IJCPE Vol.9 No.1 (March 2008)  31 

 

 
Iraqi Journal of Chemical and Petroleum Engineering 

 Vol.9 No.1 (March 2008) 31-34 
ISSN: 1997-4884 

Experimental Studies on the Benification of Fine Solids by Forth 
Flotation 

 

Muna Yousif Abdul-ahad 

Environmental Engineering Department - College of Engineering - University of Baghdad – Iraq 

Abstract 

In this paper, the experiments were carried out in laboratory flotation cell treating solid fines. The effect of 

variables such as collector oil dosage, pine oil dosage and solid content of the feed slurry have been investigated on the 

flotation characteristics of low rank coal. Attempts have also been made to develop some empirical Eq. to predict the 

yield and ash content of concentrate with the operating variables, solids concentration, collector oil dosage, and pine oil 

dosage, to estimate the recovery at any operating conditions. The calculated results obtained from regression equation 

by correlating the variables with the yield and ash content of concentrate have been compared to study whether 

calculated values match closely with the experimental values by using F test at any level of significance. 

Keywords: Flotation, Solid fines treatment by flotation.

Introduction 

It has been reported in the literature, Biswal et. al. (1), 

Lynch et. al. (2), Trahar (3), Vanagamudi and Rao (4), 

and Warren (5) that the particles reach the froth phase or 

concentrate either by true flotation or by entrainment. 

True flotation occurs when the floatable particles colloid 

with the bubbles, attach with them and the resultant 

mineralized bubbles rise towards the froth level and are 

then scraped off. Entrainment Biswal et al(1),Lynch et al 

(2), Trahar (3) Warren(5) when non-floatable particles 

enter in the water present in between the spaces of the 

bubbles and continue to move upwards. During the 

traverse, large particles drop back to the pulp phase 

becomes of higher mass, whereas, fine gangue continues 

to move and ultimately reports to the froth Vanagamudi 

and Rao (4). Hence, entrainment is non-selective and has 

determinal effect on flotation. Warren(5) found that in a 

batch flotation, the recovery of floatable mineral at a 

particular interval of time is linearly related to the weight 

of water recovered in a system in which experiments are 

carried out by varying the height of froth coloumn, rate 

and depth of froth removed. 

Froth flotation is the oldest physical separation type 

and has the advantages of relatively low power 

consumption per unit mass of material processed and a 

proven capacity to handle higher tonnage rates of solids, 

than the newer oil agglomeration procedures. The 

obvious disadvantages of froth flotation are its tendency 

to entrain very fine materials and the production of a wet 

froth. Both effects can potentially be reduced by a cleaner 

float using a hydrocarbon entrainer, but first it is 

necessary to establish the best performance of the 

roughing float. Low rank coals have a high volatile 

content and a high H/C ratio. A demineralized low-rank 

coal would thus appear to be an excellent feed-stock for 

liquefactions, combustion, and of several possible uses 

would be as the solid component in a coal-oil mixture. 

In this paper a mathematical approach based on 

correlations between   variables affecting  flotation 

process for the yield of concentrate (Y) and ash content 

of concentrate (A)  respectively using multiple linear 

regression Kennedy&Neville (6),Francis(7), Klugh (8), & 

Mohrotra & Saxena (9). 

  

 

University of Baghdad 

College of Engineering 
Iraqi Journal of Chemical 

and Petroleum Engineering 

 



Experimental studies on the benification of fine solids by forth flotation 

IJCPE Vol.9 No.1 (March 2008) 32 

Correlation between variables and yield of 

concentrate: 

The process parameters can be correlated with the yield 

of concentrate by an equation of the form:    

                                                                                                   

Y=k0 (X1)
 k1

 (X2)
k
2 (X3)

k
3                                               (1) 

 

Correlation between variables and ash content of 

concentrate: 

 

A= J0 (X1)
J
1 (X2)

J
2 (X3)

J
3                                               (2) 

 (2)    

Where (Y) represents yield% of concentrate, (A) 

represents ash% content of the concentrate, and X1, X2, 
and X3 represent solids concentration, collector oil 

dosage (Kg/t) and pine oil dosage (Kg/t) respectively. 

The constants k0, k1, k2, k3, J0, J1, J2 & J3, are evaluated 

from the principle of multiple linear least squares 

regression analysis, for which STATISTICA program 

package is used for any number of constants present in 

regression Eq. using the experimental data. 

The prediction of concentrate yield%, and ash% can be 

made for any given value of solid concentrate, collector 

oil dosage and pine oil dosage respectively within the 

experimental limit. 

Fisher
'
s F-Test Kennedy & Neville (6), Francis (7) & 

Klugh (8) is used to see how the predicted Eq. of the 

concentrate yield, and ash are fitted to the experimental 

values. The statistic F is given by: 

 

F= 
2

2

Y

X

S

S
                                                              (3) 

 

where 

2

11

2
)(

)1(

1 1
XX

n
S

n

i

iX



 



                                   (4)     

).....(
1

11

1

n
XX

n
X                                               (5) 

2

12

2
)(

)1(

1 2
YY

n
S

n

j

jY



 



                                     (6) 

).....(
1

11

2

n
YY

n
Y                                                  (7)                        

 

After F is found for yield of concentrate, and ash. The 

tabulated value of F for 5% level of significance and 

degrees of freedom d.f., f1 and f2 is Fp. 

