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Virginia Tech | terms by means of Young’s equation. If the angle at the initial stage is believed to equal
equilibrium contact angle, then equation [11] reduces to the more commonly seen
W =γ
πR2( 1−cosθ)2
[12]
A LV
Equation [12] for work of adhesion overestimates the energy of detachment with the
difference between experimental and calculated increasing with contact angle. Equation
[12] is also valid in the rare case where there is no contact angle hysteresis.
Work of adhesion (equation [11]) was compared to the measured energies of the
detachment process. The experimental energy, E , was found to be similar to the work of
2
adhesion, see Table 2 below.
Table 2 - Work of adhesion and experimental energy comparison
θ θ E , J E , J E - E , J W , J % error
R Eq 2 necking 2 necking A
39.688 50.063 3.673E-08 7.771E-09 2.896E-08 2.560E-08 11.6%
43.118 56.588 5.970E-08 1.582E-08 4.387E-08 3.883E-08 11.5%
52.267 64.984 1.002E-07 2.972E-08 7.044E-08 6.800E-08 3.5%
However, if the energy of bubble necking as previously described is subtracted from E ,
2
then work of adhesion corresponds almost exactly to the measured energy (% error in the
table is the error between W and E minus the necking energy). This further supports the
A 2
previous claim that E represents the energy of detachment and E is simply the energy
2 1
barrier to detachment.
OTS Layer Modification With pH
The detachment force was measured over a wide pH range to observe its effect. This led
to the finding of a pH dependence of the OTS layer on a silica surface. As pH in the bulk
solution increases the hydrophobicity of the coating increases (see Figure 7). As the pH
further increases, the detachment energy was observed dropping off drastically.
24 |
Virginia Tech | OTS was used because it forms a well ordered hydrophobic layer on the silicon surface
(Cohen et al. 1986; Gun et al. 1984; Gun and Sagiv 1986; Maoz and Sagiv 1984; Maoz
and Sagiv 1987a; Maoz and Sagiv 1987b). These OTS layers have been shown to be
very resilient, resisting change in temperature, bulk solution chemistry, and even physical
abrasion (DePalma and Tillman 1989; Iimura and Kato 2000). The adsorption reaction
involves the formation of covalent bonds between the polar head group and SiOH- groups
on the surface (Sagiv 1980; Tripp 1991; Tripp and Hair 1995; Zhao and Kopelman 1996).
Polymerization between adsorbed sylil groups to form Si-O-Si networks has been
reported (Zhao and Kopelman 1996). This seems unlikely due to the large space between
≡Si-OH groups on the surface (Zhuravlev 1987). Rather, the formation of –Si-O-Si-
groups between OTS molecules and an adsorbed water layer on the quartz surface is
more likely (Parikh et al. 1994; Parikh et al. 1997; Silberzan et al. 1991; Ye et al. 2001;
Zhao and Kopelman 1996). This layer begins the ordering of the water molecules at the
OTS coated surface, which is the nature of the hydrophobic behavior of the solid.
At acidic pH, the orientation of the water molecules at the substrate is reversed (Ye et al.
2001), which leads to a less ordered molecular structure of the water molecules in the
bulk interface, thereby reducing the hydrophobic nature of the overall surface. This
explains the slightly lower detachment force seen at acidic pH. As pH increases,
detachment force increases until a peak at pH 9.5. The sudden drop following this peak
is due to partial etching of the OTS layer at alkaline pH. IN the event of a ‘perfect’
monolayer, the molecules are packed too tight and prevent the penetration of OH- ions.
But etching can occur at defects in the OTS layer, and continues as more surface is
uncovered (Iimura and Kato 2000; Wasserman et al. 1989). This explains the sharp drop
in detachment force at alkaline pH.
The possibility of increased energy barrier with increasing pH has been analyzed as
another source for the increase in detachment force and energy. OTS coated surfaces
have been shown to behave similarly (electrokinetically) to bare silica with changing pH
(Murray et al. 1991). In other words, the amorphous nature of silica is conserved on a
coated surface.
25 |
Virginia Tech | The electrostatic bubble-particle interaction can be determined using the following
relationship (Shaw 1992).
( )
πεεRR ψ2 +ψ2 2ψψ 1+e−κH ( )
V E = 0 4(1 R2 +R1 ) 2 ψ2 +1 ψ2 2 ln 1−e−κH +ln 1−e−2κH
[13]
1 2 1 2
Where Ψ and Ψ represent the Stern potentials of the particle and air bubble of radii R
1 2 1
and R , respectively, ε is the dielectric constant of the medium, 1/κ the Debye length.
2
Surface potential values from literature were used for the calculations (Li and
Somasundaran 1992; Li 1958; Yiantsios S. G. and Karabelas A. J. 1995)
1.4E-14
1.2E-14
1.0E-14
8.0E-15
6.0E-15
4.0E-15
2.0E-15
0.0E+00
2 3 4 5 6 7 8 9 10 11 12 13 14
pH
26
J
,noitcaretnI
citatsortcelE
Figure 14 - Electrostatic interaction between a 2mm particle and a flat bubble
As Figure 14 indicates the peak repulsion is at pH 9.5. However, the interaction energy
only amounts to 1.2 x 10-14 J, which is about 107 times lower than the interaction energies
associated with these detachment processes. Thus, the energy of detachment variation at
pH 9.5 is due to modification of the OTS layer and the water layer at the silica surface. |
Virginia Tech | Summary & Conclusion
The Sigma 70 surface tensiometer was found to provide an accurate and reproducible
method of measuring the force and energy of the bubble-sphere detachment process.
Much better results were obtained when using a flat bubble, but this could be remedied
(in the round bubble experiment) if extreme precaution was taken to ensure that a smaller
bubble was the exact same size for each experiment.
Bubble-particle detachment is a three step process. The first step is the bubble stretching,
which is directly related to surface tension and contact angle hysteresis. This also
represents the energy barrier to detachment. The bubble stretching energy also
corresponds to the energy required to move the three-phase-contact line. Once advancing
contact angle is reached, the second step of detachment begins. The energy spent as the
TPC line ‘slides’ off the particle is equivalent to the calculated work of adhesion. The
third step of detachment is bubble necking. This part of the detachment process occurs as
the ratio of contact radius to particle height above the flat bubble datum becomes too
small to support a stable interface. Evidence of bubble necking increased with contact
angle.
The complete detachment process can be modeled using numerical solutions to the
Young-Laplace equation for vapor-liquid interface shape. The stretching portion of
detachment is modeled by assuming that contact radius is constant and contact angle
increases from receding to advancing. When advancing contact angle is reached the
sliding and necking portions of detachment are modeled together assuming that contact
angle is constant and contact radius is decreasing.
Silane coating of silica surfaces can be modified by pH. As pH increases, the
hydrophobicity of the surface also increases until pH ≈9.5 due to modification of the
water layer on the silica surface. Once pH increases past 9.5, the detachment energy
decreases dramatically as the OTS layer is etched off the surface.
27 |
Virginia Tech | High-speed photographic studies of bubble
formation, growth and detachment from
hydrophobic surfaces
Hubert C.R. Schimann
Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University,
Blacksburg, VA, 24061, USA
Abstract
Bubble particle detachment is the main limiting factor in coarse particle flotation.
Detachment occurs when forces on the bubble-particle aggregate in a flotation cell
overcome the strength of adhesion. Strength of adhesion depends on the particle contact
angle, surface energy and roughness, and surface tension of the liquid media. Surface
energy and roughness determine contact angle hysteresis, which causes the activation
energy for detachment. Bubble detachment from a flat hydrophobic surface submerged
in water was studied using a 1 kHz CCD camera. Images provided the data for
thermodynamic and force calculations from the bubble shape size and movement on the
plate. The measured energy of detachment was divided into the two parts: activation
energy and work of adhesion. The measured work of adhesion compared favorably with
calculated values.
Keywords: bubble detachment, octadecyltrichlorosilane, hysteresis, submerged plate
Introduction
Froth flotation is widely used in the mining industry to separate valuable minerals from
other materials in their host environment. Minerals are separated by attaching themselves
to rising air bubbles in the flotation cell and then recovered at the top of the cell. The ore
must be ground small enough so that flotation can proceed (e.g. <.5 mm diameter).
Coarse particle flotation provides opportunities for reduced grinding costs, increased
recoveries and simplified flow-sheet designs (by eliminating certain classifying and other
steps); all leading to increased throughput.
31 |
Virginia Tech | Flotation is a function of the probability of particle collection (Sutherland 1948);
P = P ⋅P ( 1−P ) [14]
C A D
where P , P , and P are the probabilities of collision, adhesion, and detachment
C A D
respectively. The probability of collision depends on hydrodynamic effects in the
flotation cell. The probabilities of adhesion and detachment are a combination of
hydrodynamic effects and surface chemistry of the bubble and particle. Since surface
chemistry is not affected by particle size, the probability of adhesion is mostly a function
of hydrodynamics and increases with particle size. Probability of detachment is then the
main limiting factor in coarse particle flotation.
Detachment of a bubble from a submerged plate has previously been studied using
various methods such as the single hole plate or simply a submerged plate (Byakova et al.
2003; Eckmann and Cavanagh 2003; Jones et al. 1999; Li et al. 2002; Li and Quiang
1998; Nahra and Kamotani 2003). However, these studies do not adequately describe the
detachment process with regards to a flotation application. Many others have also
observed bubbles at a submerged capillary tip rather than a plate to study formation and
detachment (Churaev et al. 2002; Keen and Blake 1996; Ouz and Zeng 1997; Yang et al.
2001). These do not properly describe detachment as seen in flotation as the bubble
cannot spread past the boundaries of the capillary tip.
Theory
The detachment of an air bubble from a flat surface submerged in water is dependent on
contact angle, surface energy of the solid and water surface tension. Contact angle
determines the size of the contact area between bubble and surface. Surface tension may
be regarded as a force vector along the bubble wall at the three phase contact (TPC) line.
This surface tension multiplied by the contact perimeter represents the tenacity of the
bubble adhesion onto the surface.
32 |
Virginia Tech | Surface energy of the solid (Eskilsson and Yaminsky 1998) and roughness determine
contact angle hysteresis. Hysteresis is the difference between advancing and receding
contact angle. When a water drop slides down a glass window, for example, the bottom
part of the drop forms a larger contact angle (taken through the water, between the
tangent to the drop wall and the glass surface) then the top part. The bottom portion is
advancing on the glass surface and is said to be the advancing contact angle. The top
portion is retreating and is said to be the receding contact angle. In the same fashion,
when a bubble first attaches to a solid in water, the bubble spreads on the surface at the
receding contact angle (water is receding from the surface). As the bubble detaches and
the contact area shrinks it does so at the advancing contact angle. When the bubble is at
steady state with the surface, neither spreading nor detaching, it is at equilibrium contact
angle, which is the average of receding and advancing angles.
Detachment involves the shrinking of the contact area as the air bubble retreats from the
surface. The TPC line must be at advancing contact angle for the initial inward
movement to begin. Thus hysteresis plays a determining role along with contact angle in
the detachment process.
The bubble contact diameter on a flat surface is dominated by the contact angle (Lin
1994). Subsequently, the final size of the bubble before detachment depends on surface
energy of the solid, liquid interfacial tension, and contact angle. The contact angle as
reported by (Lin 1994) was always 90° at detachment. However, the angle at detachment
should be the advancing angle or slightly larger if the TPC line is moving very rapidly.
The plate in this study represents a large smooth hydrophobic particle on which the TPC
spreading is not limited by physical characteristics of the solid. The contact area is then
controlled strictly by surface energy of the plate and interfacial tension of the media. The
role of surface tension was thoroughly explained in experiments with oil drops on a
submerged horizontal plate (Chatterjee 2002).
33 |
Virginia Tech | The forces acting on a bubble attached to a horizontal plate submerged in water are the
buoyancy force and surface tension force. At high flow rates the bubble momentum also
contributes to detachment, but this is not the case here. The buoyant force of the bubble
must overcome the interfacial tension for detachment to proceed. Once the interfacial
tension force is overcome, the TPC line shifts from equilibrium to advancing angle
whence the bubble begins to retract from the surface until complete detachment.
Experimental Methods
All the reagents used in the experiment were at least ACS grade and were obtained from
either Fisher Scientific or Alfa Aesar. The plate consisted of a 25.4 mm x 25.4 mm x 1.0
mm silicon wafer donated by the Virginia Tech Materials Science department. Holes
(diameter = 0.6mm) were drilled through the center of these plates using an ultrasonic
cutting machine. Plate surface roughness was measured to be about 0.5 nm by profiling
the surface with an atomic force microscope. These plates were then methylated with
octadecyltrichlorosilane (OTS) to create hydrophobic surfaces. The methylation
procedure consists of washing the samples for 1hr in Piranha solution (30% H O :70%
2 2
H2SO ) at 60 – 70°C. The samples are then rinsed in Nanopure water and immersed in a
4
10-5M silane solution in toluene for 30 – 90 minutes depending on the target contact
angle. The samples are then removed from the solution and first rinsed with chloroform
to remove any excess toluene from the surface, then acetone to remove any physisorbed
silane. Following this, the samples are placed in acetone in an ultrasonic bath for at least
20 min. This breaks up any amalgams of polymerized silane which may have
accumulated at the silica surface, thereby creating a more uniform silane coating. The
samples are stored in Nanopure water in sealed containers until the experiment. The
roughness of coated plates was also measured and was found to be less than 1 nm,
indicating a consistent silane coating. The above method was used to produce plates with
contact angles of 85°, 95°, and 97°. The surface energies of the plates were determined
from contact angle measurements of formamide, diiodomethane and water on the
surfaces, using the method as outlined by (van Oss et al. 1987).
34 |
Virginia Tech | Figure 15 - Silicon plate support
The experiment involved submerging a horizontal plate with a hole drilled through the
center in a water filled cell. The plate was attached to a Teflon support as shown in
Figure 15, connected to an air source. Bubbles were produced at the orifice as air was
fed through the system. The size of the orifice was kept constant, 0.6 mm diameter, as
plates of different hydrophobicity were used. The size of the orifice has been shown to
not affect the bubble characteristics as long as it is relatively small when compared to the
bubble diameter (Datta et al. 1950). The relationship of cell size with bubble shape was
also investigated and found to affect the bubble only under specific conditions which
satisfy the following equation (Hughes et al. 1955)
A ρc2
v ≈ 0 g [15]
c g∆ρ
where, v is the cell volume, A is the area of orifice, ρ is the gas density, c is the velocity
c 0 g
of sound in the gas, g is the acceleration of gravity, and ∆ρ is the density difference
between air and water. The cell used in this experiment was outside this range.
The experiments were recorded using a Phantom V4.0 CCD camera (Photo-Sonics Inc.)
at 1000 frames per second. These digital images were analyzed to measure the bubble-
surface contact area, dynamic contact angle, and bubble surface areas for thermodynamic
35 |
Virginia Tech | Figure 17 - Stages of bubble growth and detachment on methylated silicon wafer
In Figure 17(a) the bubble is still in the orifice, giving the reader an idea of the relative
size of the hole compared to the contact area. As more air is fed through, the bubble wall
breaks and attaches to the methylated surface in Figure 17(b). Here, the bubble forms the
receding contact angle with the wafer as it spreads across the surface (i.e. water is
receding from the surface). In Figure 17(c), the bubble has reached its maximum contact
area. From this point on, the contact angle begins to increase until advancing contact
angle is reached as shown in Figure 17(d). Once advancing contact angle is reached,
water begins to advance on the silica surface. This is the beginning of the detachment
process. Figure 17 (e) and (f) show the bubble as it is about to detach and once it has
detached.
Between points (c) and (d), the buoyancy force keeps increasing. The energy spent
during this time, while the contact area remains constant, is the energy required to shift
the contact angle from receding to equilibrium and then advancing.
37 |
Virginia Tech | Figure 19 - Initial and final stages of bubble detachment
Figure 19 displays the initial and final energy states used to calculate the work of
adhesion. The initial state represents the equilibrium state of the bubble and surface.
Thus the bubble is at equilibrium contact angle with the surface. The work of adhesion
calculation assumes that the bubble volume doesn’t change between initial and final
states. From this constant volume, the initial bubble radius, R was calculated using the
B
final volume.
π
( ) 2( )
V = 3R2 + R − R2 −R2 R − R2 −R2 [16]
6 C B B C B B C
Equation [16] determines the volume, V, of the bubble where R is bubble radius and R
B C
is the contact radius. The volume is then used in equation [17] to determine the change in
liquid-vapor interface. Equation [18] is used to calculate the contact area as is represents
the change in solid-vapor and solid-liquid interface.
2 ( )
3V 3
∆A =4π −2πR R − R2 −R2 [17]
LV 4π
B B B C
A =πR2sin2θ [18]
C B
W =∆A γ + A (γ −γ ) [19]
A LV LV C SV SL
Equation [19] calculates the work of adhesion (in Joules) for the system, where γ , γ
LV SV
and γ are the liquid-vapor, solid-vapor, and solid-liquid interfacial tensions. The
SL
39 |
Virginia Tech | volume of the bubble at equilibrium position was used to calculate the work of adhesion,
which was compared with experimental detachment energy measurements.
The moving centroid method was used to measure the energy of the detachment. This
method involves integrating the force applied by the bubble onto the surface over the
distance traveled by the bubble centroid in the vertical direction, as shown in equation
[21].
F =2πR γ sinθ [20]
γ C LV
E
=∫y
2F dy [21]
γ
y
1
F is the vertical component of the surface tension multiplied by the contact perimeter as
γ
shown in equation [20]. For the detachment process to begin F must overcome F.
B γ
Where, F represents the buoyancy force of the bubble.
B
When these two forces are equal the bubble is at equilibrium position and the bubble
forms the equilibrium contact angle with the wafer surface. For the detachment process
to begin, the TPC line must be shifted to advancing angle. E is the activation energy
1
required to shift the TPC line, and thereby begin the detachment process. The beginning
of the detachment process is marked in Figure 20 by the sudden decrease in contact area.
The energy spent from this point on until complete detachment represents the work of
adhesion portion of the energy of detachment, E .
2
40 |
Virginia Tech | Figure 20 - Moving centroid method of energy of detachment calculation (θ = 97°)
Table 3 shows the energies calculated by the centroid method and how they compare to
the work of adhesion calculated for these systems. As demonstrated, E showed good
2
correlation to the theoretical work of adhesion.
