NUMERICAL PROBLEMS RELATED TO MINERAL BENEFICIATION - 1 NATIONAL INSTITUTE OF TECHNOLOGY, JAMSHEDPUR COMPILED BY: DEVESH MUKHERJEE 178/11 GAURAV SINGH 197/11 ABHISHEK ANAND 205/11 UNDER THE GUIDANCE OF Dr. RANJIT PRASAD

THE DIFFERENT OPERATIONS/PROCESSES NECESSARY TO CONVERT AN ORE FROM A RAW, CRUDE FORM TO A PROCESSABLE FORM ARE CALLED UNIT OPERATIONS. THESE UNIT OPERATIONS COMES UNDER THE BROAD SPECTRUM OF MINERAL PROCESSING/BENIFICIATION. UNIT OPERATIONS

Mineral processing can involve three general types of unit operations: 1. comminution (particle size reduction) 2. sizing 3. classification TYPES OF UNIT OPERATIONS

1. Comminution is particle size reduction of materials. 2. Comminution may be carried out on either dry materials or slurries. 3. Crushing and grinding are the two primary comminution processes. 4. Crushing is carried out on run-of- mine ore, while, grinding is carried out after crushing. 1. COMMINUTION

1. The maximum capacity of rolls can be calculated by assuming the feed material is completely occupy the space between the rolls, so that Max. Capacity = 190 N D W ρ S(kg h -1 ) Where N= roll speed (rpm), D= roll diameter (m), W= roll width(m), ρ= bulk density of the feed material(kg m -3 ) and S= the gap between the rolls(m). NUMERICAL PROBLEMS

2. THE ESTIMATION OF THE POWER REQUIREMENTS FOR CRUSHING AND GRINDING: For the reduction from size d 1 to d 0 the total work W, is given by W = W 0 – W 1 = (K/d 0^ 1/2 – K/d 1^ 1/2) (kWh tonne-1) To eliminate the constant K, a term referred to as the work index, W i, is defined as the total work to reduce a particle from an infinite size to 100 µm. substituting in the above equation, W i = K/100^1/2 – 0 The general equation is then given as W = 10W i (1/d 0^ 1/2 – 1/d 1^ 1/2)

1. Sizing is the general term for separation of particles according to their size. 2. The selection of materials on the basis of their relative sizes can be carried out By the use of physical barriers or screens. Through the differential movement of solid particles through fluids, commonly referred to as classification. 2. SIZING

TYPES OF SCREENS: 1. GRIZZLIES 2. MULTI DECK 3. VIBRATORY 4. WIRE MESH SCREENING

1. The probability, P, of a spherical particle diameter d 0, passing through an aperture, assuming the particle does not touch the screen before passing through, can be calculated as follows: P = (D A – d 0 ) 2 / (D A + D W ) 2 Where, D A = side length of square aperture D W = thickness of the wire surrounding the aperture. NUMERICAL PROBLEMS

2. A preliminary estimate may be made of screen size using formulae of the type A = (F X percent undersize) / (100.C.K d K h.S1.S2.S3.S4) Where, A = net screening area (m 2 ) F = total feed to screen deck (th -1 ) C = basic screen capacity (m 3 h -1 ) passing through 1 m 2 of screen at the desired aperture size

K d = oversize bed depth correction factor K h = half size factor based on percentage of total feed smaller than one half the width of the aperture. S1 = deck location factor S2 = material shape factor S3 = material weight factor S4 = aperture shape factor.

It refers to sizing operations that exploit the differences in settling velocities exhibited by particles of different size. These may include: 1. gas cyclones 2. rotating trommels 3. rake classifiers 4. fluidised classifiers CLASSIFICATION CLASSIFIER

1. The summation of the forces gives the resultant acceleration of a particle in the fluid ΣF = M dv/dt = F g + F c - F b + F d F g = Mg (gravitational acceleration) F c = Mw 2 r (centrifugal force) w=angular velocity of particle r=radius of the path followed by the particle The buoyancy forces after Archimedes principle are given by: NUMERICAL PROBLEMS

