University
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Virginia Tech | 0.175
0.15
0.125
0.1
0.075
0.05
0.025
0
10 100 1000
d (µm)
p
Figure 9. Effect of contact angle on the flotation rate constant.
Higher contact angles increase the work of adhesion, which decreases
the probability of detachment. This increases the rate constant. It
should be noted that contact angles and hydrophobic force constants
are directly related. Both increase or decrease the rate constant in
tandem.
be a combined effect of bubble size and energy input on the rate constant that shows the same
effect as industrial machines.
Figure 9 and Figure 10 show the effects of surface chemistry parameters. The outcome
of varying the contact angle, along with the particle diameter, can be found in Figure 9. As the
angle increases, the rate constant increases. This is due, mostly, to the work of adhesion. A
higher contact angle increases the work of adhesion, which in turn makes a greater “energy
barrier” for detachment. This greater “energy barrier” decreases the probability of detachment
and increases the rate constant. It should also be noted that the contact angle and hydrophobic
force constant are related (Rabinovich and Yoon 1994; Yoon and Ravishankar 1994; Yoon and
Ravishankar 1996; Vivek 1998; Pazhianur 1999). The contact angle and hydrophobic force
constant, which are directly proportional, will both increase or decrease the rate constant in
tandem.
The final surface force parameter that was varied is the surface tension. This is shown in
Figure 10, along with the effect of particle diameter. Similar to the contact angle, the effects
shown here are entirely due to the work of adhesion. A higher surface tension increases the work
of adhesion, which makes it harder for particles to become detached. Therefore, the probability
of detachment decreases, with increasing surface tension, and the rate constant increases.
It should be noted that all simulations that were run show a maximum, of the rate
constant at, approximately, a particle diameter of 100 microns. This is seen in industrial flotation
cells and is a good sign as to the validity of the model and the assumptions used to derive the
model.
38
)1-nim(
k
d = 1 mm
b θ = 60°
γlv = 60.0 mN/m
εsp = 2 kW/m3
ζp = -20 mV
ζb = -30 mV
κ-1 = 96.0 nm
ρp = 2.475 g/cm3
θ = 50°
θ = 40° |
Virginia Tech | 0.06
0.05
0.04
0.03
0.02
0.01
0
10 100 1000
d (µm)
p
These simulations show that surface chemistry parameters play as important a role in
flotation as physical parameters. An analysis of flotation cannot be conducted while only
looking at the physical characteristics of the flotation machinery and the feed to that machinery.
The chemical interactions between all aspects of flotation must be considered. This includes
water chemistry and surface chemistry. A big determining factor in flotation is the hydrophobic
force. This manifests itself in the hydrophobic force constant and contact angle. If this force is
omitted, a flotation equation cannot be considered universal and will only be valid in a very few
situations. The current equation incorporates all current surface chemistry as well as
hydrodynamic knowledge. Although the current model does predict trends that are seen in
industry, a more precise knowledge of the effect of froth on the rate constant will provide a more
robust and applicable model.
Conclusions
A flotation model was developed that can predict trends in the flotation of solid particles.
The model incorporates hydrodynamic as well as surface chemistry parameters in a turbulent
environment. A collision frequency is used, along with a probability of collection and a froth
recovery factor to calculate the rate of particles that are recovered per unit volume per unit time.
The collision frequency is calculated using a model proposed by Abrahamson. Both probability
of attachment and probability of detachment, which combine to form the probability of
collection, compare surface energy values with the kinetic energies of the particles and bubbles
to determine their respective probabilities. The kinetic energies of the particles and bubbles
come from the turbulent energies of eddies directly affecting the attachment and detachment of
the particles and bubbles. The froth recovery factor is calculated using a modification of a model
39
)1-nim(
k
γlv = 70 mN/m
db = 1 mm
θ = 45°
60 mN/m εsp = 2 kW/m3
κ-1 = 96 nm
ζp = -20 mV
ζb = -30 mV
ρp = 2.475 g/cm3
50 mN/m
Figure 10. Effect of liquid-vapor surface tension on the flotation
rate constant. Higher surface tensions increase the work of
adhesion and decrease the probability of detachment. This
increases the overall rate constant. |
Virginia Tech | given by Gorain el al. (1998). The modification takes into account the particle size as well as a
maximum froth recovery determined by bubble size.
Simulations were run that found phenomena similar to those found in industrial flotation
cells. From these simulations, the surface chemistry parameters were deemed as important as the
physical parameters of the flotation system. One of the most important of the surface chemistry
parameters was the hydrophobic force. This influences both the hydrophobic force constant,
which in turn influences the contact angle; the contact angle having a large impact on the rate
constant. Further refinement of the model is necessary to incorporate a better understanding of
the froth section of flotation. The current model can predict trends found in the flotation
industry.
Nomenclature
1 subscript – refers to particle
2 subscript – refers to bubble
3 subscript – refers to liquid
B constant
C constant equal to 2.0
0
d diameter of collision [m]
12
d diameter of i [m]
i
d diameter of particle [m]
p
d diameter of neutrally buoyant particle [m]
p-n
E surface energy barrier [J]
1
E kinetic energy of detachment [J]
k-D
E kinetic energy of attachment [J]
k-A
H critical rupture thickness [m]
c
h froth height [m]
f
k rate constant [min-1]
m mass of particle or bubble [kg]
i
N number density of i – number per unit volume [m-3]
i
P probability of attachment [-]
A
P probability of detachment [-]
D
P particle effect – retention time [-]
fr
r radius of bubble – slurry-froth interface [m]
2-0
r radius of bubble – top of froth [m]
2-f
Re Reynolds number of bubble [-]
b
R froth recovery factor [-]
F
r radius of subscript i [m]
i
R radius of impeller [m]
Imp
R maximum froth recovery [-]
max
S surface area rate – slurry-froth interface [s-1]
0
S surface area rate – within slurry [s-1]
b
S surface area rate – top of froth [s-1]
f
St Stokes number [-]
U2 large scale turbulent kinetic energy [m2·s-2]
T-large
U2 attachment turbulent kinetic energy [m2·s-2]
T-A
40 |
Virginia Tech | A Comprehensive Model for Flotation under Turbulent Flow
Conditions: Verification
I. M. Sherrell
Abstract
A flotation model has been proposed that is applicable in a turbulent environment. The model
takes into account hydrodynamics of the flotation cell as well as all relevant surface forces (van
der Waals, electrostatic, and hydrophobic) by use of the Extended DLVO theory. The flotation
model includes probabilities for attachment, detachment, and froth recovery as well as a collision
frequency. Flotation experiments have been conducted to verify this model. Model results are
close to experimental values, which lead to the conclusion that the model can predict the
flotation rate constant in other circumstances, such as industrial (e.g., coal and mineral) flotation.
Introduction
Industrial flotation is a turbulent process that separates one material from another. In
most cases, this includes one solid particle from another solid particle. The process is used,
among others, to separate plastics in the recycling industry, decontaminate soil, separate carbon
from fly ash, etc. Most importantly, it is used to upgrade minerals in the mining industry.
Flotation begins with the introduction of air into a slurry. Certain particles (hydrophobic)
are able to attach to bubbles formed from this air. The bubbles then travel vertically and are
collected, while the slurry continues to travel horizontally. The process, essentially, separates
material based on its ability to attach to air bubbles. This is the driving factor in flotation.
Modeling of this process, which would be beneficial in the application of flotation as well
as the design of the flotation process, is very complex due to the three phases found in the
flotation machines as well as the turbulent environment in which flotation occurs. To complicate
matters, surface forces must be taken into account. Modification of these forces, by the addition
of surfactants, allows the process to be more efficient and in some cases is the only mechanism
allowing the process to take place.
Surface forces play a crucial role in the attachment and detachment processes between a
particle and bubble. Proper modeling of these forces is vital to having a general flotation model.
The DLVO theory models some of the surface forces seen in flotation. This theory combines the
van der Waals force and the electrostatic force into a total surface force. The problem with the
DLVO theory is the lack of any hydrophobic force parameter, which is known to be a major
contributor to surface forces between particles and bubbles in a water medium (Yoon and Mao
1996; Yoon 2000). The extended DLVO theory incorporates this third force (hydrophobic) into
the DLVO theory.
The most rigorous flotation model, to date, dealing with all three surface forces
(electrostatic, van der Waals, and hydrophobic) was proposed by Mao and Yoon (1997).
44 |
Virginia Tech | 2
1 ⎡3 4Re0.72⎤⎛ r ⎞ ⎛ E ⎞⎡ ⎛ W +E ⎞⎤
k = S ⎢ + b ⎥⎜ 1 ⎟ exp⎜− 1 ⎟⎢1−exp⎜− A 1 ⎟⎥ [1]
4 b ⎣2 15 ⎦⎝r
2
⎠ ⎝ E
k−A
⎠⎢⎣ ⎝ E
k−D
⎠⎥⎦
The model is based upon first principles in a quiescent environment and agrees well with
experimental data. The problem of this model is its applicability to industrial applications where
turbulence is encountered. This model did provide a key basis for the current model by the use
of the extended DLVO theory and its relationship to the energies of the system.
Model
The current flotation model was first proposed by Sherrell and Yoon (To be submitted -
summer 2004). Assuming that the rate process is first order (Kelsall 1961; Arbiter and Harris
1962; Mao and Yoon 1997) and that the rate is equal to the number of collisions between
particles and bubbles (βN N ) that lead to attachment (P ), once attached do not detach (1-P ),
1 2 A D
and are able to rise within the froth (R ), leads to Equation [2].
F
k =βN P (1−P )R [2]
2 A D F
Equation [2] gives the rate constant for the turbulent flotation process and is a function of both
the hydrodynamics of the flotation cell and surface forces of the particles and bubbles by the
inclusion of the collision frequency kernel, β, probability of attachment, P , probability of
A
detachment, P , and the froth recovery, R .
D F
Collision Frequency
Knowing that the environment within a flotation cell is highly turbulent, collisions that
occur within this environment occur for reasons far different than ones that occur in laminar
flows. Mao and Yoon (1997) modeled laminar collisions using the volume that the bubble
travels through and the percent solids of the slurry. A collision efficiency was then applied that
accounted for streamline effects. In turbulent flows, particles and bubbles deviate from the fluid
path. This deviation is measured by the Stokes number; a ratio of the particle relaxation
(response) time to the smallest fluid relaxation time (Kolmogorov timescale).
Two mechanisms account for turbulent collisions; the shear and accelerative mechanisms.
The shear mechanism accounts for relative motions of particles (fluid, solid, or gas) in a shear
field. These collisions always occur in a turbulent field, even among fluid particles. Collisions
between particles with Stokes numbers less than 1 occur by shear only. The accelerative
mechanism accounts for inertial effects due to large and/or heavy particles. Collisions due to the
accelerative mechanism occur above a Stokes number of 1 where there is some lag between the
particle and fluid.
Sundaram and Collins (1997) ran a numerical simulation of real world collisions and
found that for Stokes numbers above 1, a model proposed by Abrahamson (1975) provided more
reliable results. Abrahamson’s model is based entirely on the accelerative mechanism of
collision and assumes a Stokes number of infinity. A combination of shear and accelerative
mechanisms (Williams and Crane 1983; Kruis and Kusters 1997) is assumed to provide the best
results for flotation collisions, but no current shear/accelerative models can account for both
heavier and lighter than the surrounding fluid particle collisions. Since most particles in flotation
have a Stokes number greater than 1, Abrahamson’s model is currently used (Equation [3]).
( )
Z =232π12N N d2 U2 +U2 [3]
12 1 2 12 1 2
45 |
Virginia Tech | 80
60
40
20
0
-20
-40
-60
-80
0 50 100 150 200
Separation Distance, H (nm)
The particle turbulent root-mean-squared velocity, U2 , within this model is given by Liepe and
i
Moeckel (1976). The bubble turbulent mean-squared velocity is given by Lee et al. (1987).
Particle Collection
The attachment and detachment processes are both influenced by surface properties of the
particles and bubbles as well as hydrodynamics of the system. Surface energies are modeled
based upon the Extended DLVO theory. This incorporates the electrostatic, V , van der Waals
E
(dispersion), V , and hydrophobic, V , surface forces (Rabinovich and Churaev 1979; Shaw
D H
1992; Mao and Yoon 1997). V is a function of hydrophobic force constants (K and K ),
H 131 232
which can be obtained from experimental results (Rabinovich and Yoon 1994; Yoon and
Ravishankar 1994; Yoon and Mao 1996; Yoon and Ravishankar 1996; Yoon, Flinn et al. 1997;
Vivek 1998; Pazhianur 1999; Yoon and Aksoy 1999). The surface forces are additive and
combine to form the total energy of interaction, V , as shown in Figure 1.
T
The probability of attachment is dependent on the energy barrier that must be overcome
and the kinetic energy of attachment, E .
k-A
⎛ E ⎞
P =exp⎜− 1 ⎟ [4]
A E
⎝ ⎠
k−A
For attachment there exists a maximum repulsive (positive) energy, E , that must be overcome.
1
This maximum energy occurs at the critical rupture thickness, H . Nothing prevents the particle
c
and bubble from adhering once H is overcome due to the continuous drop in surface energy at
c
smaller separation distances.
The probability of detachment is dependent on the kinetic energy of detachment, E ,
k-D
and the work of adhesion, W , which must be overcome for detachment to occur (Figure 1).
A
46
)J(
7101x
V
V
E
V
T
E
1
V
D
H
C
W
V A
H
Figure 1. Surface energy vs. distance of separation between two
particles (i.e. particle-bubble) |
Virginia Tech | ⎛ W ⎞
P =exp⎜− A ⎟ [5]
D E
⎝ ⎠
k−D
The work of adhesion is the energy required to return the free energy of interaction to a zero
value, which, in turn, is the energy needed to take apart a bubble-particle aggregate into a
separate bubble and particle. This energy is obtained thermodynamically by surface tensions
(gas-solid, gas-liquid, solid-liquid) and their respective areas. A well known model used by Mao
(1997)
W
=γπr2(1−cosθ)2
[6]
A lv 1
assumes that the bubble surface is completely flat. Since the bubble and particle sizes are within
two orders of magnitude of each other, a more accurate approach to calculate W would be to
A
assume a spherical bubble attached to a spherical particle. With simple geometry, this can easily
be worked out and the current model uses this approach.
Contact angles, used within Equation [6], are known to be smaller for spherical particles
than corresponding flat plate measurements (Preuss and Butt 1998). There can be up to a 10
degree contact angle reduction for colloidal sized particles. The contact angle used in Equation
[6] is usually obtained by measurements upon flat plates. Since it is assumed that this reduction
is a function of particle size and that particles in flotation are much larger than colloidal sized
particles, a constant 5 degree reduction is included in this model.
The energies for the attachment and detachment processes that will overcome these
energy barriers are provided by the turbulence within the flotation cell. Energy input into the
cell (through the impeller) is transferred from the largest turbulent scale (corresponding to the
impeller size) to the smallest turbulent scale (Kolmogorov microscale). A certain range of these
eddy sizes will have an effect on the particles and give them their turbulent kinetic energies.
Kolmogorov theory predicts, for homogenous turbulence, that energy will cascade from
the largest scales to the smallest scales. The largest scale (impeller) produces the largest energy
which then is transferred (at a slope of -5/3 on log-log scale) to the small scale where it is
dissipated. With the addition of bubbles the slope is found to be -8/3 (Wang, Lee et al. 1990).
Particles are also found to reduce the theoretically predicted slope (Buurman 1990). It is
assumed that with a combination of all three phases, the slope will follow the -8/3 prediction for
a two-phase flow.
Eddies corresponding to the particle/bubble size through the Kolmogorov microscale will
allow the particle and bubble to deviate from the fluid flow. The fluid within this range will
have a different relaxation time than the particles and bubbles, as opposed to large eddies, where
bubbles and particles follow their movement. This out of phase motion allows the particles and
bubbles to move independent of each other and will produce collisions. It is assumed that the
average amount of this energy (U2 ) over the associated wave numbers directly corresponds to
T-A
the particle and bubble attachment energy as shown in Equation [7], where m and m are the
1 2
particle and bubble masses respectively.
1
E = (m +m )U2 [7]
k−A 2 1 2 T−A
Large eddies, on the other hand, provide the energy for detachment. For detachment,
bubbles and particles are already combined and, therefore, do not need a corresponding
relaxation time as they do in the attachment process. Since all aggregates are subjected to large
eddies, and these eddies contain the largest energies within the system, they provide the greatest
energy for detachment. Detachment follows from the centrifugal motion of these eddies, in
47 |
Virginia Tech | which bubbles travel in towards the center of vortices while particles travel outward (Chahine
1995; Crowe and Trout 1995).
1
E = (m +m )U2 [8]
k−D 2 1 2 T−D
The turbulent energy corresponding to the largest eddy is equal to the turbulent detachment
kinetic energy, U2 .
T−D
Froth Recovery
Froth recovery, R, is the percentage of particles that enter the froth and subsequently pass
f
through the froth and are collected. All particles not recovered from the froth are returned to the
slurry or never truly enter the froth phase. A simple approach of modeling this is to consider
only the particles attached to the bubble surface. The only factor affecting the bubble surface
would then be the coalescence of bubbles and loss of surface area. Once bubbles coalesce, a
portion of their carrying capacity, for that volume of air, is lost. Once that carrying capacity is
lost, it is assumed that those particles that were attached will drain back into the slurry. This
provides a maximum froth recovery barrier that can not be overcome. It should be noted that this
does not take into account entrainment, but only accounts for attached particles. This loss of
surface area is equal to the ratio of the final and initial froth bubble sizes.
S ⎛3V ⎞ ⎛3V ⎞ r
R = f =⎜ g ⎟ ⎜ g ⎟= 2−0 [9]
max S ⎜r ⎟ r r
0 ⎝ 2−f ⎠ ⎝ 2−0 ⎠ 2−f
To theoretically model three-phase froths liquid and gas effects as well as particle size,
shape, smoothness, hydrophobicity, contact angle, and concentration must be taken into account
(Harris 1982; Knapp 1990; Johansson and Pugh 1992; Aveyard, Binks et al. 1999). Froth
recovery is also thought to be a function of these variables, with particle size having a large
effect. An empirical model proposed by Gorain et al. (1998) is thought to give the best results
for froth recovery, to date.
( )
R =exp −ατ [10]
F f
Equation [10] is a function of the froth retention time, τ, and a parameter, α, that incorporates
f
both physical and chemical properties of the froth (Mathe, Harris et al. 1998). Froth retention
time is usually defined as the ratio of the froth height to superficial air flow rate, V . α is an
g
empirical parameter that must be determined by experiments, for each system. α usually ranges,
in industrial flotation cells, between 0.1 and 0.5 (Gorain, Harris et al. 1998).