Where 

f1 = number of observations (n1-1) 

f2 = number of observations (n2-1) 

Fp =tabulated value of F 

Thus if F<FP, then it shows a good agreement between 

the experimental and calculated values of yield of 

concentrate and calculated values of ash content of 

concentrate. 

 

Experimental Work 

Coal as a product of degradation of vegetable matter 

was prepared. The liberation size of ash in the coal was 

estimated at around below 100 microns and classified 

using standard test sieves. The size and ash distribution of 

sample used in these studies are given in Table 1. 

 

Table 1 Size analysis of sample 

Ash% Weight% Size, microns 

35.45 28.3 -100+75 

40.58 22.8 -75+45 

50.70 48.9 -45 

42.24 100.0 Total 

         

The flotation tests were carried out in a batch 

laboratory flotation system as shown below: 

 
Fig. 1 Experimental setup 

 

The flotation cell of 2.5 L capacity using the 

conditions: (1) mixing time for preparation of slurry 

=3min, (2) conditioning time =5 min, (3) impeller speed 

=1400 rpm, and (4) time of collection = 90 sec. 

The pulp was conditioned with diesel oil (collector) for 

5 min and after conditioning, pine oil (frother) was added 

at appropriate dose and solids concentration was 

maintained by adding required quantity of water. Then, 

aeration was started by operating the air valve at a 

pressure of 400 kPa  and the froth floated concentrate was 

collected for 90s .The concentrate and tailings were then 

dewatered, dried, weighed, sub- sampled and ash content 

of each sample was determined. All the tests were carried 

out using the above procedure by varying operating 

conditions (Table 2). 

 



Muna Yousif Abdul-ahad  

IJCPE Vol.9 No.1 (March 2008) 33 

Table 2 Operating conditions of the variables. 

 
 Operating 

conditions of 

variables 

SL.no 

Fixed operating conditions  

Pine oil 
dosage 

Kg/t 

Collector 
dosage 

 kg/t 

Solids 
concentration 

% 

 

    
1.0 2.0 _ Solids 

concentration% 

(10,15,20,25) 

1 

     

1.0 _ 25 Collector oil 

dosage kg/t 
(0.5,1.0,1.5,2.0) 

2 

     

_ 2.0 25 Pine oil dosage 
kg/t 

(0.15,0.5,0.75,1.0) 

3 

     

 

 

Table 3 Comparison of experimental and predicted values 

of the test data. 
 

 Operating variable SL.

no 

                          
Predicted 

Experimental 

Cleans Tails Cleans 

As

h 
% 

Yie

ld 
% 

Ash 

% 

Yie

ld 
% 

As

h 
% 

Yiel

d 
% 

 

20.

13 

35.

56 

45.0

0 

70.

55 

20.

55 

35.5

5 

10.

00 

Solid 

concentratio
n 

% 

 
 

Collector  

oil dosage 
kg/t 

 

 
  

Pine oil 

dosage 
kg/t 

 
 

1. 

30.

24 

40.

42 

50.0

0 

67

.00 

30.

55 

40.5

5 

15.

00 

 

28.
67 

45.
36 

50.5
5 

55.
55 

28.
00 

45.0
0 

20.
00 

25.

02 

38.

06 

48.5

0 

65

.5 5 

25.

00 

38.0

0 

25.

00 
       

21.

89 

26.

00 

43.7

8 

72.

87 

20.

53 

27.5

5 

0.5

0 

2. 

26.

00 

35.

15 

49.1

0 

70.

15 

26.

55 

30.8

3 

1.0

0 

 

27.
10 

37.
05 

50.0
1 

59.
86 

24.
57 

42.1
5 

1.5
0 

26.
00 

41.
08 

48.9
6 

63.
11 

27.
36 

35.8
2 

2.0
0 

        

24.

00 

31.

05 

48.0

0 

70.

13 

20.

97 

29.8

4 

0.1

5 

3. 

26.
09 

36.
00 

51.0
3 

68.
01 

25.
03 

34.1
0 

0.5
0 

 

23.

98 
26.

75 

38.

01 
36.

98 

50.0

0 
49.0

0 

58.

99 
58.

95 

27.

10 
27.

00 

41.0

8 
47.0

3 

0.7

5 
1.0

0 

 

 

Results and Discussion 

 The regression equations using the experimental data 
given in Table 3 were applied for the correlations 

assumed above in Eq. 1 and 2 respectively to evaluate the 

constants for the concentrate yield% and ash content% of 

concentrate. Fisher’s F-tests were used to see how Eq. 1 

and 2 were fitted to the experimental values as follows: 

 

The relation between concentrate yield and the 

variables reduces to: 

 

Y= 23.002 (X1)
0.130

(X2)
0.330

(X3)
0.120

                               (8) 

    

A graphical representation for the experimental and 

predicted values of the test data for different solid 

concentration% collector oil dosage Kg/t are shown in 

Fig. 2 to 4. 

