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Virginia Tech | Master Thesis of Jing Niu
Chapter 4 Conclusion and Future Work
4.1 Conclusion
The results obtained in this study showed that over 99% of dissolved NaCl and MgCl
2
can be removed from artificial produced water in laboratory experiments. This was
achieved in a process involving a single-stage hydrate formation step, followed by a
single-step solid-liquid separation (or dewatering).
1) The CO consumption for the removal of both MgCl and CaCl is much lower
2 2 2
than that for the removal of NaCl.
2) There is no correlation between the TDS of artificial produced water and the
induction time.
3) The results show that the %Reduction of NaCl increases with centrifugation time
and rotational speed (rpm). The removal efficiency with increasing rpm is due to
the increase in the G-force.
4) The %Reduction of NaCl achieved by filtration was substantially larger than
achieved by centrifugation. The %Reduction increased with increasing filtration
time as anticipated.
5) The %Reduction of MgCl was over 99% after filtration.
2
6) The %Reduction of CaCl increased substantially after the hydrate crystals were
2
crushed and filtered. After reducing the particle size further by
grinding, %Reduction reached 90%, indicating that the finer the particle size, the
higher the extent of cleaning.
7) The concentration range of TDS that can be handled by this process is much
larger than the range at which reverse osmosis can be used. Thus, the use of this
new process should help minimize the steps involved in for removing TDS from
produced water.
69 |
Virginia Tech | CHAPTER 3
CONTACT ANGLES OF POWDERS FROM HEAT OF IMMERSION
3.1 INTRODUCTION
Many industrial processes depend on controlling the hydrophobicity of the solids
involved. These include flotation (1-3), wetting (4), filtration (5), adhesion (6) etc. The most
commonly used measure of hydrophobicity is water contact angle (θ) (7-9). It can be readily
measured by placing a drop of water on the surface of a solid of interest, and measure the
angle through the aqueous phase at the three-phase contact. In using this method, known as
sessile drop technique, it is necessary that the solid surface be flat and smooth. To meet
these requirements, a mineral specimen is cut by a diamond saw and polished with an
abrasive powder such as alumina. It is well known, however, that mineral surfaces
particularly those of sulfide minerals undergo significant chemical changes and atomic
rearrangements during polishing. Therefore, it would be more desirable to measure contact
angles directly on powdered samples. Some times, the solids of interest exist only in
powdered form, in which case the sessile drop technique cannot be used for contact angle
measurements. It is also unreliable and impractical to use the conventional contact angle
measurement techniques for the characterization of fine powders such as fillers, pigments
and fibers.
For powdered samples, capillary rise technique is widely used (10-12). In this
technique, a powdered solid is packed into a capillary tubing, one end of which is
subsequently immersed into a liquid of known surface tension. The liquid will rise through
the capillaries formed in between the particles within the tubing. The distance, l, traveled by
the liquid as a function of time t is measured. If one knows the mean radius r* of the
capillaries present in the tubing, he can calculate the contact angle using the Washburn
equation (13, 14):
γ r*tcosθ
l2 = LV [3.1]
2η
98 |
Virginia Tech | where η is the liquid viscosity. One can determine r* with a liquid which completely wets
the powder, i.e., θ=0. One problem with this technique is the uncertainty associated with
determining r*. There is no guarantee that the value of r* determined with a completely
wetting liquid is the same as that determined by a less than completely wetting liquid. Also,
the method of using the Washburn equation gives only advancing contact angles rather than
equilibrium angles.
The Washburn equation is also used in thin layer wicking method (15-16). In this
technique, a powdered sample is deposited on a glass slide and dried. One end of the slide
coated with the dry powder is immersed in wetting liquid, and the rate at which the liquid
rises along the height of the slide is measured.
The contact angle of a powdered sample can also be measured by compressing it into
a pellet. The measured values may vary depending on the roughness and porosity of the
pellet. There is also a concern that the particles in the top layer of a pellet may be deformed
during compression, which may also affect the measurement (17).
Another method of determining the contact angles of powders is to measure the heat
of immersional wetting in various testing liquids, e.g. water, formamide etc. In this
technique, a powdered sample is degassed to remove the pre-adsorbed water and then
immersed in liquid (11, 18-22). In general, the more hydrophobic a solid is, the lower the
heat of immersion in water. Thus, one should be able to obtain the values of contact angles
from the heats of immersion in water. Different investigators use different methods of
calculating contact angles from the heat of immersion (20-22). Some of the methods
reported in the literature used gross assumptions, which may be the source of inaccuracy in
determining water contact angles.
It was the purpose of this chapter to develop a method of determining the contact
angles of powdered talc samples from the values of calorimetric heats of immersion
measurements. It is based on using a more rigorous thermodynamic relation. The contact
angles were then used to determine the surface free energies of the talc samples using the
Van Oss-Chaudhury-Good equation.
99 |
Virginia Tech | 3.2 THEORY
3.2.1 Contact Angles from Heat of Immersion
In the present work, a Microscal flow microcalorimeter was used to measure the heat
effect (h) created when a powdered sample was immersed in liquid. By dividing h with the
i i
total surface area of the sample used in the experiment, one obtains the heat of immersional
wetting enthalpy (-∆H) given in units of mJ/m2.
i
In the wetting experiment, a powdered sample was evacuated before the immersion.
Therefore, the free energy (∆G) of immersion is given by the following relationship:
i
∆G =γ −γ [3.2]
i SL S
where γ is the solid-liquid interfacial tension and γ is the surface free energy of the solid,
SL S
which is in equilibrium with its own vapor.
The enthalpy of immersion (∆H) determined using the heat of immersion
i
measurements can be related to ∆G as follows:
i
d∆G
∆H = ∆G −T i [3.3]
i i dT
p
where T is the absolute temperature. Substituting Eq. [3.2] into Eq. [3.3], one obtains:
( )
( )
d γ −γ
∆H = γ −γ −T SL S [3.4]
i SL S dT
p
One can substitute γ -γ with -γcosθ from Young’s equation to obtain:
SL S L
100 |
Virginia Tech | ∂(γ cosθ)
∆H =−γ cosθ+T LV
i LV ∂T
p
∂γ ∂cosθ
=−γ cosθ+Tcosθ LV +γ [3.5]
LV ∂T LV ∂T
p p
∂γ ∂cosθ
=−cosθγ −T LV +γ T
LV ∂T LV ∂T
p p
where θ is the contact angle.
Since the enthalpy of the liquid (H ) is given by
L
∂γ
H =γ −T LV , [3.6]
L LV ∂T
p
Eq. [3.5] is reduced to:
∂cosθ
∆H = −H cosθ+γ T [3.7]
i L LV ∂T
p
Solving Eq. [3.7] for cosθ, one obtains the following relationship:
1 ∂cosθ
cosθ= γ T −∆H [3.8]
H LV ∂T i
L p
which is a first-order differential equation with respect to cosθ.
There are no analytical solutions for Eq. [3.8]. Numerical solutions are possible,
provided that a value of contact angle is known at one particular temperature. Nevertheless,
Eq. [3.8] can be useful for determining θ from the value of ∆H determined using a
i
calorimeter. For this to be possible, it is necessary to have the values of H , γ and ∂cosθ/∂T
L LV
101 |
Virginia Tech | for a given liquid at a given temperature. The first two are usually available in the literature,
and the temperature coefficient of contact angles can be determined from experiment.
There are several ways of determining temperature coefficient of cosθ. First, one
measures θ on polished talc samples as a function of temperature and determine ∂cosθ/∂T
experimentally. An assumption made here is that although contact angle may change when it
is pulverized, its temperature coefficient may remain the same. Second, the contact angle of
a powdered sample is measured by pressing it into a pellet. Again, the pressed talc sample
may have a different contact angle from that of loose powders. However, its temperature
coefficient may be assumed to remain the same. Third, the contact angles of powdered
samples are measured using the capillary rise technique. This technique gives advancing
rather than equilibrium contact angles. If one uses this technique to determine ∂cosθ/∂T, an
implicit assumption is that the temperature coefficients of the equilibrium and the advancing
angles are the same.
3.2.2 Van Oss-Chaudhury-Good (VCG) Equation
The contact angles obtained from microcalorimetric measurements can be used for
characterizing the talc surface in terms of its surface free energy components. Essentially,
the method of characterizing the talc surface is based on using the Van Oss-Good-Chaudhury
equation (23-25):
( )
( )
1+cos θγ =2 γLWγLW + γ+γ− + γ−γ+ , [3.9]
L S L S L S L
which is useful for determining the surface free energy (γ ) and its components (i.e., γ LW,
S S
γ +, and γ -) on a solid surface. To obtain these values, it is necessary to determine contact
S S
angles of three different liquids of known properties (in terms of γ +, γ -, γ LW) on the surface
L L L
of the solid of interest. One can then set up three equations with three unknowns, which can
be solved to obtain the values of γ LW, γ +, and γ -. Once the values of γ LW, γ +, and γ - are
S S S S S S
known, one can determine the values of γ AB and γ using the following equations:
S S
102 |
Virginia Tech | γ =γLW +γAB
S S S
[3.10]
=γLW +2 γ+γ−
S S S
Thus, the values of γ , γLW, γAB, γ+, and γ− for each talc surface can be determined
S S S S S
using Eqs. [3.9] and [3.10].
3.3 EXPERIMENTAL
3.3.1 Materials
A run-of-the-mine (ROM) talc sample from Montana was received from Luzenac
America. It was crushed to -50 mm using a hand-held hammer. One part was kept for
contact angle measurements using the sessile drop and the Wilhelmy plate techniques on flat
surfaces, while the other part was ground to -150 µm using an agate mortar and pestle. The
ground samples were used for i) heat of immersion measurement using a flow
microcalorimeter and ii) contact angle measurements using the capillary rise technique.
A number of powdered talc samples were also obtained from Luzenac America.
These commercial products were named: i) Yellowstone, ii) Mistron-100, iii) Mistron Vapor-
P, and iv) Select-A-Sorb. These samples were used in the present work as received.
In the present work, four different solvents were used for the heat of immersion
measurements. These include: toluen, n-heptane, formamide and water. All of them were
HPLC grade. Toluen and n-heptane were obtained from Aldrich Chemical Company and,
formamide was purchased from Fisher Scientific. They were dried overnight over 3 to 12
mesh Davidson 3-A molecular sieves before use. All heats of immersion measurements were
conducted using Nanopure water produced from a Barnsted Nanopure II water purification
system. All the glassware was oven-dried for at least 24 hours at 75 oC prior to use. The
syringe, calorimeter cell, fittings and the teflon tubing lines of the microcalorimeter were
cleaned using HPLC grade acetone (Fisher Scientific) after each run. Heat of immersion
experiments were conducted at 20±2 oC.
103 |
Virginia Tech | 3.3.2 Experimental Apparatus and Procedure
Heats of immersion measurements were conducted using a flow microcalorimeter
(FMC) from Microscal, United Kingdom, as shown in Figure 3.1. A schematic diagram of
the microcalorimeter is illustrated in Figure 3.2. A calorimeter cell, made of Teflon, was
placed in a metal block, which was insulated from the ambient by mineral wool. Two glass-
encapsulated thermistors were placed inside the cell to monitor the changes in temperature of
the sample, and two reference thermistors were placed in the metal block outside the cell.
The calorimeter was calibrated by means of a calibration coil, which was placed in the
sample bed. The entire unit was housed in a draft-proof enclosure to reduce the effect of
temperature fluctuations in the ambient.
In each measurement, a talc sample was dried overnight in an oven at 110 oC. A
known amount (usually 0.05-0.15 gram) of the dried sample was placed in the calorimeter
cell, and degassed for at least 30 minutes under vacuum (<5 mbar) at ambient temperature.
The vacuum system consisted of a vacuum pump and a liquid nitrogen vapor trap. The
solvent was then introduced to the calorimeter cell at a steady flow rate of 3.3 ml/h by means
of a syringe micropump, and the heat effect was recorded by means of a strip chart recorder
and a PC. Thermal equilibrium was reached usually 8 to 30 minutes, depending on the
powder and liquid used. The recorded experimental data was analyzed using the Microscal
Calorimeter Digital Output-Processing System (CALDOS). This program enables the
analysis of the calibration and experimental data and converts the raw downloaded data into
the heat of immersion (h).
i
3.4 RESULTS AND DISCUSSION
3.4.1 Surface Area and Particle Size
Table 3.1 gives the values of the BET specific surface area and average particle size
(d ) for the samples used in the present work. The surface area measurements were
50
conducted using a Nova-1000 Surface Area Analyzer (Quantachrome Corporation) with
nitrogen as adsorbate. The value of d was determined by sieve analysis for the Montana
50
talc, while those of the rest of the samples were provided from Luzenac America. Figure 3.3
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Virginia Tech | shows a plot of surface area vs. 1/d . As shown, most of the points are in line suggesting
50
that as the particle size goes down the surface area increases in a linear fashion.
3.4.2 Heats of Immersion
Figure 3.4 shows a typical thermogram obtained from the flow microcalorimeter.
Also shown is a thermogram created calibration purposes. This particular experiment is for
the heat of immersion of a run-of-mine Montana talc sample in water.
Table 3.2 shows the results of the heats of immersion measurements conducted on the
various talc samples using water, formamide, toluene and n-heptane as the test liquids. The
surface tensions and their components for the liquids (γ LW, γ AB, γ +, γ -) are given in
L L L L
Chapter 2 (Table 2.1).
As shown in Table 3.2, the values of heat of immersion enthalpies in water were in
the range from 220-322 mJ/m2. It is interesting that the enthalpy of immersion in water was
related to the particle size of the sample. As shown, it was most negative with the run-of-
mine Montana talc sample (d =63 µm), and the least negative with Select-A-Sorb (d =3.5
50 50
µm). This observation may be related to the fact that the finer the particles, the larger the
aspect ratio. The particles with higher aspect ratios should give lower heats of immersion, as
larger proportions of the surface area are due to the basal plane that is hydrophobic.
The value of heat of immersion enthalpy in water obtained for the run-of-mine
Montana talc is comparable to those reported by Malandrini et al (20) for a variety of run-of-
mine European talc samples. However, the values obtained with very fine talc powders (e.g.
Select-A-Sorb, Mistron Vapor-P) were substantially lower than reported by the same authors
(20). The lower values of heat of immersion enthalpies in water obtained with fine samples
should be attributed to the increased hydrophobicity of talc surface upon grinding.
As shown in Table 3.2, a similar relationship can also be established between the
particle size and the heat of immersion enthalpies for formamide. As shown, the enthalpy of
immersion was most negative with the run-of-mine Montana talc sample (156.7 mJ/m2), and
the least negative with Select-A-Sorb (42.9 mJ/m2). Since formamide is known to be the
most basic polar liquid, the results indicate that the surface acidity of the particles increases
with increasing particle size. It should be pointed out that the heats of immersion obtained
here are substantially lower than those reported by Malandrini et al (20) for formamide. The
105 |
Virginia Tech | discrepancy may be attributed to the differences in origin, particle size, sample preparation
technique etc.
It can also be seen from Table 3.2 that the values of heat of immersion enthalpies for
n-heptane were in the range from 66.4-88.2 mJ/m2. Note that n-heptane interacts only with
the basal surface of talc and the interaction between talc surface and n-heptane is only
through the Lifshitz-van der Waals interaction. Therefore, the heat of immersion given in
terms of mJ/m2 should be more or less the same. The data suggest that the basal surface of
Mistron Vapor-P is most hydrophobic.
3.4.3 Contact Angles From Heat of Immersion
Eq. [3.8] was used to calculate the contact angles of water and formamide on the
powdered talc samples. In using this equation, the values of ∆H given in Table 3.2 were
i
used, while the values of H for water (119.16 mJ/m2) and formamide (107.8 mJ/m2) were
L
taken form the literature (26). The surface tension values were taken from Table 2.1. The
values of ∂cosθ/∂T both for water and formamide were determined by conducting contact
angle measurements as a function of temperature.
Figure 3.4 shows the results of the contact angle measurements for water conducted
on the flat Montana talc specimen using the Wilhelmy plate technique in the temperature
range of 15-25oC. Figure 3.5 shows the results of the same measurements obtained for
formamide. Wilhelmy plate technique gives both advancing and receding angles. For the
powdered samples, the contact angle measurements were conducted using the capillary rise
technique, and the results are given in Figure 3.6 for water and in Figure 3.7 for formamide,
respectively. It is commonly believed that the capillary rise technique gives advancing
contact angles (17). As shown, contact angles decreased with increasing temperature. From
the slope, the values of ∂cosθ/∂T were obtained and are given in Table 3.3 for water and
Table 3.4 for formamide, respectively.
As it can be seen in Table 3.3, for the Montana talc sample, the Wilhelmy plate
technique gave a substantially higher value of ∂cosθ/∂T than the capillary rise technique.
This discrepancy may be explained as follows. It is likely that the flat Montana talc sample
may have more hydrophilic sites exposed on the surface. As has already been discussed in
Chapter 2, the finer a talc sample is, the more hydrophobic it becomes. This was attributed to
106 |
Virginia Tech | the likelihood that talc particles break preferentially along the basal plane, thereby exposing a
larger proportion of the hydrophobic basal planes. Thus, the smaller the particle size, the
more hydrophobic the particles would become, and less strongly the water molecules would
adsorb on the surface. As the temperature increases, the bonding between the water and the
hydrophilic surface should become weaker. Therefore, ∂θ/∂T should be negative, as shown
in the present work. They should become more negative when a talc surface becomes more
hydrophilic. Indeed, the results given in Figure 3.6 shows that ∂θ/∂T becomes increasingly
negative with decreasing θ.
It is interesting to note that the values of ∂cosθ/∂T obtained for formamide are in the
same order of magnitude with those obtained for water. As shown in Table 3.4, the values of
∂cosθ/∂T determined using capillary rise technique were substantially higher than those
obtained using the Wilhelmy plate technique, which is similar to those obtained with water.
The results given in Table 3.4 also suggest that the adsorption strength of the formamide
molecules decreases with decreasing particle size. Therefore, as shown in Figure 3.7, the
slope of ∂θ/∂T becomes less negative with decreasing particle size.
For the reasons given above, it was decided to use the values of ∂cosθ/∂T obtained
using the capillary rise technique rather than those from Wilhelmy plate technique for
calculating water and formamide contact angles (θ) from the values of -∆H using Equation
i
[3.8]. The calculated contact angle values for water are given in Table 3.5, while those
obtained for formamide are given in Table 3.6. Also shown in the tables for comparison are
the values of θ obtained using the capillary rise and Wilhelmy plate methods.
