Pipeline Flow of Settling
Slurries
Presentation to Institution of Engineers Australia (Mechanical Branch)
Jeff Bremer - 23 rd April 2008
Overview and Aims
1. Explain physical laws underlying the behaviour of settling
solids in slurry pipeline flow.
2. Compare theories associated with pipeline flow. Why are
there so many?
3. Show where and how the theories disagree.
4. Present some preliminary results from recent work
(J. Bremer, V.Lim & R.Gandhi )
??
QUESTIONS
1. Where and why are slurry pipelines used?
2. What is a settling slurry?
3. What are the main features in pipeline flow?
4. Engineers are good at using theoretical and empirical “best
fit” theories. What’s the problem?
5. What are the underlying equations and physical phenomena?
6. What are the theories of pipeline flow?
7. What do we know that is right, and can we easilly confirm that
we have the “right answer”?
8. What’s the latest, and where to in future?
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
L
D
HW
=
head loss due to friction
(m)
f
=
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
Head Loss
HW P
2
v
ρg
2g
H1 = 1 + + z1 P
2
v
ρg
2g
H2 = 2 + + z1
Pipe Flow
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.
Hydraulic gradient, i (m/m )
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 Velocity , 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
350
H M = HW + H S
Frictional Head
Loss due to
solids - Hs
)r
300
e
ta
W
‐
m
(s 250
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
⎡V 2 ρ
⎤
iM − iW
CD ⎥
= 82.⎢
CV .iW
⎣ gD ρS − ρ
⎦
Durand, R. 1952. The Hydraulic Transportation of Coal and Other Materials in Pipes. Colloq. of National Coal Board,
London.
−1.5
Durand Theory – (contd)
Head Loss , 5mm gravel,Cv=10%, DN400 Pipe
500
1. Durand’s Theory is purely correlative.
H M = HW + H S
450
400
350
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
r) 300
te
a
‐W
m
( 250
s o
L d
a
e
H 200
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)
i M − iW
C V .iW
⎡V 2
ρ
= 8 2.⎢
⎣ gD ρ S − ρ
φ = 8 2 . ψ − 1 .5
H
M
= H W (1 + C V . 8 2 .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
L 400
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 function of Reynolds number for smooth spheres
and cylinders (Munson et al. 2002, 582)
Known correlations
to correction CD
based on shape
effect
Slip Velocity to Produce drag force FD
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
e
ta
‐W
(m
s 250
o
L d
a
e 200
H
Hs
Frictional Head
Loss due to
solids - Hs
HW
Frictional Head Loss due to
wall friction of carrier fluid
with pipe- HW
50
0
6.00
+ H
S
Settling Slurry
100
4.00
W
Water
150
2.00
= H
H M = 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 << Hw
•
In Durand Theory in the limit Hs
zero
Comparison of Theories
H e a d Lo s s , 5 m m gra ve l,C v= 1 0 % , D N 4 0 0 P ip e x 1 0 0 0 m
800
700
600
500
)
m
( s
Lo
400
d
a
e
H
L azar u s N e ilso n
W ilso n A d d ie C lift D u r an d
300
200
100
0
0
2
4
6
8
10
12
14
16
18
20
F lo w V e lo cit y (m / s)
Location of The Deposition Velocity and Head Loss at Deposition is
the Key to having an accurate 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
a 200
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 tests on 400 µm sand. Pressure gradient = 0.5 x sliding fr friction 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 fM for the mixture against the “base”
friction factor fB 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
Hydraulic gradient, i (m/m )
V1
V2
V4
V3 =Vdep
Settling Slurry
Water
Carrier
Mean Velocity , 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 constan
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
4 × 10 −5
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
4 × 10 −5
Virtual Experiment – Results
Deposition Velocity
Deposition Velocity – Average Error 0.05 %
-- Maximum Error 0.42 %
4 × 10 −5
Virtual Experiment – Results
Head Loss at The Deposition Point
Head Loss
– Average Error 0.55 %
-- Maximum Error 1.8 %
4 × 10 −5
Conclusions
1. Not “all is well” with the theory of slurry transport.
2. There is considerable disagreement amongst theories
regarding
1. Deposition velocity
2. Head Loss at Deposition
3. There is no clear agreement on the forces and friction
associated with various mechanisms, (e.g. fluidised bed,
heterogeneous flow, homogeneous flow etc) or the velocities
at which they occur.
4. Many of the theories “blow up” when large particles are
involved. Say > 2mm. Comparison between calculations at
these sizes indicates a need for model studies in future
developments.
5. Where possible don’t pump at sizes > 150 µm.