JJR 04-04-2006SLURRY PUMPING CALCULATIONS

NON-SETTLINGVery Fine Homogeneous - see Category AVery Fine Homogeneous - see Advanced Methods

SETTLINGFine Heterogeneous - Category A - Low CwFine Heterogeneous - Category B - High Cw

Coarse Heterogeneous - Category C - Low CwCoarse Heterogeneous - Category D - High Cw

Complex Slurries

Paterson & Cook Graeme Addie Lazarus & Neilson Metzner & Reed Wasp

Category A - Durand Formula - Simple Sand-like Slurries

This is an empirical method of estimating Hf and is not precise. In absence of test data it provides a reasonably accurate estimate for many practical slurry pumping applicatons.

The assumption that all can be calculated on the basis of clear water - and then multiplied by 2 or 3 through a HR factor for motor selection - has its limitations.Experience is essential to correctly interpret the various fudge factors.

Also it doesn't feel right to do pipe loss calculations for a fluid which doesn't reflect concentration and increased viscous friction loss.But the calculations are simple and do bridge the gap between simple slurries and those needing further test data and more advanced design

The above calculations are based on the Durand Formula and simple variations.

A variety of methods are available for assessing friction losses in more complex slurries - including the following

Hanks & Dadia Warman Technical Bulletin No 14 - Oct 1991 Dodge Metzner

Hatch

This Workbook is based on the Warman Slurry Pumping Handbook - which is adequate for simple slurries of low to medium concentration. These slurries do not include added viscocity effects due to high fines components.More advanced analysis of slurries is beyond the scope of the simple Durand based approach presented in this Workbook.

Advanced slurries are a specialist subject which should be referred to Consultants. Many have specialised software to analyse specific slurry pumping problems.

Particle Size Cw

<50 um <35<50 >35 Significant Viscosity

50 - 300 um <4050 - 300 >40

>300 um <20 Suction Dredging>300 >20

De Beers Kimberlite slurries SoftwareGIW-KSP Slurry Pipeline Design ManualImprovement on DurantLaminar flow in slurriesLarge diameter coal-water slurries

Bingham fluidsNon-Newtonian SlurriesNon-Newtonian turbulent flow

FFDS Fluid Flow Design Software

JJR 04-04-2006HOMOGENEOUS SLURRIES (NON-SETTLING)

VERY FINE PARTICLES - ALL LESS THAN 50 UM

Low Cw - design as Category A

High Cw - check Yield Stress or Viscosity characteristics for effect on Friction Head - refer to advanced literature.

JJR 04-04-2006CATEGORY A HETEROGENEOUS SLURRIES

PARTICLES 50 - 300 umConcentration Cw 0 to 40%

SG of Dry Solids 2650 kg/m3SG of Liquid 1000 kg/m3ID of pipe 150 mm Area 0.017671 m2Particle Size - d50 Average 211 umSlurry SG 1.23Concentration by weight -- Cw 30 %Concentration by volume -- Cv 14 %

FL - Limiting Velocity Factor 1.04 from Chart

High deposit risk at 0.7 VL 1.60 m/s Solids deposit in line - increased Hf over waterSettling Velocity VL 2.29 m/s Limit at which solids deposit - Hf above water

2.98 m/s Hf close to water above this velocity

Slurry Flow 176.2 m3/h 0.048944 m3/s

Velocity in pipe 2.77 m/s

Kinematic Viscocity - water 1.00 mm2/s

Use Durand Formula for limiting settling velocity VL

Hf values equal to water if V exceeds 1.3 VL

Absolute Viscosity - water 0.00100 Ns/m2 1 cP

Reynolds Number - water 415453

Darcy friction factor 0.017 From Pipe Friction page or Chart for waterEquivalent Length of pipe 116.75 m

Friction Loss Hf 5.17 m

Solids deposit in line - increased Hf over waterLimit at which solids deposit - Hf above water

JJR 04-04-2006CATEGORY BHETEROGENEOUS SLURRIES - HIGH Cw

PARTICLES 50 - 300 umHigh Concentration Cw over 40%

1

2

Estimate using Category A Durand Formual

Adjust for high concentration using additional Chart Factors and experience

The true value of Hf may be double or more the estimated values.Provide reserves of speed and power at the motor.

JJR 04-04-2006CATEGORY C COARSE HETEROGENEOUS SLURRIES - LOW Cw

PARTICLES OVER 300 umConcentration Cw 0-20%

1

2

Usually suction dredging application for gravel and/or coarse sand

Estimate using Category A Durand Formual

For VL and higher velocities take friction as 10% higher than water

JJR 04-04-2006CATEGORY DCOARSE HETEROGENEOUS SLURRIES - HIGH Cw

PARTICLES OVER 300 umConcentration Cw over 20%

1

2

Estimate using Category A Durand Formual

Adjust for high concentration using additional Chart Factors and experience

Hf may vary from Category A Durand to three times or more.Provide reserves of speed and power at the motor.

JR 25-03-2008FRICTION FACTOR - ALL FLUIDS

Pipe Internal Diameter - D 150 mmEffective roughness - e 0.05 mmFlow Rate - Q 176.2 m3/h

Flow Rate - Q 48.94 l/sSlurry SG 1.23

Slurry Density - rho 1230 kg/m3Viscosity - mu 1 cP

Area - A 17671 mm2Velocity - V 2.77 m/s

Reynolds Number - Water 4.15E+05Relative Roughness e/D 0.000333

Churchill FormulaB 1.967E-17 A1 5.057E-05 A2 0.00009 A3 7113.745

A.ln 8.869784A 2.59E+21

Friction Factorf.c - Churchill 0.0021f - Fanning - 2 x f.c 0.0042f.d - Darcy - 4 x f 0.0168

Reference

SW Churchill - Friction factor equation spans all fluid-flow regimesUniversity of PennsylvaniaChemical Engineering - Nov 7 - 1977

Absolute Roughness e - mm

Concrete 0.30 to 3.0Cast Iron 0.26PE - coarse slurry 0.26Galvanised iron 0.15PE - fine slurry 0.15Asphalted cast iron 0.12Commercial steel 0.045 to 0.05PE & PVC non abrasi 0.0015Drawn tube - hydrau 0.0015

Water Properties Absolute

Temperature deg.C Density rho Viscosity cP

0 999.8 1.8010 999.7 1.3020 998.2 1.1030 995.6 0.8040 992.2 0.6960 983.2 0.49

100 958.3 0.48

SW Churchill - Friction factor equation spans all fluid-flow regimes