 = 0.00118 rN2 ### Centrifugal Particle Setting Rate Msap = Fc – Fb – Fd Fc – centrifugal force Fb = buoyancy force Fd = drag force The terminal settling velocity of a particle in a centrifugal field and under Stokes laminar flow conditions can be expressed as: νt = rw2d2(ρs-ρf)/18μ ### Centrifugal Force Effect ### Enhanced Gravity Separators ### Falcon Concentrator Flowing film separation principles. Bed is controlled by the width of the overflow lip. High density particles removed by a series of valves placed along the circumference of the bow. Centrifugal forces up to 300 g’s. Capacities up to 100 tph and around 2200 gpm. ### Knelson Concentrator Fluidized bed separation principles. Fluidization water is injected through two rings located at the top of a bowl. High density particles settle against the fluidization water and removed by valves placed along the circumference. Around 60 G’s of force applied. Capacities up to 100 tph. ### Altair Centrifugal Jig Rotating bowl contains a cylindrical screen with a lip, whose height can be adjusted to vary the natural depth of the ragging bed. Pressurized water is injected under the bed periodically through the four pulse-blocks to cause alternating dilation and contraction of the ragging and feed bed ### Circuit Boards ### Gold Processing ### Ft Knox Gold Processing Circuit ## AMIT 145: Lesson 3 Dense Medium Separation ## Reading ### DM Vessels • Utilizes a suspension of magnetite to adjust the medium density to a value that is between coal and the ash bearing material. • The medium density correlates to the required separation density needed to achieve a desired product grade. • Feed to a heavy media vessel is injected perpendicular to the elongated width of the vessel • Float material travels across the vessel or is removed by a flight conveyor to one end. • The high density particles sink and moved chain conveyor to other end. DM Vessel Types Deep Baths • Wemco Cone • Tromp Vessel • Chance Cone Shallow Baths • Peters • Daniels Drum Baths • Teska • Tromp • Wemco #### Shallow DM Vessels This lecture will deal mostly with the Shallows Baths since they are the most common in the U.S. Cost effective for +1/4-in raw coal feed. • Low capital cost • Low operating cost • Ability to handle large amounts of refuse • Adaptability to all types of coal • Wide range of separating densities • Very efficient of a broad particle size range #### Daniels Dense Medium Vessel #### Shallow DM Vessel Sizing • Length is based on how many feet of overflow weir is required to effective carry the coarse material into the product overflow stream. • Width is established based on the amount of reject needed to be removed by the drag flight conveyors. • A general rule is that the length should be based on 25 tons/hr of feed material for every foot of overflow weir. • Example: A 500 ton/hr feed stream would require a 20-ft weir length. • This rule is based on a separation gravity below 1.55 and a 50% yield to the product stream. #### DM Vessel Width • The width is based on the capacity of the flight conveyors which can be estimated by the following table. Appropriate Refuse Capacity (short tons/hr) Height of Flights (inches)48-in Conveyor Width54-in Conveyor Width60-in Conveyor Width 8260300330 9300330370 10330370400 • Capacity values are based on a flight speed of 68 feet/min. • Conveyor capacity could be increased by either a change in speed or an increase in the number of flights up to a critical value. • However, the wear rates of the conveyor and vessel parts increase exponentially as the refuse chain speed exceeds 74 feet/min. #### DM Vessel Operation Prior to feeding coal to the DMV, the correct dense medium is pumped into the vessel through the feed washer manifold and the purge hoppers. The vessel is filled until it is freely overflowing. The proper inflow of medium can be estimated to be 260 gallons/min for every foot of overflow weir length. • For example, a 15 ft weir length vessel would require a dense medium flow rate of 15 ft x 260 gpm/ft = 3900 gallons/min • To check for proper flow, one can physically measure the fluid depth overflowing the weir. The proper depth is 3 ¾-in. The coal is then fed to the HMV through the Feed Manifold. The depth that the feed is injected should be minimized to avoid possible bypass of light particles to the tailings stream. A feed sink plate is used to direct the feed downward into the vessel so that particles do not ‘raft’ across the width of the bath. • If the refuse particles tend to adhere to the coal particles, the plate should be adjusted downward where higher currents are present. • The plate is a high wear item and thus should be checked periodically. Approximately 10% of the dense medium enters through the purge hoppers. • Provides a gentle up-current which helps stabilize the medium. • The purge hopper also serves as the drain when the HMV is shut down. #### DM Vessel: Low Density By-Pass Causes may include: • In-sufficient upward flow medium; • Plugged purge hoppers; • Deep feed injection; • Unstable medium; • Overflow weir overload; • False reading caused by laminated middlings. 260 gpm/ft of weir length. 10% of medium needs to report through the purge hoppers. Overflow depth = 3-¾ inch Weir length = 25 tph/ft #### DM Vessel: High Density By-Pass Causes may include: • Excessive upward flow of medium; • Worn sink plate; • Overload of high-density material in feed; • Viscous medium; • Excessive or un-equal medium flow in feed side manifolds; • Large amount of material below the bottom size in the feed. Adequate conveyor capacity is needed by flight number, dimensions and speed. Medium contamination less than 10%. ### Dense-Medium Cyclones (DMC) Dense medium cyclones (DMC) have been found to be effective in treating particle size fractions between 3-inch and 100 mesh, however, not typical done in a single unit. The DMC application for treating 16 x 100 mesh material is limited due to significant magnetite loss resulting from inefficiencies on the drain-and-rinse screens. The ability to treat particle sizes from 3 to 1 inch is a result of the development of large diameter DMC units in the late 1990’s. Cyclone diameters greater than 1 meter are currently available having mass throughput capacities approaching 500 tons/hour. ### DM Circuit Trends The ability to efficiently treat a large particle size range of 3 inch to 16 mesh in one process unit has revolutionized the design of coal preparation plants by reducing the number of required circuits. ### Large Diameter DMC Performance Comparisons GoonyellaRiverside Particle Size (mm)Twin 710 mm Cyclones EpSingle 1 m Cyclones EpTwin 710 mm Cyclones EpSingle 1 m Cyclones Ep +16 16 x 4 4 x 2 2 x 0.5 0.028 0.030 0.038 0.055 0.025 0.026 0.028 0.045 0.020 0.025 0.045 0.070 0.014 0.020 0.026 0.049 16 mm = 4 in.; 4 mm = 1 inch; 2mm = 0.5 in.; .5 mm = 0.127 in. ### DM Cyclone Like classifying cyclones, an air core is needed through the middle of the cyclone to ensure proper directional movement of the inner fluid toward the Vortex Finder. Unlike classifying cyclones, DMC units must be installed in a near horizontal position, which is typically 10o from horizontal. #### DM Cyclone Operation The reason for the near horizontal position is that, in the vertical position, the gravitational pull on the dense medium results in a slumping of the medium toward the apex, which pinches the air core. Under a ‘slumping’ condition, the separation efficiency would be very sensitive to inlet pressure and medium viscosity. Other factors favoring a horizontal orientation include the ease of piping for both gravity-fed and pump-fed systems and a reduction in head-room requirements. DM Cyclone Dimensions – DM Cyclone Diameter, Dc  Inlet Diameter, Di = 0.20 x Dc Vortex Finder Diameter, Do = 0.43 x Dc Apex Diameter, Du = 0.30 - 0.40 x Dc Inlet Pressure = 10 - 20 psi Included Angle = 20° Inclination Angle = 10° Feed Medium-toCoal Ratio = 5:1 #### Operating Conditions Critical Parameters for Good Heavy-Media Cyclone Operation • Operation Head • Media Splits • Media Quality • Orifice Diameters • Internal Geometry #### Operating Head (pressure) #### Gauge Pressure to Operating Head Operating Head • Nominal Operating Head = 9 Cyclone Diameters Example: 8.26” Ø ÷12 x 9 Dc = 19.5 Ft. of Head (LCH) • Always Convert Gauge Pressure to Feet of Head. Example: 12.7 PSIG ÷ 1.50 SG = 8.47 PSIG (H2O) 8.47 PSIG x 2.31 = 19.5 ft of Head (LCH) Operating Conditions Can Trim Head Requirements • High Densities or Large Inlets May Permit Higher operating Heads • Lower Densities or Small Inlets May Require Lower Operating Heads • Important to Consult Supplier on these Issues #### Required Feed Pressure @ 9 Operating Heads Heavy-Media-Cyclone Pressure Required to Maintain 9 Dc at Various Media Densities ### Media Split • Generally Media Split Should Follow Coal Yield on a volume Basis • Lower Densities Normally Require Lower Media Splits to Overflow • Decision to Adjust Media Split Requires Careful Study • Media Split Influenced by Coal Yield • Normally, Media Split Change Related to Apex Enlargement. #### Measuring Media Split • Measure Media Density of Feed, Overflow, and Underflow Media • Calculate Media Split by the following Equation: $\frac{SG_{Underflow}&space;-&space;SG_{Feed}}{SG_{Underflow}&space;-&space;SG_{Overflow}}&space;x&space;100&space;=&space;\textup{Media&space;Split&space;to&space;Overflow&space;(v/v)}$ #### Typical Feed Volumetric Capacities Dense-Medium Cyclone Diameter (inches)Volumetric Feed Rate (gallons/min)Feed Mass Flow Rate (tons/hr) 20132575 261750140 302600208 333800304 405200416 #### DM Cyclone Circuit #### Operating Condition Factors Feed Pressure Low feed pressures of 10 to 20 psi are used to maintain a stable magnetite suspension and reduce wear. However, excessively low pressures can lead to high density particles, especially slab shaped, by-passing to the overflow product stream. Feed Flow Rate The volumetric feed flow rate that can be processed by a DMC is a function of • Cyclone diameter strongly; • Feed pressure strongly; • Apex diameter slightly. Interestingly, medium density has no effect on feed rate. ### Medium-to-Coal Ratio Medium -to -Coal Ratio=Volume of Medium: Volume of Coal For example, the feed rate to a DM separator is 400 ton/hr of coal which has a relative density of 1.60. The desired medium to coal ratio is 5:1. Determine the amount of medium needed in gallons/min with the example below: Coal Volume = (400 tons⁄(hr) (2000 lbs⁄ton)) / ((62.4 lbs⁄ft3 ) (1.60) (60 min⁄(hr))(0.1337/ft3⁄(hr)))=999 gpm Medium requirement = 5 x 999=4995 gpm The ratio minimum in the feed is related to hindered settling effects. High solid concentrations slow the movement of particles to their respective process streams leading to inefficiencies ### Apex-to-Vortex Diameter Ration As you may recall, it is advantageous to minimize the Apex-to- Vortex Finder diameter ratio (DU/DO) to reduce the effects of ultrafine by-pass. In DMC units, the DU/DO ratio is generally higher and can approach a value of unity. As the DU/DO ratio approaches unity, the overflow rate falls and the underflow rate increases. ### DM Cyclone: High Density By-Pass Causes may include: • Vortex Finder Wear; • Low feed pressure; • High Vortex: Apex • diameter ratio; • High feed M:C ratio; • Overload of high-density • material in feed; • Viscous medium; • Large amount of material below the bottom size in the feed. To ensure proper operation, the medium-to-coal ratio in the underflow should be maintained above 1:1. Medium contamination less than 10%. Causes include: • Vortex Finder overload; • Apex Wear; • Unstable medium. Vortex Finder Overloading exists when the vortex finder is too small to accept all of the floatable material reporting in the feed stream. When a low volumetric amount of medium reports to the overflow, coarse low- density particles are unable to exit. Medium-to-coal ratio in the overflow stream should be maintained above 2.5:1. Medium split should approximately equal the medium split. ### Particle Retention & Surging Particle retention in DMC units occur due to density gradients being formed within the unit. Retention occurs because particles of a given density, typically the middle density fractions, have the inability to penetrate the high density layers and report to the underflow stream. As such, they remain trapped between density layers. If the feed medium-to-coal ratio is low (< 6.0) and the feed contains significant amounts of near density