Factors affecting the hydraulic performance of slurries

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Temples Cap Blas

Reprint

of a Paper Presented at a Technical Conference of

THE INSTITUTION OF ENGINEERS, AUSTRALIA

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Factors Affecting the Hydraulic Performance of Slurries

by A. D. THOMAS, B.E. (Hons.), Ph.D M.D. Research Company Pty Limited

She median particle size and the particle size distribution have on the hydraulic behaviour of the Before a slurry pipeline can be optimised, the effect that changes in solids concentration, must be known. paper examines in turn the effects that changes in these three variables has on both the pressure gradient and the critical deposit velocity. The effects are discussed qualitatively illustrated with experimental data for various slurries. Some available methods of predicting these effects are discussed but it is concluded that generally pipe loop tests are necessary if accurate predictions are required.

1 INTRODUCTION 3 EFFECT ON PRESSURE GRADIENT AND DEPOSIT

VELOCITY OF REDUCTION IN THE MEDIAN PART-

The transport of coal and other minerals by ICLE SIZE pumping them along pipelines in slurry form is a proven commercial alternative to more conventional (a) Effect on Pressure Gradient means of transport. The design of a slurry pipeline involves consideration of many factors such as concentration of solids, median particle size, particle size distribution, pipe diameter, operating 400 velocity etc. For a particular selected pipe diameter changes in the solids concentration, median part- 300 icle size, and particle size distribution will all alter the hydraulic performance of a slurry. Ref 11 optimise a pipeline design the effects that changes in the above variables have on the operating press -ure drop must be known. The operating pressure 200 dictated by the necessity to operate at a generally necessitates operating in the turbulent although some slurries having a high pro- Ref velocity slightly above the deposit velocity. This tration do operate successfully in the laminar deposit velocity the most economic one is the one portion of very fine particles and a high Obviously if two slurries have the same mm H20 / m even though that slurry may have a higher pressure

gradient than the other at higher velocities. Ret 3

with the lowest pressure gradient at that velocity NOTATION J volume Fanning friction factor Pipe diameter Gravitational acceleration Pressure gradient of slurry Solids concentration-fraction by PRESSURE GRADIENT 100 50 Sand 1 0•68 mm 0•90 mm 0-046 mm 0-20 mm Thet Pressure gradient of a heterogeneous slurry Thom Pressure gradient of a homogeneous 30 2 3 slurry Pressure gradient of water flowing at VELOCITY m/sec the same mean velocity as the slurry Specific gravity of solids Mean velocity of slurry Fig. 1 Effect of changes in median m Density of slurry mixture particle size. Vertical lines Density of water indicate deposit velocities. m Viscosity of mixture D = 50 mm, C = 18%

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Figure 1 shows experimental results for sand Although the above examples illustrate the slurries of concentration 18% by volume in a 50 mm desirability of fine particles it does not follow diameter pipe. It can be seen that as the median that the optimum slurry is the one with the finest particle size is decreased the slurry behaves more possible particles. Once the particle size is homogeneously ie., more as a single phase fluid. reduced below about 10 microns colloidal effects The operating point on each curve is determined become increasingly important and these may by the deposit velocity which is that velocity at cause a large increase in viscosity. Not only which the larger particles are no longer maintained does this increase in viscosity mean larger press in suspension and begin to form a stationary bed -ure gradients even though the slurry is behaving on the bottom of the pipe. homogeneously but it also means that the velocity operate at a velocity slightly (say 0.3m/sec) at which transition to laminar flow occurs is above that velocity. Reducing the particle size raised. The possible effect of reducing the from 0,9 mm to 0.046 mm has resulted in the operat particle size too much is shown schematically in -ing velocity being reduced from 2,35 m/sec to figure 3. 1.40 m/sec while the pressure gradient has been reduced by 50% from 240mm HO/m to 49mm H,0/m. Obviously the use of fine particles results considerable savings in pumping power. also a great reduction in pipe wear as the velocity and the particle above advantages of operating slurry must be weighed against the cost of crushing and grinding the material and the possible disadvantages of such fine material as the end Generally speaking all long distance pipelines (say greater than 30 km) operate with homogeneous type slurries. and 200 to 300 microns for coal (S.G. 1.35). 30 microns for iron ore (S.G. = 5.0) Typical median part- LOG Laminar

concentration of 45% in a 160 mm pipe. effect of changes in the median size of Ф Water

particles is illustrated in Figure 2 for a volume size from 4,3 mm to 0.25 mm has reduced the operating velocity from 3 m/sec to 1.7 m/sec and the pressure gradient from 97mm HO/metre to 31mm H20/metre.

LOG V

100 Ref 11

Fig. 3 Schematic diagram indicating disadvantages of too fine particles.

