Pip ipe eli line ne Flo low w of o f Se Sett ttli ling ng Slurries
P resentat resentation ion to to Inst Instit itut ution ion of Engineers Engineers Aust Australia (Mechanical (Mechanical Branch)
J eff Br Bre emer - 23 rd Ap Aprril 2008
Overview and Aims 1. E xplai plain n phy physical sical laws laws underly underlying ing the behav behaviour iour of sett settling solids in slurry pipeline flow. 2. Com ompar pare e theor theories ies associat associated ed wit ith h pipel pipeline ine flow flow.. Why are there so many? 3. S ho how w whe here re an and d how how the the heor ories ies disagr disagree. ee. 4. P resent som some e prelim prelimina inary ry result results s from rece recent nt work (J . Brem Bremer er,, V.L V.Lim im & R.G .Gan andh dhii )
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Overview and Aims 1. E xplai plain n phy physical sical laws laws underly underlying ing the behav behaviour iour of sett settling solids in slurry pipeline flow. 2. Com ompar pare e theor theories ies associat associated ed wit ith h pipel pipeline ine flow flow.. Why are there so many? 3. S ho how w whe here re an and d how how the the heor ories ies disagr disagree. ee. 4. P resent som some e prelim prelimina inary ry result results s from rece recent nt work (J . Brem Bremer er,, V.L V.Lim im & R.G .Gan andh dhii )
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QUESTIONS 1. Wh Wher ere e and and why why ar are e slurry slurry pi pipe pelin lines es used? used? 2. Wh What at is a set settli lin ng slu slurrry? 3. Wha Whatt are the the main main feat featur ures es in pipelin pipeline e flow? flow? 4. E ng ngineer ineers s are good at using theor heoret etical ical and em empir pirical ical “best fit” fit ” theor heories. ies. What’s the problem? 5. What are the the und underly erlying ing equ equat ations ions and ph physical ysical phenom phenomena? ena? 6. Wha Whatt ar are e the the theo heorie ries s of pipe pipelin line e flow flow? ? 7. Wha What do we know that is right, and can we easilly confirm that we have the “right answer”? 8. Wha Whatt’s the the latest latest,, and wher where e to to in fut futur ure? e?
Slurry Pipelines Slurry pipelines are used mostly for “short haul”duties, e.g. dredging (~300m ), process plants (~300m) and tailings (~3 km) In some “long haul duties”, minerals are pumped many hundreds of kilometres.
Alumbrera copper concentrate pipeline (316 km), Argentina
ENGINEERED BY PSI Photo’s with permission of PSI Australia Pty. Ltd., 66 Kings Park Rd.,West Perth, WA 6005,Tel. no. (08) 9463-6606.
Slurry Pipelines Each type of duty has its own “best operation point”, where the size of the particles and the tendency to settle has a strong impact on capital and operating cost.
ENGINEERED BY PSI Photo’s with permission of PSI Australia Pty. Ltd., 66 Kings Park Rd.,West Perth, WA 6005,Tel. no. (08) 9463-6606.
Settling Slurries
Non Settling Slurries contain particles that remain in suspension for a long time
NON-SETTLING
Settling Slurries contain particles that will fall and settle at the bottom of a container
SETTLING
•
Particles <40 µm
Particles >40 µm
•
Viscosity modified by particles
Wide range of sizes from
•
Increasingly non-Newtonian as concentration increases
Small (suspensions) 40 µm Medium (transition) 200 µm Large (heterogeneous) 2 mm Very Large (hetero “ “ ) 5 mm
Transport velocity must increase as size increases
~200 µm ~ 2 mm ~ 5 mm ~>200 mm?
Settling Slurries
SETTLING Particles >40 µm Wide range of sizes from Small (suspensions) 40 µm Medium (transition) 200 µm Large (heterogeneous) 2 mm Very Large (hetero “ “ ) 5 mm
~200 µm ~ 2 mm ~ 5 mm ~>200 mm?
Transport velocity must increase as size increases
Settling Slurries
SETTLING Particles >40 µm Wide range of sizes from Small (suspensions) 40 µm Medium (transition) 200 µm Large (heterogeneous) 2 mm Very Large (hetero “ “ ) 5 mm
Dead Donkeys?
~200 µm ~ 2 mm ~ 5 mm ~>200 mm?
