CalcCvr Page 1 of 41

file:///tt/file_convert/54776fe3b4af9faf368b45fa/document.xls 04/09/2023

CALCULATION COVER SHEET Date: 9-Apr-23Author: Revision

Project: Calc No:Title: Sizing and Selection of Hydrocyclones using Richard Arterburn method

http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

Purpose:

Basis / Assumptions:

Method:

Disclaimer:

To provide a basis for first-pass hydrocyclone sizing for mineral processing applications.

Method is based on The Sizing and Section of Hydrocyclones by Richard Arterburn. The source paper is available from the Krebs website at this address (current as of Sept 2006):http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

The selection procedure begins with a "normal" cyclone geometry, as described by Arterburn, and 20°C feed slurry consisting of water and solids with specific gravity 2.65. "Normal" pressure drop is defined as 69 kPa and feed concentration is less than 1% solids by volume.

Next, the selection applies factors to account for the effects of actual solids size, density, slurry %solids, liquid viscosity, and pressure drop.

Then the desired flow rate is compared the performance of standard cyclone sizes. A selection of a standard size then determines the number of operating cyclones.

This spreadsheet is presented "As Is" and no warrantee is made to the correctness, applicability, or validity. The method described has been used in standard engineering practice but it is the sole responsibility of the engineer using this calculation to confirm its applicability to any application.

The author of this spreadsheet accepts no responsibility for the correctness or suitability of any results derived from this spreadsheet's use.

1

A B C D E F G H I123456789

101112131415161718192021222324252627282930313233343536373839404142434445

Input Column Calculation Column

Optional:10 °C

Dynamic viscosity = 1.307 cP, density = 999.7 kg/m³

Liquid density 999.7 kg/m³ 1.000 SGLiquid viscosity 1.307 cP 1.307 cP

Feed solids density 2.65 SG 2.650 SGFeed solids content 54.6 %solids w/w 31.2 %solids v/v

Desired overflow is 80 % passing 150 µm 150 µm

Optional: Special look up tableStandard mesh sizes US sieve series

100 mesh = 149 µm

33.6 ft waterDesired pressure drop 100 kPa 100.0 kPa

14.5 psi

Desired feed flow rate 8683 m³/h 8,683 m³/h38,234 usgpm

D50c (application) = 150 * 1.25 = 188 µm

Feed correction factor C1 [(53 - %Solids v/v)/53]^(-1.43) 3.56

Pressure correction factor C2 3.27 * (pressure drop)^(-0.28) 0.89

SG correction factor C3 (1.65 / [SGs - SGw] )^0.5 1.00

Other correction factor C4 1 1.00

D50c (base) = D50c (application) / C1 / C2 / C3 / C4 59 µm

"Ideal" cyclone diameter to achieve this D50c (base) 99 cm39 inch

recommendActual cyclone diameter (from typical sizes in Fig 9) 76.0 91.0 cm

36 inch

Actual throughput of a single cyclone of this size 945.3 m³/h4162 usgpm

Number of operating cyclones required 9.2 , round up= 10

Special look up table: Water viscosity at temp

Add spares 20% extra 2

Total number of cyclones for this application 12

Summary: To achieve 8,683 m³/h and a product size 80% passing 150 µm operating at 100 kParequires 12 x 91 cm diameter cyclones (10 operating, 2 standby).

EQUATION 1: PARTICLE RECOVERY CURVESsource: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

This table is a prediction of the cyclone recovery of classified material to underflow and is useful for prediction of underflow particle size distribution.Note that unclassified material (carry-under) also reports to the underfowand must be accounted for to constitute a complete underflow size distribution.The carry-under calculation is not performed in this spreadsheet and must be estimated manually.

Rr = recovery to underflow on corrected basisX = particle diameter / D50c particle diameter

From previous page, D50c = 59 µmFrom previous page, C factors = 3.2

Particle X Reduced Particlesize, µm recovery size, µm

(corrected) (corrected) (uncorrected)200 3.4 100% 636141 2.4 100% 450100 1.7 94% 318

71 1.2 69% 22550 0.8 35% 15935 0.6 16% 11225 0.4 8% 8018 0.3 4% 5612 0.2 2% 40

9 0.1 2% 28

Or, enter a particle size to see its corrected recovery:US sieve series

100 mesh = 149 µm

size, µm X recovery149 2.5 100%

0 100 200 300 400 500 600 700

0%

20%

40%

60%

80%

100%

Eqn 1: Predicted cyclone performance

Column D Column D

Particle size, µm

Re

co

ve

ry t

o u

nd

erf

low

Note: actual recovery does not consider carry-under of overflow materialinto the underflow's interstitial spaces. Manually add an appropriate amountof carry-under to constitute a realistic underflow size distribution (eg. Fig 3).