It can be seen from Table 3.5 that the values of water contact angles determined from
the heat of immersion data are in the range of 66 to 78o. These are substantially larger than
the values of 29-59o reported by Malandrini et al (20) for several different European talc
samples at 20 oC. These authors also used the heats of immersion methods. The low contact
angles of the European talc samples agrees with the fact that their heats of immersion values
were larger than those of the North American talc samples measured in the present work.
For example, the European talc samples gave the values of heats of immersion to be in the
range of 311 to 356 mJ/m2, whereas the North American talc samples gave the values as low
as 220 mJ/m2 (for Select-A-Sorb powder). These results indicate that North American talc
samples are more hydrophobic than the European talc. The level of impurities (e.g. chlorite)
107 |
Virginia Tech | found in European talc samples is higher than the North American talc. That should have an
effect on the surface hydrophobicity of talc.
The contact angles obtained from the heat of immersion measurements may be
considered to be equilibrium angles, as was suggested by Spagnolo, et al (21) and Yan, et al
(22). In this regard, they should be smaller than those obtained using the capillary rise
technique. This is actually the case with the Montana talc and Select-A-Sorb samples.
However, the values of contact angles obtained for the Yellowstone, Mistron-100, and
Mistron Vapor-P using the heat of immersion technique are close to those obtained using the
capillary rise technique, which gives advancing angles. The only possible explanation may
be that the surfaces of these samples were smoother and more homogenous than the others, in
which case the difference between advancing and equilibrium angles can be small.
The contact angles given in Table 3.6 for formamide show somewhat different trend.
The advancing contact angle value obtained using capillary rise technique with Montana talc
and Mistron-100 powders are higher than those of equilibrium contact angles obtained from
microcalorimetric measurements. The values of contact angles for the other powders are
close to each other, suggesting the smoothness and homogeneity of these surfaces.
One of the most important advantages of using the heat of immersion technique over
the capillary rise technique is probably that it gives more reproducible results. As shown in
Tables 3.5 and 3.6, the former gave considerably smaller margins of error. It seems that it is
as reproducible as the Wilhelmy plate technique. However, the latter cannot be used for
powdered samples.
The data given in Figure 3.7 shows an interesting trend. As talc samples become
more hydrophobic the θ vs. T plots becomes increasingly flat. With Select-A-Sorb, whose
θ≈90o, the ∂θ/∂T (and, hence, ∂cosθ/∂T) zero. It follows then that Eq. [3.8] is reduced to
∆H
cosθ= − i , [3.11]
H
L
which in turn suggests that heat of immersion (-∆H) should become zero at θ=90o. Eq. [3.9]
i
suggests also that at θ>90o, the heat effect should become endothermic. Spagnolo et al (21)
indeed showed experimentally that the heats of immersion of two fluorinated hydrocarbon
108 |
Virginia Tech | powders in water became endothermic. The two fluorinated hydrocarbons had water contact
angles of 120 and 125o. This finding suggest that water molecules are not bonded strongly at
θ>90o.
3.4.4 Surface Free Energy Components of Talc from Microcalorimetric Measurements
The values of contact angles obtained from microcalorimetric measurements, as given
in Table 3.5 for water and Table 3.6 for formamide, were used for determining the surface
free energies (γ ) of the talc samples and their components (γ LW, γ AB, γ +, γ -) using Van
S S S S S
Oss-Chaudhury-Good equation (Eq. [3.9]). To do this, it was necessary to determine the
contact angles of three different liquids of known properties (in terms of γ +, γ -, γ LW) on the
L L L
surface of the solid of interest. Thus, the values of γ LW, γ +, and γ - could be calculated by
S S S
solving three equations simultaneously.
Table 3.5 and 3.6 give the contact angle values for water and formamide,
respectively. For the calculation, n-heptane was chosen to be the third liquid. However, the
contact angle measurements conducted with n-heptane showed that it completely spreads
over the talc surface, thus yielding a zero contact angle value. Since n-heptane completely
spreads over talc, it was not possible to determine θ from ∆H as we don’t have the value of
i
∂cosθ/∂T. For this reason, the value of γ LW on the talc surface was determined from the
S
value of heat of immersion enthalpies for n-heptane using the equation derived as follows:
Van Oss et al (23, 27-28) showed that the interfacial tension (γ ) at a solid-liquid
SL
interface can be given by the following relationship:
( )
γ =γ +γ −2 γLWγLW + γ+γ− + γ−γ+ [3.12]
SL S L S L S L S L
Substituting Eq. [3.12] into Eq. [3.2], one obtains:
( )
∆G =γ −2 γLWγLW + γ+γ− + γ−γ+ [3.13]
i L S L S L S L
For an apolar liquid interacting with a solid, Eq. [3.13] becomes:
109 |
Virginia Tech | ∆G =γ −2 γLWγLW [3.14]
i L S L
Eq. [3.14] suggests that as the value of γ LW becomes smaller, the Gibbs free energy
S
of immersion becomes also smaller, indicating the surface hydrophobicity of the solid.
Substituting Eq. [3.14] into Eq. [3.3] and differentiating it with respect to
temperature, one obtains,
∂γ ∂ γLW ∂ γLW
∆H =γ −2 γLWγLW −T L +2T γLW S +2T γLW L [3.15]
i L L S ∂T L ∂T S ∂T
which was originally derived by Fowkes (19). This equation allows one to determine γ LW
S
from the values of heat of immersion (-∆H), γ , γ LW, and the temperature coefficients of the
i L L
liquid and solid involved. The temperature coefficients of γ and γ LW are usually available
L L
from the literature, while that of γ LW may be assumed to be zero (19). In using Eq. [3.15],
S
the values of ∂γ /∂T = 0.098 and ∂γLW /∂T =0.098 for n-heptane were taken from the
L L
literature (26). The heats of immersion values (-∆H) for n-heptane were taken from Table
i
3.2.
Table 3.7 shows the values of γ + and γ - obtained by solving Eq. [3.9], along with the
S S
values of γ LW determined using Eq. [3.15]. The values of γ AB and γ given in the last two
S S S
columns of the table were obtained using Eq. [3.10].
As shown, the value of γ - is much higher than the value of γ + for all five talc
S S
samples studied. The results given in this table also suggest that the value of γ - may change
S
from one talc to another, while the value of γ + remains practically constant. Likewise, the
S
surface free energy components obtained from the direct contact angle measurements using
various techniques showed that a talc surface free energy contains both acid and basic
component, the basic component being in the majority (see Chapter 2). Thus, the results
obtained from the microcalorimetric measurements are in good agreement with those
obtained using other methods.
Also shown, the surface free energy of all of the five talc samples studied consists
predominantly of Lifshitz-van der Waals surface free energy component (γ LW). The values
S
110 |
Virginia Tech | of γ AB are small. This explains why the surface of talc is nonpolar or hydrophobic. The
S
results given in Table 3.7 also suggest that the surface free energy (γ ) of talc decreases with
S
decreasing particle size, which is consistent with those observed using other methods, as
reported in Chapter 2.
Furthermore, the results presented in this chapter and also in the previous chapters
suggest that the value of heat of immersion enthalpy in water is strictly dependent on the
surface hydrophobicity (θ ). From this standpoint, a relationship was established between
a
advancing water contact angles measured using various direct measurement techniques (e.g.
capillary rise, thin layer wicking) and, the heat of immersion enthalpies and the surface free
energy parameters of various talc powders. The results are summarized in Figure 3.9, where
the values of heat of immersion enthalpies were taken from Table 3.2, the values of θ were
a
obtained from Tables 2.6 and 2.7 and the values of γ , γ LW, γ -, γ + and γ AB were taken from
S S S S S
Tables 2.10 and 2.12.
Figure 3.9 shows that the value of heat of immersion enthalpy decreases as θ
a
increases. It has to be pointed out that the increase in the value of θ is primarily achieved
a
due to a decrease in the value of γ LW and, hence, a decrease in the value of γ . For example,
S S
γ LW was 31.0 mJ/m2 at θ =82o and further decreased to a value of 17.8 mJ/m2 at θ =89.4o.
S a a
On the other hand, γ AB remained practically constant at the whole contact angle range.
S
According to Figure 3.9, the value of γ - increases, while the value of γ + slightly
S S
decreases with increasing θ . Since the γ AB is given by γAB =2 γ+γ− (Eq. [3.10]), it
a S S S S
should be expected that the value of γ AB should remain unchanged as one of the components
S
in Eq. [3.10] increases, while the other decreases. It may be questioned what really causes an
increase in the value of γ - and a decrease in the value of γ + with increased θ . It has already
S S a
been shown that the area of hydrophobic basal plane surfaces increases and the area of
hydrophilic edge surfaces decreases as the surface becomes more hydrophobic, i.e, θ
a
increases. Therefore, one plausible explanation for the increase in the value of γ - with
S
increased θ would be that the surfaces of basal planes contains predominantly the basic
a
component (γ -), while the edge surfaces contains mainly the acidic component (γ +). This
S S
point will be made clear in the next chapter.
111 |
Virginia Tech | 3.5 CONCLUSIONS
An improved method of determining the contact angles of water and formamide on
powdered samples has been presented in the present work. It is based on measuring the heats
of immersion, and calculating contact angles using a rigorous thermodynamic relation. The
method of calculating contact angles was tested on a series of talc samples from Luzenac
America. The results obtained using the calorimetric method are comparable to those
obtained using the capillary rise technique. However, the calorimetric technique produced
more reproducible results.
The contact angle data obtained from the microcalorimetric measurements have been
used to determine the surface free energies (γ ) and their components (γ LW, γ -, γ +) for five
S S S S
different talc samples from Luzenac America. The results show that the van der Waals
component (γ LW) comprises the largest part of the surface free energy with small acid-base
S
components, which explains the hydrophobic properties of talc. The surface free energy data
also show that all of the talc samples are basic, which suggests that they can serve as
excellent adsorbents for acidic adsorbates.
The data obtained in the present work show that the smaller the particle size, the more
hydrophobic a talc sample becomes. This observation may be attributed to the likelihood
that the small particles have higher aspect ratios, which in turn may be ascribed to the
preferential breakage of talc particles along the basal plane.
The results showed that the surface of talc contains both basic and acidic sites.
However, the number of basic sites is much larger than the number of acidic sites as defined
from the contact angle measurements and by the application of VCG equation.
As a general trend, the γ LW component of surface free energy decreases with
S
decreasing particle size, and so does the value of γ . However, the γ LW component remains
S S
practically constant. A linkage between particle hydrophobicity and surface free energy
components was established. The more the hydrophobic surface is the lower the γ is.
S
3.6 REFERENCES
1. Aplan, F. F., and Fuerstenau, D. W., Froth Flotation, 50th Anniversary Volume, Ed.: D.
W. Fuersteanu, AIME, New York, 1962.
112 |
Virginia Tech | Improving Efficiencies in Water-Based Separators Using
Mathematical Analysis Tools
by
Jaisen N. Kohmuench
Committee Chairman: Gerald H. Luttrell
Department of Mining and Minerals Engineering
(ABSTRACT)
A better understanding of several mineral processing devices and applications was gained
through studies conducted with mathematical analysis tools. Linear circuit analysis and
population balance modeling were utilized to remedy inefficiencies found in a number of popular
mineral processing water-based unit operations. Improvements were made in areas, including
unit capacity and separation efficiency.
One process-engineering tool, known as linear circuit analysis, identified an alternative
coal spiral circuit configuration that offered improved performance while maintaining a
reasonable circulating load. In light of this finding, a full-scale test circuit was installed and
evaluated at an existing coal preparation facility. Data obtained from the plant tests indicate that
the new spiral circuit can simultaneously reduce cut-point and improve separation efficiency.
A mathematical population balance model has also been developed which accurately
simulates a novel hindered-bed separator. This device utilizes a tangential feed presentation
system to improve the performance of conventional teeter-bed separators. Investigations
utilizing the mathematical model were carried out and have predicted solid feed rates of up to 71
tph/m2 (6 tph/ft2) can be achieved at acceptable efficiencies. The model also predicts that the |
Virginia Tech | unfavorable impact of operating at low feed percent solids is severely reduced by the innovative
feed presentation design. Tracer studies have verified that this system allows excess feed water
to cross over the top of the separator without entering the separation chamber, thereby reducing
turbulence.
A hindered-bed separator population balance model was also developed whose results
were utilized to improve the efficiencies encountered when using a teeter-bed separator as a
mineral concentrator. It was found that by altering the apparent density of one of the feed
components, the efficiency of the gravity separation could be greatly improved. These results
led to the development of a new separator which segregates particles based on differences in
mass after the selective attachment of air bubbles to the hydrophobic component of the feed
stream. Proof-of-concept and in-plant testing indicate that significant improvements in
separation efficiency can be achieved using this air-assisted teeter-bed system. The in-plant test
data suggest that in some cases, recoveries of the plus 35 mesh plant feed material can be
increased by more than 40% through the application of this new technology.
iii |
Virginia Tech | ACKNOWLEDGEMENTS
The author wishes to express his deepest thanks and gratitude to Dr. Gerald H. Luttrell
for his guidance and advice during this investigation. The opportunity to work on a project of
such breadth was greatly appreciated as was the freedom allowed the author in completing this
research. The author also wishes to thank the rest of the Luttrell Clan, Kay, Sarah, and Greg, for
their fellowship and friendship.
The author is also grateful to Dr. Greg Adel for his friendship and advice, especially his
counsel in the area of population balance modeling. Thank you also is expressed to Dr. Roe-
Hoan Yoon for his helpful suggestions and recommendations.
A sincere thank you is also expressed to Dr. Mike Mankosa for his friendship and
guidance. His in-field instruction and insight were invaluable. Thanks also to Cathy Mankosa,
his wife, for her continued support and encouragement.
Thanks are also expressed to several companies whose support, both monetary and
otherwise, made this work possible. This gratitude is expressed to Eriez Magnetics, PCS
Phosphate, and the Pittston Coal Management Company. Individual thanks must also be
expressed to Mr. Joe Shoniker, Mr. Fred Stanley and particularly, Mr. Richard Merwin.
The author wishes to acknowledge Wayne and Billy Slusser for their technical advice,
assistance, and instruction. Their effort and ability are greatly appreciated.
The author would like to thank his parents, William and Carolyn Kohmuench, for their
continued support and encouragement. And finally, the author expresses his deepest
appreciation to his wife, and most loyal fan, Kathryn, for her support, encouragement and love.
iv |
Virginia Tech | ORGANIZATION
This dissertation is separated into three major chapters, each addressing a different aspect
of improving efficiency in water-based separations. Chapter 1 discusses alternative circuitry
which can improve overall spiral performance in coal preparation plants. Chapter 2 addresses
the development of an efficient novel hindered-bed classifier. In Chapter 3, the improvements
gained by the addition of air to hindered-bed density separators are discussed.
A great majority of each chapter has been constructed from articles that the author has
published in several journals and proceedings. As a result, there is a literature review and a
reference section for each of the three major chapters in this dissertation. Listed below are the
reference data for the works from which these chapters were constructed.
Chapter 1: Improving Spiral Performance Using Circuit Analysis.
1) Luttrell, G.H., Kohmuench, J.N., Stanley, F.L. and Trump, G.D., 1998. "Improving
Spiral Performance Using Circuit Analysis," SME Annual Meeting and Exhibit, Orlando,
Florida, March 9-11, 1998, Preprint No. 98-161, 8 pp, (accepted on basis of abstract).
2) Luttrell, G.H., Kohmuench, J.N., Stanley, F.L. and Trump, G.D., 1998. "Improving
Spiral Performance Using Circuit Analysis," Minerals and Metallurgical Processing,
November 1998, Vol. 15, No. 4, pp. 16-21, (full peer review).
3) Luttrell, G.H., Kohmuench, J.N., Stanley, F.L. and Trump, G.D., 1999. "An Evaluation
of Multi-Stage Spiral Circuits," Proceedings, 16th International Coal Preparation
Conference and Exhibit, Lexington, Kentucky, April 27-29, 1999, pp.79-88, (accepted on
basis of abstract).
x |
Virginia Tech | CHAPTER 1
Improving Spiral Performance Using Circuit Analysis
1.1 Introduction
Spirals have become one of the most effective and low-cost methods for cleaning 1 mm x
100 mesh coals. Unfortunately, the specific gravity cut-points obtained using spirals are
typically much higher than those employed by the coarse coal dense medium circuits. This
imbalance creates either a loss of clean coal or a decrease in product quality. Also, water-based
separators such as spirals tend to be much less efficient than dense medium devices due to
misplaced coal and refuse. As a result, spirals are often used in multi-stage circuits in which the
clean coal and/or middling streams from primary spirals are rewashed using secondary spirals.
Plant operators are then faced with the decision to either (i) discard the secondary middlings and
sacrifice yield or (ii) retain the middlings and accept a lower coal quality.
Studies carried out at Virginia Tech indicate that a third alternative exists for handling the
middlings problem. This option involves the use of a rougher-cleaner configuration in which the
middlings from the cleaner spirals are recycled back to the feed of the rougher spirals.
Preliminary analyses indicate that this approach can improve separation efficiency (i.e., lower
Ep) while simultaneously reducing cut-point.
1 |
Virginia Tech | 1.2 Literature Review
Since its introduction by Humphreys in the 1940’s (Thompson et al., 1990), spirals have
proved to be a cost effective and efficient means of concentrating a variety of ores. Their
success can be attributed to the fact that they are perceived as environmentally friendly, rugged,
compact, and cost effective (Kapur et al., 1998). During the 1980’s, there had been an increased
interest in recovering coal fines. Since then, spirals have become a common method for the
concentration of 0.1 mm – 3 mm coal. Spirals are able to maintain high combustible recoveries
while treating material too coarse for flotation and too fine for dense media separation.
Nonetheless, coal spiral efficiencies have not been able to match the separation results generally
found in metalliferous concentration processes (Holland-Batt, 1995).
A spiral is comprised of helical conduit of semicircular cross-sections (Wills, 1992).
Feed is introduced at the top of the spiral between 15-45% solids and is allowed to flow
downward. Complex mechanisms, including the combined effects of centrifugal force,
differential particle settling rates, interstitial trickling, and possibly hindered-settling (Mills,
1978), effect the stratification of particles. Generally, high density material reports to the inner
edge of the spiral, while lower density material reports to the highwall of the spiral.
Classification can also occur, predominantly misplacing the coarse, high density particles to the
outer edge of the spiral. The center of the spiral trough contains any middling material present in
the feed. The schematic cross-section seen in Figure 1.1 illustrates this separation. The band of
high density material that forms near the inner edge can be removed through the use of
adjustable splitters. Ep (Ecart Probable) values generally range between 0.10 and 0.15, with cut-
points ranging between 1.70 and 2.00 SG.