material, the amount of particle retention can be significant. However, as long as the particles are continuously removed through one stream or the other, the effect of particle retention is minimal. Large particles, however, tend to build up large loads in the cyclone and then spontaneously release the load through the apex. This process is called surging and rarely occurs when the feed top size is below 15 mm. ### Cond. #1: Low-Density Gradient (Stable Medium) ### Cond. #1: High-Density Gradient (Unstable Medium) ### Particle Retention and Surging Coarse particle retention and surging are characterized by the following partition curve. To reduce or eliminate particle retention, the difference between the medium density of the overflow and underflow streams (ρu – ρo) should be less than 0.40 RD units. To reduce the density difference, the following actions can be used: • Reduce inlet pressure; • Reduce magnetite particle size; • Increase DMC diameter; • Increase apex diameter; • Increase the feed medium- to-coal ratio; • Reduce feed particle size ### High Medium Viscosity He and Laskowski showed how medium viscosity negatively affects efficiency. Increase in medium density and contamination as well as a decrease in magnetite particle size elevates viscosity. Less than 20 centipoise is recommended. Results in: • Low medium differential; • Low ash in the finer fractions of the rejects; • High ash in the finer fractions of the clean coal product. ### DM Cyclone Design The following model was developed by the JKMRC Research Center in Australia and described by Chris Wood (1990). The model and steps of the scale-up procedure will be presented through the development and solution of an example problem. ### DMC Design Example: A preparation plant is being designed to treat 700 ton/hr of ROM coal containing an average of 5% moisture (air-dried basis). A nominal 30 x 0.5 mm fraction comprises 80% of the total ROM feed and will be cleaned using DMC units. The required product grade is 7.5%. The washability analysis of the feed material is provided in the following table. #### Solid Density Determination #### Step 1: Estimate the Required Separation Density and Yield • Determine from washability data the mass yield and relative density required to achieve the desired product grade. • In the example, a relative density of 1.39 will provide the required 7.5% ash content while recovering 69% of the feed mass. #### Step 2: Estimate the Densities of the Feed, Clean Coal and Rejects • The average densities of the feed, product and tailings can be estimated from the washability data since high accuracy is not required in this step. • In this manner, the average densities are determined for each density fraction in the feed and the overall average density is obtained by the summation of the mass units divided by the sum of all volume units comprising the given material. • For the feed, the average relative density is 1.45 which is obtain from the column (i) at 100% yield. • In similar manner, the clean coal density achieved with a 1.39 separation density is approximately 1.31. • Thus, the tailings density can be determined using a volume conservation balance expression: $\frac{mass\:&space;of\:&space;feed}{density\:&space;of\:&space;feed}&space;=&space;\frac{mass\:&space;of\:&space;floats}{density\:&space;of\:&space;floats}&space;+&space;\frac{mass\:&space;of\:&space;sinks}{density\:&space;of\:&space;sinks}$ $\frac{100}{1.45}&space;=&space;\frac{69}{1.31}&space;+&space;\frac{(100-69)}{density\:&space;of\:&space;sinks}$ Density of sinks = 1.93 #### Step 3: Flow Rates of Feed, Overflow (Clean Coal) and Underflow (Reject) • The volumetric rate of solids in each process stream, which excludes medium, can be determined by relating mass flow to the DMC units to the average density of each stream. • w is the fractional content of feed in the given size fraction and ф the fractional surface moisture. • Based the feed flow rate and a feed medium-to-coal ratio of 4:1, the minimum feed slurry flow rate, QF, can be determined. #### Step 4: Selection of the Number and Geometry of DMCs • To avoid blockages in the cyclone inlet, it is recommended that the 95% passing size of the feed not exceed (0.05 x DC). • Therefore, in the example, the cyclone diameter should be at least (30 mm/0.05) = 600 mm. Thus, for a 610 mm cyclone, the inlet diameter will be (0.2 x 610 =) 122 mm. • Since the volumetric split of feed solids is approximately 23% to underflow and the common apex diameter is (0.10 x DC) only passes 10% of the feed volume to the underflow, a larger apex of 0.35 x DC will be considered. • According to the JKMRC DMC model, the volumetric flow rate to a DMC can be estimated by the following expression: Qf = 2.87 (10– 5) DC2.30 ρ0.46 [Du/Do]0.17 • In which Dc, Du and Do are the cyclone, apex and vortex finder diameters, respectively (mm) and P the inlet pressure expressed in terms of cyclone diameters. #### Step 5: Feed Volumetric Capacity • The inlet pressure in terms of ‘cyclone diameters’ can be determined from a gauge placed on a cyclone at a vertical distance s. The reading in kPa can be used to determine the required units of P using the following expression: $P&space;=&space;\frac{(102)(\frac{kPa}{\rho&space;_{fs}})&space;+&space;(s)}{D_{c}}$ where the vertical distance above the cyclone, s, is in mm and rfs is the relative density of the feed slurry, which can be approximated by the medium density. • Three commercially available cyclone diameters will be evaluated in an effort to select the optimum size, i.e., 610, 711 and 813 mm. • Using P = 9 diameters, the flow rates and the required number of cyclones for treating QF = 1835 m3/hr was determined and the data provided in the following table Required Capacity (m3/hr)Dc (mm)QF (m3/hr)Required Number of DMC unitsExcess Capacity (%) 1835610193105 1835711276820 1835813374622 • With the 711 and 813 DMC units, sufficient capacity could be provided by 7 or 5 units, respectively. • Plant layouts typically use DMC units in pairs, so 6 and 8 units were chosen for the two larger cyclones. • Selection between the options would be based on expected over capacity needs, raw coal distribution problems and costs of pumps, screens and other ancillary equipment. • For this example, eight 711 mm cyclones will be selected. • The volumetric yield of feed slurry to the underflow stream can be determined using the expression: $\frac{Q_{U}}{Q_{F}}&space;=&space;9.29&space;D_{c}^{-0.31}&space;P^{-0.48}&space;\left&space;(&space;\frac{D_{U}}{D_{O}}&space;\right&space;)^{4.16}$ • In the example, the volumetric split is: $\frac{Q_{U}}{Q_{F}}&space;=&space;9.29&space;(711)^{-0.31&space;(9)^{-0.46}}\left&space;(&space;\frac{0.35}{0.43}&space;\right&space;)^{4.16}&space;=&space;0.188$ • Thus, the volumetric flow rate to the underflow and overflow streams of each cyclone in the example are: $Q_{U}&space;=&space;\left&space;(&space;276\frac{m^{3}}{hr}&space;\right&space;)\left&space;(&space;0.188&space;\right&space;)&space;=&space;52\frac{m^{3}}{hr}$$Q_{O}&space;=&space;\left&space;(&space;276\frac{m^{3}}{hr}&space;\right&space;)\left&space;(&space;1&space;-&space;0.188&space;\right&space;)&space;=&space;224\frac{m^{3}}{hr}$ • Medium-to-Coal ratio is essentially a measure of the percent solids in the slurry if one considers the magnetite suspension a pure fluid. • As such, the ratio is determined on a volumetric basis. $M&space;-&space;to&space;-&space;C&space;=&space;\left&space;(&space;Q_{F}&space;-&space;\frac{total\:&space;Q_{FS}}{n}&space;\right&space;)&space;/&space;\left&space;(&space;\frac{total\:&space;Q_{FS}}{n}&space;\right&space;)$ QFS is the total volumetric flow rate of solids (no medium) that is required to be treated by DMC units, QF the volumetric slurry feed flow rate for each cyclone under the given conditions and n is the total number of cyclones. $Feed\:&space;M&space;-&space;to\:&space;C\:&space;ratio&space;=&space;\left&space;(&space;276&space;-&space;\frac{376}{8}&space;\right&space;)&space;/&space;\left&space;(&space;\frac{376}{8}&space;\right&space;)&space;=&space;4.9:1$$Underflow\:&space;M&space;-&space;to&space;-&space;C&space;=&space;\left&space;(&space;52&space;-&space;\frac{86}{8}&space;\right&space;)&space;/&space;\left&space;(&space;\frac{86}{8}&space;\right&space;)&space;=&space;3.8:1$$Overflow\:&space;M&space;-&space;to&space;-&space;C&space;=&space;\left&space;(&space;224&space;-&space;\frac{280}{8}&space;\right&space;)&space;/&space;\left&space;(&space;\frac{280}{8}&space;\right&space;)&space;=&space;5.4:1$ • As shown, each of the medium-to-coal ratios are above the minimum recommended values needed to avoid surging and vortex flow problems. • A minimum of 2/3 of the medium should report to the overflow to ensure the ability to recover the coal to the vortex by using a smaller apex. #### Step 6: Magnetite Grade, Underflow & Overflow Medium Densities and Differential • As described previously, it is important that the medium density between the underflow and overflow streams be maintained at a value less than 0.4 to minimize the negative effects of particle retention and surging. • As expected, the fineness of the magnetite has a critical role in determining the density difference and the parameter p in the model reflects the Rosin-Rammler intercept. • Finer magnetite reduces the differential, however magnetite recovery becomes a concern. • In considering the density differential, one must be concerned with the required medium density (ρm) with respect to the estimated separation density (ρ50) as determined from wash ability analysis. • Typically, (ρ50 – ρm) is approximately 0.10. Therefore, in our example, ρm= 1.29. • The expressions developed to estimate the underflow (ρu) and overflow (ρo) density values (minus the coal) are: • Typically, a medium density of 1.29 is considered low and suspension stability concerns exist. Use of an ultrafine magnetite may be needed. • However, let us consider a coarser ‘superfine’ magnetite first, which, if proven applicable, would reduce magnetite losses. For a superfine magnetite, p (i. e., the 63.2% passing size) is 31 microns. Therefore, (ρU – ρO) is 0.54, which is too high and would lead to severe particle retention and surging. • As such, a finer magnetite should be considered. The p value for a typical ultrafine magnetite is 26 microns. • Redoing the calculations results in:ρU =1.54ρO=1.20 • Thus, the finer magnetite reduced the differential to 0.34, which is within the acceptable range #### Step 7: Feed Medium Density Check • To check the selection of the feed medium density was correct, which was based on an approximation of the difference between the required separation density and the medium density, the following expression is utilized:ρ50= ρm +0.125+0.154 ρu-0.215 ρo = 1.29+ 0.125 +0.154(1.54)-0.215(1.20) = 1.39 • Since 1.39 is the desired separation density, we can stop. • However, if the value did not equal the required density, step 6 would be repeated with a different ρf value until agreement is realized. • This separation density value reflects performance achieved on the +4mm particles while finer particles are expected to achieve higher values. #### Step 8: Separation Performance Predictions versus Particle Size • From the empirical data, researchers at JKMRC developed the following relationship which shows the separation density (ρ50d) achieved on each particle size fraction (mean size =d in mm) below 4 mm as compared to the separation density predicted for the +4 mm (ρ 50):ρ50 d = ρ50 + 0.0674 [1/d – 1/10] • The corresponding probable error for each fraction can be estimated from the expression:Ep=0.033 ρ50 / d ### Separation Density & Efficiency vs. Particle Size • Quality generally described by the % -44 micron.e.g.; • U.S.Grade B =95% passing 44 microns is most often used • Required magnetics content >97%. ### Magnetite Amount Required • Determination of the required amount per 1 m3 of water Density of Water = 1000 kg/m3; 1 m3 of Water = 1000 kg Magnetite Density = 5170 kg/m3 • For example, a 400 tph feed to a dense medium process equates to a volumetric flow rate of 1000 gallons/min or 3.785 m3/min. At a 4:1 medium-to-coal ratio, the volume of medium is 15.14 m3/min. • To achieve a ρm = 1.50 RD, the required amount of magnetite in the medium is 704 kg per m3 of medium or 10664 kg/min = 10.7 tonnes/min. ### Magnetite Losses Magnetite costs have become a significant operating expense with the prices ranging from$160-\$300/ton.

