Cyclone
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Contents
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:
 Define the cut point of the cyclone
 Use the Krebs method to calculate the cut point
 Use the Plitt method to calculate the cut point
 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.
Notes:
 In SysCAD 9.3 this model has been replaced by the Hydrocyclone model.
 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 Optional 
Input Output 
Number of Connections  Description  
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
 The model will simulate a hydrocyclone using one of the four user defined methods  'Define d_{50}', 'Efficiency Curve', 'Krebbs' and 'Plitt' These are described below.
 The 'Efficiency Curve' method allows the user to define the fraction of material in each size interval that will report to the cyclone overflow.
 The other three methods use the d_{50} 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.
 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.
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 d_{50}, the sharpness [math]\alpha[/math] and the required percentage solids in the under flow from the unit.
The model then uses the d_{50} defined by the user to calculate the fraction of solids in each size interval reporting to the underflow using the following equations:
 [math]\mathbf{\mathit{x=\frac{Particle_diameter}{d_{50}}}}[/math]
 where Particle_diameter  geometric mean of the size interval
 [math]y^1=\frac{e^{\alpha x}1}{e^{\alpha x} + e^\alpha2}[/math]
where:
y^{1}
= recovery to underflow on a corrected basis
 [math]\mathbf{\mathit{ y=y^1 +R_f (1y^1)}}[/math]
where:
y
= actual recovery to underflow
R_{f}
= 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 d_{50} of the cyclone from the following equations^{1}:
(1) [math]\mathbf{\mathit{d_{50}=d_{50}(Base)\times C_1\times C_2\times C_3\times Factor}}[/math]
where Factor is a correction factor to account for differences in the cyclone geometry from the 'optimum' dimensions.
(2) [math]\mathbf{\mathit{d_{50}(Base)=2.84\times D_c^{0.66}}}[/math]
where: 
d_{50}(Base) 
= the cut size a "standard cyclone" can achieve, in microns. 
Dc 
= cyclone diameter, in cm 
(3) [math]\mathbf{\mathit{C_1=\begin{pmatrix}\frac{53C_v}{53}\end{pmatrix}^{1.43}}}[/math]
where: 
C_{1} 
= Correction for the influence of cyclone feed concentration 
C_{v} 
= Feed solids volume concentration (%) 
(4) [math]\mathbf{\mathit{C_2=3.27\times \boldsymbol{\Delta}P^{0.28}}}[/math]
where: 
C_{2} 
= Correction for the influence of pressure drop 
DP 
= Pressure drop across the cyclone in kPa  calculated in (5) using Plitt method 
(5) [math]\mathbf{\mathit{\boldsymbol{\Delta}P=\frac{1.88\times Q^{1.78}\times exp(0.0055\times C_v)}{D_c^{0.37}\times D_i^{0.94}\times h^{0.28}\times (D_u^2+D_o^2)^{0.87}}}}[/math]
where: 
Q 
= feed slurry volumetric flowrate per cyclone in l/min 
C_{v} 
= Feed solids volume concentration (%)  
D_{C} 
= Diameter of cyclone  
D_{I} 
= Diameter of cyclone inlet = 0.2 * D_{C}  
D_{U} 
= Diameter of cyclone underflow, or apex = 0.15 * D_{C}  
D_{O} 
= Diameter of cyclone overflow, or vortex finder = 0.3 * D_{C}  
h 
= Free vortex height of cyclone = 1.5 * D_{c} 
All the cyclone dimensions are in cm. These values are for an 'Optimum Cyclone'^{ 2 }. 
(6) [math]\mathbf{\mathit{C_3=\begin{pmatrix}\frac{1.65}{G_SG_L}\end{pmatrix}^{0.5}}}[/math]
where:  
C_{3}  = Correction for the influence of SG 
G_{S }  = SG of solids 
G_{L }  = SG of liquids 
The model then uses the d_{50}, 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}: 
 [math]\mathbf{\mathit{x=\frac{Particle_diameter}{d_{50}}}}[/math]
 where Particle_diameter  geometric mean of the size interval
 [math]\mathbf{\mathit{y^1=\frac{exp(4x)1}{exp(4x)+exp(4)2}}}[/math]
where:
y
= recovery to underflow on a corrected basis
 [math]\mathbf{\mathit{ y=y^1 +R_f (1y^1)}}[/math]
where:
y
= actual recovery to underflow
R_{f}
= fraction of feed liquid reporting to the underflow product
Assumptions (Krebs)
 The cyclone has 'optimum' dimensions, as given in equation 5 above.