80 Vertical dashes indicate deposit E Coal velocities, Rings indicate operating 1 4-30 mm velocity. 0-25mm

Reducing the particle size from that of curve A to that of curve B has resulted in a reduction in the operating velocity and pressure

40 gradient. Further size reduction has resulted

in a large increase in viscosity which has raised the laminar transition velocity with the conseq- The onset of colloidal effects may also signify the start of non-Newtonian behaviour

PRESSURE Water uent higher operating velocity and pressure whereby the slurry may exhibit an appreciable the simplified approach of Figure 3 but the gen- Such behaviour will complicate 20 eral fact remains that there is a lower limit to

particle size as far as optimum slurry performance is concerned. However some colloidal effects, and consequent increased viscosity, can be beneficial in reducing the settling tendency of the

VELOCITY m/sec large particles. pipelines operate as a homogeneous slurry with Most commercial long distance

enough fine particles present to give a small amount of non-Newtonian behaviour. The proportion of fine particles necessary to achieve this

Fig. 2 Effect of changes in median balance depends on the specific gravity of the particle size. Vertical lines solids and their surface chemical properties. indicate deposit velocities. For coal it has been found that it is necessary D = 160 mm, C= 45% to have about 15 to 25% of the particles less

than 325 mesh (44 microns).

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(b) Effect on Deposit Velocity 4 EFFECT OF CHANGES IN SIZE DISTRIBUTION Since the deposit velocity dictates the (a) On Pressure Gradient operating point it is desirable to know how changes in particle size will affect the deposit velocity: The previous section has discussed the For coarse heterogeneous slurries an often used effect of changes in the median size. The questrelationship is that of Durand (Ref. 1) ion arises as to what is the effect of altering

the size distribution. Experimental data is (1) scarce but from the little that there is available it appears that providing the distribution of

where F is a function of particle size and is sizes approximately follows the Rosin-Rammler smaller indicates that the deposit velocity is lower for for reduced particle size. This equation distribution (Ref. 2) as produced by most crushing and grinding operations the operating pressure smaller particles and smaller pipe diameters. On drop will be roughly the same for all distributthe other hand for homogeneous type slurries the ions having the same median size. transition to laminar flow becomes of increasing importance in dictating the deposit velocity. In 300 this case assuming Newtonian behaviour laminar Sand = 0-2 mm transition occurs at Re = 2000 which means that

Rosin - Rammler

VD= 2000 M/D Pm (2)

This equation indicates that the deposit velocity is raised as the particles are reduced in 1•4 diameter is decreased. becomes greater) and as the pipe The two equations predict 150 - C 0-5 opposite effects and which one applies will depend w111 become increasingly important with the result heterogeneous slurries equation (1) will apply and the deposit velocity will vary approximately as on the fineness of the particles. For fine homogeneous slurries equation (2) For coarse, GRADIENT mm H2O 200 100 - A 4-3

of that there will be less dependence on diameter. This is illustrated by Figure 4. PRESSURE Water

50 1 1-5 3

Fig.5 Results of tests on three different

0-2 mm Sand sand slurries, all having same

median size (taken from Ref. 3)

DEPOSIT VELOCITY m/sec 1. 0 1 0-03 mm Iron Ore I I range from the narrow size distribution of sand amounts of spread. microns, to sand C which ranges from under 1 A which has a range of from 100 microns to 300 same median size of 0.2 mm but with differing The effect is illustrated by experiments D = 50 mm, C = 24% Saskatchewan Research Council different sands all with the The three size distributions VELOCITY m/sec 0•5 pressure gradient of these four slurries in a to a top size of 7000 microns (7 mm). The

50 mm diameter pipe is shown in Figure 5 for a

50 100 200 300 volume concentration of 24%. PIPE DIAMETER mm ence in operating pressure is about 15% (between

sand A and sand B) although the narrow size range sand (sand A) is seen to have a higher deposit

Fig. 4 Variation of deposit velocity velocity than the other three. Fig 6 shows results with pipe diameter - two types of for a 250 mm pipe for sand A and sand B for the slurries. From Ref. 3 same concentration. Once again there is no great

difference between the behaviour of the two

The deposit velocity of sand, having a median In the practical situation one starts off with size of 0.2 mm (equivalent to coal of about 1 mm coarse material, say coal, which then needs to be say) varies approximately as/D in agreement with crushed to allow pipelining. equation (1). The results for a fine iron ore distance applications this slurry of median particle size 30 microns (equivale for homogeneous type behaviour -nt to coal of about 0.200 mm say) show how the with a small amount of non-Newtonian properties. opposing effect of equation (2) has reduced the As mentioned previously for coal this means a diameter dependence such that the deposit velocity size of 200 to 300 microns with about 15% is almost independent of diameter. to 25% less than 325 mesh (44 microns). Using

