25/6/2018 Cyclone - SysCAD Documentation
Cyclone
From SysCAD Documentation
Navigation: Main Page -> Models -> Size Distribution Models
Contents
1 General Description
2 Diagram
3 Inputs and Outputs
4 Model Theory
4.1 Efficiency Curve
4.2 Define Cut Point
4.3 Krebs Model
4.3.1 Assumptions (Krebs)
4.4 Plitt Model
4.4.1 Assumptions (Plitt)
4.5 References
5 Data Sections
5.1 Summary of Data Sections
5.2 Cyclone Page
5.3 Requirements
5.4 Define Cut Size
5.5 Krebs
5.6 Plitt
5.7 Efficiency Curve
5.8 Common Data Fields
5.9 Partition Curve Section
6 Adding this Model to a Project
General Description
This model is used to simulate either a single hydrocyclone, or a cluster of hydrocyclones. The main
requirement for using this model is that the feed must contain solids with size distribution information. The
model will calculate the split of solids between the under and over flows based on the cut point (either
calculated or defined) and the size distribution of the feed stream.
The unit allows the user to define the cyclone in one of four ways:
1. Define the cut point of the cyclone
2. Use the Krebs method to calculate the cut point
3. Use the Plitt method to calculate the cut point
4. Define the partition curve of the cyclone
The first option allows the user to set the cut point without any further knowledge of the cyclone. The second
and third options require the user to define the cyclone dimensions. These dimensions are then used to calculate
the cut point and partition curve of the cyclone.
In the case of the Plitt method, the model will also calculate the liquid split between the over and under flows.
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Notes:
1. In SysCAD 9.3 this model has been replaced by the Hydrocyclone model.
2. This unit cannot be used to model a gas cyclone.
Diagram
The diagram shows the default drawing of the cyclone, with all of the streams that are available for operation of
the unit. The physical location of the streams connecting to the cyclone is unimportant. The user may connect
the streams to any position on the unit.
Inputs and Outputs
Label Required Input Number of Connections Description
Optional Output
Min Max.
Feed Required In 1 1 The slurry feed to the cyclone
OverFlow Requuired Out 1 1 The over flow from the unit
UnderFlow Required Out 1 1 The under flow from the unit
Model Theory
1. The model will simulate a hydrocyclone using one of the four user defined methods - 'Define d50',
'Efficiency Curve', 'Krebbs' and 'Plitt' These are described below.
2. The 'Efficiency Curve' method allows the user to define the fraction of material in each size interval that
will report to the cyclone overflow.
3. The other three methods use the d50 value, either calculated or defined by the user, to determine the
solids separation. The value is defined as the particle size that has a 50% chance of reporting to the
cyclone underflow. The majority of the particles finer than this size will report to the overflow, while the
majority of those coarser will report to the cyclone underflow.
4. The user may also define the number of cyclones in the cluster. The default value, and the minimum
number, is 1. This allows the model to calculate the pressure drop across each cyclone by dividing the
flow to the model by the number of cyclones in the cluster. This allows the user to model a number of
cyclones with a single drawing.
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Efficiency Curve
The user defines the Efficiency Curve of the cyclone by entering the fraction of material in each size interval
that will report to the cyclone overflow. This will normally be the Actual efficiency curve, which takes into
account the bypassing of fines to the underflow with the liquid. An example of an Efficiency curve is shown
below:
The user also defines the fraction of solids in the Cyclone underflow, as this allows the model to calculate the
liquid split across the cyclone.
Define Cut Point
The user defines the cut point of the cyclone, the d50, the sharpness α and the required percentage solids in the
under flow from the unit.
The model then uses the d50 defined by the user to calculate the fraction of solids in each size interval reporting
to the underflow using the following equations:
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Particle − diameter
x =
d 50
where Particle_diameter - geometric mean of the size interval
αx
e − 1
1
y =
αx α
e + e − 2
where: y1 = recovery to underflow on a corrected basis
1 1
y = y + Rf (1 − y )
where: y = actual recovery to underflow
Rf = fraction of feed liquid reporting to the underflow product
Krebs Model
The user defines the cyclone diameter, the percentage solids in the cyclone under flow and a correction factor
for the cyclone geometry, if necessary.
