# Template:Separ Model Theory

The Solid-Liquid Separator allows the user to define the solid-liquid separation with a high degree of flexibility, including the ability to allow specified species to bypass the separation calculations.

Note: To minimise input fields, some requirement combinations for solid-liquid separation necessitate swapping the OF and UF definitions and connections.

e.g. A settler requiring a defined Recovery to OF and OF Solids Fraction may be defined by swapping the OF/UF connections and choosing "Recovery to UF" and "UF Solids Fraction".

### Solids Density - Erf Cut Density Method

If this method is chosen, SysCAD uses the error function along with the solid species density, user specified SolidsCutDensity and Sharpness to determine how much of each solid species is sent to the Overflow and Underflow streams.

The fraction of a particular solid species which is sent to the Overflow stream is calculated as follows:

$Frac=0.5 * (1-erf(Sharpness*(Rho-SolidsCutDensity)/1000))$

 where: Frac = Calculated fraction of the solid species reporting to Underflow Sharpness = User specified separation curve sharpness Rho = The density of each solids species SolidsCutDensity = User specified Solids Cut Density

The standard Error Function (erf) is used:

$\operatorname{erf}(z) = \frac{2}{\sqrt{\Pi}}\int\limits_{0}^{z}e^{-t^2} dt\,$

### Bypass Species

Often in a plant one, or more, of the solid species will behave differently in a unit operation to the other solid species.

Examples:

1. A stream may contain a mixture of Salts species (KCl, NaCl, MgCl2, etc) and Gypsum. The gypsum will tend to float on the surface in thickeners, and hence the user may require the ability to send all of the gypsum to the thickener overflow. This model allows the user to do this by specifying the bypass Method = Bypass to OverFlow, Gypsum as a 'Bypass' species, with 100% reporting to the overflow.
2. A stream containing a number of species must sent to a solid-Liquid separator (e.g. a thickener, or filter), but the user wishes to specify the split to both the Underflow and the Overflow of one of the species - say 10% of species B reports to the Overflow and the remaining 90% reports to the Underflow. The user specifies the bypass Method = Bypass to Both, species B as the bypass species, Bypass Fraction = 100% and Fraction to Overflow = 10%.
Note: If the Bypass to Overflow method was used with Bypass Fraction = 10%, then 10% of species B would be bypassed to the overflow, with the remaining 90% of species B reporting to the Solid-Liquid calculation block. Hence, some of the remaining species B might be sent to the overflow, depending on how the Solid-Liquid calculation block was configured.

The Examples below demonstrate one of the Separation methods used with the Bypass species functionality:

 Solid-Liquid Separator Settings: SplitMethod: Solid Separation SolidsSeparMethod: Recovery to UF SolidsToUFReqd: 95% UFSolidsMethod: UF Solids Fraction UFSolidsFracReqd: 60%

Note: All values in the tables below are mass flows as t/h.

Description Total Solids Species A(s) Species B(s) Liquids Diagram
Feed 100 90 10 100
Example 1: No Bypass
Overflow 5 4.5 0.5 36.67
Underflow 95 85.5 9.5 63.33

Example 2: Overflow Bypass Species B Bypass = 10%
ByPassSeparCalcs NOT enabled (Overflow satisfies requirements)
Overflow 5 3.64 1.36 36.67
Underflow 95 86.36 8.64 63.33
ByPassSeparCalcs enabled (Internal stream 1A satisfies requirements)
Overflow 5.95 4.5 1.45 37.3
Underflow 94.05 85.5 8.55 62.7
Example 3: Underflow Bypass Species B Bypass = 10%
ByPassSeparCalcs NOT enabled (Underflow satisfies requirements)
Overflow 5 4.55 0.45 36.67
Underflow 95 85.45 9.55 63.33
ByPassSeparCalcs enabled (Internal stream 2A satisfies requirements)
Overflow 4.95 4.5 0.45 37.3
Underflow 95.05 85.5 9.55 62.7
Example 4: Bypass to Both Species B: Bypass Fraction = 100% and Fraction to Overflow = 50% (This method is only available in Build 135 and later)
ByPassSeparCalcs NOT enabled (Under and Over flow streams satisfy requirements)
Overflow 5 0 5 36.67
Underflow 95 90 5 63.33
ByPassSeparCalcs enabled (Internal streams 1A and 2A satisfy requirements)
Overflow 9.5 4.5 5 43
Underflow 90.5 85.5 5 57