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The effect of fine particles on slurry transport processes
Minera£~" Engineering, Vol. 10, No. 4, pp. 427-439, 1997
Pergamon PIhS0892-6875(97)00019-8
THE EFFECT
OF FINE PARTICLES
© 1997 Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved
ON SLURRY TRANSPORT
0892-6875/97$17.o0+o.0o
PROCESSES
Y.S. FANGARY§, A.S. ABDEL GHANI§, S.M. EL HAGGARt and R.A. WILLIAMS* § Mechanical Power Department, Faculty of Engineering, Ain Shams University, Abbassia-Cairo, Egypt t Mechanical Engineering Department, American University in Cairo, E1 Tahrir-Cairo, Egypt :~ Camborne School of Mines, University of Exeter, Redruth, Cornwall, TR15 3SE, UK (Received 24 October 1996; accepted 21 January 1997)
ABSTRACT
The effect of varying the proportion offine particulates in a polydisperse phosphate slurry on pressure losses during hydraulic transportation is described. Experimental data showing the benefits which can be derived by tailoring the particle size distribution are presented. Regions of optimal operation are identified for pipe diameters of 1, 1.5 and 2 inch for solids loadings of 1.45 % by volume. New qualitative phenomenological correlations are proposed to describe the results. ©1997 Published by Elsevier Science Ltd Keywords Industrial minerals; tailings; particle size
INTRODUCTION The transport of slurries by pipelines is widespread in the minerals, chemical, food, water and other industries. For transport in the locality of the processing plant the orientation of the pipelines is invariably horizontal or vertical. In long distance conveying the pipelines are horizontal or inclined. The design of the pipeline and pumping systems is often based on knowledge of the solid concentration and expected size distribution but often without having access to any detailed information on possible variations in the size distribution. In other cases, as in the transportation of minerals from mining sites to the processing plant, or from the mill to the smelter, the particle size may often vary according to variations in the comminution process. Use of a dense phase medium to transport slurry was discussed by Charles & Charles [1], using sand particles suspended in a water/clay mixture containing 30-50% clay by weight. This resulted in the reduction of power requirement for transporting the slurry by approximately 6 %. However other studies have reported opposite effects. For instance it was reported that for sand suspended in 40 wt % china clay the head loss increased [2]. 427
428
Y.s. Fangary et al.
An experimental study was carried to compare the use of clay and limestone on hydraulic characteristics when transporting silica sand [3]. The results showed that a remarkable reduction occurred when clay was added to carrier fluid, whereas the use of limestone did not show an appreciable reduction in pressure drop. A minimum pressure drop for a given value of delivered concentration was found when varying the concentration of fine particles in carrier fluid [4]. For this study a value of 30 wt % of clay gave a minimum pressure drop. A theoretical study was performed to compare the actual size distribution of sand and coal with the theoretical size distribution proposed to obtain optimum transport conditions [5] (i.e. minimum pressure drop for a given delivered slurry concentration). A difference was found between the two curves which showed that optimum flow conditions can be achieved by varying size d i s t r i b u t i o n of the material to be transported. Another theoretical study discussed the effect of presence of fine particles on the transport process [6]. An optimum condition can be found based on ratio of the fines to coarse particles. In this case the fine particles were defined as those of size less than 50 /~m. An assumption was made that due to presence of fine particles, at high solids concentration, the flow could be treated as pseudo-homogeneous non-Newtonian flow. Modelling of slurry flow took account of the presence of fine particles [7,8] by suggesting that the presence of fine particles vary the density of carrier fluid thus affecting the terminal fall velocity of particles which is of primary importance in calculating the threshold velocity (i.e. the minimum flow velocity required to keep solid panicles suspended). Two main arguments are often made against the tailoring of size distribution in industrial practice. First, the cost of grinding to manipulate the fine particle distribution to achieve the desired medium compared with the saving in power required to transport the slurry. One possible means of reducing any further power required for extra grinding can be provided exploiting the inherent degradation of solids in the circulating pump(s). Indeed, the correct choice of pump type and size can be made to maximize such effects to encourage the production of fines in some circumstances [9]. Secondly, the utilization of fine material may necessitate additional downstream equipment and complications in separating fine material from carrier fluid. In this study the size distribution of slurries was changed by varying the tail of distribution curve by increasing the percentage of fines in the population. Using this approach the cost of any grinding required is then minimized as excess fine particles are produced when raw material is extracted. Several techniques [9-11] are now used to separate fine particles efficiently, hence there are few reasons not to pursue the approach of tailoring the particle size distribution in order to optimize transportation.
HYDRAULIC MEASUREMENTS
Test Rig The test rig Figure 1, used for experiments consisted of a mixing tank of 0.47 m 3 capacity, in which the solid particles were mixed with carrier fluid (water) and agitated by means of slurry ejected from nozzles at different angles Figure 2. This arrangement was adopted to prevent the rapid settling of solid particles in the tank and to break-up any agglomerates that could present in the powder during addition of solid particles. Three test pipe sections of different diameters were used to measure the pressure drop of slurry, having diameters of 1", 1.5" and 2", shown in Figure 1 as sections A, B and C respectively, each section of length 6 m. The pressure drop was measured in section A by means of pressure transducers (PR9390/25, Philips), placed a distance of 155 pipe diameters apart. For test sections B and C, inverted U-tube manometers were used to measure the pressure drop, with pressure taps placed a distance of 133 and 103 pipe diameters apart, respectively. Flow rate was measured by diverting the flow into a measuring tank of known volume (0.017 m 3) and recording the time required to fill this tank, with accuracy of 2%.
Slurry transport processes
429
Concentration of solids in the conveyor was measured by using a weigh tank technique and counter flow loop shown in Figure 1. The flow in the main circuit was maintained by 10 horse power centrifugal pump (pump A). Flow control was achieved using a ball valve. Circulation of the slurry inside the mixing tank was via a 1.5 horse power centrifugal pump (pump B), fed from the upper third of the tank, where the concentration of solid particles are considerably lower and pumping it again to the tank through the nozzles shown in Figure 2.
(11)
(4) (s)
(3~)
(e)~/.~
(s) (7)
1. Mixing tank 4. Control valve 7. Section D 10. Section C
230 23D 0D
:_-/
(o)
2. Measuring tank 5. Circulating pump 8. Section E 11. Counter flow loop
(t2) 3. Main pump 6. Section A 9. Section B 12. Pressure taps in counter flow loop
Fig. 1 Schematic diagram of the experimental test rig.