The model calculates the d50 of the cyclone from the following equations1:
(1) d 50 = d 50 (Base) × C1 × C2 × C3 × Factor
where Factor is a correction factor to account for differences in the cyclone geometry from the 'optimum'
dimensions.
(2) d 50 (Base) = 2.84 × D c
0.66
where: d50(Base) = the cut size a "standard cyclone" can achieve, in microns.
Dc = cyclone diameter, in cm
−1.43
53−Cv
(3) C1 = ( )
53
where: C1 = Correction for the influence of cyclone feed concentration
Cv = Feed solids volume concentration (%)
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(4) C2 = 3.27 × ΔP
−0.28
where: C2 = Correction for the influence of pressure drop
DP = Pressure drop across the cyclone in kPa - calculated in (5) using Plitt method
1.78
1.88 × Q × exp(0.0055 × Cv )
(5) ΔP =
0.37 0.94 2 2
0.28 0.87
Dc × D × h × (D u + D o )
i
where: Q = feed slurry volumetric flow-rate per cyclone in l/min
Cv = Feed solids volume concentration (%)
DC = Diameter of cyclone
DI = Diameter of cyclone inlet = 0.2 * DC
DU = Diameter of cyclone underflow, or apex = 0.15 * DC
DO = Diameter of cyclone overflow, or vortex finder = 0.3 * DC
h = Free vortex height of cyclone = 1.5 * Dc
All the cyclone dimensions are in cm. These values are for an 'Optimum Cyclone' 2 .
0.5
1.65
(6) C3 = (
GS −GL
)
C3 = Correction for the influence of SG
where: G
S = SG of solids
GL = SG of liquids
The model then uses the d50, either defined as in 4.1 or calculated in 4.2, to calculate the fraction of solids in
each size range using the following equations 2,3:
Particle − diameter
x =
d 50
where Particle_diameter - geometric mean of the size interval
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exp(4x) − 1
1
y =
exp(4x) + exp(4) − 2
where: y = recovery to underflow on a corrected basis
1 1
y = y + Rf (1 − y )
where: y = actual recovery to underflow
Rf = fraction of feed liquid reporting to the underflow product
Assumptions (Krebs)
1. The cyclone has 'optimum' dimensions, as given in equation 5 above.
2. The mass weighted mean of the solids density is used to determine the cut point.
Plitt Model
The user defines all of the cyclone dimensions and the model then calculates the d50 in microns, the pressure
drop across the cyclone and the liquid distribution between the over and under flows.
The following equations are used to determine the cyclone operation3:
(7) d50 Calculation
0.46 0.6 1.21
50.5 ∗ D c ∗ D ∗ Do ∗ exp(0.063 ∗ Cv )
i
d 50 = Factor ∗ { }
0.71 0.38 0.45 0.5
Du ∗ h ∗ Q ∗ (ρ s − ρ l )
where d50 is in microns
Dc- Cyclone diameter, cm
Di - Cyclone feed inlet diameter, cm
Do- Cyclone overflow or Vortex finder diameter, cm
Du- Cyclone underflow or Apex diameter, cm
h - Free vortex height in cyclone, cm
Q - Volumetric flow rate of each cyclone feed at temperature,l/min
Cv - Volumetric percent of solids in feed slurry at temperature
ρs - Solids density at Temperature (t/m3)
ρl - Liquid density at Temperature (t/m3)
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Factor - d50 correction factor.