The statistic F is calculated as 1.104 for yield of 

concentrate. The tabulated value of F for 5% level of 

significance and degree of freedom d.f. =11 and f2 =11 is 

Fp =3. In this case also F< Fp results in a good agreement 

between the experimental and calculated values of yield 

of concentrate given in Table 3. 

 

20

30

40

50

60

70

80

5 10 15 20 25 30

Solid concentration%

E
x
p

e
ri

m
e

n
ta

l 
a

n
d

 p
re

d
ic

te
d

 v
a

lu
e

s
 o

f 
y
ie

ld
%

 a
n

d
 a

s
h

%

Experimental
cleans yield%

Experimental
cleans ash%

Experimental
tails yield%

Experimental
tails ash%

Predicted
cleans yield%

Predicted
cleans ash%

 
Fig. 2 Experimental and predicted values of the test data 

for different solid concentrations% 



Experimental studies on the benification of fine solids by forth flotation 

IJCPE Vol.9 No.1 (March 2008) 34 

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5

Collector oil dosage kg/t

E
x
p
e
ri
m

e
n
ta

l 
a
n
d
 p

re
d
ic

te
d
 v

a
lu

e
s
 f

o
r 

c
le

a
n
s
 a

n
d
 t

a
il
s
 o

f 
y
ie

ld
%

 a
n
d
 

a
s
h
%

Experimental

cleans yield%

Experimental

cleans ash%

Experimental tails

yield%

Experimental tails

ash%

Predicted cleans

yield%

Predicted cleans

ash%

 
Fig. 3 Experimental and predicted values of the test data 

for different collector oil dosages kg/t 

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Pine oil dosage kg/t

E
x
p

e
ri

m
e

n
ta

l 
a

n
d

 p
re

d
ic

te
d

 v
a

lu
e

s
 o

f 
y
ie

ld
%

 a
n

d
 a

s
h

%

Experimental cleans

yield%

Experimental cleans

ash%

Experimental tails

yield%

Experimental tails

ash%

Predicted cleans yield%

Predicted cleans ash%

 
Fig. 4 Experimental and predicted values of the test data 

for different pine oil dosages kg/t 

 

The relation between concentrate yield and the 

variables reduces to: 

 

A=18.983 (X1)
0.101

 (X2)
0.120

 (X3)
0.100

                              (9) 

  

The standard deviation of the percent errors in the 

equation above is 0.054  

The statistic F is calculated as 0.987 for ash content of 

concentrate. The tabulated value of F for 5% level of 

significance and degree of freedom d.f. =11 and f2 =11 is 

Fp =3. In this case also F< Fp results in a good agreement 

between the experimental and calculated values of yield 

of concentrate given in Table 3.   

The graphical representations of experimental and 

predicted values of the test data are shown in Fig. 2 to 4.  

 

Conclusions 

It may be concluded that when the experimental data 

were correlated with the operating variables through a 

regression equation then the estimated regression 

equation was found to fit within experimental limits and 

the same was tested and verified by using Fishers F- test 

at 5% level of significance. 

References 

1. S.K.Biswal, P.S.R. Reddy, and S.K. Bhaumik,” Some 
aspects on entrainment in Coal Flotation.” The Indian 

Mining and Engineering Journal, Vol.41. No. 5, May 

2002, p 39. 

2. A.J.Lynch, N.W.Johnson, E.V.Manlaping and 
C.G.Thorne,”Mineral and Coal Flotation Circuits and 

Their Simulation.” Elsevier Scientific Publishing Co., 

Amsterdam, 1981. 

3. W.J. Trahar,”A Rational Interpolation of Role of 
Particle Size in Flotation.” International Journal of 

Mineral Processing, Vol.8, 1981, p289. 

4. M.Vanagamudi and T.C.Rao,”A Model for the 
Prediction of Fines Recovery in Batch Coal 

Flotation.” Mineral Engineering Vol.2, 1989, p185. 

5. L.J.Warren,”Determination of the Contributions of 
True Flotation and Entrainment in Batch Flotation 

Tests.” International Journal of Mineral Processing, 

Vol. 14, 1985, p33. 

6. J. B. Kennedy & A. M. Neville, "Basic statistical 
methods for engineers & scientists", 2nd edition, 
Crowell, 1976. 

7. A.Francis, "Advanced level statistics", ST (P) L TO, 
1979. 

8. H. E. Klugh, "Statistics: he essentials for research", 
2nd edition, Wiley, 1974. 

9. S. P. Mehrotra & A. K. Saxena, “Studies on Froth 
Flotation of Coal”, Int. J. Miner. Processes, 10 (1983) 

255.