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-ure gradient will increase for coarse particles

mm H2o/m 50 Sand d50 = 0-2 mm gradient above that for water flowing alone at the same velocity is directly proportional to the (say greater than 1mm for coal). Evidence suggests that the incremental increase in pressure As the concentration is increased the press GRADIENT в type (Ref. 1) assume such a relationship. For a volumetric concentration, Equations of the Durand particular slurry the Durand equation is given by PRESSURE 25 2 Water until eventually it will behave like a single uced the slurry will behave more homogeneously phase Newtonian fluid, Equation (3) can not be As the particle size is progressively red- (3) VELOCITY m/sec applied to such a slurry. For such a slurry single Fig. 6 Results of tests on two different phase Newtonian methods can be used to describe sands having the same median size the behaviour.

= 250 mm, C = 24% ie., hom = 2f Pm V/g D (4)

average values less than 44 microns the Rosin-Rammler distribution of 250 microns for the d where f is the Fanning friction factor and depends is such that only 2% of particles are greater than on the Reynolds Number. For low concentrations This is fortunate since the reciprocating it often occurs that the increase in viscosity is pumps used in long distance applications can gener about the same as the increase in density -ally not handle particles greater than about 3mm. the Reynolds Number remains the same as that of Of course other factors such as coking properties water. For such a slurry equation (4) indicates for coking coal may make it desirable to operate with a coarser particle size.

(b) On Deposit Velocity hom = Pm w= 1+ C(s - 1)] " (5)

The effect that changes in the particle size distribution have on the deposit velocity has which is similar to equation (3) for particular received little attention in the literature. The slurry, pipe diameter and velocity. results of Fig.5 show that for a sand slurry of median particle size 0.2 mm a moderate width size Equations (3) & (5) describe the flow of distribution (sand B) had a lower deposit velocity heterogeneous and homogeneous slurries respectthan the narrow size sand (sand A) but not as low ively providing the concentration is low (say less as the wider size sand. However sands A and B when than 30%) and there are no colloidal effects. For tested in a 250 mm pipe showed the reverse slurries of particle size such that the behaviour and sand A had the lowest deposit velocity. (Fig.6) is between these two extremes it has been suggest The differences are not large however and as with -ed (Ref, 5) that the simple addition of equations the pressure gradient, providing the Rosin-Rammler (3) and (5) adequately describe the behaviour type distribution is followed the median particle size is probably the dominating factor determining the deposit velocity.

Obviously this equation still retains the linear-

The Effect of Particle Size Distribution on ity with respect to concentration, For higher Dense Phase Slurry Behaviour concentrations and when very fine particles are present no such linear relationship will exist

As the concentration of a slurry is increased although often the error in assuming linearity is

to very high values approaching the maximum packing not great. the region termed dense phase behaviour is reached. At these concentrations (above about 50% (b) The Effect of Concentration Changes on the by volume) most slurries will flow in laminar flow Deposit Velocity settling occurring even at very low velocit -ies. It is usually considered that the pressure For a heterogeneous type slurry where equatgradients associated with such concentrations are ion (1) applies changes in concentration have little too high for practical applications. However an effect on the deposit velocity. This is illustrat interesting paper by Elliot & Glidden (Ref. 4) -ed in Fig.4 by the sand slurry results. The range that the pressure gradient could be reduced of deposit velocities shown covers concentrations by adjusting the size distribution, They found from 12% to 36%. However if the slurry is a homothat the size distribution which gave the minimum geneous type and if the concentration is high voidage also gave the lowest pressure gradient. enough equation (2) will become this paper was published there does not appear deposit velocity will then increase with increasto have been any further work done on this interest ing concentration because of the necessity to -ing aspect of slurry behaviour. operate in the turbulent regime. Of course if no

deposition occurs under laminar flow then operation in that regime is entirely feasible. Generally

THE EFFECT OF CHANGES IN CONCENTRATION this requires extremely fine particles although (a) The Effect of Concentration Changes on the concentration approaches the maximum packing it can occur for coarser particles providing Pressure Gradient sity. This is the region of dense phase transport.

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6 AVAILABLE METHODS OF PREDICTING SLURRY median size were shown to be of secondary import- BEHAVIOUR ance. The pressure gradient was shown to increase

with increasing concentration. At low concentrat-

(a) Pressure Gradient Prediction ions this increase was roughly linear with conc-

entration but at higher concentrations and with

Methods of predicting the pressure drop of finer particles a non-linear increase would occur. slurries are still far from satisfactory especi- The discussion revealed that with the present ally if large diameter pipes are involved. Heterostate of knowledge pipe loop tests are usually geneous or semi-heterogeneous slurries would not necessary, if accurate prediction of slurry behav normally be considered for long distance applicat- - iour is required. ions but are used over short distances. Equations of the form of equation (6) can be used for those ACKNOWLEDGEMENTS slurries and methods described in refs. (5) and(6) are of some use. However the different methods The author wishes to thank M.D. Research often give widely varying estimates and pipe loop Company for permission to publish this paper. tests are usually needed if an accurate prediction is required. If the pipe loop tests are performed 9 REFERENCES in pipes of smaller diameter than that proposed the results must be scaled up to larger diameters. 1. DURAND,R. Basic Relationships of the A recent paper by the author (Ref. 7) reviews Transportation of Solids in Pipes-Experi available scale-up methods and proposes a compre- -mental Research. Proc. Int. Assoc. for hensive scale-up procedure suitable for all types Hyd. Research, Uni. of Minnesota, Sept

1953, pp. 89-103.