Pipeline Flow of Newtonian Liquids ΔP HW = ρg
L V2 = f D 2g
Darcy-Weisbach equation f
HW
=
head loss due to friction
(m)
=
friction factor
(dimensionless)
L
=
length of pipe
(m)
D
=
internal diameter of pipe
(m)
g
=
accelaration due to gravity
(m /s)
V
=
mean Flow velocity
(m/s)
2
Moody Diagram HeadLoss HW
H1 =
P1
ρg
+
2 v 2g
+ z1 H2 =
P2
ρg
+
2 v 2g
+ z1
PipeFlow
C.Y. O’Connor Pipeline c.a. 1899
Features of Settling Slurry Pipeline Flow
Fixed Bed
Fluidised Fluidised Bed
Homogeneous Homogeneous Flow
Heterogeneous Heterogeneous Flow
1. Size does matter.
)
m / m ( i
, t n e i
d a r g c i l u a r d y H
V1
V2
V4
V3 =Vdep
Settling Slurry
•
Larger particles require increased transport velocity
•
Smaller particles (particularly fines <40 µm) can modify viscosity. Helps to suspend larger particles.
2. Flow velocity generates turbulence which keeps particles suspended.
Water Carrier Mean Veloci ty , V (m/s)
3. The system curve has a minimum that bounds different flow / friction processes
Newitt’s Classification of Slurry Pipeline Flow
Solids
Concentration
Newitt et al (1955) described a range of flow flow/deposition phenomena after observing sand and coal particles in 25mm Perspex pipes. His classifications are still used today. Newitt, D. M., J . F. Richardson, M. Abbott, and R. B. Turtle. 1955. Hydraulic Conveying of Solids in Horizontal Pipes. Trans. Institution of Chemical Engineers 33: 94-113.
Frictional Head loss Mechanisms Head Loss , 5mm gravel,Cv=10%, DN400 Pipe 500
•
Since we understand the behaviour of water (the carrier) we can calculate the frictional head losses caused by wall friction - HW
•
The remainder must be friction losses between
450
400
H M = HW + HS
350
Frictional Head Loss due to solids - Hs
r) 300 e ta W ‐ m ( 250 s o L d a e 200 H
Water
Settling Slurry Deposition Point
150
Frictional Head Loss due to wall friction of carrier fluid with pipe- HW
100
(a) particles and fluid
50
0 0.00
2.00
4.00
6.00
8.00
10.00
12.00
Flow Velocity (m/s)
14.00
16.00
18.00
20.00
(b) particles and pipe wall (c) particle-particle collisions.
Durand Theory -1952
φ = 82.ψ−1.5
⎡V2 ρ ⎤ iM − iW CD ⎥ = 82.⎢ CV .iW ⎣ gD ρS − ρ ⎦
Durand, R. 1952. The Hydraulic Transpo rtatio n of Coal and Other Materials i n Pipes. Colloq . of National Coal Board, London.
−1.5
Durand Theory – (contd) Head Loss , 5mm gravel,Cv=10%, DN400 Pipe 500
400
350
)r 300 te a ‐W m ( 250 s o L d a e 200 H
1. Durand’s Theory is purely correlative.
H M = HW + HS
450
2. The curve fit was for 305 points, for sand and coal running between 200 µm and 25 mm.
Frictional Head Loss due to solids - Hs
Water
Settling Slurry Deposition Point
150
4. As transport velocity becomes large, the slurry curve converges to water head loss from above.
Frictional Head Loss due to wall friction of carrier fluid with pipe- HW
100
3. The results are in “Head of Carrier Fluid” – usually water.
50
0 0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
Flow Velocity (m/s)
⎡V2 i M − iW ρ = 82.⎢ C V .iW ⎣ gD ρ S − ρ
φ=
82.ψ
− 1.5
H M = H W (1 + C V .82.ψ − 1.5 )
⎤ CD ⎥ ⎦
− 1.5
“Nothing proves that such a formula is rigorously exact. Doubtless exists a more accurate and more complex means of notation, but the one given above groups quite favourably”
More Theories (To name a Few) Correlation
1. Durand – 1952 2. Homogeneous Mixture Theory 3. Newitt et. Al - 1955 4. Rose and Duckworth – 1969
Correlation
5. Heyden and Stelson - 1971
Correlation
6. Volcado and Charles 1972
Correlation
7. Wasp et al - 1977
Part theory part correlation Correlation
8. Lazarus – Neilson 1978 9. Wilson - 1992 10. Wilson Addie & Clift 1997 In Current Use Not in Use
No Problem – “I’ve got a Computer” Head Loss at 6.6 m/s , 5mm gravel, Cv=10% DN400 Pipe x 1000m 800 700 600
) 500 m ( s o 400 L d a e H 300
Lazarus ‐ Neilson Wilson‐Addie‐Clift Durand
200
Water
100 0 0
2
4
6
Flow Velocity (m/s)
8
10
Answers Using commonly accepted theories can vary by several hundred percent – AND MORE!
