The influence of coarse particles on the rheology of fine-particle slurries

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Rheology in the Mineral Industry II

March 14-19, 1999 Kahuku, Oahu, Hawaii United Engineering Foundation

THE INFLUENCE OF COARSE PARTICLES ON THE RHEOLOGY

OF FINE PARTICLE SLURRIES

Allan D. Thomas Slurry Systems Pty Limited 7 Cantwell Rd, Lochinvar, NSW 2321, Australia T:61 2 4930 7309; F:61 2 4930 7770; E: [email protected]

ABSTRACT: The influence of coarse particles on the rheology of fine particle slurries is studied based on well known expressions for the effect of rigid particles on the viscosity of a Newtonian fluid. Recent rheology measurements involving addition of various sands to slimes slurries are used to develop semi-theoretical correlations. The developed equations are shown to describe the trends evident with more common continuous particle size distribution slurries. This is illustrated by recent rheology measurements on 14 different mineral slurries.

INTRODUCTION

Slurries of interest in the mineral industry can range from all colloidal, clay type slurries, to wide particle size distribution ball mill products, to gapped particle size distributions consisting of almost mono-sized grannular material suspended in a clay slurry. The rheology of all three types can be measured in a viscometer. For colloidal sized particles the principal forces determining the rheology are attractive forces dependant on surface chemistry and molecular dispersion forces. The relative strength of the attractive and the rheology increases with decreasing particle size and chemical influences such as pH are important. For coarser particles (say greater than 10 microns), hydrodynamic and dispersive forces determines the rheology,Makosko (1). For a given solids concentration with decreas a ice interparticle reaction forces largely determine the rheology.

COARSE PARTICLES IN NEWTONIAN FLUIDS

When solid particles are suspended in a Newtonian fluid the viscosity is increased. Einstein (2) first analysed the hydrodynamic effect of dilute concentrations of spheres arriving at the classic equation: M/M= 1 + 2.5C, (1) Numerous extensions of this equation have since been proposed. For example D.G. Thomas (3) measured the viscosity of numerous suspensions and developed the empirical equation: M/M= 1 + 2.5C, + 10.05 C.? + 0.00273 exp(16.6 C,) (2)

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In modelling the effect of both sperical and non-spherical particles and mono and wide particle size distributions, a key parameter is the ratio C/Comax where Cumax is the volume concentration at the maximum packing density. For example Landel et al (4) found that the following equation (3) described the influence of a range of spherical and non-sperical particles having both mono and wide size distributions. Equation 3, with Comax = 0.75, approximates equation 2.

MIM, = (1 - C/Crmax) 25 (3)

Most of the experimental data supporting the above equations was obtained in small scale rotational or tube viscometers. Data obtained in larger diameter pipes by the present author, Thomas (5), (g), (Z) and Shook et al (8), also support these results. These authors tested various size sands in high viscosity Newtonian fluids in horizontal pipes. Under laminar flow conditions the sand slowly settles and for coarse particles in low viscosity fluids a moving or stationary bed forms. Data pertaining to these conditions cannot be used in comparing with equations 2 and 3. Only data for which the ratio of fluid viscosity to particle size was sufficiently large to ensure near homogeneous flow were used. The test data were plotted as pressure gradient versus velocity on log-log co-ordinates. This enabled the laminar and turbulent flow regimes to be identified. Laminar flow slurry data which paralled the laminar flow fluid only curve were judged as flowing near homogeneously. Using this criteria the following data were used to compare with equation 2: Thomas (5,6,Z) (105 mm pipe); 0.82 mm sand in 270 mPas fluid, C. = 0.12; 0.13 mm sand in 2000 mPas fluid, C, = 0.06; 0.13 mm sand in 160 mPas fluid, C, = 0.10. Shook et al (8) (52.5 mm pipe): 0.18 mm sand in 38 mPas fluid, C. = 0.30; 0.18 mm sand in 38 mPas fluid, C. = 0.36; 0.18 mm sand in 38 mPas fluid, C. = 0.42 The results are shown in Figure 1. Also shown in Figure 1 is the predicted relationship according to equation 2 and equation 3 (with Cumax = 0.75). The data confirm the general trends predicted by equations 2 and 3.

