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HEAVY MINERALS 2003164

sample was loaded into the pressure vessel and dischargedthrough the tube at a controlled flow rate (Qm). Pressureloss and flow rate were recorded, allowing the velocity andwall shear stress to be determined directly. The measureddata is presented in a conventional pseudo-shear diagram,which is a plot of pseudo-shear rate (Γ ) versus wall shearstress (τo), where:

[1]

[2]

and V  = mean mixture velocity (m/s) = Qm /A D = internal pipe diameter (m)∆P f  = pipeline pressure loss due to friction (Pa) L = pipeline length (m).

A typical data set and pseudo-shear diagram is shown inFigure 1.

The slurry is best modelled using the yield pseudo-plasticmodel in which the yield stress (τ y), fluid consistency index(K ), and flow behaviour index (n) are determined iterativelyfrom a pseudo-shear diagram (Γ  and τo known) using thefollowing relation (Govier and Aziz, 1972):

[3]

The rheological parameters established for each residuesample are correlated against the volume concentration of solids (Cv), determined from the following relation:

[4]

where S w = 0.9982 , relative density of water at 20°CS m = slurry relative density

S s = solids relative density, 2.61.

Effect of pump shearing

The analysis of the tailings was based on the thickenerunderflow pump suction and discharge data only. Thecombined measured suction and discharge pseudo-sheardiagram for a typical thickener (thickener No. 2) is shownin Figure 2. It is seen that the slurry at the suction side has aslightly lower yield stress than the discharge slurry. This isattributed to shearing of the slurry and generation of ultra

fine particles. The suction and discharge data have beenmodelled separately to account for these differences.From Figure 2 it is evident that the residue slurry is found

to be shear thinning i.e. the apparent viscosity decreaseswith increasing shear rate. Furthermore it may be seen thatfor similar slurry densities the rheology increases from thesuction to the discharge. This would imply that the slurryexhibits time dependent behaviour in which the rheologyincreases with exposure to shear.

Results obtained for a sample from the pilot plant pumpsuction and centrifugal and peristaltic pump discharge arepresented in Figure 3. From the results it is evident thatboth the centrifugal pump and peristaltic pump increase theslurry rheology when compared with the data obtained fromthe common suction manifold. This is more pronounced in

the centrifugal pump and is attributed to higher shearintensity in the centrifugal pump.

Figure 4 presents the slurry yield stress, Figure 5 the fluidconsistency index, and Figure 6 the flow behaviour index asa function of solids concentration by volume. All theparameters are based on the underflow pump suction anddischarge data. The rheological parameters were determinedfrom the measured data using Equation [3].

Since there is a difference between the pump suction anddischarge samples, these are identified separately on thegraphs. From these charts it is observed that the yield stressfor the discharge data is generally higher than the suctiondata; however, the fluid consistency index and flowbehaviour index parameters remain relatively constant.

C S S 

S S v

m w

s W 

=  −

−

Γ = =           −( )

−( )+

  +  −( )

+  +

+

+8 4 1

3 12

2 1 1

3

11

1

22

V 

 D

n

K 

n n n

o

n

o y

n

o y

 y

o y  y

τ τ τ 

τ τ 

τ 

τ τ    τ 

τ o f  D P

 L=   ∆

4

Γ =8V 

 D

Figure 1. Typical data and pseudo-shear diagram

0 200 400 600 800 1000

Pseudo-Shear Rate, 8V/D (s-1)

Sample: Thickener 1 Underflowρm: 1.181 t/m3

   W  a

   l   l   S   h  e  a  r   S   t  r  e  s  s ,       τ

  o   (   P  a   )

200

180

160

140

120

100

80

60

40

20

0

Pseudo-shear Wall Shear

Rate Stress

(s-1) (Pa)

986.0 145.0

896.8 142.0

783.7 139.1

645.7 134.3

539.9 129.6

449.1 125.0

374.9 120.7

318.1 116.8

267.9 112.8

222.9 108.6

183.9 104.6

157.5 100.8

126.3 96.9

104.3 93.0

83.4 89.2

67.2 83.4

57.6 79.6

44.2 72.0

38.3 68.2

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VARIABLE RHEOLOGY OF HEAVY MINERAL TAILINGS 165

Figure 2: Test tesults for thickener No. 2 suction and discharge

Figure 3: Test results for the pilot plant at one density

Figure 4: Slurry yield stress versus solids concentration by volume

0 100 200 300 400 500 600 700 800 900 1000Pseudo-Shear Rate, 8V/D (s-1)

1.240 t/m3 Suction 1.223 t/m3 Suction 1.161 t/m3 Suction

1.224 t/m3 Discharge 1.203 t/m3 Discharge 1.166 t/m3 Discharge

   W  a

   l   l   S   h  e  a  r   S   t  r  e  s  s ,       τ

  o   (   P  a   )

200

180

160

140

120

100

80

6040

20

0

0 200 400 600 800 1000

Pseudo-Shear Rate, 8V/D (s-1)

ρm=1.241 t/m3

Centrifugal Pump discharge Peristaltic Pump Discharge Common Pump suction

   W  a   l   l   S   h  e  a  r   S   t  r  e  s  s ,       τ

  o   (   P  a   )

400

350

300

250

200

150

100

50

0

0% 2% 4% 6% 8% 10% 12% 14|% 16% 18% 20%

Volume Fraction of Solids, Cv(%)

Suction Data Discharge Data Suction Model Discharge Model

   W  a   l   l   S   h  e  a  r   S   t  r  e  s  s ,       τ

  o   (   P  a   )

100

90

80

70

60

50

40

30

20

10

0

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HEAVY MINERALS 2003166

Conclusions

• The residue slurry behaves as a time dependent yieldpseudo-plastic fluid i.e. it exhibits shear thinningbehaviour, and the rheology increases with exposure tointense shearing (as in a centrifugal pump)

• The rheological parameters have been determined asfunctions of the volumetric concentration of solids

• The slurry rheology tends to increase as it passesthrough a pump (increase in yield stress). The increasein rheology is attributed to the generation of fineparticles during shear. This effect is decreasedconsiderably as the density decreases

• The rheology of the slurry measured at the discharge of 

a centrifugal pump is greater than the rheology

measured at the discharge of a peristaltic pump on acommon manifold. The difference is attributed to themore intense shear in the centrifugal pump

• Finally it is concluded that pumping the residue in ahigh shear pump, such as a centrifugal pump, will notreduce the residue yield stress but rather increase it.

References

GOVIER, G.W. and AZIZ, K. The flow of complex mixtures in pipes. Von Nostrand Reinhold Company,1972.

Figure 5. Fluid consistency index versus solids concentration by volume

Figure 6. Flow behaviour index versus solids vehicle concentration by volume

0% 2% 4% 6% 8% 10% 12% 14|% 16% 18% 20%

Volume Fraction of Solids, Cv(%)

Suction Data Discharge Data Fitted Model

   F   l  u   i   d   C  o  n  s   i  s   t  e  n

  c  y   I  n   d  e  x ,

   K   (   P  a .  s  n   )

14

12

10

8

6

4

2

0

0% 2% 4% 6% 8% 10% 12% 14|% 16% 18% 20%

Volume Fraction of Solids, Cv(%)

Suction Data Discharge Data Fitted Model

   f   l  o  w   B  e   h  a  v   i  o  u  r   I  n   d  e  x ,  n

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0