PImp B
.fme~ It A.&
Fig.2 Flow diagram of mixing circuit and nozzle arrangement in mixing tank. Experimental Procedure On starting the pumps the flow control valve Figure 1 was fully open, then dry powder was introduced into the mixing tank. The slurry was mixed and circulated allowing two minutes to reach a steady state
430
Y.s. Fangaryet
al.
condition. The pressure drop in the three test sections was then recorded. The flow was then diverted from the main mixing tank to the measuring tank to measure the flow rate and volumetric solid concentration. The volumetric concentration of the mixture was determined by weighing the measuring tank. Since the volume of the sampling tank was known hence the density of the mixture could be calculated. After collecting the sample the flow control valve was set to another position and another set of data were recorded. Material Characteristics Phosphate material from Sebbaeia, Egypt were used in the tests. Measurements were made on four particle size distributions A, B, C and D shown in Figure 3. To further illustrate the percentage of each class of sizes forming each powder the distributions are also shown in a cumulative form versus sieve size, Figure 3(b). Powders C and D are mixtures of powders A and B. The mixing ratio of A and B to produce powders and D are given in Table 1.
1 0.8 0.6
.t , |
.
.
.
.
Powder A . Powder B -- - -- - Powder C .... Powder D
0.4 0.2 0 0.01
0.1 1 Particle size ( ~ )
10
(a)
1 0.8 e~
0.6 0.4 0.2
IIIII
il_l II
I. IIH
I;rFr' / I 1'
Illll I i
Powder211
0 0.01
0.1 1 Sieve opening (nun)
Powder,D, 10
(b) Fig.3 (a) Cumulative particle size distributions of powders used in experimental work, and (b) corresponding frequency distribution. The Rosin Rammler correlation was used to fit the size distribution and to indicate the breadth of the size distribution: Ps=l-exp(d/d0) N
(1)
Slurry transportprocesses
431
where Ps is the fraction of powder of diameter d coarser than the sieve size d. The Rosin Rammler uniformity coefficient N gives an indication about the width of size distribution. Values of N were approximately 0.7 for a broad size distribution and N > 2 indicates a narrow size distribution. The coefficient d o is the second fitting parameter (sometimes referred to as the absolute size constant) was found to have a value of 5.57.
TABLE 1 Properties of powders used in experiments.
Material
ds0 (#m)
0 (kg/m 3)
wt% of A
wt% of B
Rosin Rammler coeff (N), (eqn. 1)
A
250
2500
100
0
1.300
B
< 74
2695
0
100
1.996
C
90
2597
50
50
1.674
D
< 74
2646
25
75
1.924
Material A was transported in concentrations of 0.72%, 3% and 4.73% by volume. Material B was transported in concentrations of 3.18% and 4.66% by volume. Materials C and D were transported in concentration of 1.45 % by volume.
RESULTS Transport of fine and coarse particles at constant concentration Based on theoretical assumption that for the same operating conditions reducing the size of particles will decrease the pressure loss [12]. To test this hypothesis measurements were made for constant solids concentrations and flow velocities. Measurements on slurry A at concentration of 3% and 4.73% were compared with data obtained for slurry B at solids concentration of 3.18% and 4.66 respectively. Figure 4(a) and (b) shows the result of comparison for the 1" pipe. It is evident that, unexpectedly, the pressure drop in case of coarse slurries flow is lower than for the fine particles slurry flow. For flow in 1.5 " pipe the pressure drop using coarse particles is higher than in case of fine particles as shown in Figure 4(c,d). Increasing the concentration form 3% to 4.7% here increases the difference between pressure drops obtained for materials A and B. These trends are also observed in hydrotransport in the 2 " pipe, Figures 4(e,f), where the difference between the two size distributions is marked. Effect of varying the ratio of fine to coarse particles on pressure drop The effect of varying the ratio of fine to coarse particles for the same concentration of 1.45 % on the pressure drop velocity characteristics was examined using two mixtures with 25 wt% coarse particles (powder C) and the other having 50% coarse (powder D). Figure 5(a) shows the comparison between the two mixtures in the 1 " pipe. The suspension containing the largest amount of fines gave lower pressure drop. Figure 5(b) shows that for the 1.5 " pipe increasing the fines content decreases the pressure loss. Hence both Figures indicate that finer slurries exhibit a lower pressure drop, although the differences in magnitudes are small. Whereas in the case of 2 " pipe, increasing coarse particle content increases the pressure drop markedly with velocity. This increase of pressure drop with velocity is gradual in case of slurries possessing a higher fine particles, Figure 5(c ).
432
Y . S . Fangary et al.
300.
O
300 •- - - - O m r ~ 250. [ O O m ~ C ~ a = t ~
u~,,,.u,
2~.
200-
I x wnlpiuamc'~-aml
2[.10.
n z ~
I x ~ ,l~t7
,I
x-a~
1150,
~ 100-
X -X II
~x
X
100. 50.
0
0
w
|
i
i
|
1
2
3
4
5
6
i
i
1
2
3
i
i
4
5
Velocity, V(m's) ~b)
V~nty, V(mS) (a) 50, 40.
40.
0
30,
D[] ~
vE2o 10'
10. 0
w
g
|
i
w
1
L5
2
0 2.5
i
i
w
i
0.5
1
1.5
2
Velocity,V(mts) (c)
2.5
Vdcdty, V(n~)
(d)
~°
50[~
40-
Gear vwta"
~
]
[] cm~ puedesC~r,=3
(lmr~tmr It liImel~RidesC%=4.7 |
o []O
[]
~2o. xxX
an
[]
13°
[] []
d~
[]
[]
[]
/
10
10-
0 0
| 0.4
i 0,8
! 1.2
V ~ t y , V(m~) (e)
0. L6
0
e OA
!
lit8
1.2
1.6
Vdoeity, V(nCs)
(0
Fig.4 Comparison of headloss for fine (B) and coarse (A) slurries of similar solids concentration: ~ 3 % (a, c, e) and - 4.7% (b, d, f) for pipe diameters of 1" (a, d), 11/2" (c, d) and 2" (e, f). To demonstrate clearly the effect of increasing the proportion of fines in the transported slurry on pressure drop, a comparison between slurry of coarse particles at two concentrations (0.72% and 3 %) and between a mixture of coarse and fine particles with concentration of 1.45 % was made. Figures 6(a,b,c) show the results for 1, 1.5, and 2 " pipes, respectively. For the 1 " pipe, Figure 6(a), 6(b), the flow characteristics coarse slurry (powder A) at concentration coarse particle
there is no clear difference between the slurries. For the 1.5 " pipe, Figure of slurries C and D lie between the boundaries determined by the flow of concentrations 0,72% and 3% with slurry approaching the trend of low slurry i.e. at a concentration of 0.72%.
The curve for the slurry with a low proportion of fines approaches that of the coarse 3 % slurry at high velocities. Similarly for the 2 " pipe. The experimental data for the 1.5 and 2 "pipes were correlated using the dimensionless groups used earlier by [13], where in this work i w was replaced by if and C was divided by (l_Cf) to account for the effect of the increasing percentage of fine particles.
Slurry~anspoa processes
433
110.