Given the fact that there is a maximum recovery that can not be overcome, a modification
of Gorain’s model is proposed. All recoveries calculated using equation [10] must then be scaled
using the maximum froth recovery (Equation [9]).
r
( )
R = 2−0 exp −ατ [11]
F r f
2−f
It is also known that particles within a flotation froth have varying retention times, due to,
in large part, particle size (Mathe, Harris et al. 1998). Average retention time within a froth is
the ratio of froth height, h, to superficial air flow rate (Gorain, Harris et al. 1998). Knowing that
f
small particles within a liquid environment follow the flow, small particles are thought to have a
froth retention time equal to the average retention time within the froth. It is also known that
larger particles have a more difficult time traveling upward in the froth (Bikerman 1973). It is
48 |
Virginia Tech | proposed that certain particles take longer to travel through the froth due to their size and
density. Knowing this, a froth retention time model is proposed
h
τ ( d ) = f P [12]
f p V fr
g
that is a function of particle size, d , and takes this into account by the addition of a froth particle
p
effect, P .
fr
The particle effect on the retention time is given the functional form
⎛ d ⎞
P =exp⎜B p ⎟ [13]
fr ⎜ d ⎟
⎝ p−n ⎠
where B is a constant and d is the particle diameter that, when attached to a given bubble size,
p-n
the bubble-particle aggregate has a neutral buoyancy. The neutrally buoyant particle, d ,
p-n
affecting Equation [13] is used to take into account the buoyancy of the bubble with an attached
particle. Smaller or less dense particles allow the bubble to travel upward within the froth more
quickly. The smaller a given particle is compared to the neutrally buoyant particle size, the
closer the particle effect is to 1. Therefore, the closer the particle is to following the fluid (or
bubble) flow the closer the particle retention time is to the average retention time within the
froth. The larger or more dense the particle is compared to the neutrally buoyant particle, the
greater the particle effect becomes. Large particles will take longer to travel through the froth, if
they travel through the froth at all. Particle effect, using this functional form, must always be
greater than 1 and therefore, particle froth retention time must always be equal to or greater than
the average froth retention time. B is thought to be a function of frother type and cell-dynamics
and is found empirically for each system.
Experimental
Sample
Model verification was carried out by continuous flotation experiments. These
experiments were performed using samples obtained from Potters Industries Inc. The samples
were Ballotini impact beads which are ground soda-lime glass used in sandblasting. These were
already sized and at least 80% spherical. Three different sizes were obtained: 40x70 mesh
(Potters spec AA), 70x140 mesh (Potters spec AD), and 170x325 mesh (Potters spec AH). No
preparation of the sample was required, beyond what the experimental procedure entails.
To measure contact angle of the particles, a flat surface was desired. A representative
portion of the glass particles was melted in an oven at 800ºC. These large glass pieces
(approximately 12mm x 12mm) were then ground flat on two sides. One side was polished,
eventually using a 2400 grit polishing cloth. Contact angles were easily measured using these
polished surfaces.
Surfactants
Cetyl (hexadecyl) trimethyl ammonium bromide (C TAB) was used as a collector due to
16
the wide Ph fluctuations it can encounter and still perform satisfactorily, as well as ease of use.
This was obtained from Sigma-Aldrich. Polypropylene glycol with an average molecular weight
of 425 (PPG-425) was used as a frother. This was also obtained from Sigma-Aldrich.
49 |
Virginia Tech | Frother Addition
Recirculating
load
Mixer
Mixing Tank
Flotation Cell
Feed
Tailings
Product
Air
Figure 2. Flotation circuit schematic
Continuous Testing
Testing was run on a continuous flotation circuit. This produces steady-state conditions
in which the flotation environment is not constantly changing and a flotation rate constant is not
arbitrarily set, as in batch tests (De Bruyn and Modi 1956; Jowett and Safvi 1960; Mehrotra and
Padmanabhan 1990). Continuous testing is both more difficult to setup and takes longer than
batch testing to perform, but results in more representative and reproducible data. Batch testing
data is difficult to collect because it must be collected in a short period of time, with steady state
never being reached. This brings into question what conditions are affecting the batch flotation
tests. Rate constants are constantly changing, while some believe that the flotation rate order
may also change (Brown and Smith 1953-54). This is not the case with a continuous flotation
circuit.
Experimental Setup
A diagram of the flotation circuit is shown in Figure 2. All feed to the flotation cell
comes from the mixing tank. The contents of the mixing tank are recirculated from the bottom
of the tank to the top. The combination of the mixer, within the tank, and the recirculating load
provides a well mixed environment in the mixing tank. This allows ideal conditioning, where
collector adsorption on particles is as equal as possible, as well as constant feed grade to the
flotation cell. A constant feed grade is needed to reach steady state in the continuous cell. The
contact angle samples are also placed within the conditioning tank so that they are conditioned
along with the sample being tested. They were held in the mixing tank within a perforated
plexiglass container which was retrieved after each flotation test was complete.
Feed is pumped out of the recirculating load using a variable speed Masterflex peristaltic
pump. This rate is approximately 1.33 L/min, which gives an average residence time (before the
introduction of air) within the 2L cell of 1.5 minutes. Before the feed enters the cell, frother is
introduced to obtain a dosage of 10ppm.
The flotation cell is modeled after the Rushton flotation cell (Rushton, Costich et al.
1950; Deglon, O'Connor et al. 1997; Armenante, Mazzarotta et al. 1999; Jenne and Reuss 1999)
as shown in Figure 3, where H/D = 1, d/D = 1/3, and w/D = 1/10. The height of the impeller off
the bottom of the cell, h, was set at 4mm for these tests. The h/D ratio in a typical Rushton cell
50 |
Virginia Tech | Impeller shaft
Baffle
w
Feed
H
h
Product
Tailings
Air input
Sintered d
glass plate
D
Figure 3. Flotation cell dimensions.
is 1/2, however h needed to be smaller than in a typical Rushton cell for the impeller to create
small bubbles, from the air coming through the sintered plate, as well as mix large particles,
which settle on the bottom of the cell. The height of the impeller still provided excellent mixing
as shown by a dye tracer. Four baffles were evenly spaced within the cell, at a height 0.5 inches
above the slurry level. A Rushton impeller was used with a diameter of 2.0 inches, which is
slightly larger than the desired d diameter of 1.83 inches given from the above ratios. The actual
dimensions of the flotation cell are as follows; D = 5.5 inches, H = 6.0 inches, d = 2.0 inches, w
= 0.55 inches, h = 0.16 inches. H given here is the height of the baffles, while the liquid was
kept below this height.
Feed entered the flotation cell mid-way up one side. On the opposite side, tailings were
pumped from the bottom of the cell with a variable speed peristaltic pump. The pump speed was
adjusted so that froth height was minimized and constant. Air was introduced through the
bottom of the cell using compressed gas and a flow meter. All tests were kept at the same
constant air rate. Air entered a chamber below the cell which was connected to the main cell by
a plexiglass partition which contained a sintered glass plate. The sintered glass plate (porosity C)
was obtained from Ace Glass. Air flowed through the plate and was broken up by the plate itself
and the action of the impeller situated directly over top of the plate. Mixing within the cell was
accomplished by a Lightnin Labmaster L1U10F mixer using a R100 Rushton impeller.
Sampling positions were located as shown in Figure 4 for the feed, product, and tailings.
The feed sample was situated where there was a direct drop in the material so that a flow diverter
was not needed. Any diversion of a contained flow might cause pressure differences which
would lead to different flow rates. The design of the system accommodated this so that correct
rates could be measured for the feed as well as the tailings and product. The product was
measured at the output of the launder around the cell, which collected the freely overflowing
product from the cell. Tailings were collected at the output of the tailings pump.
51 |
Virginia Tech | Frother Addition
Feed
Tailings
Product
Air
Sampling point
Figure 4. Sampling points around flotation cell.
Experimental Procedure
All samples were reused for subsequent tests so that particle size, as well as particle
surface chemistry did not drastically change between tests. This required the cleaning of
samples between tests. All glass samples were placed in an H SO bath overnight. The acid was
2 4
then drained using a glass fiber filter and rinsed three times. The sample was then placed in a
bucket and filled with water to dilute any leftover acid. The bucket was then drained, making
sure particles had settled to the bottom, and the process was repeated until a natural pH reading
was obtained (usually 5 repetitions). The glass particles were then placed within the mixing tank
and water was added until the correct percent solids (by volume) was reached.
Contact angle samples were rinsed with deionized water, after being cleaned in the acid
bath, and a deionized water contact angle was measured to determine if all samples were
properly cleaned. The samples were then placed within a plexiglass holder which was
subsequently placed within the mixing tank.
Once all samples were within the mixing tank, the mixer and recirculating pump were
turned on. C TAB was then added, at the desired concentration, and left to condition for at least
16
10 minutes. When conditioning was complete, the feed and frother pump were turned on,
airflow was set to the desired flow reading and the Lightnin mixer was turned on to the desired
speed setting.
Once steady state was reached, all desired measurements were taken. Torque and rpm
measurements, used to calculate energy input, were taken directly from the Lightnin mixer. A
pressure differential reading, used for air holdup calculations, was taken between two points
within the cell using a Comark C9553 pressure meter. Three full data sets were taken for each
test.
Once the test was complete, the contact angle samples were removed from the mixing
tank along with a representative sample of the solids and liquid from the tank, for zeta potential
and contact angle measurements.
52 |
Virginia Tech | Table 1. Flotation test variables
Particle Particle Size – Contact Angle - Impeller % Solids (by
Test #
Category approx. (mm) approx. (deg) RPM volume)
1 AA 300 25 1200 8.5
2 AD 140 25 1200 8.5
3 AH 65 25 1200 8.5
4 AA 300 33 1200 8.5
5 AD 140 33 1200 8.5
6 AH 65 33 1200 8.5
7 AA 300 40 1200 8.5
8 AD 140 40 1200 8.5
9 AH 65 40 1200 8.5
10 AA 300 33 900 8.5
11 AD 140 33 900 8.5
12 AH 65 33 900 8.5
13 AA 300 33 1500 8.5
14 AD 140 33 1500 8.5
15 AH 65 33 1500 8.5
16 AA 300 33 1200 5
17 AD 140 33 1200 5
18 AH 65 33 1200 5
19 AA 300 33 1200 12
20 AD 140 33 1200 12
21 AH 65 33 1200 12
Sample Analysis
Variables
The effects of 4 different variables were examined during these tests. These include
particle size, contact angle, energy input, and feed concentration. A layout of the tests is shown
in Table 1. Some tests were run twice due to variations in the measured and desired contact
angles. A high, medium and low value for each variable was desired, with a medium baseline
comparable for all tests.
Rate Constant
After mass balancing all flow rate data, the rate constant was determined. The typical
formula used in flotation is
kτ
R= [14]
1+kτ
where R is recovery and τ is average retention time within the cell. This formula assumes perfect
mixing and can be rewritten by substituting R=Pp/Ff for the recovery.
Pp
k = [15]
( )
τFf −Pp
P and F are the flow rates of the product and feed respectively while p and f are the grades of
those flow rates. By assuming that steady state has been reached and substituting in the tailings
mass flow rate (Tt), the rate constant is then given by Equation [16].
Pp
k = [16]
τTt
This formula is valid only for single input and single output processes. Within an industrial
flotation process, the flow rate of the froth is much less than the tailings flow rate, and the above
53 |
Virginia Tech | Pp Pp Pp
k = = = [17]
Vv Vt τFt
As can be seen, the only difference between Equation [16] and [17] are the flow rates T and F. If
a single output stream at steady state is assumed, Equation [17] reduces to [16]. Since this is not
the case for these experiments, the more general form of the equation ([17]) is being used. Rate
constants are shown in Table 2.
Air Fraction
Air fraction was determined from the difference between the two pressure differential
readings taken during the flotation tests. One reading was obtained with air in the system, while
the other was taken without. Knowing the percent solids (%S) within the cell (before the
addition of air), as well as the densities of the solid (ρ), liquid (ρ) and air (ρ), the air fraction
1 3 2
(%A) can be calculated using Equation [18].
∆P −∆P
%A= A S [18]
( ( ))
ghρ ρ%S +ρ 1−%S
2 1 3
The percent solids within the cell was assumed to be the tailings percent solids. If the cell is
perfectly mixed, the tailings concentration is equal to the cell concentration.
Surface Tension
Surface tension was determined with a KSV Sigma 70 tensiometer using the Du Nouy
ring method. Since surface tension is temperature sensitive, the liquid samples were stored in a
refrigerator until a measurement could be performed. They were then taken from the refrigerator
and allowed to reach their corresponding experimental temperature. A 25 mL sample was placed
within a plastic container which was positioned within the machine. C TAB is surface active on
16
the liquid-vapor interface and therefore affects surface tension. C TAB also adheres to glass.
16
To keep the amount of C TAB in solution constant throughout the test and therefore have a
16
constant surface tension, a plastic container was used.
Contact Angle
Contact angle measurements were performed using a Rame-Hart Model 100 goniometer
which employs the sessile drop method. The glass samples were rinsed to clear particles from
the surface, dried with nitrogen and then placed upon the viewing stage. A sample of the liquid
from the mixing tank was used to determine the contact angle. The average of, at least, 5
measurements were obtained for each glass particle. Three glass particles were used per
flotation test. All three glass particle values were then averaged together to get one contact angle
per test. The average contact angle values can be found in Table 2.
Zeta Potential
The zeta potential of the particles were measured using a Lazer Zee model 501 zeta
potential meter. A representative sample from the mixing tank was set within an ultrasonic bath
for 10 minutes to break up any particle aggregates. The sample container was then shaken up, let
to sit for one minute so that large particles would settle, and a sample was taken near the top of
the container. This procedure reduced the particle size being measured, which results in a better
measurement from this zeta potential meter. The sample was then measured at least 5 times,
with the voltage being applied for, at most, 2 seconds per measurement. This reduced the
amount of sample heating which leads to false measurements. One sample was used per test.
55 |
Virginia Tech | Valve
Glass
plate
Viewing
area
Plexiglass Hollow
box tube
Figure 5. Bubble sampling device.
Particle Size
Particle size is very important for model prediction as well as data representation. This
measurement was taken using a Microtrac X100 which employs a laser diffraction analysis and
light scattering technique. This technique gives a very reliable measurement for spherical
particles and the analyzer measures well within the tested particles’ size range.
The sauter mean size was the desired output from this machine. The particle measuring
program could not do this automatically, so a number distribution of particle sizes was measured
per sample. The number distribution was then converted into the sauter mean size.
The sauter mean size is the particle size that has the same surface area to volume ratio as
the entire sample’s surface area to volume ratio. This is commonly used in fluid dynamic
modeling as well as froth modeling. The sauter particle size for each test can be found in Table
2.
Bubble Size
A representative bubble size was determined for the frother dosage used (10ppm), as well
as sintered plate porosity, impeller type and diameter, and air flow rate. This was found by
running the flotation setup in exactly the same way as it was in the flotation tests, with the
exception of particles. This data was not recorded during the flotation tests because of the time
consumed in taking the measurements as well as the fact that particles would have blocked the
measuring device. The long time of this test would have resulted in the sample being exhausted
mid-way through the bubble size test. A pure water test, with only the addition of frother, could
be run continuously, with out a mixing tank. For these reasons, it was thought best to run these
tests without particles so that a more reproducible as well as feasible experiment could be
performed. The bubble size determined in this test is assumed to be the bubble size within the
flotation tests, although it is known that particles can affect the formation of bubbles and
therefore bubble size.
56 |
Virginia Tech | Figure 6. Original and modified bubble pictures.
Once steady state was reached, a sampling device (Figure 5) was lowered into the
flotation cell. The device is comprised of two glass plates held in place by a plexiglass box.
This provides bubble and liquid containment as well as a viewing area for the bubbles. A hollow
plexiglass tube is attached to one end of the box while the other end has a valve. When the valve
is opened, and at the bottom of the device, water can be introduced, through the valve end, until
water completely fills the device. The valve can then be closed, the device inverted, and the tube
can be inserted into the flotation cell. The sealed, liquid-filled container allows bubbles to travel
upward, through the plexiglass tubing into the glass-plate viewing area. Pressure measuring
positions were made available in the middle of the viewing area and at the bottom of the hollow
tube.
Following this procedure, to view bubbles within the flotation cell, digital pictures were
taken of those bubbles so that a size analysis could be performed. These digital pictures were
imported into Photoshop where they were manipulated into black and white clearly discernible
250
200
150
100
50
0
57
10.0 90.0 71.0 52.0 33.0 14.0 94.0 75.0 56.0 37.0 18.0 98.0 79.0
Bubble Diameter (mm)
elbbuB
fo
rebmuN
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
gnissaP
tnecreP
Figure 7. Bubble size population distribution with a Sauter mean
size of 467.4 microns |
Virginia Tech | Contact Angle
100
10
1
0.1
0.01
0.001
0.0001
0.0001 0.001 0.01 0.1 1 10 100
Experimental Rate Constant (min-1)
Figure 8. Relationship between experimental and theoretical rate
constants with variations in contact angle.
bubble images. An example of this is shown in Figure 6. Bubbles that were indistinct or
overlapping were deleted from the picture.
After the clear bubble images were prepared, they were imported into a Matlab program
which determined the size of each bubble. Knowing the size of each bubble, under those
operating conditions, the sauter size was determined. A graphical representation of the
population distribution of the bubble size is shown in Figure 7.
The pressure differential between the inlet of the tube and the viewing area was also
recorded. This gives the pressure difference between the measuring area, where the bubble size
is now known, and within the cell, where the actual bubble size is desired. The pressure
difference was found to be negligible and did not affect the bubble size.
Results
Once all parameters for the model were determined, the rate constants were calculated
using Equation [2] and can be found in Table 2. A fit was done for the variable B in the froth
recovery section of the model. B is 4.7 for this machine and frother type. The relationship
between experimental and theoretical rate constants is shown in Figure 8 through Figure 11.
Figure 8 shows the relationship between the experimental and theoretical rate constants
with variations in contact angle. Overall there is good agreement between the two. As can be
seen, as contact angle increases (corresponding to high rate constants) there is excellent
agreement between experimental and theoretical rate constants. With lower rate constants, and
therefore lower contact angles, more scattering of the data is apparent. This shows the sensitivity
of the rate constant to contact angle. With slight variations between measured and actual contact
angles, great differences are seen in values of rate constants. These variations may be due to
incomplete collector adsorption due to conditioning time or mixing as well as errors in
measurement. It should be noted that other input variables will have errors which may cause
58
)1n-im(
tnatsnoC
etaR
laciteroehT |
Virginia Tech | Energy Dissipation
100
10
1
0.1
0.01
0.001
0.0001
0.0001 0.001 0.01 0.1 1 10 100
Experimental Rate Constant (min-1)
Figure 11. Relationship between experimental and theoretical rate
constants with variations in energy dissipation.
available for measuring contact angle would not have perceived these fluctuations.
