Pipeline Transport of Settling Slurries

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 PipelinesEach 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 PSIPhoto’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 mmLarge (heterogeneous) 2 mm ~ 5 mmVery Large (hetero “ “ ) 5 mm ~ >200 mm?

Transport velocity must increase as size increases

Settling Slurries




Transport velocity must increase as size increases

Settling Slurries

Dead Donkeys?




Pipeline Flow of Newtonian Liquids

HW = gPρΔ

= g

VDLf

2

2

Darcy-Weisbach equation

H1 =g

P1

ρ +

g2

2v + z1

H2 =g

P2

ρ +

g2

2v + z1

Head LossHW

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)

DLf

Moody Diagram

C.Y. O’Connor Pipeline c.a. 1899

Features of Settling Slurry Pipeline Flow

Mean Velocity , V (m/s)

Hyd

raul

ic g

radi

ent,

i (m

/m)

Settling Slurry

Carrier

Fixed Bed

Fluidised Heterogeneous Homogeneous

V1 V2 V3 =Vdep V4

Water

HeterogeneousFlow

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.

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100

150

200

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0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

Head Los (m‐Water)

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

SWM HHH +=

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

5.12

.82.

−

⎥⎦

⎤⎢⎣

⎡ρ−ρ

ρ=

−D

SWV

WM CgDV

iCii

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”

5.12

.8 2.

−

⎥⎦

⎤⎢⎣

⎡ρ−ρ

ρ=

−D

SWV

WM Cg DV

iCii

5.1.8 2 −ψ=φ

).82.1( 5.1−ψ+= VWM CHH

0

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100

150

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500

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)


Water

Settling Slurry

Deposition Point



SWM HHH +=

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!

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800

0 2 4 6 8 10

Head Los (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


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


Turbulent fluctuation of particle velocity in the direction of flow




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500

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)


Water

Settling Slurry

Deposition Point

HW

Hs

SWM HHH +=Solids concentration approaches input concentration Hs=constant

).82.1( 5.1−ψ+= VWM CHH

• 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 = gPρΔ

= g

VDLf

2

2

Comparison of Theories

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

Head Los (m)

F low Ve locit y (m / s)

Head Loss , 5mm grave l,C v=10% , DN400 P ipe x 1000m

L azaru s Ne ilson

W ilson A dd ie C lift Du rand

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

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0.00 2.00 4.00 6.00 8.00 10.00

Head loss (m)

Velocity m/s

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

Wilson Addie Clift DurandLazarus NeilsonWater

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 bemore 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 VelocityCollaborators : J. Bremer (SKM) , Vincent Lim (K.J. Beer), Ramesh Gandhi (PSI – California)

Mean Velocity , V (m/s)

Hyd

raul

ic g

radi

ent,

i (m

/m)

Settling Slurry

Carrier

Fixed Bed

Fluidised Heterogeneous Homogeneous

V1 V2 V3 =Vdep V4

Water

Heterogeneous

Flow

Fluidised Bed

Homogeneous 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)


Pesky mean path length constan


All terms in the final equation are rearranged to solve for theSlip 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

5104 −×

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

Virtual Experiment – ResultsDeposition Velocity

5104 −×

Deposition Velocity – Average Error 0.05 %-- Maximum Error 0.42 %

Virtual Experiment – ResultsHead Loss at The Deposition Point

5104 −×

Head Loss – Average Error 0.55 %-- Maximum Error 1.8 %

Conclusions

5104 −×

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.

Documents

Pipeline Transport of Settling Slurries