Magnetite loss ranges from 0.50 – 3.0 kg/tonne of feed (1 – 6 lb/ton) and will depend on:

• Fineness of the
• magnetite;
• Fineness of the coal;
• Magnetic separator
• efficiency;
• Magnetite recovery circuit design.

Most of the loss occurs at the drain and rinse screen.

The majority of the lost magnetite is associated with adhesion to the particles in the clean coal and reject streams.

An expression was developed by the Dutch State Mines researchers that quantifies the amount of magnetite Qm (liters/ton) adhering to the coal and reject as a function of particle size ds (mm) and density ρs:

$Q_{m}&space;=&space;\frac{950}{d_{s}&space;\times&space;\rho&space;_{s}}$

For example, consider the typical particle size ranges reporting to the dense medium vessel (100 x 10 mm) and dense medium cyclones (10 x 1 mm). The arithmetic mean particle sizes are 55 mm and 5.5 mm, respectively. The relative particle density is about 1.35.

Vessel Product:
$Q_{m}&space;=&space;\frac{950}{55&space;\times&space;1.35}&space;=&space;12.79\:&space;liters/ton&space;=&space;0.0128\:&space;m^{3}/ton$

$=0.0128\:&space;m^{3}/ton&space;\times&space;5000&space;kg/m^{3}&space;=&space;64&space;kg/ton$

Dense Medium Cyclone Product:
$Q_{m}&space;=&space;\frac{950}{55&space;\times&space;1.35}&space;=&space;12.79\:&space;liters/ton&space;=&space;0.1279\:&space;m^{3}/ton$

$=&space;0.1279&space;\times&space;5000.0&space;=&space;640kg/ton$

Obviously, if drainage only was used to recover the magnitude, a tremendous magnetite loss would be realized, even for the coarse coal application.

Typical losses: 0.5 kg/ton of coarse feed and 1.0 kg/ton of fine feed.

### Rinse Water Requirements

• The rinse screen portion of the drain-and-rinse screen used to recover magnetite uses shower boxes and water sprays. Water boxes tend to be more efficient for magnetite recovery.
• The amount of water required is a function of the screen area and varies between 20 m3/hour/m of screen width to 65 m3/hour/m.
• The amount of water is less for the shower box as compared to water sprays as shown by the following equations, which were developed by the DSM researchers
Shower Boxes:

$Q_{W}&space;=&space;\frac{3}{d_{s}\:&space;\times&space;\:&space;\rho&space;_{s}}&space;m^{3}/ton$

Water Sprays:

$Q_{W}&space;=&space;\frac{9}{d_{s}\:&space;\times&space;\:&space;\rho&space;_{s}}&space;m^{3}/ton$