Table 3 – Moving centroid detachment energies and theoretical work of adhesion
Sample I II
Contact angle (hysteresis) 95° (32°) 97° (18°)
E 6.794 x 10-7 J 5.435 x 10-7 J
1
E 1.034 x 10-6 J 1.378 x 10-6 J
2
E 1.714 x 10-6 J 1.922 x 10-6 J
total
Theoretical W 1.132 x 10-6 J 1.325 x 10-6 J
A
% Error, (W vs E ) 8.66% 4.00%
A 2
These measurements clearly demonstrate the importance of contact angle hysteresis.
While sample II had a larger equilibrium contact angle, since sample I had more
hysteresis, it required much more energy to detach.
Measured surface energies during the experiment provided a third method for energy of
detachment determination. This method simply involves calculating the total surface free
energy of the system for each frame in the experiment film. The energy difference
41 |
Virginia Tech | between equilibrium and complete detachment was then used as the energy of
detachment.
Figure 21 - Surface free energy of bubble and plate system
Figure 21 demonstrates the use of instant surface free energies to measure the energy of
detachment. The free energy difference between equilibrium (frame -513) and beginning
of detachment (frame -507) is equivalent to the activation energy, E . The free energy
1
difference between beginning of detachment (frame -507) and complete detachment is
equivalent to the work of adhesion or E . Note that at detachment the free energy dips
2
slightly. This drop represents an exothermic process. Nature constantly seeks to reach
lowest energy state. When detachment starts until one frame before detachment the free
energy is increasing because an energy input is provided by the extra air being fed to the
bubble. The instant before detachment, the bubble has reached its maximum stable size.
This means that detaching rather than still growing allows the bubble to reach a lower
energy state, thereby creating an instantaneous process.
42 |
Virginia Tech | Table 4 – Surface free energy detachment and theoretical work of adhesion
Sample I II
Contact angle (hysteresis) 95° (32°) 97° (18°)
E 7.863 x 10-7 J 5.279 x 10-7 J
1
E 9.924 x 10-7 J 1.097 x 10-6 J
2
E 1.779 x 10-6 J 1.625 x 10-6 J
total
Theoretical W 1.132 x 10-6 J 1.325 x 10-6 J
A
% Error, (W vs E ) 12.33% 17.14%
A 2
The measured values shown in Table 4 again demonstrate the importance of contact
angle hysteresis. Although sample I has a slightly smaller measured work of adhesion,
E , it benefits from larger hysteresis, leading to larger activation energy, E , and
2 1
ultimately a larger overall energy of detachment.
Summary & Conclusion
A submerged plate with a single orifice was successfully used to measure force and
energy of detachment of a single bubble from a hydrophobic surface. The detachment
force was obtained from buoyancy of the bubble, which was measured using image
analysis of the experiment. Bubble equilibrium with the plate is reached when the
buoyant force of the bubble is equivalent to the force due to surface tension.
Detachment energy was successfully measured using both the moving centroid method
and surface free energy measurements also from image analysis. These methods clearly
outlined the multiphase nature of the bubble detachment process. The first phase of
detachment is shifting of the TPC line from equilibrium to advancing contact angle. The
energy spent in doing so is referred to as the activation energy. The second phase occurs
when the TPC slides inward until complete detachment. This subsequent component of
the detachment process corresponds to the work of adhesion. Thus, if hysteresis is
present the bubble-particle interaction is not a reversible process. The measured
activation energy showed direct correlation to contact angle hysteresis and subsequent
detachment energy corresponded closely to the calculated work of adhesion.
43 |
Virginia Tech | Detachment of silica spheres from large air
bubbles in cetyltrimethylammonium
bromide solutions
Hubert C.R. Schimann
Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University,
Blacksburg, VA, 24061, USA
Abstract
Bubble particle detachment is the main limiting factor in coarse particle flotation.
Detachment occurs when forces on the bubble-particle aggregate in a flotation cell
overcome its adhesive force. The strength of adhesion depends on contact angle, surface
tension, and contact angle hysteresis. Detachment forces and energies were measured
between a surfactant coated silica sphere and a flat bubble as a function of the surfactant
concentration. A digital camera was used to measure the contact radius of the bubble on
the sphere, to calculate the receding contact angle. The forces were used to calculate
contact angles which were compared to Wilhelmy plate measurements on glass slides.
The measured energy was separated into the energy barrier and the detachment energy
which was compared to the theoretical work of adhesion.
Keywords: Bubble-particle detachment force, cetyltrimethylammonium bromide,
hysteresis
Introduction
Froth flotation is widely used in the mining industry to separate valuable minerals from
other materials in their host environment. Minerals are separated by attaching themselves
to rising air bubbles in the flotation cell and then recovered at the top of the cell. The ore
must be ground small enough so that flotation can proceed (e.g. <.5 mm diameter).
Coarse particle flotation provides opportunities for reduced grinding costs, increased
recoveries and simplified flow-sheet designs (by eliminating certain classifying and other
steps); all leading to increased throughput.
47 |
Virginia Tech | Flotation is a function of the probability of particle collection (Sutherland 1948).
P = P ⋅P ( 1−P ) [22]
C A D
Where, P , P , and P are the probabilities of collision, adhesion, and detachment
C A D
respectively. The probability of collision depends on hydrodynamic effects in the
flotation cell. The probabilities of adhesion and detachment are a combination of
hydrodynamic effects and surface chemistry of the bubble and particle. Since surface
chemistry is not affected by particle size, the probability of adhesion is mostly a function
of hydrodynamics and increases with particle size. Probability of detachment is then the
main limiting factor in coarse particle flotation.
Cationic surfactants such as cetlytrimethylammonium bromide (C TAB) easily attach to
16
the negatively charged silica surface. The C TAB molecules attach to the silanol groups
16
at the glass surface which provide the negative sites. The sphere becomes more
hydrophobic as more surfactant is adsorbed onto the surface. The density of the silanol
groups determines the maximum possible C TAB density on the surface. As these
16
negative sites are filled the surface is neutralized. The surfactant concentration where
this occurs is the point of zero charge (pzc). Further C TAB adsorption occurs as
16
concentration is increased through attraction between the hydrophobic tails. This creates
a densely packed second layer on the sphere with the polar heads pointing toward
solution, thereby decreasing the overall hydrophobicity of the sphere. Increasing the
C TAB concentration also decreases the surface tension of the aqueous solution. This is
16
similar to increasing the frother concentration in a flotation cell.
Theory
Detachment force
The total force exerted by the flat bubble onto the sphere is a function of the contact
radius and angle formed at the interface. Figure 22 illustrates the geometry involved in
the force equation derivation.
48 |
Virginia Tech | Figure 22 - Flat bubble - sphere detachment geometry
F =2πr γ cosϕ [23]
tpc lv
Equation [23] calculates the total force exerted by the bubble onto the sphere in the
vertical direction due to surface tension, where γ is the surface tension. The contact
lv
radius, r , is a function of the receding contact angle, θ . When the sphere first
tpc r
penetrates the bubble, water recedes from the solid surface. The TPC spreads on the
solid until it is pinned at the radius of contact and settles at receding contact angle (Preuss
and Butt 1998b). From Figure 22 it can be seen that the angle between the tangent at the
contact line and the horizontal is equal to α. Thus, r = Rsinθ. The TPC line stays
tpc r
pinned until advancing contact angle is reached. At advancing contact angle,
ϕ=π2−θ +θ. The total force necessary to move the TPC on the sphere surface is
a r
then
π
F =2πRsinθ⋅γ cos −θ +θ [24]
r lv 2 a r
Work of adhesion
The measured energy was compared to the calculated work of adhesion for a sphere and
flat bubble interaction. Work of adhesion was calculated with the following equation:
49 |
Virginia Tech | ( )
W =γ πR2 sin2θ −2cosθ 1−cosθ [25]
A LV R Eq R
where R is the radius of the sphere and θ and θ are the receding and equilibrium
R Eq
contact angles respectively. The work of adhesion calculation describes the change in
free energies between the initial and final states as described in Figure 13.
Figure 23 - Sphere - flat bubble work of adhesion calculation
Equation [11] assumes that the initial state is receding contact angle, and the equilibrium
contact angle is used to cancel out the solid-liquid and solid-vapor interfacial tension
terms by means of Young’s equation. If the angle at the initial stage is believed to equal
equilibrium contact angle, then equation [11] reduces to the more commonly seen
W =γ πR2( 1−cosθ)2 [26]
A LV
Equation [12] for work of adhesion overestimates the energy of detachment with the
difference between experimental and calculated increasing with contact angle. Equation
[12] is also valid in the rare case where there is no contact angle hysteresis.
Equations [24] and [11] illustrate the importance of contact angle hysteresis in the
detachment process. Hysteresis is caused by surface roughness (Adamson 1997;
Israelachvili 1991) and by surface energy of the solid (Chibowski 2003). The C TAB
16
molecules adsorb onto the silica surface in patches or domains, thereby creating
chemically heterogeneous surfaces than can lead to increased hysteresis.
50 |
Virginia Tech | Surfactant adsorption at the solid-liquid-vapor interface during movement of the solid
across the liquid vapor interface can also cause hysteresis. During Wilhelmy plate
measurements of advancing and receding contact angles, a surfactant coated plate is
introduced vertically into aqueous surfactant solution. The liquid vapor boundary
depresses as the solid is pushed down past the water surface. The meniscus created by
this depression will form the advancing contact angle with the plate, and remain at that
angle as the plate is lowered further into the solution. CTAB molecules in the solution
will orient themselves at the TPC so as to have the hydrophobic tail onto the solid to
escape the water (Yaminsky and Ninham 1999). This phenomenon leads to increased
pinning of the TPC line and consequently larger advancing contact angles.
Experimental Methods
Forces were measured using a Sigma 70 Surface tensiometer (KSV Instruments Ltd.).
This equipment was a hanging balance with a resolution of 1 µN. The bubble-particle
interactions were photographed by a 4.0M pixel S4 digital camera (Canon Inc.) equipped
with a reversed 50 mm AF NIKKOR (Nikon Corporation) lens (which allows it to act as
a macro lens).
Soda lime glass spheres with a mean diameter of 2007 µm ± 40 µm (Duke Scientific
Corporation) were used in the experiment. The diameter of these spheres was verified
with a micrometer as shown in Table 5.
Table 5 - Sample dimensions
Sphere Diameter, µm
A 1991
B 2008
C 2004
Before treatment, the spheres were washed for 1hr in Piranha solution (30% H O :70%
2 2
H SO ) at 60-70°C before treatment. Once washed the spheres were stored in a sealed
2 4
container filled with Nanopure water. All measurements were done at 20°C ± 0.5°.
51 |
Virginia Tech | A sphere was then fixed to the end of a glass hook, which was manufactured by the
Virginia Tech glass shop, using Crytalbond™ 509 glue (Electron Microscopy Sciences).
The sphere was then suspended in a solution of cetyltrimethylammonium bromide
(C TAB) for two hours to create a hydrophobic surface.
16
Figure 24 - Surface tension of C TAB Figure 25 - Contact angle of C TAB
16 16
aqueous solutions aqueous solutions on glass
C TAB should reach equilibrium concentration on the glass surface after 1h (Yaminsky
16
and Yaminskaya 1995). Solution concentrations ranged from 10-6M to 10-3M. Samples
were first treated with the 10-6M solution and force measurements were taken
immediately after. Between measurements the samples were soaked in successively
higher concentrations of C TAB. The purity of the C TAB (Fluka) was verified by
16 16
testing the surface tension of a range of concentrations to identify the critical micelle
concentration. The surface tension was measured using the same tensiometer equipped
with a Du Nouy ring (Pt-Ir-ring made to DIN 53914-80 and ASTM D 971 specifications,
also by KSV Instruments Ltd.). Figure 24 indicates a critical micelle concentration
(CMC) of 9 x 10-4 M, which is in accordance with literature (Frank and Garoff 1996; Liu
et al. 2001). The steady surface tension of the aqueous solution above the CMC also
indicates an uncontaminated surfactant. The surface tension of pure water was measured
at 72.6 mN/m.
52 |
Virginia Tech | Glass plates (Fisher Scientific) were cleaned and treated with C TAB using the same
16
methods earlier described to obtain contact angle measurements for various
concentrations. Advancing and receding contact angles were measured using the
Wilhelmy plate principle with the KSV Sigma 70. The contact angles thus obtained can
be seen in Figure 25. These measurements were also in agreement with literature
(Janczuk et al. 1999).
The measured contact angles were also used to determine the surface free energy, γ of
s,
the glass using equation [27] (Chibowski 2003).
( 1+cosθ)2
γ =γ( cosθ−cosθ) a [27]
s l r a ( 1+cosθ)2 −( 1+cosθ)2
r a
Where, γ is the surface tension of water, and θ and θ are the receding and advancing
l r a
contact angle respectively.
To perform the force measurements, the sphere was suspended from the tensiometer
above a flat bubble. The bubble was created using a PTFE rod, with a cone bored out in
the center, connected to a syringe that provided the air for the bubble as shown in Figure
6. The bubble support sat in a rectangular glass cell filled with water on top of a
mechanical stage that could be moved vertically at 1 mm/min to bring the bubble and
particle into contact and then detach them.
53 |
Virginia Tech | Figure 26 - Flat bubble apparatus Figure 27- Detachment force curve
The tensiometer was connected to a computer to record force and distances every .25 s.
The reported distance is the relative position of the mechanical stage. Although the
actual position is not known, the distance traveled during the detachment process (used
for energy calculations) is still recorded.
A typical output curve from the surface tensiometer is shown in Figure 27. The
detachment force is measured as the difference between the maximum and the baseline.
The baseline is the force at which the sphere is detached. This is the force exerted on the
instrument from the weight of the sphere only. The energy is taken as the integral of the
force applied across the distance from equilibrium to detachment. Equilibrium is shown
in the figure as x . It is the point at which the bubble is neither pushing up nor pulling
0
down on the sphere.
Results & Discussion
Detachment forces at increasing surfactant concentration are shown in Figure 28 for the
three spheres. Sphere A measurements were stopped at 10-4 M because the sphere
became unglued from the glass hook.
54 |
Virginia Tech | As shown in Figure 29 the calculated contact angles differed considerably from the flat
plate measurements. Some differences in contact angle based on the solid shape have
been reported before (Preuss and Butt 1998b). The contact angle on a sphere can be 10°
smaller for the same surface on a flat plate. This phenomenon was reported for low
contact angle surfaces.
The dynamic nature of C TAB adsorption at the TPC line is also a factor explaining the
16
difference in measurements on the sphere and flat plate. As concentration increases, the
dynamic contact angle behavior may be explained by Gibbs’ adsorption equation.
dγ
− =Γ [28]
dµ
Where µ is the chemical potential and Γ is the adsorption. The force on a solid partially
immersed in water minus the buoyancy can be expressed as the wetting tension (Eriksson
et al. 1996).
τ=γ −γ [29]
sv sl
Equation [29] can be substituted into equation [28] to obtain equation [30] (Yaminsky
1994).
∂τ
− =Γ −Γ [30]
∂µ sv sl
Thus, the slope of the wetting tension isotherm represents the competition for adsorption
of C TAB molecules at the solid-liquid and solid-vapor interface.
16
56 |
Virginia Tech | Figure 30 - (a) Wetting tension isotherm and (b) Adsorption difference isotherm
The wetting tension isotherm was graphed as shown in Figure 30(a) to find the slope of
the line, which is shown in Figure 30(b). The derivative of the wetting tension isotherm
does not produce the adsorption difference isotherm but is still useful as the sign of the
derivative and the relative magnitude are still represented. The competition between
solid-vapor and solid-liquid interface for C TAB adsorption explains the variation in
16
contact angle and detachment force with increasing concentration. Hysteresis increases
linearly with concentration until about 10-4M. The linear relationship is reflected in the
adsorption isotherm as the slope only decreases slightly until about 10-4M. Beyond this
point the slope magnitude increases sharply as the solid-vapor interface begins to adsorb
less C TAB compared to the solid-liquid interface. As the adsorption difference
16
approaches zero and becomes negative, the hysteresis plateaus and then begins to
decrease.
When the sphere comes into contact with the bubble, and the TPC line spreads over the
solid surface the C TAB molecules migrate out of the water onto the dry surface. This
16
creates a high concentration gradient of surfactant molecules at the dry boundary,
allowing the C TAB hydrophobic tails to escape the water. This accumulation creates a
16
band of increased hydrophobicity on the sphere. These bands then create a surface more
prone to pinning for subsequent experiments, thereby increasing hysteresis.
Hysteresis from surface domains
57 |
Virginia Tech | An atomic force microscope was used to produce images of C TAB coated silica
16
surfaces. Silica wafers were coated with a range of C TAB concentration using the
16
same procedure previously described. Silica wafers were used because they provide a
very smooth surface (mean roughness was ≈ 0.2 nm) on which chemical heterogeneity
could be observed. The sphere surface was too rough (50 – 75 nm roughness) to easily
see C TAB molecules, which are only 20Å long. Figure 31 shows the AFM images
16
which provide a qualitative justification for contact angle hysteresis. The patches on
these images were about 20Å high which indicated that they were probably the beginning
of the C TAB monolayer formation. As the concentration is increased, the domains
16
seem to grow larger and more frequent. This provides local hysdrophobic sites for the
TPC line to get pinned, which in turn leads to increased hysteresis.
Figure 31 - AFM images of (a) 1x10-5M, (b) 3x10-5M, (c)
5x10-5M, (d) 1x10-4M C TAB coated silica wafer. Each
16
square is 5µm x 5µm.
Energy calculations
The energy of detachment was compared with the work of adhesion calculated with
equation [11]. The detachment force curve is split into two sections, the stretching or
energy barrier, E , and the sliding, E . E is the energy spent shifting the TPC line from
1 2 1
58 |
Virginia Tech | Increasing collector dosage increases the contact angle leading to higher detachment
energies. Increasing frother decreases contact angle but this is compensated by the
increase in bubble tensile strength. However, if surface tension is decreased too much,
the bubbles are too strong and do not rupture easily to adhere properly to the hydrophobic
particles.
Summary & Conclusion
Bubble-particle detachment energy was successfully measured as indicated by the good
correlation with the theoretical work of adhesion. Total detachment energy is larger than
the work of adhesion because the energy barrier for movement of the TPC line must be
overcome before detachment will begin. The energy barrier is directly related to contact
angle hysteresis. It is the energy spent shifting the TPC line from receding to advancing
contact angle. The close relation between hysteresis and detachment force was also
demonstrated.
Contact angle hysteresis is affected by the dynamic nature of C TAB adsorption at the
16
solid-liquid-vapor interface. C TAB adsorption at the solid-vapor interface during
16
sphere-bubble attachment and during Wilhelmy plate measurements created
discrepancies between contact angle measurements at the same concentrations.
