Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 1005-1011
Published Online October 2012 (http://www.SciRP.org/journal/jmmce)
Application of High Tension Roll Separator for the
Separation of Titanium Bearing Minerals: Process
Modeling and Optimization
Srijith Mohanan*, Sunil Kumar Tripathy, Y. Ramamurthy, C. Raghu Kumar
Tata Steel Limited, Jamshedpur, India
Received April 20, 2012; revised May 23, 2012; accepted June 3, 2012
The High Tension Roll Separator (HTRS) is one of the main electrostatic unit operations employed to separate titanium
minerals like ilmenite, rutile and leucoxene which behave as conducting from zircon, sillimanite, garnet and monazite
which behave as non-conducting minerals when a high potential difference is applied. Three process inputs, namely roll
speed, feed material temperature and roll speed have been optimized. Experiments were conducted based on the Box-
Behnken factorial design; the results were analyzed using response surface methodology (RSM). A new term, called
Operational Quality Index (OQI) has been defined as a process output, which is maximized by quadratic programming,
to obtain the optimum operating conditions. The maximum value of OQI obtained under the constraints of grade >96%
and recovery >98% is 195.53, at the following operating conditions—Temperature: 102˚C, Feed Rate: 1.75 tph and Roll
Speed: 132 rpm. Under these conditions, the grade and recovery obtained are 96.6% and 98.9% respectively.
Keywords: High Tension Roll Separator; Response Surface Methodology; Titanium; Box-Behnken Design
Significant research has been dedicated, over the past de-
cade, to enhance plant performance and efficiency to
economically concentrate titanium bearing minerals from
beach sand deposit. The heavy mineral industry employs
different unit operations, in series, to produce high grade
titanium minerals (ilmenite, rutile, etc.), with the focus
on maximizing recovery, along with the quality. The
High Tension Roll Separator (HTRS) is one of the main
electrostatic unit operations employed to separate con-
ducting from non-conducting fractions. Titanium mi-
nerals like ilmenite, rutile and leucoxene behave as con-
ducting whereas zircon, sillimanite, garnet and monazite
behave as non-conducting minerals when a high potential
difference is applied.
HTRS are conventional ionizing field separators utiliz-
ing a grounded roll to neutralize the charge of the feed
material, when passed through high voltage ionizing field.
The conducting particles lose their charge to the grounded
roll and follow a trajectory depending on the centrifugal
force developed by the speed of the rotor. The non-con-
ducting particles are pinned to the roll, transported fur-
ther and removed by mechanical means like brush or by
high voltage AC wiper [1-5]. HTRS is of two types
—static and dynamic. The operation efficiency of HTRS
depends on the suitable selection of process variables at
which the response reaches its optimum, in this case the
maximum value. In the present work Response Surface
Methodology (RSM) has been used as the optimization
tool. This has been widely used as a dependable method
of process optimization [6-10]. “Design of Experiments”
strategies are available in literature, to be used based on
the objective of the work, such as randomized block de-
signs [8,10]. For evaluation of process variables, the two
level factorial designs together with response surface
methodology has been used because these techniques use
factors with more than three levels, and in this way they
can establish quadratic models using central composite,
Box-Behnken and Doehlert design .
The Box-Behnken design followed by the use of RSM
has been proposed for the present study. RSM has been
widely used for modeling and optimization of process
parameters, in particular chemical and pharmaceutical
systems [11-18], with limited application in the field of
mineral processing. A basic understanding of the factors
that influence the separation in a HTRS is well estab-
lished from classical works [19-21]. In mineral pro-
cessing, grade and recovery are the important output pa-
rameters which will designate the efficiency of the pro-
cess/separation with variable process inputs. Maximizing
these two variable outputs should be the basic aim of any
Copyright © 2012 SciRes. JMMCE
S. MOHANAN ET AL.
research in the field of mineral processing.
The HTRS parameters that affect the separation are the
roll speed, feed rate, temperature of the feed material,
intensity of the applied potential, splitter division plates,
humidity, the feed characteristics such as mineral surface
condition, and feed size distribution [1,2]. In the current
work, an attempt is made to optimize three process vari-
ables of prime importance, namely roll speed, feed rate
and temperature of the feed, which are predicted to play a
significant role in concentrating titanium minerals (ilme-
nite, rutile, etc.). In any process plant, under a given set
of operating conditions, the grade and recovery are fixed
and it is a well-established knowledge that both grade
and recovery are inversely related. High grade material
can be obtained with very low recovery, which may not
be desirable. The reverse of this also holds true. To
circumvent this problem, it is proposed to create an index
that represents the grade and recovery obtained under the
same operating conditions. The value of the process para-
meters that maximize this index are the true optimum
operating conditions. Optimization studies are carried out
by using quadratic programming by the mathematical
software package MATLAB 7.1.