• Typically, sprays are used for the coarse products where the total screen area is low while shower boxes are employed in fine particle rinsing.
• Water is added in stages. About 4/5ths of the water is recirculation water, generally from the overflow of the magnetic separators.
• Clean water is added in the last sprays/boxes just prior to discharging the screen.
• The capacity of a drain-and-rinse screen can be estimated by the Sauter diameter, which is a measurement based on the amount of particle surface area.
• The Sauter diameter is determined by dividing the mass in each size fraction by the mean particle size of the size fraction, which essentially provides the average amount of surface area for a given amount of mass.
ABCDC/D
Particle Size FractionOpening (mm)Weight (%)Arithmetic Mean Particle Size
3/8" x 4M4.7615.567.142.18
4M x 8M2.3612.133.563.41
8M x 16M1.188.451.774.77
16M x 30M0.605.550.896.24
Total41.6916.60
Sum (C/D)/41.69 = 0.398
Sauter Mean Diameter = 2.51
• Total length is about 4.8m long with the first 1.2m being a sieve bend with 0.5mm openings and 3.6m being a horizontal screen.
• Typical sieve bend capacity = 105 to 135m3/h/m2 of screen area.
• The drain-and-rinse screen capacity can be estimated by the following formula:
$C&space;=&space;4.03&space;\left&space;[&space;(\mathit{SMD})2x\rho&space;_{S}^{2}&space;\right&space;]^{1/3}&space;x&space;Ao/17.5$Dutch States Mine Equation
C = screen discharge capacity (tons/hr/ft of effective width)
ρs = relative density (sp.gr.) of the solids
Ao = open area of screen surface
• The D&R screen capacity determined from the equation can be multiplied by a factor of 1.4 to estimate the capacity of banana screens in a drain-and-rinse application
• Effective width = Nominal width – 0.5ft
• Example: Clean coal drain-and-rinse screen, ρs = 1.35
$C&space;=&space;4.03&space;\left&space;[&space;(2.51)2x1.352&space;\right&space;]^{1/3}&space;x&space;30.0/17.5$
=15.6 tons/hr/ft
8ft screen = 117 tons/hr

### Magnetic Separators

Typically a Wet-Low Intensity Drum Separator.

• Approximately 750 Gauss (High-Gradient Rare Earth Drums = 21,000 Gauss or 2.1 Tesla.

Commonly employ 0.9 and 1.2 meter diameter units that range up to 3 meters in width

Two types of tank styles exist, i.e.,

• Concurrent
• Counter-rotation

The counter-rotation unit is the most popular due to elevated magnetite recovery.

### Magnetic Separator Capacity

In the counter-rotation unit, the drum rotates against the inward flow of dilute medium. As the medium passes through a slot having a preset depth, magnetite is attracted to the drum. The drum can be adjusted to obtain different medium depths.

Losses are typically no more than 0.25 grams/liter of non-magnetic product.

Wet Drum Capacity in Dense-Medium Recovery Applications Counter-Rotation; Grade E Magnetite; Feed Solids < 13% by weight.

## AMIT 145: Lesson 2 Classifying Cyclones

Classifying cyclones are the most commonly used technology for achieving particle size separations below 300 microns.

Classifying cyclones are comprised of a cylindrical section and a conical section.  The length of the conical section has been found to significantly effect particle size separations

### Cyclone Fundamentals

A tangential feed injection is used to induce a centrifugal force, which accelerates the particle size settling kinetics.

Coarse particles report to the outer wall of the cyclone and spiral downward toward the apex or spigot via the motion of the fluid stream.

Due to a constricted apex, the volume reporting to the underflow stream is restricted and thus a portion of the stream is forced to reverse direction and move upward along a low pressure zone toward the Vortex Finder.  The upward moving flow carries the fine particles to the overflow stream.

### Design

The magnitude of the applied centrifugal force increases with a decrease in cyclone diameter. As such, the cyclone diameter selected for a given application is associated with the desired size separation.

In mineral applications. it is generally stated that a certain size cut is desired which would imply that the majority (i.e., 95%) of underflow solids has a size greater than the target cut point and the overflow has a majority less than the desired cut point.

However, design models are based on the particle size that has a 50% probability of reporting to the overflow or underflow stream.

It is generally recognized the small particle size separations require small diameter hydrocyclones. For geometrically equivalent cyclones, the mean particle size separation (d50) is a function of the cyclone diameter, i.e.,

d50(c) = DCX

where the value of x has been debatable and vary from model to model as shown below:

• 1.875 → Krebs-Mular-Jull Model (1978);
• 1.8 → Plitt’s Model (1976);
• 1.36 to 1.52 → Bradley’s Model (1965).

### D50(c) Versus Overflow Size Relationship

As previously mentioned, mineral applications require a separation whereby a material finer than the desired cut point reports to the overflow whereas design is based on the d50(c).

A relationship between the d50(c) and the overflow size was developed by Arterbury (1976).

For example, it is typically desired to achieve a 100 mesh (150 micron) separation.

• 95% -100 mesh in overflow.
• Multiplier = 0.73.
• Target d50(c) = 150 x0.73 = 110 microns
Required Overflow Size (% passing)Multiplier
98.80.54
95.00.73
90.00.91
80.01.25
70.01.67
60.02.08
50.02.78

### d50 Versus 95% Finer

• Particle size distributions of the feed, underflow and overflow streams.
• d95 (overflow) = 95 microns.
• d95 (underflow & feed) = 750
• Due to inefficiencies, every particle in the feed has a probability of reporting to either the underflow or overflow streams.
• The particle size having a 50% chance of reporting to either stream is the d50.

### Plitt Equation

A commonly used design model used for applications in the mineral industry was design by Plitt (1976), i.e.,

$d_{50(c)}&space;=&space;\frac{14.8D_{C}^{0.6}&space;D_{i}^{0.6}&space;D_{O}^{1.21}&space;exp(0.063v)}{D_{U}^{0.71}h^{0.36}&space;Q^{0.45}(\rho_s&space;-&space;\rho_w)^{0.5}}$

$Q&space;=&space;\frac{0.021P^{0.56}&space;D_{C}^{0.21}&space;D_{i}^{0.53}&space;h^{0.16}&space;(D_{U}^{2}&space;+&space;D_{O}^{2})}{exp(0.0031V)}$

in which d50(c) is in microns, Q in m3/hour, Dc , Di , Du and Do the cyclone cylinder, inlet, spigot and vortex finder diameters in centimeters, h the distance in cm from the bottom of the vortex finder to the top of the apex, P the feed pressure in kPa (1 psi = 6.895 kPa), ρs the density of solids in grams/cm3, and V the volumetric percent solids concentration in the feed.

The definition of a ‘typical’ cyclone is:

1. Inlet area ≈7% of the cross-sectional area of the cylindrical chamber.
2. Vortex Finder diameter = 30% of the cyclone diameter.
3. Apex diameter = 10%-35% of the cyclone diameter.
4. Cone Angle = 10° – 20°

### Classifying Cyclone Design (Krebs Engineers)

Krebs Engineers approach cyclone design similar to screen design.

Cyclone design is based on the d50(c) achieved using a typical cyclone under standardize conditions, i.e.,

• Medium = water at 20°C & 1 centipoise
• Solids density= 2.65
• Solids concentration < 1%.
• Pressure drop = 10 psi.

The base d50(c) can be estimated by the expression:

d50(c) (base)=2.84DC0.66

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### Krebs Cyclone Design

The actual d50(C) can be determined from the expression:

d50(c) (actual) = D50(c) (base) x π1m CPm x π1n CDn

in which CPm are the correction factors for m process variables and CPn the design related factors.

Process variable include feed solids content, solids density, pressure drop and slurry viscosity.

Cyclone design parameters include cyclone diameter, vortex finder diameter, spigot diameter, length of cylinder, cyclone, cyclone angle and mounting angle.

### Pressure Drop Correction

Pressure drop within a given operation can be adjusted through a change in volumetric feed rate.

• Variable feed pumps.
• Valves on feed lines which opens or closes the flow to cyclones in a bank.

A change in feed pressure has a relatively small effect on the d50(c).

The expression for the determination of the correction factor is:

CP(pressure) = 3.27p-0.28

Where P is the pressure drop in kPa

### Solid Density Correction

The rate that a charged particle moves in a fluid under centrifugal forge is a function of particle density.

Higher density particles move at a faster rate toward the cyclone wall. As such, the d50(c) for high density particles is lower.

The correction factor for solid density is:

CP(density) = [1.65/(ρsm)]-0.5

Where ρs and ρm are the densities of the solid and medium in gm/cm3.

### Cyclone Design Corrections

Inlet Diameter

• Effects both feed flow rate capacity and d50(c).
• Manufacturers can provide different sizes and shapes to meet flow rate capacities.
• In general, an increase in inlet size elevates capacity and the d50(c).

Cylinder Length

• Increasing length results in greater retention time which should reduce d50(c).
• Typically, the cylinder length is equal to the cyclone diameter.

Large cyclones (>660 mm) use shorter cylinder lengths.

#### Cone Section

Cone angles vary from 6° to 90°

20° cone angle has been the standard; however, 10° is common for cyclones in the mineral industry

High cone angles are typically used to achieve very coarse particle size separations

Longer 10° cones achieve higher retention times and finer, more efficient size separations.

Recently, Krebs Engineers developed the qMax cyclone which incorporates a dual slope cone, i.e., a 10° at the interface between the cylinder and the cone and a 6° angle at the bottom of the cone. Retrofitting a standard cyclone allows lower d50(c).