2 |
Virginia Tech | Figure 1.1 – Cross-section of a spiral trough flow (Chedgy et al., 1990).
Several improvements in coal spiral performance have been seen over the years. Recent
studies have concentrated on optimizing the number of turns required on a spiral. This effort is
an attempt to standardize the required number of turns needed on a spiral for different ores. As
recent as the 1960’s, Australian coal spirals had as few as 2 full turns, while modern spirals can
employ as many as 7 turns to achieve the required separation (Holland-Batt, 1995).
Improvements in mineral spiral efficiencies have also been noted by Edward, et al.
(1993) after the removal of products and subsequent repulping of the remaining flow after
approximately four spiral turns. Generally, without repulping, the spiral flow can reach steady-
state after only two turns. However, the recovery of the mineral can continue slowly for up to
four or more turns. Repulping the spiral flow after only a few turns can restore the initial high
3 |
Virginia Tech | rate of recovery (Holland-Batt, 1995). Several spiral manufacturers have introduced designs that
have successfully incorporated repulping.
Repulping in coal applications is less effective. When treating coal, the number of
necessary turns increases due to the relatively low specific gravity of the pulp. For instance, if a
mineral spiral, treating 4.0 SG material, requires 2 to 3 turns in order to effectively make a
separation, it can be expected that a coal spiral will need 5 to 6 turns. Repulping after only 3
turns can destroy a partial separation occurring in the finer material which would normally
require 6 turns to complete. In addition, repulpers in mineral spirals add solids and water to the
concentrate zone, while repulpers in coal spiral applications add slurry to the reject zone thereby
decreasing combustible recovery. Holland-Batt (1995) confirmed this in his work, which
showed repulpers do not improve efficiency in coal spiral separations, and can actually decrease
efficiency.
Studies have also shown that the feed rate, especially the total volumetric flow,
introduced onto a spiral can greatly affect the performance of a spiral. Walsh and Kelly (1992)
have stated in their work that the total mass feed rate is among one of the most important factors
for determining coal spiral capacity. Their work goes on to show that for any feed pulp density,
there is an associated optimum feed rate. Further studies by Holland-Batt (1990) show that there
is indeed a performance envelope that is greatly affected by slurry density, and further indicates
that a more dominant control of spiral performance is seen when combining slurry density with
the solids flow rate (i.e., volumetric feed rate). As volumetric feed rate is increased, an increasing
amount of entrained material will report to the outer wall and effectively reduce efficiency.
These misplaced particles find it hard to escape the high velocity flow regimes and ultimately
report to the clean coal product.
4 |
Virginia Tech | Unexpectedly, little or no literature was found in the area of advanced coal spiral
circuitry for the reason of improving separation efficiency. However, there were a few
exceptions. A new process, utilizing rotating spirals, was studied by Holland-Batt (1992). His
studies suggest that by rotating the downward volumetric flow (the spiral flow turns over itself
during its descent), rotating spirals can improve the separation potentials by applying one or
more additional force to the flowing film of particles. These studies were an extension of work
completed in the early 1980’s. Ultimately, it was found that the finer feed particles benefited
from a flow that rotated over itself. Unfortunately, little or no improvement was found for the
coarser feed particles.
Another advance in spiral circuitry was the advent of the compound spiral. The
compound spiral is essentially a two-stage, middlings reclean circuit arranged on one column
(MacNamara et al., 1995, 1996). A short primary and short secondary spiral are positioned on
the same center tube, where a first stage clean and reject product can be removed, after which,
the first stage middlings are repulped and retreated on the secondary spiral. Advantages of this
design include lower cut-points, reduced floor space, elimination of interstage pumping, and
improved recovery (Weldon et al., 1997).
6 |
Virginia Tech | 1.3 Theoretical Framework
1.3.1 Circuit Analysis
Circuit analysis can be used to evaluate the overall effectiveness of various
configurations of unit operations in mineral and coal processing circuits. This powerful tool,
which was first developed and advocated by Meloy (1983), has regretfully seen only limited
application in the analysis of coal processing circuits. Strictly speaking, this method can only be
applied if particle-particle interactions do not influence the probability that a particle will report
to a particular stream. In other words, the partition (or Tromp) curve should remain unchanged
during variations in the characteristics of the feed stream. This assumption is generally valid for
dense medium separations. This may also be a reasonable assumption for water-based processes
such as spirals provided that the changes in feed characteristics are not too large. In fact, circuit
analysis will always provide useful insight into how unit operations should be configured in a
multi-stage circuit, even if the exact numerical predictions are not completely accurate.
Consider the one-stage unit operation shown below. The concentrate-to-feed ratio is
given by:
C/F = P [1.1]
As a result, the mass of particles of a given property reporting to either the concentrate (C) or
refuse (R) streams can be calculated as seen in Figure 1.3:
F
C
C = (P) F
R R = (1-P) F
Figure 1.3 - Analysis of a single-stage separator.
7 |
Virginia Tech | where P is a dimensionless probability function that selects particles to report to a given stream
based on their physical properties. For density-based separations, the probability function can
often be estimated from an S-shaped transition function commonly referred to as the Lynch-Rao
equation (1975), i.e.:
P =
(ea -1)/(ea X+ea
-2) [1.2]
in which X is the SG/SG ratio and a is a sharpness index. Note that the specific gravity cut-
50
point (SG ) is represented by a value of X=1 at which P=0.5.
50
The slope of the probability function evaluated at X=1 can be used to represent the
separation efficiency of the process. The slope is obtained by taking the derivative of the
concentrate-to-feed ratio at X=1. For the Lynch-Rao (1975) equation, this gives:
¶ (C/F)/¶ X = ¶ P/¶ X = a ea / (4-4ea )) [1.3]
However, efficiencies of dense medium separators are more commonly reported in terms of an
Ecart probable error (Ep). Ep values may be calculated directly from the probability function
using the expression:
Ep = SG (X -X ) / 2 [1.4]
50 25 75
where X and X are defined at P=0.25 and P=0.75, respectively. Therefore, the following
25 75
approximation may be used in this case:
¶ (C/F)/¶ X = ¶ P/¶ X » D P/D X = -0.25 SG /Ep [1.5]
50
8 |
Virginia Tech | According to this analysis, the separation efficiency (defined by the slope of the circuit partition
curve) of a rougher-cleaner circuit should be 1.33 times that of the single-stage circuit.
The relative efficiencies of other circuit configurations can be evaluated by circuit
analysis using the same approach. Several of these are summarized in Table 1.1. As shown, the
standard rougher-cleaner (Circuit 2) and rougher-scavenger (Circuit 3) configurations each have
efficiencies 1.33 times greater than the single-stage process. Note that the rougher-scavenger-
cleaner (Circuit 4) configuration incorporating three stages has an efficiency that is twice that of
the single-stage process.
The most common multi-stage spiral circuit used in industry today is the rougher-cleaner
configuration (Circuit 5). However, unlike the circuits discussed above, the cleaner spirals are
used to treat only the middlings from the rougher spirals. The clean coal streams from both
spirals are combined to produce an overall clean product, while both reject streams are discarded.
The circuit is normally configured so that no cleaner middlings are produced and no products are
recycled. Surprisingly, circuit analysis indicates that this configuration is no more efficient than
a single-stage unit. In fact, no improvement in efficiency is obtained even when both the rougher
concentrate and middlings streams are passed to the cleaner spirals (Circuit 6). According to
circuit analysis, the only configurations inherently capable of improving separation efficiency are
those which have product streams that are recycled back to the feed of a previous stage. These
recycle streams are shown as the dotted lines in Table 1.1.
10 |
Virginia Tech | The results of the linear circuit analyses should not be taken to imply that traditional
multi-stage spiral circuits have no value. The primary advantage of these traditional circuits is
that they provide an effective means for reducing the specific gravity cut-point (SG ) below that
50
which may be achieved using a single-stage spiral. Furthermore, the “preferred” configurations
identified by circuit analysis are not practical for spiral circuits due to large circulating loads and
the excessive number of spirals required.
Despite the practical shortcomings of recycle streams, the final configuration (Circuit 7)
included in Table 1.1 does appear to merit further study. In this circuit, both the concentrate and
middlings products from the rougher unit are passed to the cleaner unit. The clean stream from
the cleaner unit is taken as final product, while the cleaner refuse is combined with the rougher
refuse and discarded. The middlings stream from the cleaner spiral is recycled back to the head
of the rougher unit. As shown in Table 1.1, this configuration is capable of an efficiency that is
approximately 1.22 times that of the single-stage circuit. While not as efficient as a “true”
rougher-cleaner circuit, this configuration substantially reduces the amount of material that must
be recycled. In fact, this configuration was found to be the only practical circuit capable of
simultaneously improving separation efficiency while reducing cut-point.
1.3.2 Direct Procedure to Determine Optimum Circuitry
An alternative method exists for investigating these trends not only with respect to
efficiency, but also separation cut-point. Consider the popular coal spiral circuit shown in Figure
1.5. In this circuit, only the middling material is rewashed in the secondary spirals.
12 |
Virginia Tech | M S C = C + C
P P S
C C = F(P )
S P PC
F P C R S C S = M P(P SC)
P M = F(P -P )
P PR PC
R
P
Figure 1.5 - Schematic of middlings reclean circuit.
Similar to the previous section, P , P , and P are the dimensionless probability functions that
PC PR SC
select particles to report to a given stream. Namely, these are the partition values for the primary
spiral clean product, primary spiral refuse product and secondary spiral clean product,
respectively. By simple algebraic substitution described above, the overall concentrate-to-feed
ratio (C/F=P ) at a given specific gravity for this particular circuit can be represented as:
T
P = P + P (P – P ) [1.10]
T PC SC PR PC
Once a partition expression is established for a bank of spirals, Equation [1.10] can be
easily expanded by utilizing a transition function to depict the separations that occur within a
bank or circuit of spirals. A sigmoid equation was used for all of the preliminary calculations,
due to its symmetrical representation of an S-shaped partition (Tromp) curve that will not
"flatten out" at higher specific gravities. According to the sigmoid model, the partition curve for
a density separation may be represented by the following exponential transition function:
P = 1/(1+exp ((SG-SG )/a )) [1.11]
50 s
where P is the partition factor, a is an empirical fitting constant, and SG-SG is the specific
s 50
gravity cut-point of the separation subtracted from the specific gravity of interest. A value of
13 |
Virginia Tech | 0.0911 for a was found to provide a reasonable fit with experimental data available in the
s
technical literature. By substituting the sigmoid partition function for each of the separations
represented in Equation [1.10], the overall partition expression for this circuit now becomes:
P = 1/(1+exp ((SG-SG )/a ))+1/(1+exp ((SG-SG )/a ))*
T 50 s 50 s
PC SC
[1/(1+exp ((SG-SG )/a ))-1/(1+exp ((SG-SG )/a ))] [1.12]
50 s 50 s
PR PC
where SG , SG , and SG are the specific gravity cut-points for the primary spiral clean
50 50 50
PC SC PR
coal, secondary spiral clean coal, and the primary spiral refuse products.
An example of partition data for a two-stage, middlings reclean spiral circuit is shown in
Figure 1.6. This simulated data depict separations where the clean and refuse splitter positions
on the primary spirals are set for specific gravity cuts of a 1.6 and 2.0 SG, respectively. The
inner and outer splitter settings on the secondary spirals are set for an SG of 1.67. The fitting
50
constant (a ) is 0.0911.
s
Suppose the specific gravity in question was at a 1.75 SG. By simple substitution into
Equation [1.12], the partition factor for this circuit can be calculated as 0.390. Simply stated,
only 39% of the 1.75 SG material is reporting to the clean coal launder. If the overall cut-point
of the circuit is needed, then it is only required to sweep through specific gravities until P is
equal to 0.5. The cut-point for this circuit was found to be 1.715 SG. More importantly, these
findings resulted independently of feed washability.
To validate this procedure for directly calculating circuit concentrate-to-feed ratios,
circuit partition factors were calculated both directly and through an iterative simulation
technique, which utilized feed coal washability. This was completed for the middling rewash
circuit described in Figure 1.5. The results can be seen in Table 1.2. For each technique, the
14 |
Virginia Tech | Clearly, as seen in Table 1.2, this alternative method of determining circuit partition
factors is mathematically equivalent to the simulation method which utilized feed coal
washability. The consistency of the directly calculated and simulated partition values verifies
that for any specific gravity cut-point, a circuit partition value can be calculated. This also
indicates that circuit results such as SG , SG , and SG can be ascertained by simply varying
25 50 75
the specific gravity of interest (SG in Equation [1.12]) until the indicated partition value equals
0.25, 0.50, and 0.75, respectively. More importantly, the Ecart Probable Error (Ep) and cut-point
(SG ) of the entire circuit can be determined completely independent of feed coal washability.
50
Naturally, the results will be more accurate provided that a proper transition function is used.
It becomes obvious that Equation [1.12] would be more useful in the form:
ƒ
SG = (P, a , SG , SG , SG ) [1.13]
50 50 50
PC PR SC
where the specific gravity of interest is a function of the circuit partition factor (P), the fitting
constant (a ), and the specific gravity cut-points for the primary and secondary spirals, as
indicated by splitter position. Unfortunately, the complexity of the ensuing mathematical
expressions prevented accomplishment of this task.
Mathematica, a powerful mathematical software package, was utilized in an effort to
achieve this goal. In order to derive an equation for the specific gravity of interest, the term SG
had to be separated from the other variables present in the partition expression (i.e., P and a ).
Mathematica had great difficulty in completing this task, and was only able to successfully
calculate an equation for one of the circuits discussed above. Unfortunately, the form of the
exponential expressions constrained Mathematica to solve for SG using inverse functions. This
16 |
Virginia Tech | made solutions nearly impossible to obtain. On the occasion that Mathematica was successful in
deriving an expression for SG as a function of the remaining variables (i.e., splitter position), the
solution was not unique, and its sheer length made it impractical to use. Some calculated
solutions reached several pages in length. Discussions with several mathematical authorities
confirmed that a practical solution, unique or otherwise, was not possible.
1.3.2.1 Reid Equation
The sigmoid and Lynch-Rao (1975) partition functions were utilized throughout the
preliminary calculations and concept validation to represent density-based separations.
However, a more suitable partition model was needed to accurately depict spiral separations that,
when represented as Tromp curves, tend to be asymmetrical and "flatten out" at higher specific
gravity cut-points. A partition model developed by Reid (1971) was found to provide a
reasonably good fit to experimental data available in the technical literature. This exponential
transition function is given by:
C/F = P = exp{ln(0.5)(SG/SG )m} [1.14]
Reid Reid 50
in which m is an empirical fitting constant.
The Reid transition function is plotted adjacent to actual plant data in Figure 1.7. It
should be noted that the normalized data could not be well fit using either the sigmoid transition
function, or the Lynch-Rao (1975) expression. This is due to the inability of the symmetrical
Lynch-Rao or sigmoid models to fit asymmetrical partition data.
Using the Reid partition function, Equation [1.12] (expression for the circuit shown in
Figure 1.5) can now be rewritten as:
17 |
Virginia Tech | 1.8(a) and 1.8(b). When operating these two-stage circuits, plant operators must decide whether
to discard the secondary middlings and sacrifice yield, or retain the middlings and accept a lower
clean coal quality. The theoretical studies conducted earlier utilizing linear circuit analysis
suggest that a third alternative exists for handling the middlings stream. This option involves the
use of a primary-secondary spiral configuration in which the middlings from the secondary
spirals are recycled back to the feed of the primary spirals. Figures 1.9(a) and 1.9(b) provide
illustrations of these particular configurations.
Table 1.3 highlights key differences between these four circuits. In the case of the
traditional circuit (Figure 1.8(a)), the secondary spirals are used to treat only the middlings
product from the primary spirals. The clean coal streams from both the primary and secondary
spirals are combined to produce a total clean product, while both the primary and secondary
reject streams are discarded. The traditional circuit is normally configured so that the secondary
middlings are sent to the reject stream, although it may also be diverted into the clean coal
product if the quality is acceptable. The modified traditional circuit (Figure 1.8(b)) is similar to
this configuration except that the primary clean coal is also rewashed with the primary middlings
using the secondary spirals. The modified traditional circuit does require more secondary spirals
than the traditional circuit, but may prove beneficial if significant amounts of high ash material
are misplaced into the total clean coal product by the primary spirals. The circuits that
incorporate middling recycle streams (Figures 1.9(a) and 1.9(b)) are essentially identical to the
traditional and modified traditional circuits except that the secondary middlings are passed back
to the primary spiral feed.
19 |
Virginia Tech | Table 1.3 - Description of two-stage spiral circuits.
Figure Circuit Configuration Primary Clean Secondary Middlings
1.8(a) Traditional To Clean To Refuse (or Clean)
1.8(b) Modified Traditional To Secondary To Refuse (or Clean)
1.9(a) Traditional (with Recycle) To Clean To Feed
1.9(b) Modified Traditional (with Recycle) To Secondary To Feed
In order to quantify the improvements gained by utilizing recycle streams, these four
“popular” coal spiral circuits described above were investigated using the direct method of
determining circuit partition values, as described in the previous sections. These circuits were
compared in terms of overall specific gravity cut-point and separation efficiency as defined by
Ep. Microsoft Excel, which can readily solve iterative problems, was used to carry out the
comparisons in a spreadsheet based format. For each test, the primary and secondary spiral clean
and refuse cut-points were varied for all SG combinations between 1.6 and 2.0 SG, inclusive.
50
Although specific gravity cut-points approaching 1.6 SG are considerably difficult if not
impossible to obtain for a given spiral in a typical operation, the theoretical results yield
important insights.
To simulate a circuit with no recycle streams, the clean and refuse specific gravity cut-
points for the secondary spiral (SG and SG , respectively) were held equal. Because both
50 50
SC SR
cut-points were the same, no middlings product was created. In contrast, to simulate a recycle
stream, the cut-points of the secondary unit were allowed to vary, where SG £ SG . For
50 50
SC SR
each variation and circuit, the SG and Ep were recorded and plotted. Figures 1.10(a) and
50
1.10(b) show a typical example of results that were obtained for the circuit shown in Figure
21 |
Virginia Tech | The resultant charts for the circuits seen in Figures 1.8(a), 1.8(b), and 1.9(a) were also
completed, but are not shown here. Instead, for comparison purposes, the lowest possible
specific gravity cut-points and peak efficiencies for each circuit are shown in Table 1.4. It must
be noted that optimization of splitter positions is necessary since the splitter positions that yield
the lowest possible circuit cut-point do not necessarily maximize efficiency (i.e., minimize Ep).