16

15 •THOMAS (1978, 1979) + SHOOK ET AL (1973)

14 13 12

VISCOSITY RATIO EQUATION 3 (Cmax = 0.75) *

- I EQUATION 2

2 1

5 10 15 20 25 30 35 40 45 50

VOLUME CONCENTRATION SAND (%)

FIGURE 1. VISCOSITY RATIO VERSUS VOLUME CONCENTRATION

SAND IN NEWTONIAN FLUIDS IN 50 & 100 mm PIPES

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COARSE PARTICLES IN NON-NEWTONIAN VEHICLE SLURRIES

Bingham Parameter Variation with Volume Concentration of Coarse Particles The rheology of slurries is often described by the Bingham Plastic model: = = I, + Mp T (4) The addition of coarse particles to a colloidal non-Newtonian Bingham Plastic clay slurry can be expected to increase the rheology of the clay slurry. Thomas (2) presented limited data which indicated that both the Yield Stress and the Plastic Viscosity increase in a

similar manner as described above for coarse particles in Newtonian fluids.

The author has recently completed two series of tests on mine tailings which involved addition of sand to slimes slurries. The results of these tests can be used to further investigate the effect of coarse particles. The testwork was conducted in a Contraves Rheomat 115 rotational viscometer. Two bob and cup systems were used. The "A" System used a bob of diameter 48.56 mm and a cup diameter of 48.10 mm giving a gap of 1.27 mm. The "B" system used a bob of 30.00 mm diameter and a cup of diameter 32.50 mm giving a gap of 1.25 mm. Shear rates ranged from 41.8 sec to 661 sec!. The Series 1 tests involved testing four different sands in a minus 10 micron slimes slurry. The Series 2 tests involved testing one sand in a minus 45 micron slimes slurry. Details of the sand properties are summarised in Table 1.

TABLE 1 SAND PROPERTIES

Pso Size Pso Size Pro Size (Microns) (Microns) (Microns)

Series 1 Tests Sand SG 3.93 Minus 600 micron sand 470 350 160 Minus 425 micron sand 360 230 105 Minus 300 micron sand 220 150 80 600 x 300 micron sand 520 450 350 Series 2 Tests Sand SG 2.86 Minus 600 micron sand 430 320 200 The tests were conducted rapidly to minimise any effects due to sand settling in the viscometer gap during the test. If settling effects were evident the sample was mixed at Series 1 tests at low slimes concentrations were clearly influenced by settling of the sand each shear rate increment during the test. In spite of these precautions some results in the

and 600 x 300 micron sands respectively, being rejected. It can be noted that for all data included, the slimes Yield Stress was about an order of magnitude higher than that required for static stability as given by the following equation,Thomas, (10). i.e. all slurries were completely stable under static conditions with the slimes Yield Stress preventing sand settling. Ty (slimes) ≥ 0.092 g d (Ps - pv) (5)

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The viscometer data were analysed using the Bingham Plastic model. All data closely followed the Bingham model at shear rates above 100 sec!. For shear rates below 100 sec! the data deviated from the Bingham model and this low shear rate data was not used. The Bingham parameters were determined for the slimes alone at various slimes concentrations and for various additions of sand. Figure 2 shows the Yield Stress ratio versus the volume concentration of sand for the Series 1 and 2 tests. The Yield Stress ratio is the Yield Stress measured with sand addition divided by the Yield Stress of the slimes alone. The data for Series 1 and 2 tests apply to a range of slimes concentrations. Also shown in Figure 2 are results for 0.2 mm sand in clay in a 9.41 mm diameter pipe,Thomas (11), zircon flour in clay measured in a rotational viscometer, Thomas (9), and minus 20 mm coal in a 152 mm diameter pipe, Duckworth et al (12). Given the range of test conditions all results are remarkably consistent. The data of Figure 2 are best fitted by the following equation analagous with equation 3 with kCumax = 0.9 rather than Comax = 0.75 which applied in Figure 1. Ty (sand + slimes) / Ty (slimes) = (1 - C,/kCumax)?s (6) where k is a correlating parameter. The product Cymax is used to correlate data such as in Figure 2. Inclusion of Comax provides a physical rationale to predict the likely rheology of say a wide size distribution sand based on narrow size distribution sand data. Because of the relatively narrow particle size distributions of most of the sands tested Comax will be around 0.6, so the product kCymax = 0.9 indicates a k value around 1.5.