#### Vortex Finder

• Primary role is to control the size separation and the flow leaving the cyclone.
• Extended below the inlet to prevent feed bypass
• Size can range from 20% – 45% of the cyclone diameter
• Large vortex finders increase capacity and elevates the d50(c)
• The expression to determine the correction factor is:

$\frac{CD&space;(vortex)&space;-&space;D_{o}}{(0.3D_{c})^{0.6}}$

#### Apex Diameter

• Must be large enough to allow passage of the expected amount of flow.
• Has some effect on the d50(c).
• Correct size is typically selected after the cyclone size and number has been determined and a material balance has been performed.
• The pattern of the discharge is indicative of performance: a) a wide angle indicates unacceptable solids content and ‘roping’ conditions represent excessive solids content and poor performance

### Volumetric Feed Flow Rate

The volumetric feed rate to a cyclone is directly related to the pressure drop across the cyclone.

As such, the pressure drop used for determining the d50(c) is applied to determine the feed flow rate per cyclone.

To determine the number of cyclones needed, the total flow rate of the stream is divided by the allowable flow rate per cyclone (see attached graph).

The data shown in the graph was obtained using water. Therefore, the determination of the number of cyclones will be a slight over estimation.

#### Design Example

A classifying cyclone system is needed to achieve a 150 micron (100 mesh) separation. The total volumetric flow rate to the system is 5000 gpm at a solids content of 5% by weight (ρp=1.02). At an average relative solids density of 1.3, the solids mass flow rate equates to 64 tons/hr. The desired operating pressure is 12 psi (82.7 kPa). A standard vortex finder size will be used.

#### Performance Prediction

The efficiency of a classifying cyclone is typically measured by the slope of the partition curve plotted on the basis of the probability of a particle reporting to the underflow stream versus particle size.

A more direct efficiency measurement from the partition curve is the imperfection value (I):

I = d75 – d25 / 2d50

in which d75, d50, and d25 are the particle sizes having 75%, 50%, and 25% probabilities, respectively, of reporting to the underflow stream

#### Example: Partition Curve Development

The mass yield of solids to the underflow has been determined to be 63% using the two-product formula. A particle size analyses of samples collected from the underflow and overflow streams have been completed and the results provided:

#### Actual Partition Curve

A plot of Column [7] versus Column [1] forms the Actual Partition Curve which is shown in the following figure.

### Ultrafine By-Pass

An inherent inefficiency of classifying cyclones is that the water recovered in the coarse underflow stream carries ultrafine particles that should be in the overflow stream. The by-pass is typically referred as ultrafine by-pass.

From the figure in the previous slide, the amount of ultrafine by-pass is indicated by the probability corresponding to the smallest size fraction, which is around 26%.

In general, an increase in water recovery results in an increase in the amount of ultrafine by-pass.

A worn apex will result in an increase in water recovery and thus increase ultrafine by-pass.

In design, it is commonly desired to minimize the apex size to limit water recovery. Solid concentrations as high as 50% by weight can be achieved without roping conditions.

Since ultrafine by-pass is not related to the actual separation of particles based on the applied forces within the cyclone, the effect of ultrafine by- pass on the Actual Partition curve is removed before measuring the true efficiency by the Imperfection value (Eq. 10-9).

The correction for ultrafine by-pass results in the Corrected Partition Curve.

#### Correction Partition Curve

The equation for determining the corrected Partition Number is:

$Y'&space;=&space;\frac{Y&space;-&space;R_{1}}{1&space;-&space;R_{1}&space;-&space;R_{2}}$

In which Y’ is the corrected partition number, U the actual partition number, R1 the fractional amount of ultrafines by-passing to the underflow stream and R2 the fractional amount of coarse particles by-passing to the overflow stream.

The by-pass of coarse material to the overflow stream is rare but may occur due to a worn vortex finder.

R2 = 0 can be assumed in most cases.

#### Example

Based on the curve projection, the estimated amount of ultrafine by-pass in the example was about 26%.

Using the equation above, the corrected partition number for each size fraction can be determined.

123
Mean Particle Size (microns)Actual Partition NumberCorrected Partition Number
1200100.00100.00
850100.00100.00
600100.00100.00
425100.00100.00
30097.3596.42
21298.2897.68
15089.3485.59
10665.9053.92
7549.9932.42
5335.9013.38

### Reduced Efficiency Curves

Lynch and Rao (1965) found that classifying cyclone efficiencies are more easily evaluated and compared over a range of cyclone geometries and operating conditions using a Reduced Efficiency Curve.

The Reduce Efficiency curve is a plot of the corrected partition numbers versus (d/d50(c)).

### Separation Performance Projection

Lynch and Rao found that the Reduced Efficiency Curve can be modeled by the following expression:

#### $Y'&space;=&space;\frac{exp&space;(ax)&space;-&space;1}{exp(\alpha&space;x)&space;+&space;exp&space;(\alpha&space;)&space;-&space;2}$

in which x is the d/d50(c) and a is the curve slope and the value is indicative of the classification efficiency.

Typical α values are between 2 and 4.

The equation above can be used to predict the performance of a classifying cyclone by assuming a value for α.

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#### Example: Performance Prediction

Given a feed particle size distribution and an alpha value of 2.5, predict the performance of a cyclone. The amount of ultrafine by-pass is assumed to be 20% by weight.

123456 = 2*57= 6/(Σ6)
Mean Particle Size (microns)Weight (%)d/d50(c)Corrected Partition NumberActual Partition NumberUnderflow Weight (%)Normalized Underflow Weight (%)
12002.40121.001.002.403.90
8507.508.51.001.007.5012.18
6008.9061.001.008.9014.45
4256.404.251.001.006.4010.39
3006.9031.001.006.8911.19
2124.302.120.970.974.196.80
1504.501.50.820.863.866.28
1064.001.060.550.642.554.14
753.400.750.310.451.522.46
5351.700.530.170.3417.3628.20
Total100.0061.57100.00

Feed

• Qf = 5000 gpm; Mf = 64 tph

Underflow

• Solids Yield to Underflow = 61.57%
• Mu = 64 tph (0.6157) = 39.4 tph
• Assume a desired underflow solids content of 40%
• Total Mass Flow = 39.4/0.40 = 98.5 tph
• Calculated Pulp Density = 1.176 (based on ρp = 1.6)
• Qu = 335 gpm → 335 gpm/6 = 56 gpm/cyclone
• Apex Diameter → 2 inches (from graph)

Overflow

• Mo = 24.6 tph
• Qo = 4665 gpm → 778 gpm/cyclone

Transporting the slurry into and out of the cyclone circuit requires a line velocity of 7 – 10 ft/sec (200 – 300 cm/sec) to keep particles suspended.

Feed enters a center chamber for distribution where the slurry velocity should be reduced to 2 – 3 ft/sec (60 – 90 cm/sec) to ensure good distribution.

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## AMIT 145: Lesson 1 Industrial Screens

### Industrial Screens

• A 20° inclined screen is typically used for pre­ screening and sizing applications.
• Decreasing the inclination slows the movement across the table thereby decreasing capacity but improving efficiency.
• Above 12 mm, dry screening is preferred.
• Below 12 mm, wet screening using a low-pressure water spray is preferred with a water flow rate of 0.8- 1.4 m3/t/h.
• Actual water requirements dependent on application.

### Screening Fundamentals

The most commonly used method for separating particles based on particle size is screening.

In screening, two basic processes are taking place.

1. Stratification -The process whereby the large particles rise to the top of the   vibrating material bed while the small particles shift through the voids and   form the bottom of the bed.
2. Probability of Separation – The process of particles reporting to the screen   apertures or openings and passing through if the particle size is less than the   aperture

### Screen Motion

The processes of particle stratification and probability are caused by the vibration of the screen.

On inclined screens, the vibration is caused by a circular motion in a vertical plane of 1/8 to 1/2- inch amplitude at 700 to 1000 cycles/min. The vibration lifts the particles up, thereby, causing stratification. The incline will cascade the particles down the slope and introduce the probability of particle passage through the screen.

Horizontal screens, which are used only when height restrictions prohibit inclined screens, transfer the material using a straight line motion at an angle of  approximately 45 degrees to the horizontal. This motion lifts the particles up from the screen surface and moves the particles toward the discharge end.

### Screen Feed Rate Factors

For a given feed rate, the width of the screen is selected to control the bed depth and achieve the optimum stratification.

Rule of thumb :

• For particles weighing 100 lbs/ft3 or greater, the bed depth at discharge should never be greater than 4 times the aperture size in the screen.
• For particles less than 100 lbs/ft3, the bed depth is limited to 3 times the opening size.

Other factors controlling stratification include:

1. Material travel rate (length/time) is a function of:
1. material specifications;
2. screening media specifications;
3. depth of bed;
4. stroke characteristics;
5. slope of screen.
2. Stroke characteristics
1. amplitude;
2. direction of rotation;
3. type of motion;
4. frequency.
3. Surface moisture – high surface moisture hinders stratification.

### Screening Probability

Upon stratification, the particles having a size less than the smaller screen aperture pass through the screen to the underflow.

Obviously, Particles having a size significantly smaller than the aperture size pass through easily.