(8) Pressure Drop across the Cyclone in kPa
1.78
1.88 ∗ Q ∗ exp(0.0055 ∗ Cv )
ΔP = PressFactor ∗
0.37 0.94 2 2
0.28 0.87
Dc ∗ D ∗ h ∗ (D u + D o )
i
where PressFactor - Pressure drop correction factor (This is also named Pressure_Factor3 in SysCAD)
(9) Pressure drop across cyclone, in metres of feed slurry
ΔP
H =
gravity ∗ ρ Feed
(10) Recovery of feed volume to the underflow product
S
Rv =
S + 1
where
Du
3.31 0.54 2 2 0.36
1.9 ∗ ( ) ∗ h ∗ (D u + D o ) ∗ exp(0.0054 ∗ Cv )
Do
S = SFactor ∗
0.24 1.11
H ∗ Dc
where SFactor - S correction factor (This is also named Sharp_Factor4 in SysCAD)
(11) Sharpness Separation
0.15
2
Dc ∗ h
m = SharpFactor ∗ 1.94 ∗ exp [(−1.58 ∗ Rv ) ∗ ( ) ]
Q
where: Rv - Recovery of feed volume to the underflow product
SharpFactor - Sharpness correction factor (This is also named Sharp_Factor2 in SysCAD)
Q - Volumetric flow rate of each cyclone feed at temperature, l/min
The user may choose either the Lynch or the Rosin-Rammler equation to calculate the solids size distribution
across the cyclone.
Lynch
(12) Recovery to underflow on a corrected basis for the size interval
di
exp (a ) − 1
d50
′
y =
i
di
exp (a ) + exp(a) − 2
d50
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where: di - geometric mean of the size interval
a = 1.54 * m - 0.47
m - measure of the sharpness of separation
Rosin-Rammler
(13) Recovery to underflow on a corrected basis for the size interval
m
di
′
y = 1 − exp(−0.693147 × ( ) )
i
d 50
where di - geometric mean of the size interval
m - measure of the sharpness of separation.
The actual recovery to the underflow, y, is then calculated using the same equation for both methods:
′ ′
y = y + Rf (1 − y )
where Rf = fraction of feed liquid reporting to the underflow product
Assumptions (Plitt)
1. The pressure drop equation assumes free discharge from both the under and over flows from the cyclone.
2. The mass weighted mean of the solids density is used to determine the cut point.
3. Q in the sharpness equation is the total volumetric flow into the cyclones.
References
R.A.Arterburn, The Sizing and Selection of Hydrocyclones, Metallurgical Handbook.
D.T.Tarr, Practical application of liquid cyclones in mineral dressing problems, Krebs Engineers
documentation. October 1965
L.R.Plitt, A mathematical model of the hydrocyclone classifier, CIM Bulletin, December 1976
T.P.Napier-Munn, Mineral Comminution Circuits: Their Operation and Optimisation, 1999
Data Sections
The default sections and variable names are described in detail in the following tables. The default Cyclone
access window consists of 4 sections. This number may increase or decrease, based on user configuration.
Summary of Data Sections
1. Cyclone-1 tab - Contains general information relating to the unit.
2. PartCrv tab - This second tab displays the partition curve data for the cyclone.
3. Info tab - Contains general settings for the unit and allows the user to include documentation about the
unit and create Hyperlinks to external documents.
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4. Links tab, contains a summary table for all the input and output streams.
5. Audit tab - Contains summary information required for Mass and Energy balance. See Model Examples
for enthalpy calculation Examples.
Cyclone Page
Class: Cyclone-1 - The first tab page in the access window will have this name.
Symbol / Tag Input / Calc Description/Calculated Variables / Options
Common First Data Section
Requirements
SplitMethod / Method The user only needs to specify the actual d50 of the cyclone
DefineCutSize
and the percent solids in the underflow.
The unit uses the Krebs model to calculate the operating
parameters of the cyclone. The user specifies the cyclone
Krebs diameter and the percent solids in the underflow. The model
calculates the d50 of the cyclone.
The unit uses the Plitt model to calculate the operating
parameters of the cyclone. The user specifies the all of the
Plitt physical parameters of the cyclone. The model calculates the
d50 of the cyclone and the liquid split to the under and over
flows.
The unit uses a user specified Efficiency Curve (or partition
curve) to calculate the separation of the solids. The user also
Efficiency specifies the fraction of solids in the Cyclone underflow. The
Curve model calculates the Actual d50 of the cyclone and the liquid
split to the under and over flows.