 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 d_{50} 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 operation^{3}:
(7) d_{50} Calculation
[math]\mathbf{\mathit{d_{50}=Factor*\left\{\frac{50.5*D_c^{0.46}*D_i^{0.6}*D_o^{1.21}*exp(0.063*C_v)}{D_u^{0.71}*h^{0.38}*Q^{0.45}*(\rho_s\rho_l)^{0.5}}\right\}}}[/math]
where d_{50} is in microns
 D_{c} Cyclone diameter, cm
 D_{i}  Cyclone feed inlet diameter, cm
 D_{o} Cyclone overflow or Vortex finder diameter, cm
 D_{u} 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
 C_{v}  Volumetric percent of solids in feed slurry at temperature
 [math]\mathbf{\mathit{\rho_s}}[/math]  Solids density at Temperature (t/m^{3})
 [math]\mathbf{\mathit{\rho_l}}[/math]  Liquid density at Temperature (t/m^{3})
 Factor  d_{50} correction factor.
(8) Pressure Drop across the Cyclone in kPa
 [math]\mathbf{\mathit{ \Delta P =PressFactor*\frac{1.88*Q^{1.78}*exp(0.0055*C_v)} {D_{c}^{0.37}*D_{i}^{0.94}*h^{0.28}*(D_u^2+D_o^2)^{0.87} }}}[/math]
 where PressFactor  Pressure drop correction factor (This is also named Pressure_Factor3 in SysCAD)
(9) Pressure drop across cyclone, in metres of feed slurry
 [math]\mathbf{\mathit{H=\frac{\Delta P}{gravity*\rho_{Feed}}}}[/math]
(10) Recovery of feed volume to the underflow product
 [math]\mathbf{\mathit{R_v=\frac{S}{S+1}}}[/math]
 where
 [math]\mathbf{\mathit{S = SFactor* \frac{1.9*(\frac{D_u}{D_o})^{3.31}*h^{0.54}*(D_u^2+D_o^2)^{0.36}*exp(0.0054*C_v)} {H^{0.24}*D_c^{1.11}}}}[/math]
 where SFactor  S correction factor (This is also named Sharp_Factor4 in SysCAD)
(11) Sharpness Separation
_{ [math]\mathbf{\mathit{m=SharpFactor*1.94*exp\left[(1.58*R_v)*\left(\frac{D_c^2*h}{Q} \right)^{0.15}\right]}}[/math] }
where: R_{v}  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 RosinRammler equation to calculate the solids size distribution across the cyclone.
Lynch
(12) Recovery to underflow on a corrected basis for the size interval
 [math]\mathbf{\mathit{y_i'=\frac{exp\left(a\frac{d_i}{d_{50}}\right)1}{exp\left(a\frac{d_i}{d_{50}}\right)+exp(a)2}}}[/math]
where: d_{i}  geometric mean of the size interval
 a = 1.54 * m  0.47
 m  measure of the sharpness of separation
RosinRammler
(13) Recovery to underflow on a corrected basis for the size interval
 [math]\mathbf{\mathit{y_i'=1\exp\left(0.693147\times\left(\frac{d_i}{d_{50}} \right)^m\right)}}[/math]
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:
 [math]\mathbf{\mathit{y=y'+R_f(1y')}}[/math]
where R_{f} = fraction of feed liquid reporting to the underflow product
Assumptions (Plitt)
 The pressure drop equation assumes free discharge from both the under and over flows from the cyclone.
 The mass weighted mean of the solids density is used to determine the cut point.
 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.NapierMunn, 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
 Cyclone1 tab  Contains general information relating to the unit.
 PartCrv tab  This second tab displays the partition curve data for the cyclone.
 Info tab  Contains general settings for the unit and allows the user to include documentation about the unit and create Hyperlinks to external documents.
 Links tab, contains a summary table for all the input and output streams.
 Audit tab  Contains summary information required for Mass and Energy balance. See Model Examples for enthalpy calculation Examples.
Cyclone Page
Unit Type: Cyclone1  The first tab page in the access window will have this name.
Symbol / Tag 
Input / Calc 
Description/Calculated Variables / Options  
Requirements  
SplitMethod / Method  DefineCutSize  The user only needs to specify the actual d_{50} of the cyclone and the percent solids in the underflow.  
Krebs  The unit uses the Krebs model to calculate the operating parameters of the cyclone. The user specifies the cyclone diameter and the percent solids in the underflow. The model calculates the d_{50} of the cyclone.  
Plitt  The unit uses the Plitt model to calculate the operating parameters of the cyclone. The user specifies the all of the physical parameters of the cyclone. The model calculates the d_{50} of the cyclone and the liquid split to the under and over flows.  