F b =Mρ f g/ρ s (gravitational acceleration) F b =Mρ f rw 2 /ρ s (centrifugal acceleration) ρ f =density of fluid ρ s =density of solid F d =1/2f d ρ f v 2 A F d =drag force f d =drag coefficient or friction factor v=particle velocity A=characteristic area of the particle usually taken to be the projected cross-section F b =Mρ f g/ρ s (gravitational acceleration) F b =Mρ f rw 2 /ρ s (centrifugal acceleration) ρ f =density of fluid ρ s =density of solid F d =1/2f d ρ f v 2 A F d =drag force f d =drag coefficient or friction factor v=particle velocity A=characteristic area of the particle usually taken to be the projected cross-section

2. Considering the condition when the particle reaches its terminal velocity v ∞, i.e. it is no longer accelerating, dv/dt=0 and for a spherical particle, M = πd 3 ρ s /6, therefore, v ∞ = d 2 /18 (ρ s -ρ f )g/η (laminar flow, Re 800)

1. Concentration is defined as the number of moles of a solute in a volume of the solution. 2. There are a number of ways to increase the concentration of the wanted minerals: in any particular case the method chosen will depend on the relative physical and surface chemical properties of the mineral and the gangue. 3. CONCENTRATION

1. IN GRAVITY CONCENTRATION, THE PARTICLES CAN BE CLASSIFIED BASED ON THEIR SPECIFIC GRAVITY. 2. AIR IS THE MAIN FLUID MEDIUM FOR THE PROCESS 3. Of the gravity separation processes, the spiral concentrators and circular jigs are two of the most economical due to their simplicity and use of space. USE: WILFLEY TABLES. a. GRAVITY CONCENTRATION WILFLEY TABLE

1. The motion of particles in relatively dilute slurries was considered and a general description of the forces acting on a single particle moving in a fluid derived. If the initial acceleration of the particles as they start to fall is considered, then since v=0, dv/dt initial = {(ρ s -ρ f )/ ρ s }g = {1-ρ f /ρ s }g This expression indicates that, unlike the terminal velocities of the particles, the initial acceleration of the particles is independent of the particle size. This process, known as differential acceleration, may be exploited by designing equipment which provides frequent accelerating opportunities for the particles. NUMERICAL PROBLEMS

1. There are two main types of electrostatic separators: a.) electrodynamic separators (force of gravity) b.) electrostatic separators (force of electrostatic attraction) 2. There are three important mechanisms by which particles may acquire a surface charge: 1) contact electrification 2) conductive induction, and 3) ion bombardment b. ELECTROSTATIC SEPARATION

1. The force between a charged particle and a grounded surface is given by the equation, F=e + e - /4πξ 0 ξ r y 2 Where, e - =total negative charge on particle e + =corresponding positive image charge y=distance between the charged particle and the grounded surface ξ 0 =permittivity of free space ξ r =relative permittivity of the medium. NUMERICAL PROBLEMS

1. The process of separating magnetic substances from the non-magnetic substances in a mixture with the help of a magnet is called magnetic separation. 2. This separation technique can be useful in mining iron as it is attracted to a magnet. 3. The raw ore, after calcination is fed onto a moving belt which passed underneath two pairs of electromagnets under which further belts ran at right angles to the feed belt. c. MAGNETIC SEPARATION

1. The magnitude of the interaction of a material with a magnetic field is often described in terms of its magnetic susceptibility,X which is given by, X=H/M The magnetic field intensity,B,is given by, B=µ 0 (H+M) Where: µ 0 =magnetic permeability of a vacuum H=applied magnetic field M=intensity of magnetization of material NUMERICAL PROBLEMS

The particle is assumed to behave as if it were a small magnet of pole strength,p, and of length,l, equal to the particle diameter. In a uniform magnetic field,H, the force on the S pole of the magnet is pH, the force on the N pole is –pH. The net force on the particle in the field is then zero. 2. In a magnetic field of gradient dH/dx, the force on the S pole is pH. The force on the N pole is –p(H-ldH/dx). The net magnetic force on the particle,Fm, is then,

Fm=pl dH/dx The magnetization, M=p/a, where a is cross-sectional area of the particle. Since M=XH(mean) Where H (mean)= the mean field strength P=aXH(mean) Substituting for P, then the net force on the particle is given by Fm=VXH(mean) dH/dx Where V is the volume of the particle.