In other words, the results in Table 1.4 are independent of one another. For example, the
modified traditional circuit with recycle is capable of achieving a minimum specific gravity cut-
point of 1.53. This circuit is also capable of maintaining a minimum Ep of 0.094. However,
these two results are generally not obtainable at the same primary refuse and secondary clean
coal splitter positions.
Table 1.4 - Circuit comparisons for Ep and SG using the Reid partition model.
50
Circuit Circuit Label Description Min. Min.
Figure SG Ep
50
1.8(a) Traditional Middling Rewash 1.60 0.105
1.8(b) Modified Traditional Clean & Midds Rewash 1.48 0.128
1.9(a) Traditional w/Recycle Middling Rewash w/Recycle 1.76 0.086
1.9(b) Modified Traditional Clean & Midds Rewash 1.53 0.094
w/Recycle w/Recycle
The results recorded in Table 1.4 indicate several findings. Incorporating a recycle
stream raises the maximum possible efficiency of a circuit by increasing the probability that the
material being treated will report to the correct streams. By adding a recycle stream to the circuit
shown in Figure 1.8(a), the Ep dropped from 0.105 to 0.086. By adding a recycle stream to the
circuit shown in Figure 1.9(a), the Ep dropped from 0.128 to 0.094. These results are indicative
of efficiency increases of approximately 18% and 26%, respectively. However, by adding a
23 |
Virginia Tech | recycle stream, the lowest possible specific gravity cut-point of the circuit will rise slightly due
to the multiple passes of middling material in the circulating load that will now report to the
concentrate.
According to linear circuit analysis, the efficiencies of the traditional and modified
traditional circuits (Figures 1.8(a) and 1.8(b), respectively) should be relatively equal. However,
these results indicate that the modified traditional circuit has a slightly lower maximum
efficiency than the traditional circuit. This is most likely due to the increased loading of near
gravity material on the secondary spiral that is more difficult to treat. Nevertheless, allowing
more material to pass from the primary spiral to the secondary spiral for recleaning lowers the
minimum circuit SG dramatically. For example, without any recycle streams, recleaning the
50
concentrate and middlings (Figure 1.8(b)) from the primary unit lowered the SG of the circuit
50
from 1.60 to 1.48 SG when compared to exclusively recleaning the middlings material (Figure
1.8(a)). This same finding holds true when recycle streams are utilized, as seen in comparing
circuits shown in Figures 1.9(a) and 1.9(b). For these circuits, sending the concentrate and
middlings material to the secondary spiral units yields a potential SG reduction of 23 SG points
50
(i.e., a cut-point of 1.76 versus 1.53).
Though there are advantages to the recycle configurations that incorporate exclusive
rewashing of the middlings from the primary spirals, the greatest advantage comes from utilizing
recycle configurations that rewash both the concentrate and middlings from the primary spirals.
These configurations lower the Ep, but more importantly lower the specific gravity cut-point of
the entire spiral circuit. By bringing the normally high spiral circuit SG closer to the cut-points
50
found in the plant circuits that treat coarser material at greater tonnages, plant yields and
24 |
Virginia Tech | efficiencies become maximized. In addition, the gravities in the more efficient dense medium
circuits can now be incrementally raised resulting in an increase in total plant yield.
1.4 Circuit Testing
1.4.1 Site Description
The Winoc preparation plant located in southern West Virginia was identified as an ideal
site for the installation of a prototype test circuit for the proposed rougher-cleaner spirals with
middlings recycle. The feed coals treated at this plant contain a relatively high proportion of
middlings that tend to make small improvements in efficiency highly profitable.
The plant flowsheet for the spiral circuit is shown in Figure 1.11. The circuit is fed 1 mm
x 100 mesh material from a bank of 38 cm (15-inch) classifying cyclones. Cyclone underflow
travels to a distributor that overflows into six sets of triple-start MDL-4 spirals. The clean coal
and middlings streams from the rougher spirals flow by gravity into a cleaner feed sump. This
material is then pumped up to a second distributor that feeds six sets of triple-start MDL-4 spirals
located on the next floor. The clean coal from the cleaner spirals are taken as final product,
while the reject streams from both the rougher and cleaner spirals are discarded. The cleaner
middlings are allowed to flow by gravity back to the feed of the rougher spiral bank.
25 |
Virginia Tech | Cyclone Feed
(-1 mm)
Cyclones Cleaner
Spirals
To Thickener
Clean
(-100 M)
Coal
Cleaner
Rougher Refuse
Spirals
Sample
Sump/
Point
Pump
Rougher
Refuse
Figure 1.11 – Winoc coal preparation plant rougher-cleaner spiral circuit.
1.4.2 Test Program
Three separate sets of detailed tests were performed to evaluate the circuit. The first run
(Test #1) involved the sampling of the complete rougher-cleaner circuit with partial recycle. In
the second run (Test #2), the splitters on the cleaner spiral were adjusted so as to produce no
middlings stream. The results obtained from this test run would be similar to those obtained
from the widely used traditional rougher-spiral circuit. Finally, a third test run (Test #3) was
performed under the same conditions as the second test run, but at a significantly reduced plant
feed rate. It is well known that reducing the feed tonnage can significantly reduce the SG cut-
point for spirals (Mikhail et al., 1988). Therefore, data from the third run was used to determine
whether the SG cut-point could be more effectively reduced using (i) rougher spirals in series
26 |
Virginia Tech | 1.4.3 Experimental Results
Data from each test was collected and used to construct partition curves for each spiral
configuration. The partition curves for Tests #1, #2, and #3 can be seen plotted in Figures 1.12,
1.13, and 1.14, respectively. Partition curves were constructed for the rougher, cleaner and
combined circuit performance in each test case. The data presented in these figures indicate that
the rougher bank of spirals for each configuration consistently operated at a higher cut-point than
the corresponding cleaner bank of spirals. This dissimilarity was less pronounced in Test #3,
where a significantly lower feed rate was utilized. This outcome is a direct result of the
corresponding decrease in volumetric feed flow rate. A lower volumetric feed flow rate
decreases the effect of the centrifugal force exerted on the slurry particles, resulting in a lower
percentage of material reporting to the clean coal launder. This lower recovery reflects a lower
cut-point.
Figures 1.12, 1.13, and 1.14 also illustrate that the overall efficiency of test circuit #1 is
superior to that of test circuit #2. This is seen when comparing the relative steepness (Ep) of
each of the corresponding combined circuit partition curves. It also appears that the overall
efficiency of test circuit #3 was relatively high in comparison to both test circuit #1 and #2.
Unfortunately, twice as many spirals would be required to obtain this efficiency since Test #3
was conducted at a feed rate half of that utilized in Test #1 or #2.
28 |
Virginia Tech | 1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
Specific Gravity
30
rotcaF
noititraP
Rougher
Cleaner
Combined
Figure 1.14 – Test #3 experimental partition data.
Tables 1.7 and 1.8 summarize the performance data seen in Figures 1.12, 1.13, and 1.14.
The key comparisons are highlighted as bold numbers for each case. The data shown in the first
column of Table 1.7 indicate that a reduction in feed rate (Test #3) reduced the SG for the
50
rougher spirals from 1.95-1.97 down to 1.82. However, this cut-point was still considerably
higher than the 1.63-1.65 SG values obtained using the rougher-cleaner circuits (Tests #1 and
#2). It was possible to achieve SG of 1.55 for Test #3, but only at half of the feed rate (or with
50
twice the number of spirals) used in Tests #1 and #2. These results demonstrate that a greater
reduction in SG cut-point can be achieved with a rougher-cleaner circuit than with a single-
50
stage circuit. Rougher-cleaner circuits are highly recommended for this reason. |
Virginia Tech | Table 1.7 - SG values obtained from the spiral tests.
50
Run Rougher Cleaner Overall
Test #1 1.97 1.66 1.65
Test #2 1.95 1.70 1.63
Test #3 1.82 1.65 1.55
Table 1.8 - Ep values obtained from the spiral tests.
Run Rougher Cleaner Overall
Test #1 0.16 0.25 0.16
Test #2 0.15 0.25 0.20
Test #3 0.17 0.25 0.18
Table 1.8 shows that the Ep values for the rougher spirals remained relatively constant at
about 0.16 + 0.01. The Ep values were even more consistent for the cleaner spirals, although a
worse Ep (i.e., Ep=0.25) was obtained. This suggests that the greater loading of near-gravity
material adversely impacted the shape of the partition curve for the cleaner spirals. As a result,
the overall Ep values for the traditional rougher-cleaner spiral circuit (Test #2) are worse than
those obtained using single-stage spirals. Thus, a portion of the gain achieved by reducing the
cut-point is lost as a result of the lower overall circuit efficiency. On the other hand, data from
the modified rougher-cleaner circuit (Test #1) suggests that good efficiencies (i.e., Ep=0.16) can
be maintained through the use of a middlings recycle stream. It is also worth noting that the ratio
of the Ep values for Tests #1 and #2 is 1.25 (i.e., 0.20/0.16). This value is close to the theoretical
ratio of 1.22 predicted by circuit analysis.
31 |
Virginia Tech | 1.5 Circuit Simulations
Natural variations in the washabilities of the feed coal made it difficult to calculate the
exact improvement offered by the new rougher-cleaner circuit. To overcome this limitation, a
series of partition model simulations were conducted using a fixed set of “typical” washability
data for the plant. This was accomplished by developing regression equations for the
experimental partition curves obtained in each of the three test runs.
To properly simulate both the rougher and cleaner circuits, two different fitting
expressions were required. The most adequate fitting expressions are shown as bold lines in
Figures 1.15 and 1.16 for both the rougher and cleaner circuits, respectively. For the rougher
spiral, the “best fit” to the rougher partition factor (P ) was obtained using the transition function
R
advocated by Reid (1971):
P = exp{-0.693 (SG/SG )m} [1.16]
R 50
in which m is an empirical fitting constant.
Shown in Figure 1.15 is the plant data for the rougher spiral circuit. Also shown are the
“best-fit” curves for the Reid (1971) and popular Lynch-Rao (1975) equations. The rougher
spiral circuit data tended to be asymmetrical. In a spiral separation, material at a lower specific
gravity is efficiently partitioned to the clean coal launder; however, the slightly raised tail is an
indication of how spirals tend to misplace coarse, high density material to the clean coal product
stream. Since the Lynch-Rao equation is a symmetrical transition function, it did not fit the data
well.
Unlike the rougher spiral circuit, the Reid (1971) equation was not an adequate fitting
expression for the cleaner spiral circuit (See Figure 1.16). In this circuit, the increased amount of
32 |
Virginia Tech | near-gravity material caused an even higher lift in tail of the partition data. The near-gravity
material present in the cleaner spiral circuit makes an efficient separation more difficult to obtain
as evidenced by the “flatter” partition data of the cleaner spiral circuit in comparison to the
rougher spiral circuit.
For the cleaner spiral, a modified version of the Reid expression had to be developed in
order to obtain the “best fit” to the cleaner partition factor (P ), , i.e.:
C
P = 1- exp{-0.693 / (SG/SG )n} [1.17]
C 50
in which n is an empirical fitting constant. Equation [1.17] is plotted along with actual plant data
in Figure 1.16. Both the Reid (1971) and Lynch-Rao (1975) equations are also plotted. It can
easily be seen that neither the Lynch-Rao nor the Reid equation adequately fit the data for the
cleaner spiral circuit. The modified Reid expression permits the low gravity portion of the
partition curve to remain relatively steep, while allowing the tail of the partition curve to lift.
Consequently, this equation accurately predicts how a coal spiral will misplace an increased
amount of high gravity and/or middling particles when treating a feed material of a tight specific
gravity range.
33 |
Virginia Tech | Circuit simulations were performed for each of the three test runs using partition factors
obtained from Equations [1.16] and [1.17]. The experimental feed washability data obtained
during Test #2 was used in all of the simulations. Two sets of simulations were conducted. In
the first set, clean coal yield and ash was calculated using the actual SG cut-points from the
experimental runs. In the second set, the SG cut-points were adjusted slightly so that a consistent
product ash of 11.75% was obtained. The simulation results are summarized in Table 1.9.
Table 1.9 - Summary of simulation results.
Simulated Yield Ash Ep Organic
Circuit (%) (%) Efficiency
Using Actual Cut-Points:
Test #1 59.47 11.87 0.15 92.8
Test #2 55.27 11.66 0.19 86.2
Test #3 62.30 13.08 0.17 79.2
Using Adjusted Cut-Points:
Test #1 59.27 11.75 0.15 92.5
Test #2 55.40 11.75 0.18 86.4
Test #3 --- --- --- ---
The simulation results conducted using actual plant cut-points indicate that the rougher-
cleaner circuit with middlings recycle would produce a 59.47% yield at 11.87% ash. This result
compares favorably to the 55.27% yield and 11.66% ash that would be obtained using the
rougher-cleaner without recycle. In contrast, the simulation of Test #3 for the rougher spiral
circuit only (with no recleaning stages) operated under actual plant cut-points produced the
highest yield of 62.30%, but at a relatively high ash of 13.08%. Although the organic
35 |
Virginia Tech | efficiencies for these simulation runs have been reported in Table 1.9, these values cannot be
directly compared because of the variations in clean coal ash content.
In order to improve the comparisons, a second set of simulations was conducted in which
the cut-points for the rougher spirals were adjusted so that a constant clean coal ash of 11.75%
was obtained in each case. Unfortunately, it was not possible to achieve an ash value this low for
the rougher spiral circuit only (Test #3) since it would require a substantial adjustment to the SG
cut-point to a value below that which is realistically achievable. On the other hand, only minor
adjustments to the SG values were necessary to achieve 11.75% ash for the rougher-cleaner
configurations. As shown in Table 1.9, the circuit with the middlings recycle (Test #1) produced
a yield of 59.27% at an organic efficiency of 92.8% compared to a yield of only 55.40% at an
organic efficiency of 86.2% for the circuit with no middlings recycle (Test #2). This represents a
yield increase of 3.87% at the same ash content. For a typical 3-shift operation with a circuit
feed rate of about 40 tonne/hr (44 ton/hr), this represents a revenue increase of approximately
$255,000 annually (i.e., 44 ton/hr x 3.87% x $25/ton x 6000 hr/yr = $255,000). Preliminary
economic analyses show that this additional revenue would offer an attractive payback on the
capital investment required to purchase additional spirals.
Finally, a few comments need to be made regarding the Ep values obtained from the
simulation runs. According to the circuit analyses conducted in the introductory section of this
chapter, the rougher-cleaner circuit with middlings recycle was expected to be 1.22 times more
efficient than the same circuit without a middlings recycle stream. A comparison of the values
reported in Table 1.9 for the circuit simulations shows that an Ep ratio of 1.20 was achieved (i.e.,
0.18 / 0.15 = 1.20). The close agreement between these Ep ratios further supports the use of
linear circuit analysis as an effective tool for evaluating spiral circuit performance. For
36 |
Virginia Tech | 1.6 Conclusions
1. A theoretical study was conducted using linear circuit analysis to evaluate a variety of
different multi-stage spiral circuits. The study suggested that a modified rougher-cleaner
circuit incorporating a middlings recycle stream offered the best option for improving
spiral separation efficiency while maintaining a reasonable circulating load.
2. Linear circuit analysis allowed for the derivation of an alternative method for determining
the partition expression of a given spiral circuit without the requirement of a washability
based simulation. Moreover and more importantly, the efficiency (Ep) and cut-point
(SG ), of a given spiral circuit can be calculated independent of washability provided a
50
proper transition function (i.e., Reid, Lynch-Rao, and/or modified Reid expressions) is
used to simulate the mineral separation.
3. A two-stage spiral test circuit was installed at the Winoc preparation plant located in
southern West Virginia. The test circuit was designed so that a variety of different circuit
configurations could be compared under actual plant conditions.
4. For an equivalent number of spirals, the in-plant spiral test data indicate that rougher-
cleaner circuits operated in series are superior to parallel circuits for reducing the SG .
50
This capability is needed so that the spiral circuit cut-point can be brought into line with
the cut-points realized in the coarse coal dense medium circuits.
5. Test data was used to develop regression equations that were used to simulate the
experimental partition curve data produced during the on-site circuit testing. While a
38 |
Virginia Tech | rougher spiral circuit separation could be simulated using an equation developed by Reid
(1971), a new, modified version of this equation was developed to properly simulate
cleaner spiral circuits that generally treat large amounts of near-gravity material.
6. The in-plant test results also suggest that the SG for rougher-cleaner spiral circuits
50
operated with and without a middlings recycle are very similar (i.e., » 1.65 SG in this
case). However, the separation efficiency (as measured by Ep) was approximately 1.25
times higher for the circuit incorporating a middlings recycle stream. This ratio compares
favorably with the theoretical ratio of 1.22 predicted by linear circuit analysis and a ratio
of 1.20 obtained from partition simulations.
7. Preliminary calculations suggest that the rougher-cleaner spiral with middlings recycle is
capable of increasing circuit yield by 3.86% at the same ash. For a typical plant, this
would represent about $255,000 of additional revenues annually. Economic analyses
suggest that this additional revenue would offer an attractive payback on the capital
investment.
39 |
Virginia Tech | CHAPTER 2
Improving Performance of Hindered-Bed Separators
2.1 Introduction
Hindered-bed hydraulic separators have been used in mineral processing applications for
years. Simply stated, a hindered-bed separator is a vessel in which feed settles against an evenly
distributed upward flow of water or other fluidizing medium. Typically, these devices are used
for size classification, however, if the feed size distribution is within acceptable limits, hindered-
bed separators can be used for the concentration of particles based on differences in density.
A simplified schematic of a typical hindered-bed separator is shown in Figure 2.1. Most
hindered-bed separators utilize a downcomer to introduce feed material to the system. This
material enters the feed zone and may encounter either free or hindered settling conditions,
depending on the concentration of particles in the separator. The settling particles form a
fluidized bed (teeter-bed) above the fluidization water injection point. Material is then
segregated based on terminal, hindered-settling velocities. Slower settling material reports to the
top of the teeter-bed while the faster settling particles descend to the bottom of the teeter-zone.
Specifically, low density and fine material reports to the overflow, while coarse and high density
material report to the underflow. Particles that settle through the teeter-bed enter a dewatering
cone and are discharged through an underflow control valve. The rate of underflow discharge is
regulated using a PID control loop.