°'-
[] tane matenal%~O by
150
X
-.I nm
III 100
X O C]~
0
I
1
0
X
T
f
T
2
3
4
Vdocity,V(m's) (a)
25.
[]
~20-
x
C)X- ~
15. r,1) 10. 5 0
I
i
0.5
0
I
1 W ~ i t y , V(m's)
1.5
2
(b) 25 20-
=
[] X
15
Free~
~'~75by~ht~ th X [] - X xX
lO. 5 0 0
I
I
0.2
0.4
I
I
0.6 0.8 Vdodty, V(nCs)
I
|
1
1.2
1.4
(c) Fig.5 Effect of varying the percentage of fine particles in the transported materialon headloss in (a) 1", (b) 1 i/~,, , and ( c ) 2" pipes.
434
Y.S. Fangary et
al.
i i+ Z [ + 2 / m (C/(1 -C+.))
(2)
gD(S -1)
where Z and m are constants of values 96 and 1.18 respectively, if is calculated from: fV 2 if =
where,
f=~
(3)
2gD
/Pro:o]
(4)
and/3 are constants found to have values of 0.033 and 0.104 respectively. 250 []
'h
0 Coarse particle with C % :0.72 200,
O Coarse particles with C% : 3
X Fine par tiles % =50
£
150,
~
100 ,
X4>,X o
X Fine pattie les% =75
4~
~m xOxX
50.
XOX
X
IlK
0 1
2
3
Velocity, V(m/s)
(a) 50
0
~ ~
45 40
[] Coarse particle with C % s0.72 J
35 30
X Fine psrtiles% s$O
25
OCoarse particles with C%=3 X Fine parti¢ lea% m75
20
0 x
15 10
x
5 0
x
v
X
0.5
:'b
o 4>
I
[]
0 O O
X•
X~ 1 ~ X
1
1.5
2
2.5
Velocity, V(m/s)
(b) 35 30
nComrse particle with C% s0.72
4>
0 Coarse plr ticles with C % =3 25 ~
20
O
X Fine par tiles% =SO X F i n e psrtic les%=75 o
10
x
X
[]
D
x
5
X
X°
~
0 0.2
0.4
0.6
0,8
!
1.2
1.4
Velocity, V(m/s)
(c)
Fig.6 Headloss for transport of coarse particulates at concentrations of 0.72% and 3% and for two different mixtures of coarse/ fine particles with overall concentration 1.45 % solids in (a) 1", (b) 11/2 ", and ( c ) 2" pipes.
Slurry transport processes
435
The density and viscosity can be modified to take the effect of fine particles into account [14]:
(5)
Pm = P, (I +Cf(S-1))
~1.m = ~1,I[1
+2.5Cf+10.05C2+16.6exp(0.00273Cf)]
(6)
Another correlation was developed for the prediction of coarse panicles phosphate slurries [15]: i -i w
=
131Fr-,.2
(7)
iwC where
Fr -
V2 gD(S-1)
(8)
Eqns. 2 and 7 were compared with experimental data as shown in Figures 7(a-d) for powders C and D. The Figures further support comments made earlier in discussing Figures 5 and 6.
40.
[
40
l]qx dkla
3~,
~ l~dm
30.
°"
• Olmi~i7
J
~20, lOi 5, 0 0
"~
I
I
I
0.5
1
1,5
...' o,"°
¢
°,~ t°°+
1 Q5
O/
0
I 1
I 1.5
2
~ixity,"4u/s)
x~Joaty,v(ms) (a)
(b)
40,
40-
26, 30,
30-
20,
2o
10,
IO
E ".,) 15i
]
~ l~xdm Gm~l~m2 .. " G~ndellea7
..,,' ,," ,,'"
•~
.d"
5, 0
I
I
I
O.5
1
1.5
'Velocity,V(nVs)
(c)
0 0
I
I
I
0.5
1
1.5
' ~ d y , 'V(m's)
(d)
Fig.7 Comparison of experimental headloss data with correlations (2) and (7) at a solids concentration of 1.45% for: powder C (a) IIA " (b) 2" pipes; and for powder D ( c ) 1 1/2" and (d) 2" pipe.
436
Y . S . F a n g a r y et al.
A comparison between correlation 2 and 7 is shown in Figure 8. It is clear that increasing the percentage of fines does not have the required effect on pressure loss if the operating velocity is within the range of 0.6 to 1.2 m/s for the 1.5 " pipe, since in this range the transportation properties of coarse particles is more effective predicted using correlation 7. The trends for the 2 " pipe showed that increasing percentage of fine particles is useful at any operating velocity except for concentrations < 10%. 100 90. 80. 70.
I00 90 80
70 60 50 40 30 20 10 0
40. 20. 10. 0 0
O.S
1 Velocity, V(m/s)
1.5
2
0.5
l Vdocity, V(m/s)
(a)
(b)
200180140" O 12010080.
0
50 45 4O 35 3O 20 L~ 10 5
40200 0
1.5
0
O~
1
LS
2
O.S
Vdodty, V(m/s)
1
L5
2
Vel~:ity, V(m/s)
(c)
(d)
2OO
~f
1801~014O120100806040-
180
160 140
0
120
411
0
0
0
0.$
i
l..q
2
0.5
Velocity, V(m/s)
1
1.5
Vdoclt3,, V(m/s)
(e)
(f)
I Correlation
2 Cf%
=25
.
Correlation
2 Cf%
:75%
~Correlatloo
.
.
.
Correlation
2
Ct%
:50
7
Fig.8 Comparison of pressure drop-velocity correlations (2) and (7) for flow in 11/2" pipe (a, c, e) and 2" pipe (b, d, e) for volume concentrations of 5% (a, b). 10% (c, d) and 20% (e, f) for slurries containing different percentages of fine particles (eqn. 2).