With increasing C TAB concentration, the contact angle of the sphere was increased
16
while bulk solution surface tension was decreased. This clearly showed the careful
balance between frother and collector dosages that must be optimized in coarse particle
flotation.
60 |
Virginia Tech | DEVELOPMENT AND VALIDATION OF A SIMULATOR BASED ON A
FIRST-PRINCIPLE FLOTATION MODEL
GAURAV SONI
ABSTRACT
A first-principle flotation model was derived at Virginia Tech from the basic mechanisms
involved in the bubble-particle and bubble-bubble interactions occurring in a flotation cell (Yoon
and Mao, 1996; Sherrell and Yoon, 2005; Do, H, 2010). The model consists of a series of analytical
equations for bubble generation, bubble-particle collision, attachment, detachment, and froth phase
recovery. The process of bubble-particle attachment has been modelled on the premise that bubble-
particle attachment occurs when the disjoining pressure of the thin liquid in a wetting films formed
between particle and bubble is negative, as was first suggested by Laskowski and Kitchener
(1969). These provisions allow for the flotation model to incorporate various chemistry parameters
such as zeta-potentials, contact angles, surface tension in addition to the physical and
hydrodynamic parameters such as particle size, bubble size, and energy dissipation rate.
In the present work, the effects of both hydrodynamic and chemistry parameters have been
studied using the model-based computer simulator. A series of laboratory batch flotation
experiments carried out on mono-sized glass beads validated the simulation results. The flotation
feeds were characterized in terms of particle size, contact angle, and Hamaker constant, and the
flotation experiments were conducted at different energy dissipation rates, gas rates, froth heights.
The flotation tests were also carried out on mixtures of hydrophobic silica and hydrophilic
magnetite particles, so that the grades of the flotation products can be readily determined by
magnetic separation. The experimental results are in good agreement with the model predictions
both in terms of grade and recovery. |
Virginia Tech | Nomenclature and Symbols
RC- Rougher Circuit
RSC- Rougher Scavenger Circuit
RSCC- Rougher Scavenger Cleaner Circuit
DLVO – Derjaguin and Landau, Verwey and Overbeek
MIBC – Methyl Isobutyl Carbinol
DAH – Dodecylamine hydrochloride
OTS – Octadecyltrichlorosilane
d – Particle diameter
1
d – Bubble diameter
2
d – Collision diameter
12
d – Diameter of bubbles entering the froth phase
2-0
d – Diameter of bubbles at the top
2-f
E – Kinetic energy of attachment
k
E’ – Kinetic energy of detachment
k
h – Height of the froth
f
K – Hydrophobic force constant between the bubble and particle
132
K – Hydrophobic force constant between two particles
131
K – Hydrophobic force constant between two bubbles
232
m – Mass of the paticle
1
m – Mass of the bubble
2
n – Number of cells in the bank
N – Number of particles attached to each bubble
P – Probability of attachment
a
P – Probability of collision
c
P – Probability of detachment
d
P – Probability of bubble-particle aggregates transferring from the pulp to the froth
t
P – probability of bubble-particle aggregate surviving the froth phase.
f
r – Radius of the particle
1
r – Radius of the bubble
2
R – Bank recovery
R – Pulp zone recovery
p
R – Froth zone recovery
f
R – Maximum theoretical water recovery
w
Re – Reynolds number
S – Superficial gas velocity, rate of gas addition
b
t – Retention time per flotation cell
𝑢̅ – Particle RMS velocity
1
𝑢̅ – Bubble RMS velocity
2
U – Velocity of a particle approaching a bubble at the critical rupture distance
Hc
vi |
Virginia Tech | Chapter 1: FLOTATION
History of Flotation
Froth flotation is undoubtedly the most important process for the separation and
concentration of fine coal and mineral particles. Apart from a century of operation in the mining
industry, flotation is also utilized for waste water treatment for different petro-chemical plants and
de-inking in paper recycling.
The industrial revolution of the nineteenth century and the need to commercially better the
mining process caused the process of floatation to gain momentum in its development over three
phases in history. During the latter part of nineteenth century the technology found small scale
applications in washing away of gangue from raw ore. The process bettered itself over the next
quarter century when the need to concentrate fine sulphide particles led to the research efforts for
floating zinc and lead minerals. The mining industry benefited hugely from the flotation techniques
developed in the nineteenth century, leading to extensive increase in mineral production yield and
quality.
William Haynes (Lynch et al, 2005) can be credited to be the pioneer with regards the
flotation concept. He was the first to patent his idea of flotation as a method to separate minerals,
claiming that sulphides could be agglomerated by oil and non-sulphides could be removed by
washing, in a powdered ore.
The commercial viability of the floatation method was tested by the Bessel brothers in
Dresden Germany in their floatation plant, used to clean graphite ore. This was in the late
nineteenth century. The first plant to process sulphide ores, was based on Carrie Everson’s work,
who patented her work, while working on small scale flotation plants.
True industrialization of the process of floatation, from being a research topic at
laboratories to a more commercially valuable tool, occurred in the early twentieth century.
The above, however had relied on use of oil for the floatation process. Although the
research in the field of floatation, spearheaded the commercial, the needed economic surge was
yet to reach its potential. The work done at BHP, Australia, to monetize the extraction of zinc from
its ore by improving concentration, resulted in furthering the bettering of the extraction process.
Work at BHP and work by other contemporaries on bulk extraction using flotation proved to be a
commercial success in the early twentieth century. Efforts were now being channelized to cater
1 |
Virginia Tech | for selective differential floatation, a method achieved by controlling the incoming air flow rate to
the ore mixture being processed.
It was in 1911, that James Hyde had the first floatation operation installed in the US, at
Basin Montana (Fuerstenau, 2005). This step sparked an instant uprise in the use of flotation to
improve the ore processing.
The introduction of chemical reagents and the trending process of selective flotation,
towards the mid twentieth century brought about more widespread use and appreciation of flotation
as an economically viable tool. Thus, while chemical floatation increased the ore tonnage, the use
of selective floatation brought about increase in the concentration ratios.
Flotation Process
Flotation is a three phase physico-chemical separation (Wills, 1997). The process is based
on separating hydrophobic particles from hydrophilic ones dispersed in water by selectively
attaching the former onto the surface of air bubbles. Specific reagents are added to the slurry prior
to flotation process to accentuate the differences in surface properties of the desired mineral and
gangue, thus allowing better separation both in terms of selectivity and recovery.
Naturally or rendered hydrophobic particles are attached to the air bubbles in the pulp
phase, which are also hydrophobic in nature (Yoon and Aksoy, 1999; Yoon and Wang, 2006), and
forms the bubble-particle aggregates. Thermodynamically, for bubble-particle attachment to be
feasible the Gibbs free energy of attachment must be negative. The Gibbs free energy can be given
in terms of interfacial tension as
G (cos1) (1)
lv
2
lv
is the interfacial tension between liquid and air, and θ is the contact angle at the three phase
contact. Thermodynamically, feasibility occurs when the contact angle is greater than zero. Higher
the value of contact angle, more negative is Gibbs free energy. Hence the contact angle is a major
deciding factor for bubble-particle attachment in the pulp phase.
The air bubble loaded with various composition of particle rises through the pulp and enters
the froth phase at the bottom. Froth is a three phase system, where polyhedral bubbles are separated
by thin film walls (lamellae) which form the plateau borders .Froth zone acts as pseudo second
beneficiation unit which is a more efficient process than the pulp zone. (Ata et al., 2002, Schultz
et al, 1991). As the air bubble rises through the froth phase bubble, coalescence occurs, which |
Virginia Tech | decreases the bubble surface area rate and hence the carrying capacity. Reduction in bubble surface
area and shock generated due to coalescence causes less hydrophobic particles to attach to bubble-
particle aggregates and to drop back to the pulp zone or collection zone (Falutsu and Dobby, 1989,
Moys, 1978).
Recovery in froth zone is contributed by two mechanism: recovery due to attachment or
true flotation and entrainment. True floatation occurs when the rising bubble is attached to the
hydrophobic particles in the pulp phase and the bubble-particle aggregated formed survives the
froth phase and report to concentrate. While entrainment occurs when the particle is trapped
between the spaces of bubbles and recovered without attachment. Entrainment recoveries are
directly proportional to the water recovery to concentrate launder. (Warren, 1985)
Only hydrophobic particles are recovered through the true flotation, it is a selective process.
On the other hand, entrainment is non-selective and undesirable. Ultra-fine particles are more
easily entrapped and reports as flotation concentrate due to entrainment (Fuerstenau, 1980).
Equipment and Reagents
The main purpose of a flotation machine is to increase the contact between the air bubbles
and the ore feed. The entire process of aerating the feed, can thus be achieved in different ways.
The types of flotation methods can be characterized based on a number of factors. Different authors
use unique characterization point to differentiate the types. The floatation machines can be broadly
categorized into three groups based on the floatation rates achieved through the process (lynch et
al, 2005). The three types are: floatation columns (pneumatic flotation machines), mechanically
agitated floatation machines and the high intensity machines. The floatation columns are the ones
with the lowest flotation rate constants. The feed enters the column at the top and as it makes its
way downward, it makes contact with air bubbles generated at the base. The flotation cell, in this
case, acts both as the collection zone and the disengagement zone.
In the mechanically agitated floatation machine, which are medium intensity floatation
devices, there exists an external agitation machine which helps the feed to be in suspension and
causes a rotary motion which leads to induced bubble formation in the feed. The final type of
flotation machine is the high intensity types, in which there exists an external agitation mechanism
which brings the feed pulp in contact with fine air bubbles. In this case, the external contactor is
the collection zone while the tank itself is the disengagement zone. Historically, these are the most
advanced types of flotation machines.
3 |
Virginia Tech | Method of air introduction is another feature which can be used to characterize the
machines (Brewis, 1996, Young, 1982). Thus, we can have five types based on this
characterization type: the mechanical, pneumatic, dissolved air, vacuum and electro-flotation. A
further classification can be seen in the self-aerated type of flotation devices which disperse and
generate bubbles by self-aeration through an orifice.
In flotation, different chemical reagents are used to modify the surface properties of the
minerals and alter the flotation environment. Collectors are surface active organic reagents which
selectively adsorbs on the mineral surfaces and impart hydrophobic characteristics to the mineral
surface. Increase in particle surface hydrophobicity encourages the possibility of particle
attachment to the air bubble. However, an excessive concentration of collector decreases the
hydrophobicity of mineral surface due to development of collector multilayer. Frothers are used
to adsorb onto the air-water interface and reduce the surface tension of water, therefore promoting
reasonable stable froth, whereas excessive use of frothers can result in formation of highly stable
form. Modifiers are classified as activators, depressants and pH modifiers. Activators are used to
enhance the collector adsorption on particular mineral surface, while depressants prevent the
adsorption of the collector onto the undesired mineral surface.
Flotation Modeling
Flotation is multi-phase separation process which involves much complex micro process,
each differentiating the mineral particles of different size distribution and liberation based on their
hydrodynamic and surface properties. The complication of mechanism and interdependence of
these micro process makes the quantitative predictive modelling unusually difficult.
There are several commercial or academics flotation available and utilized to predict or
evaluate the flotation performance of a unit or flotation circuit like, Aminpro-Flot (Aminpro),
HSC (Outotec), iGS (SGS MinnovEX) ,JKSimFloat (JKTech), SUPASIM (Eurus), USIM PAC
(Caspeo) ,limn.
JKSimFloat is a general purpose graphical software package for the simulation of flotation
plant operations. It is being developed at Julius Kruttschnitt Mineral Research Centre (JKMRC)
as part of AMIRA P9 Project. JKSimFloat was first released as a MS-DOS program in 1993.
Presently software is available in three different version with the advance version (JKSimFloat
V6.4PLUS ) offering the capability to included your own flotation model.
4 |
Virginia Tech | The software treats each stream to be composed of different particle class, a collection of
particle that are considered to have properties. The recovery of particles class is considered to
combination of true flotation and entrainment. The model describes continuous flotation cell as
pseudo first order rate kinetics using a continuously stirred tank reactor (CSTR) model. The
recovery is given as (Savassi, 1998):
5
R
i (1
P .S .Ri
b
P .Si
b
f
. R
.
f
.(1
. ) (1
R )w
R
w
)
E N
E
T
N
. R
T
w
. R
w
(2)
where P – ore floatability for component i, S – bubble surface area flux (min-1) ,R – froth
i b f
recovery ,τ - residence time (min) ,R – water recovery ,ENT – degree of entrainment .
w
Limitation of this approach is that it model parameters are derived from the experimental
data using batch tests data and surveying. Hence the simulation prediction is greatly depends on
the collection of good experimental data and sampling efficiency.
Amelunxen Mineral Processing Ltd. (Aminpro) provides process simulation models for
flotation and grinding circuit design. Aminopro-Float (flotation model) is based on pseudo-
empirical approach where prior conducted flotation tests serves as data-bank to predict the
recoveries for a particular size fraction having specific floatability. It can be used to determine the
economic optimum circuit as capital cost and operating cost for circuit is also computed
simultaneously.
Limn is spreadsheet based simulation tool which provides flow sheet balancing solution.
Limn incorporates extensive models for communication, gravity and size separation, but it lacks
an efficient flotation model. Flotation recovery is determined by using a tromp curve, where Ep
and Rho50 values are entered manually to match the experimental concentrate yields and grade.
SUPASIM flotation simulation model is developed by Eurus Mineral Consultants. It is
based on Kelsall’s equation of two rate constant-
R100 1exp k t 1expk t (3)
f s
where is slow floating fraction, k
f
is fast floating rate, k
s
is slow floating rate. These
parameters are estimated by laboratory batch rate tests and Scale-up algorithms are used to
simulate the full-scale, continuous flotation plant performance. |
Virginia Tech | USIM PAC is user friendly steady state process simulation software packaged developed
by BRGM and commercialized since 1986. It incorporates different flotation models and classify
them as ‘performance’ model and predictive models.( Villeneuve et al, 1995). Performance models
are basic approach for material balance calculations, while predictive models are based on kinetic
approach.
Two kinetic constant model considers the feed to compose of three sub population, non-
floating, fast floating and slow floating. In perfect mix condition flotation is described as-
6
F
fj
F
j
R i n f
j j
1
1
1
k s
j
1
j
1
1
1
k f
j
(4)
F
fj
is flow rate of mineral j in the froth, F
j
is the flow rate of mineral j in the feed, R i n f
j
is the
maximum possible recovery of mineral j in the froth,
j
is the proportion mineral j having slow
flotation and capable of floating, is the residence time.
Another approach is distributed kinetic constant, where rate constant is considered to be
function of particle size and recovery is determined through first order rate kinetics in perfect mix
condition.
F f
ij
F
ij
R i n f
f
1
1
1
k
ij
(5)
F f
ij
is flow rate of mineral j and size class i in the froth, F f
ij
is flow rate of mineral j and size
class i in the feed,
k
ij x 0i
j.5 1
x
ix
l
j
1 .5
. e x p
x
2
e
. x
j
i
2
(6)
x
i
is average size in size fraction I, is adjustment parameter for mineral j, xl is largest floating
j j
particle size for mineral j, x e
j
is easiest floating particle size for mineral j.
Recovery due to entrainment ( R
ij
) is givens as
R P.R (7)
ij ij w |
Virginia Tech | Chapter 2: FLOTATION MODEL
Derivation of First-Order Rate Equation
Many researchers modeled flotation as a first-order process (Sutherland, 1948; Tomlinson
and Fleming, 1963),
𝑑𝑁
1 = −𝑘𝑁 [8]
1
𝑑𝑡
in which flotation rate is shown to be proportional to the number of particles 1 (N ) in a cell, with
1
k representing its rate constant. It has been shown that k is given by the following relationship
(Mao and Yoon, 1996),
1
𝑘 = 𝑆 𝑃 [1]
𝑏
4
In general, probability of flotation, P, is given by
𝑃 = 𝑃 𝑃(1−𝑃 )𝑃 𝑃 [10]
𝑎 𝑐 𝑑 𝑡 𝑓
where P represents the probability of attachment, P the collision probability, P the probability
a c d
of detachment in pulp phase, P the probability of bubble-particle aggregate being transferred to
t
the froth phase at the pulp-froth interface, and P represents the probability of bubble-particle
f
aggregate not being broken and surviving the froth phase.
In the past, the flotation process was often modeled as a first-order process with a single
rate constant for the recovery processes occurring in both the pulp and froth phases of a flotation
cell and viewed flotation effectively as a single-phase process. However, the cell consists of two
different phases, i.e., pulp and froth, each having distinctly different recovery mechanisms.
Therefore, it would be better to develop two different model and fine ways to combine them in the
end.
When considering the pulp phase only, the first-order rate equation may be given as
𝑑𝑁
1 = −𝑘 𝑁 [11]
𝑝 1
𝑑𝑡
8 |
Virginia Tech | Under quiescent conditions, P can be readily determined from stream functions for water around
c
air bubbles (Luttrell and Yoon, 1992). Under turbulent conditions, however, most investigators
use Abrahamson’s collision model (1975),
𝑍 = 23/2𝜋1/2𝑁 𝑁 𝑑2 √𝑢̅2 +𝑢̅2 [12]
12 1 2 12 1 2
which was derived considering random collision under highly turbulent conditions and is
applicable for particles with very large Stokes numbers. In Eq. 12, Z is the frequency of collision
12
(number of collisions per unit time) between particles 1 and bubbles 2; N and N are the number
1 2
densities of particles and bubbles, respectively; d is the collision diameter (sum of radii of
12
bubbles and particles); and 𝑢̅ and 𝑢̅ are the RMS velocities of the particles and bubbles,
1 2
respectively.
The flotation rate equation for pulp phase under the turbulent flow conditions can then be
written as
𝑑𝑁1
= −𝑍 𝑃 [13]
12
𝑑𝑡
The probability of forming bubble-particle aggregates in the pulp phase and the aggregates
successfully entering the pulp phase should be gives as
𝑃 = 𝑃 𝑃(1−𝑃 )𝑃 [14]
𝑎 𝑐 𝑑 𝑡
Substituting Eqs.12 and 14 into Eq. 13, one obtains,
𝑑𝑁1 = −23/2𝜋1/2𝑁 𝑁 𝑑2 √𝑢̅2 +𝑢̅2𝑃 𝑃(1−𝑃 )𝑃 [15]
𝑑𝑡 1 2 12 1 2 𝑎 𝑐 𝑑 𝑡
which is a second-order flotation rate equation with respect to N and N and is applicable for large
1 2
particles with high Stokes numbers. In flotation, bubble-particle collision is not completely
random. Smaller particles follow the stream lines around bubbles. Further, the trajectories of
bubbles and particles may not be completely random even for coarse particles. Therefore,
appropriate corrections may be necessary particularly in the areas outside the rotor-stator
mechanisms. In effect, the P of Eq. 16 serves as a correction factor for the hard-core, random
c
collision model of Abramson (Eq.12). Luttrell and Yoon, 1989 has derived a collision probability
model which was further modified by Do, 2010,
9 |
Virginia Tech | 3
𝑃 =
tanh2(√3
(1+
16𝑅𝑒
)
(𝑑1))
[16]
𝑐 2 1+0.249𝑅𝑒0.56 𝑑2
where Re represents the Reynolds number. In the present work, Eq. [16] has been used as the P
c
for the bubble-particle interactions in the pulp zone.