The effect of percent solids can be seen in Figure 9 and Figure 10. Figure 9 shows wide
variations between theoretical and experimental rate constants. This is mostly due to 2 data sets;
19-a and 19-b from Table 2. These data sets are the high percent solids, large particle size tests.
Two full tests were run for test number 19 because the particles were difficult to keep in
suspension. With this particle size and percent solids, the mixing action of the impeller was
inadequate. This is the reason for the discrepancy between the experimental and theoretical rate
constants. The model predictions are based upon the assumption that there is complete mixing.
Other effects may become noticeable when mixing is not adequate.
Knowing that there was error in these 2 tests, they were removed from the analysis. This
is shown in Figure 10, which displays excellent agreement between theoretical and experimental
rate constants. Knowing that removal of incomplete mixing data resulted in agreement between
experiment and theory tells a great deal about the assumption of mixing for model use.
Adequate mixing must be present for the model to predict rate constants accurately.
Figure 11 shows the relationship between theoretical and experimental rate constants
while energy input was varied. The energy was varied by increasing or reducing the speed of the
mixer within the flotation cell. Overall there is good agreement between the experimental and
theoretical values.
Overall, there is good agreement between the experimental and theoretical data, although
there are fluctuations within data sets. This is mostly due to errors in measuring input data.
Reliable input data is seen to be a problem in these tests, with errors compounding due to the
many variables measured. For the model to be useful in real world applications many data sets
must be taken, to average out this error, or very reliable input data must be obtained.
60
)1n-im(
tnatsnoC
etaR
laciteroehT |
Virginia Tech | Conclusions
A first order turbulent flotation rate equation has been proposed and verified
experimentally. The rate model encompasses both hydrodynamic and surface force effects,
which are incorporated into the collision frequency, probability of attachment, probability of
detachment, and froth recovery sections of the model. The model is semi-empirical in nature due
to the inclusion of the froth recovery. No froth recovery model has been proposed that is purely
theoretical, so a well known and reliable empirical model has been incorporated into the present
rate model.
Experimental verification has been performed with good results. Model calculations are
similar to experimental data. A result of the rate calculations was the understanding that input
data must be very reliable to use this model. Also, adequate mixing must be observed for the
model to be reliable. With this knowledge, the current rate equation can be used to predict
output from an industrial flotation process. The model can be very helpful in the optimization of
plant performance and flotation equipment design.
Nomenclature
%A air fraction [-]
%S percent solids without air - by vol. [-]
1 subscript – refers to particle
2 subscript – refers to bubble
3 subscript – refers to liquid
B constant [-]
d diameter of collision [m]
12
d diameter of particle [m]
p
d diameter of neutrally buoyant particle [m]
p-n
E surface energy barrier [J]
1
E kinetic energy of attachment [J]
k-A
E kinetic energy of detachment [J]
k-D
F feed flow rate [m3·s-1]
f feed grade [-]
g gravity [m·s-2]
h distance between pressure readings [m]
h froth height [m]
f
k rate constant [min-1]
m mass of particle or bubble [kg]
i
N number density of i – number per unit volume [m-3]
i
P product flow rate [m3·s-1]
p product grade [-]
P probability of attachment [-]
A
P probability of detachment [-]
D
P particle effect – retention time [-]
fr
R recovery [-]
r radius of bubble – slurry-froth interface [m]
2-0
r radius of bubble – top of froth [m]
2-f
61 |
Virginia Tech | Summary
The primary objective of this research was to derive a generic turbulent flotation
model based as much as possible upon first principles. This was accomplished by
incorporating models of the collision frequency, probability of attachment, probability of
detachment, and froth recovery into one model for the rate constant of the entire flotation
process.
Collision frequency - The collision frequency model used is typical to other
flotation models in existence. It assumes a Stokes number of infinity, which is not true in
flotation for either particles or bubbles, but has been shown to be close to real world
situations for much lower Stokes numbers. This was based upon numerical simulations
performed by previous researchers.
A review of the collision frequency models relating to flotation, existing in the
literature to date, was also given. The most relevant, current model available for flotation
was presented with all applicable assumptions. An area that has not been studied within
the fluid mechanics profession was pointed out. This included the collision of particles
and bubbles within a liquid environment. No present model can account for the differing
densities between these three phases.
Probability of attachment - The probability of attachment related the surface
forces of interaction, based upon the extended DLVO theory, to the turbulent energy of
attachment. The energy of attachment was assumed to be that of an average vortex
between the kolmogorov microscale and the particle/bubble scale.
Probability of detachment – The probability of detachment relates the work of
adhesion to the maximum turbulent energy available within the system for detachment.
The work of adhesion was calculated by the thermodynamic change in energy based upon
the change in area between the final and initial conditions of detachment and the
respective surface tensions of those areas. The maximum scale for the detachment
turbulent energy was given as the impeller size with the detachment energy equal to the
turbulent energy at this scale.
Froth recovery - Once the particle has intersected the froth, there is a certain
probability that the particle will travel through the froth and exit into the product as
6 5 |
Virginia Tech | opposed to re-entering the slurry or never truly entering the froth. A form of a well
known empirical model was used for this probability which is a function of average
residence time within the froth. A function of the particle residence time was proposed as
well as a maximum froth recovery.
The flotation model was verified by experiments performed in an idealized
flotation cell. The cell was based upon a typical Rushton flotation cell with slight
modifications to dimensional ratios due to mixing effects. Ground silica particles were
floated using cetyl trimethyl ammonium bromide as the collector and polypropylene
glycol (M = 425) as the frother. Once the froth recovery parameter was fit to the
N
experimental data, there was good agreement between the theoretical and experimental
rate constants across the entire range of variables tested, which includes particle diameter,
contact angle, percent solids, and energy input.
Theoretical trends were predicted using the derived flotation rate equation. The
effects of particle size, bubble size, energy input, contact angle, and liquid-vapor surface
tension were shown. Trends and values predicted by the model were similar to those
seen in industrial situations. This shows the usefulness of the model with control and
prediction capabilities for running industrial processes as well as the design of those
processes.
6 6 |
Virginia Tech | Recommendations for Future Work
Based upon the knowledge gained from this investigation, the following are
considered excellent areas for further research.
(1) Froth recovery (particle froth residence time) – The development of a non-
empirical froth recovery model will greatly benefit the proposed flotation
equation. The current equation is empirical with no theoretical basis. Also, the
one parameter that must be fit in the current flotation equation is included within
the froth recovery model. This parameter is used to calculate the particle
residence time within the forth. When this parameter can be replaced by known
input variables and a theoretical froth recovery model can be derived, a truly
universal slurry and froth flotation model will be available. The current model is
only universal within the slurry.
(2) Collision frequencies of particles and bubbles – The derivation of a collision
frequency that can account for particles and bubbles is needed for future flotation
models. Currently, only two phases are accounted for in collision frequencies.
This is not the case in flotation, where three phases are encountered. The effect of
all three phases on the collision frequency must be accounted for, as well as the
full range of Stokes numbers encountered in flotation.
(3) Combined effect of particles and bubbles on turbulence – The individual
effects of particles and bubbles on the turbulent energy spectrum have been
previously predicted and verified. The combined effect of two phases on a third
has not. Since a similar relationship exists between air and water and solid and
water, the assumption was made that the combined air-solid effects on water are
equal. This may not be the case. Further research into this will verify or disprove
this assumption.
(4) Attachment and detachment energies – The proposed attachment and
detachment energies are based upon the turbulent energy spectrum and what that
spectrum can affect. Although the scales given can affect the particles and
bubbles, the exact magnitude of the energy imparted to them might vary from the
6 7 |
Virginia Tech | EVALUATION OF METHODS FOR IMPROVING
CLASSIFYING CYCLONE PERFORMANCE
by
Dongcheol Shin
Committee Chairman: Gerald H. Luttrell
Department of Mining and Minerals Engineering
ABSTRACT
Most mineral and coal processing plants are forced to size their particulate streams in
order to maximize the efficiency of their unit operations. Classifiers are generally considered to
be more practical than screens for fine sizing, but the separation efficiency decreases
dramatically for particles smaller than approximately 150 µm. In addition, classifiers commonly
suffer from bypass, which occurs when a portion of the ultrafine particles (slimes) are misplaced
by hydraulic carryover into the oversize product. The unwanted misplacement can have a large
adverse impact on downstream separation processes. One method of reducing bypass is to inject
water into the cyclone apex. Unfortunately, existing water injection systems tend to substantially
increase the particle cut size, which makes it unacceptable for ultrafine sizing applications. A
new apex washing technology was developed to reduce the bypass of ultrafine material to the
hydrocyclone underflow while maintaining particle size cuts in the 25-50 µm size range.
Another method of reducing bypass is to retreat the cyclone underflow using multiple
stages of classifiers. However, natural variations in the physical properties of the feed make it
difficult to calculate the exact improvement offered by multistage classification in experimental
studies. Therefore, several mathematical equations for multistage classification circuits were
evaluated using mathematical tools to calculate the expected impact of multistage hydrocyclone
circuits on overall cut size, separation efficiency and bypass. These studies suggest that a two-
stage circuit which retreats primary underflow and recycles secondary overflow offers the best
balance between reducing bypass and maintaining a small cut size and high efficiency. |
Virginia Tech | ACKNOWLEDGMENTS
The author would like to express the deepest appreciation to his advisor, Dr. Gerald H.
Luttrell, for his guidance and advice during this investigation. His invaluable knowledge and
experience in mineral processing gave the author a lot of motivation to complete this research.
Deepest appreciation also goes to Dr. Roe-Hoan Yoon for his suggestions and recommendations.
The author is also grateful to Dr. Greg Adel for his class teaching in the area of population
balance modeling. The author is also thanks to Dr. Tom Novak for his guidance in graduate
school life.
A sincere thank you is also expressed to Dr. Jinming Zhang for his friendship and
guidance. Special thanks are also expressed to James Waddell and Robert Bratton for their
technical suggestions and assistance during this investigation. Thanks are extended to Baris
Yazgan, Todd Burchett, Chris Barbee, Kwangmin Kim, Hyunsun Do, Jinhong Zhang, Nini Ma
and Jialin Wang for their friendship.
Thanks are also expressed to several companies whose support made this work possible.
This gratitude is expressed to Toms Creek Coal Company, Coal Clean Company, Middle Fork
Processing, Krebs Engineers and Morris Coker Equipment. Individual thanks must also be
expressed to Mr. Robert Moorhead at Krebs Engineers.
The author would like to thank his parents, Yoonseok Shin and Kyunghee Choi, for their
continued support and encouragement. The author would like to thank his brother, Jinuk Shin,
for his encouragement. The author would like to thank to Myoung-Sin Kim, Dr. Roe-Hoan
Yoon’s wife, for her moral support during the author’s stay in Blacksburg. The author especially
expresses his deepest appreciation to his wife, Jaehee Song, for her support, encouragement and
love. Thanks and loves are expressed to Kate Jiyoung Shin, his adorable daughter, for being with
the author and his wife.
iii |
Virginia Tech | CHAPTER 1 - DEVELOPMENT OF A NEW WATER-INJECTION
SYSTEM FOR CLASSIFYING CYCLONES
1.1 Introduction
1.1.1 Background
Most mineral and coal processing plants are forced to size their particulate streams in
order to maximize the efficiency of their unit operations. These sizing techniques commonly
include various types of screens and classifiers. Screens exploit differences in the physical
dimensions of particles by allowing fines to pass through a perforated plate or open mesh while
coarser solids are retained. Unfortunately, screening systems are generally limited to particle size
separations coarser than approximately 250 µm due to limitations associated with capacity and
blinding. Hydraulic classifiers, which include both static and centrifugal devices, are generally
employed for finer size separations. Hydraulic classifiers exploit differences in the settling rates
of particles and are influenced by factors such as particle shape and density as well as particle
size. Classifiers are generally considered to be more practical than screens for fine sizing, but the
separation efficiency decreases dramatically for particles smaller than approximately 150 µm
(Heiskanen, 1993). In addition, classifiers commonly suffer from bypass, which occurs when a
portion of the ultrafine particles (slimes) are misplaced by hydraulic carryover into the oversize
product. The unwanted misplacement can have a large adverse impact on downstream separation
processes.
1.1.2 Objectives
The primary objective of the work outlined in this chapter is to evaluate a new apex
washing system for hydrocyclone classification. The new technology is designed to reduce the
1 |
Virginia Tech | 1.2 Experimental
1.2.1 Description of the Water-Injection System
Water-injected apex systems have been shown to be capable of reducing the bypass of
ultrafine particles that are misplaced to the hydrocyclone underflow. Unfortunately, past studies
have shown that existing water injection systems tend to substantially increase the particle
cutsize, which makes these systems unacceptable for many ultrafine sizing applications. In
addition, existing systems typically require large amounts of clarified injection water that may
not be readily available in industrial plants. In light of these problems, a new type of water-
injected cyclone technology was designed by Krebs Engineers to overcome some of the inherent
limitations associated with existing apex washing systems. In particular, the system was designed
to efficiently reduce the bypass of ultrafine particles to the underflow while maintaining a
relatively small particle cutsize.
The new water-injected apex consists of three parts (see Figure 1.1). The top section
consists of a grooved flange that is used to attach the apex to the bottom of a 6-inch (15.2-cm)
diameter Krebs G-Max hydrocyclone. The middle portion consists of interchangeable chambers
that serve as the body of the water-injected apex. Finally, the bottom part consists of the
underflow port (apex finder) and a tangential wash water inlet port. The cutaway view provided
in Figure 1.1 provides an example of the dimensions used for one possible combination of these
various components. For testing purposes, three interchangeable sections for Chamber A were
constructed with a height of 2.5 inches and three different inner diameters of 3.5, 4.0 and 4.5
inches. Likewise, nine different components for Chamber B were constructed with three different
inner diameters (i.e., 3.0, 3.5 and 4.0 inches) and three different inlet diameters (i.e., 0.50, 0.75
and 1.00 inches) so that all possible combinations of diameters and inlets could be evaluated.
3 |
Virginia Tech | testing to better match the feed solids content of slurry typically treated by desliming cyclones at
operating plant sites in the coal industry.
1.2.3.2 Preliminary Testing
Several preliminary test runs were conducted to determine the appropriate vortex finder
size for the test program. In these tests, the effects of vortex finder and apex geometries on
pressure drop and volumetric flow rate were evaluated. These initial experiments were carried
out using water and minus 100 mesh coal slurry having a solids content of approximately 4.6%
solids by weight. The pressure drop across the cyclone was measured by taking the difference
between the feed pressure at the cyclone inlet and the overflow pressure at the vortex outlet. The
effects of changes to the hydrocyclone geometry on pressure drop and volumetric flow rate are
summarized in Figure 1.5.
PRESSURE DR OP & USGPM
200
180
160
140
120
100
80
60
40
20
0
1 10 100
PRESSURE DROP (PSI)
Figure 1.5 – Flow and pressure response as a function of apex and vortex sizes for the 6-inch
(15.2-cm) diameter Krebs G-Max cyclone used in the test program.
8
ETARWOLF
CIRTEMULOV
Apex ø1.25 (VFø2.5, coal slurry)
Apex ø1.0 (VFø2.5, coal slurry)
Apex ø0.75 (VFø2.5, coal slurry)
Apex ø1.25 (VFø2.5, water)
Apex ø1.0 (VFø2.5, water)
Apex ø0.75 (VFø2.5, water)
Apex ø1.25 (VFø1.5, coal slurry)
Apex ø1.0 (VFø1.5, coal slurry)
Apex ø0.75 (VFø1.5, coal slurry)
Apex ø1.25 (VFø1.5, water)
Apex ø1.0 (VFø1.5, water)
Apex ø0.75 (VFø1.5, water) |
Virginia Tech | The data provided in Figure 1.5 show that the size of the vortex finder and pressure drop
is interdependent. In addition, the data demonstrate that the hydrocyclone can pass more slurry at
a given pressure than water. A larger vortex finder results in a lower pressure drop for the same
volume or a greater capacity for the same pressure drop. Conversely, a small diameter vortex
finder result in a larger pressure drop for the same volume. Although particle size analyses were
not conducted on these particular samples, an increase in cyclone pressure drop usually leads to a
higher volumetric throughput and a finer particle cut size (Svarovsky, 1984). Therefore, based on
these results, a 1.5-inch (3.8-cm) diameter vortex finder was selected for the test program since it
could provide a higher pressure drop at given volumetric flow rate for the new water-injected
apex system.
A few preliminary test runs were also performed to compare the performance of the
standard conventional apex and the water-injected apex prior to the initiation of extensive
detailed testing. These initial tests were conducted using a 1.5-inch (3.8-cm) diameter vortex
finer and a constant 120 GPM volumetric slurry flow rate. The experiments were carried out
using water and minus 100 mesh coal slurry having a solids content of approximately 4.5%
solids by weight. The resultant test data shown in Figure 1.6 indicate that the new water-injected
apex has the ability to achieve much better classification performance with a low pressure drop.
In fact, the particle size partition curve obtained at a pressure drop of 26 PSI with a 1-inch
diameter water-washed apex was nearly identical to the curve obtained at a much higher pressure
drop of 32 PSI with a smaller 0.75-inch diameter conventional apex. The ability to operate with a
larger apex has substantial advantages in term of being less prone to plugging. In addition, these
results suggest that the new water-injection apex may make it possible to achieve finer particle
size separations with larger diameter (higher capacity) cyclones in the future.
9 |
Virginia Tech | analysis. Particle size analysis was performed by wet sieving particles larger than 45 µm (325
mesh) and by laser analysis (Microtrac) of particles finer than 45 µm (325 mesh).
The sample point for the feed stream was the discharge of slurry from the return line that
circulated back to the slurry sump. Sample points for the underflow and overflow streams were
cut by the linear proportional cutter located inside the automated sampler. The total volume of
each slurry sample was reduced to a manageable volume by representatively subdividing the
slurry into smaller lots using a wet rotary slurry splitter. Because of the use of a closed-loop
system, the addition of injection water increased the volume of circulating slurry which, in turn,
raised the sump level and reduced the feed solids content. To overcome this problem, a small
dosage of flocculant was added to the circulating feed sump after each series of test runs to
quickly aggregate and settle coal particles. Once settled, some of the clarified water at the top of
the sump was pumped out to restore the solids content of the feed slurry back to the desired
range of 4.5-5.0% by weight. Comparison studies showed that the required flocculant dosage
was too low to impact the sizing performance of the hydrocyclone due to the high levels of shear
within the centrifugal feed pump, piping network and cyclone.