Efficiency Curve  The unit uses a user specified Efficiency Curve (or partition curve) to calculate the separation of the solids. The user also specifies the fraction of solids in the Cyclone underflow. The model calculates the Actual d_{50} of the cyclone and the liquid split to the under and over flows.  
No_Of_cyclones / NumCyclones 
Input 
The number of cyclones in the bank. This allows the user to 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 d_{50} of the cyclone.  
UnderFlowSolids / UFSolids  Input  The percentage of solids in the cyclone underflow.  
Sharpness / Alpha  Input  The required sharpness (default 4.0).  
Krebs  
CycloneDiam / Diam  Input  The diameter of the cyclone.  
CorrectionFactor / Factor  Input  This is the correction factor to account for differences in the cyclone geometry from the 'optimum' dimensions. This is 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.  
OldFeedConcCalc  Input  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 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 d_{50} of the cyclone.  
InterSectPt  Output  The calculated intersection point of the cyclone. This is the size at which the cumulative percentage oversize of the 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.  
Height / h  Input  The free vortex height of the cyclone, defined as the distance from the bottom of the vortex finder to the top of the underflow orifice.
h = Total length of the cyclone  vortex length  
ApplyScale  Input  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 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  RosinRammler  The method by which the model calculates the sharpness of separation. Please see Equation (13) in the Plitt Model Theory.  
Lynch  The method by which the model calculates the sharpness of separation. The Lynch method will give a slightly more sharp separation than the RosinRammler method. Please see Equation (12) in the Plitt Model Theory.  
OldLiqSplitCalc  Tick Box  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) 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 untick this box.  
Factors  
d50_Factor1 / Factor  Input  This Factor is used to adjust the d_{50} of the cyclone. Increasing this value will increase the d_{50} used in the calculations, and hence increase the amount of solids reporting to the cyclone Overflow. Please see Equation (7) in the Plitt Model Theory.  
Sharp_Factor2 / SharpFactor  Input  Sharpness Factor is used to adjust "m". Increasing this value will increase the sharpness of separation and more of the coarse particles will report to the underflow. Please see Equation (11) in the Plitt Model Theory.  
Pressure_Factor3 / PressFactor  Input  Press Factor is used to adjust "dP". Increasing this value will increase the pressure drop across the cyclone and hence change the size recovery of the cyclone. Please see Equation (8) in the Plitt Model Theory.  
S_Factor4 / SFactor  Input  SFactor is used to adjust "S", which influences the recovery of feed volume to the cyclone underflow. Increasing this value will increase the recovery to the cyclone underflow. Please see Equation (10) in the Plitt Model Theory.  
OFLiq_Factor5 / OFLiqCorrFac  Input  Overflow liquid correction factor, used to adjust the liquid split to the overflow.
Liquid to Overflow = OFLiqCorrFac * Calculated Liquid to Overflow.  
Results:  
d50  Output  The calculated d_{50} of the cyclone.  
PressDrop  Output  The calculated pressure drop across the cyclone.  
S  Output  The calculated ratio of the underflow volumetric flow to the overflow volumetric flow. Please see Equation (10) in the Plitt Model Theory.  
Rv  Output  Recovery of feed volume to the underflow.  
Sharpness / m  Output  The efficiency exponent in efficiency curve. This is a measure of the sharpness of separation of the cyclone.  
Alpha  Output  The alpha term calculated when using the Lynch sharpness 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  
QvPerCyclone  Output  The feed volume flow per cyclone (equal to total feed volume flow if NumCyclones is equal to 1).  
SolidsVolFrac / VolFrac  Output  The volumetric fraction of solids in the cyclone feed at feed conditions.  
UnderFlow_Solids / UFSolids  Output  The fraction of solids in the cyclone underflow stream.  
OverFlow_Solids / OFSolids  Output  The fraction of solids in the cyclone overflow stream.  
UnderFlow_SolidsConc@25 / UFSolConc25  Output  The solids concentration at 25°C in the cyclone underflow stream.  
OverFlow_SolidsConc@25 / OFSolConc25  Output  The solids concentration at 25°C in the cyclone overflow stream.  
UnderFlow_SolidsRecovery / UFSolRec  Output  The fraction of feed solids that reports to the cyclone underflow stream.  
OF_Liq_Split / OFLiqSplit  Output  The fraction of feed liquids that reports to the cyclone overflow stream.  
UF_Liq_Split / UFLiqSplit  Output  The fraction of feed liquids that reports to the cyclone 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.
Tag / Symbol  Input or Calc  Description 
The black rectangle at the top of the page is for display purposes only.
 
Log > Lin  Button  This button toggles the x display between log and ln. 
Auto > Fixed Scale  Button  This button toggles the display between auto scaling and user defined fixed 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.