If N >> N or N remains constant during flotation, Eq. 15 becomes a pseudo-first-order
2 1 2
flotation rate equation with respect to N . From Eqs. 11 and 15, one can then write an expression
1
for the first-order rate constant in the pulp zone (k ) in the following form,
p
𝑘 = 23/2𝜋1/2𝑁 𝑁 𝑑2 √𝑢̅2 +𝑢̅2𝑃 𝑃(1−𝑃 )𝑃 = 𝑍 ⁄𝑁 𝑃 [17]
𝑝 1 2 12 1 2 𝑎 𝑐 𝑑 𝑡 12 1
Bubble Generation Model
The diameters of bubbles (2r ) were calculated using the bubble generation model derived
2
by Schulze(1984),
0.6
2.11γ
𝑑 = ( 𝑙𝑣) [18]
2 𝜌3𝜀 𝑏0.66
where γ is the surface tension of the water in a flotation cell, ρ is the density of the water, and ε
lv 3 b
is the energy dissipation rate in the bubble generation zone. In the present work, it is assumed that
air bubbles are generated at the high energy dissipation zone in and around the rotor/stator
assembly, which has 5 to 30 times larger energy dissipation rates than the mean energy dissipation
rate (ε ) of a cell (Schulze 1984). In the present work, we assumed that the energy dissipation rate
in the bubble generation zone is 15 times larger than the mean.
RMS Velocities
The RMS velocity of the particles is calculated using the following relationship,
𝑢̅ =
0.4𝜀4/9𝑑 17/9 (𝜌1−𝜌3)2/3
[19]
1 𝜐1/3 𝜌3
where ε is the energy dissipation rate, d is the particle diameter, ν is the kinematic viscosity of
1
water, ρ is the density of the particle, and ρ is the density of water (Schubert 1999).
1 3
10 |
Virginia Tech | can be used for bubble-particle interactions (Pan and Yoon, 2010). Figure 2-1 shows a plot of all
of the surface forces acting between a mineral particle and an air bubble.
By using Eq. 26, we obtained the hydrophobic force constant (K ) between two
131
hydrophobic surfaces using the following relation,
𝐾 = 𝑎𝑒𝑏 𝑘𝜃 [27]
131
where a and b are constants which vary with contact angle, θ (Pazhianur and Yoon, 2003). Table
k
2-1 gives the values of a and b at different ranges of contact angles.
k
In determining P using Eq. 21, we calculated E using the following relation,
a k
𝐸 = 0.5𝑚 (𝑈 ) 2 [28]
𝑘 1 𝐻𝑐
where m is the mass of the particle, and U is the velocity of a particle approaching a bubble at
1 Hc
the critical rupture distance (H ). This velocity may be found by the following relation,
c
𝑈 =
𝑢̅
1 [2]
𝐻𝑐
𝛽
where β is the drag coefficient in the boundary layer of the bubble (Goren and O'Neill, 1971),
which in turn can be obtained as follows (Luttrell and Yoon, 1992),
0.83
𝛽 =
0.37(𝑟1)
[30]
𝐻
which has been derived from the Reynolds lubrication theory.
2.4.2 Probability of Collision
Luttrell and Yoon (1992) derived an expression for P , which has been modified slightly
c
to ensure that P < 1(Do 2010). Eq. (16) above gives an expression for P used in the present work.
c c
Table 2-1: Values of a and for b different range of contact angles
k
a b
k
> 92.28° 6.327x10-27 0.2127
92.28° > θ > 86.89° 4.888x10-44 0.6441
< 86.89° 2.732x10-21 0.04136
13 |
Virginia Tech | 2.4.3 Probability of Detachment
The probability of detachment was calculated using the following expression (Yoon and
Mao, 1986),
𝑃 = exp
(−𝑊𝑎+𝐸1)
[31]
𝑑 𝐸′
𝑘
where W is the work of adhesion, and E’ is the kinetic energy of detachment. W can be obtained
a k a
from the following relation,
𝑊 = γ π 𝑟2(1−cos𝜃)2 [32]
𝑎 𝑙𝑣 1
where γ is the surface tension of water, r is the radius of the particle, and θ is the contact angle.
lv 1
By using Eq.(32), the kinetic energy of detachment (𝐸′) has been calculated using the
𝑘
following relation(Do 2010),
2
𝐸′ = 0.5𝑚 ((𝑑 +𝑑 )√𝜀/𝜈) [33]
𝑘 1 1 2
where is the energy dissipation rate and is the kinematic viscosity.
Froth Recovery Model
Once particles enter the froth phase, the more hydrophobic particles survive the froth phase
and reach the launder while the less hydrophobic particles drop back to the pulp phase. The
probability of survival (R) is given as (Do, 2010),
f
𝑅
𝑓
=
𝑑2−0𝑒−𝑁 𝑑6 2ℎ −𝑓 0(1− 𝑑𝑑 22 −− 𝑓0)( 𝑑𝑑 2−1 0)2
+𝑅
𝑤𝑒−0.0325(𝜌 𝜌3 1−1)−63000𝑑1
[34]
𝑑
2−𝑓
where d is the diameter of the bubbles entering the froth phase at the bottom, d the bubble
2,0 2,f
diameter at the top, N the number of particles attached to each bubble, h the froth height, R the
f w
maximum theoretical water recovery, ρ the density of water, and ρ is the particle density. The
3 1
first term of Eq. 34 represents the recovery due to attachment, while the second term represents
the recovery due to entrainment (Do 2010).
By considering flow balance, one can derive the following relationship,
14 |
Virginia Tech | 𝑄𝑎𝑖𝑟⁄𝑄𝑙𝑖𝑞
𝑅 = 𝑜𝑢𝑡 𝑖𝑛 [35]
𝑤 1 ⁄𝐸−1
𝑙
where 𝑄𝑎𝑖𝑟 is the volumetric flow rate of air leaving the cell, 𝑄𝑙𝑖𝑞 the flow rate of pulp entering
𝑜𝑢𝑡 𝑖𝑛
the cell, and 𝐸 is the fraction of water entering a froth launder. The values of these parameters can
𝑙
be readily measured or are readily available in operating plants.
Overall Recovery
Figure 2-2 shows a mass balance of materials around a flotation cell, in which R is the
p
fractional recovery in the pulp phase and R is the fractional recovery in the froth phase. As between
f
the pulp and froth zones of a flotation cell. One can readily find that the overall recovery, R, can
be calculated using the following relation,
𝑅 =
𝑅𝑝𝑅
𝑓 [36]
𝑅𝑝𝑅 𝑓+1−𝑅𝑝
In a mechanically-agitated flotation cell, the R can be calculated as follows,
p
𝑅 =
𝑘𝑝𝑡
[37]
𝑝
1+𝑘𝑝𝑡
where k is the flotation rate constant in the pulp phase. Eq. (36) is for perfectly mixed reactor
p
(flotation cell) as is the case with a mechanically-agitated individual cell in a flotation bank.
For a plug-flow reactor, R can be calculated using the following relation
p
𝑅 = 1−𝑒−𝑘𝑝𝑡 [38]
𝑝
15 |
Virginia Tech | Chapter 3: MODEL PREDICTIONS
The flotation model discussed in the previous chapter is developed from first principles of
surface chemistry and hydrodynamics of bubble-particle interactions. The parameters affecting
the hydrodynamic properties include particle size, bubble size, energy dissipation rate, etc., while
the parameters affecting the surface chemistry are composed of contact angle (θ), zeta-potential,
Hamaker constant (A ), and surface tension (γ). Thus, the model can predict flotation recovery
131
and grade from both physical and chemical parameters. In the present work, the flotation feed is
represented as a matrix of different particle size and properties such as contact angle, -potential,
and degree of liberation. The flotation rate constant (k ), recovery, and grade are then calculated
p
using the flotation model.
Standalone Flotation Model
Effects of different parameters such as contact angle, particle size, froth height, superficial
gas velocity and zeta potential of particle on flotation recovery are studied. Table 3-1 shows the
model parameters used for model predictions and simulation.
3.1.1 Contact angle
Figure 3-1 shows the effect of contact angle and particle size on the recovery of sphalerite
flotation. At a given contact angle, a series of so-called ‘elephant’ curves have been obtained as
reported by Trahar and Warren (1976) and Gaudin (1931). The experimental recovery vs. log
particle size curves show long tails and sharp nose at the fine and large particle sizes, respectively.
The difficulties in floating coarse particles began at particle sizes above 125 µm (100 mesh),
while fine particle recoveries decline at 10 µm. The simulation results obtained in the present
Table 3-1: Values of the input parameters used in flotation simulation
Variable Value
Specific Power (kW/m3) 1.5
Superficial Gas Rate (cm/sec) 2.0
Froth Height (cm) 8
Bubble Zeta Potential (mV) -30
Flotation Time (min) 2.5
Particle Zeta Potential (mV) -15
Specific Density (sphalerite) 4.1
Slurry Fraction (%) 10
17 |
Virginia Tech | Figure 3-1: Effect of contact angle and particle size on recovery. Input parameters: energy dissipation rate,
1.5 kW/m3; aeration rate, 2 cm/s; S.G. = 3.1, 20 mg/L MIBC; ζ-potential, -15 mV; 2.5 min
retention time, 8 cm froth height.
work show also that the problems of floating for both the coarse and fine particles can be overcome
by increasing the contact angles of particles. Particle hydrophobicity along with bubble size and
particle size represents the three of the most important parameters in flotation. It also shows that
the higher the contact angles are, higher the recoveries. Note also that the maximum flotation
occurs at the particle sizes in the range of 20 to 105 µm.
Eqs.26 and 27 show that hydrophobic force constant for bubble-particle interaction (K )
132
increases with increasing contact angle. The role of hydrophobic force is to decrease the energy
barrier (E ), which in turn causes the probability of bubble-particle attachment (P ) and hence
1 a
increase the flotation rate constant (k ) and recovery
p
3.1.2 Froth height
Figure 3-2 shows a contour plot for the changes in recovery with respect to froth height
and particle size. It can be seen that the recovery of the coarse particles decreases with increase in
the froth height. As the bubble particle aggregates rises through the froth phase in a flotation cell,
bubble surface area decreases due to bubble coalescence, which in turn increases the chances of
18 |
Virginia Tech | Figure 3-2: Effect of froth height on recovery. Input parameters: energy dissipation rate, 1.5 kW/m3;
aeration rate- 2 cm/s; S.G. , 3.1; frother, 20 mg/L MIBC; ζ-potential, -15 mV; 2.5 min
retention time, θ =45°.
bubble particle detachment. The froth recovery factor (R) decreases more for the coarser particles,
f
hence the overall recovery decreases.
3.1.3 Superficial gas rate
Figure 3-3 shows a contour plot for the recovery as functions of superficial gas rate (v )
g
and particle size (d ). The plot shows that with a rise in the airflow rate, the recovery increased at
1
a given particle size. Many researcher have reported similar results for industrial column flotation
in the past (Yianatos, Bergh, and Cortes,1988).
3.1.4 Zeta potential
Figure 3-4 shows the effects of particle ζ-potentials and particle size on flotation recovery.
As shown in Figure 3-4 Effect of ζ-potential on recovery. Input parameters: energy dissipation
rate, 1.5 kW/m3; aeration rate- 2 cm/s; S.G. , 3.1; frother, 20 mg/L MIBC; 2.5 min retention time,
froth height- 8 cm, θ =45°., fine particle flotation benefits from a decrease in the negative ζ-
potential of particles, which can be attributed to a decrease in energy barrier (E ) for bubble-
1
particle interaction. It is well known that the ζ-potential of both air bubbles and mineral particles
are negative particularly in sulfide flotation. By reducing the electrostatic repulsion between
particles and bubbles, one can reduce the energy barrier for bubble-particle attachment and hence
increase the flotation rate. As shown in Eq. (21) a decrease in energy barrier (E ) should increase
1
19
P a r tic le S iz e ( m )
)
m
c
(
t
h
g
ei
H
h
t
o
r F
3
2
2
1
1
0
5
0
5
0
5
5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
9
8
7
6
5
4
3
2
1
0
0
0
0
0
0
0
0
0
0 |
Virginia Tech | Flotation Circuits Simulation
In this section effect of circuit arrangement and operating parameters on chalcopyrite
recovery was studied. The objective was to be able to generate a recovery versus grade curves
which could be used to compare the performance of the different flotation circuits. It was assumed
that the contact angle of chalcopyrite feed varies linearly with the feed grade. Table 3-2 shows the
operating parameter used for simulation.
Circuit arrangement:
Three circuits arrangement were considered for the simulation purpose.
i) Rougher Circuit (RC)
Figure 3-5: Rougher Circuit
A 6 cell rougher circuit, as shown in Figure 3-5 was studied. Tailings of each preceding
flotation cell acted as the feed to the next flotation cell.
ii) Rougher Scavenger Circuits (RSC)
Figure 3-6 shows the rougher-scavenger circuit used for simulation. The circuit comprises
of twelve flotation cells. The first six cells act as the rougher, while the next six cells act as the
21
F
C
T
F
C
T
F
C
T
F
C
T
F
C
T
F
C
C
T
T
F C F C F C F C F C F C F C F C F C F C F C F C
T T T T T T T T T T T T
T
C
Figure 3-6: Rougher scavenger circuit |
Virginia Tech | dotted lines represent the grade-recovery curve for contact angle of 60º, while the solid line
represent the grade recovery curve for 90º contact angle. Numbers above the curves represent the
optimum residence times (residence times at the inflection points or ‘shoulders’ of the curves).
Specific energy was kept constant at 3kW/m3 for this particular set of simulation.
Comparison of the results given in Figure 3-8 show that the RSCC circuit gives a better
result than the SC and RSC circuits, which is in agreement to typical industrial practices. It can
also be deduced that, with an increase in the contact angle, the circuit performance increases, for
all the other parameters being constant. Furthermore, the contact angle increase causes the
optimum residence time to decrease, which is an important advantage of using a stronger flotation
collector.
3.2.2 Specific energy
Effect of changing the specific energy input to flotation was studied by plotting the grade-
recovery curves. Figure 3-9 shows that an increase in the energy dissipation rate (𝜀)̅ from 1 kW/m3
23
1 0
8
6
4
2
0
0
0
0
0
0
0
3 K W
/
C
C
m
u
u3
1
=
=
0
6
9
0
0
o
o
9 m
6
2 0
R
1
g
8
r
1 1
S c
3
v
3
6
0
2 2
C ln
)
%
(
y
r
e
v
o
c
e
R
G r a d e ( % )
Figure 3-8: Effect of contact angle on chalcopyrite grade –recovery curve. Input parameters:
energy dissipation rate, 3 kW/m3; aeration rate, 0.5 cm/s; θ (Cu) = 60° & 90°; 20 cm
froth height; ζ = -8 mV. |
Virginia Tech | Chapter 4: MODEL VALIDATION WITH EXPERIMENTAL DATA
Chalcopyrite Batch Flotation
Studies were conducted by Muganda et al. (2010) to show the effect of particle size and
contact angle on the flotation recovery of chalcopyrite in a series of laboratory-scale batch flotation
tests. While specific details of this experiment can be found in the original paper, the test
parameters relevant to simulator can be found in Table 4-1. The specific power input (kW/m3) was
calculated by assuming a power number of 1.1 and a gassed-to-ungassed power ratio of 0.7. These
assumptions are also supported by data elsewhere in the literature (Sawant, 1981). During feed
preparation for the batch flotation tests, chalcopyrite was treated in pre-cleaning stages without the
addition of collector to reduce the silica to very low levels.
In these tests, Muganda et al. conducted flotation tests on pure chalcopyrite samples of
different size fractions of known advancing contact angles. For the laboratory tests, the contact
angles of different size fractions were manipulated by thermal oxidation and/or conditioning with
100
80
)
%
(
y
r 60
e
v
o
c
e
R
m 40
u
m
xi Contact Angle
a 36-40
M
20 66-70
71-75
0
1 10 100 1000
Particle Size (µm)
Figure 4-1: Effect of contact angles on the recovery of pure chalcopyrite particles of different
contact angles. Experimental data are from Muganda, et al. (2011), and the curves are
from simulation.
29 |
Virginia Tech | 1.0
P
a
0.8
y 0.6 1-P
t d
i
l
i
b
a
b
o
r 0.4
P P
c
0.2
0.0
1 10 100
Particle Size (m)
Figure 4-2: Effect of particle size on probabilities (Pa, Pd & Pc); energy dissipation rate, 15 kW/m3; ζ = -
77 mV; θ = 35°.
potassium amyl xanthate. The Washburn method was used to measure the advancing contact
angles.
The flotation tests were conducted at 0.3 cm/s superficial gas rate and 1 cm froth height.
Figure 4-1 shows the size-by-size recoveries obtained at three different ranges of contact angles,
i.e., = 36-40o, 66-70o, and 71-75o. The solid lines represent the results of the simulations carried
out using these contact angles, while the points represent the experimental data. Note here that
data presented were due to ‘true’ flotation, meaning that the authors subtracted the recoveries due
to entrainment from the experimental recoveries. Since Muganda, et al. did not report the values
of -potentials, we used the values of -77 mV for minerals and -30 mV for air bubbles. The fit
between the Muganda, et al.’s experimental and our simulation results is reasonable. The
discrepancies observed at the finer and coarser particle sizes may be due to the possible errors
associated in the method of correcting the experimental data for the recovery due to entrainment.
The data presented in Figure 4-1 show that the higher the contact angles, the higher the recoveries,
and that the optimum flotation occurs at the particle sizes in the range of 20 to 105 µm.