All of the detailed tests were conducted using a volumetric feed slurry flow rate of 100
GPM, which typically provided a pressure drop across the cyclone of 21 PSI. Figure 1.5
indicates that this pressure drop is appropriate for the 6-inch (15.2-cm) diameter hydrocyclone
used in this study. The detailed tests were run in accordance with a Box-Behnken parametric test
matrix developed using the Design Expert™ software package. Four parameters were varied (i.e.,
water injection flow rate, apex outlet diameter, apex inlet diameter and apex chamber diameter)
to create a 30 point test matrix for the water-injected apex system. The lower, middle and upper
settings for each of these parameters are summarized in Table 1.1. As shown, the water injection
11 |
Virginia Tech | 1.3 Results and Discussion
1.3.1 Parametric Study Results
To fully investigate the effects of the operating and geometric parameters on sizing
performance, regression equations for cutsize and bypass were obtained from the Box-Behnken
parametric study using the Design-ExpertTM software. The resultant linear regression equations
obtained for cutsize and bypass are shown in Table 1.2. The input variables used in the uncoded
expressions are entered as true units of measure (GPM and inches), while the coded values are
entered as normalized units ranging between -1 and +1 (see Table 1.2).
The overall data analysis suggested that the effects of water injection flow rate, apex inlet
diameter, apex chamber diameter and apex outlet diameter were all interrelated. Nevertheless, a
simple linear model was selected for the regression analysis since it still provided a relatively
good fit to the experimental data. As shown in Figure 1.8, the cutsize and bypass values
predicted by the linear model were in reasonably good agreement with the experimentally
determined values. More importantly, the linear model maximizes the numerical significance of
Table 1.2 – Regression expressions obtained from the Box-Behnken parametric study.
Uncoded Expressions Coded Expressions
Cut Size = Cut size =
+61.84083 +30.43
+0.32717 Water Injection Rate +4.91 Water Injection Rate
-1.66000 Apex Inlet -0.42 Apex Inlet
-3.15667 Apex Chamber -1.58 Apex Chamber
-22.44333 Apex Outlet -5.61 Apex Outlet
Bypass = Bypass=
-0.43483 +0.26
-0.0062222 Water Injection Rate -0.093 Water Injection Rate
-0.02333 Apex Inlet -0.005833 Apex Inlet
+0.055000 Apex Chamber +0.027 Apex Chamber
+0.58667 Apex Outlet +0.15 Apex Outlet
14 |
Virginia Tech | Figure 1.8 – Correlation between actual and predicted cut size and bypass.
the main effect for each variable. As such, the coefficients in the regression equations are more
meaningful for a linear model than for other higher term (quadratic or cubic) models that could
have been used in the statistical analysis.
The regression expressions indicate that both the water injection flow rate and apex outlet
diameter are significant terms in the linear models for cutsize and bypass since the coded
coefficients are relatively large. The expressions show that a smaller apex outlet diameter and
higher water injection rate produce a larger particle cutsize and smaller bypass. On the other
hand, the coded expressions show that the apex inlet diameter and chamber diameter are not
significant in either of the linear models. As such, these parameters do not have a significant
influence on either the cutsize or bypass obtained using the water-injected apex system.
To further illustrate the effects described above, the linear regression data was plotted to
show the correlations between the water injection rate and the two responses of primary interest
(i.e., cutsize and bypass). The plots for water injection rate and apex outlet diameter are shown in
Figures 1.9 and 1.10, respectively. The large value for Pearson’s correlation coefficient (R2 )
15 |
Virginia Tech | 1.3.2 Verification Results
The results of the parametric study indicate that water injection rate has the largest
overall impact on the partitioning performance provided by the water injected apex. Therefore, to
better examine the influence of this parameter on the two significant responses (i.e. cutsize and
bypass), an additional set of four tests were conducted at water injection rates of 0, 10, 20 and 30
GPM. All other geometric variables were held constant at their central point as specified in the
detailed test matrix. The resultant data, which are plotted in Figure 1.12, shows that increasing
the water injection rate produces a larger particle cutsize and lower bypass. Particle cutsize
increased steadily from 23.20, 25.41, 30.41 and 38.07 µm as the injection water flow rate
increased. Likewise, the bypass of ultrafines to the underflow decreased steadily from 0.32, 0.24,
Figure 1.12 – Partitioning performance as a function of water injection rate under central
point conditions (0.75 inch apex inlet, 4 inch chamber, 1 inch outlet).
18 |
Virginia Tech | 0.20 and 0.09 as the water injection rate increased. These opposing trends demonstrate the trade-
off between cutsize and bypass that must be considered when using a water-injected apex.
1.3.3 Optimization Results
Several series of statistical analyses were conducted using the Design-ExpertTM software
to identify the optimum settings of controllable variables that minimize bypass for a desired
cutsize range. The optimization was carried out over the same range of controllable variables as
used in the detailed test matrix. As such, the water injection flow rate was varied from 0 to 30
GPM, apex inlet diameter was varied from 0.5 to 1 inch, apex chamber diameter was varied from
3.5 to 4.5 inches, and apex outlet diameter was varied from 0.75 to 1.25 inches. Five different
cutsize ranges were considered in the optimization, i.e., 20~25 µm, 25~30 µm, 30~35 µm, 35~40
µm and 40~45 µm. The combination of variables that provided the smallest bypass was
considered the best solution among several optimized solutions obtained for each cutsize range.
For cases in which many optimized solutions were found, a secondary objective of a lower water
injection rate was used to select the best combination of controllable variables. Once the
optimum solution was identified for each cutsize range, three-dimensional (3D) response surface
plots were created so that the influence of the two most significant variables (i.e., water-injection
rate and apex outlet diameter) could be visualized at the optimum settings for the two remaining
variables (i.e., apex inlet diameter and chamber diameter).
The results of the optimization runs are summarized in Tables 1.3-1.7 for each of the five
size ranges examined in this study. The corresponding response surface plots for each of these
tables are also provided in Figures 1.13-1.22. For ease of comparison, the optimum values are
also summarized in Table 1.8.
19 |
Virginia Tech | Table 1.8 – Summary of optimal conditions needed for different cutsize ranges.
Apex
Desired Injection Apex Apex Inlet Expected Expected
Chamber
Size Range Rate Outlet Diameter Cut Size Bypass
Diameter
(Microns (GPM) (Inch) (Inch) (Microns) --
(Inch)
20-25 11.78 1.25 0.87 4.02 23.56 0.4247
25-30 13.58 1.03 0.78 4.11 28.98 0.2908
30-35 18.50 0.99 0.96 4.24 30.71 0.2416
35-40 25.40 0.85 0.70 4.36 36.09 0.1309
40-45 29.77 0.76 0.81 3.94 40.77 0.0231
1.3.3.1 Optimum Conditions for the 20-25 µm Size Range
The best solution (i.e., combination of water injection rate, apex outlet diameter, apex
inlet diameter and apex chamber diameter) for the 20-25 µm size range is shown in Table 1.8.
For this very small cutsize, it was necessary to employ a low water injection rate and large apex
outlet diameter. As a result, the bypass value was very high at nearly 0.42. These results suggest
that it is not possible to achieve such a small cutsize with this technology unless other
operational parameters not examined in the study are changed (i.e., hydrocyclone geometry, feed
inlet pressure, feed inlet diameter, etc.).
1.3.3.2 Optimum Conditions for the 25-30 µm Size Range
The best solution (i.e., combination of water injection rate, apex outlet diameter, apex
inlet diameter and apex chamber diameter) for the 25-30 µm size range is shown in Table 1.8.
Again, the only way to achieve the small cutsize range was to operate with a relatively low water
injection rate (13.6 GPM) and relatively large apex outlet (1.03 inches). The amount of bypass
25 |
Virginia Tech | was somewhat lower for this case compared to finer 20-25 µm size range (i.e., 0.29 versus 0.42);
however, the bypass was still relatively large compared to the project goal of achieving bypass
values of less than 0.10-0.15. Nonetheless, these results are considered an improvement over
those typically provided by hydrocyclone deslime circuits that currently operate in the coal
industry. These industrial circuits typically provide cutsizes in the 40-45 µm size range with
bypass values of 0.30-0.35. Thus, the water-injected apex makes it possible to attain a smaller
cutsize with a similar bypass to that of current industrial circuits.
1.3.3.3 Optimum Conditions for the 30-35 µm Size Range
The best solution (i.e., combination of water injection rate, apex outlet diameter, apex
inlet diameter and apex chamber diameter) for the 30-35 µm size range is shown in Table 1.8. In
this case, the somewhat larger cutsize range made it possible to operate with a higher water flow
rate so that the bypass could be reduced below 0.25. This operating range is attractive since it
provides a smaller cutsize that typically found in industrial plants (i.e., normally 40-45 µm) with
significantly less bypass (i.e., normally 30-35%).
1.3.3.4 Optimum Conditions for the 35-40 µm Size Range
The best solution (i.e., combination of water injection rate, apex outlet diameter, apex
inlet diameter and apex chamber diameter) for the 35-40 µm size range is shown in Table 1.8.
The performance obtained in this particular operating range represents a considerable
improvement over that normally achieved in industrial plants. The low bypass of 0.13 for this
case can be attributed to the use of a higher water injection rate (25.4 GPM) and smaller apex
outlet diameter (0.85 inches). Furthermore, the cutsize is smaller (by about 5 µm) than that
26 |
Virginia Tech | typically obtained in industrial circuits which utilize conventional hydrocyclones that do not
employ the water injected apex technologies. Therefore, this operating point is considered to be a
very attractive for many of the deslime cyclone circuits that are currently operating in the coal
industry. The use of the new apex washing system would be expected to improve product quality
(due to less bypass) and improve coal recovery (due to the smaller cutsize).
1.3.3.5 Optimum Conditions for the 40-45 µm Size Range
The best solution (i.e., combination of water injection rate, apex outlet diameter, apex
inlet diameter and apex chamber diameter) for the 40-45 µm size range is shown in Table 1.8.
This particular range of cutsize values represents the range that is typically achieved in industrial
deslime cyclone circuits. For this practical range, a very low bypass of just over 0.02 could be
realized by using a water injection flow rate approaching the maximum tested value of 30 GPM.
To achieve the low bypass, a relatively small apex outlet diameter of 0.76 inches had to be used.
The exceptionally low bypass makes this operating point attractive for cases in which the
misplacement of slimes must be avoided in order to make the best possible quality for the final
product. Such applications would include deslime circuits ahead of flotation and product sizing
cyclones installed downstream of fine (100x325 mesh) spirals utilized in some industrial plants.
1.3.3.6 Bypass and Cutsize Correlation Under Optimum Conditions
Several important observations can be made based on the information gathered from the
optimization study. The study indicates that there are no solutions (i.e., no combination of
controllable variables) that provide cutsize values below 20 µm or above 50 µm. This finding
should be expected since none of the cutsize values determined experimentally was found to fall
27 |
Virginia Tech | in these ranges. More importantly, the study showed a very strong negative correlation between
cutsize and bypass when operating under optimal conditions. This trend can be seen by the data
plotted in Figure 1.23 for the entire set of optimized test runs conducted in the parametric study.
The Pearson correlation coefficient (R2) value of near unity (R2=0.99) shows an almost
perfect correlation between cutsize and bypass. As such, this plot can be used to estimate the
minimum amount of bypass that can be achieved for a target cutsize. As shown, a reduction in
bypass to 0.1 or lower using the water-injected apex will force the cutsize to increase to
approximately 37 µm or larger. This operating point will likely require a modestly high water
rate (e.g., 26 GPM) and small apex outlet diameter (e.g., 0.8 inches). Likewise, the regression
line shows that a bypass of less than 0.05 dictates a larger cutsize of 40 µm or larger. This
requires a higher water flow rate approaching 30 GPM and relatively small apex approaching
0.75 inches.
Figure 1.23 – Correlation between predicted cutsize and bypass.
28 |
Virginia Tech | 1.4 Summary and Conclusions
A parametric study was performed to evaluate a new water-injected apex system. The
study indicated that apex outlet diameter and water injection flow rate have the main effect on
minimizing the bypass of ultrafine particles to the underflow. The effects of apex inlet diameter
and apex chamber diameter where not found to be important variables for the range of
dimensions examined in this study. When operated under optimum conditions, the new apex
washing system makes it possible to reduce ultrafine bypass from a typical range of 30~35%
down to approximately 2% when operated within a cutsize range of 40-45 um. A smaller cutsize
range was possible when using less injection water and larger apex outlets, but these changes
tended to rapidly increase the amount of bypass. In fact, a near perfect linear correlation was
observed between cutsize and bypass when operating under the optimum settings of apex
geometry and water flow rate that were needed to minimize bypass.
29 |
Virginia Tech | CHAPTER 2 – MATHEMATICAL SOLUTIONS TO PARITIONING
EQUATIONS FOR MULTISTAGE CLASSIFICATION CIRCUITS
2.1 Introduction
2.1.1 Background
Classification processes are used in a wide variety of applications in both the mineral
processing and coal preparation industries. Both static tank and centrifugal separators are used
primarily for the purpose of sorting particles according to size based on differences in settling
rates. In some applications, the classification processes may be used in multistage circuits that
are specifically designed to minimize the misplacement of particles and improve separation
efficiency. For hydraulic classifiers, scavenging circuits can be used to reduce unwanted losses
of coarse particles by retreating the undersize stream using one or more additional stages of
separation. Likewise, cleaning circuits can be used to improve the quality of the coarse product
by retreating the oversize stream in one or more additional units designed to reduce the
inadvertent bypass of fine materials.
In most cases, the natural variations in the physical properties of the feed particles (i.e.,
density, conductivity, magnetic susceptibility, washability) make it difficult to experimentally
determine the extent of the improvement offered by multistage classification circuits. To
overcome this problem, an evaluation of multistage separation circuits was performed in this
study using a mathematical approach. An S-shaped partition function, which has been advocated
for describing hydrocyclone efficiency curves (Lynch and Rao, 1975), was used for all of the
performance calculations conducted in this work. According to this expression, the partition
curve for a separation may be represented by the following exponential transition function:
32 |
Virginia Tech | exp[αZ]−1
P = [2.1.1]
exp[αZ]+exp[α]−2
where P is probability function to a particular stream, α is the sharpness of separation, and Z
is the ratio of the particle size ( X ) to particle size cutpoint ( X ) (i.e.,Z = X / X ). It is
50 50
generally assumed that the bypass is independent of particle size and equals the water recovery
from the feed to the underflow (oversize) product. This condition assumes that the fraction of the
feed water recovered in the underflow stream carries an equivalent fraction of the feed solids.
Austin and Klimpel (1981) argue that there is no fundamental reason why, in general, this should
be so, and show data where the bypass is clearly not equal to the water recovery. Svarovsky
(1992) and Braun and Bohnet (1990) assume that the bypass equals the fraction of the feed slurry
reporting to the underflow. This assumption is not commonly used, but is a close approximation
to the water recovery at low feed solids concentrations and is more readily measured. The
generalized equation for simulating overall bypass of multistage classification circuits is
obtained by using a following equation:
P =(P* −Bp)/(1−Bp) [2.1.2]
where P and P* represent the corrected and actual probability functions, respectively, and Bp
is the bypass of ultrafine particles to underflow. The actual probability can be obtained by simply
adding water entrainment to corrected probability function.
2.1.2 Linear Circuit Analysis
A comparison of the performance of different configurations of multistage circuits can be
accomplished using a mathematical approach called linear circuit analysis (LCA). This
technique, which was first advocated by Meloy (1983), is one of the most powerful tools for
33 |
Virginia Tech | analyzing processing circuits. The LCA approach has been used to improve the performance of
processing circuits in variety of industrial applications (Luttrell et al., 1998). LCA can only be
applied if particle-particle interactions do not influence the probability that a particle will report
to a particular stream, i.e. the partition curve should remain unchanged in each stage of
separation. This assumption is reasonably valid for most classification separators provided that
the machine is functioning within its recommended operating limits (e.g., feed solids content is
not too high). Based on this assumption, circuit analysis will provide not only useful insight into
how unit operations should be configured in a multistage circuit, but also numerical solutions
that predict overall circuit performance.
2.1.3 Objectives
The primary objective of the work outlined in this chapter is to use partition models and
linear circuit analysis to derive analytical expressions that can be used to directly calculate key
indicators that describe the separation performance of multistage classification circuits. For
hydraulic classifiers, some of the specific indicators of interest include particle cutsize, bypass
and separation efficiency. Due to the complexity of the mathematics involved, a commercial
software package known as Mathematica was used to algebraically solve most of the
performance expressions developed in this study. In addition, the accuracy of the analytical
expressions was evaluated by means of direct numerical simulations conducted using iterative
models developed in an Excel spreadsheet format.
34 |
Virginia Tech | 2.2 Mathematical Software
2.2.1 Mathematica Simulations
Mathematica, a powerful mathematical software package, was utilized to derive general
mathematical equations for the multistage classification circuits and to calculate their overall
particle cutsize and separation efficiency. For the purpose of this study, multistage classification
circuits represent a combination of processing units that include two-stage and three-stage
circuits that incorporate underflow reprocessing, overflow reprocessing, recycle and no recycle.
The “preferred” configurations identified by circuit analysis are limited in this study to three or
less units for practical reasons.
To derive the generalized equations for multistage classification circuits, the combined
probability function for two-stage and three-stage circuits was calculated from the individual
probability function for a single-stage unit using the linear circuit analysis (LCA) methodology.
The combined probability function was entered, simplified and then generalized by the
Mathematica software package. The combined probability function for the multistage circuits
followed the generalized form given by:
P = f(α,X ) [2.2.1]
50
where P is a probability function (fraction reporting to underflow), α is the separation
sharpness, and X is the separation cutsize for each unit. All of the probability equations were
50
found to be expressed as complex exponential functions, which are non-algebraic and non-linear.
