Pipeline Flow of Settling Slurries Presentation to Institution of - - PowerPoint PPT Presentation

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

Settling Slurries contain particles that will fall and settle at the bottom of a container Non Settling Slurries contain particles that remain in suspension for a long time

NON-SETTLING

• Particles < 40 µm
• Viscosity modified by

particles

• Increasingly non-Newtonian

as concentration increases

SETTLING

Particles > 40 µm Wide range of sizes from Small (suspensions) 40 µm ~ 200 µm Medium (transition) 200 µm ~ 2 mm Large (heterogeneous) 2 mm ~ 5 mm Very Large (hetero “ “ ) 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 ~ 200 µm Medium (transition) 200 µm ~ 2 mm Large (heterogeneous) 2 mm ~ 5 mm Very Large (hetero “ “ ) 5 mm ~ >200 mm?

Transport velocity must increase as size increases

Settling Slurries

Dead Donkeys?

SETTLING

Particles > 40 µm Wide range of sizes from Small (suspensions) 40 µm ~ 200 µm Medium (transition) 200 µm ~ 2 mm Large (heterogeneous) 2 mm ~ 5 mm Very Large (hetero “ “ ) 5 mm ~ >200 mm?

Pipeline Flow of Newtonian Liquids

HW = g P ρ Δ

=

g V D L f 2

2

Darcy-Weisbach equation

H

1 =

g P

1

ρ

+

g 2 2 v + z

1

H

2 =

g P

2

ρ

+

g 2 2 v + z

1

H ead Loss H

W

Pipe Flow

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 (m2/s)

V

= mean Flow velocity (m/s)

D L f

Moody Diagram C.Y. O’Connor Pipeline c.a. 1899

Features of Settling Slurry Pipeline Flow

Mean Velocity , V (m/s) Hydraulic gradient, i (m/m )

Settling Slurry Carrier

Fixed Bed Fluidised Heterogeneous Homogeneous V1 V2 V3 =Vdep V4 Water Heterogeneous Flow Fluidised Bed Homogeneous Flow

1. Size does matter.

• 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. 3. The system curve has a minimum that bounds different flow / friction processes

Newitt’s Classification of Slurry Pipeline Flow

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.

Solids Concentration

Frictional Head loss Mechanisms

• 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 (a) particles and fluid (b) particles and pipe wall (c) particle-particle collisions.

50 100 150 200 250 300 350 400 450 500 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 H e a d L

• s

( m ‐ W a t e r ) Flow Velocity (m/s)

Head Loss , 5mm gravel,Cv=10%, DN400 Pipe

Water Settling Slurry Deposition Point

Frictional Head Loss due to wall friction of carrier fluid with pipe- HW Frictional Head Loss due to solids - Hs S W M

H H H + =

Durand Theory -1952

Durand, R. 1952. The Hydraulic Transportation of Coal and Other Materials in Pipes. Colloq. of National Coal Board, London.

5 . 1

. 82

−

ψ = φ

5 . 1 2

. 82 .

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ρ − ρ ρ = −

D S W V W M

C gD V i C i i

Durand Theory – (contd)

1. Durand’s Theory is purely correlative. 2. The curve fit was for 305 points, for sand and coal running between 200 µm and 25 mm. 3. The results are in “Head of Carrier Fluid” – usually water. 4. As transport velocity becomes large, the slurry curve converges to water head loss from above. “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”

5 . 1 2

. 82 .

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ρ − ρ ρ = −

D S W V W M

C gD V i C i i

5 . 1

. 8 2

−

ψ = φ ) . 82 . 1 (

5 . 1 −

ψ + =

V W M

C H H

50 100 150 200 250 300 350 400 450 500 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 H e a d L

• s

( m ‐ W a t e r ) Flow Velocity (m/s)

Head Loss , 5mm gravel,Cv=10%, DN400 Pipe

Water Settling Slurry Deposition Point

Frictional Head Loss due to wall friction of carrier fluid with pipe- HW Frictional Head Loss due to solids - Hs

S W M

H H H + =

More Theories

(To name a Few)

• 1. Durand – 1952
• 2. Homogeneous Mixture Theory
• 3. Newitt et. Al - 1955
• 4. Rose and Duckworth – 1969
• 5. Heyden and Stelson - 1971
• 6. Volcado and Charles 1972
• 7. Wasp et al - 1977
• 8. Lazarus – Neilson 1978
• 9. Wilson - 1992
• 10. Wilson Addie & Clift 1997

Correlation Correlation Correlation Correlation Correlation In Current Use Part theory part correlation Not in Use

No Problem – “I’ve got a Computer”

Answers Using commonly accepted theories can vary by several hundred percent – AND MORE!

100 200 300 400 500 600 700 800 2 4 6 8 10 H e a d L

• s

( m ) Flow Velocity (m/s)

Head Loss at 6.6 m/s , 5mm gravel, Cv=10% DN400 Pipe x 1000m

Lazarus ‐ Neilson Wilson‐Addie‐Clift Durand Water

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

Frictional Head Loss due to wall friction of carrier fluid with pipe- HW Frictional Head Loss due to solids - Hs

50 100 150 200 250 300 350 400 450 500 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 H e a d L

• s

( m ‐ W a t e r ) Flow Velocity (m/s)

Head Loss , 5mm gravel,Cv=10%, DN400 Pipe

Water Settling Slurry Deposition Point

HW Hs

S W M

H H H + =

Solids concentration approaches input concentration Hs=constant

) . 82 . 1 (

5 . 1 −

ψ + =

V W M

C H H

• 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

HW = g P ρ Δ

=

g V D L f 2

2

Comparison of Theories

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 H e a d L

• s

( m ) Flow V e locity (m /s)

Head Loss , 5m m gravel,Cv=10% , DN 400 Pipe x 1000m

L azarus Ne ilson W ilson A ddie Clift Durand

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

Agreement is less critical at 100 µm

50 100 150 200 250 300 350 400 450 500 0.00 2.00 4.00 6.00 8.00 10.00 H e a d l

• s

s ( m ) Velocity m/s

Head Loss, 100µm particle, Cv=10%, DN100 pipe x 1000m

Wilson Addie Clift Durand Lazarus Neilson Water

Slope M

Wilson Addie and Clift Theory

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)

Mean Velocity , V (m/s) Hydraulic gradient, i (m/m )

Settling Slurry Carrier

Fixed Bed Fluidised Heterogeneous Homogeneous V1 V2 V3 =Vdep V4 Water

Heterogeneou s Flow Fluidise d Bed Homogeneou s Flow

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

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

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 Pipe diameter (D) 0.1 0.9 m Particle density (ρp) 2,160 4,000 kg/m3 Particle size (d) (40 μm) 0.02 (20 mm) m Concentration by volume (Cv) 0.05 0.4 Pipe length (L) 1,000 m Pipe roughness Smooth

5

10 4

−

×

200 Virtual data points (deposition velocity, and pressure at the deposition point) obtained using Durand equation to

Virtual Experiment – Results Deposition Velocity

5

10 4

−

×

Deposition Velocity – Average Error 0.05 %

• - Maximum Error 0.42 %

Virtual Experiment – Results Head Loss at The Deposition Point

5

10 4

−

×

Head Loss – Average Error 0.55 %

• - Maximum Error 1.8 %

Conclusions

5

10 4

−

×

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.