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 α 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:

[math]\displaystyle{ Frac=0.5 * \left( 1- \operatorname{erf} \, \left( \alpha* \left( Rho \, - \, \operatorname{SolidsCutDensity} \right) /1000 \right) \right) }[/math]

where:	Frac	= Calculated fraction of the solid species reporting to Underflow
	α	= User specified separation curve efficiency parameter or sharpness (ErfAlpha)
	Rho	= The density of each solids species
	SolidsCutDensity	= User specified Solids Cut Density

The standard Error Function (erf) is used:

[math]\displaystyle{ \operatorname{erf}(z) = \dfrac{2}{\sqrt{\Pi}} \,\int\limits_{0}^{z} \, e^{-t^2} \, dt }[/math]

Solids Density - Logistic Cut Density Method

Recovery to underflow for a given solid species i:

[math]\displaystyle{ \mathbf{\mathit{R_i=\cfrac{exp\left(\alpha \, \cfrac{Rho_i}{SolidsCutDensity }\right)-1}{exp\left(\alpha \, \cfrac{Rho_i}{SolidsCutDensity }\right)+exp(\alpha)-2}}} }[/math]

where:	Rhoi	= Density of solids species i
	α	= User specified separation curve efficiency parameter or sharpness (LogisticAlpha)
	Rho	= The density of each solids species
	SolidsCutDensity	= User specified Solids Cut Density. For a species with this density, there is a 50% split to underflow.

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.

	Example 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.
	Example 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%. 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.
	Results Table: If the BypassSeparCalcs tickbox is enabled, the Slurry Separation Results table displayed on the Separ page is for the internal streams, before the addition of the bypassed species, it will be displayed with the text "(excluding bypass)". User should note that the composition of the actual Overflow and Underflow stream may be different to the results shown in the results table as they will include the bypassed species.

The Examples below demonstrate one of the Separation methods used with the Bypass species functionality and the use of the BypassSeparCals tickbox:

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) see Note in Bypass Species
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) see Note in Bypass Species
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%
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) see Note in Bypass Species.
Overflow	9.5	4.5	5	43
Underflow	90.5	85.5	5	57