For long distance pipelines economic consider- 2. ROSIN, P and RAMMLER,E. The Laws Governations generally dictate that the slurries be homo ing the Fineness of Powdered Coal. The -geneous ie., pseudo single phase fluids exhibit- Institute of Fuel, Oct. 1933 pp. 29-112. ing either Newtonian or non-Newtonian behaviour. If reliable viscometer tests are available there 3. EXPERIMENTAL STUDIES ON SOLIDS PIPEare a number of methods which will allow predict LINING OF CANADIAN COMMODITIES. Series of -ion of pipeline behaviour. Most of these reports by Saskatchewan Research Council are discussed by Kenchington (Ref.8). He concludfor Canadian Transport Commission and ed that the prediction of the turbulent pressure the Transportation Development Agency. drop by these methods was probably accurate enough 1973/1974. although prediction of the transition velocity was not so reliable, For a viscous high concent- 4. ELLIOT, D.E. and GLIDDON,B.J. Hydraulic ration slurry where the transition velocity Transport of Coal at High Concentrations. the velocity range of likely operation this PrOC. ist Int. Conf. on the Hyd, Transpserious shortcoming. Kenchington ort of Solids in Pipes (Hydrotransport 1) combination of viscometer methods and pipe 1oop Paper G2, Organised by B.H.R.A. and held tests. Scaling up of pipe loop tests on homogenat Uni, of Warwick, U.K. (Ist-4th Sept) slurries is best done using 1970. -osed by Bowen (Ref. 9). Examples of the use the Bowen scale-up method are given in Bowens 5. CHARLES, M.E. Transport of Solids by Pipe

line Hydrotransport 1 Paper A3.

(b) Deposit Velocity 6. WASP,E.J. AUDE, T.C., SEITER, R.H. and There have been a multitude of methods prop- THOMPSON, T.L. Hetero-Homogeneous solids-

Liquids Flow in the Turbulent Regime Int,

osed for prediction of the deposit velocity Symp. on Solid-Liquid Flow in Pipes and heterogeneous and semi-heterogeneous slurries. its Application to Solid Waste Collect- Fifty five of these methods have been recently ion and Removal, Philadelphia,Penn., discussed by Carleton and Cheng (Ref, 10) among U.S.A. (4th-6th March 1968). them the method proposed by Durand (equation 1). They concluded that at present there is no reli- 7. THOMAS, A.D. Scale-up Methods for Pipeable method available. Once again pipe 1oop line Transport of Slurries. To be publis tests are invariably required for accurate estim- -hed in Int. J. of Min, Processing. ation. For homogeneous slurries the laminar transition velocity generally coincides with the 8. KENCHINGTON, J.M. The Prediction of Pressdeposit velocity so that the remarks made in the ure Drop in Slurry Pipelines. Multiphase previous section are relevant ie., that for Systems Symp. Org. jointly by I.Chem. E. accurate determination of the transition velocity & I. Mech, E., Paper II, Uni. Strathclyde, pipe loop tests are generally necessary. U.K. April 1974. 7 CONCLUSIONS 9. BOWEN, R.L. (Jnr), 1961, Series of articles

in Chem, Engng., June 12, p. 243, June 26,

The general behaviour of slurries has been p.127, July 10, p.147, July 24, p. 143, described and the qualitative effect of changes in Aug 7, p.129, Aug 21, p.119, Sept 4, the median particle size, particle size distrib- P. 131. ution and concentration are discussed. As the median particle size is reduced a slurry behaves 10. CARLETON, A.J. and CHENG, D.C.H. Design increasingly more like a homogeneous fluid. Velocities for Hydraulic Conveying of Pseudo-homogeneity is reached at median particle Settling Suspensions, Hydrotransport 3, sizes ranging from about 250 microns for coal to Paper E5, Colorado School of Mines, Golden, about 30 microns for iron ore. The median part- Colorado, 15th-17th May 1974. icle size was seen to largely dictate the type of slurry behaviour and changes in the particle 11. THOMAS, A.D., Unpublished work at size distribution whilst maintaining the same M.D. Research Co.

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