Slurry transport processes
437
DISCUSSION Solid particles in the suspension affect the nature of the turbulent structure of the fluid which in turn is responsible for the macroscopic hydraulic characteristics. However the complexity of calculating such effects theoretically is intractable at present. It was noticed that flow of fine particles (Powder B) in 1 " pipe gave higher pressure drop than that of coarse particles (Powder A) Figure 4(a). The flow in this pipe is considered to be a pseudo-homogeneous flow as the hydraulic characteristics for both slurries approaches that of clear water, hence the reason for this trend can be explained by assuming that coarse particles having comparably larger size than that of free particles thus their ability to damp turbulent eddies is greater and thus decreases the losses within the fluid leading to a lower pressure drop. It must be noted that the level of turbulence was reduced to a level which did not affect the support of particles in the fluid. The case is different when fine particles are present in the solid powder. These fines mix with the carrier fluid thus modifying its properties (i.e. density and viscosity), as given in equations 4 and 5. From these equations it is clear that increasing fine particles increase both density and viscosity of carrier fluid. This has the opposite effect on flow of coarse particles within a slurry. If the density is increased, the relative density between solid particles and carrier fluid is decreased hence buoyancy effects are enhanced resulting in improved support and suspension of particles. Increasing the viscosity increases the ability of the fluid to damp turbulent eddies required to support coarse particles leading to rapid settling of coarse particles.These phenomena explain the trends of slurries C and D in the 2 " pipe, Figures 7(b) and 7(d). In Figure 7(b) powder C contains 38 wt% of coarse particles and 62 wt% of fine particles. Thus at low velocities and increased viscosity the turbulence is damped leading to rapid settling of particles and a rise in pressure loss, as most of coarse particles in this case will be transported as sliding bed. Whereas in the case of powder D, Figure 7(d), where the amount of fine particles is 82 wt% and coarse particles 18 wt%, the presence of fine particles increases the density of the fluid in such a way that the increase of viscosity do not affect the turbulence and coarse particles are transported as a fully suspended load. A further improvement to the correlation proposed in this paper (eqn. 2) could be based on combining the two-layer model of [16] with the model of [12].The resultant correlation could be a form of: i -
fV2 " +K,(C-Cf-C) 2gD
W
+K2C(S-1)
(9)
--V-
where
f
=(X
OmVD ] -~
(lo)
Pm W is the terminal particle settling velocity and could be determined using the correlation [17]: W
= W0(1 - C ) m
(11)
The contact load is calculated by:
(12)
where the first term takes in the right hand side of the correlation takes into account the change in carrier fluid properties due to presence of fine particles, the second term contributes to the pressure loss due to
438
Y.s. Fangaryet aL
the fraction of solid particles transported as suspended load. The last term contributes to the pressure losses due the fraction of solids transported as sliding bed. This approach offers a possible means of producing a unified correlation including critical velocity effects not encompased in equations 2 and 7, but requires experimental verification.
CONCLUSIONS At high velocities the pressure loss for fine particles are higher than that for coarse particles. This can be explained as the fine particles have higher tendency to mix with carrier fluid to form pseudo-homogeneous fluid of higher density, yet the turbulence in the flow is not damped. In case of coarse particles, the slurry has nearly the same density as that of fine particles mixed with carrier fluid, but in this case the coarse particles tends to damp turbulence inside the moving fluid flow. Mixing fine and coarse particles while keeping the total output solids concentration constant can cause the hydraulic curve of this slurry to move towards hydraulic curve of coarse particles slurry either at higher or lower volumetric concentrations than that of the mixture. This work shows that the variation of fine particles percentage in poweder to be transported by pipelines could lead to reduction in pressure loss provided that correct percentages of fine powder were chosen. This has important practical implications for the design and operation of conveying systems.
REFERENCES
1.
2.
.
.
.
.
7. 8. 9. 10. 11. 12. 13.
Charles, M.E. & Charles, R.A., The use of heavy media in the pipeline transport of particulate solids. In Advances in Solid-Liquid Flow in Pipes and Its Applications, ed. I. Zandi. Pergamon Press, Oxford, UK, 187-197 (1971). Kenchnington, J.M., Prediction of critical conditions for pipelines flow of settling particles in a heavy medium. Hydrotransport 4, BHRA Fluid Engineering, Cranfield, Bedford, England. 31-48 (1976). Hisamitsu, N., Shoji, Y. & Kswugi, S., Effect of added fine particles on flow properties of settling slurries. Hydrotransport 5, BHRA Fluid Engineering, Cranfield, Bedford, England. 29-49 (1978). Sakamoto, M., Mase, M., Nagawa, Y., Uchida, K. & Kamino, Y., A hydraulic transport study of coarse materials including fine particles with hydrohoist. Hydrotransport 5, BHRA Fluid Engineering, Cranfield, Bedford, England. 79-90 (1978). Hou, H.C., Investigation of optimal grain disstribution for transprt with high concentration. Hydrotransport 10, BHRA Fluid Engineering, Cranfield, Bedford, England. 177-183 (1986). Hou, H.C., On the optimal concentration of fine particles in hydrotransport. Hydrotransport 11, BHRA Fluid Engineering, Cranfield, Bedford, England. 285-294 (1988). Gillies, R.G., Shook, C.A. & Wilson, K.C., An improved two-layer model for horizontal slurry pipeline flow. Can. J. Chem. Eng., 69, 173-178 (1991), Wilson, K.C., Clift, R. Addie, G..R. & Maffett, J., Effect of broad particle grading on slurry stratification ratio and scale-up. Powder Technol., 61, 165-172 (1990). Brown, N.I. & Heywood, N.I., Slurry Handling: Design of Solid-Liquid Systems. Elsevier Science Publishers, London. (1991). Shook, C.A. & Roco, M.C., Slurry Flow Principles and Practice. Butterwoth-Heinemann, Boston. (1991). Jacobs, B.E.A., Design of Slurry Transport Systems. Elsevier Applied Science, London. (1990). Newitt, D.M., Richardson, J.F., Abbott, M. & Turtle, R.B., Hydraulic conveying of solids in horizontal pipes. Trans. lnstn. Chem. Engrs., 33, 93-113 (1955). Durand, R. & Condolios, E., Experimental study of the hydraulic transport of coal and solid materials in pipes. Proc. Colloq. On The Hydraulic Transport of Coal, National Board, UK, 39-55
Slurry transport processes
14. 15. 16. 17.
(1952). Thomas, D.G., Transport Characteristics of Suspensions:VIII. A note of the viscosity of newtonian suspensions of uniform spherical particles. J. Colloid. Sci., 20, 267-277 (1965). Fangary, Y.S., Study of The Effect of Some Properties of Two Phase Liquid Solid Flow On The Design of Slurry Pipelines. M.Sc. Thesis, Ain Shams Univ., Cairo- Egypt. (1995). Wilson, K.C., Slip point of beds in solid-liquid pipeline flow. Proc. ASCE, J. Hyd. Div., 97, 1665-1679 (1070). Richardson, J.F. & Zaki, W.N., Sedimentation and fluidization. Trans Inst. Chem. Engrs., 32, 35-52 (1954).