Therefore, to get a solution (i.e., to find α andX ) from the combined equations for multistage
50
circuits, the built-in “FindRoot” function was used in Mathematica. This function can search for
a numerical solution to complex non-algebraic equations by Newton’s method. To find a solution
to an equation of the form f(x) =0 using Newton’s method, the algorithm starts atx = 0, then
35 |
Virginia Tech | uses knowledge of the derivative f ′to take a sequence of steps toward a solution. Each new
calculated point x that the algorithm tries is found from the previous point x using the
n n−1
formulax = x − f(x )/ f ′(x ).
n n−1 n−1 n−1
When searching for a solution, the particle cutsize (X ) was represented by a value of
50
X at which P=0.5. Likewise, the separation sharpness was expressed as follows:
X 2X
α=1.0986 50 =1.0986 50 [2.2.2]
Ep X − X
75 25
where Ep is the Ecart probable error (another criterion for the separation efficiency) and X
25
and X are the particle sizes defined at P=0.25 and P=0.75, respectively. If the values ofX ,
75 25
X and X are known, the particle cutsize and separation sharpness (or Ecart probable error)
50 75
can be determined numerically. The formations of the “FindRoot” function that are related
withX , X and X are as follows:
25 50 75
FindRoot[P ==0.5,{X,X }] [2.2.3]
0
FindRoot[P ==0.25,{X,X }] [2.2.4]
0
FindRoot[P ==0.75,{X,X }] [2.2.5]
0
These formations instruct the program to search for an X value that numerically satisfies the
equation “P ==0.5 or 0.25 or 0.75” starting with X=X .
0
For the cases involving the probability function with bypass, the following equation was
used to calculate the overall probability function:
P =(P* −Bp)/(1−Bp) [2.2.6]
36 |
Virginia Tech | where P* represents the actual probability function (with entrainment), P is the corrected
probability function (no entrainment), and Bp is the ultrafine misplacement to underflow for
each unit. This equation can be rearranged to provide the following expression forP*:
P* =(1−Bp)P+Bp [2.2.7]
In a manner similar to deriving equations for multistage circuits for overall cutsize and
separation efficiency, the equations for multistage circuits can be generalized for determining the
overall bypass. The combined probability function for multistage circuits that include bypass
followed the generalized form given by:
P* = f(α,X ,φ ) [2.2.8]
50 L
where P* is probability function that includes bypass. The termsα, X and φ represent the
50 L
separation sharpness, cutsize, and ultrafine size bypass (misplacement) to underflow for each
unit, respectively. The overall bypass for a specific circuit configuration can be calculated by
setting this probability function (P*) equal to 0 within the “FindRoot” function.
Unfortunately, the Mathematica software package had great difficulty in deriving an
equation for the specific particle size of interest due to the complexity of the equations involved.
The form of the exponential expressions constrained Mathematica to solve for X using inverse
functions. This made solutions nearly impossible to obtain. Therefore, in order to derive an
equation for the specific particle size of interest, the term X had to be separated from the other
variables present in the partition expression. The following functions are related with the specific
particle size of interest:
X = f(P,α) [2.2.9]
50
X = f(P*,α,φ ) [2.2.10]
50 L
37 |
Virginia Tech | separation sharpness (α) to be enter for each unit in the circuit. The interconnection of the
various streams between units A, B and C can be varied using a series of six dropdown menus
(C), which indicate where each of the two products from each separator should report. The
probability to underflow for each unit is calculated from Equation [2.2.11] in the left most
columns (D), (E) and (F). These probabilities are used with the feed tonnage distribution
(yellow-shaded column) to calculate the tonnage entering and exiting each unit A, B and C. The
calculated tonnage values are then used to determine the overall partition probabilities (G) for the
combined circuitry using the simple relationship:
UnderflowTonnage for ith SizeClass
Probability to Underflow= [2.2.12]
Feed Tonnage for ith SizeClass
The partition curves (H) are then obtained by plotting the mean size (C) as a function of the
combined partition values (G), as well as the individual partition values (D), (E) and (F) for each
unit. The overall cutsize and separation efficiency for the multistage circuit is reported as a
summary output (B).
The predictions obtained from the theoretical equations derived from Mathematica for
determining the circuit partition factors were found to be equivalent to the simulation results
obtained from the Excel simulation spreadsheet. The exact agreement between the Mathematica
and Excel partition values verifies that, for any particle cutsize and separation sharpness, a circuit
partition curve can be calculated analytically from the probabilities without the need to know the
feed size distribution. This finding is extremely important since most investigators do not realize
that simulations based on partitioning probabilities are independent of the physical properties of
the feed stream. In other words, the same cutsize and efficiency will be obtained from the
simulations routines regardless of what feed size distribution is entered. Only the product size
distributions will change in response to changes in the feed size distribution.
39 |
Virginia Tech | 2.3 Results
2.3.1 Underflow Reprocessing Circuit Without Recycle
2.3.1.1 Two-Stage Circuit Analysis
The underlying principle of LCA is that all particles that enter a separator as feed (F ) are
selected to report to either the concentrate (C ) or tailing (T ) streams by a dimensionless
probability function ( P ). This can be mathematically described for a two-stage underflow
reprocessing circuit without recycle as shown in Figure 2.2. In this case,P and P represent the
0 1
partition probabilities for the primary and secondary units, respectively. By simple algebraic
calculation, the oversize-to-feed ratio ( T F = P ) for this particular circuit can be
T,under
represented as:
P = P P [2.3.1]
T,under 0 1
This equation can be easily expanded using a transition function to quantify the separation
probability that occurs for each separator. If a standard classification model is used (Lynch and
Rao, 1977), then the partition for each unit in the circuit can be calculated using:
Figure 2.2 – Schematic of a two-stage underflow reprocessing circuit without recycle.
40 |
Virginia Tech | eαZ −1
P = [2.3.2]
eαZ +eα−2
where P is the partition factor, α is a sharpness value and Z represent the normalized size
given by X X . By substituting the partition function given by Equation [2.3.2] into the
50
separation probabilities represented in Equation [2.3.1], the overall partition expression for this
circuit now becomes:
eα 0Z0 −1 eα 1Z1−1
P =
T
eα0+eα0 Z0 −2 eα1+eα1 Z1−2
[2.3.3]
H LH L
where α and α are the sharpness values and Z and Z are the normalized size for the primary
0 1 0 1
H LH L
and secondary separators, respectively. This equation represents the combined partitioning
probability for a two-stage underflow reprocessing circuit without any recycle streams.
To check the validity of Equation [2.3.3], a comparison was made between the analytical
solution and a simulation results obtained using the spreadsheet program described previously.
The partitioning data selected for use in this validation procedure are shown in Figure 2.3. For
each technique, the primary and secondary separators were set to make a respective cutsize of
150 and 106µm. The separation sharpness values for the primary and secondary units were also
set at different values of 2.748 and 3.661, respectively. By substituting these values into the
Equation [2.3.3], the overall partition expression for this circuit becomes:
e0.01831X −1 e0.0345X−1
P =
T
13.588+e0.01831 X 36.939+e0.0345 X
[2.3.4]
H LH L
A comparison of the partitioning results obtained using this expression and those obtained from
H LH L
the Excel simulations are summarized in Table 2.1. As should be expected, the Mathematica
solution for determining circuit partition factors is mathematically equivalent to the Excel
simulation (which utilized feed properties). The good agreement between the Mathematica and
41 |
Virginia Tech | Figure 2.3 – Example of the partitioning response of the two-stage circuit underflow
reprocessing circuit without recycle.
Excel partition values verifies that for any particle cutsize, a circuit partition value can be
calculated. This also indicates that important size values, such as X , X , and X , can be
25 50 75
back-calculated from Equation [2.3.4] by varying X until the desired values of P are found.
More importantly, important performance indicators, such as the separation sharpness (α) and
cutsize (X ), can be determined for the entire circuit completely independent of feed properties.
50
As discussed previously, Mathematica can be used to perform the calculations required to
determine the important performance indicators for the two-stage circuit. In trying to find
solution to this equation, Newton’s method was used to determine the values of X needed to
identify the cutsize (X ) and calculate the separation sharpness (α). To accomplish this goal,
50
the appropriate X values were determined using the “FindRoot” function which searches for a
42 |
Virginia Tech | In this case, the primary, secondary and tertiary separators were set to make separations at the
particle cutsize of 150, 106 and 75µm with separation sharpness values of 2.748, 3.661 and
3.663, respectively. The partition values calculated from Mathematica and Excel were again
found to exactly agree for this circuit. The cutsize and separation sharpness for total circuit was
found to be 165.55 µm and 4.135, respectively. Once again, the analytical solution shows that
the cutsize for the combined circuit is larger than that obtained for either of the single unit
operations.
3.3.2 Underflow Reprocessing Circuit With Recycle
2.3.2.1 Two-Stage Circuit Analysis
The approach described above can also be used to evaluate the effects of recycle streams
on the performance of multistage circuits. This type of assessment is traditionally much more
difficult to perform with standard simulation routines since it requires several iterations to find a
stable solution. However, no such problem exists for analytical solutions obtained using linear
circuit analysis.
Consider the two-stage underflow reprocessing circuit with recycle shown in Figure 2.5.
Once again, P and P represent the dimensionless probability functions that select particles to
0 1
report to a given stream. By simple algebraic substitution, the overall oversize-to-feed ratio
(T F = P ) for this particular circuit can be calculated as:
T,under
P = P P (1−P +P P) [2.3.11]
T,under 0 1 0 0 1
By substituting Equation [2.3.2] into this expression, the overall partition expression for this
circuit becomes:
45 |
Virginia Tech | Figure 2.5 – Schematic of a two-stage underflow reprocessing circuit with recycle.
−1+eα 0Z0 −1+eα 1Z1
P =
T
3−2eα0−eα0 Z0−eα1−2eα1 Z1+eα0+α1+eα0+α1 Z1+eα0 Z0+α1 Z1
[2.3.12]
H LH L
To check the validity of this expression, a comparative solution was again obtained from the
Excel spreadsheet simulation routine. In this case, the primary, secondary and tertiary separators
were set to make a cutsize of 150, 106 and 75 µm with separation sharpness values of 2.748,
3.661 and 3.663, respectively. As expected, both the Mathematica and Excel partition values
were in perfect agreement for this three-stage circuit. The cutsize and separation sharpness for
total circuit was found to be 158.30 µm and 3.717, respectively. In this case, the increase in
cutsize created by the use of a two-stage circuit is less with a recycle stream than without a
recycle stream (i.e., 158.30 versus 164.54µm).
2.3.2.2 Three-Stage Circuit Analysis
In this case, an analytical solution to the partitioning performance of a three-stage circuit
with recycle was derived using linear circuit analysis. A schematic of the three-stage circuit is
46 |
Virginia Tech | when substituting Equation [2.3.2] into the expression derived from linear circuit analysis. For
verification purposes, the primary, secondary and tertiary separator were set to make separations
at cutsize values of 150, 106 and 75 µm with separation sharpness values of 2.748, 3.661 and
3.663, respectively. The Mathematica and Excel partition values were again found to be
consistent for this circuit, indicating that the analytical solution was indeed accurate. The cutsize
and separation sharpness for total circuit were found to be 158.32 µm and 3.737, respectively,
based on the input values selected for the individual units. It is important to notice that cutsize of
158.32 µm obtained with this three-stage circuit with recycle streams was substantially smaller
than the cutsize of 165.55 µm obtained for the three-stage circuit without recycle. Thus, the use
of recycle streams suppresses the impact of increasing cutsize for multistage circuits in which the
underflow stream is retreated to reduce bypass.
2.3.3 Overflow Reprocessing Circuit Without Recycle
2.3.3.1 Two-Stage Circuit Analysis
Several series of calculations were also performed to quantify the partitioning behavior of
Figure 2.7 – Schematic of a two-stage overflow reprocessing circuit without recycle.
48 |
Virginia Tech | circuits in which one or more of the overflow (undersize) streams were reprocessed. In the first
example, a two-stage overflow reprocessing circuit without recycle was evaluated as shown in
Figure 2.7. For this configuration, the overall oversize-to-feed ratio (T F = P ) is:
T,under
P = P +P −P P [2.3.15]
T,under 0 1 0 1
Substituting Equation [2.3.2] into this expression gives the overall partition expression as:
−1+(cid:198)α0 Z0
−1+(cid:198)α1 Z1 1− −2+− (cid:198)1 α+ 0(cid:198) +α (cid:198)0 αZ 00
Z0
P = +
T
−2+(cid:198)α0+(cid:198)α0 Z0 −2+(cid:198)α1+(cid:198)α1 Z1 [2.3.16]
H LJ N
Both the Mathematica and Excel solutions for the partition values were identical, indicating
again that the analytical solution was accurate. In this case, the primary and secondary separators
were set to provide respective cutsize values of 150 and 106 µm and respective separation
sharpness values of 2.748 and 3.661. Based on these input values, the cutsize and separation
sharpness for the total circuit was found to be 87.06 µm and 2.805, respectively. In this case, the
use of a two-stage circuit to retreat the undersize product reduced the overall cutsize compared to
the cutsize .
2.3.3.2 Three-Stage Circuit Analysis
Figure 2.8 shows the layout for a three-stage overflow reprocessing circuit without
recycle. The overall oversize-to-feed ratio (T F = P ) for this circuit can be calculated from
T,under
linear circuit analysis as:
P = P +P +P −P P −P P −PP + P PP [2.3.17]
T,under 0 1 2 0 1 0 2 1 2 0 1 2
Similar to the previous section, the overall partition expression for this circuit becomes:
49 |
Virginia Tech | n
P T= P N−1
N=1 [2.4.4]
where n is n‰umber of classification separators in the circuit. When considering bypass, the
generalized equation for this circuit can be obtained as:
n
∗ ∗
P = P
T N−1
N=1 [2.4.5]
where the pro‰ bability (P*) for single-stage, two-stage and three-stage units can be expressed as:
P* =(1−Bp)P+Bp [2.4.6]
As indicated previously, the respective values of P and P* represent the corrected and actual
probability functions for the circuit and Bp represents the bypass of fine particles to the
underflow stream. The probability functions (P) for each separator can be estimated based on
the empirical formula (Lynch and Rao, 1977):
eαZ −1
P= [2.4.7]
eαZ +eα−2
where α is the separation sharpness and Z=X/X is the normalized particle size, i.e., the ratio of
50
the actual particle size of interest (X) divided by the cutsize (X ).
50
2.4.2 Underflow Reprocessing Circuit With Recycle
Generic configurations of underflow reprocessing circuits without recycle are shown in
Figure 2.12. The probability functions calculated by linear circuit analysis for each circuit are as
follows. The single-stage probability can be expressed as follows:
P = P [2.4.8]
T 0
The two-stage probability can be expressed as follows:
55 |
Virginia Tech | P T=P 0+ 1−P 0 P 1 [2.4.17]
Likewise, the partitioning probability for a three-stage can be expressed as follows:
H L
P T=P 0+P 1+P 2−P 0 P 1−P 0 P 2−P 1 P 2+P 0 P 1 P 2 [2.4.18]
This equation can be further simplified to:
P T=P 0+ 1−P 0 P 1+ 1−P 0 1−P 1 P 2 [2.4.19]
From these equations, a generalized expression for this specific type of circuit incorporating n
H L H LH L
unit operations can be obtained by inspection. The partitioning probability for circuits without
bypass is given as:
n n
n n n
P T=P 0+P n−1 1−P N−2 − 1−P N−2 +P n−2 1−P N−3
N=2
N=2
N=3
N=2 N=3
[2.4.20]
i y
j i y i yz
while the partitioningj j j jj p„ robj j jjab‰ ilitH y for circL uz z zzits „ withj j jj ‰ bypH ass is givLz z zzenz z z zz as: ‚H L
k k { k {{
n n
n n n
∗ ∗ ∗ ∗ ∗ ∗ ∗
P =P +P 1−P − 1−P +P 1−P
T 0 n−1 N−2 N−2 n−2 N−3
N=2 N=2 N=3
N=2 N=3 [2.4.21]
i y
j i y i yz
The values of Pand j j j jjP„ * inj j jj t‰ hesH e expresL sz z zz ion „ reprj j jj e‰ senH t the parL tiz z zz tiz z z zzoning pr‚ obH abilities L for each unit
k k { k {{
operation with and without bypass, respectively.
2.4.4 Overflow Reprocessing Circuit With Recycle
Generic configurations of underflow reprocessing circuit without recycle are as shown in
Figure 2.14. The probability functions for the single-, two- and three-stage circuits can be
mathematically represented as follows. The single-stage probability can be expressed as:
P = P [2.4.22]
T 0
The two-stage probability, which can be expressed as:
58 |
Virginia Tech | Figure 2.14 – Generic configurations of overflow reprocessing circuits with recycle.
P
0
P T=
1−P 1+P 1 P 0 [2.4.23]
This equation can be further simplified to:
P
0
P =
T
1− 1−P 0 P 1 [2.4.24]
The three-stage probability, which can be expressed as:
H L
P −P P +P P P
0 0 2 0 1 2
P T=
1−P 1−P 2+P 0P 1+P 1P 2 [2.4.25]
This equation can also be further simplified to:
P 1− 1−P P
0 1 2
P =
T
1− 1−P 0 P 1− 1−P 1 P 2 [2.4.26]
H H L L
The generalized equation of this specific type of circuit can be obtained as follows for cases in
H L H L
which bypass is ignored.
n n
P T= P 0 1− P N−1 1−P N−2 1− P N−1 1−P N−2
N=3 N=2 [2.4.27]
i i yy i y
j j zz j z
Likewise, thj jje gej jjnera‚lized eqHuation oLfz zz z zzthìis j jjspec‚ific typHe of circLuz zzit can be obtained as follows for
k k {{ k {
cases in which bypass is considered.
59 |
Virginia Tech | 2.5 Summary and Conclusions
Linear circuit analysis was combined with an empirical model of particle classification to
derive analytical expressions that describe the partitioning performance of multistage circuits.
Due to the complexity of the mathematical functions, a software package known as Mathematica
was used to perform the required computations dictated by linear circuit analysis. Although
Mathematica had great difficulty in deriving analytical equations for a specific particle size of
interest, this powerful tool still provided a convenient platform for searching for solutions via
Newton’s method. In addition, this approach provided useful insight into how unit operations
should be configured in multistage circuits to reduce bypass and manipulate cutsize.
The partitioning data derived from Mathematica provided values that were identical to
those obtained from simulations performed using a traditional partition model developed using
an Excel spreadsheet. The perfect agreement between these two diverse approaches verifies that
circuit partition values can be accurately calculated using a direct analytical approach and
without the need for simulation. As such, critical values of particle size (e.g., X , X and
25 50
X ) that are important in describing the performance of classification units, can be back-
75
calculated from the partitioning equations derived by linear circuit analysis. This ability confirms
that the two most important performance indicators, i.e., cutsize (X ) and separation sharpness
50
(α), can be determined for the combined circuit completely independent of feed properties.