However, the probability of P of a particle passing through the screen in one trial decreases as the particle size approaches the aperture size, i.e,

$P&space;=&space;\left&space;[&space;\frac{(a&space;-x)}{(a&space;+&space;b)}&space;\right&space;]^{2}$

a = screen opening size;
x = particle diameter
b = diameter of wire

The probability of a particle being retained on a screen during a single trial Q is:

Q = 1-p     [equation 4.2]

There, the overall probability of a particle being retained on a screen R is:

$R&space;=&space;\left&space;\{&space;1-\left&space;[&space;\frac{(a&space;-&space;x)}{(a&space;+&space;b)}&space;\right&space;]^{2}&space;\right&space;\}^{2}$     [equation 4.3]

m = number of screen trials which is a function of screen length, amplitude and frequency and assumes good stratification.

According to this simplistic model, the value of P increases with:

1. Increasing screen opening a;
2. Decreasing particle size x;
3. Decreasing wire diameter b.

### Screening Concepts

Also note that the probability P would increase over several trials m, and that m can be increased by increasing the length of the screen. Therefore, a perfect screening can only be achieved from an infinitely long screen.

However, the number of trials m possible on a given screen is a function of the amount of open area, As, available.

As – a2 / (a+b)2 = for square apertures

The amount of open area decreases significantly with a decrease in aperture size, e.g., 60% to 30%.

Screen manufacturers are using advanced materials and unique screen designs to increase open area.

### Perfect Screening vs. Reality

As mentioned previously, a 100% screening efficiency is not commercially practical since a screen of infinite length would be required.

A “perfect” separation is typically defined from a sieve analysis in which the sample is vibrated on a sieve for a period of 1 to 3 minutes. This is equivalent to approximately 90- to 180-feet long screen. A screen length of 24 feet is the largest manufactured screen.

The “commercial perfect” screening practice is typically based on efficiency values in the order of 90% to 95%, indicating that 5% to 10% of the undersize particles report to the screen overflow.

### Screen Blinding Effects

Screen blinding reduces the number of openings in the screen, thereby decreasing the number of successful trials m.

Blinding is typically caused by particles having a 50% chance of passing through the screen. The critical particle size range that causes blinding is

0.5 < X/a < 1.5

Therefore, sizing of material having a large portion of material in the size class should be avoided.

High moisture and clay in the feed causes binding

### Mass Flow Rate Through a Screen

The mass flow rate at which particles flow through the screen varies as a function of distance from the feed point.

• From position a – b, the vibration of the screen causes the particles to stratify and the part1cle passage rate increases with distance .
• From position b – c, a maximum mass flow rate through the screen occurs and is referred to as “saturation screening”. This is due to the passage of the particles having a size significantly smaller than the aperture size.

From position c – d, the flow rate through the screen sharply declines since only those particles having a low probability remain.

### Feed Rate vs. Efficiency

As previously mentioned, screens are designed to treat a given mass flow rate at which point a maximum screening efficiency value is obtained as shown below:

1. At very low feed flow rates, screening efficiency increases with the feed rate. This is due to the fact that a sufficient amount of coarse particles is required to prevent excessive bouncing caused by screen vibration.
2. At the point “a”, screening efficiency achieves an optimum value.
3. Feed rates greater than the optimum value result in a decline in screening efficiency due to an increasing bed thickness and the inability of the undersize particles to report to the underflow stream, i.e., mass flow rate through the screen is limited.

### Screening Efficiency

Several definitions of screening efficiency exist, of which selected indexes are provided in the following sections.

### Screening efficiency equation

Manufacturers express screening efficiency in terms of the content of undersize in the overflow b when the overflow is considered the product.

E = 100 – b     [equation 4.4]

or

E = [% (or tph) of feed which is oversize/%(or tph) of feed which passes over] x 100

For example, assume a sieve analysis of the screen overflow revealed that 9% of the screen overflow is undersize material. According to the equation, the screen efficiency is 100 – 9 = 91%.

### Two product formula - Oversize

Screening efficiency can also be determined by using the two product formula.

According to the two product formula, the recovery of oversize material to the screen overflow can be calculated using the following expression:

RO = OO / Ff = o(f-u) / f(o-u)     [equation 4.5]

Where o, u, and f are the contents of the oversize material in the screen overflow, underflow and feed streams, respectively.

### Two product formula - Undersize

Likewise, the corresponding recovery of undersize material to the screen underflow is:

Ru – (1-u) (o-f) / (1-f) (o-u)     [equation 4.6]

Thus, the overall screening efficiency E is the product of Ro and Ru or:

E = 0(f-u) / f(o-u)2 x(1-u) (o-f) / (1-f)     [equation 4.7]

It should be noted that if no apertures are deformed or broken, then the concentration of oversize in the underflow stream is approximately zero and, thus, Eq. [4.7] reduces to Eq. [4-6]:

### Performance Prediction & Efficiency Assessment

Partition curves are also commonly used to determine the separation efficiency whereby the Imperfection Value ” ” can be obtained:

I = d75 – d25 / 2d50     [equation 4.8]

where the d75, d50, and d25 are the particle sizes that have a 75%, 50%, and 25% chance of reporting to the overflow stream.

Partition curves from a screening process are most useful for predicting the outcome for each size fraction comprising the feed. Thus, an overall knowledge of the overflow and underflow stream compositions can be obtained.

### Prediction Screen Performance

Whiten and White (1997) defined a partition curve model for single deck screens based on screen open area (fa) and an efficiency parameter (TRN) that is a function of the number of trial events on the screen, i.e.,

Y(x) – exp[ -TRN (fo) (1 – x / d)2]     [equation 4.9]

where Y is the actual partition number in terms of the probability to the overflow stream, TRN the efficiency parameter, fa the fractional open area, and d the screen aperture size.

As shown, screening efficiency improves with an increasing TRN value.

• TRN is a function of feed rate and the decking material. For rubber decking, an optimum feed rate exists.
• Fractional open area has the same effect on screening efficiency as the TRN value.

An inclined screen deck with a 2 mm aperture is being used to achieve a size separation for a given material. Assume a TRN value of 10 and no ultra-fine particle agglomeration or sliming, predict the particle size distribution of the overflow and underflow streams given the following feed size distribution.

#### Predict the Particle Size Distribution Given:

Particle Size Fraction (mm)Weight (tph)
+230
2 x 125
1 x 0.620
0.6 x 0.310
0.3 x 0.155
-0.1510

#### Distribution Solutions

123-1*2 4=1-3
Particle Size (mm)Feed Weight (ton.hr)Partition # (Eq. 10)Overflow (tph)Overflow (%)Underflow (tph)Underflow (%)
+2301.00030.0060.040.000.00
2 x 1250.65116.2832.588.7217.43
1 x 0.6200.1533.066.1316.9433.85
0.6 x 0.3100.0450.450.909.5519.09
0.3 x 0.1550.0180.090.184.919.81
-0.15100.0080.080.169.9219.82
10049.96100.0050.04100.00

#### Screen Selection

Screen selection is based on the overall screen area required to achieve efficient screening at a given mass throughput capacity .

• Length of screen is important for ensuring the number of trials needed to achieve the desired mass throughput capacity and to provide sufficient screen underflow capacity.
• Width is important for ensuring proper bed depth so as to provide sufficient stratification.
• Length of screen should be at least two times the width for good practical design.

#### Screen Area

The required screen area A can be determined by the expression:

A = Fu / TC     [equation 4.10]

F = the feed rate in tons per hour,

u = the percentage of material in the feed liner than the screen opening,

T = screen capacity in terms of the throughput (tons/hour) passing through the screen per linear foot;

C = represents correction factors for the screen capacity based on variations from the standard (or default) parameter values, i.e,

= C1 x C2 x C3 x C4 x C5 x C6 x C7 x C8 x C9 x C10 x C11     [equation 4.11]

The value for u can be obtained from the cumulative percent finer curve representing the particle size distribution of the screen feed.

#### Correction Factors

CorrectionsDefinitions
C1Mass factor
C2Open area factor
C3% Oversize material in feed
C4% Undersize (fines) in feed
C5Screen efficiency factor
C6Deck factor
C7Screen factor

#### Screen Capacity, T

Standardized Screen Capacity

Gluck assumes bulk density=  1.6 t/m3

Nordberg (Metso): 50% oversize in feed, size, 25% half size, 20° slope, 92%-95%  efficiency.

Osborne: 60°/o open area.

#### Mass Correction Factor, C1

Standard factors were developed using normal vibrating speeds using a material having a density of 1.602 t/m3.

Where the solid density is different, the following correction is applied:
C1 = ρ / 1.602

#### Open Area Correction Factor, C2

Corrects for percentage of available open area.

The standard percentage of open area for a given aperture size is provided by the manufacturer capacity plot.

C2 = Pa / Pr     [equation 4-12]

Pa = actual % open area,

Pr = rated % open area obtained from plot

Pa = 100 A1 A2 / (A1 + W1) (A2 + W2)    for rectangular openings
[equation 4-13]

Pa = 100 A2 / (A + W)2   for square openings     [equation 4-14]

Pa = 100 A / (A + W)    for wedge wire     [equation 4-15]

A = aperture or screen opening

W = wire or bar diameter

#### Correction Factor for Oversize, C3

25% oversize is the standard and any different value affects the stratification process

#### Correction for Undersize, C4

Defined as the percent less than half the screen aperture and the standard is 40%.