30 |
Virginia Tech | 1.0
P
a
0.8
y
t 0.6
i
l
i
b
1-P
a d
b
o
r 0.4
P
0.2
P
c
0.0
10 20 30 40 50 60 70 80 90
Contact Angle
Figure 4-3: Effect of contact angle on probabilities (Pa, Pd & Pc): energy dissipation rate, 15 kW/m3; ζ = -
77 mV; Particle size = 20 µm.
An advantage of using a first-principle model for flotation simulation is to analyze the
various mechanisms involved. Figure 4-2 shows the probabilities of collision (P ), attachment
c
(P ), and detachment (P ). As shown, both P and P decreases with particle size, while P increases
a d a c d
with particle size. Thus, the difficulty in floating fine particles is due to the low collision and
attachment probabilities, while the difficulty in floating coarse particles is due to detachment.
Figure 4-3 shows the effect of contact angle () on the probabilities of attachment (P ),
a
detachment (P ) and collision (P ). As shown, P is independent of contact angle, while the
d c c
probability of not being detached, i.e., (1-P ), increases with , which can be attributed to
d
increasing work of adhesion (W ) as shown in Eq. [32].
a
31 |
Virginia Tech | The lines represent the simulation results, while the points represent the experimental recoveries.
A reasonably good fit can be seen between the experimental and simulation results.
Batch Silica Flotation
Closely controlled laboratory flotation tests were performed on mono-sized glass beads to
validate the simulator outcome over various feed properties and operating conditions. Flotation
experiments were conducted on mono-sized glass beads using a 1.2 liter laboratory scale Denver
flotation machine. The particle sizes of the beads were in the range of 35 to 119 µm. Dodecylamine
hydrochloride (DAH) was used as collector while MIBC was added as frother. To maintain a
uniformity in all laboratory tests, a 4 x 10-6 M DAH-in-ethanol solution was prepared as a stock
solution. A known volume of the stock solution was used in flotation and contact angle
measurement. Table 4-2 summarizes the flotation conditions.
For contact angle measurements, a clean and polished glass plate was conditioned in the
solution for two minutes prior to the measurements. The standard goniometer-based on sessile
drop technique was used for all the contact angle measurements. The process involved vertical
dropping of a water droplet on to the surface of the prepared silica plate. The surface was then
captured by high resolution camera and then analyzed using Ramé–hart Model 250. To ensure the
correct measurement of contact angles, each measurement was repeated five times on each glass
plate and the average value for the contact angle was calculated. In flotation tests, regulated
pressurized air was introduced to a flotation cell through the impeller shaft and rotor and the
superficial gas rate was monitored by means of a flow meter (GFM, Aalborg make).
Table 4-2: Operating parameters for silica batch flotation experiments
Variable Value
Rotational Speed (RPM) 850
Froth Height (cm) 1.5
Specific Power (kW/m3) 2.71
Flotation Time (min) 0.5 - 4
Superficial Gas Rate (cm/s) 1
Cell Volume (L) 1.2
Frother Type MIBC
34 |
Virginia Tech | A known quantity (120 g) of glass beads was added to the 1.2 liter Devner flotation cell
and agitated for 30 seconds in the presence of MIBC and DAH. The agitation was stopped and the
pH was measured, after which the slurry was agitated again for another 1 minute without air. After
the 1 minute conditioning time, air was introduced to commence flotation. Each flotation
experiment lasted for 4 minutes, during which time a set of five samples were collected. The first
three sample were collected at interval of 30 seconds, followed by two progressively long intervals
(1min and 1.5 min). The collected flotation products were dried in an oven and weighed. From the
weight, flotation recoveries were calculated. The results were plotted as a function of time to obtain
kinetic information.
Effect of particle size on silica flotation recovery is shown in Figure 4-6. Laboratory scale
flotation tests were conducted on pure glass spheres of different particle size (35, 71 and 119 µm).
The flotation test were conducted at 1cm/s superficial gas rate, 1.5 cm of froth height, and 2.5
kW/m3 energy dissipation rate. The solid line represents the simulation results while the points
represents the experimental cumulative recoveries. The experimental data fit reasonably well with
the simulations result.
100
119
71
80
%) 35
(
y
r 60
e
v
o
c
e
R
e
v 40
ati
ul = 51
m
3
u kW/m
C
20 V = 1 cm/s
g
Froth Height = 1.5 cm
0
0 1 2 3 4
Flotation Time (min)
Figure 4-6: Effect of particle size on the kinetics of silica flotation.
35 |
Virginia Tech | 100
9.71 (1300)
80 6.72 (1150)
2.71 kW/m
(850 RPM)
) 60
%
(
y
r
ove
S.G. = 2.5
c 40
e
R = 38
V = 1 cm/s
g
20
d = 35 m
1
Froth Height = 1.5 cm
0
0 1 2 3 4
Time (min)
Figure 4-7: Effects of energy dissipation on the kinetics of silica flotation: particle size, 35 µm.
Figure 4-7 shows the effect of specific energy input on the recovery of silica particles. In
these experiments, 35 µm silica particles were used, with the Denver flotation machine operating
at 850, 1150 and 1300 RPM. As shown, the flotation kinetics and hence the recovery increases
with increasing energy input. Note here that the simulation results are in reasonable agreements
with the experimental dada, validating the first-principle model and the simulation results obtained
in the present work.
Figure 4-8 shows that the values of P , P , and P as calculated using the model under the
a c d
experimental conditions employed in the flotation experiments. As shown, both P and P
a c
increased with increasing energy dissipation rate (𝜀)̅ , while the probability of not being detached
(1-P ) increases with 𝜀.̅ The flotation recovery increased with increasing energy input shows that
d
the detrimental impact of particle detachment is overcome by the beneficial effects of P and P .
a c
36 |
Virginia Tech | Selective Flotation
In another set of flotation tests were carried out on a mixed feed consisting of 10% silica
(SiO ) and 90% magnetite (Fe O ) by weight. The glass beads were mono-sized particles with a
2 3 4
designated size of 75 µm, while that of magnetite was a -75+53 µm fraction. The latter sample was
obtained from the Alpha Chemicals. The glass beads were cleaned in a Piranha solution at 70ºC in
order to remove all the contamination. The particles were then rinsed three to four times with
ultrapure water in an ultrasonic bath. The glass beads were then dried in an oven. The dried samples
were then immersed in a freshly prepared 2x10−5 M octadecyltrichlorosilane (OTS)-in-toluene
solution for a given period time. A glass slide was immersed in the same solution so that the contact
angles of the glass beads and glass slide were the same. After the immersion, the excess OTS was
removed from the silylated surfaces by quickly washing the plates and particles sequentially with
chloroform, acetone and pure water. After the excess OTS had been removed, the silylated plates
38
1 0
8
6
4
2
0
0
0
0
0
0
0
= 6 1
5
1
1
2
S
V
d
F
.G . = 2 .5
2 .5 k W
= 1 c mg
= 3 5 m1r
o th H e ig
3
/m/s
h
3
t = 1 .5 c m
4
) %
(
y
r
e
v
o
c
e
R
e
v
ti
a
ul
m
u
C
F lo ta tio n T im e ( m in )
Figure 4-9: The effects of contact angle on the kinetics of silica flotation: particle size, 35 µm. |
Virginia Tech | were blow-dried using a stream of pure nitrogen. The hydrophobicity was controlled by controlling
the time of contact between the glass spheres and OTS solution.
The equilibrium, advancing, and receding contact angles were determined using the sessile
drop technique by means of a contact angle goniometer. With a given silica plate, the
measurements were repeated five times and averaged.
The flotation tests were carried out on the 1:9 mixtures of hydrophobized silica and
magnetite particles using the Denver laboratory flotation machine with a 1.2 liter flotation cell. In
each test, 120 grams of the mixture and MIBC were added to the cell and conditioned for 30
seconds. After the agitation, the pH of solution was measured. The slurry was agitated further for
another minute without air, after which a regulated air flow was introduced to commence the
flotation test for a total of 4 minutes. Five samples were collected. The first three samples were
collected at intervals of 30 seconds, followed by two progressively longer intervals (1 min and 1.5
min). The flotation recoveries were determined from the timed weights of the froth products. The
results were plotted as a function of time in order to produce standard kinetic curves. Both the
flotation concentrate and tails were subjected to magnetic separation to determine the product
grades.
The first set of flotation tests were conducted by varying the impeller speed in the range of
850, 1,050 and 1,300 RPM, while keeping all other variables constant. Figure 4-10 shows the
effects of the RPM, or energy dissipation rate (𝜀)̅ , on the recovery of silica and magnetite. As
shown, silica floated much faster than magnetite because the former was hydrophobic. The silica
samples were hydrophobized in a 2x10−5 M OTS-in-toluene solution for 30 seconds to obtain an
equilibrium contact angle of 61o.
Note here that the increase in 𝜀 ̅ does not change the recovery of the hydrophobic silica.
However, the recovery of the hydrophilic magnetite increased with increasing𝜀.̅ The net result is
that the grade of froth product decreased with increasing 𝜀.̅ Figure 4-11 shows the grade-recovery
curves in the flotation experiments. Also shown in the figure are the simulated grade-recovery
curves. The experimental results obtained at the lower energy dissipation rates are lower than the
simulated, while the results obtained at the higher dissipation rates show an excellent agreement.
The discrepancy observed at the lower energy dissipation rates may be due to the possibility that
the silica-magnetite mixtures were not fully suspended.
39 |
Virginia Tech | Figure 4-12 shows a set of selective flotation tests conducted on the 1:9 hydrophobic silica-
hydrophilic magnetite mixed particle suspension by varying the superficial gas rate. The
equilibrium contact angle of the silica was 63º after 30 seconds of contact time with a 2x10−5 M
OTS-in-toluene solution. As expected, the silica recoveries were higher at 1.0 cm/sec gas rate than
at 0.5 cm/s gas rate. Similar results were reported by Yang and Aldrich (2006). The solid lines
show the simulation results obtained assuming that the magnetite contact angle was 7o. Reasonable
agreements were obtained at the longer flotation time. At the shorter flotation times, the simulated
results were lower than the experimental results. Figure 4-13 shows the grade vs. recovery curves
obtained on the basis of the data presented in Figure 4-12. The simulated and predicted results are
in reasonable agreement.
41
1 0
8
6
4
2
0
0
0
0
0
0
0 1 2 3
M
S
a
ilic
0
1
g n
a
.5.0
e
c m
c m
tite
4
/s/s
)
%
(
y
r
e
v
o
c
e
R
F lo t a t io n T im e ( m in )
Figure 4-12: The effects of superficial gas rate on the kinetics of silica and magnetite flotation: energy
dissipation rate, 2.71 kW/m3; aeration rate, 1 cm/s; 1.5 cm froth height; θsilica = 64°,
θmag= 7°. |
Virginia Tech | Figure 4-14 shows the results of two sets of flotation tests conducted on the 1:9 mixtures
of hydrophobic silica and hydrophilic magnetite. In one test, the silca sample had a contact angle
of 51o and in the other the contact angle as 61o. As has already been noted, the contact angle was
controlled by controlling the immersion time in a 2x10-5 M OTS-in-toluene solution. As expected,
hydrophobic silica particles floated much faster than the hydrophilic magnetite. Also, the
recoveries of the silica particles with = 61o were higher than those of the silica with = 52o. It
is interesting to find that the magnetite particles floated better in the presence of the less
hydrophobic particles. This finding may be explained by the likelihood that the magnetite particles
may have a lesser competition with the silica particles when the latter is less hydrophobic. This
phenomenon has not been reflected in the model development. Therefore, the simulation did not
fit the experimental data well. For this reason, no simulation results are presented in Figure 4-14.
43 |
Virginia Tech | Chapter 5: CONCLUSION
General Conclusion
Flotation models are an important tool to develop better understanding of the flotation
process. The first-principle model developed in the present work can be used to evaluate the
performance of a flotation machine or flotation circuit without the need of extensive laboratory
experiments. A unique advantage of the model/simulator developed in the present work is that for
the first time one can predict flotation results from both the hydrodynamic and chemistry
parameters. The model has been validated from a series of carefully controlled flotation
experiments. Further, the simulation results presented in this communication are consistent with
the flotation practice.
Recommendations for Future Work
While the simulation shows reasonable fit with the experimental data, they may not be
sufficient. Model is made of some assumptions and simplification, which could be improved while
considering following suggestions-
Include an analytical expression for bubble coarsening in the froth (or foam) phase.
Include a model to predict the contact angle of particle based on liberation analysis.
Incorporate the effect of hydrophobic coagulation.
Develop the model to relate zeta-potential with pH and contact angle with dosages with
collector dosages.
Take effect of presence of other particles of different species on bubble coverage.
44 |
Virginia Tech | IDENTIFICATION OF IMPROVED STRATIGIES
FOR PROCESSING FINE COAL
by
Zulfiqar Ali
ABSTRACT
In modern coal preparation plants, solid-solid and solid-liquid separation processes used
to treat fine coal are least efficient and most costly operations. For example, field studies indicate
that the froth flotation process, which is normally used to treat minus (-0.2 mm) fine coal, often
recovers less than 65 to 70% of the organic matter in this size range. Fine coal separation
processes are also inherently less effective in removing pyrite than that of coarse coal
separations. Moreover, while fines may represent 10% or less of the total run-of-mine feed, this
size fraction often contains one-third or more of the total moisture in the delivered product. In
order to address these issues, several multistage coal processing circuits were set up and
experimentally tested to demonstrate the potential improvements in fine coal upgrading that may
be realistically achievable using an “optimized” fine coal processing flowsheet. On the basis of
results obtained from this research, engineering criteria was also developed that may be used to
identify optimum circuit configurations for the processing different fine coal streams.
In the current study, several fine coal cleaning alternatives were evaluated in laboratory,
bench-scale and pilot-scale test programs. Fine coal processes compared in the first phase of this
work included spirals, water-only cyclones, teeter-bed separators and froth flotation. The
performance of each technology was compared based on separation efficiencies derived from
combustible rejection versus ash rejection plots. The resulting data was used to identify size
ranges most appropriate for the various alternative processes. As a follow-up to this effort, a |
Virginia Tech | second phase of pilot-scale and in-plant testing was conducted to identify new types of spiral
circuit configurations that improve fine coal separations. The experimental data from this effort
indicates that a four-stage spiral with second- and fourth-stage middlings recycle offered the best
option for improved separation efficiency, clean coal yield and combustible recovery. The newly
developed spiral circuitry was capable of increasing cumulative clean coal yield by 1.9 % at the
same clean coal ash as compared to that of achieved using existing conventional compound
spiral technology. Moreover, the experimental results also proved that slurry repluping after two
turns is not effective in improving separation performance of spiral circuits.
The third phase of work conducted in this study focused on the development of methods
for improving the partitioning of pyrite within fine coal circuits. The investigation, which
included both laboratory and pilot-scale test programs, indicated that density-based separations
are generally effective in reducing sulfur due to the large density difference between pyrite and
coal. On the other hand, the data also showed that sulfur rejections obtained in froth flotation are
often poor due to the natural floatability of pyrite. Unfortunately, engineering analyses showed
that pyrite removal from the flotation feed using density separators would be impractical due to
the large volumetric flow of slurry that would need to be treated. On the other hand, further
analyses indicated that the preferential partitioning of pyrite to the underflow streams of
classifying cyclones and fine wire sieves could be exploited to concentrate pyrite into low-
volume secondary streams that could be treated in a cost effective manner to remove pyrite prior
to flotation. Therefore, on the basis of results obtained from this experimental study, a combined
flotation-spiral circuitry was developed for enhanced ash and sulfur rejections from fine coal
circuits.
iii |
Virginia Tech | ACKNOWLEDGEMENTS
It is my pleasure to acknowledge everyone who contributed directly or indirectly to
complete this research work. First of all, my special thanks to my research advisor, Dr. Jerry
Luttrell, who was always there for guidance, suggestions, help, support and encouragement
during my research work at Virginia Tech. Jerry, it was an honor for me to work with you and
there is no doubt in saying that this work would not have been possible without you. I am also
truly indebted and thankful to my respected committee members, Dr. Greg Adel, Dr. Emily
Sarver and Dr. Jaisen Kohmuench for their valuable comments, suggestions and advices.
During my experimental work, Bob Bratton was there to help whenever I was stuck.
Thank you Bob, for your invaluable help and suggestions to improve my research work. My
thanks and appreciation was due to Jim Waddell and John Matherly for their invaluable help
during experimental set up. Special thanks are due to Kathryn Dew, Carol Trutt and to Gwen
Davis for their administrative assistance throughout my graduate studies.
I would like to thank Alpha Natural Resources, Arch Coal, Inc. and their employees for
assisting in my in-plant experimental testing programs. I am also obliged to the management and
employees of Cardinal, Knight Hawk, Prairie Eagle and Creek palm preparation plants for
providing much needed fine coal samples for my experiments. Appreciation is also extended to
Eriez Manufacturing for their assistance during teeter-bed and HydroFloat™ testing.
The financial support provided by the University of Engineering and Technology, Lahore,
Pakistan and Taggarat Global LLC and Nano Drying Technologies LLC is greatly
acknowledged.
I would also like to thank many friends for their nice company throughout my stay in
Blacksburg namely Jawad Raza, Imran Akhtar, Shamim Javid, Arshad Mehmood, Karim Akhtar,
vi |
Virginia Tech | CHAPTER 1 - INTRODUCTION
1.1 Motivation
Coal is one of the most abundantly available energy sources in the world and is found
almost in every country. The top five largest proven reserves of coal are in the United States,
Russia, China, Australia and India, respectively. Table 1.1 shows the distribution of proven coal
reserves. Currently, there are over 860 billion tonnes of proven coal reserves. In 2010, world coal
consumption grew by 7.6% and now coal accounts for 29.6% of world total energy, 40% of
world electricity and 66% of world steel production (BP, 2011).
The United States leads the world with a little over 237 billion short tons of recoverable
coal reserves, i.e., approximately 27.6% of the total world coal reserves. It is estimated that at the
current production rate of 984.6 million tonnes per year (USEIA, 2010), the U.S. reserves would
last for 240 years. Coal is the largest single fuel used for electricity generation in the U.S. and
accounts for 42% of electric power generation. Since 2000, about 90% of all the coal consumed
in U.S. has been used for electric power generation as shown by Figure 1.1.
Run-of-mine coal often contains inorganic impurities in the form of mineral matter. The
mineral matter consists of noncombustible materials such as shale, slate and clay. These
unwanted contaminants reduce the coal heating value, leave behind an undesirable ash residue,
and increase the transporting cost of coal. These impurities can also alter the suitability of coal
for the manufacture of metallurgical coke or generation of petrochemicals and synthetic fuels.