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• SERIES 1 TESTS • SERIES 2 TESTS

11 X THOMAS (1978/2) A THOMAS (1981)

10 & DUCKWORTH ET AL (1983)

RATIO YIELD STRESS A U 0 v ∞ 9 EQUATION 6 (kCvmax = 0.75)

2 EQUATION 6 (kCymax = 0.9) 1

5 10 15 20 25 30 35 40 45 50

VOLUME CONCENTRATION SAND (%)

FIGURE 2. YIELD STRESS RATIO - (SAND+SLIMES)/SLIMES

Figure 3 shows an analagous plot for the same data for the ratio of the Plastic Viscosity with coarse particles and the Plastic Viscosity of the vehicle slurry alone. Compared with Figure 2 there is considerably greater scatter in the results. The effect of coarse particle addition can be correlated by the following equation (7), analagous with Equation 3. Equation 7 predictions with kComax = 0.6 and 0.9 roughly encompass the range of results. Mp (sand + slimes) / Mp (slimes) = (1 - C,/kCymax) 25 (7)

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20

19 • SERIES 1 TESTS • SERIES 2 TESTS

18 X THOMAS (1978/2) A THOMAS (1981)

17 X DUCKWORTH ET AL (1983)

1 5 1 4

RATIO PLASTIC VISCOSITY 16 EQUATION 7 (kCvmax = 0.6);

0. 6

* EQUATION 7 (KCmax = 0.9)

1 5 10 15 20 25 30 35 40 45 50

VOLUME CONCENTRATION SAND (%)

FIGURE 3. PLASTIC VISCOSITY RATIO (SAND + SLIMES)/SLIMES

Bingham Parameter Variation with Total Solids Concentration Figures 2 and 3 show the Yield Stress and Plastic Viscosity ratios plotted against volume concentration of coarse particles. An alternative method of presentation involves plotting the measured Yield Stress and Plastic Viscosity against total solids concentration. In this case the ratio of coarse particle volume to total solids volume (x) is a parameter. Figure 4 shows the Series 2 test Yield Stress results plotted in this manner. The data show that, for any given total volume concentration, increasing ratio of sand addition results in a decrease in Yield Stress. For example at a total volume concentration of 20% the slimes alone exhibit a Yield Stress around 85 Pa. Addition of sand in the ratio x = of 20%. Increasing the ratio of sand to x = 0.384 results in a Yield Stress of around 12 0.189 results in the Yield Stress decreasing to 37 Pa at the same total solids concentration Pa at 20% total concentration. This behaviour is as expected and is a reflection of the physical fact that for any given total solids concentration the rheology of a slurry increases with decreasing particle size or decreases with increasing particle size. Increasing addition of sand to the slimes increases the average particle size and therefore decreases the Yield Stress. An important trend evident in Figure 4 is that the slope of the Yield Stress versus total allowing for the different X and Y axis scales). As increasing ratios of sand are added the slope progressively increases to approximately 11.5 at the highest ratio x = 0.789. It is well known that the Yield Stress of colloidal slurries is generally correlated by an equation of the following form: Ty (slimes) = A C," (8)

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Although there is considerable scatter, the slimes data in Figure 4 are approximated by an eqation of this form, with A = 7.45 x 105 and n = 5.61. Yield stress is in Pascals and C, is the volume fraction of slimes solids expressed as a fraction. Equation 8 infers a straight line plot of log ty versus log C, and is a well known relationship. Perhaps not so well known is that with slimes Yield Stress correlated by a straight line, addition of sand results in the Yield Stress versus volume concentration plot following a slightly more curved path. This is evident from a close inspection of Figure 4 data. The reduction in Yield Stress for a given total concentration and the increase in the slope of the log ty versus log C, as the mean particle size increases, are both predicted by application of equation 6 as is revealed by the following analysis. Also predicted is the change in behaviour from a straight line relationship for colloidal slurries to a slightly more curved relationship as coarse particles are added. It was previously seen in Figure 2 that the effect on the Yield Stress of sand addition was correlated by equation 6 with Comax = 0.9. Combining equations 6 and 8 we arrive at the following equation (9) for the Yield Stress of the total mixture.