42 |
Virginia Tech | Feed
Overflow
Fluidization Water
Underflow
PID
Control
Loop
Figure 2.1 - Schematic diagram of a conventional hindered-bed separator.
More recently, a new hindered-bed classifier separator has been developed that utilizes an
innovative feed presentation system. This device, which is known as the CrossFlow separator, is
shown in Figure 2.2. The CrossFlow utilizes a tangential, low-velocity feed entry system that
introduces slurry at the top of the classifier. This approach allows feed water to travel across the
top of the unit and report to the overflow launder with minimal disturbance of the fluidization
water within the separation chamber. To reduce the velocity of the feed flow, the feed stream
enters a side well before flowing into the separation chamber. The feed then overflows into the
top of the device. Solids settle into the separation chamber as they travel between the feed entry
point and overflow launder. The result of this feed presentation system is the elimination of
excess feed water in the separation chamber, which can adversely effect separation efficiency.
43 |
Virginia Tech | 2.2 Literature Review
2.2.1 General
Hydraulic classifiers are primarily categorized by the method in which the coarse
material is discharged from the separation zone of the unit (Heiskanen, 1993). The first category
is marked by a lack of underflow (or coarse fraction) control. This causes an underflow stream
of such high velocity to occur that no fluidized bed forms and no gradation of particles (by size
and density) manifests. The second group of hydraulic classifiers is marked by an attempt to
control the underflow discharge generally causing the appearance of a teeter-bed. Classifiers can
be further subdivided into mechanical or non-mechanical categories. In mechanical classifiers,
the underflow discharge is removed via mechanical means. In non-mechanical classifiers, the
underflow stream is removed through mass-action and gravity.
The CrossFlow separator is a non-mechanical, hindered-settling, counter-current
hydraulic classifier that utilizes a teeter-bed. There are several other classifying devices that fall
under this description, including the Floatex fluidized-bed classifier (or Floatex Density
(cid:226)
Separator) and the allflux separator. In these classifiers, the underflow rate is restricted and a
teeter-column is formed by solids settling against elutriation water (teeter-water) that is fed
evenly across the entire cross-section of the unit. Generally, coarse particles are graded in order
of decreasing terminal velocity (Heiskanen, 1993), with the coarser particles settling through the
teeter-bed, and the finer particles reporting to the overflow. The high interstitial velocities of
water traveling between the particles in the teeter-bed ensure that there is little bypass of fines to
the underflow. In fact, these types of classifiers often produce very clean underflows
(Schwalbach, 1965).
45 |
Virginia Tech | Typically, teeter-bed classifiers are capable of separations as coarse as 800 microns and
as fine as 75 microns (Littler, 1986). According to Heiskanen (1993), when the separation is
coarser than 800 microns, efficiencies drop dramatically as the separator begins to act as an
elutriator. When separations finer than 100 microns are conducted, low capacities become an
issue. Solid capacities typically range from 10 to 40 tph/m2 (0.85-3.40 tph/ft2) depending on the
cut-point of the separation. Generally, as separations become coarser, the solids capacity
increases, and the opposite is true for finer separations.
Littler (1986) utilized a Floatex hindered-settling classifier and essentially summarized
the effects on classifier performance of operating at different separation cut-points. It is stated
that the Floatex separator is considered to be the most advanced commercial separator for
hydraulic particle classification and is able to treat material whose size is between what would be
considered optimal for either screens (coarse) or hydrocyclones (fine). A schematic of this
device can be seen below in Figure 2.3. As shown, mineral slurry is introduced to the teeter
chamber through a downcomer. A differential pressure cell and discharge valve controls the
bed-level in the unit. According to Littler (1986), there is a discernable drop in efficiency
(normally 80-90%) as the nominal mesh of the separation is increased from 140 to 16 mesh
(U.S). These results reflect the response of the Floatex separator, however, the same general
trend can be found in any hindered-bed classifier.
46 |
Virginia Tech | Improving the sharpness of classification has many benefits. The greatest of these
benefits is the reduction of misplaced material to the product stream. With less misplacement,
more properly sized material (an amount proportional to the total reduction of misplace
material), can now report to the product launder. Littler (1986) goes on to state that improved
classification can be beneficial to closed-circuit grinding, by reducing circulating load and
improving the gradation of material that is treated in other downstream processes (i.e., flotation).
Since the advent of the original hydraulic classifier in 1927 by Fahrenwald (Taggart,
1950), hydraulic separators have been used most extensively in the classification of material
based on hindered-settling phenomena. However, it has been shown that these devices can also
be effectively applied to gravity separations provided that the size distribution of the feed is
within acceptable limits, depending on the application (Heiskanen, 1993). An example of
successful density applications using hindered-bed separators can be seen in fine and coarse coal
processing, (Reed et al., 1995; Honaker, 1996) mineral sands beneficiation (Mankosa et al.,
1995), and the recycling of chopped wire (Mankosa and Carver, 1995). Wills (1992) considers
this gravity concentration component, commonly found in hindered-bed classifiers, an “added
increment.” According to Bethell (1988), the cleaning efficiency of a teeter-bed separator is
limited to a feed size range of 6 to 1 when used as a gravity separation device. This is due to the
fact that when treating wider size distributions, coarse, low density material will be misplaced to
the underflow due to its net greater sizing effect. In the same way, extremely fine, high density
material will report to the overflow irrespective of its overall density. This inherent disadvantage
is further discussed in Chapter 3 of this dissertation.
48 |
Virginia Tech | 2.2.2 Hindered-Settling
In teeter-bed applications, the free settling rates of particles are greatly reduced. This is
in response to the presence of other particles that cause either particle-to-particle collisions
and/or “near-misses” (Littler, 1986). As the size of the particle decreases, the reduction in the
settling rate of that particle increases. According to Littler (1986), the hindered-settling
phenomenon begins to take place at approximately 20% solids by mass. Classification utilizing
hindered-settling is an improvement over free-settling classification due to the fact that less fine
material can become entrapped by coarse particles that settle more slowly through a teeter-bed.
In free-settling applications, coarse material can settle quickly enough to entrain fine particles to
the underflow.
According to Zimmel (1983, 1990) five effects occur as the volume fraction of solids (f )
in a slurry increases. This includes a decrease in the cross sectional area available for the
elutriation fluid (teeter water) which results in an increased net velocity as seen by the settling
particles. The apparent viscosity of the pulp is also increased. This increase of apparent specific
gravity toward the specific gravity of the particles causes a reduction of gravitational force
effects on the individual particles. The last two effects include an increase of wall hindrance
and the occurrence of hydrodynamic diffusion.
The apparent slurry viscosity is very important in determining the hindered-settling
velocities of particles. When treating a slurry containing particles in the size ranges generally
used in mineral processing classification applications, many other factors and variables can also
be significant. The most important factors being the volume concentration of solids, particle size
and particle shape (Heiskanen, 1993). There are various expressions available in the literature
49 |
Virginia Tech | that describes slurry viscosity. Einstein derived the following equation for apparent viscosity
(h ):
h =1+2.5f [2.2]
where f is the fraction of solids by volume. Heiskanen and Laapas (1979) and Laapas (1983)
later went on to modify this formula with an empirical correction as seen below.
h =1+2.5f +14.1f
2+0.00273e16.6f
[2.3]
Rutgers (1962) derived a simple equation for pulp viscosity in the form of the Arrhenius
equation as seen here:
h = h exp(kf ) [2.4]
w
where h is the viscosity of water or other fluidizing medium. The variable, k, is a fitting
w
parameter which has been given values of 5 (John and Goyal, 1975) to 14 (Plitt, 1976). This
equation provides values similar to the equations listed above when k is approximately 5.
In 1989, Swanson suggested this semi-empirical equation:
2f +f
h =h max
w 2( f - f ) [2.5]
max
where f is the highest fraction of solids by volume obtainable for a specific material. An
max
incredible amount of work was found in the literature on determining this variable, f .
max
Disappointingly, most of the conclusions have been empirical in nature.
50 |
Virginia Tech | According to Sudduth (1993), many attempts have been made to predict the optimum size
distribution for packing material, but little work has been completed on determining the exact
value of the attainable maximum fraction of solids (Yu and Standish, 1993). As early as 1930, it
was concluded that size ratios of particle components was an extremely important factor in
determining the maximum packing of solids (Furnas, 1931; Westman and Hugill, 1930). The
most definitive work was completed by McGeary (1961), nevertheless it can be considered
empirical in nature, as it requires direct measurement and is only applicable for ideal spherical
particle systems. However, in his work, the packed density for monosized spherical particles
was approximately 62.5% that of the crystal density of the solid. Sudduth (1993) was able to
match the results summarized by McGeary by utilizing the size ratios of the first to nth size
fraction of a dry mineral sample in determining the maximum obtainable packing of solids.
Sudduth (1993) used an empirical process in choosing the proper value for n.
According to Low and Bhattacharya (1984), the determination of f has been calculated
max
from direct measurements and even graphical estimation. Work in estimating these values was
conducted by Lewis and Nielsen (1969) who concluded that the maximum concentration of
solids was far more accurately determined in air than in water. Another conclusion demonstrated
was that as particles increased in aggregation, the maximum packing of solids decreased. This
was a direct result of a lack of sphericity of the particles.
Other methods for determining the maximum concentration of particles include direct
measurement through sedimentation (Robinson, 1957) and a least square regression of the
experimental data. Essentially, most reliable means of determining f are empirical in nature.
max
According to Yu and Standish (1993), the packing density of the system is affected by
both the solids volumes as well as their particle size distribution. Yu and Standish (1988, 1991)
51 |
Virginia Tech | further demonstrate that linear models can satisfactorily predict the solids packing with the use of
a discrete or simple continuous size distribution. However, recent work by Swanson (1999) in
the area of hindered-settling phenomena advocates the determination of the maximum
concentration of solids through the direct measurement of teeter-bed expansion when
transitioning between a fully settled and fully elutriated state.
In modeling hindered-bed separations, several equations have been developed and
utilized for determining the hindered-velocity of a particle (v). Masliyah (1979) utilizes the
t
expression:
gd2(
r - r
)
( )
v = s f a F a [2.6]
t 18h f
f
where g is the force due to gravity, d is the diameter of the particle, r is the density of the solids,
s
r is the density of the fluidizing medium, a is the suspension voidage (1-f ), and h is the
f f f
viscosity of the fluid. The term F(a ) describes a function that accounts for particle
concentration. Usually, this function is in the form described by Richardson and Zaki (1954).
The above equation is for a laminar flow regime and can be corrected for non-stokes flow
as seen below:
( )
gd2 r - r
v = ( s susp )a F( a ) [2.7]
t f
18h 1+0.15Re0.687
f
where r is the apparent density of the suspension and Re is the Reynolds number (Masliyah,
susp
1979). Reynolds number can be calculated as:
52 |
Virginia Tech | 2.3 Comparative Studies
2.3.1 In-Plant and Laboratory Testing
The CrossFlow concept was originally investigated in the laboratory, by way of a lab-
scale separator. The laboratory setup is shown in Figure 2.4. This laboratory test unit was
constructed out of Plexiglas and has a cross-sectional area of 8 in2 (0.005 m2). The clear nature
of the Plexiglas allowed for the optical determination of varying flow regimes and the presence
of turbulence. A vibratory feeder was used to provide a constant feed flow rate to the separator.
A control loop, consisting of a PID controller, pressure sensor, and underflow pneumatic valve
was employed to maintain a constant bed level within the unit. A traditional downcomer could
be installed, which would allow this lab-scale unit to operate like a conventional teeter-bed
separator.
It was apparent, even at the earliest stages of experimentation, that efficiencies and
capacities for applications using teeter-bed separators could be improved with the CrossFlow
device. The earliest tests compared the conventional teeter-bed separator against the CrossFlow
separator at relatively benign test conditions. These initial investigations were completed using
either passing 14 mesh aggregate limestone or phosphate ore. Feed solids rates ranged from 1.0
to 2.3 tph/ft2 at a feed percent solids of approximately 50%. Figure 2.5 shows the results of these
initial comparative tests. For an array of separation cut-points at the solid feed rates described, it
can easily be seen that the CrossFlow has a tendency to perform slightly better in terms of
separation efficiency. The separation efficiency was defined as either Ecart Probable (Ep) or
Imperfection as calculated in Equations [2.13] and [2.14].
d - d
Ep = 75 25 [2.13]
2
55 |
Virginia Tech | 0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.20 0.30 0.40 0.50 0.60
Separation Cut-Point (mm)
57
pE
CrossFlow
Conventional
Figure 2.5 - Initial comparative test data.
The results shown in Figure 2.5 are representative of a multitude of random tests where
the variables, including feed rate, elutriation water rate, bed-level, and feed percent solids are not
necessarily equal. In an effort to fairly compare this data, points where these variables are
consistent for both separators are graphed below in Figures 2.6 and 2.7.
Figure 2.6 reveals that for tests where all variables are equal, the CrossFlow separator
repeatedly produced classification results higher in efficiency than that realized using a
conventional feed system. It is also interesting to note that the separation cut-point is generally
greater in the conventional separator tests, as seen in Figure 2.7. These results suggest that less
feed water is entering the separation chamber of the CrossFlow unit. In a conventional feed
system, the total volume of feed water is introduced directly into the separation chamber, adding
velocity to the rising current of elutriation water in the upper portion of the classifier. This
increase in velocity can increase the cut-point of the separation. |
Virginia Tech | Only an incremental improvement in efficiency can be seen at the low feed rates utilized
in the initial laboratory tests. Further test work was completed in a north Florida phosphate
beneficiation plant where constant high rates of feed solids could be provided. For these tests, a
2 x 2 ft. (0.6 x 0.6 m) CrossFlow unit was constructed out of steel. Like the lab-scale unit, a PID
controller coupled with an air-actuated underflow valve and pressure sensor was used to control
bed level. In these investigations, the CrossFlow separator was compared to a Krebs Whirlsizer,
which had been previously installed at the plant. Both units were fed from a bank of dewatering
cyclones. Feed percent solids were highly variable, ranging from 20 to 60%.
Results for this test work can be seen in Figure 2.8. In this figure, efficiency
(Imperfection) is shown as a function of solids feed rate. Much like the original laboratory tests,
the CrossFlow separator demonstrated the potential for increased efficiency when compared to
the Whirlsizer. More importantly, the data show that the CrossFlow is less affected by increases
in feed solid rates (especially in excess of 6.0 tph/ft2) than a more traditional water-based
classifier.
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.0 2.0 4.0 6.0 8.0 10.0
2
Feed Rate (tph/ft )
59
noitcefrepmI
Whirlsizer
CrossFlow
Figure 2.8 - CrossFlow and Whirlsizer solids feed rate test comparison. |
Virginia Tech | It can be seen (Figure 2.9) that the CrossFlow unit is able to maintain high levels of
heavy mineral recovery at significantly higher capacities than the identical unit with a more
conventional feed introduction system. Specifically, the CrossFlow unit was able to achieve a
heavy mineral recovery of 95% at a solids feed rate of 23 tph/m2 (1.94 tph/ft2) compared to 13
tph/m2 (1.09 tph/ft2) with the conventional system.
2.3.2 Tracer Studies
In an effort to explain the evident capacity and efficiency improvements of the
CrossFlow feed presentation system over traditional feed systems, tracer studies were conducted.
These studies investigated both the overflow and underflow streams for both “traditional” and
“CrossFlow” feed configurations. The laboratory-scale separator was utilized in this effort. For
comparative purposes, it was important to keep the operating conditions (i.e., solids feed rate,
feed percent solids, elutriation water rate and bed-level) consistent while conducting these tests.
The most important of these variables was volumetric feed rate. It was found that relatively
coarse, dry silica sand could be fed at a constant rate from a vibratory feeder. This, in
conjunction with make-up water flow meters, facilitated a constant volumetric feed to the
separator.
Liquid residence times were calculated using the method advocated by Mankosa (1990).
In this method, a conductivity probe was used to measure the salinity (conductance) of the
overflow stream. Incremental samples of the stream were then taken with respect to time
(seconds) and assayed for concentration (% or ppt) of tracer. The data is normally corrected for
background or residual salinity, and then mathematically normalized with respect to the original
tracer concentration. Plotting time versus normalized concentration yields a response curve from
61 |
Virginia Tech | which the initial tracer concentration can be calculated by summing the area under this curve.
The mean residence time, t , is then calculated from Equation [2.15]:
m
(cid:229) C t D t
t = i i [2.15]
m (cid:229) C D t
i
where C represents the concentration (salinity) at a time increment, t.
i i
In order to determine the non-liquid mean residence times for a particle from the feed
reporting to either the underflow or overflow stream of the separator, a modification had to be
made to this procedure. In determining the mean residence time of solids from the feed that
should report to the overflow, a particle had to be used, whose size and density assured its
appearance in the overflow launder. Likewise, a very dense particle tracer that would settle
through the teeter-bed was needed for determining the mean residence time of the feed solids
that should appear in the underflow launder.
To track solids reporting to the underflow of the separator, a dense, monosized, titanium
mineral sand was used as a tracer. This titanium mineral sand was dense enough to settle against
the upward current of elutriation water. A spike of titanium sand (approximately 100 grams) was
added to the feed stream of the separator. Samples were taken of the underflow stream with
respect to time and assayed for heavy mineral content. The calculated mean residence times for
particles reporting to the underflow stream are summarized in Table 2.1.
It can be seen in Table 2.1 that the mean residence time to the underflow for both the
CrossFlow separator and a conventionally fed hindered-bed separator are nearly identical. Two
tests were conducted for each configuration. There was some disparity between the first and
second tests, which can most likely be contributed to the size of the separation chamber in
conjunction with the rapidity with which the automatic control valve reacted. The PID loop
62 |
Virginia Tech | controller was extremely sensitive to variations in the feed rate, which was magnified by the
small size of the separator. Consequently, as the underflow control valve responded, the internal
flow regimes were altered, varying slightly differently for each test. Nevertheless, the average
values of the mean residence times were relatively consistent. This finding suggests that the
improved efficiency of the CrossFlow separator (i) cannot be attributed to an extended residence
time in the teeter-bed and (ii) may be due to differences in how particles overflow the unit.
Table 2.1 - Mean underflow residence time for CrossFlow and conventional combinations.
Test Mean Residence Time (sec)
No. CrossFlow Conventional
1 33.05 31.23
2 29.66 34.48
Average 31.36 32.86
In order to investigate the behavior of the overflow stream, it was necessary to determine
the retention time of both the water and the solids associated with the feed. This was necessary
since it has been argued that the CrossFlow feed presentation system allows for the rapid
removal of excess feed water from the separator without the entrainment of solids. A salt tracer
(NaCl) was used to track the liquid accompanying the feed and to determine its residence time.