Response Surface Methodology
Response Surface Methodology (RSM) is collection of
statistical and mathematical methods that are useful for
modeling and analyzing problems. In this technique, the
main objective is to optimize the response surface that is
influenced by various process parameters. The RSM also
quantifies the relationship between the controllable input
parameters and the obtained response surfaces .
The design procedure of RSM is
1) Designing of a series of experiments for adequate
and reliable measurement of the response of interest.
2) Developing a mathematical model of the second
order response surface with the best fittings.
3) Finding the optimal set of experimental parameters
that produce a maximum or minimum value of response.
4) Representing the direct and interactive effects of
process parameters through two and three dimensional
If all variables are assumed to be measurable then the
response surface can be expressed as:
where y is the output of the system, and xi the variables
of action called factors.
The objective is to optimize the response y with an as-
sumption that the independent variables are continuous
and controllable through the experimentation. It is also
required to find a suitable approximation for the true fun-
ctional relationship between independent variables and
the response surface, typically a second-order model is
utilized in response surface methodology [7,22,23].
where x1, x2, ... , xk are input factors which influence the
response y; β0, βii (i = 1, 2, ..., k), βij (i = 1,2, ... k; j = 1,
2, .. ., k) are unknown parameters and ε is a random error.
The β coefficients, which should be determined in the
second-order model, are obtained by the least square
method. Generally Equation (2) can be written in matrix
where Y is defined to be a matrix of measured values, X
to be a matrix of independent variables. The matrixes β
and ε consist of coefficients and errors, respectively. The
solution of Equation (3) can be obtained from the above
matrix equation as
where X' is the transpose of the matrix X and (X'.X)−1 is
the inverse of the matrix X'.X. The coefficients, i.e. the
main effect (βi) and two-factors interactions (βij) can be
estimated from the experimental results by computer
simulation programming applying least squares method
using MATLAB 7.1. [6,22,23].
2. Materials and Methods
The mineral sample used for this study was taken from
the Kuduremozhi region of Tamil Nadu, India. The sam-
ple was initially deslimed in the laboratory using hydro-
cyclone test rig and then concentrated by multistep gra-
vity concentration using spiral concentrator to achieve
the desired heavy mineral concentrate i.e. more than 90%
heavy minerals . Thus the obtained heavy mineral
concentrate has been subjected for the particle size
analysis, X-ray diffraction studies, and mineralogical
studies. Particle-size measurement of the sand sample
was performed using standard laboratory Sieve Shaker.
The size distribution of the sample is given in Table 1.
As it can be elucidated from Table 1, about 90.5% of the
material is having size less than 500 µm; it may also be
noted that about 25.5% of the sample is having the size
below 125 µm. In order to obtain a closed sized feed
material, the sample was subjected to screening using
500 µm as top screen and 125 µm as the bottom screen.
Oversize of 500 µm and undersize of 125 µm were re-
moved. Only −500 + 125 µm size fraction was used for
the experimental work. The feed sample has been sub-
jected for the X-ray diffraction study for the identifica-
tion of the mineral phases which has been shown in Fig-
ure 1. From Figure 1, it is revealed that the sample con-
tains ilmenite as a major mineral and rutile, monazite,
Copyright © 2012 SciRes. JMMCE
S. MOHANAN ET AL. 1007
TABLE 1. SIZE DISTRIBUTION OF FEED SAMPLE.
Mesh size (µm) Weight (%) Cumulative weight %
−600 + 500 7.6 100
−500 + 425 15.8 92.4
−425 + 355 22.1 76.6
−355 + 250 17.2 54.5
−250 + 125 11.8 37.3
−125 + 100 6.1 25.5
−100 + 75 3.9 19.4
−75 15.5 15.5
View within article
Figure 1. XRD pattern of the mineral sand sample (✚:
ilmenite; : sillimanite; : rutile; •: zircon; ■: quartz; ▲:
garnet; and ♦: monazite).
zircon, garnet, sillimanite and quartz minerals are present
in minor quantity. The mineralogical studies were carried
out for the sample using a Leica petrological optical mi-
croscope, to quantify the different minerals. The minera-
logical assemblage of the feed sample has been tabulated
in Table 2. From Table 2, it is observed that the feed
sample contains 74.5% of titanium bearing minerals such
as ilmenite and rutile as conducting minerals and remain-
ing minerals such as monazite, zircon, garnet sillimanite
and quartz are non-conducting.
