Slurry Pumping.xls

JJR 04-04-2006 SLURRY PUMPING CALCULATIONS Particle Size NON-SETTLING  Very Fine Homogeneous Homogeneous - see Category A   Very Fine Homogeneous Homogeneous - see Advanced Methods

<50 um <50

SETTLING Fine Heterogeneous - Category A - Low Cw Fine Heterogeneous - Category B - High Cw

50 - 300 um 50 - 300

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

>300 um >300

Category A - Durand Formula - Simple Sand-like Slurries This is an empirical method 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 do pipe loss calculations 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 Complex Slurries 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 Paterson & Cook  Graeme Addie Lazarus & Neilson Metzner & Reed

De Beers Kimb GIWGIW-KS KSP P Slu Slurr rr Improvement Lami Lamina narr flo flow wi

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

Large diameter Bingham fluids Non-Newtonia Non-Newtonia

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 sc ope 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.   Hatch FFDS Fluid Flo

Cw <35 >35

Significant Viscosity

<40 >40 <20 >20

 

Suction Dredging

rlite slurries Software Pipeline Design Manual n Durant slurries

coal-water slurries

Slurries  turbulent flow

Design Software

JJR 04-04-2006 HOMOGENEOUS 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 04-04-2006 CATEGORY A HETEROGENEOUS SLURRIES PARTICLES 50 - 300 um Concentration Cw 0 to 40% Use Durand Formula for limiting settling velocity VL SG of Dry Solids SG of Liquid ID of pipe Particle Size - d50 Average Slurry SG Concentration by weight -- Cw Concentration by volume -- Cv

2650 1000 150 211 1.23 30 14

FL - Limiting Velocity Factor

1.04 from Chart

High deposit risk at 0.7 VL Settling Velocity VL Hf values equal to water if V exceeds 1.3 VL

1.60 m/s 2.29 m/s

Solids deposit in line - increased Hf over water 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

 Velocity in pipe

kg/m3 kg/m3 mm um

Area

0.017671 m2

% %

2.77 m/s

0.048944 m3/s

Kinematic Viscocity - water  Absolute Viscosity - water Reynolds Number - water Darcy friction factor Equivalent Length of pipe Friction Loss Hf 

1.00 mm2/s 0.00100 Ns/m2

1 cP

415453 0.017 116.75 m 5.17 m

From Pipe Friction page or Chart for water

JJR 04-04-2006 CATEGORY B HETEROGENEOUS SLURRIES - HIGH Cw PARTICLES 50 - 300 um High Concentration Cw over 40% Estimate using Category A Durand 1 Formual  Adjust for high concentration using additional Chart Factors and 2 experience The true value of Hf may be double or more the estimated values. Provide reserves of speed and power at the motor.

JJR 04-04-2006 CATEGORY C COARSE HETEROGENEOUS SLURRIES - LOW Cw PARTICLES OVER 300 um Concentration Cw 0-20% Usually suction dredging application for gravel and/or coarse sand Estimate using Category A 1 Durand Formual For VL and higher velocities take friction as 10% higher 2 than water

JJR 04-04-2006 CATEGORY D COARSE HETEROGENEOUS SLURRIES - HIGH Cw PARTICLES OVER 300 um Concentration Cw over 20% Estimate using Category A 1 Durand Formual  Adjust for high concentration using additional Chart Factors and 2 experience Hf may vary from Category A Durand to three times or more. Provide reserves of speed and power at the motor.

JR 25-03-2008 FRICTION FACTOR - ALL FLUIDS Absolute Roughness

Pipe Internal Diameter - D Effective roughness - e Flow Rate - Q Flow Rate - Q Slurry SG Slurry Density - rho  Viscosity - mu

150 mm 0.05 mm 176.2 m3/h 48.94 l/s 1.23 1230 kg/m3 1 cP

 Area - A  Velocity - V

17671 mm2 2.77 m/s

Concrete Cast Iron PE - coarse slurry Galvanised iron PE - fine slurry Asphalted cast iron Commercial steel PE & PVC non abra Drawn tube - hydra

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

Churchill Formula B 1.97E-17 A1 5.06E-05 A2 0.00009 A3 7113.745

Temperature deg.C

  A.ln 8.869784  A 2.59E+21 Friction Factor f.c - Churchill f - Fanning - 2 x f.c f.d - Darcy - 4 x f

0.0021 0.0042 0.0168

Reference

SW Churchill - Friction factor equation spans all fluid-flow regimes University of Pennsylvania Chemical Engineering - Nov 7 - 1977

0 10 20 30 40 60 100

- mm

0.30 to 3.0 0.26 0.26 0.15 0.15 0.12 0.045 to 0.05 0.0015 0.0015

Absolute Density rho

999.8 999.7 998.2 995.6 992.2 983.2 958.3

Viscosity cP

1.80 1.30 1.10 0.80 0.69 0.49 0.48