No_Of_cyclones / The number of cyclones in the bank. This allows the user to
Input
NumCyclones emulate a bank of cyclones in a single unit.
The parameters in the access window change depending on the cyclone model chosen by the user. The input
parameters for each model will be detailed separately below. Where a model has output parameters that are
only displayed for that particular model, these are also shown individually.
Define Cut Size
Cut_Size / CutSize Input The required d50 of the cyclone.
UnderFlowSolids / UFSolids Input The percentage of solids in the cyclone underflow.
Sharpness / Alpha Input The required sharpness (default 4.0).
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Krebs
CycloneDiam / Diam Input The diameter of the cyclone.
This is the correction factor to account for differences in the
cyclone geometry from the 'optimum' dimensions. This is
CorrectionFactor / Factor Input
used to adjust the calculated cut point of the cyclone. The
default value is 1. (See Equation (1) in the Krebs theory)
UnderFlowSolids / UFSolids Input The percentage of solids in the cyclone underflow.
Cv (Feed solids volume concentration) in calculation of
correction factor C1 was incorrect by a factor of 100.
Calculation has been corrected, but for backward
OldFeedConcCalc Input compatibility of tuned existing projects the old (incorrect)
calculation can be used if this option is selected. C1 in turn
effects d50 calculation which drives the separation. Option is
new to Build 135.19957 and Build 136.19935.
Results:
Calc_d50 Output The calculated d50 of the cyclone.
The calculated intersection point of the cyclone. This is the
size at which the cumulative percentage oversize of the
InterSectPt Output
underflow is equal to the cumulative percentage undersize in
the overflow.
Pressure_Drop / CalcDP Output The calculated pressure drop across the cyclone.
Plitt
Cyclone_Diameter / Dc Input The diameter of the cyclone.
Inlet_Diameter / Di Input The inside diameter of the cyclone feed inlet.
Vortex_Diameter / Do Input The inside diameter of the overflow or the vortex finder.
Spigot_Diameter / Du Input The inside diameter of the underflow or the spigot diameter.
The free vortex height of the cyclone, defined as the distance
from the bottom of the vortex finder to the top of the
Height / h Input underflow orifice.
h = Total length of the cyclone - vortex length
This is used as a "once off" factor to scale all of the values in
"Dc", "Di", "Do", "Du" and "h" as a group. The user types a
ApplyScale Input value into ApplyScale and SysCAD will scale the values in
"Dc", "Di", "Do", "Du" and "h" by that value and then reset
ApplyScale to "*".
SharpEqn The method by which the model calculates the sharpness of
Rosin-
separation. Please see Equation (13) in the Plitt Model
Rammler
Theory.
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Lynch The method by which the model calculates the sharpness of
separation. The Lynch method will give a slightly more sharp
separation than the Rosin-Rammler method. Please see
Equation (12) in the Plitt Model Theory.
OldLiqSplitCalc This is only available in builds 134.11986 and later. Prior to
this build the liquid split calculation in the Plitt model was
incorrect. This has now been corrected. However, for
backward compatibility, users may enable the old (incorrect)
Tick Box
liquid split calculation.
Note: In new projects this will be disabled by default. In old
projects it will be enabled, and hence users will not see a
change in their results, unless they un-tick this box.
Factors
This Factor is used to adjust the d50 of the cyclone.
Increasing this value will increase the d50 used in the
d50_Factor1 / Factor Input calculations, and hence increase the amount of solids
reporting to the cyclone Overflow. Please see Equation (7) in
the Plitt Model Theory.
Sharpness Factor is used to adjust "m". Increasing this value
will increase the sharpness of separation and more of the
Sharp_Factor2 / SharpFactor Input
coarse particles will report to the underflow. Please see
Equation (11) in the Plitt Model Theory.
Press Factor is used to adjust "dP". Increasing this value will
Pressure_Factor3 / increase the pressure drop across the cyclone and hence
Input
PressFactor change the size recovery of the cyclone. Please see Equation
(8) in the Plitt Model Theory.