Ty (total [1-(xC/kCvmax)J25 (9)

Thomas (2) developed an analagous equation but based on a different expression than that in equation 6. The full lines through the data in Figure 4 represent the predicted Yield Stress using equation 9. The predicted Yield Stress is close to the measured Yield Stress. A similar expression as equation 9 can be developed for the Plastic Viscosity. The Plastic Viscosity of colloidal slurries is often correlated by the following equation: Mp = exp(B V,) (10) Combining equations 7 and 10 we derive the following equation.

Mp=[1-x/(1+V/(kCmax|25 exp[B (1-x)V, (11)

The applicability of this equation is illustrated in Figure 5 which shows the Series 2 Test data plotted as Plastic Viscosity versus total solids Volume Ratio with the volume ratio of sand to total solids, x, as parameter. The dashed lines represent curves fitted to the data whilst the full lines are predicted curves using equation 9 with B = 17.7 and kCmax= 0.75. This value of kComax is in the middle of the 0.60 and 0.90 extremes shown in Figure 3. The predicted behaviour does not fit the data as well as was seen for the Yield Stress (Figure 4) as was previously seen in relation to Figure 3. Nevertheless the predicted trends are correct. As the sand ratio increases the slope of the curve decreases and this is predicted by equation 9. Equation 9 also predicts a slightly curved relationship which is also evident in the data. For any given total Volume Ratio the Plastic Viscosity decreases as the sand ratio increases. The Importance of the Ratio /M, A useful parameter which characterises the degree of non-Newtonian behaviour of a slurry is the ratio of Yield Stress to Plastic Viscosity. For a slurry containing a high

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proportion of coarse particles the Yield Stress will be low and the yMp ratio will be low. Conversely for a highly non-Newtonian clay slurry this ratio is high. These trends are evident in Figure 6 which shows the ty/M, ratio versus the calculated mean size for Series 2 test results. The Tyl, ratio is that applying at a Yield Stress of 10 Pa. A Yield Stress of 10 Pa was selected since typical mineral slurry pumping involves a Yield Stress around this magnitude.

10,000 10,000

• SLIMES ALONE • x = 0.189 • SLIMES ALONE +-× = 0.189

× x = 0.384 • × = 0.583 *x = 0.384 #-x = 0.583 A X = 0.685 X x = 0.789 *-x = 0.685 -4-x = 0.789

1,000 INCREASING MEAN PARTICLE SIZE

100

YIELD STRESS (Pa) 10 SLOPE 11.5 PLASTIC VISCOSITY (mPas) 1,000 100

SLOPE 5.6

SLIMES ALONE

• SLIMES ALONE

10 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

TOTAL VOLUME CONCENTRATION (%) TOTAL VOLUME RATIO

FIGURE 4. YIELD STRESS VS VOLUME CONC. FIGURE 5. PLASTIC VISCOSITY VS VOLUME RATIO

SERIES 2 TESTS SAND IN SLIMES SERIES 2 TESTS SAND IN SLIMES

With the Yield Stress in Pascals and the Plastic Viscosity in Pascal seconds the units of "y/Mp are sec!. The mean size is calculated by assuming the mean size of the minus 45 micron slimes is 10 microns. Because of the overwhelming influence of the sand on the mean size the combined mean size is not very sensitive to assumed mean size of the slimes. For example assuming a mean slimes particle size of 1 micron instead of 10 microns makes little difference to the calculated total mean size. Figure 6 illustrates the expected trend for the ty/f, ratio to decrease as the mean particle size increases. In the limit of very coarse particles the ratio tends to zero indicating Newtonian behaviour. Also shown in Figure 6 is the predicted relationship using equations 9 and 11. The predicted behaviour shows less reduction in the ty/Mp ratio. This is explained by the fact that the Yield Stress selected for the comparison, t, = 10, is lower than the measured Yield Stress values (see Figure 4). Hence both the Yield Stress and Plastic Viscosity data have had to be extrapolated to considerably lower concentrations and volume ratios where the predicted behaviour diverges significantly from the indicated experimental behaviour.