The feed solids reporting to the overflow were tracked using a limestone tracer. The appearance
of the limestone tracer in the overflow was assured due to its small size and lower density. In
each test, the limestone and salt tracers were added at the same time. Similar to the process in
the underflow tracer studies, incremental samples of the overflow stream were then taken with
respect to time (seconds) and assayed for concentration (%).
63 |
Virginia Tech | The mean residence times of the liquid and solids from the feed that report to the
overflow launder are reported in Table 2.2. The solid samples were screened at 50 mesh to
provide a fine and coarse fraction. The data suggest that the CrossFlow system reduces the mean
residence time of the feed water by nearly half. Upon closer examination, it can also be seen that
the solids reporting to the overflow of the CrossFlow separator arrive faster than those in a
conventional hindered-bed separator.
Table 2.2 - Mean overflow residence time for CrossFlow and conventional combinations.
Fraction Mean Residence Time (sec)
CrossFlow Conventional
Water (Salt Solution) 6.08 11.31
Solids (-50 mesh) 14.61 15.94
Solids (+50 mesh) 11.07 17.19
Plotting of the residence time curves for each of the separator configurations shows that
each of the units acts extremely different. These residence time curves for the conventional and
CrossFlow separators can be seen in Figures 2.10 and 2.11, respectively. According to Figure
2.10, feed water takes several seconds to appear in the overflow launder in a conventional
configuration. The water is followed after a short time by the finest material (-50 mesh), and
then the coarsest material (+50 mesh). There appears to be a distinct delay between the
emergence of each tracer in the overflow stream. This suggests that in a conventional hindered-
bed design, a separation is occurring to overflow material prior to its appearance in the launder.
According to the data given in Figure 2.11, there appears to be no separation between the
coarse and fine material reporting to the overflow in the CrossFlow separator. As in a
conventional feed system, the CrossFlow separator allows for the quick removal of liquid
64 |
Virginia Tech | associated with the feed stream. In contrast to the conventional system, the fine and coarse
material reporting to the overflow exits the system at nearly the identical time and with like
mixing, as indicated by the similar curves (Levenspiel, 1962). This lack of separation is
providing the CrossFlow separator with an increased rate of rejection of material that should
report to the overflow. This essentially increases the apparent size (volume) of the device
available for separating a greater number and tighter size range of particles.
In a conventional hindered-bed unit, separator volume is being inefficiently utilized for
the partitioning of material that should report to the overflow. Consequently, a wider size
distribution of particles is being treated, causing an increase in particle interference and
interstitial velocities. Conversely, in the CrossFlow, a greater amount of separator volume is
being utilized for treating a greater number of particles closer to the cut-point of the separation.
The increased amount of closely sized material in the separation chamber should decrease
particle interference and the range of interstitial velocities encountered by any particle within the
system. Essentially, the system becomes more homogeneous and less turbulent.
65 |
Virginia Tech | 2.4 Population Balance Model
2.4.1 Model Description
A mathematical population balance model has been developed at Virginia Tech to help
understand this new tangentially fed hindered-bed separator. This model utilizes general
equations for hindered settling in transitional flow regimes to accurately predict overflow and
underflow partitions, particle size distributions, and component recovery data. Input data include
feed rate, percent feed solids (by mass), feed size distribution (up to 9 size fractions), density of
components in the feed stream (up to 2 components), fluidization water rate, and underflow
discharge rate.
The CrossFlow model was principally constructed as a series of well-mixed zones. These
zones represent three distinct sections that have dissimilar mixing patterns and flow regimes.
Therefore, each section must be modeled accordingly. The three primary sections include the
feed inlet, teeter-bed, and underflow areas. Figure 2.12 depicts these primary sections and flows
for the CrossFlow separator.
The model was constructed using the Microsoft Excel(cid:228) spreadsheet, which is a powerful
engineering tool capable of performing iterative calculations (including compound iterations).
Advantages of using Excel include instant graphing of results, and more importantly, ease of
troubleshooting. Results of tens of thousands of calculations are readily seen in an array of
spreadsheet cells where mistakes and erroneous coding errors are easily seen and corrected.
67 |
Virginia Tech | An experiment with dye was conducted to view the flow patterns in the feed section of
the separator. The Plexiglas lab-scale unit, previously described, was utilized in these
experiments. A photograph of one test run can be seen in Figure 2.14. From this experiment, it
was determined that the feed water predominantly travels in two directions, either across the top
of the classifier, or it is drawn directly down into the separator at the feed inlet point via drag.
The drag created by the settling of the feed solids is responsible for the downward flow. The
influx of solids and the associated liquid hinder the fluidization water from entering into the first
five vertical zones of the feed section. This downward flow (Q ) of liquid induced by the settling
d
solids was determined to be proportional to the total volumetric concentration of settling
particles within that zone as seen in Equation [2.16]. Test work to date indicates that this
proportionality constant (X) has an approximate value of 12-15.
Q = X (U A) [2.16]
d(zone) p zone
where U = hindered settling velocity
p
A = area through which solids settle.
The upward flow of fluidization water that enters each zone is shown as Qx . This flow
n
is counter-acted by both the flow induced by solids settling (Q ) and by the horizontal flows (Q)
d l
that can move to or from adjacent cells. Material suspended within the teeter-bed acts like a
distributor for the rising teeter water, evenly distributing Qx over the entire cross-section of the
n
unit for each level of the feed inlet area. The horizontal flows can be calculated by conducting a
flow balance for each zone within the feed section, given the elutriation water rate (Q ), feed rate
w
(Q), and the underflow discharge rate (Q ).
f u
70 |
Virginia Tech | Start
Input Calculate
Increase time
Operational Apparent by D t:
and Density Viscosity in all
t = t+D t
Data Zones
Input
Separator
Calculate U for
Geometry p
all Size/Density
Classes for all
zones.
Input
Feed Size and
Component Are U P & Re Yes
Distribution Data Self-Consistent for
Calculate Beta Calculate Reynolds All Zones?
Factor for All Zones Number for all Zones
and Size/Density for each Size/Density
Reset time & Classes Class.
Zone
Concentrations
to Zero No - Iterate
Calculate Balance all Zones with
FO lov ine w r T a o el fl e OV teo v rl e u Zrm f olo ne w etr i &c R Zoe ofs nSp ee o fc l oidt r st o a i ln lC / Soo iun zt ec oe /Dn f et er naa scti iho tyn D F Be l aote lw ar nm s Zc fi e on ro ne om e fL Fa F et le o er w dal VD ae lute e Zr s om f noi en r s e F Q eeD d
Classes
Calculate the New
Concentration of Solids
for each Zone
Is the New
Concentration
of Solids for each Zone No
and every Size &
Calculate Partition Density Class Equal
Data to the Old
Concentration?
Yes
Calculate Efficiency
Data
End
Calculate Product
Recovery & Particle
Size Distribution Data
Figure 2.16 – Flowchart illustrating procedure needed to complete the population balance model.
75 |
Virginia Tech | 2.4.3 Model Validation
Over sixty laboratory tests were conducted to validate the population model. A minus 1.5
mm aggregate limestone was used as the testing material. The feed size distribution is provided
in Table 2.3. The validation tests were performed over a wide range of operating conditions.
Feed rates generally ranged from 0.5 tph/ft2 (5.93 tph/m2) to over 6 tph/ft2 (71.2 tph/m2). Feed
percent solids (by mass) ranged from 35 to 65 percent. Various cut-points were obtained by
either raising or lowering bed pressure and/or fluidization water rate. Cut-points ranged from a
low of 0.257 mm to a high of 0.700 mm.
Table 2.3 - Particle size distribution of limestone used in laboratory validation test work.
Particle Size Mass
(Tyler Mesh) (%)
+14 33.76
14 x 20 17.85
20 x 28 13.28
28 x 35 10.34
35 x 48 7.92
48 x 65 5.75
65 x 100 3.50
-100 7.61
It is obvious that settled material would pack closest in the dewatering cone of the
CrossFlow separator where there is no elutriation. It is appropriate that as the cut-point (d ) of
50
the separation changes, so does the size distribution of the underflow stream, and hence the
maximum possible concentration of particles at the underflow (f ). Fine material will
max
generally fill voids that occur between coarser material, but as more fine material reports to the
76 |
Virginia Tech | overflow of a hydraulic classifier, these voids will remain proportionally empty. Yu and
Standish (1993) discuss that both the fractional solid volumes and the particle size distribution
affect the maximum packing density. In their work, it is stated that mathematical models are
only recently relating particle size distribution to packing density; however, these linear models
have been used to accurately predict the packing density of solids provided a simple continuous
or discrete size distribution is available.
The maximum packing of solids was determined semi-empirically. Several laboratory
tests were conducted and subsequently simulated using the CrossFlow model. The f term was
max
varied until the simulated cut-point results were consistent with the laboratory cut-point results.
The d /f relationship was then graphed as shown in Figure 2.17.
50 max
In general, a linear correlation was found to exist between the maximum volumetric
concentration of solids (f ) and the target cut-point (d ). A linear fit to this data yielded an R2
max 50
value of 0.87. The three outlying data points that do not fit this data well, occurred at extremely
high feed rates of over 7 tph/ft2 (83.1 tph/m2). It is believed that, at this feed rate, the separator is
approaching its capacity limit and the necessary increase in fluidization water causes the entire
teeter-bed to act as a fluid, thereby causing deviation from the linear relationship.
Due to the apparent linearity, the f and d relationship can be determined by
max 50
conducting as few as two laboratory control tests. One test must provide a coarse cut-point,
while the other a fine cut-point. Once this relationship is known, it can be incorporated into the
CrossFlow model.
77 |
Virginia Tech | 0.30
0.25
0.20
0.15
0.10
0 1 2 3 4 5 6 7 8
Feed Rate (tph/ft2)
84
noitcefrepmI
0.5 mm Cut-Point
0.35 mm Cut-Point
Figure 2.22 - Effect of solids feed rate on Imperfection.
Efficiency (Ep) is better for the finer separation; however, the imperfection for the
coarser separation tends to be slightly superior. Nonetheless, the average imperfection of both
the coarse and fine separations increases from 0.200 to 0.280 as feed rate increases from 23.76
tph/m2 (2 tph/ft2) to 71.2 tph/m2 (6 tph/ft2). Unlike other hydraulic classifiers, the CrossFlow
separator is capable of high throughput capacities at acceptable efficiencies. Heiskanen (1993)
states that the solids capacities for hydraulic classifiers are only typically in the range of 10
tph/m2 to 40 tph/m2 for fine and coarse separations, respectively.
The effect of feed percent solids (by mass) on Ep and cut-point was simulated at two
different feed rates, 23.76 tph/m2 (2.0 tph/ft2) and 43.82 tph/m2 (3.7 tph/ft2). To complete these
tests, the solids feed rate and fluidization water rate were all held constant. It was also necessary
to hold the underflow volumetric flow rate constant as the feed percent solids were varied from a
low of 20% to a high of 80%. |
Virginia Tech | 2.5 Conclusions
1. Comparative studies completed in the laboratory and in-plant suggested that the
CrossFlow feed presentation system offers several advantages over traditional hindered-
bed separator feed systems. These advantages include increased capacity and separation
efficiency.
2. Solid and liquid tracer studies suggest that the unique feeding system used by the
CrossFlow is capable of rapidly discharging excess feed water and fines that should
report to the overflow. Comparative test work indicates that conventional teeter-bed
separators are less efficient in segregating this overflow material prior to discharge.
3. A mathematical population balance model was developed to simulate the CrossFlow
separator. Validation tests show a good correlation between laboratory results and model
simulations. Consistent results were found for separation cut-point (d ), Ecart Probable
50
(Ep), and Imperfection.
4. A correlation between the target cut-point (d ) and the maximum concentration by
50
volume of solids (f ) was confirmed. This linear relationship appears to vary with
max
material, feed size distribution, and ultimately the cut-point of the separation.
5. The mathematical model has shown that the CrossFlow separator can maintain an
acceptable and less varied efficiency over a number of different operating conditions,
including low feed percent solids (approaching 25% by mass) and feed solids rates in
excess of 6 tph/ft2 (71.2 tph/m2).
88 |
Virginia Tech | CHAPTER 3
Improving Coarse Particle Recovery in Hindered-Bed Separators
3.1 Introduction
Hindered-bed separators are commonly used in the minerals industry as gravity
concentration devices. These units can be employed for mineral concentration provided that the
particle size range and density differences are within acceptable limits. However, these
separators often suffer from the misplacement of low density coarse particles to the high density
underflow. This shortcoming is due to the accumulation of coarse, low density particles that
gather at the top of the teeter bed. These particles are too light to penetrate the teeter bed, but are
too heavy to be carried by the rising water into the overflow launder. These particles are
ultimately forced downward by mass action to the discharge as more particles accumulate at the
top of the teeter bed. This inherent inefficiency can be partially corrected by increasing the teeter
water velocity to convey the coarse, low density solids to the overflow. Unfortunately, the
higher water rates will cause fine, high density solids to be misplaced to the overflow launder,
thereby reducing the separation efficiency.
To overcome the shortcomings of traditional hindered-bed separators, a novel device
known as the HydroFloat separator was developed based on flotation fundamentals. As shown
in Figure 3.1, the HydroFloat unit consists of a rectangular tank subdivided into an upper
separation chamber and a lower dewatering cone. The device operates much like a traditional
hindered-bed separator with the feed settling against an upward current of fluidization water.
The fluidization (teeter) water is supplied through a network of pipes that extend across the
bottom of the entire cross-sectional area of the separation chamber. However, in the case of the
94 |
Virginia Tech | HydroFloat separator, the teeter bed is continuously aerated by injecting compressed air and a
small amount of frothing agent into the fluidization water. The gas is dispersed into small air
bubbles by circulating the water through a high-shear mixer in a closed-loop configuration with a
centrifugal pump. The air bubbles become attached to the hydrophobic particles within the teeter
bed, thereby reducing their effective density. The particles may be naturally hydrophobic or
made hydrophobic through the addition of flotation collectors. The lighter bubble-particle
aggregates rise to the top of the denser teeter bed and overflow the top of the separation chamber.
Unlike flotation, the bubble-particle aggregates do not need to have sufficient buoyancy to rise to
the top of the cell. Instead, the teetering effect of the hindered bed forces the low density
agglomerates to overflow into the product launder. Hydrophilic particles that do not attach to the
air bubbles continue to move down through the teeter bed and eventually settle into the
dewatering cone. These particles are discharged as a high solids stream (e.g., 75% solids)
through a control valve at the bottom of the separator. The valve is actuated in response to a
control signal provided by a pressure transducer mounted on the side of the separation chamber.
This configuration allows a constant effective density to be maintained within the teeter bed.
The HydroFloat separator can be theoretically applied to any system where differences in
apparent density can be created by the selective attachment of air bubbles. Although not a
requirement, the preferred mode of operation would be to make the low density component
hydrophobic so that the greatest difference in specific gravity would be achieved. Compared to
traditional froth flotation processes, the HydroFloat separator offers several important
advantages for treating coarser material, including enhanced bubble-particle contacting,
increased residence time, lower axial mixing/cell turbulence, and reduced air consumption.
95 |
Virginia Tech | 3.2 Literature Review
3.2.1 General
The improved recovery of coarse particles has long been a goal within the minerals
processing industry. An array of studies has been conducted in an effort to overcome the
inefficiencies found in modern processes and equipment. These studies range in scope from
simple force investigation to the introduction of novel equipment. Advancements in chemistry
and conditioning have also been developed and employed at a number of installations.
3.2.1.1 Recovery by Flotation
Research on the relationship between particle size and floatability began as early as 1931
with work conducted by Gaudin, et al. showing that coarse and extremely fine material is more
difficult to treat when compared to intermediate sizes. Twenty years after this original work,
Morris (1952) arrived at the same conclusion, that particle size is one of the most important
factors in the recovery of ores by flotation. An illustration of this trend is seen in Figure 3.2.
Generally, recovery is low for the finest particles (d <20m m), and is at a maximum for
p
intermediate sized particles. A definite decrease in recovery occurs as the particle diameters
continue to increase in size. This reduction in recovery on the fine and coarse ends is indicative
of a reduction in the flotation rate of the particles (Jameson, 1977). It can be seen that the
efficiency of the froth flotation process deteriorates rapidly when operating in the extremely fine
or coarse particle size ranges. This is especially so when operating below 10m m and above
200m m. These findings might suggest that current conventional flotation practices are only
fundamentally optimal for the recovery of particles smaller than 65 mesh.
97 |
Virginia Tech | Research conducted by Schulze (1977) determined that the flotation of a mineral is a
resultant of forces acting on a bubble and particle in a flotation system. These forces include
gravity, buoyancy, hydrostatic pressure, capillary compression, tension, and shear forces induced
by the system. According to Schulze, particles in diameter of several millimeters should float (in
the absence of turbulence) provided the contact angles are in excess of 50°. Later work by
Schulze (1984) shows that turbulent conditions, similar to those found in mechanical flotation
cells, drastically reduce the upper size limit of floatable material. Several other investigations
support these findings (Bensley and Nicol, 1985; Soto, 1988). This research has demonstrated
that turbulent conditions reduced the maximum floatable size to one tenth of that found in non-
turbulent conditions (Ives, 1984; Ahmed and Jameson, 1989).
The recovery of fine and intermediate sized particles is a product of two phenomena,
flotation and entrainment. However, coarse material is recovered solely by genuine flotation
(Trahar, 1981). The low recovery of coarse particles can be attributed to several factors.
Robinson (1959) observed that when coarse and fine particles are combined in one system, the
result is a low surface coverage of collector on all particles in response to the magnitude of
surface area generated by fine material. Generally, a lower floatability is realized for the coarser
particles. Unlike fine material, coarse particles are not as capable of floating at low collector
dosages. Data also suggest that when a soft mineral is attritted, overall particle surface area is
substantially increased by the presence of slimes. This causes a considerable increase in reagent
consumption and a reduction of floatability in some ores (Soto and Iwasaki, 1986).
Another theory is that small particles have a higher rate of flotation and, therefore, crowd
out coarse particles from the air bubbles. Soto and Barbery (1991) disagree with this assessment,
speculating that the poor recovery of coarse material is strictly a result of detachment. They
99 |
Virginia Tech | further advocate the use of separate circuits for fine and coarse processing in an effort to
optimize the conditions necessary for increased recovery.