1 |
Virginia Tech | 100
90
80
70
60
50
40
30
20
10
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Excess surface moisture also reduces the heating value of coal, leads to severe handling
and freezing problems and increases the overall transportation costs of coal to consumer sites
(Kaytaz et al., 1994). Therefore, strict limitations on the heating value, ash and moisture contents
of purchased coal are imposed in coal purchasing agreements.
Coal processing is an important step to satisfy the run-of-mine coal quality specifications
as per end-user demand. Coal processing also removes impurities such as sulfur and trace
elements like mercury, thus cleaned coal is more environmentally friendly. In short, coal
processing increases the heating value, lowers the transport cost, reduces the particulate
emissions and improves the marketability of the run-of-mine coal. There are 286 coal processing
plants in the United States, which cleaned approximately 67% (660 million short tons per year)
of the total coal consumed in the United States (Coal Age, 2010).
)%(
noitpmusnoC
laoC
Year
Electric Power Coke Plants Other Industrial Residental & Commercial
Figure 1.1 Coal consumption by sectors from 2000 to 2010 (US EIA, 2011).
2 |
Virginia Tech | Although not shown in Figure 1.2, coal processing usually starts with crushing, i.e., run-of-mine
coal lumps that are too large to pass through the processing plant are crushed down to an
appropriate size. The crushed coal is then separated into appropriate size fractions as coarse,
small, fine and ultrafine. Screens are employed for sizing coarser particles, while combinations
of sieves and classifying cyclones are used for sizing finer particles. Figure 1.3 shows coal
particles sizing equipment for various size ranges.
The objective of coal processing is to separate impurities from valuable carbonaceous
material. In order to remove these impurities, modern coal processing plants incorporate a
number of solid-solid separation methods such as dense medium vessels, water-only cyclones,
teeter bed separators, coal spirals and froth flotation. Figure 1.3 shows the effectiveness of
different types of conventional coal cleaning separators relative to the coal particles sizes.
The final step of coal preparation is solid-liquid separation, or dewatering, which
removes unwanted surface moisture and produces a relatively dry concentrate. Dewatering
methods are broadly classified in to three main groups: sedimentation, filtration and thermal
drying (Wills & Napier-Munn, 2006). Primarily screens are used to remove excess moisture
from coarser (+5 mm) coal particles. Finer particles, which used to have higher moisture contents
than that of coarser ones due to their greater surface area, are dewatered using centrifugal
methods or filtration systems (Luttrell et al., 2007). Figure 1.3 shows several different types of
mechanical dewatering methods for different ranges of particle sizes.
5 |
Virginia Tech | Figure 1.3 Range of coal particle sizes that can be effectively treated by conventional coal
processing methods (Luttrell, 2012).
1.2 Problem Statement
The solid-solid and solid-liquid separation processes used to treat fine (-1 mm) coal are
the least efficient and most costly operations used in modern coal processing facilities (Figure
1.4). Field studies indicate that the froth flotation process, which is normally used to recover coal
finer than 0.1-0.2 mm, often recover less than 65 to 70% of the organic matter in this size range.
Moreover, this surface based separation process is inherently less effective in removing pyrite
than density based separation processes used to treat coarse coal. The lower particle size that can
be effectively treated by water based density separators is severely limited by the low mass of
small particles. Moreover, fines often represent 10 percent or less of the total run-of-mine feed.
However, this size fraction may contain one third or more of the total moisture of the delivered
6 |
Virginia Tech | well as various types of surface-based separators such as conventional or column flotation
machines. In many cases, the separation processes are used in multistage circuits and are
integrated with various types of classification operations either before or after the cleaning step.
In addition to technical and economic reasons, operator preferences and vendor biases also
appear to contribute to the large variations that are observed in how fine coal is cleaned and
dewatered. As a result, a standard “optimum” flowsheet for fine coal processing, which can be
flexible and adaptable to accommodate changes in feed coal characteristics, does not exist at this
time.
1.3 Research Objectives
The objective of this research is to develop an engineering criterion that can be used to
identify optimum circuit configurations for the processing of fine coal streams. This dissertation
describes several potential improvements in fine coal processing circuitry. Several multistage
circuits, including laboratory, bench-scale, pilot scale-and in-plant test circuits, were set up and
tested to demonstrate the potential improvements in fine coal recovery that may be realistically
achievable using an “optimized” fine coal processing flowsheet. This research work also focused
on the development, testing and evaluation of a modified compound spiral to treat fine coal
feedstocks. A new combined flotation-spiral circuitry for desulfurization of high sulfur fine coal
was also developed and experimentally tested. Finally, this research work also evaluated an
innovative fine coal dewatering technique called Nano Drying Technology (NDT™). This
innovative process is capable of physically removing moisture from fine coal at ambient
temperature using molecular sieve technology.
8 |
Virginia Tech | 1.4 Contributions
The key contributions of this research and development work are as follows:
• Developed an improved fine coal processing circuitry based on feed size characteristics.
• Developed an expanded stage compound spiral circuit (4-3-4-3 turn spiral circuit with
second and fourth stage middlings recycle).
• Developed a new and innovative enhanced fine coal sulfur rejection circuit using
combined spiral-flotation circuitry.
• Evaluated the effectiveness of a new low-temperature fine coal drying process.
1.5 Dissertation Organization
This dissertation is composed of seven chapters. The first chapter “Chapter 1 -
Introduction” provides an introduction to the research topic, a detailed problem statement and a
listing of research objectives. The second chapter “Chapter 2 - Literature Review” is a brief
report on current status of research on fine coal processing. Specifically, this chapter describes in
detail the research and developments in coal spiral technology (i.e., history, construction, design
variables and operating variables). A brief introduction of several other fine coal processing
separators used in this research work is also included in the literature review.
The next four chapters focus on the experimental testing and engineering evaluation of
various new approaches for fine coal cleaning and dewatering. The first of these chapters
“Chapter 3 - Performance Comparison of Fine Coal Cleaning Alternatives” discusses all the
laboratory-scale and pilot-scale test results obtained from the detailed testing of common
technologies used to clean fine coal (i.e., spirals, teeter bed separators, water-only cyclones and
froth flotation). The resultant data suggest, for the particular coal investigated in this study, that
the most effective processes for each size range were generally (i) froth flotation for feeds finer
9 |
Virginia Tech | than about 0.3 mm, (ii) spirals for feeds sized to 1 x 0.3 mm, and (iii) teeter-bed systems
(particularly the HydroFloat™ technology) for feeds larger than 1 mm. Water-only cyclones are
not recommended as stand-alone units due to the potential for high coal losses when secondary
back-up units are not available within the plant circuitry.
The next chapter “Chapter 4 - Engineering Development of Expanded Stage Compound
Spiral” provides results of field tests conducted with a prototype compound spiral that was
modified to improve coal recovery and enhance the selectivity of fine coal processing. Detailed
in-plant experimental tests results, along with separation performance data comparisons, are
presented in this chapter for five different spiral circuit configurations. The performance
comparison indicates that, amongst all the spiral circuits tested, a modified compound spiral with
more cleaning stages and partial middlings recycle is the best option for improved separation
efficiency, clean coal yield and combustible recovery. Preliminary calculations indicate that this
new modified spiral circuit is capable of increasing the clean coal yield by 1.9%, while
maintaining the same ash contents as achieved by existing compound spiral circuits.
This spiral technology research was further expanded in the next chapter “Chapter 5 -
Enhanced Sulfur Rejection Using Combined Spiral Flotation Circuits” to investigate new
methods for improving fine coal desulfurization. Specifically, this chapter discusses the
experimental set up, test results, and technical evaluation of an innovative combined spiral-
flotation circuitry. This chapter also describes in detail the study conducted to evaluate the
partitioning of pyrite within fine coal circuits. The sulfur and ash separation performances of
different fine coal cleaning alternatives were also presented and compared. On the basis of this
study, a spiral followed by a froth flotation cleaning process is recommended for the cleaning of
high sulfur ultrafine (minus 0.25 mm) coal feeds. This chapter describes the rationale for the
10 |
Virginia Tech | design of this new fine coal cleaning circuit and finally a generic flowsheet is also proposed for
any coal preparation plant treating high sulfur ultrafine coal feeds.
The next chapter “Chapter 6 - Engineering Development of Micro Sieve Drying Process”
discusses the theoretical basis for an innovative fine coal drying process. Experimental results
obtained from bench- and pilot-scale testing of this novel approach to fine coal dewatering are
also presented and discussed in this chapter. The results obtained from the experimental work
indicates that the NDT™ system can effectively dewater fine (1 mm x 0) coal from slightly more
than 30% surface moisture to single-digit values. Test data obtained using a pilot-scale NDT™
plant further validated this capability using a continuous prototype facility. The data presented in
this chapter also showed that the performance of the NDT™ system is not dictated or constrained
by particle size, i.e., it works equally well on 1 mm x 0 coal as it does on 325 mesh x 0 coal.
The seventh and final chapter of the dissertation “Chapter 7 – Summary and
Conclusions” provides an overall summary of the findings, conclusions and recommendations
resulting from this research and development study.
11 |
Virginia Tech | CHAPTER 2 - REVIEW OF LITERATURE
2.1 Fine Coal Processing
Coal loss during fine (-1 mm) coal processing is perhaps the greatest among all other size
fractions. For example, froth flotation processes typically recover only 60-80% of the organic
matter contained in fine coal feeds (Bethell, 1998). A study conducted by Cavallaro et al. (1991)
indicates that the reserves of low-ash coal in the central Appalachian region could be nearly
doubled by efficiently cleaning at a particle topsize of 1 mm (Figure 2.1). Moreover, surface-
based separation processes, such as froth flotation, which are generally used to treat fine (0.15 x
0.044 mm) coal, are less effective in removing pyritic sulfur than density-based processes used to
treat the coarser sizes of coal (Adel and Wang, 2005). Therefore, fine coal desulfurization is
often poor in many coal processing facilities treating high sulfur run-of-mine coal seams.
Field studies indicate that the yield
and quality of clean coal products from fine
coal circuitry may be significantly increased
by improving the efficiency obtained for
particle size separations at 150- and 45-μm.
Unfortunately, screens used for sizing fine
particles, and particularly those finer than
0.5 mm, tend to blind easily, wear quickly
and suffer from low throughput and poor
efficiency (Mohanty, 2003). Another
problem associated with fine coal screening
Figure 2.1 Effect of decreasing top size on
coal availability (Cavallero et al., 1991).
Used under fair use, 2012.
15 |
Virginia Tech | is the inefficient removal of ultrafine mineral sediments, such as high-ash clay particles, from
fine coal feeds (Mohanty et al., 2002). Moreover, fine (-1 mm) coal particles may represent as
little as 10% of the total run-of-mine coal, but often contain one-third or more of the total
moisture in the final coal product. Existing fine coal dewatering processes, such as filtration,
centrifuges and thermal drying, are expensive and consume large amounts of energy (Osborne,
1988; Le Roux et al., 2005). The lack of an efficient, inexpensive and safe drying process is one
of the primary reasons that about 2 billion tons of fine coal was discarded by the United States
coal preparation plants into waste impoundments (Orr, 2002).
2.2 Spirals
2.2.1 Spiral Technology
A spiral is composed of a helical channel of modified semicircular cross-section wound
around central column. These are flowing film concentrators and have been found varied
applications in coal and mineral processing industry. Generally, a feed pulp containing between
15 to 45% solids by weight and in the size range of 3 mm to 75 µm is introduced at the top end
of spiral trough. The pulp then gradually flows spirally downwards and, during this motion, the
particles tend to stratify into different streams depending upon their particle size and specific
gravity. Separation is achieved by the combined action of stratification, film sizing and
centrifugal/gravitational forces. Finally, adjustable splitters and/or cutters are used to divert the
separated particles into clean, middlings and refuse streams (Davies et al., 1991; Wills and
Napier-Munn, 2006). Figure 2.2 is a schematic cross-section of a coal spiral trough. In addition,
coal spirals have been successfully used for the treatment of iron ore, chromite, heavy mineral
sand deposits.
16 |
Virginia Tech | Figure 2.2 Cross-section of flow through a spiral trough.
Spirals are considered as one of the simplest, most effective and lowest cost fine (1 x 0.15
mm) coal processing technology (Kohmuench, 2000). Coal cleaning using spiral concentrators
was started back in 1947 when Hudson Coal Company installed 48 spirals to clean fine
anthracite coal in eastern Pennsylvania. During the 1950s, a number of researchers tried to use
spirals to clean fine bituminous coal, but their attempts were not successful (Denin & Wilson,
1948). Finally, since first introducing design changes in the 1980s that made spirals larger
(which improve throughput capacity) and lighter (due to fiberglass and urethane construction),
spiral separators have become one of the most popular fine coal cleaning separators. Apart from
their simplicity, coal spirals have many other advantages such as low capital and operating cost,
simple to operate, no moving parts, no regent requirements, stable cut point with size, good clean
coal recovery and high reject ash levels. On the flip side, spirals have low throughput capacity
17 |
Virginia Tech | compared to other water-based separators such as water-only cyclones. Spirals also operate with
a relatively high specific gravity cut point and can treat only a very limited feed size range
(MacHunter et al., 2003; Luttrell et al., 2003).
2.2.2 Historical Development
The concept of separation by spirals dates back to 1943 when Humphreys Mineral
Industries introduced their first spiral for concentrating mineral ores. These early units were used
to upgrade a wide variety of ores including gold, silver, tin, ilmenite, rutile, zircon, monazite,
iron, barite, fluorspar, mica and phosphate (Davies et al., 1991; Leonard, 1991). For many years
following the introduction of the first units, spirals tended to be used only for comparatively easy
separations. However, subsequent research and development by different spiral manufacturers
around the world led to much wider use of spirals in mineral processing applications and
eventually to their adoption for the coal cleaning (Richard et al., 1985).
The early spirals utilized relatively simple profiles and were designed with a single start
and 4-6 turns. These units were constructed from semicircular sections that were bolted together.
One of the disadvantages of early spiral separators is that they were constructed from cast iron
and weighed about one tonne each. In Australia, sand miners used truck tire sections that were
cut and reattached together to form a spiral instead of using excessively heavy spirals. In 1947,
spirals made from asbestos reinforced concrete were introduced for rutile and zircon extraction.
The decade of 1950 marked a major advance in spiral technology when Ernst Reichert used
fiberglass as a construction material for spirals. The use of fiberglass made it possible to made
light weight, non -corrosive continuous helices and allowed two or three helices to be mounted
on one central column (Davies et al., 1991, Hunter et al., 1985). Another development in the
subsequent spirals is the replacement of rotating disc cutters for concentrate removal with the
18 |
Virginia Tech | concentrate cut from the pulp stream by finger-type splitters. All early designs used wash-water
channels to overcome the sanding/beaching problem of inner trough section. In late 1970s and
early 1980s, Australian researchers came up with modified spiral geometry that resulted in
complete wash-waterless light-weight spirals (Richards & Palmer, 1997). The most recent breed
of spiral is made of fiberglass spray-coated with polyurethane (Das et al., 2007).
2.2.3 Particle Separation Mechanism
While spirals are conceptually very simple in terms of design, the particle separation
mechanism that occurs along the flow path is relatively complex. Feed slurry introduced at the
top of the spiral gradually flows downward under gravity through the spiral trough. Within the
rotating flowing film, coal particles are subjected to gravitational, centrifugal and Bagnold forces
(Bagnold, 1954; Kapur and Meloy, 1999). The combined action of these forces causes lighter
particles to move towards the outer wall and the denser particles move to the central column.
The particle separation mechanism on spirals has been a continuous source of confusion
in the literature. Some researchers believe that there are two basic types of fluid flow along a
spiral trough, which are (i) a primary axially downward flow and (ii) a secondary cross channel
flow (Figure 2.3). The hydraulic phenomenon responsible for both of these flows has been
explained by a number of researches (Holland-Batt, 1990, 1992, 1994, 1998; Richards and
Palmer, 1997; Kapur and Meloy, 1998). According to Holland-Batt (1990), the interaction
between the fluid flow and the particles results in separation of particles of different densities.
On one hand, light particles are carried in the cross flow from the inner region of the trough
towards the outer region and settle at the bottom of the channel. In this case, light particles are
picked up and carried down by the primary flow, which eventually transport the particles out of
the separator. On the other hand, dense particles in the outer region quickly fall to the bottom of
19 |
Virginia Tech | the channel and are carried towards the inner region by the cross flow. These dense particles are
too heavy to be picked up and carried back into the outer region. Hence, dense remain in the
inner region and are carried by the primary flow down the separator (Holland-Batt, 1989).
Richards and Palmer (1997) divided the cross section of the spiral trough into three zones
as shown in Figure 2.3. The inner zone is occupied by a bed of slow moving heavy particles. In
the outer region, or recovery zone, heavy particles must settle into lower layers in order to be
transported towards the center of the spirals. The intermediate transition zone contains composite
“middlings” particles and is located between the inner and outer zones (Richards and Palmer,
1997).
Figure 2.3 Separation mechanism and primary and secondary flow pattern on a spiral
trough (Richards & Palmer, 1997). Used under fair use, 2012.
According to Luttrell et al. (2007), the above mentioned description of particle separation
fails to recognize two counter-rotating flows that actually present across the spiral profile. These
20 |
Virginia Tech | two rotating flows converge along a line of separation as shown by Figure 2.4. The clockwise
flow in the lower rotation zone is responsible for moving lighter particles towards the outer wall
of the spiral. Heavier particles contained in this flowing stream settle down and are carried
inward towards to the inner side of the spiral trough. The clockwise rotation is responsible for
providing a dense concentrate that is relatively free of light particles. In contrast, the counter
clockwise flow in the upper rotating section stratifies particles along the outer wall according to
density. Unfortunately, some denser particles in the upper flow zone settle against the wall and
are trapped there by rising current of the counter clockwise flow. Studies indicate that these
entrapped high density particles rarely cross from the upper to the lower flow zones and
eventually report with the low density product regardless of density. To eliminate these
entrapped particles, Luttrell et al. (2000) recommends recleaning of primary low-density product
using a secondary stage of spirals.
Figure 2.4 Separation regions across a spiral profile (Luttrell et al., 2007).
Used under fair use, 2012.