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600

400 SLURRIES HAVING A CONTINUOUS PARTICLE SIZE DISTRIBUTION RATIO YIELD STRESS/PLASTIC VISCOSITY 200 FIGURE 6. RATIO YIELD STRESS / PLASTIC VISCOSITY 50 AT YIELD STRESS = 10 Pa CALCULATED MEAN SIZE (MICRONS) SERIES 2 TESTS SAND IN SLIMES 100 150 PREDICTED USING EQUATIONS 9 & 11 200 250 300 The slurries discussed in Section 3 have a "gapped" particle size distribution in that there is little material between the sand sizes and the colloidal sized slimes. The majority of slurries of interest in the mineral processing industries have a more continous particle size distribution resulting from comminution. In this case it is not so easy to separate them into a coarse sand fraction and a slimes fraction. Nevertheless the rheological behaviour of the continuous size distribution slurries follows similar trends as outlined in Section 3. Figure 7 shows test results obtained by the author in recent years on 14 different slurries all having continous size distributions. The plots of Yield Stress versus concentration follow similar trends as were indicated in Figure 4 for a sand in slimes "gapped" slurry. These trends are: A decrease in Yield Stress with increasing mean particle size for any particular concentration; and an increase in the slope of the Yield Stress versus concentration plot for increasing mean particle size. Figure 8 is a plot of Plastic Viscosity versus Volume Ratio for the same 14 slurries. This plot can be compared with Figure 5. Similar trends are evident, namely: The same trend of a decrease in Plastic Viscosity with increasing mean size for any particular concentration is evident in both figures. Also evident is the reduced slope of the plot as the mean particle size increases. Figure 9 shows a plot of the ty/up ratio versus mean particle size for the 14 different slurries. Also included is the ty/up ratio for the Series 2 tests which were previously shown in Figure 6. Both sets of data show a reduction in the tylM, ratio as the mean particle size increases. However the wide size distribution test results show a stronger

decrease in the Ty/M, ratio with mean particle size than the previous "gapped" size Series

2 tests. This is a reflection of the marked differences in particle size distribution of the continuous size distribution slurries and "gapped" size distributions applicable to the Series 2 tests. A more complete analysis would include a distribution parameter to further characterise each slurry in addition to the mean particle size used here.

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100

1,000

INCREASING MEAN PARTIGLE SIZE

YIELD STRESS (Pa) 10 NEEASING MEAN PARTICLE SIZE PLASTIC VISCOSITY (mPas) 1

0.1 1 10 100 1

VOLUME CONCENTRATION (%) 0.2 0.4 0.6 0.8 1 1.2 1.4

VOLUME RATIO

* ZING CONC. d80=7.5M + NICKEL ORE d80 = 10M * NICKEL ORE d80=10.1M # LEAD CONC. d80= 16M

* NICKEL ORE 080=23M * LEAD CONC. d80=25M * MAGNETITE d80 = 35M * COPPER CONC. d80= 47M

° COPPER TAILS d80=56M FLYASH d80 = 80M # MAGNESITE d80 = 165M #SILICA d80 = 170M

*PHOSPHATE d80=220M • MAGNESITE d80=400M

FIGURE 7. YIELD STRESS VERSUS VOLUME CONCENTRATION FIGURE 8. PLASTIC VISCOSITY VERSUS VOLUME RATIO CONTINUOUS SIZE DISTRIBUTION SLURRIES CONTINUOUS SIZE DISTRIBUTION SLURRIES

§ 1,400€ ≥ 1,600 • SERIES 2 TESTS XVARIOUS WIDE SIZE DIST

PLASTI AT YIELD STRESS = 10 Pa

RATIO YIELD STRESS TO 200 400 0 0 SERIES 2 TESTS & WIDE SIZE DISTRIBUTION SLURRIES FIGURE 9. RATIO YIELD STRESS/PLASTIC VISCOSITY 50 CALCULATED MEAN SIZE (MICRONS) 100 150 200 250 300