Several new devices have been produced and tested for the sole purpose of improving the
recovery of coarse particles. Harris, et al. (1992) tested a hybrid mechanical flotation column,
which is essentially a cross between a conventional cell and a column flotation cell. In this
device, a column is mounted above an impeller type agitator. The column component offers the
advantage of an upper quiescent section optimal for flotation, while the mechanical impeller
offers the ability of reattachment and increased collection of any non-attached coarse material in
the lower zone. When compared to a release analysis curve, this hybrid mechanical column out-
performed a conventional flotation cell, but was equivalent to a traditional flotation column.
Improvements in coarse particle recovery have also been seen with the advent of non-
mechanical flotation cells. Success has been observed when using column flotation (i.e., Flotair,
Microcel, and CPT cells), Lang launders, Skin flotation, and the negative-bias flotation column.
Column flotation offers several advantages that can be useful in any application. Barbery (1984)
advocates that columns have no mechanical parts, easy automation and control, low turbulence,
easy bubble size control, simple flow patterns, well-defined hydrodynamic conditions and high
throughput. These advantages translate to ease of maintenance, scale-up, modeling, and a
reduction of short-circuiting usually witnessed in conventional flotation.
3.2.1.2 Recovery by Gravity Concentration
Water-based gravity concentration devices are used extensively throughout the minerals
industry to concentrate high density particles from a mixture of high and low density material.
Although many devices have been developed over the years, a technique gaining in popularity is
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Virginia Tech | hindered/fluidized-bed separators. These separators, traditionally used for classification, work
reasonably well for mineral concentration if the particle size range and density difference are
within acceptable limits (Bethel, 1988; Mankosa et al., 1995; Reed et al., 1995).
Separators, such as coal spirals and water-only cyclones, have been widely used in the
coal preparation industry to upgrade coal feeds in the intermediate particle size range (e.g., 2 x
0.15 mm). Particles of this size are generally too small to be handled in conventional dense
medium circuits and too coarse to be efficiently recovered by froth flotation circuits.
Unfortunately, water-based separators often provide lower separation efficiency when compared
to other plant circuits. For example, while water-only cyclones tend to misplace significant
amounts of larger, low-ash coal particles to the reject stream, spirals tend to misplace coarse,
high ash particles to the clean coal stream. Spiral circuits also generally suffer from high
specific gravity cut-points, however they also tend to maintain high combustible recoveries. As a
result, water-based separators are often used in multi-stage circuits in an attempt to deal with
misplaced coal or rock (as described in Chapter 1).
A great deal of research has been devoted to the study of fluidized-beds and their use in
gas/solid contacting and in liquid/solid applications. Studies describing the latter have typically
focused on the classification aspects of fluidized-bed separators and less so on mineral
concentration. Recent work has shown that fluidized-bed separators can be used to effectively
separate mineral assemblages that have components with different densities. For instance, coal
can be separated from ash forming components (Honaker, 1996), silica from iron ore, and silica
from various heavy minerals such as zircon and ilmenite (McKnight et al., 1996). Results from
these studies indicate that efficient concentration can be achieved if the particle size ratio (top
size to bottom size) is less than 3 or 4 to 1 and in a range from 200 mesh to several millimeters.
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Virginia Tech | Unfortunately, this is seldom the case and, as a result, separation efficiency is poor. To correct
this shortcoming, the valuable component (i.e., coal, iron ore, ilmenite and zircon) frequently
must be reprocessed to achieve the desired quality.
As stated previously, a hindered-bed separator is a vessel in which water is evenly
introduced across the base of the separator and rises upward. The separator typically has an
aspect ratio of two or more and is equipped with a means of discharging solids through the
bottom of the unit. Rising water and solids flow over the top of the separator and are collected in
a launder. Solids are typically introduced in the upper portion of the vessel and begin to settle at
a rate defined by the particle size and density. The coarse, higher density particles settle against
the rising flow of water and build a bed of teetering solids. This bed of high density solids has
an apparent density much higher than the teetering fluid (i.e., water). Since particle settling
velocity is driven by the density difference between the solid and liquid phase, the settling
velocity of the particles is reduced by the increase in apparent density of the teetering bed. As a
result, the low density component of the feed resists penetrating the bed and remains in the upper
portion of the separator where it is transported to the overflow launder by the rising teeter water.
Hindered-bed separators are also well recognized as low turbulence devices. For this
reason, they are used extensively for particulate processing as either gas/solid or liquid/solid
contact devices (Heiskanen, 1993). The high solids concentration in the separator limits particle
mobility. As a result, particles move through the separation chamber in a “plug flow” manner.
Previous work has shown that this type of motion results in an increase in process recovery due
to reduced back-mixing (Doby and Finch, 1990). Furthermore, particle detachment is also
minimized due to a reduction in localized turbulence.
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Virginia Tech | The concept of improving coarse particle recovery through the use of bubble-particle
attachment in a rising current separator (flotation column) has been previously demonstrated
(Laskowski, 1995; Barbery, 1989). Unfortunately, these approaches used an open-column
reactor operating in the free, not hindered, settling regime. As a result, these configurations do
not have the advantages associated with a teeter-bed approach. The distinctive advantage of
utilizing a teeter-bed is the greatly improved hydrodynamic environment within the separator.
To recognize this advantage, the fundamental difference between free and hindered-settling
conditions must be examined.
Particle settling is generally recognized as falling into one of two categories: free or
hindered-settling. Under free settling conditions, individual particles do not affect the settling
behavior of adjacent particles and, as such, the pulp has the rheological characteristic of the fluid.
Furthermore, the settling velocity is determined by particle size and particle density. Hindered-
settling is fundamentally different. At high solids concentrations, adjacent particles collide with
each other influencing the settling characteristics. The settling path is greatly obstructed
reducing particle velocity. Additionally, the high solids concentration increases the apparent
viscosity and specific gravity of the pulp, thus further reducing particle settling. As a result, the
acceleration of particles becomes more important than the terminal velocity. This collision
phenomenon is the most important aspect of hindered-settling and provides favorable
hydrodynamic conditions that cannot be achieved in open-tank reactors, such as conventional
column cells. Specifically, particle collection rate, retention time and cell turbulence are all
improved.
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Virginia Tech | 3.2.1.3 Phosphate Recovery
The United States is the world’s largest producer of phosphate rock, accounting for
approximately 45 million tons of marketable product valued at more than $1.1 billion annually
(United States Geological Survey, Mineral Commodity Summaries, January 1999).
Approximately 83% of this production can be attributed to mines located in Florida and North
Carolina. The major U.S. producers are located in Florida and include Cargill Fertilizer, Inc., CF
Industries, Inc., IMC-Agrico, Inc., Agrifos, LCC, and PCS Phosphate, Inc. Of these, IMC-
Agrico is by far the largest single producer in the state.
Prior to marketing, the run-of-mine phosphate matrix must be upgraded to separate the
valuable phosphate grains from other impurities. The first stage of processing involves
desliming at 150 mesh to remove fine clays. Although 20-30% of the phosphate contained in the
matrix is present in the fine fraction, technologies currently do not exist that permit this material
to be recovered in a cost-effective manner. The oversize material from the desliming stage is
typically screened to recover a coarse (plus 14 mesh) high-grade pebble product. The remaining
14 x 150 mesh fraction is typically classified into coarse (e.g., 14 x 35 mesh) and fine (e.g., 35 x
150 mesh) fractions that are upgraded using conventional flotation machines, column flotation
cells, or other novel techniques such as belt flotation (Moudgil and Gupta, 1989). The fine
fraction (35 x 150 mesh) generally responds very well to upgrading and, in most cases,
conventional flotation technologies can be used to produce acceptable concentrate grades with
recoveries in excess of 90%. On the other hand, high recoveries are often difficult to maintain
for the coarser (14 x 35 mesh) fraction. In fact, prior work has shown that the recovery of coarse
particles (e.g., >30 mesh) can be less than 50% in many industrial operations (Davis and Hood,
1992). For example, Figure 3.3 illustrates the sharp reduction in recovery as particle size
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Virginia Tech | Existing column cells used in the phosphate industry also have performance limitations
due to mechanical design. In most cases, air is introduced using “venturi-type” aspirators that
require a great deal of water. The majority of this aeration water reports to the column overflow
product. This aeration water carries undesired gangue material into the froth product.
Additionally, the column aeration rate is intrinsically dependent upon the aspirator water flow
rate. As a result, an increase in aeration rate requires an increase in water flow rate which, in
turn, can have a detrimental effect on performance. Based on these limitations, it is apparent that
a flotation system is required that incorporates quiescent hydrodynamic conditions and provides
for a de-coupling of the aeration system from external water supplies.
One well-known method of improving flotation performance is to classify the feed into
narrow size fractions and to float each size fraction separately. This technique, which is
commonly referred to as split-feed flotation, has several potential advantages such as higher
throughput capacity, lower reagent requirements and improved separation efficiency. Split-feed
flotation has been successfully applied to a wide variety of flotation systems including coal,
phosphate, potash and industrial minerals (Soto and Barbery, 1991).
The United States Bureau of Mines (USBM) conducted one of the most comprehensive
studies of the coarse particle recovery problem in the phosphate industry (Davis and Hood,
1993). This investigation involved the sampling of seven Florida phosphate operations to
identify sources of phosphate losses that occur during beneficiation. According to this field
survey, approximately 50 million tons of flotation tailings are discarded each year in the
phosphate industry. Although the tailings contain only 4% of the matrix phosphate, more than
half of the phosphate in the tailings is concentrated in the plus 28 mesh fraction. In all seven
plants, the coarse fraction was higher in grade than overall feed to the flotation circuits. In some
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Virginia Tech | cases, the grade of the plus 28 mesh fraction in the tailings approached 20% P O . The USBM
2 5
study indicated that the flotation recovery of the plus 35 mesh fraction averaged only 60% for the
seven sites included in the survey. Furthermore, the study concluded that of the seven phosphate
operations, none have been successful in efficiently recovering the coarse phosphate particles.
There have been several attempts to improve the poor recovery of coarse (16 x 35 mesh)
phosphate grains through the addition of improved flotation reagents. One such study, which
was funded by the Florida Institute of Phosphate Research (FIPR), was completed by the
University of Florida in early 1992 (FIPR Project 86-02-067). These investigators also noted that
the flotation of coarse phosphate is difficult and normally yields recoveries of only 60% or less
when using flotation. The goal of the FIPR study was to determine whether the recovery of
coarse phosphate could be enhanced via collector emulsification and froth modification achieved
by frothers and fines addition. Plant tests conducted as part of this project showed that the
appropriate selection of reagents could improve the recovery of coarse phosphate (16 x 35 mesh)
by up to 6 percentage points. Furthermore, plant tests conducted with emulsified collector
provided recovery gains as large as 10 percent in select cases. Unfortunately, reports of follow-
up work by industry which support these findings have not yet been published.
In 1988, FIPR also provided financial support (FIPR Project 02-070-098) to the Canadian
Laval University to determine the mechanisms involved in coarse particle flotation and to
explain the low recoveries of such particles when treated by conventional froth flotation. In light
of this study, these investigators proposed the development of a modified low turbulence device
for the flotation of coarse phosphate particles. Laboratory tests indicated that this approach was
capable of achieving recoveries greater than 99% for coarse phosphate feeds. In addition, the
investigators noted that this approach did not suffer from high reagent costs associated with other
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Virginia Tech | strategies designed to overcome the coarse particle recovery problem. Although the preliminary
data was extremely promising, this work was unfortunately never carried through to industrial
plant trials due to problems with the sparging system and tailing discharge system.
Building on these early findings, Soto and Barbery (1991) have recently developed a
negative bias flotation column that improves coarse particle recovery (Barbery, 1989). It was
surmised that the only factors preventing conventional columns from being ideally suited for
coarse particle recovery were wash water flow and a thick froth layer. Wash water is used in
column flotation to “wash” fine gangue (i.e., clays) from the product froth. However, wash
water can also propel coarse particles back into the pulp resulting in a loss of recovery. Soto and
Barbery (1991) removed this wash water resulting in a negative bias flow (i.e., net flow rising
upwards). An added flow of elutriation water aids in propelling coarse particles to the overflow
by inducing drag on any bubble-particle in the pulp. In fact, Barbery (1989) has been able to
demonstrate a four-fold improvement in coarse particle recovery when utilizing negative bias.
Essentially, this device is operated in a flooded manner and in the absence of a froth zone.
Several other similar devices have also been developed (i.e., Laskowski, 1995).
A number of alternative processes have been used by industry in an attempt to improve
the recovery of the coarser particles. These techniques include gravitational devices such as
tables, launders, spirals and belt conveyors that have been modified to perform skin-flotation
(Moudgil and Barnett, 1979). Although some of these units have been successfully used in
industry, they normally must be supplemented with scavenging flotation cells to maintain
acceptable levels of performance (Moudgil and Barnett, 1979; Lawver et al., 1984).
Furthermore, these units typically require excessive maintenance, have low throughput
capacities, and suffer from high operating costs. Reagent consumption can also be a major
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Virginia Tech | drawback, as up to 10 lbs/ton of chemical can sometimes be needed to facilitate skin-flotation
(Keating, 1999). Despite these shortcomings, the increased recovery of coarse phosphate matrix
can offer several benefits.
One of the most obvious advantages of improved coarse particle recovery would be the
increased production of phosphate rock from reserves currently being mined. For example, a
survey of one Florida plant indicated that 7-15% of the plant feed was present in the plus 35
mesh fraction (Mankosa et al., 1999). At a 2,000 tph feed rate, this fraction represents 140-300
tph of flotation feed. An improvement in coarse particle recovery from 60% to 90% would
represent an additional 50-100 tph of phosphate concentrate. This tonnage corresponds to an
additional $7.5-15 million of corporate revenues. This incremental tonnage and income could be
produced without additional mining or reserve depletion.
3.2.1.4 Carbon/Coal Recovery
In 1993, the total world coal reserves were estimated at over 1,039,182 tons, of which
23% were estimated to be in the United States alone (Kawatra, 1995). Prior to sale, run-of-mine
coal is generally upgraded in order to remove ash bearing minerals and to increase the BTU
value of the clean coal product. The removal of sulfur bearing minerals has also become of
greater importance since the advent of the United States Clean Air Act, which restricts the
emission of sulfur dioxide from coal fired power plants.
In a general flowsheet, a coal feed is crushed to a top-size of a few inches and then
further classified into several size fractions. The largest of these size fractions, approximately 2
inch x 6 mesh, is predominantly treated in dense media processes. Dense medium bathes and
cyclones are the most popular and most efficient; they are capable of Ep (efficiency) values
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Virginia Tech | approaching 0.02. The 6 x 65 mesh size fraction is generally processed in coal spirals or water-
only cyclones, while the passing 65 mesh size fraction is generally treated with flotation.
Coal spirals suffer from specific gravity cut-points that are typically much higher than
those employed by the coarse coal dense medium circuits. This imbalance creates either a loss
of clean coal or a decrease in product quality. Spirals are capable of minimizing the rejection of
these coarser, low-ash particles due to the buffering action of the flowing film on particle
classification. Water-only cyclones tend to misplace significant amounts of larger, low-ash coal
particles to the reject stream due to the size classification within the cyclone. Because of this
particle misplacement, these water-based separators tend to be much less efficient
(approximately 0.16 Ep) than dense medium devices. Further discussion on this topic is found in
Chapter 1, Sections 1.1 and 1.2.
Froth flotation is used almost exclusively for the upgrading of coal in the passing 65
mesh size range. However, the maximum floatable size of coal particles depends on several
variables, including coal rank, collector addition, pulp density, cell turbulence, and retention
time. In coarse particle flotation, a bubble will rise through the pulp and encounter a particle of
coal and/or gangue. If the particle is hydrophobic, and if it passes within a close enough range of
the bubble, the particle will adhere to the bubble. Once attached, the particle will be swept to the
rear of the bubble by its relative motion through the pulp. If the force of adhesion is strong
enough, the particle will remain attached to the bubble and reach the surface.
Collision efficiencies of bubble and particles should increase as the coal particle size
increases. These probabilities dictate that capture and attachment should be expected to increase
along with recovery. However, according to Jameson, et al. (1984), this does not hold true for
the coarsest material. As a bubble unites with a coarse particle, attachment occurs. The bubble
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Virginia Tech | and particle become a bubble-particle aggregate that has a higher buoyancy effect than that of the
particle alone. Unfortunately, even after attachment, this bubble-particle aggregate may now
only have an effective buoyancy and/or density equal to that of the pulp, resulting in a loss of
combustible recovery. This effective buoyancy of the bubble-particle aggregate most likely sets
the upper limit on the maximum floatable size. Thus, the maximum floatable particle size for a
given material is anywhere between 10 and 100m m (Jameson et al., 1984).
Studies conducted by Sun and Zimmerman (1950) found that bituminous coal was able to
float at slightly larger sizes than anthracite coal particles (6.7 mm vs. 1.17mm). However, the
specific gravity of the bituminous coal was less than that of the anthracite coal, which may have
contributed to this finding. Even though these coarse particles were buoyant enough to float,
they were incapable of passing over the overflow weir into the clean coal launder due to their
size.
In studies conducted by Crawford (1936), it was shown that fine particles are more likely
to float before coarser particles. In fact, subsequent studies conducted by Brown and Smith
(1954) and Rastogi and Aplan (1985) concluded that flotation rates increase with a decrease in
particle size. The slower flotation rate of coarse coal leads to a loss in recovery of these
generally high quality, low ash particles.
Subsequent investigations by Luttrell (2000) have demonstrated how feed rate can
influence the recovery of coarse coal particles. Plotted in Figure 3.4 is the maximum floatable
particle size as a function of feed rate. It can be concluded from this plot, that if effective bubble
surface area remains constant as feed rate increases, the competition for this surface area also
increases. As a result, bubble surface area is first covered by the finer particles, which have a
higher flotation rate in comparison to the coarser particles. This phenomenon results in
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Virginia Tech | 3.3 Theoretical Framework
3.3.1 Flotation Fundamentals
The reaction, or flotation, rate for a process is indicative of the speed at which the
separation will proceed. In mineral flotation the reaction rate is controlled by several
probabilities, e.g., collision, adhesion and detachment. The attachment of particles to air bubbles
is the underlying principle upon which all flotation processes are based. This phenomenon takes
place via bubble-particle collision followed by the selective attachment of hydrophobic particles
to the bubble surface. Particles may also detach if the resultant bubble-particle aggregate is
thermodynamically unstable. According to Sutherland (1948), the attachment process may be
described by a series of mathematical probabilities given by:
P= P P (1- P ) [3.1]
c a d
in which P is the probability of collision, P the probability of adhesion, and P the probability
c a d
of detachment. The attachment and detachment probabilities are controlled by the process
surface chemistry and cell hydrodynamics, respectively. In an open (free settling) system, the
collision probability is quite low due to the low particle concentration. However, at higher
concentrations, the crowding effect within the hindered-bed increases the probability of collision.