2.2. Experimental Work
The sample was then prepared for experiments using
HTRS by initial desliming using cyclone test rig, fol-
lowed by gravity concentration with spirals to achieve
about 90% heavy mineral concentrate, containing tita-
nium bearing minerals like ilmenite, rutile and leucoxene,
while non-conducting minerals include garnet, zircon,
silimanite, monazite, other heavy minerals like pyrox-
enes and amphiboles together with free quartz. Close
sized sample of −500 + 125 microns was prepared and
used for all the experiments. A typical HTRS experiment
involved the following sequence steps:
1) Pre-heat the sand to the desired temperature.
2) Start the HTRS rotor and apply voltage.
TABLE 2. MINERAL COMPOSITION OF FEED SAMPLE.
Mineral Mass %
3) Finally, start the feeder while adjusting the splitter
The experimental program was designed to achieve
better quality and quantity by suitably selecting the pro-
cess variables. All the experiments were conducted on
laboratory model HTRS (MDL Australia make). The val-
ues along with levels of three independent process vari-
ables—temperature (X1), feed rate (X2) and roll speed (X3)
—that have been used in this study are given in Table 3.
All other parameters are kept constant throughout the
experiments. The results obtained were used for the
computer simulation programming applying least square
The levels are chosen to be in sync with plant opera-
tion data. The feed rate is suitable for the laboratory
—scale HTRS of 250mm diameter. Below 100˚C, mois-
ture is retained which affects the separation and heating
above 140˚C, leads to undesirable wastage of energy.
3. Results and Discussion
A three factor, three levels Box-Behnken design was
used to determine the responses such as grade and reco-
very of the conducting minerals. For any experiment, we
calculate the grade and recovery as process outputs.
However, since these two are inversely related, maxi-
mizing any one would not represent the optimum operat-
ing condition. Hence it is proposed to define a new index,
Operational Quality Index (OQI), given by,
Assay valueof product%
Yield%* Assayvalue oftheproduct%
Assay value ofthefeed
The ideal separation in mineral processing would have
an OQI value of 200. However, in all “real” separation
practices, OQI would be less than this value. The operat-
ing conditions that maximize OQI under constraints are
the actual optimum operating condition for the unit op-
eration. The experimental values of OQI obtained from
factorial (Box-Behnken) designed experiments are tabu-
lated in Table 4.
From the experimental results, grade and recovery are
Copyright © 2012 SciRes. JMMCE
S. MOHANAN ET AL.
TABLE 3. PROCESS VARIABLE VALUES AND LEVELS.
180.0 185.0190.0 195.0 200.0
Levels and codes
S.No Variables (−1) (0) (+1)
1 Temperature in ˚C (X1) 100 120 140
2 Feed rate in tph (X2) 1.5 2.0 2.5
3 Roll speed in rpm (X3) 120 150 180
TABLE 4. FACTORIAL DESIGN AND OQI VALUES.
3 Experimental Predicted
1 −1 −1 0 195.2 195.6
2 1 −1 0 195.2 195.2
3 −1 1 0 194.7 194.7
4 1 1 0 194.4 192.8
5 −1 0 −1 193.3 192.9
6 1 0 −1 185.6 186.7
7 −1 0 1 194.1 192.9
8 1 0 1 195.2 195.7
9 0 −1 −1 193.8 192.6
10 0 1 −1 186.8 187.2
11 0 −1 1 194.4 194.0
12 0 1 1 193.8 194.9
13 0 0 0 195.1 195.1
14 0 0 0 195.1 195.1
15 0 0 0 195.1 195.1
calculated for each experiment in order to verify the mo-
del equation and the second order response functions
representing the conducting minerals are expressed as
functions of the independent process parameters. The
calculated model equations for grade (y1), recovery (y2)
and OQI (y3) of titanium bearing minerals in the con-
ducting fraction, on the basis of coded variables are
given in Equations (5), (6) and (7) respectively
0.09 0.47 2.89
x xxx xx
A comparison between the predicted values of OQI
from Equation (7) and experimental results are made in
Figure 2, which shows that predicted values and the ob-
Figure 2. Relation between predicted and observed OQI of
titanium minerals in the conducting fraction.
served data points are in very good agreement (R2 of
In order to check the adequacy of the model in terms
of classical statistics, a plot of predicted values vs. re-
siduals is made. As discussed by Montegomery ,
there is no relation between the predicted values and the
residuals (Figure 3). In addition, a plot of cumulative
normal probability as a function of predicted values is
made, showing a satisfactory linear relationship (Figure
Effect of Variables on OQI of Conducting
As the temperature of the feed material increases at lower
roll speeds, the conducting fraction quality increases; on
the other hand, at low levels of feed material temperature,
the recovery of the conducting materials increases with
an increase in roll speed. However, to improve the
economy of the process, it is desired to keep grade above
a certain specified value and maximize recovery at this
level and this condition of operation is achieved with the
help of OQI.