NOMENCLATURE C Cc Cf
do D f g i K1 K2 m N Ps
R S V W W0
= volume fraction solids = contact load (volume fraction) = volume fraction (-74 #m) solids = Rosin Rammler coefficient (eqn. 1), (m) = pipe diameter, (m) = friction factor = gravitational acceleration = hydraulic gradient (m liquid/m pipe) = constant in equation 9 = constant in correlation 9 = constant in equation 11 = Rosin Rammler constant (eqn. 1), dependent on size distribution = fraction of solids smaller than diameter d = correlating constant, equation 12 = solids specific gravity = mean velocity of flow, (m/s) --- hindered teminal settling velocity, (m/s) = particle terminal settling velocity, (m/s)
Greek Letters Od
p
= = = =
constant in equation 4 constant in equation 4 fluid viscosity density
Subscripts f m w
439
= fines = properties of carrier fluid taking percentage of fines into account = carrier fluid alone (water)
Pergamon PIhS0892-6875(97)00019-8
THE EFFECT
OF FINE PARTICLES
© 1997 Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved
ON SLURRY TRANSPORT
0892-6875/97$17.o0+o.0o
PROCESSES
Y.S. FANGARY§, A.S. ABDEL GHANI§, S.M. EL HAGGARt and R.A. WILLIAMS* § Mechanical Power Department, Faculty of Engineering, Ain Shams University, Abbassia-Cairo, Egypt t Mechanical Engineering Department, American University in Cairo, E1 Tahrir-Cairo, Egypt :~ Camborne School of Mines, University of Exeter, Redruth, Cornwall, TR15 3SE, UK (Received 24 October 1996; accepted 21 January 1997)
ABSTRACT
The effect of varying the proportion offine particulates in a polydisperse phosphate slurry on pressure losses during hydraulic transportation is described. Experimental data showing the benefits which can be derived by tailoring the particle size distribution are presented. Regions of optimal operation are identified for pipe diameters of 1, 1.5 and 2 inch for solids loadings of 1.45 % by volume. New qualitative phenomenological correlations are proposed to describe the results. ©1997 Published by Elsevier Science Ltd Keywords Industrial minerals; tailings; particle size
INTRODUCTION The transport of slurries by pipelines is widespread in the minerals, chemical, food, water and other industries. For transport in the locality of the processing plant the orientation of the pipelines is invariably horizontal or vertical. In long distance conveying the pipelines are horizontal or inclined. The design of the pipeline and pumping systems is often based on knowledge of the solid concentration and expected size distribution but often without having access to any detailed information on possible variations in the size distribution. In other cases, as in the transportation of minerals from mining sites to the processing plant, or from the mill to the smelter, the particle size may often vary according to variations in the comminution process. Use of a dense phase medium to transport slurry was discussed by Charles & Charles [1], using sand particles suspended in a water/clay mixture containing 30-50% clay by weight. This resulted in the reduction of power requirement for transporting the slurry by approximately 6 %. However other studies have reported opposite effects. For instance it was reported that for sand suspended in 40 wt % china clay the head loss increased [2]. 427
428
Y.s. Fangary et al.
An experimental study was carried to compare the use of clay and limestone on hydraulic characteristics when transporting silica sand [3]. The results showed that a remarkable reduction occurred when clay was added to carrier fluid, whereas the use of limestone did not show an appreciable reduction in pressure drop. A minimum pressure drop for a given value of delivered concentration was found when varying the concentration of fine particles in carrier fluid [4]. For this study a value of 30 wt % of clay gave a minimum pressure drop. A theoretical study was performed to compare the actual size distribution of sand and coal with the theoretical size distribution proposed to obtain optimum transport conditions [5] (i.e. minimum pressure drop for a given delivered slurry concentration). A difference was found between the two curves which showed that optimum flow conditions can be achieved by varying size d i s t r i b u t i o n of the material to be transported. Another theoretical study discussed the effect of presence of fine particles on the transport process [6]. An optimum condition can be found based on ratio of the fines to coarse particles. In this case the fine particles were defined as those of size less than 50 /~m. An assumption was made that due to presence of fine particles, at high solids concentration, the flow could be treated as pseudo-homogeneous non-Newtonian flow. Modelling of slurry flow took account of the presence of fine particles [7,8] by suggesting that the presence of fine particles vary the density of carrier fluid thus affecting the terminal fall velocity of particles which is of primary importance in calculating the threshold velocity (i.e. the minimum flow velocity required to keep solid panicles suspended). Two main arguments are often made against the tailoring of size distribution in industrial practice. First, the cost of grinding to manipulate the fine particle distribution to achieve the desired medium compared with the saving in power required to transport the slurry. One possible means of reducing any further power required for extra grinding can be provided exploiting the inherent degradation of solids in the circulating pump(s). Indeed, the correct choice of pump type and size can be made to maximize such effects to encourage the production of fines in some circumstances [9]. Secondly, the utilization of fine material may necessitate additional downstream equipment and complications in separating fine material from carrier fluid. In this study the size distribution of slurries was changed by varying the tail of distribution curve by increasing the percentage of fines in the population. Using this approach the cost of any grinding required is then minimized as excess fine particles are produced when raw material is extracted. Several techniques [9-11] are now used to separate fine particles efficiently, hence there are few reasons not to pursue the approach of tailoring the particle size distribution in order to optimize transportation.
HYDRAULIC MEASUREMENTS
Test Rig The test rig Figure 1, used for experiments consisted of a mixing tank of 0.47 m 3 capacity, in which the solid particles were mixed with carrier fluid (water) and agitated by means of slurry ejected from nozzles at different angles Figure 2. This arrangement was adopted to prevent the rapid settling of solid particles in the tank and to break-up any agglomerates that could present in the powder during addition of solid particles. Three test pipe sections of different diameters were used to measure the pressure drop of slurry, having diameters of 1", 1.5" and 2", shown in Figure 1 as sections A, B and C respectively, each section of length 6 m. The pressure drop was measured in section A by means of pressure transducers (PR9390/25, Philips), placed a distance of 155 pipe diameters apart. For test sections B and C, inverted U-tube manometers were used to measure the pressure drop, with pressure taps placed a distance of 133 and 103 pipe diameters apart, respectively. Flow rate was measured by diverting the flow into a measuring tank of known volume (0.017 m 3) and recording the time required to fill this tank, with accuracy of 2%.
Slurry transport processes
429
Concentration of solids in the conveyor was measured by using a weigh tank technique and counter flow loop shown in Figure 1. The flow in the main circuit was maintained by 10 horse power centrifugal pump (pump A). Flow control was achieved using a ball valve. Circulation of the slurry inside the mixing tank was via a 1.5 horse power centrifugal pump (pump B), fed from the upper third of the tank, where the concentration of solid particles are considerably lower and pumping it again to the tank through the nozzles shown in Figure 2.
(11)
(4) (s)
(3~)
(e)~/.~
(s) (7)
1. Mixing tank 4. Control valve 7. Section D 10. Section C
230 23D 0D
:_-/
(o)
2. Measuring tank 5. Circulating pump 8. Section E 11. Counter flow loop
(t2) 3. Main pump 6. Section A 9. Section B 12. Pressure taps in counter flow loop
Fig. 1 Schematic diagram of the experimental test rig.