This phenomenon is due to the compression of the fluid streamlines around the bubbles as they
rise through the teeter-bed. The increased probability of collision can result in reaction rates that
are several orders of magnitude higher than found in conventional flotation.
After a particle contacts a bubble, the particle is swept over the bubble surface for a finite
period of time known as the sliding time. During this period, the thin liquid film separating the
bubble and particle must rupture if particle adhesion is to occur. This “sliding time” is a
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Virginia Tech | reflection of the hydrodynamics of the system and is primarily a function of the particle and
bubble sizes. On the contrary, the length of time required for the liquid film to thin sufficiently
so that rupture occurs is a measure of the chemistry of the flotation system and is commonly
referred to as the induction time. The induction time is small for hydrophobic particles (e.g., 1
msec) and may approach infinity for extremely hydrophilic particles.
Utilizing the induction time concept, Yoon and Luttrell (1989) derived an analytical
expression for the probability of bubble-particle adhesion (P ) as:
a
Ø (cid:239)(cid:236) - BU t (cid:239)(cid:252) ø
P =sin2Œ 2arctanexp(cid:237) b i (cid:253) œ [3.2]
a Œ
º
(cid:239)(cid:238) D b(D
p
/D
p
+1)(cid:239)(cid:254) œ
ß
in which D is the particle diameter, D is the bubble diameter, t is the induction time, U is the
p b i b
differential velocity between the bubble and particle, and B is a constant that varies depending on
the particular flow regime (as dictated by Reynolds number). In most cases, U is simply
b
assumed to be the terminal rise velocity of the bubble. Since Equation [3.2] is expressed as a
sine function, the calculated value of P will always fall between zero and unity, the correct
a
limits for probabilities.
To illustrate the effect that particle size has on the probability of adhesion, and hence
recovery, P was plotted as a function of particle size for different levels of induction time
a
(hydrophobicity) as seen in Figure 3.6. As expected, P increases sharply as the induction time
a
is reduced from 5 to 1 msec. It is illustrated that for a given value of t, P decreases steadily as
i a
the particle size increases. The reduced P value is due to the fact that larger particles tend to
a
slide more rapidly over the bubble surface since they project further out into the high velocity
region of the streamlines that pass over the bubble surface. However, it can be concluded that if
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Virginia Tech | (size, density, composition and shape), and cell agitation intensity. Theoretical D * values have
p
been calculated by Schulze (1984) from the tensile and shear stresses acting on bubble-particle
aggregates under homogenous turbulence. The degree of turbulence was quantified in terms of
the induced root mean square velocity (RMSV).
A study conducted by Schulze (1984) concluded that turbulence had a tremendous effect
on the recovery of coarse particles. A typical set of results obtained by Schulze is presented in
Figure 3.7. In this figure, the maximum floatable particle size is shown as a function of
turbulence (RMSV) and contact angle. According to this data, the maximum size of particles
that may be recovered by flotation increases by more than an order of magnitude when changing
from high to low turbulence. In fact, according to Barbery (1984), the optimum conditions for
coarse particle flotation occur when cell agitation intensity is reduced to a point just sufficient to
maintain the particles in suspension (i.e., teeter-bed conditions).
10
1
0.1
0.01
0 20 40 60 80 100
Contact Angle (°)
118
)mm(
eziS
elcitraP
Low Turbulence
(Static Condition)
Medium Turbulence
(RMSV = 0.2 m/sec)
High Turbulence
(RMSV = 1.0 m/sec)
Figure 3.7 - Influence of turbulence on the maximum particle size that may be recovered by froth
flotation (after Schulze, 1984). |
Virginia Tech | The maximum floatable particle size is also effected by buoyancy. In froth flotation, the
bubble-particle aggregate must have sufficient buoyancy to be lifted to the surface of the pulp.
Mathematically, the maximum particle diameter (D ) that may be floated may be estimated
max
from:
1/3
(cid:230) r (cid:246)
D = D (cid:231) f (cid:247) [3.4]
max b (cid:231) r - r (cid:247)
Ł p f ł
in which r and r are the densities of the particle and fluid, respectively. This expression
p f
suggests that 1 mm diameter bubbles are capable of carrying particles up to approximately 0.85
mm before the critical buoyancy limit is exceeded (r = 2.5 gm/cm3).
p
Particle retention time can also greatly influence the recovery of coarse particles. The
mixers-in-series model provides a convenient framework for analyzing this phenomenon (Arbiter
and Harris, 1962; Bull, 1966). According to this model, the cumulative fractional recovery (R)
of a given particle species can be determined using the expression:
( )
R=1- 1+kt - n [3.5]
p
in which k is the flotation rate constant, t is the particle residence time and n is the number of
p
equivalent mixers. Figure 3.8 shows recovery determined from Equation [3.5] for different
values of n as a function of the dimensionless product kt . In most cases, n is assumed to be
p
equal to the number of cells in the flotation bank. This assumption is generally valid for a cell-
to-cell flotation bank. However, the magnitude of n is typically smaller for flow-through
flotation banks that have a significant amount of intermixing. The appropriate value of n can be
119 |
Virginia Tech | K is approximately equal to one and may be ignored. For vertical flow cells such as columns, K
may be estimated from:
K = Q s {Co- CurrentMode} [3.7]
U A+Q
p s
K = Q s {Counter- CurrentMode} [3.8]
U A- Q
p s
in which U is the particle settling velocity and A is the cross-sectional area of the flotation cell.
p
In most flotation processes, feed particles move with the fluid flow towards the discharge point
(co-current mode). A counter-current arrangement has obvious advantages since the settling
velocity is reduced by the upward flow of liquid resulting in a higher retention time. Hindered-
settling, as previously explained, provides an environment in which the particles never achieve
their terminal free-fall velocity. As a result, the effective particle velocity through the cell is
greatly reduced providing a significant increase in retention time as compared to a free-settling
system.
Finally, the rate constant (k) is the most important term in determining flotation
performance. Studies conducted by Yoon, et al. (1997) indicate that this parameter can be
mathematically described by:
k = 1 PS [3.9]
4 b
in which P is the probability of bubble-particle attachment and S is the superficial bubble
b
surface area rate. The latter can be calculated directly using:
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Virginia Tech | 6 Q g
S = [3.10]
b
D A
b c
in which Q is the volumetric gas flow rate, D is the bubble diameter, and A is the cell cross-
g b c
sectional area (Yoon et al., 1997). Equations [3.9] and [3.10] suggest that the same flotation rate
constant (k) can be maintained at a lower overall gas rate (Q ) provided that the attachment
g
probability (P) increases accordingly.
3.3.2 Theoretical Advantages of the HydroFloat Cell
The HydroFloat cell is a flotation device that operates much like a traditional hindered-
bed separator with feed settling against an upward current of fluidization water. However, unlike
a conventional teeter-bed separator, the HydroFloat cell is continuously aerated by injecting
compressed air and a small amount of frothing agent into the fluidization water. As previously
described, the small air bubbles are evenly dispersed into the cell and attach to the hydrophobic
particles within the teeter-bed. These bubble-particle aggregates have an effective density much
lower than that of the sole particle. These bubble-particle aggregates rise to the top of the denser
teeter-bed and overflow from the top of the separation chamber. Hydrophilic particles that do
not attach to the air bubbles continue to move down through the teeter-bed and eventually settle
into the dewatering cone and are discharged. Compared to traditional froth flotation processes,
the HydroFloat separator offers several important advantages for treating coarser material,
including enhanced bubble-particle contacting, increased residence time, lower axial mixing/cell
turbulence, and reduced air consumption.
According to Equation [3.2], the probability of attachment increases as the differential
velocity between bubbles and particles (U ) is reduced. Unlike conditions found in froth
b
flotation where particles are allowed to settle freely opposite the direction of rising bubbles, the
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Virginia Tech | hindered-settling/rise conditions realized within the teeter-bed of the HydroFloat cell slows the
velocity at which bubbles and particles travel. As dictated by Equation [3.2], the reduced
velocity will increase the probability of adhesion (P ), thereby enhancing flotation recovery. As
a
shown in Figure 3.6, this phenomenon is particularly important for coarse particles that tend to
suffer from low P values.
a
Greater recovery can also be realized utilizing the HydroFloat separator due to a decrease
in the probability of detachment (P ). This decrease in detachment is a direct result of the
d
reduction of localized turbulence generally seen in hindered-bed separators. As stated
previously, the optimum conditions for coarse particle flotation occur when cell agitation
intensity is reduced to a point just sufficient to maintain the particles in suspension. Thus, a
teeter-bed is an ideal environment for minimizing particle detachment (Barbery, 1984).
The HydroFloat cell is both a flotation device and a density separator. The use of a
teeter-bed makes it possible to achieve separations based on small differences between the
density of free suspended particles and the density of bubble-particle aggregates. As a result,
separations can be achieved even if the buoyancy of the bubble-particle aggregate is too small to
lift the particle load. In other words, the density of the bubble-particle aggregate need only be
smaller than the effective density of the teeter-bed to achieve a separation. This capability
eliminates the buoyancy limitation described by Equation [3.4]. This feature is important for
very large particles that are difficult to carry to the top of a conventional flotation pulp.
The HydroFloat cell also operates under nearly plug-flow conditions because of the low
degree of axial mixing afforded by the uniform distribution of particles across the teeter-bed. As
a result, the cell operates as if it were comprised of a large number of cells in series (i.e., high
value of n). As shown in Figure 3.8, this characteristic allows a single unit to achieve the same
123 |
Virginia Tech | recovery as a multi-cell bank of conventional cells (all other conditions equal). In other words,
the HydroFloat cell makes more effective use of the available cell volume than well-mixed
conventional cells or open columns.
The hindered-bed environment also influences particle retention time (t ), and hence,
p
particle recovery. In most flotation processes, feed particles move with the fluid flow towards
the discharge point (co-current mode). In contrast, particles move in the opposite direction to the
fluid flow within the HydroFloat cell (counter-current mode). As dictated by Equations [3.6] and
[3.8], the fluidization water within a hindered-settling regime provides a significant increase in
the particle retention time. The longer retention time allows good recoveries to be maintained
without increasing cell volume.
The HydroFloat separator can be theoretically applied to any system where differences in
apparent density can be created by the selective attachment of air bubbles. In summary,
compared to traditional froth flotation processes, the HydroFloat separator offers several
important advantages for treating coarser feed streams. These include:
• Improved Attachment: The differential velocity between bubbles and particles is greatly
reduced by the hindered settling/rise conditions within the teeter-bed of the HydroFloat
separator. Consequently, the reduced velocity will increase the contact time between bubbles
and particles, thereby promoting the probability of adhesion and enhancing flotation
recovery. This phenomenon is particularly important for coarse particles. The high solids
concentration within the teeter-bed will also improve recovery by increasing the collision
probability between bubbles and particles (Yoon and Luttrell, 1986).
124 |
Virginia Tech | • Reduced Turbulence: According to Barbery (1984), the optimum conditions for coarse
particle flotation occur when cell agitation intensity is reduced to a point just sufficient to
maintain the particles in suspension. Woodburn (1971) and Schultz (1984) have also shown
that reduced cell turbulence significantly increases the maximum particle size limit for
effective flotation. The use of fluidization water in the HydroFloat separator makes it
possible to keep particles dispersed and in suspension without the intense random agitation
required by mechanical flotation machines.
• No Buoyancy Limitation: Unlike traditional flotation processes, the HydroFloat cell is both a
flotation device and a density separator. The use of a teeter-bed makes it possible to achieve
separations based on small differences between the density of free suspended particles and
the density of bubble-particle aggregates. As a result, separations can be achieved even if the
buoyancy of the bubble-particle aggregate is too small to lift the aggregate from the surface
of the teeter-bed. This capability eliminates the buoyancy limitation and is particularly
important for very large particles that are difficult to carry to the top of a conventional
flotation pulp.
• Plug-Flow Conditions: The HydroFloat cell operates under nearly plug-flow conditions
because of the low degree of axial mixing afforded by the uniform distribution of particles
across the teeter-bed. Consequently, the cell operates as if it were comprised of a large
number of cells in series. Provided that all other conditions are equal, this characteristic
allows a single unit to achieve the same recovery as a multi-cell bank of conventional cells
(Arbiter and Harris, 1962; Mankosa et al., 1992). In other words, the HydroFloat cell makes
125 |
Virginia Tech | 3.4 Population Balance Model
3.4.1 Model Description
A population balance model was developed and utilized in an effort to more fully
understand the HydroFloat separator. Although fundamentals of flotation were used in
developing the HydroFloat separator, the actual separation of particles is accomplished by
gravity, based on density differences of components in the feed stream after the selective
attachment of air bubbles. These bubbles change the apparent density of the hydrophobic
components so that the gravity separation can be enhanced.
The HydroFloat model was constructed much like the population balance model of the
CrossFlow separator developed in the previous chapter. The HydroFloat model utilizes general
equations for hindered-settling in transitional flow regimes to accurately predict overflow and
underflow partitions, particle size distributions, and component recovery data. Input data include
feed rate, percent feed solids (by mass), feed size distribution (up to 9 size fractions), density of
components in the feed stream (up to 2 components), fluidization water rate, and underflow
discharge rate. The general geometry and feed characteristics of these units are nearly identical.
This model was also constructed as a series of zones occurring in three distinct sections. These
primary sections include the feed inlet, the teeter-bed, and the underflow area. An illustration of
these primary sections has already been presented in Figure 2.12.
The Microsoft spreadsheet, Excel, was used for all calculations. This powerful software
package is capable of performing the iterative calculations required to solve the steady-state
equations necessary to model the HydroFloat separator.
127 |
Virginia Tech | 3.4.1.1 Feed Section
The configuration of zones in the feed section of the HydroFloat separator was arranged
similarly to that of the CrossFlow separator model. Again, the cross-flowing action of the feed
water and solids necessitated the need for a 5 x 5 configuration as seen in Figure 2.13. If an
inadequate number of zones was utilized, particles could be incorrectly partitioned and
mathematically misplaced into overflow or underflow launders.
As shown in Figure 2.13, the upward flow of fluidization water that enters each zone is
shown as Q . This flow is counteracted by both the flow induced by solids settling (Q ) and by
xn d
the horizontal flows (Q) that can move to or from adjacent cells. Material suspended within the
l
teeter-bed acts like a distributor for the rising teeter water, evenly distributing Qx over the entire
n
cross-section of the unit for each level of the feed inlet area. The horizontal flows can be
calculated by conducting a flow balance for each zone within the feed section, given the
elutriation water rate (Q ), feed rate (Q), and the underflow discharge rate (Q ).
w f u
Unlike the previous CrossFlow model, an assumption had to be made when modeling the
feed section of the HydroFloat separator. In this separator, bubbles attach to hydrophobic
particles creating bubble-particle aggregates. From visual inspection, it can be concluded that
these agglomerates are created in the feed section of the separator and rarely penetrate the teeter-
bed or underflow sections. It is not known how the attachment of air bubbles will affect the
rise/sink characteristics of these agglomerates. Consequently, it was assumed that after contact
and subsequent attachment of an air bubble or bubbles, the rise/sink characteristics of these
agglomerates would be equal to that of a particle of equivalent apparent size and density.
128 |
Virginia Tech | 3.4.1.2 Teeter-Bed and Underflow Sections
The teeter-bed and underflow sections of the HydroFloat were also arranged similarly to
that of the previous CrossFlow model. This configuration can be seen in Figure 2.15. A
transition zone, to which fluidization water flow is added, separates these two sections. This
fluidization flow makes a split in this transition zone, with the majority of the water rising up
through the teeter-bed. This fluid flow assists the activated bubble-particle aggregates in rising
from the top of the teeter-bed into the overflow launder.
In the HydroFloat separator, small air bubbles are introduced into the unit along with the
elutriation water. The bubbles that rise up through the teeter-bed occupy a certain fraction of
volume within the separation chamber and consequently alter the apparent gravity of the teeter-
bed. It can be concluded that changes in air fraction within the separation chamber can be
affected by a large number of variables (i.e., average bubble size, average particle size in the
teeter-bed, frother addition, elutriation water flow rate, etc.). Incorporating these variables into
the general hindered-bed population balance model would add impractical complexities to the
already burdensome computer code. Consequently it was assumed that the rising bubbles had no
overall effect on the teeter-bed characteristics. This assumption may be inaccurate; however,
conclusions drawn from trends while using this model can nevertheless provide useful insight
into the advantages offered by the HydroFloat separator.
3.4.2 Calculations
Similar to the CrossFlow population balance model, an iterative dynamic technique (i.e.,
finite differencing) was used to solve for changes in concentration of particles over time for each
zone of the HydroFloat separator. Using the general equations for hindered-settling in
129 |
Virginia Tech | transitional flow regimes presented in Chapter 2, component recovery/rejection data could be
calculated. The volumetric flows and solids from each zone were mass-balanced with respect to
one another using the laws of mass conservation (steady-state flow). This technique is also
discussed in length in Chapter 2.
3.4.3 Modeling Insight and Investigation
In an effort to illustrate the advantages offered by the HydroFloat for recovering coarse
particles, a separation of two components was simulated. Feed stream characteristics were
inputted into the model. This feed consisted of two density components and was divided into
nine size fractions. Both components had an equivalent and flat particle size distribution. The
feed rate was assumed to be 2.5 tph/ft2 at an elutriation water rate of 26.75 gal/ft2. Simulations
were conducted while varying the density ratio of the two components. The density of the first
component was reduced (from 3.0 to 1.25 SG) while maintaining the density of the second
component constant (3.0 SG).
The results of these simulations are presented in Figure 3.9. It can easily be seen that as
the density ratio (r /r ) decreases, the recovery of coarse particles increases. At a density ratio
1 2
of 0.75, only 12% of the plus 0.71 mm material (+20 mesh) reported to the overflow. This
density ratio is typically found in applications where a 2.25 SG material is being separated from
a 3.00 SG material (i.e., mineral sands). However, using air bubbles, the density ratio (r /r )
1 2
can be altered to 0.50. At this ratio, nearly 72% of the coarse, lower density material is now
recovered to the overflow launder. These results are analogous to recovering the coarse, low
density material that is typically lost in a conventional hindered-bed density separator. As
presented in Figure 3.10, this change in apparent density of one component can represent an
increase in total circuit recovery of nearly 22.5%. Naturally, additional improvements in overall
130 |
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