The analytical approach outlined in this study also made it possible to derive generic
expressions for partitioning probability for generalized circuits that reprocess either overflow
(undersize) or underflow (oversize). These expressions indicate that classification performance is
indeed improved through the proper application of multistage circuits and that recycling of
61 |
Virginia Tech | VITA
Dongcheol Shin was born in Pusan, South Korea on the 19th day of September, 1972. He
graduated from Haksung High School in the winter of 1991. The following spring, he was
granted admission to Dong-A university, where he went on to gain a Bachelor of Engineering
degree in Mineral and Mining Engineering. During his time as an undergraduate, he was
involved in some projects of ventilation and rock mechanics. In addition, he had served Korean
government at infantry military for 2 years. After graduating in the winter of 1998, he remained
at Dong-A university to pursue a Master of Engineering degree in Mineral and Mining
Engineering with an emphasis in development of environmental material for a waste water
treatment. He completed his degree in the winter of 2000 and he had worked at the same
university as Business Incubator Manager for 1 year. He learned what principal of economics is
in detail from this job. His life of Mineral Processing was beginning after this job. He got chance
to get an internship to be considered mineral processing industry from Korean Institute of
Geoscience and Mineral Resources (KIGAM), the only government research center of a mineral
processing. After internship, he was granted admission to Virginia Polytechnic Institute and State
University (Virginia Tech) to pursue a Master of Science degree in Mineral and Mining
Engineering with an emphasis in a mineral processing. Upon completion of his thesis of Master
of Science, Dongcheol is preparing to get a job offer in mining industry and will begin his
professional career as a process engineer in the United States.
168 |
Virginia Tech | ABSTRACT
Column flotation cells have become increasingly popular in the coal industry due
to their ability to improve flotation selectivity. The improvement can be largely
attributed to the use of froth washing, which minimizes the nonselective entrainment of
ultrafine minerals matter into the froth product. Unfortunately, the practice of adding
wash water in conventional flotation machines has been largely unsuccessful in industrial
trials. In order to better understand the causes of these failures, a detailed in-plant test
program was undertaken to evaluate the use of froth washing at an operating coal
preparation plant. The tests included detailed circuit audits (solid and liquid mass
balances), salt tracer studies, and release analyses. The data collected from these tests
have been used to develop criteria that describe when and how froth washing may be
successfully applied in industrial flotation circuits.
A second series of tests was developed to look at other alternatives to froth
washing and their effectiveness. This involved two-staged flotation circuitry. A two-
staged approach was developed because the existing flotation cells did not have enough
residence time to support froth washing. The process owner wanted to evaluate possible
alternatives to column cell flotation. The testing included release analysis testing as well
as a detailed series of tests with percent solids control to the secondary flotation unit.
I |
Virginia Tech | ACKNOWLEDGMENTS
The author would like to thank first and foremost his Maker, for without Him
nothing is possible, but with Him all things are possible.
Many thanks to Dr. Gerald H. Luttrell for his time, guidance, much patience, and
for seeing the author’s potential. If it hadn’t been for his encouragement, this degree
would not have been started. Sincere appreciation is expressed to Dr. Greg T. Adel, for
his expertise and guidance. Dr. Adel’s modeling classes provided some of the author’s
most used tools. The author would also like to express sincere thanks to Dr Roe- Hoan
Yoon, for his expertise in flotation chemistry. His help in understanding of acid base
interactions has been most helpful.
The author would like to express special thanks to Dr. Peter Bethell for his
encouragement and advice. Dr. Bethell was instrumental in organizing the plant support
at A.T. Massey Coal Corporation. Many thanks to the plant staff at the three sites,
particularly Bret Plymal, Randy Grimes, Jeffrey Walkup, and Lance. Without their
support, the wash water systems would not have been in place.
The author would like to express gratitude to A. T. Massey Coal Corporation as
well as Pittston Coal Corporation for their financial support. Special thanks to Fred
Stanley and Van Davis for giving of their time and expertise.
The author would like to thank Ian Sherrell, Matt & Colleen Eisenmann, and
Ramazan Asmatulu for providing stress relief and faithful encouragement during this
II |
Virginia Tech | Chapter 1
INTRODUCTION
1.1 - Background
There are two primary mechanisms by which particles may be recovered in a
froth product during flotation. These are (i) direct attachment to air bubbles and (ii)
hydraulic entrainment in the froth product water. Direct attachment is a selective process
that occurs as a result of differences in the wettability between coal (which dislikes
water) and mineral matter (which likes water). Although this phenomenon is a selective
process, composite (middlings) particles containing both coal and mineral matter can be
recovered by this mechanism due to the presence of the coal inclusions.
The recovery of particles by hydraulic entrainment is a nonselective process
resulting from the carryover of fine particles with the water that reports to the froth
launder and is an inherent problem in froth flotation. Studies have shown that the rate at
which ash reports to the froth product is directly related to the mass rate of froth water
(Lynch et al., 1981). In the mineral industry, hydraulic entrainment has traditionally
been minimized using multiple stages of cleaner flotation to dilute the concentration of
the impurities in the flotation feed. This approach is generally not practical in the coal
industry due to the large capital costs of multi-stage circuits. Consequently, column
flotation has become the preferred alternative to multi-stage cleaning for the coal
industry. Column cells are able to significantly reduce the entrainment problem through
the addition of a counter-current flow of wash water to the top of the froth. Studies
suggest that less than 1% of the feed pulp (and associated fine clay) will report to the
1 |
Virginia Tech | froth product in a well-operated column (Luttrell et al., 1999). Consequently, the wash
water allows column cells to produce a high-grade concentrate in a single stage of
flotation.
Although many column installations now exist, the coal industry has been rather
hesitant in adopting the column flotation technology. One of the major reasons for this
reluctance is the comparatively low market value of fine coal. This situation makes it
difficult for operators to justify the higher capital and operating costs for columns,
particularly if the expenditure is for the replacement of existing conventional cells. In
addition, many coal operators generally have the perception that columns are more
difficult to operate, entail greater amounts of maintenance, and require complicated
ancillary systems for compressed air and wash water.
A less costly alternative to the installation of column cells is to adapt the froth-
washing concept to existing conventional flotation machines. This approach has already
been evaluated in pilot-scale and industrial circuits in the mineral industry (Kaya and
Laplante, 1990). Unfortunately, attempts to apply this approach in the coal industry have
been largely unsuccessful. Studies suggest that conventional froths are generally too
shallow to allow the wash water to be effective. Furthermore, coal recovery is often
adversely impacted by attempts to deepen the froth by lowering the pulp level. The
recovery loss can be attributed to increased particle detachment (due to froth instability)
and lower bubble-particle attachment (due to less pulp volume and shorter residence
time). This suggests that wash water can be effectively applied only to conventional
flotation systems that have sufficient excess capacity to offset the recovery problems
created by the lower froth stability and shorter residence time. Stronger frothing agents
2 |
Virginia Tech | 2.2 - Overview of How Particles Enter Froth
Material enters the froth by two main effects: true flotation, and mechanical
means. A floatable particle’s principle means of reporting to the froth is by true flotation,
caused by bubble attachment and levitation, although any hydrophobic particle may
report to froth by the same means as a hydrophilic particle would (Kaya et al., 1990). For
nonfloatable (hydrophilic) particles, hydraulic entrainment, such as carryover by wake,
mechanical entrainment due to turbulence, or slime coatings are possible means of
transportation to the froth phase (Jowett, 1966). All particles in a conventional froth,
either hydrophobic or hydrophilic, may leave the froth by two means: drainage back into
the pulp or removal in the concentrate (Bisshop and White, 1976).
Similarly, Kaya et al., (1990) distinguished the way that water enters the froth
into three categories. The first route is one in which the water is entrained by a boundary
layer around each bubble, which is described as the bubble walls dragging the water with
it. The second form of water entrainment is in the wakes of bubble clusters. The third
method of water carryover into the froth is by entrapment of water between bubble
clusters (Smith and Warren, 1989). Unfortunately, little information is available about
mechanisms such as entrapment (Gaudin, 1957) and carrier flotation (Greene and Duke,
1962), (Subrahmanyam and Forssberg, 1988b). For the rest of this discussion, the term
entrainment will be used to describe all mechanical (i.e. nonselective) processes for both
water and particles.
5 |
Virginia Tech | 2.3 - Entrainment
2.3.1 – Overview
Finch et al., (1989) showed that entrained particles and water recovery have a
proportional relationship for conventional mechanical cells. The thickness of the liquid
films that surround bubbles was proposed by Klassen and Tikhonov (1964) to directly
correlate to the amount of entrainment. Warren(1985) expanded this to say that recovery
of floatable components will vary linearly with the amount of water recovered. When
these lines were extrapolated, they intercepted the mineral recovery axis at a positive
value, depending on the material being studied. However, when lines of nonfloatable
material were plotted, the extrapolation showed an intercept at the origin. Others such as
Lynch et al. (1981) also observed this trend (Warren, 1985).
Studies on the effect of particle densities on entrainment were conducted by
Kirjavainen (1989). They showed that, for particles that could be assumed spherical
(quartz and chromite), hydraulic entrainment will increase as material density decreases.
Material mass was found to determine the degree of entrainment, whereas pulp density
was found to have no bearing on degree of entrainment. For materials with different
shape factors, such as phlogopite, the degree of entrainment was found to increase
strongly with pulp densities over 10%. Regardless of pulp density, the phlogopite was
found to have a higher degree of entrainment than the quartz or chromite. Kirjavainen
(1989) concluded that the principle difference was due to the hydrodynamic response of
the material shape.
From this study, it was proposed that the hydraulic entrainment of nonfloatable
material was a statistical phenomenon. The nonfloatable recovery could then be
6 |
Virginia Tech | described by a simple probability model where no other assumptions are needed
(Kirjavainen, 1989).
Other work, such as Subrahmanyam and Forssberg (1989b), agreed with
Kirjavainen, and represented the process by the equation: R= e R . R is the
g g water g
recovery of fine gangue, and R is the recovery of water, each of which is for a given
water
time, and R is for a given size. The degree of entrainment e , is the slope of the plot of
g g
the recovery of water versus the recovery of solids (Subrahmanyam and Forssberg,
1988b).
When considering particles that are neither gangue nor floatable material but are
locked, limited flotation can occur. These particles can be recovered due to incomplete
liberation, incomplete depression of the gangue, or by coflocculation with other floatable
particles (Coburn, 1985). From this, Szatkowski (1987) concluded (in contrast to
Kirjavainen (1987)) that the amount of gangue reporting to concentrate is a function of
the concentration in the pulp.
2.3.2 - Size Effects
Numerous studies have been conducted on the effect of size on entrainment of
nonfloatable material. Jowett (1966) found that fine free gangue recovery is proportional
to its concentration in the pulp; similarly Kaya et al., (1990) pointed out that as fineness
increases, gangue recovery increases. Others correlated fineness to decreased selectivity
(Kirjavainen, 1989).
Work by Bisshop and White (1976) found that particle drain-back into the pulp at
any size is directly related to the froth residence time. Kirjavainen (1989) further broke
down gangue recovery into 1-micrometer-size intervals to determine the differences.
7 |
Virginia Tech | Recovery in any size class is proportional to the amount of floated water, with the finest
particles closely reflecting the water flow.
Mechanical separation of particles without the addition of collectors was found to
be more active in particles with less than 3-5 micron diameters. From this work, it is
assumed that the mechanical separation of fine particles is due to their very slow settling
rates in water (Klassen and Tikhonov, 1964). Others pointed out that, with increases in
recovery in the coarsest particles in coal feeds, there is a corresponding progressive
increase in recovery of ultrafine particles (Miller, 1969).
Fine particles have been shown to be transported into the froth not only by
entrainment but also as slime coatings on the surface of valuable minerals (Waksmundzki
et al., 1972). The degree of entrainment depends on the size of the material being
entrained. As a particle size decreases, the degree of entrainment increases (Warren,
1985). Also, as the particle size becomes coarser, not only is the degree of entrainment
lessened, but the correlation is not always linear (Engelbrecht and Woodburn, 1975). For
ultrafine particles, test work has shown the degree of entrainment for some hydrophobic
particles to be very close to that of hydrophilic gangue (Warren, 1985).
2.3.3 - Frother Effects
Frothers have been studied for many effects such as recovery, froth stability, and
product grade. Frothers also play an important role in the nonselective entrainment of
particles. The degree of entrainment of slime particles depends not only on the
concentration of the frother but also on its nature (Klassen and Tikhonov, 1964).
Subrahmanyam and Forssberg (1988a) concurred and added that the characteristics of
frother usage control the water recovery and, therefore, indirectly control entrainment.
8 |
Virginia Tech | Work done by Szatkowski (1987) with hematite ore found that average bubble
size strongly affects the selectivity of the flotation. Other factors include the standard
deviation of the bubble size as well as particle size. For these tests, frother concentration
was used to control the average bubble size. Frother concentration also influenced froth
formation rate. As the froth formation rate was increased, the amount of gangue
recovered also increased (Szatkowski, 1987).
Similar testing by Laplante et al. (1983) showed that the overall transfer
selectivity will be maximum when the rate limiting factor is the transfer from the slurry
to the froth. Conversely, overall selectivity will be minimized when the transfer from the
froth cell lip is rate limiting.
2.3.4 - Liquid Lamella Thickness Effects
Liquid lamella thickness is the thickness of the water layers that separate
individual bubbles in a froth. Their thickness determines the carrying capacity of
entrained particles, as well as the stability of the froth. As a lamella thickness approaches
the size of the particles attached to the bubbles, the amount of drainage reaches its
maximum without causing bubble coalescence. For incomplete drainage, the lamella
thickness will be greater than that of the particles held by the bubbles (Flynn and
Woodburn, 1987).
As the particles being held by bubbles decrease in size, the corresponding well-
drained lamella thickness decreases. Heram (1981) proposed the froth liquid lamella
thickness theory to explain low selectivity in separating ultrafine particles. The theory
states that the grade of concentrate attainable is related to the water recovered in the froth.
The amount of water recovered is determined by the liquid lamella thickness. Using this
9 |
Virginia Tech | as a basis, the maximum acceptable lamella thickness required for ultrafine separation is
10 micrometers. This is due to the non-settling nature of ultrafine particles and their ease
of entrainment.
Others concurred with the liquid lamella theory that, as the liquid lamella
increases, so also does the probability of recovering entrained material (Subrahmanyam
and Forssberg, 1988b). The thickness of the liquid lamella was found to be in direct
correlation to the amount of frother used in the system. Therefore using excess frother
lessens the efficiency of the flotation process (Waksmundzki et al., 1972).
2.3.5 - Froth Depth
Between the flotation rate coefficient and froth depth, there exists a linear
relationship that has a negative gradient. Simply put, as froth depth increases, flotation
rate decreases. This was documented by Engelbrecht and Woodburn (1975), and
Laplante et al. (1983). Feteris et al., (1987) both confirmed these results and added that
the probability of drainage depends linearly on froth depth.
Deep froths have been found to promote selectivity in flotation due to increased
coalescence. The coalescence causes the particles to detach as well as reattach to bubbles
below (Finch et al., 1989). Distribution studies within deep froths have led to stressing
the importance of both mobility and drainage (Cutting et al., 1981). Gangue entrainment
has been linked with shallow froth depth as well as increased gas rate (Kaya et al., 1990).
2.4 - Froth Drainage
Froth drainage is known to be one of the irreversible processes that occur in all
froths. This is facilitated by capillary suction created by pressure differentials as well as
10 |
Virginia Tech | gravity (Kaya et al., 1990). Szatkowski (1987) described these capillaries as channels
between the mineralized bubbles, the length and diameter of which determine the rate
that gangue is drained. Effective drainage can only occur from the froth layers close to
the froth pulp interface.
Cutting et al. (1986) split drainage into two categories: film drainage and column
drainage. Film drainage is defined as the drainage of water and solids around the air
bubble and is characterized as a slow process that occurs over the entire froth volume.
Column drainage is described as an area of rapid descent of material in a single vertical
zone, which is started by an accumulation of solids that invert the hydraulic gradient in
the froth, is usually limited to about 1 cm2 in area, and may start at any point in the froth
column. Column drainage is often initiated by froth mobility, whereas tranquil
conditions encourage steady (film) drainage. Through these studies, it was determined
that the drainage rate of water always exceeds that of the solids (Cutting et al., 1982).
The amount of froth drainage is highly dependant upon the froth residence time as
shown by Bisshop and White (1976) and Cutting et al. (1986). Both agreed that the
amount of recovery of material by the froth is governed by the residence time of the
froth. The effects of drainage as well as residence time are greater for coarse particles
(Bisshop and White, 1976).
High particulate solids in the froth were found to significantly reduce the drainage
rate of water from a froth, creating a stabilizing effect (Engel and Smitham, 1987). Wash
water has been found to reduce overloading, which can increase drainage without
reducing froth stability (Kaya et al., 1990).
11 |
Virginia Tech | Comparing the work of Cutting et al. (1986), Moys (1978, 1984), Kuzkin et al.
(1983), and Subrahmanyam and Forssberg, (1988b), all agreed that, while froth drainage
is good, it can lead to instability. Well-drained froths also do not flow well, requiring the
use of mechanical means of removal (i.e. paddles). This in turn greatly increases the
losses of recovery. Therefore, any removal of well-drained froths should target removal
of only the upper layers of froth to minimize any losses.
2.5 - Froth Residence Time
Most agree that froth residence time plays a vital role in froth drainage as well as
recovery of mineral. Bisshop and White (1976) labeled it as the single most important
factor in drainage from the froth. Others listed it as a controlling factor along with
drainage rate in maximizing gangue rejection (Kaya et al., 1990), (Szatkowski, 1987).
Only Miller (1969) preferred a short residence time coupled with froth washing as a
means of cleaning coal froth.
In general, the froth residence time depends on two factors: froth depth and rate of
froth formation (Szatkowski, 1987).
12 |
Virginia Tech | 2.6 - Prevention of Entrainment
Several alternate methods of reducing entrainment with wash waterless systems
have been made. One such system was a froth vibration system (Kaya, et al., 1990). The
system induced vibrations into the froth column to stimulate drainage. Although the
system did aid in drainage, it did so at the expense of recovery. The system was
compared to a wash water system and the benefits were less than that of wash water. The
vibratory system did have an additive effect when coupled with the wash water system
(Kaya et al., 1990). Other systems tested include rod barriers in the froth phase (Degner
and Sabey, 1988), or ultrasonic vibrations to encourage coalescence and slow the froth
phase (Kaya and Laplante, 1988).