PImp B
.fme~ It A.&
Fig.2 Flow diagram of mixing circuit and nozzle arrangement in mixing tank. Experimental Procedure On starting the pumps the flow control valve Figure 1 was fully open, then dry powder was introduced into the mixing tank. The slurry was mixed and circulated allowing two minutes to reach a steady state
430
Y.s. Fangaryet
al.
condition. The pressure drop in the three test sections was then recorded. The flow was then diverted from the main mixing tank to the measuring tank to measure the flow rate and volumetric solid concentration. The volumetric concentration of the mixture was determined by weighing the measuring tank. Since the volume of the sampling tank was known hence the density of the mixture could be calculated. After collecting the sample the flow control valve was set to another position and another set of data were recorded. Material Characteristics Phosphate material from Sebbaeia, Egypt were used in the tests. Measurements were made on four particle size distributions A, B, C and D shown in Figure 3. To further illustrate the percentage of each class of sizes forming each powder the distributions are also shown in a cumulative form versus sieve size, Figure 3(b). Powders C and D are mixtures of powders A and B. The mixing ratio of A and B to produce powders and D are given in Table 1.
1 0.8 0.6
.t , |
.
.
.
.
Powder A . Powder B -- - -- - Powder C .... Powder D
0.4 0.2 0 0.01
0.1 1 Particle size ( ~ )
10
(a)
1 0.8 e~
0.6 0.4 0.2
IIIII
il_l II
I. IIH
I;rFr' / I 1'
Illll I i
Powder211
0 0.01
0.1 1 Sieve opening (nun)
Powder,D, 10
(b) Fig.3 (a) Cumulative particle size distributions of powders used in experimental work, and (b) corresponding frequency distribution. The Rosin Rammler correlation was used to fit the size distribution and to indicate the breadth of the size distribution: Ps=l-exp(d/d0) N
(1)
Slurry transportprocesses
431
where Ps is the fraction of powder of diameter d coarser than the sieve size d. The Rosin Rammler uniformity coefficient N gives an indication about the width of size distribution. Values of N were approximately 0.7 for a broad size distribution and N > 2 indicates a narrow size distribution. The coefficient d o is the second fitting parameter (sometimes referred to as the absolute size constant) was found to have a value of 5.57.
TABLE 1 Properties of powders used in experiments.
Material
ds0 (#m)
0 (kg/m 3)
wt% of A
wt% of B
Rosin Rammler coeff (N), (eqn. 1)
A
250
2500
100
0
1.300
B
< 74
2695
0
100
1.996
C
90
2597
50
50
1.674
D
< 74
2646
25
75
1.924
Material A was transported in concentrations of 0.72%, 3% and 4.73% by volume. Material B was transported in concentrations of 3.18% and 4.66% by volume. Materials C and D were transported in concentration of 1.45 % by volume.
RESULTS Transport of fine and coarse particles at constant concentration Based on theoretical assumption that for the same operating conditions reducing the size of particles will decrease the pressure loss [12]. To test this hypothesis measurements were made for constant solids concentrations and flow velocities. Measurements on slurry A at concentration of 3% and 4.73% were compared with data obtained for slurry B at solids concentration of 3.18% and 4.66 respectively. Figure 4(a) and (b) shows the result of comparison for the 1" pipe. It is evident that, unexpectedly, the pressure drop in case of coarse slurries flow is lower than for the fine particles slurry flow. For flow in 1.5 " pipe the pressure drop using coarse particles is higher than in case of fine particles as shown in Figure 4(c,d). Increasing the concentration form 3% to 4.7% here increases the difference between pressure drops obtained for materials A and B. These trends are also observed in hydrotransport in the 2 " pipe, Figures 4(e,f), where the difference between the two size distributions is marked. Effect of varying the ratio of fine to coarse particles on pressure drop The effect of varying the ratio of fine to coarse particles for the same concentration of 1.45 % on the pressure drop velocity characteristics was examined using two mixtures with 25 wt% coarse particles (powder C) and the other having 50% coarse (powder D). Figure 5(a) shows the comparison between the two mixtures in the 1 " pipe. The suspension containing the largest amount of fines gave lower pressure drop. Figure 5(b) shows that for the 1.5 " pipe increasing the fines content decreases the pressure loss. Hence both Figures indicate that finer slurries exhibit a lower pressure drop, although the differences in magnitudes are small. Whereas in the case of 2 " pipe, increasing coarse particle content increases the pressure drop markedly with velocity. This increase of pressure drop with velocity is gradual in case of slurries possessing a higher fine particles, Figure 5(c ).
432
Y . S . Fangary et al.
300.
O
300 •- - - - O m r ~ 250. [ O O m ~ C ~ a = t ~
u~,,,.u,
2~.
200-
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2[.10.
n z ~
I x ~ ,l~t7
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1150,
~ 100-
X -X II
~x
X
100. 50.
0
0
w
|
i
i
|
1
2
3
4
5
6
i
i
1
2
3
i
i
4
5
Velocity, V(m's) ~b)
V~nty, V(mS) (a) 50, 40.
40.
0
30,
D[] ~
vE2o 10'
10. 0
w
g
|
i
w
1
L5
2
0 2.5
i
i
w
i
0.5
1
1.5
2
Velocity,V(mts) (c)
2.5
Vdcdty, V(n~)
(d)
~°
50[~
40-
Gear vwta"
~
]
[] cm~ puedesC~r,=3
(lmr~tmr It liImel~RidesC%=4.7 |
o []O
[]
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an
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[] []
d~
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/
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| 0.4
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! 1.2
V ~ t y , V(m~) (e)
0. L6
0
e OA
!
lit8
1.2
1.6
Vdoeity, V(nCs)
(0
Fig.4 Comparison of headloss for fine (B) and coarse (A) slurries of similar solids concentration: ~ 3 % (a, c, e) and - 4.7% (b, d, f) for pipe diameters of 1" (a, d), 11/2" (c, d) and 2" (e, f). To demonstrate clearly the effect of increasing the proportion of fines in the transported slurry on pressure drop, a comparison between slurry of coarse particles at two concentrations (0.72% and 3 %) and between a mixture of coarse and fine particles with concentration of 1.45 % was made. Figures 6(a,b,c) show the results for 1, 1.5, and 2 " pipes, respectively. For the 1 " pipe, Figure 6(a), 6(b), the flow characteristics coarse slurry (powder A) at concentration coarse particle
there is no clear difference between the slurries. For the 1.5 " pipe, Figure of slurries C and D lie between the boundaries determined by the flow of concentrations 0,72% and 3% with slurry approaching the trend of low slurry i.e. at a concentration of 0.72%.
The curve for the slurry with a low proportion of fines approaches that of the coarse 3 % slurry at high velocities. Similarly for the 2 " pipe. The experimental data for the 1.5 and 2 "pipes were correlated using the dimensionless groups used earlier by [13], where in this work i w was replaced by if and C was divided by (l_Cf) to account for the effect of the increasing percentage of fine particles.
Slurry~anspoa processes
433
110.
°'-
[] tane matenal%~O by
150
X
-.I nm
III 100
X O C]~
0
I
1
0
X
T
f
T
2
3
4
Vdocity,V(m's) (a)
25.