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CONCLUSIONS

The addition of rigid particles to a Newtonian fluid increases the viscosity. Well known expressions for this effect have been extended to the case of coarse particles added to non-Newtonian Bingham Plastic vehicle slurries. Predicted trends are confirmed by data from the literature as well as data from two series of tests recently completed by the author involving rheology measurements on various sands added to slimes slurries. Direct comparison between predictions and measurements is illustrated by plots of total Yield Stress/ Yield Stress of the slimes versus volume concentration of sand, and total Plastic Viscosity/ Plastic Viscosity of the slimes versus volume ratio of the sand. The predictive equations have also been recast in terms of total solids concentration and total solids volume ratio with the volume ratio of sand to total solids as parameter. The trends predicted with increasing sand ratio are analagous to the trends observed with more common continuous particle size distribution slurries. In particular the theory predicts the observed increase in slope of the Yield Stress versus volume concentration plot as the mean article size increases and the reduction in slope of the Plastic Viscosity versu Volume Ratio plot. The ratio of Yield Stress to Plastic Viscosity is identified as an important parameter which indicates the degree of non-Newtonian behaviour. This ratio decreases as the mean particle size increases.

NOTATION

A correlating parameter in eqn 8 B correlating parameter in eqn 10 C. fractional volume concentration of solids Comax volume concentration at maximum packing volume concentration of total solids in the slurry particle size in metres gravitational constant k correating parameter in eqns 6, 7, 9 & 10

correlating exponent in eqn 8 Volume Ratio which equals C./(1-C.)

volume ratio of sand to total solids shear rate p/Ms ratio of slurry viscosity to fluid viscosity Ps density of the solid particle in kg.m Plastic Viscosity (Co-efficient of Rigidity

Pr sear sure the slimes vehicle slurry in kg.mi?

Yield Stress Ty (slimes) Yield Stress of the slimes in Pascals

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REFERENCES

Macosko, C.W.. (1994), Rheology Principals, Measurements and Applications, VCH Publishers Inc., New York. 2. Einstein, A. Ann. Phys, 1906, 19, 289 3. Thomas, D.G. (1965), J. Colloid Sci., 20, p267 4. Landel, R.F., Moser, B.G., and Bauman, A.J. (1963), Fourth Int. Congress on Rheology, Brown Univ., Proc. Part 2, p 663. 5. Thomas, A.D. (1978/1), "Coarse Particles in a Heavy Medium - Turbulent Pressure Drop Reduction and Deposition Under Laminar Flow", Hydrotransport 5 Conf., May 8 to 11, Hannover, Paper D5. 6. Thomas, A.D. (1979/1), "Pipelining of Coarse Coal as a Stabilized Slurry - Another Viewpoint", 4th Int. Tech Conf. on Slurry Transportation, March 28-30, Las Vegas. 7. Thomas, A.D. (1979/2), "The Role of Laminar/Turbulent Transition in Determining the Critical Deposit Velocity and the Operating Pressure Gradient for Long Distance Slurry Pipelines", Hydrotransport 6 Conf., Canterbury, U.K. 8. Shook, C.A., Schriek, W., Smith, L.G., Haas, D.B., and Husband, W.H.W. (1973), Experimental Studies on the Transport of Sands in Liquids of Varying Properties in 2 and 4 Inch Pipelines, Report E73-20, Saskatchewan Research Council, Canada. 9. Thomas, A.D. (1981), "Slurry Pipeline Rheology", 2nd National Conf. on Rheology, Sydney, May 14.

10. Therines Demical Enginarion DAist pha, she fon of the act Sle ry

Chemical Engineers, Inst. of Engineers, Aust. 11. Thomas, A.D. (1978/2), Unpublished work M.D. Research Co. Pty Ltd, Sydney 12. Duckworth, R.A., Pullum, L., Lockyear, C.F., and Lenard, J. (1983), Bulk Solids Handling, V3, n4, p817.