SFactor is used to adjust "S", which influences the recovery
of feed volume to the cyclone underflow. Increasing this
S_Factor4 / SFactor Input
value will increase the recovery to the cyclone underflow.
Please see Equation (10) in the Plitt Model Theory.
Overflow liquid correction factor, used to adjust the liquid
split to the overflow.
OFLiq_Factor5 /
Input
OFLiqCorrFac Liquid to Overflow = OFLiqCorrFac * Calculated Liquid to
Overflow.
Results:
d50 Output The calculated d50 of the cyclone.
PressDrop Output The calculated pressure drop across the cyclone.
The calculated ratio of the underflow volumetric flow to the
S Output overflow volumetric flow. Please see Equation (10) in the
Plitt Model Theory.
Rv Output Recovery of feed volume to the underflow.
The efficiency exponent in efficiency curve. This is a
Sharpness / m Output
measure of the sharpness of separation of the cyclone.
Alpha Output The alpha term calculated when using the Lynch sharpness
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equation.
Rs Output Recovery of feed solids to the underflow.
Rf Output Recovery of feed liquid to the underflow.
Efficiency Curve
The user will also see a tab 'EffCrv' where they must enter the fraction of each size interval reporting to the
Cyclone overflow. An example of an Efficiency Curve is shown in Efficiency Curve Theory.
UnderFlowSolids / UFSolids Input The percentage of solids in the cyclone underflow.
Common Data Fields
The feed volume flow per cyclone (equal to total feed volume
QvPerCyclone Output
flow if NumCyclones is equal to 1).
The volumetric fraction of solids in the cyclone feed at feed
SolidsVolFrac / VolFrac Output
conditions.
UnderFlow_Solids /
Output The fraction of solids in the cyclone underflow stream.
UFSolids
OverFlow_Solids / OFSolids Output The fraction of solids in the cyclone overflow stream.
UnderFlow_SolidsConc@25 The solids concentration at 25°C in the cyclone
Output
/ UFSolConc25 underflow stream.
OverFlow_SolidsConc@25 / The solids concentration at 25°C in the cyclone overflow
Output
OFSolConc25 stream.
UnderFlow_SolidsRecovery The fraction of feed solids that reports to the cyclone
Output
/ UFSolRec underflow stream.
The fraction of feed liquids that reports to the cyclone
OF_Liq_Split / OFLiqSplit Output
overflow stream.
The fraction of feed liquids that reports to the cyclone
UF_Liq_Split / UFLiqSplit Output
underflow stream.
OF_Density / OFDens Output The overflow slurry density
UF_Density / UFDens Output The underflow slurry density
Options
ShowQFeed Tickbox Show the total feed to the cyclone.
Partition Curve Section
The Cyclone has a section showing the partition curve. The model will calculate the partition curve for the
Cyclone configuration and display it on this page.
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Tag / Symbol Input or Description
Calc
The black rectangle at the top of the page is for display purposes only.
The two white boxes below the window allow the user to configure the lower and upper display limits of the
curve.
Log > Lin Button This button toggles the x display between log and ln.
Auto > Fixed This button toggles the display between auto scaling and user defined fixed
Button
Scale scale.
Stepped > Smooth Button Toggles the display between discrete points (Stepped) and a smooth curve.
Size Intervals Button > Ascending - Clicking on this displays the values from small to large.
> Descending - Clicking on this displays the values from large to small.
Graph : On > Off Button Toggles the graphical display on and off.
Adding this Model to a Project
Insert into Configuration file
Sort either by DLL or Group.
DLL: Separ2.dll → Units/Links → Size Separation: HydroCyclone (old)
OR Group: Size Distribution → Units/Links → Size Separation: HydroCyclone (old)
See Project Configuration for more information on adding models to the configuration file.
Insert into Project
Insert Unit → Size Separation → HydroCyclone (old)
See Insert Unit for general information on inserting units.
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