A second such wash waterless system included adding a baffle grid below the
base of the froth. This system aimed at reducing turbulence between the pulp and the
froth, reducing the likelihood of entrainment. There were positive results; however,
operating difficulties outweighed the benefits (Moys, 1978).
2.7 - Froth Washing
2.7.1 – Overview
Several wash water systems have been tried in the past for both coal and mineral
flotation systems. All agree that the wash water should be added as a light rain, and not a
jet (Finch et al., 1989), (Kaya et al., 1990).
Kaya et al. conducted test work with a wash water system that targeted metallic
minerals. In this system, wash water rates were varied. At the lowest rate, recovery of
mineral increased over no washing due to better froth stability. At the medium rate, both
an added recovery and an increase in product grade were observed. At the highest wash
13 |
Virginia Tech | water rate, more entrainment of gangue particles occurred than at the medium rate. The
explanation was that at the higher wash water rates, mixing occurred within the froth, and
the wash water was not as effective. For all of the tests conducted, wash water rates were
only 7 to 12% of the feed water. Wash water was shown to increase bubble coalescence
while increasing froth drainage.
Some guidelines for placement of wash water were also given. In general, wash
water should be distributed evenly across the entire cell. However, to save water
requirements, wash water should be at least added to the cell lip adjacent to the overflow
weir (Kaya et al., 1990). Adding it to the cell lip is one of the most crucial places for
wash water because the entrainment is most severe at that point (Moys, 1978). Adding
wash water above the froth decreases gangue entrainment at higher water recovery, while
adding wash water at the froth pulp interface decreases gangue entrainment. Adding
wash water above the froth also increases the chance of water short-circuiting to the
concentrate. The height of the wash water addition above the froth should be minimized
to increase froth stability (Kaya et al., 1990).
Test work showed that adding wash water at rates above 0.4 cm/s was detrimental
to the system due to excessive mixing of the upper froth, as well as loss of cleaning. The
same phenomenon was observed with lower rates and shallower froths, masking any
selectivity increases created by the wash water (Finch et al., 1989)
One system studied employed booster plates and raising the cell weirs to change
the froth velocity profile to stabilize the froth. This reduces the froth residence time as
well as the distribution; however it allows for incorporation of wash water easily
(Koivistoinen et al, 1991), (Heiskanen and Kallioinen, 1993). Miller (1969) compared
14 |
Virginia Tech | the flotation product created by adding wash water to a single stage with that of the
standard rougher-cleaner system and found that the single stage addition of wash water is
a viable alternative to roughing and cleaning.
2.7.2 - Size Effects of Froth Washing on Coal Flotation
Froth sprinkling was compared on three size fractions of coal feed by Miller
(1969). The coarse fraction (14X48 Mesh) seemed to see little improvement from the
froth sprinkling. Only modest gains in product ash and recovery were found. For the
mid-size region (48X150 Mesh), both an increase in purity as well as a modest increase
in recovery were realized, with the 48X65 Mesh size fraction benefiting the most. For
the smallest size class (150X0 Mesh), no benefit in either quality or recovery was found.
In fact, the product quality was found to be worse than without froth sprinkling. In each
test, the best tests were considerably inferior to that obtained from the washability curves
(Miller, 1969).
15 |
Virginia Tech | Chapter 3
IN-PLANT TESTING
3.1 - Circuit RDT
3.1.1 - Residence time tests:
Residence time studies are an important tool in optimizing a plant’s performance.
Efficiency of separation depends on the physical differences between what is being
separated and how long the separation process has to occur. If the process is optimized to
maximize the physical differences between the different particles to be separated, yet
does not have sufficient time for the separation to occur, then the separation will be less
efficient. If, however, the separation is not utilizing the differences between the minerals
to its benefit, yet has ample time, the separation will not be efficient either. Being able to
measure the residence time of a process provides important clues as to the areas to
maximize the efficiency.
At the beginning of this study on froth washing, the idea of adding wash boxes to
more than one plant was discussed, assuming the testing showed that the wash boxes
provided a reduction in ash for the product. It was known from previous experience that
adding wash water reduced the recovery of coal in flotation cells. It has also been shown
that residence times of 3.5 to 4 minutes are necessary for high coal recovery. So before
wash boxes were ordered and installed in several plants, a series of residence time studies
were conducted to determine which plants were best suited for wash water systems.
For all of the residence time studies conducted for this research, a tracer of
potassium chloride salt solution was used. Depending on the volume flow of slurry
21 |
Virginia Tech | through the froth cells, 15 to 30 gallons of tracer solution would be used. The solution
was made by fully dissolving deicing salt. Care was taken so that no undissolved pieces
were left in the solution. While the salt was dissolving, a series of samples would be
taken of the tailings. A total dissolved solids (TDS) meter was used to measure the
salinity of the tailings. Conductivity meters can also be used; however for the plants
being tested, the background conductivity was too high to detect a difference made by the
tracer, so total dissolved solids was measured instead. Due to plant fluctuations as well
as meter adjustments, the process of determining the baseline concentration of TDS
usually took 10 minutes to establish. The length of time was purposefully long so that
any shifts due to cycling of plant water could be seen. This would determine the baseline
salinity of the tailings. The total tracer concentration would then have the baseline level
subtracted from it to determine the increment of added salinity.
The test was timed starting with the addition of tracer to the feed of the froth cells.
The tracer was added as rapidly as possible so that a single spike in salinity could be
traced. Samples from the tailings were drawn off every thirty seconds, and the TDS was
measured in parts per trillion. Values ranged from 0.320 ppt. to 0.700 ppt. Each test was
completed when the salinity of the tailing samples stabilized to an approximate value of
the base line. The reason this is approximate is because plant chemistry can change
depending on how quickly recycled water is returned to the froth cell feed. Baseline
drifts of as high as 0.021 ppt. have been observed.
For this work all residence times mentioned are the entire bank’s mean residence
time.
22 |
Virginia Tech | 3.1.2 – Plant 1
During the initial circuit audit at Plant 1, two residence time tests were completed
to help determine the potential that the froth cells had for adding a wash water system.
Because the system had originally been designed to handle all of the minus 100 mesh
coal, but later had the minus 325 fraction removed from the feed, it was believed that
there was ample residence time. Hence the reason for starting the work at Plant 1. The
first test was on the froth cell system with no wash water added to any of the cells. This
test showed an ample mean residence time of 8.7 minutes. The second test was
conducted with the wash water added to the last three cells (cells 3-5). This test showed a
residence time of 7.4 minutes.
After the wash boxes were added to the primary cells, a third test was completed
to see what the effect of having wash water on all of the cells (1-5). This test showed a
mean residence time of 6.3 minutes. Although this test showed a considerable loss of
residence time due to the wash water addition, there was still ample residence time for the
coal to be recovered. Figure 3.1 shows the normalized distributions of the three tests at
Plant 1. A normalized distribution curve was used when comparing the three curves
because differences in baseline concentrations as well as total concentration are present
when comparing the raw data.
23 |
Virginia Tech | 0.20
0.15
0.10
0.05
0.00
0 5 10 15 20 25
Time (min)
24
noitartnecnoC
dezilamroN
No Wash
Wash (3-5)
Wash (1-5)
Figure 3.1 – Residence time distributions obtained with and without froth washing.
3.1.3 - Plant 2
Plant 2 was the second plant that was considered for wash water systems. Two
tests were performed on the existing froth cells at Plant 2. For both of these tests, no
wash water systems had been added to the cells. The first test was conducted with bank 1
having a mean residence time of 2.5 minutes, and bank 2 having a mean residence time of
3 minutes, which Figure 3.2 illustrates. Because the froth cell circuit at Plant 2 has the
ability to vary the percent solids of the feed by adding or removing dilution water, a
second set of tests were conducted at Plant 2. The goal of this second test set was to see
if by removing all dilution water from the cells, there might be enough residence time to
warrant adding wash boxes to the cells. Then the wash water could act as the dilution |
Virginia Tech | 0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
0.0 2.5 5.0 7.5 10.0 12.5 15.0
Residence Time (min)
26
noitartnecnoC
dezilamroN
Test 2 Bank 1
Test 2 Bank 1
Figure 3.3 - Residence time distribution for Plant 2 Test 2.
3.1.4 - Plant 3
A third plant for which wash water systems were considered was Plant 3. The
froth cell system consisted of one bank of five 500-cubic-foot cells. The purpose for this
test was to see if the cells had enough residence time to warrant adding a wash water
system. Two tests were conducted on two different feed rates of the same coal, their
residence times are plotted in Figure 3.4. The first test was conducted with the plant feed
rate at 570 tph and the froth cell residence time was 3.6 minutes. The second test was
conducted a few hours later at a feed rate of 750 tph. The second test showed a mean
residence time of 5.2 minutes. The difference seen between the two tests could be partly
explained by differences in how quickly the salt tracer was added to the cells; however,
this does not account for more than a few tenths of a minute difference. |
Virginia Tech | 0.300
0.250
0.200
0.150
0.100
0.050
0.000
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Residence Time (min)
27
noitartnecnoC
dezilamroN
Goals High
Tonnage
Goals Low
Tonnage
Figure 3.4 - Residence time distributions obtained at two tonnages.
3.1.4.1 Observations:
One of the interesting findings from these residence time studies is that low
tonnage to a plant does not necessarily mean longer residence time for the froth cells.
For the Plant 3, running at a lower feed rate lowered the residence time in the froth cell.
The major contributing factor to residence time changes would be the flow rate of water
coming into the froth cells. The feed is dry coming into the plant. The amount of water
available for the plant is fixed and dictated by the system’s carrying capacity. If the
amount of coal coming into the plant is reduced, but the water addition stays the same,
then the water to coal ratio will increase. This would increase the water going to the fine
coal circuit, and possibly reduce the residence time of the froth cells.
Another observation is that different coals entering a plant will have different
residence times, even though the entire plant feed is remaining the same. This is
probably due to different mass splits of coals through the plants. |
Virginia Tech | Adding wash water reduces the amount of residence time in the cells because
wash water increases the flow rate through the cells. (Note: if the wash water is not being
effective in washing the water out of the cells, and the water is just being carried over
with the froth, then the effect of wash water on residence time will be minimal.)
Wash water when added correctly adds a net volume flow into the bank of cells.
Normal froth cells have a net volume flow out of the froth cells, created by the removal
of froth from the cell. By adding water to the cells, the total throughput is increased.
This decreases the amount of time available for a piece of coal to report to the froth. If
the froth washing is not very effective, and the added wash water is being carried over
with the froth, then the residence time that the cells have would not be reduced as much.
This might eventually become a way of measuring the effectiveness of froth washing. If
the total volume flow of feed, froth, wash water, and cell volume is known, then a
theoretical residence time can be calculated. If the residence time is longer than the
estimated residence time, then it may be an indication that the froth washing did not have
a net downward flow.
28 |
Virginia Tech | 3.2 - Circuit Audit
3.2.1 - Overview
CCllaassssiiffyyiinngg
UUllttrraaffiinneeRReeffuussee
CCyycclloonneess
FFlloottaattiioonn CCeellllss
11 22 33 44 55
FFeeeedd
SSppiirraall
FFeeeedd CClleeaann TTaaiillss
CCooaall
Figure 3.5 - Simplified flotation circuit flowsheet.
Figure 3.5 shows the layout of the industrial flotation circuit evaluated in the test
program. The flotation circuit consists of five 1000 ft3 Wemco cells arranged in series as
primary (two cells) and secondary (three cells) banks. The flotation bank was originally
designed to process minus 100-mesh feed from a single bank of classifying cyclones.
The classifying circuit was later reconfigured with a second stage of classifying cyclones
that was designed to operate at a nominal cut size of 325 mesh. The additional stage of
classification improved the performance of the flotation circuit by removing a large
portion of the fine clay slimes from the flotation feed. This configuration also reduced
the total volumetric flow of slurry that entered the flotation circuit. As a result, the
flotation bank has excess volumetric capacity that is currently not being utilized.
The plant operators had started to implement a wash water system but had not
determined the best way of running the system. The testing that they had conducted
29 |
Virginia Tech | showed low ash concentrate reporting from the first cell and increasing ash down the
bank. With this information, the plant installed a wash water system on the last three
cells. The plant hoped that by attacking the higher ash contributors, the greatest
reduction in ash could be realized. The goal of this test work was to first determine the
circuits’ capability, identify any opportunities for improvement, and implement the most
effective wash water system.
The water for the wash water system was gravity-fed from the clarified makeup
water head tank on the floor above which provides 8 ft of head to the system. The first
two series of tests (1 & 2) were completed using the wash water system on the last three
cells that the plant operators had designed. All subsequent tests utilized a set of wash
boxes on the primary cells as well. The piping for the final system was split into two
sections with the primary cells being fed first, and the remainder of the cells fed next.
The piping branched to provide water for the wash boxes on both sides of the cells. The
individual wash boxes were open on the top, and the water would flow from the pipe into
the box (Figure 3.6).
30 |
Virginia Tech | mass flow of clean coal produced by each cell. All experimental values were evaluated
using a mass balance program and mathematically adjusted to obtain an internally
consistent set of data. Flow rates or assay values that required substantial adjustment
were deemed unreliable and were eliminated from the data set.
3.2.2.1 – FLOW
A PVC sample container was constructed with an opening of 5 inches that could
be placed in such a way so as to catch an entire segment of the stream. Knowing that the
entire length of one cell was 120 inches, an approximate flow rate for each side could be
calculated. Edge effects were minimal in part due to the long length of the cell, and
partly because the paddles pushed the froth. The samples were taken at multiple points
along the edge of the cell. A minimum of 5 seconds was used for all samples to
accurately calculate a flow rate. The paddles had a cycle time of 5 seconds and were
used as a gauge of time for sample collection. Typical sample times and mass flow were
as follows (Table 3.1).
Table 3.1 - Median flow rate by cell.
Median Values
Number of Paddles Wet Sample
Cell Rotations Weight (g)
1 2 9410
2 2 7925
3 4 6400
4 4.2 4060
5 6.25 2725
35 |
Virginia Tech | When the froth was heavily loaded with coal, the sample easily flowed into the
sample collector, such as with the first three cells. If, however, the froth was not heavily
loaded, the froth bubbles were much larger and would not flow down into the sampler
easily. This effect was compounded when no wash water was used. Often, filling the
sample container multiple times was needed in order to collect a representative sample.
3.2.2.2 - Sample Collection
The method for collecting samples during a test was as follows: first, all of the
buckets with the appropriate labels were set beside each cell. Then the sampler was used
to collect the first timed sample on the first cell. This sample was collected and poured
into the bucket. The sampler was quickly rinsed out and moved to the next cell. The
second cell’s sample was taken and placed into its designated bucket. This was repeated
down one side of the bank of cells. Then the buckets were quickly moved to the other
side of the cells. There the same procedure was used to collect the samples. The same
number of paddle turns per sample were kept constant for each side, to reduce biasing
one side or the other. Sample collection time took about seven minutes per side with
about one minute delay in the middle for switching buckets, giving the total sample
collection time at 15 minutes, or about 2 times the residence time. By going down the
bank at the equivalent rate of one residence time, the samples from each cell represented
the same segment of feed as it traveled down the bank, reducing the effects of feed
variations.
During the sample collection from the individual cells, composite samples were
taken of the feed, the product, and the tails from the entire bank of cells. These samples
36 |
Virginia Tech | were collected from the automatic sampler on the floor below. The sampling rate was set
at three sample cuts per minute.
3.3.2.3 - Chemical Dosages
All of the chemical dosages were measured at the end of the last test. This was so
as not to interrupt the flow of frother and diesel to the cells while sampling was being
done. Diesel was added at the classifying cyclone overflow on the floor above. This
allowed more mixing time with the coal. The frother was added to the feed tank next to
the first cell.
3.3.2.4 - General Observations
A useful aid in determining the effectiveness of wash water is the hand drain test
(Davis, 1999). This test is a quick way of determining what the froth water is carying.
The first step is to collect a handful of froth entering a product launder. The water
portion of the froth is allowed to drain out of the first hand into the second, cupped
below. This water is examined in good light. If the water has a lot of clays in it, then the
wash water is not being effective. If the water has almost no clays in it, then the wash
water is being effective at removing clay from the product.
This method was used throughout the testing process to make a visual assessment
of the wash water effectiveness. Some tests seemed to have less clay than others, but
none of them seemed to remove all of the clays. Some tests the product contained a lot of
water, while others seemed to have less water. Each test seemed to have a similar
amount of clays left behind. One other observation is that the clays seemed to be
37 |
Virginia Tech | coagulated. This may be a function of the fact that the wash water is from the thickener
overflow, and probably still had coagulant and flocculent in it.
3.2.3 - Results
3.2.3.1 - Initial Tests (1-A, B)
As part of the initial circuit audit conducted, two tests (1-A, 1-B) were conducted
on the system to establish a baseline of where the plant was performing. Test series 1
used Powellton coal seam as the plant feed. This set of tests was a comparison of the
circuit’s performance with and without wash water on the last three cells. The entire
circuit was tested rather than only the cells with wash water. This allowed us to
determine the total impact of the wash water. The objective of this test was to determine
(1) if the wash water was effective (2) where the ash was coming from, and (3) how the
system could be improved. It was decided to conduct size by size analysis of all of the
streams to pinpoint the major contributors of ash. Also, a residence time test was
conducted with no wash water as well as with wash water added to the last three cells.
Some observations of test series 1. The first observation was that visually most of
the coal was being floated in the first two cells, and the last two cells had hardly any coal
recovery. The second observation was that the wash water was being added above the
paddles. This meant that during part of a cycle of the paddles the water was being
deflected and a section of froth was not being washed very well (Figure 3.10). Bubble
size also was much smaller where the water was being added. This raised some questions
as to the method that the wash water was being added. Was the wash water being added
in a less than ideal way? Was the height of the rain boxes too high, so that it caused the
38 |
Virginia Tech | recovery of 97.4%. This test showed that over 93% of the coal was being recovered in
the first two cells.
With wash water (test 1-B) the product ash was 10.45% with a combustible
recovery of 95.8%. Because the wash water was being added only to the last three cells
where only 6 percent of the coal was being recovered, the effectiveness of the wash water
was negligible. Using this information, it was recommended that wash water be added to
the first cells. It was also recommended that the wash boxes added to the first two cells
be made with double the hole density because of the amount of coal being recovered in
these first two cells. This would double the wash water provided to the first two cells.
The reduction of ash from a 10.48% to a 10.45% is statistically no reduction in ash. The
recovery was reduced by the wash water, by reducing the ability of the last three cells to
recover high ash as well as larger coal particles.