For better understanding, the statistical model is de-
scribed in terms of three dimensional (3D) response sur-
face plots between two independent variables and quality
of the conducting minerals at center level of the third
variable. Figure 5 shows the effects of temperature and
feed rate on OQI of the conducting fraction at center
level of roll speed. It is observed that at center level of
roll speed there is a trivial effect on OQI with tempera-
ture or feed rate variations. This is due to the fact that at
higher temperatures, grade obtained is higher. At higher
temperatures, the work function is high which results in
more pinning effect of the non-conducting particles,
thereby affecting the recovery. At higher feed rates and
lower temperatures, excessive multilayer formation re-
sults in more recovery with low grade. Hence, in this
range, the OQI values almost remain constant.
Figure 6 explains the effects of temperature and roll
speed on OQI of the conducting fraction at center level
of feed rate. The OQI of the conducting fraction in-
Copyright © 2012 SciRes. JMMCE
S. MOHANAN ET AL. 1009
186 188 190 192 194
Figure 3. Plot of predicted values of OQI vs. residuals of
Cumulative Normal Probability
Figure 4. Cumulative normal probability vs. Predicted va-
lues of OQI.
Figure 5. Response surface plots showing the effect of tem-
perature (x1) and feed rate (x2) on OQI of conducting frac-
Figure 6. Response surface plots showing the effect of tem-
perature (x1) and roll speed(x3) on OQI of conducting frac-
creases initially with increase in roll speed, because of
the drastic increase in recovery with respect to rate of
quality reduction, due to the fact that the centrifugal
force dominates the pinning force of non-conducting
particles. Further it may be inferred that the roll speed
controls the selective charging at the ionizing zone and
discharging to the rotor. With further increase in roll
speed above a certain value, there is a drastic lowering of
grade of the product.
Figure 7 shows the effects of feed rate and roll speed
at center level of temperature. It can be observed from
the figure that there is a trivial effect of feed rate on OQI
of the conducting fraction.
Maximizing the functions given by Equations (5) and
(6) is done by using the maximization toolbox in MAT-
LAB 7.1. It is observed that a maximum grade of 97.7%
is predicted under conditions of high temperature, inter-
mediate feed rate and low roll speed; however, the re-
covery is only 88.5%. On the other hand, recoveries of
around 99.8% can be achieved at low temperatures, high
roll speeds and intermediate feed rates, with a product
grade of 94.9%. In order to obtain a balance between the
recovery and grade, an attempt is made to maximize the
variable OQI, with the constraint that grade has to be
>96% and recovery >98%. The maximization is done
based on Constrained Function Optimization. It is ob-
served that the maximum value of OQI obtained under
the given constraints is 195.53. This is obtained at the
following operating conditions—Temperature: 102°C, Feed
Rate: 1.75 tph and Roll Speed: 132 rpm. Under these
operating conditions, from Equations (5) and (6), the
grade and recovery obtained are 96.6% and 98.9% re-
The primary process input parameters of a High Tension
Roll Separator (HTRS), namely the roll speed of the
rotor, feed material temperature and feed rate are opti-
mized in this study, using experimental data and qua-
dratic programming. For the optimization studies, a new
Figure 7. Response surface plots showing the effect of feed
rate (x2) and roll speed(x3) on OQI of conducting fraction.
Copyright © 2012 SciRes. JMMCE
S. MOHANAN ET AL.
output index—Operational Quality Index (OQI)—has
been applied successfully to optimize input parameters
for efficient operation. Statistical models were developed
for OQI, as well as both grade and recovery of the con-
ducting minerals individually. The predicted values ob-
tained using the models were in very good agreement
with the observed values (R2 value of 0.91 for OQI;
similar values obtained for both grade and recovery).
Process optimization, viz. maximization of OQI has been
done by keeping the constraints of grade >96% and re-
covery >98%. The maximum value of OQI obtained un-
der the given constraints is 195.53, at the following oper-
ating conditions—Temperature: 102˚C, Feed Rate: 1.75
tph and Roll Speed: 132 rpm. Under these operating
conditions, the grade and recovery obtained are 96.6%
and 98.9% respectively. Normally, the separation effi-
ciency index, which is a % recovery from the formula, is
associated with coal washing processes; while coefficient
of separation is nothing but an index derived from reco-
very/distribution percentages of concentrates and rejects.
Though these indices are useful in predicting the process
performance, using the quality and quantity of different
fractions, these are not completely significant for process
variable optimization studies. Therefore, it was found
that the concept of OQI is simple and more reliable in
Authors are thankful to Tata Steel Ltd management for
the support and permission to publish this work.
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