21 |
Virginia Tech | 2.2.4 Particle Separation Forces
The forces responsible for particle separation within a spiral trough have been studied by
a number of researchers (Atasoy and Spottiswood, 1995; Kapur and Meloy, 1999; Atasoy, 1987;
Holland-Batt and Holtham, 1992; Luttrell et al., 2000). Forces involved in the particle separation
within the spiral trough include hindered settling, interstitial trickling, centrifugal, frictional,
gravitational, drag and Bagnold forces (Bagnold, 1954; Kapur and Meloy, 1999). Among these,
the Bagnold force is distinctive. Data that shows its existence during particle separation within a
spiral trough was first shown by Holtham in 1992. He concluded that Bagnold forces arises due
to increase in inter particle interaction at high pulp densities and at high shear rates. It was also
found that Bagnold forces weaken at a solid percentage below about 50% (Holtham, 1992). The
Bagnold force is a dispersive force that is directly proportional to the shear rate and square of the
particle diameter. The Bagnold force varies along the depth of the flowing film and, depending
on its magnitude, causes particles to move upward or downward in the flowing film. Studies
show that Bagnold forces are in effect within the inner region of spiral, where particles are in
bed-load motion and the percentage solids are more than 50% (Atasoy and Spottiswood, 1995).
Kapur and Meloy (1999) concluded that amongst all the forces acting on a particle, no single
force dominates the others and, hence, separations are based on differences in the rate of change
of all these individual forces with respect to particle size, shape, density and radial position.
2.2.5 Spiral Design Parameters
Spiral design is critical to effective separation performance and has been the subject of
both experimental and computational studies over the last three decades (Kapor and Meloy,
1998; Holland-Batt, 1989; Holtham, 1990; Stokes, 2000). Primary spiral design parameters
include spiral pitch, diameter, trough slope, length and profile. Secondary design parameters
22 |
Virginia Tech | include wash-water configurations, feed box arrangements, splitters locations, repulper locations
and construction materials. The design process consists of a number of interactive stages and
usually starts with the scale-up, followed by volute shape determination, and finally with a
sanding analysis (Davies et al., 1991; Holland-Batt,1990). Some of the key design variables are
described in greater detail in the following sections.
Pitch and Diameter: The ideal pitch of a spiral trough for a particular feed type is one
that ensures particle fluidity. In general, the pitch is steeper for heavy high-density feed material
and is shallower for light particles (Davies et al., 1991). The diameter of a spiral depends upon
the capacity and the separation size. For a given separation size, the capacity of a spiral is a
function of trough area and it decreases with the particle size (Hollan-Batt, 1985). Due to the low
density and low unit value of coal, spirals used in coal applications have a lower pitch and a
larger diameter than mineral spirals (Luttrell et al., 2007).
Profile: Profile is a very important design parameter for spirals. In particular, the shape
of the inner and flatter section of a spiral controls the migration of high density particles towards
central column. The inner profile terminates and curves steeply upward at the outer side as a
vertical water-retaining wall. The profile is generally designed to give a targeted relative density
of separation, but in practice the profile often represents a compromise between fluidity and
selectivity. Davies (1991) also considered the number and method of product stream divisions
and overall pulp capacity as important parameters that influence the profile design. Optimizing
studies of profile shape, with a focus of material handling aspects, were conducted by Holland-
Batt (1995). This work discussed various profile shapes and concluded that trough shape has a
profound effect on the nature of fluid flow phenomena and, hence, on the separation efficiency
as well. This study concluded that, for a given pitch, one shape will produce excellent metallurgy
23 |
Virginia Tech | but poor material handling behavior, while other shapes may excel at transporting solids but
perform poorly in terms of separation (Holland-Batt, 1995).
Flow length: In addition to pitch and profile, spiral length is a critical parameter that has
been thoroughly investigated by a number of researchers (Davies, 1991; Kohmuench, 2000;
Wildon and MacHunter; 1997; Atasoy and Spottiswood, 1995). Length, which reflects the total
distance over which slurry travels as it passed down a spiral, is normally referenced by the
number of complete 360o turns utilized by the spiral design. This parameter should not be
confused with spiral height, which varies depending on the pitch employed. The aim of these
studies was to optimize, and perhaps standardize, the required number of turns on a spiral for an
efficient separation process for different ores. In early 1960’s, Australian coal spirals employed
as few as two full turns, while modern spirals employ as many as seven turns or more to achieve
the required separation. In general, a minimum of five to six turns are recommended to achieve
maximum separation efficiency (Holland-Batt, 1995). Other research (Weldon and MacHunter,
1997) has suggested that four turns are optimum for most spiral applications and that acceptable
separations can be achieved using even shorter two or three turn spirals, depending on the
density distribution of the feed particles (Figure 2.5). According to Atasoy and Spottiswood
(1995), the optimum length of a coal spiral is a function of feed size. Shorter spirals are more
effective for separation of coarse particles, while longer spirals are better for fine particles.
24 |
Virginia Tech | (DGR = Clean Ash/Feed Ash)
Figure 2.5 Plot for optimum number of spiral turns (showing 4, 5 and 6 turn coal spirals)
(Wildon & MacHunter, 1997). Used under fair use, 2012.
Repulping: The installation of repulpers along the spiral length generally improves the
separation efficiency of mineral spirals. The repulpers reinitiate the separation process by
capturing, mixing and reintroducing the high velocity slurry stream with the relatively sluggish
middling stream. The idea of repulping was introduced based on work originally done by
Holland-Batt in 1995. According to this study, spiral fluid flow reaches steady-state after only
two turns, while mineral recovery slowly continues for up to four or more turns. As a result,
repulpers are generally installed after three or four turns when high density products are removed
through central column. Several spiral manufacturers have introduced designs that have
successfully incorporated repulping (MacHunter et al., 2003). The effectiveness of repulping in
coal applications has drawn mixed opinions. In his PhD dissertation, Kohmuench (2000) argued
that although repulping in coal spirals reduces gravity cut point but is found to be less effective
in improving separation efficiency because the relatively low specific gravity of coal particles
25 |
Virginia Tech | requires more turns to be effectively separated. Holland-Batt (1995) also stated that repulping
can destroy a partial separation occurring with finer material and thus can decrease the separation
efficiency. Similarly, Atasoy and Spottiswood (1995) noted that if a mineral spiral treating 4.0
SG solids requires only one turn for an effective separation, then it can be expected that a coal
spiral will need approximately five or six turns to achieve a good separation.
Construction Materials: The earliest spiral was manufactured from cast iron. This practice
remained unchanged until the 1950’s when fiberglass was introduced as a construction material
for the spiral structure by Ernst Reichert. Until the late 1970’s, rubber was used as a lining
material for spiral trough and for feed and product boxes. Rubber lining was generally effective,
but expensive and difficult to apply to complex shapes. In 1980’s, sprayed polyurethane was
introduced as a lining material. Finally, in 1988, the first mono-polymer spiral was commercially
introduced, which is available in either ceramic or polyurethane. The major advantages of the
mono polymer spiral construction include improved wettability and fluidity and superior
resistance to reagents and to acid and spark attacks. Today, reverse casting is now well
established for the construction of spirals, which made it possible to accurately fabricate feed and
product boxes, splitters, repulpers and other components of the distribution and laundering
system in heavy duty sections (MacHunter et al., 2003).
Feed Box: The spiral feed box is used to introduce the slurry to the spiral trough in a
direction parallel to the walls of the trough. Ideally, the feed box should be hydraulically
designed to provide equilibrium of the flow pattern as early as possible without splashing or
surging. It is also generally accepted that the design of the feed box should facilitate the
distribution of solids evenly throughout the slurry (Holland-Batt, 1995). More recently, however,
some researchers have proposed that selective segregation and distribution of larger particles
26 |
Virginia Tech | towards the inside of the trough may be desirable to reduce unwanted entrapment of dense
particles in the high velocity flow region (Luttrell, 2012).
Product Splitters: In order to make appropriate low-density, middling and high-density
products, spirals are fitted with two adjustable splitters at the discharge end of the spiral. There
are several different types of splitters such as small finger splitters, banana splitters and slide
splitters. Splitters located at the end of the last turn are normally of the pivoting-blade type.
These splitters are placed either on the trough surface or, in some cases, may be embedded in or
positioned exterior to the trough surface. The splitters may be positioned in parallel or offset
slightly to permit total elimination of either the middlings or concentrated products. Multiple
start spirals are linked through a common shaft to control the same splitter positioning. Some
mineral spirals are also equipped with one or more auxiliary splitters to remove separated solids
(Holland-Batt, 1995).
For spiral applications in the coal industry, two splitters are used to separate coal,
middlings and refuse products. Generally, the outer splitter nearer the wall is capable of making
a density cut between 1.55 and 2.0 SG, while the inner splitter nearer the support pole can make
a density cut 1.8 and 2.4 SG (Mikhail et al., 1988). In order to maintain efficiency, a constant
density cut amongst the entire spiral bank should be targeted, which requires the position of the
splitters to be the same for all the spiral units (Luttrell, 2007). Typically, the outer splitter should
be placed to provide an acceptable clean coal product quality, which typically requires a position
of approximately 3 inches from outside wall. Likewise, the inner splitter should be placed to
provide a reject product that is acceptable for discard, which normally requires a splitter position
of approximately 10.5 inches from outside wall. The middlings product resulting from these
positions can be diverted to the clean product, refuse stream or recycled back to feed. Some
27 |
Virginia Tech | spirals have an additional primary refuse splitter, called a cutter, located after three or four turns.
The purpose of the cutter is to remove high density refuse as soon as possible so as to improve
separation efficiency and increase refuse loading capacity.
Ancillary Components: In order to collect products from main and auxiliary splitters,
some form of product receivers are also associated with the spiral assembly. Their designs vary
depending upon the manufacturer and model of spiral. The main characteristics of product
receivers include satisfactory performance in terms of wear resistance, avoidance of splashing of
products and suitable material handling characteristics (Holland-Batt, 1995). Spirals are usually
installed in multiple banks and the necessary ancillaries required for these banks include a frame
to support the spiral bank, main distributors to split feed pulp equally amongst each start and
launders to transport the concentrate, middling and tailing flows. Spiral banks are fed via an
overhead feed distributor which ideally distributes the feed slurry equally and homogenously to
every spiral unit in the bank.
2.2.6 Conventional and Compound Spirals
There are a number of spiral manufacturer around the world. Some manufacturers
incorporate proprietary features into their conventional single-stage spirals and claim that design
improves the separation performance. Studies conducted by Honaker and Wang (1991) evaluated
the separation performance of four conventional single-stage spirals made by different
manufacturers. This investigation concluded that there is a little difference in the separation
performance among all these spiral designs (Figure 2.6). Therefore, it is not surprising that most
manufacturers have instead focused much of their R&D efforts on the development of compound
spiral designs. Compound spirals incorporate two stages of spiral processing in a single spiral
assembly. Typically, compound spirals consist of three or four turns of primary spirals
28 |
Virginia Tech | 2.2.7 Spiral Operating Variables
The separating performance of spirals is greatly influenced by a number of operating
variables that are under the control of the plant operators. In coal preparation plants, spiral
circuits are not often run at their maximum separation efficiency because of poor feed sizing,
incorrect splitter settings, inappropriate solid and volumetric flow rates and uneven feed
distribution (Luttrell et al., 2000). Therefore, to avoid these issues, a brief discussion of how
these operating variables influence spiral performance is provided in the following sections.
Particle Size: There have been conflicting opinions about the optimum particle size
range for coal spiral circuitry. For coal applications, some early researchers were of the view that
the appropriate coal feed size for spirals is 3 x 0.1 mm (Kapur and Meloy, 1999; Davis et al.,
1991), while others suggest that a feed size as broad as 3 x 0.05 mm can be effectively treated by
this technology (Holland-Batt, 1992). Another point of view (Luttrell et al., 2007) is that coal
particles coarser than 1 mm or finer than 0.2 mm are not cleaned as effectively in spirals and
should instead be upgraded by dense medium processes (for plus 1 mm) and froth flotation (for
minus 0.2 mm).
Slurry Flow Rate: For an efficient separation, spirals should be provided with an adequate
and stable slurry flow rate. The optimum slurry flow rate varies according to the spiral diameter.
Typically, for most of the industrial units, the optimum flow rate is between 30-40 gallons per
minute (GPM) per start for a particle size range of 1 x 0.15 mm (Luttrell et al., 2007). A
volumetric flow rate on higher side is maintained for a coarser feeds, while a lower slurry flow
rate is required for a finer feeds (Honaker et al., 2006). At a constant tonnage of dry solids, a
lower flow rate may result in sanding or beaching problems along the spiral trough. A higher
flow can also cause high density particles to report with the water, which reduces the quality of
30 |
Virginia Tech | the low density product by lowering the separation efficiency and increasing the density cut point
(Kohmuench, 2000).
Atasoy and Spottiswood (1995) studied the effect of residence time on the separation
performance of spirals. They concluded that the residence time has a mixed effect on the
separation efficiency of the particles of different densities and size classes. For example,
residence time does not play a significant role in the separation of low-density coarse (3.35 x 1.7
mm) coal particles. In contrast, increased residence time has an unfavorable effect on higher
density (SG > 1.45) particles of the same size class because they tend to move towards the clean
coal stream with time.
Solids Feed Rate: Recent research (Luttrell et al., 2003; 2007) indicates that the density
cut point (SG ) and Ecart Probable (Ep) increases sharply with an increase in the dry solids feed
50
rate to a spiral. As shown in Figure 2.7(a), a decrease in the solids feed rate improves the product
quality (lowers the clean coal ash content), but decreases the recovery of product solids (reduces
the recovery of combustible organic matter). An increase in dry solids feed rate to more than 3
tonnes per hour per spiral start seriously impacts the separation efficiency (Holland-Batt, 1994;
Li et al., 1993). Contrary to this, some spiral manufacturers claim that their spiral designs can
handle a feed rate as high as 4.5 tonne per hour per start without impacting the separation
efficiency (Luttrell, 2012).
31 |
Virginia Tech | Figure 2.7 Effect of dry feed rate on spiral performance (a) on gravity cut-point, (b)
on separation efficiency (Luttrell et al., 2003). Used under fair use, 2012.
Feed Solids Content: At constant feed percent solids, an increase in the feed rate
increases the volumetric flow of slurry down the spiral. This increases the centrifugal force
exerted on the particles, forcing more material to report to the low density product that, in turn,
results in a higher density cut point (Mikhail et al., 1988). As shown in Figure 2.6(b), a similar
relationship between dry feed rate and cutpoint was also reported by Luttrell (2003). If the dry
tonnage is fixed, then an increase in the feed solids content decreases the slurry flow rate and
lowers the specific gravity cut point. For coal applications, this action decreases combustible
recovery and improves clean coal ash (Luttrell et al., 2003). Mikhail (1988) is of the point of
view that feed rate may actually have a greater effect on separation cut point than even splitter
position.
32 |
Virginia Tech | Feed Distribution: The maximum yield from a spiral circuit can only be realized when the
same density cut point is maintained throughout the spiral circuitry. Unfortunately, one of the
common problems faced by coal spirals operated in industrial plants is poor feed distribution.
This problem can create differences in density cut points among different spiral units in a bank
and, in extreme cases, can lead to other operational issues such as beaching and sanding. Poor
feed distribution may also block the feed distributor port, which ultimately causes variations in
the slurry flow rates (Luttrell et al., 2003, 2007).
2.2.8 Spiral Flow Modeling
Although spiral concentrators are considered to be a mature technology, there is still
room for incremental improvements in design. The most likely approach for realizing these
design improvements is through the phenomenological modeling of the fluid flow patterns and
particle interactions that occur during spiral separations. Such fundamental modeling requires the
knowledge of operating variables (e.g., volumetric and dry solid feed rates), spiral design (e.g.,
pitch, diameter and trough shape) and particle properties (e.g., density, size and shape).
A number of researchers have developed spiral models based on mechanistic phenomena
(Holland-Batt, 1989; Atasoy and Spottiswood, 1995; Glass et al., 1999; Holland-Batt and
Holtham, 1992). These models have been used to predict the motion of particles in the flowing
film over the spiral trough surface. The first such model was developed by Holland-Batt (1989).
The model was capable of predicting the dynamics of fluid regimes and estimating particle
distributions across the spiral trough after separation. This model uses the Manning equation to
describe the primary flow in the inner region and the free vortex equation for the outer region
flow (Holland-Batt, 1989). This model is computationally intensive and its output is not directly
suitable for industrial process simulations (Li et al., 1995). The modeling work done by Holland-
33 |
Virginia Tech | Batt was further extended by researchers at JKMRC and their model was capable of predicting
operational performance for a given set of feed characteristics and splitter settings.
More recently, advances in computational fluid dynamics (CFD) and discrete element
modeling (DEM) of particle-particle interactions should ultimately help to completely investigate
the separation process and to design a better spiral geometry. During the last two decades, CFD
modeling in three dimensions has been used to simulate spiral flows (Holtham, 1990; Jancar et
al., 1995; Matthews et al., 1996). The concept of turbulence has also been incorporated into the
spiral modeling (Matthews et al., 1997). One of the most recent and most advanced models for
predicting particle partitioning during spiral separations was developed by Das et al. (2007). This
modified coal spiral model was based on three principal components, i.e., spiral geometry
modeling, fluid flow analysis and equilibrium force balancing for moving particles. This model
successfully predicted the radial equilibrium distribution of particles with respect to specific
gravity and particle size (Das et al., 2007). Nevertheless, while spiral models have provided
much insight related to the mechanics of particle separation, the ability of these fundamental
models to predict actual spiral performance for arbitrary applications remains a difficult task.
Consequently, there is a room for a more realistic analysis that would provide a truly quantitative
multiphase hydrodynamic description of spiral separations (Glass et al., 1999, Das et al., 2007).
Based on insight provided by fundamental modeling, Holland-Batt (1992) came up with
idea of rotating spirals. This research proposed that separation efficiency can be improved by
rotating the downward volumetric flow. It was argued that, in rotating spirals, one or more
additional forces were acting on the flowing film of particles, which results in a better separation
process. It was found that separation efficiency of fine feed particles increases from a spiral flow
34 |
Virginia Tech | that rotated over itself but, unfortunately, little or no improvement was found for the coarser feed
particles (Holland-Batt, 1992).
2.2.9 Spiral Circuitry
Until 1990, little work has been done in the area of optimizing spiral circuitry. This
situation changed rapidly in the 1990’s with the introduction of the compound spiral. The
compound spiral is essentially a two-stage middlings reclean circuit that operates along one
central spiral column (MacNamara et al., 1995, 1996), i.e., a short primary and short secondary
spiral are positioned on the same central tube. After the first stage, the primary reject is removed
through the central column and the primary clean and middlings are repulped and retreated on
the secondary spiral. Advantages of this design include lower density cut points, reduced floor
space, elimination of interstage pumping, and improved recovery (Weldon et al., 1997).
According to Bethell (2003), common spiral circuit configurations are as follows:
• Single stage spiral circuit without recycle.
