## Hydrocyclone – syscad documentation

The model is primarily designed to split solids based on size distribution data. Therefore, the feed should 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 first two options allow the user to set the cut point without any further knowledge of the cyclone. The next three 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.

The __Hydrocyclone__ may also act as a simple splitter, where the solids in the feed to the unit do not have any size distribution data. In this case the user must select Method = ‘Simple (non PSD) Models’ and set the solids and **liquid split** to the under and over flow streams.

The diagram shows the default drawing of the __Hydrocyclone__, with all of the streams that are available for operation of the unit. The physical location of the streams connecting to the **Hydrocyclone** is unimportant. The user may connect the streams to any position on the unit.

• The other methods use the d 50 value, either calculated or defined by the user, to determine the solids separation. The d 50 is defined as the particle size that has a 50% chance of reporting to either the cyclone underflow or overflow. 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 Hydrocyclones 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 Hydrocyclones with a single drawing.

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:

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]\rho_s[/math] – Solids density at Temperature (t/m 3) [math]\rho_l[/math] – Liquid density at Temperature (t/m 3) F – d 50 correction factor.

[math]{\frac{Q}{D_c^{2}\sqrt{P/\mathit{\rho_p}}} = K_{Qo}D_c^{-0.10}(\frac{D_o}{D_c})^{0.68}(\frac{D_i}{D_c})^{0.45}(\frac{L_c}{D_c})^{0.20}\mathit{\Theta^{-0.10}}}[/math] where D c – Cyclone diameter, cm D i – Cyclone feed inlet diameter, cm D o – Cyclone overflow or Vortex finder diameter, cm K Qo – Material dependent constant for performance characteristic, P i L c – Length of the cylindrical section of the cyclone, cm P – Cyclone feed pressure, kPa Q – Cyclone throughput, l/min [math]\mathbf{\mathit{\Theta}}[/math] – full cone angle, degrees

D u – Cyclone underflow or spigot diameter, cm g – acceleration due to gravity, m/s 2 K Do – Material dependent constant for performance characteristic, P i [math]\rho_p[/math] – Density of feed pulp, (t/m 3) [math]\lambda[/math] – hindered settling factor

[math]{R_f = K_{Wo}(D_c^{-0.00})(\frac{D_o}{D_c})^{-1.19}(\frac{D_u}{D_c})^{2.40}(\frac{D_i}{D_c})^{-0.50} (\frac{L_c}{D_c})^{0.22} \mathit{\Theta^{-0.24}}(\frac{P}{\mathit{\rho_p}gD_c})^{-0.53}\mathit{\lambda^{0.27}}}[/math] where K Wo – Material dependant constant for performance characteristic, P i

The common forms of the Efficiency Curves are the Rosin-Rammler and Lynch curves. However, these have the disadvantage of not being able to model the "fishhook" since they are monotonic. Each has a single "sharpness" parameter – as the sharpness increases, the separation about the d 50 increases. (d 50 is the size which will report with equal probability to underflow or overflow, and refers to the corrected value.)

Note that the efficiency curve is not the actual recovery curve (the split between underflow and overflow). *Hydrocyclone* models assume that the fine particles do not separate, so that they effectively partition with the liquid, so that the recovery for fine particles is the same as the *liquid split* [math]R_f[/math]. This means that the recovery curve is related to the efficiency curve by [math]{{y=y’+R_f(1-y’)}}[/math] Rosin-Rammler

The user may have plant data, which they want to use to tune a particular model. Also, there are other efficiency curve models not presently implemented in **SysCAD**, such as the Cilliers model. The user could then calculate the solids partition using a PGM, or externally and supply this to the model.

Note that specifying the curve data effectively determines the d50 for the solids split. Some of the methods such as the Nagaswararo cyclone calculate the d50 – it is up to the user to ensure that the d50 for the specified split is equal to that calculated by the model (or at least understand that they are using a different d50.) **SysCAD** will display the d50 for the user curves, and this can be compared to the calculated d50.

The user specifies an Efficiency Curve (or partition curve) on the Partition Curve page, which is used 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.

The unit uses the Krebs Cyclone Model to calculate the operating parameters of the cyclone. The user specifies the cyclone diameter and, the percent solids in the underflow and the required Efficiency Curve Split Method. The model calculates the d 50 of the cyclone. The feed solids volume concentration must be greater than 53% to use this method.

The unit uses the Plitt Cyclone Model to calculate the operating parameters of the cyclone. The user specifies the all of the physical parameters of the cyclone and the required Efficiency Curve Split Method. The model calculates the d 50 of the cyclone and the liquid split to the under and over flows.

The unit uses the Nageswararao Model to calculate the operating parameters of the cyclone. The user specifies the all of the physical parameters of the cyclone and the required Efficiency Curve Split Method. The model calculates the d 50 of the cyclone and the liquid split to the under and over flows.

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. The Results fields that are common to all methods are shown in the Common Results section.

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.

Only visible if the User Defined Curves method or User Curve SplitMethod has been chosen. If ticked, allows to user to set the Corrected Partition Curve, which is applied directly to the solids separation. If not ticked, the user enters the Actual Partition Curve which is "corrected" prior to being applied to the solids separation.