#### Screen Efficiency Factor, C5

90% – 95% is considered normal for a typical woven wire screen. Colman recommends 80% – 85% for scalping operations.

#### Multi-deck Correction Factor, C6

This factor accounts for the fact that lower decks have an effectively lower screen surface area since the majority of the material from the top deck enters the next further down the screen.

It is applied to the design of each deck below the top deck.

For a n number of decks from the top, the correction factor is:

C6 = 0.9(n-1)     [equation 4-16]

#### Screen Slope Correction, C7

Corrects for the reduction in effective horizontal screen area:

Ahorizontal = A cos θ     [equation 4-17]

A = aperture length along the slope

θ – angle of inclination from horizontal

#### Correction for Aperture Slot Shape, C8

Aperture ShapeGluckColmanNordberg
L/WC8L/WC8L/WC8
Square11<2111
Rectangle>61.6>251.43-41.15
Rectangle3-61.44-251.2>41.2
Rectangle2-31.12-41.1
Circular--0.8--0.8

#### Correction for Particle Shape, C9

Elongated particles are defined as a particle having a length-to-width ratio greater than 3 and a size between 0.5 and 1.5 times the aperture size.

#### Correction for Moisture, C11

ConditionC11
Moist or dirty stone, muddy or sticky0.75
Moist ore from underground, >14% moisture0.85
Dry quarried rock <4% -10%1.00
Dry uncrushed material, dry or hot material1.25
Wet screening with sprays1.75

#### Typical Commercial Screens

Width (mm)Area (m2)|Width (mm)Area (m2)|Width (mm)Area (m2)
2540.31|15245.57|213410.41
3050.37|12195.95|182911.15
3560.43|15246.50|213411.71
3560.54|18296.69|243811.89
6100.56|15247.43|213413.01
4060.62|18297.80|243813.38
6100.74|15248.36|243814.86
4060.74|18298.92|243817.84
5080.93|21349.10|
5081.08|15249.29|
6101.11|182910.03|

The depth of the bed at the discharge end of the screen indicated the effectiveness of the bed stratification and the ability of particles to have an opportunity to pass through the screen.

The bed depth, D, in inches at the discharge end should be limited to limit to 4 times the screening opening for solid density > 100lbs/ft3 or 3 times for less than 100lbs/ft3.

The expression used to quantify D is:

D = TK/5SW     [equation 4-18]

T = tons/hour at discharge end.

K = cubic feet per ton of ore; or 2000lbs/ton divided by the solid density in lbs/ft3.

S = material travel rate in feet per minutes which is dependent on screen and material characteristics.

• Horizontal screens have travel rates of about 45 feet/minute.
• Incline screens having a 20° slope have travel rates of about 125ft/min. A reduction in slope reduces the screen capacity as shown in the following table.

W = net width of the selected screen in feet. Due to support material the net width = nominal width – 6 inches.

#### Screens Width Design

Slope Reduction% of Rated Capacity
2-1/2 degrees or less90 - 92.5
5 degrees or less80 - 85
7 - 1/2 degrees or less70 - 75
10 degrees or less60 - 65

If the selected width provides a bed thickness greater than the maximum allowable, then

1. Choose a wider screen (less length);
2. Choose a larger screen area;
3. Increase the screen inclination (increase S );
4. Use multiple decks (the use of an upper deck to remove a coarser size fraction will unload the final sizing deck).

Then, repeat the bed depth calculation.

#### Screens Width Design (Metric units)

The expression used to quantify D (mm) is:

D = 50T/3SWK     [equation 4-19]

T = metric tons of overflow material

K = bulk density of material (tjm3)

S = material travel rate in meters per minute which is dependent on screen and material characteristics.

W = effective width of screen (m). Due to support material in the net width = nominal width – 0.15.

For material of bulk density 1.6 t/m3, the bed at the feed end should not exceed 4 times the aperture size.

For material of bulk density 0.8 t/m3, the bed depth should not be greater than 2.5 – 3.0 times the aperture size.

#### Screens Design Considerations

For screen widths of 0.6 – 2.5 meters, the inclination should not be less than 16° and a maximum of about 26° for capacities 15 – 270 t/h.

When the slope is greater than 20 degrees, the capacity is markedly reduced as the effective aperture area is reduced by 0.93.

For longer screens, e.g. 4.8 meters, screen manufacturers recommend a further addition of 2 degrees and for screens of about 6 meters, 4 degrees should be added.

A function of the undersize materials ability to screen within a given period of time.

Sufficient length is needed to provide sufficient residence time to maintain desired screening efficiency.

The appropriate residence time can be determined by analyzing the screening efficiency as a function of time using a standard lab sieve shaker and the exact screen aperture that is or will be used in the plant.

Screen Design Example

A processing engineer is assigned the task of determining the screen area required to screen 200 tons/hr of minerals at a 3/4-inch particle size. The material density is 150 lb/ft3 and the Rosin/Rammler constants are R=0.5 inches and =0.8. The screen should have square openings with 5/16″ wires. Water sprays will be used. Assume an oversize velocity of 1 ft/sec.

Solution:

A = FU/TK

F = 200tph

T = ?? from graph

Underflow (%) -> Rosin-Rammler Eq.

Y = 1 – exp[-(x/R)n]

U = Y = 1 – exp[ -(0.75/0.5)0.8] = 0.749 = 0.75

Screen Example

K = KaKoKuKwKdKs

1. Open Correction Factor, Ka
Ka = Pa/Pr
Pa = 100A2 / (A + W)2 = 100 (3/4)2 / (3/4 + 5/16)2 = 49.83
From graph:
Pr = 56%
Ka = 49.8/56 = 0.889
2. Oversize Correction, Ko = 1.0 from graph
3. Undersize Correction, Ku = 1.3 from graph
Y = 1 – exp [-(0.375/0.5)0.8] = 54.8
4. Wet Screen Correction, Kw – 1.1 from table
5. Safety Correction, Ks – 0.8
6. Kd = 1
K = (0.889) (1.0) (1.3) (1.1) (0.8) = 1.017
A = (200 tph) (0.75) / (??? tph/ft2) (1.017) = 83.8 ft2
Assume 16′ x 6′ screen:
D = TK/5SW = 200 tons/hr  * 0.25 * ???ft3 /ton / 5*60ft/min * 6 ft = 0.925
Since 0.93″ < (3 x 3/4″) the chosen screen is acceptable
With 10% support:
Area = 83.8 x 1.1 = 96ft2

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## AMIT 145: Course Schedule

Tentative Lecture Topic Schedule

 Week Topic Assignments Class # 1 Syllabus, Blackboard An introduction to Industrial Screening See Blackboard Assignments Class # 2 Designing a screen and analysis of the performance See Blackboard Assignments Class # 3 Classifying cyclone design and working principles See Blackboard Assignments Class # 4 Partition curves and efficiency calculations of a Classifying Cyclone See Blackboard Assignments Class # 5 Intro to Dense media Separation, Equipment and applications See Blackboard Assignments Class # 6 Dense Media Cyclone, principle, design and applications See Blackboard Assignments Class # 7 Wash and Rinse Screens , Magnetic Separators See Blackboard Assignments Class # 8 Gravity Separation, principles and applications See Blackboard Assignments Class # 9 Equipment used in Gravity Separation See Blackboard Assignments Class # 10 Concept of Froth Flotation See Blackboard  Assignments Class # 11 Flotation Devices See Blackboard Assignments Class # 12 Application of Froth Flotation in Circuits See Blackboard Assignments Class # 13 Dewatering See Blackboard Assignments Class # 14 Clarification See Blackboard Assignments Class # 15 Concepts of Leaching See Blackboard Assignments

## COURSE INFORMATION

Title: Introduction to Mineral Beneficiation

Department/Number: AMIT 145

Credits: 3

Prerequisites: N/A

Location: Fairbanks Pipeline Training Center (FPTC) Room #2

## INSTRUCTOR INFORMATION

Name: Tathagata Ghosh, Brian Ellingson

Course Textbook:

Wills’ Mineral Processing Technology, 8th edition,
B.A Wills, James Finch PhD, Butterworth-Heinemann publisher, 2015

ISBN-13: 978-0080970530

Any Supplies Required: Notebook or 3 ring binder to store handouts

## COURSE DESCRIPTION

An overview to the field of mining beneficiation and comminution, systems and equipment used for the mining and mineral processing industry. Fundamentals of basic separation and mineral beneficiation, economic planning, environmental concerns, safety and terminology will be explored.

## GENERAL DESCRIPTION OF GOALS

The goal of the student is to gain broad knowledge of the equipment and processes used in large scale mine mill operations. The student will learn about separation and comminution equipment used, and the control and analysis operators use to control quality.