• Spirals circuitry with middlings only recycles.
• Spiral circuit with clean coal only recycles.
• Spiral circuit configuration having both clean coal and middlings recycle.
Luttrell et al. (1998) used a linear circuit analysis technique to identify the optimum spiral
circuitry for compound spirals. They studied the following four different spiral circuit
configurations:
• Single stage spiral circuit.
• Conventional rougher-cleaner circuit without recycle.
• Modified rougher cleaner circuitry with middlings recycle.
• Rougher with middlings only recleaning.
35 |
Virginia Tech | Out of the above listed spiral circuits, the modified
rougher-cleaner circuit offered the best option for
improved performance, while maintaining a
reasonable circuit load. In the modified rougher-
cleaner spiral circuit, middlings particles from the
cleaner spiral are recycled back to the feed of
rougher spiral as shown by Figure 2.8. This
circuitry not only improves the separation
efficiency, but also reduces the density cut point
(Luttrell et al., 1998). Essentially all of the
compound spirals employed within the coal Figure 2.8 Modified rougher-cleaner
spiral circuit with middlings recycle
industry now use this two-stage configuation to (Luttrell et al., 1999). Used under fair
use, 2012.
reduce the entrappment of dense particles in the
high velocity flow region and to improve the sharpness of separation via the recycling of the
middlings product back to the feed stream.
2.2.10 Spirals for Ultrafine Coal Processing
A recent development related to the use of spirals is the introduction of ultrafine (0.15 x
0.044 mm) coal spiral circuits. In these circuits, deslimed ultrafine coal slurry is introduced to a
conventional spiral at a reduced dry solids feed rate of 0.45 to 0.50 t/hr/start and lower feed
percent solids of 10 to 12% by weight. These ultrafine coal spirals are reported to achieve a cut
point of 1.8 SG and an E value of 0.20. Moreover, the ash contents were reduced from 17.35%
p
to 9.84% and total sulfur from 3.56% to 3.0%. This spiral circuit was designed specifically to
treat oxidized ultrafine coal feed, which is difficult to upgrade by surface-based froth flotation
36 |
Virginia Tech | processes (Honaker et al., 2006). So far, the results suggest that this proprietary circuitry has the
potential to be effectively used to treat well liberated low ash ultrafine coal with high pyrite
contents, but may not suitable for poor feeds having high proportions of middlings or clay
particles (Luttrell et al., 2007).
2.2.11 Spirals for High Sulfur Coal Processing
Spirals are particularly well suited to reduce the sulfur contents of the final product in
coal applications (Zeilinger, 1976). Tavares and Sampaio (1990) reported that a standard LD-9
spiral reduced the clean coal sulfur content to 2.2% from 4.2%. While spirals commonly provide
a reject stream that is rich in sulfur, the absolute removal of sulfur from the clean coal product is
typically rather low in industrial operations. One obvious reason for this is that spirals can only
remove mineral, or pyritic, sulfur and not the organic sulfur associated with the carbonaceous
fraction of the coal. The poorer rejection may also be because spirals are mainly configured for
coal recovery rather than for pyrite removal (Kawarta et al., 2001).
On one hand hydrophobic coal pyrite particles (Oxidized pyrite particles are often
hydrophobic) or partially liberated pyrites often behaves in flotation like pure coal particles and
tend to report to the froth. On other hand spirals exploit the difference between specific gravities
of coal and rock forming minerals, thus the same hydrophobic pyrite particles can be rejected by
spirals because of their relatively high density. A two stage spiral in a rougher cleaner circuit
arrangement was found to improve the coal pyrite rejection by approximately 10% compared to a
single stage spiral (Kawarta et al., 2001). Tavares and Sampaio (1990) were showed that the
sharpness and density of separation increase with the increase in particle size.
37 |
Virginia Tech | 2.3 Teeter-Bed Separators
2.3.1 Introduction
Teeter-bed separators are hydraulic classifiers that have long been recognized as low-cost
and high capacity devices for both classification and density separation. A teeter-bed separator is
used for separating particles by size and/or density using a fluidized bed. A schematic diagram of
a typical teeter-bed separator is shown in Figure 2.9. Recently, many coal preparation plants in
the United States and in Australia have started to use teeter-bed technology as an alternative to
spiral separators for fine coal cleaning (Sarkar et al., 2008). Teeter-bed separators are based on
hindered settling and were originally used for particle size classification. However, if the feed
size distribution is within acceptable limits, these classifiers can be effectively used for the
concentration of particles based on differences in density (Bethell, 1988).
Teeter-bed separators have been manufactured since 1934. It was not until the early
1960’s, however, that this unit was for the first time used for coal recovery from waste piles and
tailings ponds (Drummond et al., 2002). Originally, teeter-bed separators primarily exploited
differences in coal particle size distributions for upgrading, but later developments in the
technology has now made it possible to separate particles primarily on the basis of density
differences. Recently, a new type of teeter-bed separators known as the reflux classifier has been
introduced to the coal and mineral industries. The reflux classifier technology has been reported
to achieve density cut points as low as 1.35 SG, while maintaining good separation efficiencies
that exceed those typically reported for coal spirals (Galvin et al., 2010).
38 |
Virginia Tech | 2.3.2 Particle Settling Theory
A solid particle falling under the influence of gravity in a viscous fluid is acted upon by
three forces, i.e., a downwards acting force of gravity, an upward acting buoyancy force due to
fluid displacement and an upward drag force acting in the direction of fluid flow. According to
Taggart (1945), the free settling of particles predominates if the percentage of solids by weight is
less than 15%. However, with an increase in the proportion of solid in the pulp, the settling rate
of solid particles began to decrease in response to an increase in the interstitial fluid velocity.
This condition, which is known as hindered settling, lower the settling rate compared to free
settling conditions. Littler (1986) states that hindered settling starts when the concentration of
solids in the pulp is about 20%. Under hindered settling conditions, a modified Newton’s law can
be used to determine the approximate falling rate of the particles (Wills and Napier-Munn,
2006). Mathematically, this condition can be represented by:
[2.1]
1/2
𝑣 = 𝑘[𝑑(𝐷𝑠−𝐷𝑝)]
where, is the falling velocity of particles, is the settling constant, d is the diameter of the
falling p𝑣article, D is the particle density D 𝑘a nd D is the pulp density. The hindered settling
S S P
phenomenon minimizes particle size classification and enhances density classification. The
hindered settling ratio between two different falling particles is always greater than the free
settling ratio.
With the increase in number of settling particles, a condition called “quicksand” is
reached. Under this condition, each particle is covered only by a thin layer of water and the
solids are in a state of “full teeter.” Every particle is free to move, but cannot do so without
colliding with other particles, so the particles tend to remain in place such that the mass of
39 |
Virginia Tech | discharged as underflow. Since the size and density of the feed particles are not uniform,
particles are generally segregated according to their mass within the teeter-bed (Luttrell et al.,
2006). The upward flow of fluidization water can be adjusted in such a way that the teeter-bed is
mainly composed of “near-density” particles suspended within the separator. The height of the
fluidized bed is normally controlled by on-line adjustment of the underflow rate using an
actuated valve. A transducer monitors the bed pressure and controls the valve opening and
underflow rate based on a specified set point value. Once steady-state conditions are reached,
small and light feed particles float upward along the rising current of water and report to the
overflow, while relatively coarse and denser particles sink and report to the under flow product.
Since their invention, teeter-bed separators have gone through significant advances in the
fundamental technology. As a result, there are many different classifying units, other than a
teeter-bed, that fall under this category of separator. These include Floatex density separators,
AllFlux separators, CrossFlow™ separators, HydroFloat™ separators and Reflux classifiers.
2.3.3 CrossFlow Separator
In order to maintain a high efficiency, non-turbulent conditions must exist within a teeter-
bed separator (Heiskanen, 1993). In a conventional teeter-bed, changes in flow patterns may
exist due to the introduction of feed into the teeter-bed chamber. This flow disruption can result
in the unwanted misplacement of particles. In order to overcome this problem, a modified teeter
bed known as the CrossFlow separator was designed the Eriez Manufacturing group. Figure 2.10
shows a conceptual diagram of a CrossFlow separator. As shown in this illustration, feed slurry
enters from the side of the CrossFlow unit and flows quiescently across the top of the teeter-bed.
This unique feed arrangement avoids turbulence normally associated with systems in which feed
slurry is injected below the pulp surface and into the center of the teeter-bed.
41 |
Virginia Tech | are too heavy to be carried by the rising teeter water and too light to penetrate the fluidized bed,
accumulate at the top of the teeter-bed. Eventually, more and more particles build up at the
surface of the bed, which forces some low-density coarse particles to enter the teeter bed.
Ultimately, these particles report to underflow along with the high-density particles. This
problem can be partially corrected by increasing the velocity of the fluidization water, but higher
velocities of can cause the misplacement of high-density fine particles. As a result, conventional
teeter-bed separators are inefficient when treating feed streams with a wide particle size
distribution and/or a narrow density distribution. To overcome this shortcoming, the HydroFloat
separator was developed by the Eriez Manufacturing group.
Figure 2.11 shows a conceptual diagram of HydroFloat separator. The HydroFloat is
essentially a teeter-bed separator into which small air bubbles are also introduced into the
fluidization water. If required, frothers and collectors may also be added to the teeter water aid in
bubble production and to render the desired mineral surfaces hydrophobic. The air bubbles attach
to hydrophobic particles within the teeter bed, which effectively reduce their density. Unlike
froth flotation, these bubble-particle aggregates have insufficient buoyancy to rise on their own,
but due to the attached bubbles, are light enough to rise to the top of the top of the teeter bed and
eventually report to the overflow launder. As a result, the HydroFloat combines the high capacity
of a teeter bed with the flexibility of a froth flotation process. The HydroFloat offers many added
advantages such as enhanced bubble particle contacting, better control of particle residence time,
lower cell turbulence and reduced air consumption (Mankosa, et al., 1999, 2003).
HydroFloat separators have been successfully used in phosphate and fine coal processing
operations (Barbee, 2007; Kohmuench et al., 2003; Mankosa et al., 2003). As shown in Figure
2.12, comparative testing of a HydroFloat separator on a deslimed coal (2 x 0.15 mm) provided
43 |
Virginia Tech | Figure 2.12 Test result obtained using 2 x 0.15 mm spiral feed from central Appalachia
(Mankosa et al., 1999). Used under fair use, 2012.
2.3.5 Reflux Classifiers
A reflux classifier is a teeter-bed separator that incorporates closely spaced parallel
inclined plates that accelerate particle movement (Figure 2.13). In terms of functionality, the
inclined plates are analogous to the inclined plates used in lamella thickener technology. For
density separations, the inclined plates help to suppress the effects of particle size and enhance
the separation of particles based on differences in relative density (Nguyentranlam and Galvin,
2004). A full-scale reflux classifier operated at flow rate of 16 tph of dry solids per square meter
of cross-sectional area treating fine (2 x 0.25 mm) coal achieved an overall density cut point of
about 1.7 SG and an E value to 0.15 (Galvin et al., 2004). Reflux classifier has also been used as
P
a dry fine coal cleaner in which air was used as the fluidizing medium.
45 |
Virginia Tech | possible to effectively separate small coal particles on the basis of density, with minimal size
effects, by using a vibrated reflux classifier having air sand dense medium. An overall E value
P
of 0.07 was achieved by dry processing coal (8 x 0 mm) in a semi-batch laboratory test using a
reflux classifier (Macpherson and Galvin, 2010; Macpherson et al., 2011).
2.4 Water-Only Cyclones
2.4.1 Water-Only Cyclone Description
A water-only cyclone (WOC) is a gravity-based separator that has been used in the coal
industry since the 1950's. The major advantage of a water-only cyclone over a dense medium
cyclone is that it does not require any external feed medium (Kim and Kalima, 1998; Patil et al.,
2007). On the other hand, water-only cyclone units are limited in terms of topsize to applications
involving only fine (<3 mm) coal feeds (Weyher and Lovell, 1969; Gottfried, 1978). A typical
water-only cyclone is a variant of hydrocyclone technology. The separator consists of a tapered
conical vessel that is open at its apex and joined from the top to a cylindrical section that
incorporates a tangential feed inlet (see Figure 2.14). The tangential inlet creates a rotating flow
within the unit that induces centrifugal forces that enhance the settling of larger and denser
particles to the cyclone wall and downward out the apex. A plate is fitted to the top of the
cylindrical section and an axially mounted overflow pipe passes through this plate. The overflow
pipe is extended into the body of the cyclone by a short removable section that is called a vortex
finder. The vortex finder prevents the short-circuiting of feed directly to the overflow. Smaller
and lighter particles are transported by the rotating flow to the center of the cyclone and up and
out through the vortex finder.
When feed is introduced tangentially under pressure to a water-only cyclone, the
movements of the particles inside the cyclone slow down because of the wide conical bottom.
47 |
Virginia Tech | This phenomenon creates a crowding of particles at the conical bottom. The crowded mass of
particles assists in developing hindered settling conditions and eventually in the formation of a
dense bed of particles. Thus, the separation process is based on the hindered settling velocity of
particles in a centrifugal field. The lighter particles are unable to penetrate the bed of higher
density material and thus report through the vortex finder and report as overflow, while denser
particles are discharged as underflow from the apex (Flintoff et al., 1987).
Figure 2.14 shows a schematic comparison between a classifying cyclone and a water-
only cyclone. Unlike conventional classifying cyclones, water-only cyclone units have a wide
conical angle and a long vortex finder that extends along the length of the cylindrical body.
Water-only cyclones utilize cone angles up to 120° and more, while classifying cyclones
designed for particle sizing commonly use cone angles of 10° to 20°. 2007. The larger cone
Figure 2.14 Comparison between classifying and water-only cyclone.
48 |
Virginia Tech | and on the size and specific gravity of feed particles. As shown in Figure 2.15, they proposed a
“generalized water distribution plot” that serves as a characteristic plot for the water split from
water-only cyclones. The slope of the plot represents the percentage of feed water reporting to
the overflow.
In a similar study, Majumder et al. (2011) studied the effects of various design and
operating variables on the separation efficiency of water-only cyclones used for fine (0.5 mm x
0) coal cleaning. This study revealed that vortex finder length, vortex finder diameter and cone
angle directly control the average residence time of coal particles inside the water-only cyclone.
It was also concluded that vortex finder diameter is the most sensitive variable among all the
variables studied.
In an earlier study, Kim and Klima (1998) suggested that for proper operation, the cone
angle of a water-only cyclone should be greater than 45°. However, too wide an angle (e.g.,
180°) reduces cyclone efficiency. At concentrations higher than 20% solids, the bypass of dense
particles to the overflow increases and, hence, reduces the separation performance. Cyclone
efficiency can also be enhanced through the use of multistage water-only cyclone circuitry.
Simulations performed by Kim and Klima (1998) indicated that a three-stage recirculating
overflow/underflow circuit can achieve ferrosilicon recoveries of 97% and quartz rejections of
95%.
The separation performance of a water-only cyclone is not only affected by its geometry,
but also depends upon the operating variables. Water-only cyclones are effectively used to
process coal streams finer than 1 mm, but coal feed up to 20 mm upper size have also been tried
on cyclones. Water only cyclones are most effective for a size fraction of 0.5 mm to 0.15 mm.
Particle size fractions finer than 0.15 mm will report to over flow irrespective of their density.
50 |
Virginia Tech | Bethell and Moorhead (2003) also studied the water-only cyclone/spiral circuitry to clean
fine (1 x 0 mm) coal. This study indicated that water-only cyclone and spiral circuits are flexible
and can be configured to operate at a high separating density to maximize carbon recovery or
may also be configured to operate at a low separating density to maximize coal quality. In order
to avoid excessive recycling rates that may occur in such circuitry, they proposed that the circuit
must either be configured with no recycle or with only a spiral middlings recycle. In the case of
treating finer feeds consisting of 0.6 mm top size, spiral middlings as well as clean coal can be
recycled without any fear of excessive recycling rates. However, recycling of both the spiral
clean coal and middlings must be restricted to circuitry where the water-only cyclone separating
density is sufficiently high to keep the recycle rate acceptable.
2.5 Froth Flotation
Conventional density-based separation processes are inefficient when used to upgrade
coal particles finer than about 100 mesh (0.15 mm). Thus, for this size range, froth flotation has
become the most commonly used coal processing technique. Flotation is a physico-chemical
separation process that utilizes differences in the surface “wettability” of coal and unwanted
rock/refuse particles. Figure 2.17 is a schematic diagram of a typical conventional flotation cell.
During operation, hydrophobic coal particles attach to air bubbles and are carried to the surface
and collected as concentrate, while hydrophilic particles remain in the aerated pulp and are
eventually discharged as tailings. A conventional, or mechanical, flotation cell consists of an
agitator and tank. The agitator keeps coal particles suspended and disperses the air bubbles
throughout the pulp. The agitation also provides turbulence within the pulp that promotes
collisions and attachment of hydrophobic particles to the air bubbles.
52 |
Virginia Tech | Flotation is a complex process that involves three phase flow and has been thoroughly
discussed by many authors (King, 1982; Schulze, 1984; Fuerstenau et al., 1985; Harris et al.,
2002; Rao, 2004). The process starts with the selective attachment of particles to air bubbles. The
bubble-particle aggregate rises into a froth phase due to buoyancy forces. Some of large particles
may be detached from the bubbles before reaching the froth. The entrainment of particles in the
water phase that reports to the froth may also occur. Unlike the selective process of flotation,
entrainment is not a selective and is detrimental to the grade of the froth product.
Column flotation is an important development in the froth flotation process. A column
cell consists of a long vertical cylinder into which air is added at the bottom. These cells are not
agitated by any mechanical means. Feed slurry, which is introduced at approximately two-thirds
of the way up along the column height, travels downwards through the column against rising air
bubbles. The selectivity in column flotation is enhanced via the use of water sprays that rinse
entrained mineral matter from the froth concentrate. Figure 2.18 is a schematic diagram that
compares the distribution of water in a conventional and column cell. Ideally, none of the water
from the feed slurry ever reports in the froth concentrate in column flotation. The column
technology was developed as an alternative approach to conventional flotation cells used in
cleaner circuits of mineral plants. Columns also have become increasingly popular for the
upgrading of ultrafine coal particles (Finch, 1995). There are now many types of column
flotation cells commercially available (Finch and Dobby, 1991; Jena et al., 2008). Two of the
technologies most commonly used in the coal industry include the Microcel column developed at
Virginia Tech and the CoalPro column developed by Canadian Process Technologies (CPT).
54 |
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