[]
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x
C)X- ~
15. r,1) 10. 5 0
I
i
0.5
0
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1 W ~ i t y , V(m's)
1.5
2
(b) 25 20-
=
[] X
15
Free~
~'~75by~ht~ th X [] - X xX
lO. 5 0 0
I
I
0.2
0.4
I
I
0.6 0.8 Vdodty, V(nCs)
I
|
1
1.2
1.4
(c) Fig.5 Effect of varying the percentage of fine particles in the transported materialon headloss in (a) 1", (b) 1 i/~,, , and ( c ) 2" pipes.
434
Y.S. Fangary et
al.
i i+ Z [ + 2 / m (C/(1 -C+.))
(2)
gD(S -1)
where Z and m are constants of values 96 and 1.18 respectively, if is calculated from: fV 2 if =
where,
f=~
(3)
2gD
/Pro:o]
(4)
and/3 are constants found to have values of 0.033 and 0.104 respectively. 250 []
'h
0 Coarse particle with C % :0.72 200,
O Coarse particles with C% : 3
X Fine par tiles % =50
£
150,
~
100 ,
X4>,X o
X Fine pattie les% =75
4~
~m xOxX
50.
XOX
X
IlK
0 1
2
3
Velocity, V(m/s)
(a) 50
0
~ ~
45 40
[] Coarse particle with C % s0.72 J
35 30
X Fine psrtiles% s$O
25
OCoarse particles with C%=3 X Fine parti¢ lea% m75
20
0 x
15 10
x
5 0
x
v
X
0.5
:'b
o 4>
I
[]
0 O O
X•
X~ 1 ~ X
1
1.5
2
2.5
Velocity, V(m/s)
(b) 35 30
nComrse particle with C% s0.72
4>
0 Coarse plr ticles with C % =3 25 ~
20
O
X Fine par tiles% =SO X F i n e psrtic les%=75 o
10
x
X
[]
D
x
5
X
X°
~
0 0.2
0.4
0.6
0,8
!
1.2
1.4
Velocity, V(m/s)
(c)
Fig.6 Headloss for transport of coarse particulates at concentrations of 0.72% and 3% and for two different mixtures of coarse/ fine particles with overall concentration 1.45 % solids in (a) 1", (b) 11/2 ", and ( c ) 2" pipes.
Slurry transport processes
435
The density and viscosity can be modified to take the effect of fine particles into account [14]:
(5)
Pm = P, (I +Cf(S-1))
~1.m = ~1,I[1
+2.5Cf+10.05C2+16.6exp(0.00273Cf)]
(6)
Another correlation was developed for the prediction of coarse panicles phosphate slurries [15]: i -i w
=
131Fr-,.2
(7)
iwC where
Fr -
V2 gD(S-1)
(8)
Eqns. 2 and 7 were compared with experimental data as shown in Figures 7(a-d) for powders C and D. The Figures further support comments made earlier in discussing Figures 5 and 6.
40.
[
40
l]qx dkla
3~,
~ l~dm
30.
°"
• Olmi~i7
J
~20, lOi 5, 0 0
"~
I
I
I
0.5
1
1,5
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¢
°,~ t°°+
1 Q5
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0
I 1
I 1.5
2
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x~Joaty,v(ms) (a)
(b)
40,
40-
26, 30,
30-
20,
2o
10,
IO
E ".,) 15i
]
~ l~xdm Gm~l~m2 .. " G~ndellea7
..,,' ,," ,,'"
•~
.d"
5, 0
I
I
I
O.5
1
1.5
'Velocity,V(nVs)
(c)
0 0
I
I
I
0.5
1
1.5
' ~ d y , 'V(m's)
(d)
Fig.7 Comparison of experimental headloss data with correlations (2) and (7) at a solids concentration of 1.45% for: powder C (a) IIA " (b) 2" pipes; and for powder D ( c ) 1 1/2" and (d) 2" pipe.
436
Y . S . F a n g a r y et al.
A comparison between correlation 2 and 7 is shown in Figure 8. It is clear that increasing the percentage of fines does not have the required effect on pressure loss if the operating velocity is within the range of 0.6 to 1.2 m/s for the 1.5 " pipe, since in this range the transportation properties of coarse particles is more effective predicted using correlation 7. The trends for the 2 " pipe showed that increasing percentage of fine particles is useful at any operating velocity except for concentrations < 10%. 100 90. 80. 70.
I00 90 80
70 60 50 40 30 20 10 0
40. 20. 10. 0 0
O.S
1 Velocity, V(m/s)
1.5
2
0.5
l Vdocity, V(m/s)
(a)
(b)
200180140" O 12010080.
0
50 45 4O 35 3O 20 L~ 10 5
40200 0
1.5
0
O~
1
LS
2
O.S
Vdodty, V(m/s)
1
L5
2
Vel~:ity, V(m/s)
(c)
(d)
2OO
~f
1801~014O120100806040-
180
160 140
0
120
411
0
0
0
0.$
i
l..q
2
0.5
Velocity, V(m/s)
1
1.5
Vdoclt3,, V(m/s)
(e)
(f)
I Correlation
2 Cf%
=25
.
Correlation
2 Cf%
:75%
~Correlatloo
.
.
.
Correlation
2
Ct%
:50
7
Fig.8 Comparison of pressure drop-velocity correlations (2) and (7) for flow in 11/2" pipe (a, c, e) and 2" pipe (b, d, e) for volume concentrations of 5% (a, b). 10% (c, d) and 20% (e, f) for slurries containing different percentages of fine particles (eqn. 2).