## STUDENT LEARNING OUTCOMES/OBJECTIVES

Upon completion of this course the student will be able to:

1. Identify the role of a mill operator technician in the control of separation and comminution in the mill.
2. Understand and explain the terminology used to describe the equipment and systems in mill operations.
3. Understand and explain mine mill process drawings.
4. Students demonstrate an understanding of safety as applied to working in a mill facility
5. Students demonstrate proper safety practices around rotating equipment
6. Students demonstrate knowledge of various types of crushing equipment.
7. Students demonstrate knowledge of various types of grinding equipment circuits.
8. Students demonstrate knowledge of various types of conveyors systems.
9. Students demonstrate knowledge of various types of screen applications.
10. Students demonstrate knowledge of various types of material classifiers.

## INSTRUCTIONAL METHODS

Instructional methods will include lectures, reading assignments, homework, labs, the use of the Blackboard system, and other digital media.

## CLASS ASSIGNMENT SCHEDULE

Assignments and due dates will be provided through the Blackboard system.

## COURSE POLICIES

Students are expected to comply with the University Student Code of Conduct available for review at:

## CLASS POLICIES

### Classroom Ground Rules

1. Turn off cell phones during class. If you must maintain cell phone contact, put the ringer on vibrate and leave the class room to receive a call.
2. No laptop computers are allowed during class without instructor’s permission.
3. If you are late for class by over 15 minutes you will receive .5 attendance point. Please find a vacant seat and be seated with a minimum of disturbance to the class.
4. Respect instructor and classmates.
5. Restrict talking or conversations that do not include the entire class or add value to the class discussion.
6. If you do not understand a concept, idea, or explanation, you should ask the instructor or classmate to explain it in a different manner.
7. All tests will be administered in a closed book- no notes format.

### Homework, Class Notes, Power Point presentations, notebooks and Blackboard

Students are expected to submit legible homework written in a manner suitable for the assignment. Shorthand answers will not be accepted. Answers must communicate the content of the question. The process of writing out both the question and the answer helps the student to retain the information. As an employee you will be expected to communicate clearly in your written communications and this class expects the same level of communication.

As a student you are responsible for taking notes and making certain you understand the information presented. A notebook is a good way to capture and retain this information. Information not covered in your assigned reading will be made available in lecture, in a digital format, or in hard copy. All Class assignments will be initiated from Blackboard. (You may be directed away from Blackboard but you will start in the Blackboard Assignments folder.)

### Class Attendance and Participation

Class attendance and participation is very important for meeting the course objectives. Attendance will be taken at the start of each class. Students who are working a rotating shift schedule or missing class on a regular basis need to make prior arrangements with the instructor. The student’s participation portion of the grade is based on the quality (not frequency) of your participation. Those receiving high grades in class participation are those who:

1. Have prepared for class by completing reading assignments prior to the lecture.
2. Understand and have completed all assignments neatly, accurately and on-time.
4. Present Safety Huddle discussions.
5. Are willing to volunteer for in-class demonstrations and exercises.
6. Class participation will be an earned grade for each scheduled class. If you are late you will lose .5 point for class participation. If you are absent you lose the entire point.
7. Unexcused absences will lose one attendance point. Excused absences will lose .5 attendance point. Excused means that you notified the instructor before the beginning of class. (As you would do if you were notifying an employer.)

### Make Up work Policy

Homework and assignments turned in later than the test covering the assignment will receive zero credit and may not be evaluated. Keeping up with class work is expected. If you cannot be present for a test you should contact the instructor beforehand and schedule a time to make up the test. Tests not scheduled for make-up within a week will be scored as a 0.

### EVALUATION

A = 100-90%                                                  Exams                                     30%

B =   89-80%                                                  Homework                              20%

C =   79-70%                                                  Attendance/Participation     20%

D =   69-60%                                                  Final Exam                              30%

F =   59% or less

* Plus and minus grades will not be submitted

* The Final exam is comprehensive and will be drawn from material covered over the entire semester.

## SUPPORT SERVICES

Extensive support services are available for the student and can be found on the web at: www.uaf.edu/sssp/. Students are encouraged to form study groups with their peers. The instructor is available to assist students on an as scheduled basis. Students are encouraged to take full advantages of all these services.

### DISABILITIES SERVICES

UAF has a Disability Services office that operates in conjunction with the College of Rural and Community Development’s (CRCD) campuses and UAF eCampus. Disability Services, a part of UAF’s Center for Health and Counseling, provides academic accommodations to enrolled students who are identified as being eligible for these services.If you believe you are eligible, please visit http://www.uaf.edu/chc/disability.html on the web or contact a student affairs staff person at your nearest local campus. You can also contact Disability Services on the Fairbanks Campus at (907) 474-7043, fydso@uaf.edu.

### UAF Title IX

University of Alaska Board of Regents have clearly stated in BOR Policy that discrimination, harassment and violence will not be tolerated on any campus of the University of Alaska. If you believe you are experiencing discrimination or any form of harassment including sexual harassment/misconduct/assault, you are encouraged to report that behavior. If you disclose sexual harassment or sexual violence to a faculty member or any university employee, they must notify the UAF Title IX Coordinator about the basic facts of the incident.

1) You may confidentially disclose and access confidential counseling by contacting the UAF Health & Counseling Center at 474-7043;

2) You may access support and file a Title IX report by contacting the UAF Title IX Coordinator at 474-6600;

3) You may file a criminal complaint by contacting the University Police Department at 474-7721

## AMIT 145: Introduction to Mineral Benefication

This course provides an overview or introduction into the field of mineral beneficiation and comminution, systems and equipment used for the mineral processing industry.  Fundamentals of basic separation and mineral beneficiation, environmental concerns,  safety and terminology will be explored.

## Course Information

Credits: 3

Prerequisites: Placement in Mill Operations OE program

## Instructional Goals

1. Describe and explain the liberation and concentration principles of mineral recovery
2. Describe particle size analysis and its importance for recovery
3. Describe the reagent process and how it is used.
4. Describe flotation circuit processes and its basic operation
5. Describe the different types of dewatering circuits and their basic operation.
6. Describe the water treatment process and its basic operation.
7. Explain mill circuit capacities vs efficiency/recovery
8. Explain efficiency of mineral processing operations

## Student Outcomes

Student Outcomes
Upon successful completion of the course, the student will be able to do the following:
Assessment Procedures
This outcome will be assessed by one or more of the following:
Students demonstrate an understanding of safety as applied to working in a mill facilityPerformance answering identified mill safety test questions
Students demonstrate proper safety practices around rotating equipmentObserved performance demonstrating proper (general) safety practices required around rotating equipment
Students demonstrate knowledge of various types of liberation and concentration equipmentPerformance answering identified liberation and concentration circuit equipment test questions

Observed performance identifying various types of liberation and concentration equipment components
Students demonstrate knowledge of various types of dewatering circuitsPerformance answering identified dewatering equipment circuit test questions

Observed performance identifying various dewatering unit components
Students demonstrate knowledge of various types of froth flotation systemsPerformance answering identified froth flotation test questions

Observed performance identifying froth flotation unit components and associated equipment
Students demonstrate knowledge of reagents and their applicationsPerformance answering identified reagent application and performance questions

Observed performance identifying reagent performance and application
Students demonstrate knowledge of water treatment circuits/systems used in mill operationsPerformance answering identified water treatment process test questions

Observed performance identifying water treatment circuit components and associated equipment
Students demonstrate knowledge of efficient mill operations involving liberation, concentration, and water treatmentPerformance answering identified mill process operation and efficiency test questions

Observed performance identifying proper operation of mill processes, and ability to summarize efficiency

## Course Outline

1. Liberation and concentration principles
1. Liberation (comminution) system terminology
2. Comminution system components
3. Comminution principles/targets (particle size analysis)
4. Concentration system terminology
5. Concentration methods/principles
2. Flotation Circuits
1. Froth flotation terminology
2. Froth flotation system components
3. Froth flotation principles of operation
4. Froth flotation normal operation
5. Froth flotation analysis/control parameters
3. Dewatering circuits
1. Dewatering equipment types
2. Dewatering terminology
3. Principles of dewatering/efficiency
4. Dewatering system normal operation
5. Dewatering system abnormal operation
4. Reagents
1. Reagent terminology
2. Reagent principles/applications
3. Reagent performance measures
4. Reagent application methods
5. Reagent safety and environmental concerns
5. Mill water treatment
1. Water treatment terminology
2. Water treatment system components
3. Water treatment principles/methods
4. Water treatment environmental/efficiency concerns
6. Communition & Concentration analysis and efficiency
1. Guidelines for proper communition operation/efficiency
2. Guidelines for proper froth flotation circuit operation/efficiency
3. Guidelines for proper dewatering circuit operation/efficiency
4. Guidelines for proper water treatment operation/efficiency
5. Mill circuits process variables

## Suggested Text

Wills’ Mineral Processing Technology, 8th edition
B.A Wills, James Finch PhD, Butterworth-Heinemann publisher, 2015

## Bibliography

DACUM Research Chart for Mill Operator
Produced for Teck Alaska Inc. Red Dog Mine – June 2015
Prepared by John P. Hakala
ApprenticeshipUSA United States Department of Labor