Looking at the distribution of the coal, Table 3.2, one can see that the wash water
had little impact on the performance of the system.
Table 3.2 - Product mass by cell.
% of Product Mass
No Wash With Wash
Cell 1 57.1 55.2
Cell 2 36.7 36.9
Cell 3 4.5 5.8
Cell 4 1.2 1.6
Cell 5 0.6 0.5
The mass percentage as well as the percent ash for each size is shown in Tables
3.3, 3.4, and 3.5. For both tests the feed remained relatively constant, which is to be
expected because the time between tests was less than an hour. The concentrate analysis
40 |
Virginia Tech | with wash water is very similar to the concentrate without wash water. This can be
explained by the fact that only six percent of the concentrate was being washed.
Table 3.3 - Size by size ash and mass percentages for feed tests 1-A, B.
Feed size analysis Mean particle size Without wash-water With wash-water
Mesh Microns Weight % Ash % Weight % Ash %
Plus 48 M 351 2.27 5.72 2.76 10.35
48 x 65 M 248 6.82 4.63 6.44 5.58
65 x 100 M 175 11.33 5.05 11.07 5.17
100 x 325 M 81 37.95 14.10 35.70 15.20
Minus 325 M 41 41.63 55.64 44.03 53.22
Table 3.4 - Size by size ash and mass percentages for concentrate tests 1-A, B.
Concentrate size analysis Mean particle size Without wash-water With wash-water
Mesh Microns Weight % Ash % Weight % Ash %
Plus 48 M 351 2.82 3.04 3.16 2.87
48 x 65 M 248 8.80 3.82 8.38 3.66
65 x 100 M 175 14.60 4.09 14.68 4.14
100 x 325 M 81 45.09 6.37 43.23 6.69
Minus 325 M 41 28.70 22.94 30.55 21.45
Table 3.5 - Size by size ash and mass percentages for tailings tests 1-A, B.
Tailings size analysis Mean particle size Without wash-water With wash-water
Mesh Microns Weight % Ash % Weight % Ash %
Plus 48 M 351 0.46 59.10 1.60 53.04
48 x 65 M 248 0.33 75.08 0.80 63.86
65 x 100 M 175 0.58 84.60 0.59 78.40
100 x 325 M 81 14.52 92.96 13.87 92.04
Minus 325 M 41 84.11 92.30 83.14 88.73
The tailings analysis shows a slight difference as seen in Figure 3.11. Notice that
all of the size ranges other than 100 x 325 are slightly lower in ash for the test with the
wash water. Because these are tailings, a lower ash indicates lower recovery in that size
41 |
Virginia Tech | range. What this is saying is that wash water has a greater effect on the recovery of all
size ranges other than 100 x 325, Table 3.6.
100.00
90.00
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Plus 48 48 x 65 65 x 100 100 x Minus
M M M 325 M 325 M
Size fractions
42
%
Weight % (no wash)
Ash % (no wash)
Weight % (with wash)
Ash % (with wash)
Figure 3.11 - Comparison of tailings size and ash for tests 1-A, B.
Table 3.6 - Combustible recovery by size.
Combustible Recovery
Mesh Microns No Wash Wash Difference
Plus 48 M 351 97.93 92.19 5.74
48 x 65 M 248 99.70 98.78 0.93
65 x 100 M 175 99.81 99.69 0.12
100 x 325 M 81 99.27 99.06 0.21
Minus 325 M 41 91.82 88.62 3.20
When comparing the effects of each size class on the total ash of the cell’s
concentrate, it is easy to see that the smaller size classes especially the minus 325
contributes most of the ash. Figure 3.12 compares each of the last three cells
performance by size. The biggest difference can be seen in the performance of cell 5. |
Virginia Tech | This is due in part to the wash water on that cell, but it is also due to the cumulative effect
of all of the cells with wash water. In the last cell the difference in ash in the minus 325
fraction is over 30 percent. In comparison the difference in ash on the minus 325 ash for
the fourth cell is 27 % and for the third cell there is no difference.
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Plus 48 48 x 65 65 x 100 100 x Minus
M M M 325 M 325 M
Size
43
hsA
cell 3 ww
cell 3 nw
cell 4 ww
cell 4 nw
cell 5 ww
cell 5 nw
Figure 3.12 - Size by Ash plot for tests 1-A, B.
The purpose of the size analysis was to confirm that the ash was coming from the
high ash clay component and that the wash water was washing out the clay component
(in the minus 325 fraction). A secondary purpose was to see what size fractions the wash
water had an adverse affect on.
3.2.3.2 - Staged Frother Addition (Test 2-A, B)
In the initial tests, the effectiveness of the wash water was limited by the amount
of froth product it washed. So a second test to was used to see the results of distributing
the recovery of the bank to the cells with the wash water (cells 3-5). The plant was very |
Virginia Tech | interested in this test to see how the wash water would work before spending more
money on the primary cells. The two tests that were performed compared the cells with
wash water on the last three cells, to no wash water on any of the cells. These two tests
were conducted with a mixture of 80% Eagle and 20% Powellton coal seams feeding the
plant.
There were several methods to choose from to redistribute the froth recovery.
Weir bars, staged frother addition, reducing air consumption in the primary cells as well
as lowering pulp level in the primaries were discussed. Because the primary cells already
had the air intake openings only ¼ open, the plant operators were hesitant to reduce the
air much more. They were afraid that lowering the intake of air would end up collapsing
the froth and not allow the first two cells to recover enough coal. Lowering pulp level
was not chosen because of concerns that the combustible recovery would not be as good.
Adding weir bars were chosen, because this maintains pulp level (which keeps the same
cell volume and therefore residence time, see Figure 3.13), but it also increases the froth
depth, which increases froth drain back into the pulp. Six inches of weir bars were added
to the primary froth cells. Note adding six inches of weir bars does not increase the froth
depth by six inches due to the angle that the weir bars are added at. After the weir bars
were added and the system was allowed to stabilize, it was decided to also use a staged
frother addition in conjunction with the weir bars. Although the weir bars had moved
some of the recovery down the bank, most of the coal was still being recovered in the
first two cells.
44 |
Virginia Tech | same system settings, the product ash was reduced to 8.08, for only a 0.5 percentage
point drop in recovery.
The effect of wash water can be seen on the recovery of coal in Table 3.8. Wash
water was added to cells three four and five. In cell three, the amount of coal recovered
was reduced from 20% to 12%, similarly cell 4 had a slight decrease in coal recovery,
and cell five’s percent of product mass recovered was increased. This shows that as wash
water is added, less coal is recovered in that cell. The benefit of shifting the coal
recovery to the cells with wash water is that the tons of water recovered vs. the tons of
water used to wash the coal becomes more evenly balanced. With the recovery of
product shifted to be more evenly distributed by staged frother addition the effect of the
wash water was increased compared to the previous tests. The product ash was reduced
from 9.14% to 8.08%, a reduction of 11.6%.
Table 3.8 - Product mass split by cell with and without wash water.
% of Product Mass
No Wash With Wash
Cell 1 27.4 27.6
Cell 2 29.7 34.2
Cell 3 20.2 12.9
Cell 4 18.3 15.7
Cell 5 4.4 9.7
The effect of adding the wash water was increased over test 1 series. The
reduction of ash was greater for the overall product not just the cells where the froth was
being washed. With the results of this test it was decided to have wash boxes built for the
two primary cells. The primary cells would differ in that they would have double the
amount of holes as the secondary boxes from 150 to 302 holes. The hole spacing was
46 |
Virginia Tech | reduced in hopes that the wash water would be more evenly distributed giving a greater
washing effect.
3.2.3.3 - Wash Water on All Cells (Test 3-A, B)
Two tests were conducted with Tunnel Eagle feeding the plant, comparing the
froth system with (3-B) and without (3-A) wash water on all of the cells. This was the
first test where wash water was added on all of the cells using the new wash boxes on the
primary cells. Frother was added in stages as well. The purpose of this test was to see if
adding wash water to the primary cells would indeed have the reduction in ash that the
plant was looking for. The froth being recovered was unusually wet in appearance in
comparison to other tests to that point. The overall effect of adding wash water to all of
the cells should have been greater for this test than all of the previous tests. The
reduction in ash was far from dramatic: it was as if other factors reduced the ash of the
product more than the wash water. The goal for this test was an ash reduction of greater
than one percentage point between with wash water and without. For the previous test
(test 2) the difference in ash was almost 1 percent. For this test (3) it was about ½ of a
percent difference, shown in Table 3.9. Water recovery was a greater issue in this test.
Table 3.9 - Wash water performance for test 3-A, B.
Concentrate Combustible
ash Recovery
% %
With wash 8.56 97.64
No wash 8.98 97.07
Ash reduction (%) 4.7
47 |
Virginia Tech | 3.2.3.3.2 Small Test (Test 3-C)
A small test was used to check the overall effects of reducing the air that the
primary cells used and reducing the amount of frother used in the secondary cells. This
was a single test, intended to be compared to the test with wash water. The test was in
response to a question that the plant had about the increased frother needed to run the
cells, because of the staged frother addition. Could less frother be used in the circuit
without the performance of the circuit being compromised? The goal was to recover less
coal in the primaries thus pushing more coal, and frother, to the secondary circuit. To
accomplish this the air was reduced from ¼ to 1/8 of the intake area on the primary
circuit. The frother that was added to the secondary circuit was also reduced from
210ml/min to 170 ml/min in the secondary circuit. The frother added to the primary
circuit was kept at 206 ml/min. This reduced the amount of coal recovered in the first
two cells by a fair amount (visually). Because this was a last minute test, only grab
samples were taken of the feed the concentrate and the tailings as well as grab samples
for the first two cell concentrates. Although the overall concentrate was less desirable,
the recovery was maintained with less frother addition; see Table 3.10 for comparisons.
No flow rates or assays were measured for the secondary circuit; therefore it can only be
inferred from the data that the performance of the last three cells dropped dramatically.
Because the recovery was maintained, the coal previously recovered in the first two cells
was shifted to the last three. The amount of coal recovered was probably greater than the
wash water could remove, and so the overall clay recovery increased, increasing the
product ash.
48 |
Virginia Tech | Table 3.10 - Comparison of test 3-A, B, and C
Test No Wash With Wash Small Test With Wash
Combustible Recovery 97.6 97.1 97.0
Feed (% Ash) 21.79 21.54 22.61
Concentrate (% Ash) 8.98 8.56 9.12
Tails (% Ash) 88.54 86.26 86.50
Cell 1 (% Ash) 7.35 7.27 6.26
Cell 2 (% Ash) 9.58 8.84 6.78
Some benefits from moving the coal down the bank in this manner is that a
substantial frother savings can be achieved by pushing the coal down the bank and
allowing the frother already in the system to work in other cells.
3.2.3.4 – Comparison Testing with Eagle Coal Seam (Test 4-A, B, C, D, E)
Three tests (4-B, C, & D) were performed with wash water added on all of the
cells and frother added in stages. Weir bars were added to the first two cells to help
maintain a high froth depth. These weir bars were kept the same for all three tests. Two
more tests (4-A & E) were conducted at a later date with the same coal seam, to compare
normal pulp level without wash (test 4-A) as well as lower pulp level with wash (test 4-
E). A detailed list of the test follows, with Eagle Coal feeding the plant for all tests.
§ Test 4-A Primary cell paddles were removed and no wash water was
added.
§ Test 4-B Primary cell paddles were left on.
§ Test 4-C Primary cell paddles were removed.
§ Test 4-D Primary cell paddles were removed and froth level was increased
on all cells by lowering pulp level in the cells.
49 |
Virginia Tech | § Test 4-E Primary cell paddles were removed and froth level was increased
to a high level by lowering the pulp level in the cells.
The purpose of the first three tests was first to assess the impact of removing the
paddles on the froth washing. The second purpose was to evaluate how much could be
gained by better matching the froth flow to wash water flow and how that would impact
coal recovery. Because the goal of reaching a net bias flow of water into the cell was not
met, tests 4-A and 4-E were added at a later date to be compared with these tests.
The total test time for the initial tests took about 3 hours from the time the first
test was taken until the last test was finished. This was longer than most tests because the
paddles had to be removed from the primary cells. (Most of the delay was in taking the
paddles off, which took a little over an hour.) Sample time also increased for tests 4-C,
and 4-D because flow rate measurements could not be taken using the turn of the paddles
for a reference. The flow rate measurements instead had to be timed, which slowed down
the sample taking process.
For these three tests there was very little difference between the recovery and the
concentrate ash of the test with and without the paddles, Table 3.11. Changing the pulp
level created the biggest difference between the tests. For tests 4-A, 4-B and 4-C the
froth depth on the primary cells was kept at 14 inches, and the secondary cells at 12
inches. The froth depth was increased to 18 and 22 inches for the primary cells and 16
and 18 inches on the secondary circuit for the low level (4-D) and very low level (4-E)
tests respectively.
50 |
Virginia Tech | Table 3.11 - Comparison of test conditions for series 4 tests.
B C D E A
Test With Paddles No Paddles Low Pulp Level Very Low Level No wash
Combustible Recovery 95.3 95.8 93.1 93.1 96.1
Feed (% Ash) 32.45 30.44 31.44 30.23 31.88
Concentrate (% Ash) 9.23 9.32 8.53 8.30 9.95
Tails (% Ash) 89.02 89.03 84.42 83.43 90.32
3.3 - Discussion
3.3.1 - Water Ash Relationships
For tests 1-A and 1-B, Figure 3.14 shows the overall water ash plots for the two
tests. In this plot the tons per hour of ash reporting to concentrate are plotted against the
tons per hour of water reporting to concentrate. In an ideal situation the tons of ash
reporting to concentrate should only increase as the higher ash coal is recovered. This
would produce the shallowest slope. However as water is recovered in a conventional
flotation cell entrained particles of ash report to concentrate, this increases the amount of
ash that is collected which raises the slope. Notice the negligible difference between the
two tests. However if the points of the last three cells are compared to that of the last
three cells in the test with no wash water (1-A) the effect of the wash water (1-B) can be
seen.
51 |
Virginia Tech | 5
4
y = 0.0334x
y = 0.0359x
3
2
1 y = 0.0504x
y = 0.0277x
0
0 20 40 60 80 100 120 140 160
Water Flow (tph)
52
)mpt(
hsA
fo
etaR
ssaM
3/10/00 With Wash
3/10/00 No Wash
Linear (3/10/00 No Wash)
Linear (3/10/00 With Wash)
Figure 3.14 - Water ash plot for test series 1, Powellton coal.
Looking at the effectiveness of the wash water for test series 2 can also be seen in
the water ash plot, Figure 3.15. Similar to the previous test, the water ash relationship for
cells one and two fall in line with those that had no wash water. The last three cells
which did have wash water are clearly operating on a different level. The slope for these
last three cells are 0.0229, which is far less than the overall from the test without wash
water 0.0338. This slope is even lower than that of the last three cells for the previous
test with wash water 1-A, 0.0277. The reason for this difference is that the coal recovery
was more evenly distributed, so the amount of clay recovered to the amount of low ash
coal recovered was less than test series 1. |
Virginia Tech | 4
3.5 y = 0.0338x
3
y = 0.028x
2.5
2
1.5
y = 0.0229x
1
0.5
0
0 20 40 60 80 100 120 140
Water Flow (tph)
53
)hpt(
hsA
fo
etaR
ssaM
No Wash
With Wash
Secondary Cells
(With Wash)
Figure 3.15 - Water ash relationship for test series 2, 80% Eagle / 20% Powellton coal
blend.
For tests 3-A and 3-B, Figure 3.16 shows the difference that wash water made to
all of the cells not just the last three. This shows that the effectiveness of the wash water
was not limited to the last three cells but that all of the cells could benefit from froth
washing. The biggest difference between test series 2 and series 3 are the amount of
water that was recovered. Comparing the last point of each plot, for test 2, the most
water recovered from any one cell was 120tph, whereas for test 3, the highest water
recovery rate was 178 tph. Therefore even though the tons of ash recovered are less on a
per ton of water basis, test 3 recovered more water and with it more tons of ash. |
Virginia Tech | 5
4.5
y = 0.0236x
4
y = 0.0292x
3.5
3
2.5
2
1.5
1
0.5
0
0 50 100 150 200
Water Flow (tph)
54
)hpt(
hsA
fo
etaR
ssaM
No Wash Water
With Wash Water
Figure 3.16 - Water ash relationship for tests 3-A and 3-B, Tunnel Eagle coal.
For test series 4 one of the chief goals of the test work was to see if a better
balance of coal recovery to wash water addition could be achieved. When comparing the
concentrate produced from each of the froth cells, during the test with paddles and
without paddles the concentrate ash as well as the mass percentage stayed relatively
constant, Tables 3.12 and 3.13 respectively. Both the Low Level (3-D) and the Very
Low Level (3-E) tests had very little visual difference in flow rates for any of the cells.
For these two tests (3-D, E) it looked like all but the last cell were recovering about the
same amount of coal. Only the last cell looked a little less loaded. Usually, it is possible
to determine visually which cells are recovering more coal; often the difference is
dramatic. The tailings looked darker than usual; however they were not at an
unacceptable level. The results of these tests confirmed the visual assessment, clearly |
Virginia Tech | that the recovery of coal was shifted down the bank of cells. Shifting the coal also
increased the effectiveness of the froth washing. This is mirrored by the ratio of the
liquid recovered in the concentrate to the amount of wash water added to the cell. As the
ratio approaches 1, the amount of water being recovered equals the amount of wash water
being added. Ratios over 1 indicate a net flow downward increasing the likelihood that
the wash water completely rinsed the froth. Comparing the results of the five tests, it is
clear that the very low level test (4-E) best approached this wash water bias, Table 3.14.
None of the tests ever fully even reached equal amounts of water recovered to water
added.
Table 3.12 - Concentrate ash comparison by cell for series 4 tests.
Concentrate Ash
Cell With Paddles No Paddles Low Level Very Low No Wash
1 8.89 8.92 6.57 6.58 9.86
2 7.83 7.39 6.21 7.02 9.22
3 10.55 10.08 9.07 8.88 12.56
4 13.57 13.49 12.59 11.73 16.25
5 19.55 19.30 13.09 12.01 20.89
Table 3.13 - Concentrate mass comparison by cell for series 4 tests.
Mass % of Concentrate
Cell With Paddles No Paddles Low Level Very Low No Wash
1 43.45 43.48 22.97 31.54 56.90
2 27.86 24.07 19.71 21.76 36.04
3 18.59 18.05 30.17 28.05 4.72
4 6.63 9.52 18.28 13.19 1.45
5 3.46 4.88 8.85 5.46 0.90
55 |
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