Settling and Drag Forces on Particles
Depends on density , particle diameter, shape, Reynolds number and surface effects
Settling and Drag Forces on Particles
Particles >150 µm
Drag coefficient as a funct ion of Reynolds number for smooth spheres and cylinders (Munson et al. 2002, 582)
Known correlations to correction C D based on shape effect Slip Velocity to Produce drag force F D
Settling and Drag Forces on Particles
Turbulent fluctuation of particle velocity in the direction of flow
Settling and Drag Forces on Particles Head Loss , 5mm gravel,Cv=10%, DN400 Pipe 500
H
Solids concentration approaches input concentration Hs=constant
450
400
350
)r 300 te a W ‐ m ( 250 s o L d a e 200 H
Hs
Frictional Head Loss due to solids - Hs
Water
Settling Slurry
150
HW 100
Frictional Head Loss due to wall friction of carrier fluid with pipe- HW
50
0 2.00
4.00
6.00
= HW + HS
HM = HW(1+ CV .82.ψ−1.5)
Deposition Point
0.00
M
8.00
10.00
12.00
14.00
16.00
18.00
ΔP HW = ρg
L V2 = f D 2g
20.00
Flow Velocity (m/s)
•
In the limit the slip velocity is roughly constant as the average velocity of particles in direction of flow equals approaches the velocity of the liquid i.e.Vsolid =Vliquid the “homogeneous limit” . In other words Hs <
•
In Durand Theory in the limit Hs
zero
Comparison of Theories Head Loss , 5m m gravel,Cv=10%, DN400 Pipe x 1000m 800
700
600
500
) (m s o L 400 d a e H
Lazarus Neilson W ilson A d d i e Clift Durand
300
200
100
0 0
2
4
6
8
10
12
14
16
18
20
F l o w V e l o c i t y (m /s)
Locatio n of The Deposi tion Veloci ty and Head Los s at Deposi tion is the Key to having an accur ate Theory. Clearly the “ state of the art is not good”
Comparison of Theories Head Loss, 100µm particle, Cv=10%, DN100 pipe x 1000m 500 450 400 ) 350 m ( 300 s s o l 250 d a200 e H 150
Wilson Addie Clift Durand Lazarus Neilson Water
100 50 0 0.00
2.00
4.00
6.00
8.00
10.00
Velocity m/s
Agreement is less critical at 100 µm
Wilson Addie and Clift Theory
Slope M
Determined in t ests on 400 µm sand. Pressur e gradient = 0.5 x slidin g fr fri ctio n factor
Lazarus Nielsen Theory (1978) Lazarus Neilsen Theory is a correlation theory that claims to be more accurate than Durand and Newitt’s theories. They proposed that the mass flow rate ratio (M*), defined as the ratio of mass flow of solids to carrier fluid, should be used instead of the volumetric concentration (Cv)
Lazarus Nielsen Theory (contd) They plotted friction factor f M for the mixture against the “base” friction factor f B to develop their final correlation.
Current Work – Particle Drag & Deposition Head and Velocity Collaborators : J . Bremer (SKM) , Vincent Lim (K.J . Beer), Ramesh Gandhi (PSI – California)
Began by describing the equations of drag and pressure loss due to solids at the deposition point. Assumes : All particles fluidised at the minimum in the pressure gradient curve Fixed Bed
Fluidised Fluidise d Bed
Homogeneous Homogeneou s Flow
Heterogeneous Heterogeneou s Flow
)
m / m
(
i
, t n e i
d a r g c i l u a r d y H
V1
V2
V4
V3 =Vdep
Settling Slurry
Water Carrier Mean Velocit y , V (m/s)
Particle Drag and Deposition Velocity and Head Loss(contd)
Particle Drag and Deposition Velocity and Head Loss(contd)
Pesky mean path length consta
Particle Drag and Deposition Velocity and Head Loss(contd) All terms in the final equation are rearranged to solve for the Slip velocity V’
This is Measurable from experiment!
Particle Drag a Virtual Experiment Based on Durand Points
−5
4× 10
Particle Drag a Virtual Experiment Based on Durand Points System Parameter
Value Range
Unit
Lower
Upper
Carrier density ( ρ)
1,000
1,250
kg/m3
Carrier viscosity ( μ)
0.0008
0.001
Pa.s
0.1
0.9
m
2,160
4,000
kg/m3
(40 μm)
0.02 (20 mm)
m
0.05
0.4
Pipe diameter (D) Particle density ( ρp) Particle size (d) Concentration
by
volume (Cv) Pipe length (L) Pipe roughness
1,000
m
Smooth
200 Virtual data points (deposition velocity, and pressure at the deposition point) obtained using Durand equation to
−5
4× 10
Virtual Experiment – Results Deposition Velocity
Deposition Velocity – Average Error 0.05 % -- Maximum Error 0.42 %
−5
4× 10
Virtual Experiment – Results Head Loss at The Deposition Point
Head Loss
– Average Error 0.55 % -- Maximum Error 1.8 %