0 100 200 300 400 500 600 700

0%

20%

40%

60%

80%

100%

Eqn 1: Predicted cyclone performance

Column D Column D

Particle size, µm

Re

co

ve

ry t

o u

nd

erf

low

FIGURE 3: PARTICLE RECOVERY CURVESsource: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

FIGURE 5: CYCLONE DIAMETER VERSUS D50c FOR STANDARD CYCLONEsource: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

FIGURE 6: INFLUENCE OF FEED CONCENTRATION ON SEPARATION (C1)source: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

FIGURE 7: INFLUENCE OF PRESSURE DROP ON SEPARATION (C2)source: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

FIGURE 8: INFLUENCE OF SOLIDS SPECIFIC GRAVITY ON SEPARATION (C3)source: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

FIGURE 10: APEX CAPACITY CURVEsource: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

Cyclone Diam first point second point Slopeinch cm psi usgpm psi usgpm a

4 10 8 30 70 91 0.516 15 6 70 100 300 0.52

10 25 9 200 100 700 0.5215 38 7 300 70 1000 0.5220 51 4 500 50 2000 0.5526 66 4 1000 90 5000 0.5230 76 3 1300 93 8000 0.5333 84 5.4 2150 71.5 8000 0.5136 91 7.8 3000 50 8000 0.53

Pressure entered on InputSheet 14.5 psi

Performance of all cyclone diameters at this pressure

Cyclone Diam Flow at this pressureinch cm usgpm m³/h

Cycl_perf 4 10 40.7 9.26 15 110.5 25.1

10 25 256.4 58.215 38 439.1 99.720 51 1014.0 230.326 66 1946.1 442.030 76 2992.7 679.733 84 3553.8 807.136 91 4162.3 945.3

FIGURE 7: INFLUENCE OF PRESSURE DROP ON SEPARATIONsource: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

Table: PROPERTIES OF WATERsource: http://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html

http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html

Temperature Density°C (cp) kg/m³

Water 5 1.519 1.519 100010 1.307 1.307 999.720 1.002 1.004 998.225 0.890 0.894 997.1 This line only, source= http://www.lsbu.ac.uk/water/data.html30 0.798 0.801 995.740 0.653 0.658 992.250 0.547 0.553 988.160 0.467 0.475 983.2

Dynamic Viscosity

Kinematic Viscosity10-6 m²/s

This line only, source= http://www.lsbu.ac.uk/water/data.html

Label Factor Source

Units_flow m³/h 1L/s 3.59999712 http://www.engineeringtoolbox.com/unit-converter-d_185.htmlusgpm 0.22710085 http://www.engineeringtoolbox.com/unit-converter-d_185.html

Units_density SG 1t/m³ 1kg/m³ 0.001lb/ft³ 0.01601815 http://www.engineeringtoolbox.com/unit-converter-d_185.html

Units_size µm 1micron 1mm 1000metre 1.00E+06inch 2.54E+04

mesh µm http://www.encyclopedie-gratuite.fr/Definition/table-de-conversion.phpUSmesh 4 4760

5 40006 33607 28308 2380

10 200012 168014 141016 119018 100020 84025 71030 59035 50040 42045 35050 29760 25070 21080 177

100 149120 125140 105170 88200 74230 62270 53325 44

400 37500 31

TyMesh 9 2000 http://www.4oakton.com/TechTips/OAK_TT30.pdf#search=%22tyler%20mesh%20conversion%2210 168012 141014 119016 100020 84124 70728 59532 50035 42042 35448 29760 25065 21080 177

100 149115 125150 105170 88200 74250 63270 53325 44400 37

BritishMesh 8 2000 http://www.4oakton.com/TechTips/OAK_TT30.pdf#search=%22tyler%20mesh%20conversion%2210 168014 120016 100022 71025 60030 50035 42044 35552 30060 25072 21085 180

100 150120 125150 105170 90200 75240 63300 53

350 45

MeshTypes US USmeshTyler TyMeshBritish BritishMesh

inverseUnits_pressure kPa 1 7.500617 http://www.engineeringtoolbox.com/unit-converter-d_185.html

bar 100 0.01Atm 101.3 0.009872mm Hg 0.133 7.518797mm water 0.00981 101.9368inch Hg 3.378 0.296033inch water 0.24813896 4.03psi 6.8948 0.145037

http://www.engineeringtoolbox.com/unit-converter-d_185.htmlhttp://www.engineeringtoolbox.com/unit-converter-d_185.html

http://www.engineeringtoolbox.com/unit-converter-d_185.html

http://www.encyclopedie-gratuite.fr/Definition/table-de-conversion.php

http://www.4oakton.com/TechTips/OAK_TT30.pdf#search=%22tyler%20mesh%20conversion%22

http://www.4oakton.com/TechTips/OAK_TT30.pdf#search=%22tyler%20mesh%20conversion%22

http://www.engineeringtoolbox.com/unit-converter-d_185.html

TABLE 1: RELATIONSHIP OF D50c TO OVERFLOW SIZE DISTRIBUTIONsource: http://www.krebs.com/documents/83_sizing_select_cyclones.pdf

Multiplier

d50c_base 98.8 0.5495 0.7390 0.9180 1.2570 1.6760 2.0850 2.78

distribution