Slurry transport processes
437
DISCUSSION Solid particles in the suspension affect the nature of the turbulent structure of the fluid which in turn is responsible for the macroscopic hydraulic characteristics. However the complexity of calculating such effects theoretically is intractable at present. It was noticed that flow of fine particles (Powder B) in 1 " pipe gave higher pressure drop than that of coarse particles (Powder A) Figure 4(a). The flow in this pipe is considered to be a pseudo-homogeneous flow as the hydraulic characteristics for both slurries approaches that of clear water, hence the reason for this trend can be explained by assuming that coarse particles having comparably larger size than that of free particles thus their ability to damp turbulent eddies is greater and thus decreases the losses within the fluid leading to a lower pressure drop. It must be noted that the level of turbulence was reduced to a level which did not affect the support of particles in the fluid. The case is different when fine particles are present in the solid powder. These fines mix with the carrier fluid thus modifying its properties (i.e. density and viscosity), as given in equations 4 and 5. From these equations it is clear that increasing fine particles increase both density and viscosity of carrier fluid. This has the opposite effect on flow of coarse particles within a slurry. If the density is increased, the relative density between solid particles and carrier fluid is decreased hence buoyancy effects are enhanced resulting in improved support and suspension of particles. Increasing the viscosity increases the ability of the fluid to damp turbulent eddies required to support coarse particles leading to rapid settling of coarse particles.These phenomena explain the trends of slurries C and D in the 2 " pipe, Figures 7(b) and 7(d). In Figure 7(b) powder C contains 38 wt% of coarse particles and 62 wt% of fine particles. Thus at low velocities and increased viscosity the turbulence is damped leading to rapid settling of particles and a rise in pressure loss, as most of coarse particles in this case will be transported as sliding bed. Whereas in the case of powder D, Figure 7(d), where the amount of fine particles is 82 wt% and coarse particles 18 wt%, the presence of fine particles increases the density of the fluid in such a way that the increase of viscosity do not affect the turbulence and coarse particles are transported as a fully suspended load. A further improvement to the correlation proposed in this paper (eqn. 2) could be based on combining the two-layer model of [16] with the model of [12].The resultant correlation could be a form of: i -
fV2 " +K,(C-Cf-C) 2gD
W
+K2C(S-1)
(9)
--V-
where
f
=(X
OmVD ] -~
(lo)
Pm W is the terminal particle settling velocity and could be determined using the correlation [17]: W
= W0(1 - C ) m
(11)
The contact load is calculated by:
(12)
where the first term takes in the right hand side of the correlation takes into account the change in carrier fluid properties due to presence of fine particles, the second term contributes to the pressure loss due to
438
Y.s. Fangaryet aL
the fraction of solid particles transported as suspended load. The last term contributes to the pressure losses due the fraction of solids transported as sliding bed. This approach offers a possible means of producing a unified correlation including critical velocity effects not encompased in equations 2 and 7, but requires experimental verification.
CONCLUSIONS At high velocities the pressure loss for fine particles are higher than that for coarse particles. This can be explained as the fine particles have higher tendency to mix with carrier fluid to form pseudo-homogeneous fluid of higher density, yet the turbulence in the flow is not damped. In case of coarse particles, the slurry has nearly the same density as that of fine particles mixed with carrier fluid, but in this case the coarse particles tends to damp turbulence inside the moving fluid flow. Mixing fine and coarse particles while keeping the total output solids concentration constant can cause the hydraulic curve of this slurry to move towards hydraulic curve of coarse particles slurry either at higher or lower volumetric concentrations than that of the mixture. This work shows that the variation of fine particles percentage in poweder to be transported by pipelines could lead to reduction in pressure loss provided that correct percentages of fine powder were chosen. This has important practical implications for the design and operation of conveying systems.
REFERENCES
1.
2.
.
.
.
.
7. 8. 9. 10. 11. 12. 13.
Charles, M.E. & Charles, R.A., The use of heavy media in the pipeline transport of particulate solids. In Advances in Solid-Liquid Flow in Pipes and Its Applications, ed. I. Zandi. Pergamon Press, Oxford, UK, 187-197 (1971). Kenchnington, J.M., Prediction of critical conditions for pipelines flow of settling particles in a heavy medium. Hydrotransport 4, BHRA Fluid Engineering, Cranfield, Bedford, England. 31-48 (1976). Hisamitsu, N., Shoji, Y. & Kswugi, S., Effect of added fine particles on flow properties of settling slurries. Hydrotransport 5, BHRA Fluid Engineering, Cranfield, Bedford, England. 29-49 (1978). Sakamoto, M., Mase, M., Nagawa, Y., Uchida, K. & Kamino, Y., A hydraulic transport study of coarse materials including fine particles with hydrohoist. Hydrotransport 5, BHRA Fluid Engineering, Cranfield, Bedford, England. 79-90 (1978). Hou, H.C., Investigation of optimal grain disstribution for transprt with high concentration. Hydrotransport 10, BHRA Fluid Engineering, Cranfield, Bedford, England. 177-183 (1986). Hou, H.C., On the optimal concentration of fine particles in hydrotransport. Hydrotransport 11, BHRA Fluid Engineering, Cranfield, Bedford, England. 285-294 (1988). Gillies, R.G., Shook, C.A. & Wilson, K.C., An improved two-layer model for horizontal slurry pipeline flow. Can. J. Chem. Eng., 69, 173-178 (1991), Wilson, K.C., Clift, R. Addie, G..R. & Maffett, J., Effect of broad particle grading on slurry stratification ratio and scale-up. Powder Technol., 61, 165-172 (1990). Brown, N.I. & Heywood, N.I., Slurry Handling: Design of Solid-Liquid Systems. Elsevier Science Publishers, London. (1991). Shook, C.A. & Roco, M.C., Slurry Flow Principles and Practice. Butterwoth-Heinemann, Boston. (1991). Jacobs, B.E.A., Design of Slurry Transport Systems. Elsevier Applied Science, London. (1990). Newitt, D.M., Richardson, J.F., Abbott, M. & Turtle, R.B., Hydraulic conveying of solids in horizontal pipes. Trans. lnstn. Chem. Engrs., 33, 93-113 (1955). Durand, R. & Condolios, E., Experimental study of the hydraulic transport of coal and solid materials in pipes. Proc. Colloq. On The Hydraulic Transport of Coal, National Board, UK, 39-55
Slurry transport processes
14. 15. 16. 17.
(1952). Thomas, D.G., Transport Characteristics of Suspensions:VIII. A note of the viscosity of newtonian suspensions of uniform spherical particles. J. Colloid. Sci., 20, 267-277 (1965). Fangary, Y.S., Study of The Effect of Some Properties of Two Phase Liquid Solid Flow On The Design of Slurry Pipelines. M.Sc. Thesis, Ain Shams Univ., Cairo- Egypt. (1995). Wilson, K.C., Slip point of beds in solid-liquid pipeline flow. Proc. ASCE, J. Hyd. Div., 97, 1665-1679 (1070). Richardson, J.F. & Zaki, W.N., Sedimentation and fluidization. Trans Inst. Chem. Engrs., 32, 35-52 (1954).
NOMENCLATURE C Cc Cf
do D f g i K1 K2 m N Ps
R S V W W0
= volume fraction solids = contact load (volume fraction) = volume fraction (-74 #m) solids = Rosin Rammler coefficient (eqn. 1), (m) = pipe diameter, (m) = friction factor = gravitational acceleration = hydraulic gradient (m liquid/m pipe) = constant in equation 9 = constant in correlation 9 = constant in equation 11 = Rosin Rammler constant (eqn. 1), dependent on size distribution = fraction of solids smaller than diameter d = correlating constant, equation 12 = solids specific gravity = mean velocity of flow, (m/s) --- hindered teminal settling velocity, (m/s) = particle terminal settling velocity, (m/s)
Greek Letters Od
p
= = = =
constant in equation 4 constant in equation 4 fluid viscosity density
Subscripts f m w
439
= fines = properties of carrier fluid taking percentage of fines into account = carrier fluid alone (water)