# Solid-Liquid Separator

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## Introduction

The Solid-Liquid Separator sub-model is used in the General Separator, Evaporator and Precipitation3 models. It allows splits between two outlets based on:

• Mass Fraction
• Mass Flow
• Volume Fraction
• Volume Flow
• Solid Separation

The first four methods are similar to the GM model. The last method allows a solid liquid separation to be specified, similar to the Thickener and other Mass Separation Models.

For all methods, the user may select any number of species to bypass this logic and directly send a fraction of each species to either the underflow or overflow outlets.

## 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.

### 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 = Sharpness = Rho = SolidsCutDensity =

The erf function is:

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

### 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

## Separ Page

The page allows the user to specify the split between the Underflow and Overflow streams.

Symbol / Tag
Input / Calc
Description
Requirements
Split Method Mass Fraction The users may specify the mass fraction split between the Underflow and Overflow streams.
Mass Flow The user may specify the mass flow to either the Underflow or Overflow stream - either as total flow or on a phase basis.
Volume Fraction The users may specify the volumetric fraction split between the Underflow and Overflow streams.
Volume Flow The user may specify the Volume flow to either the Underflow or Overflow stream - either as total flow or on a phase basis.
Solid Separation The user may specify the solid split between the Underflow and Overflow streams.
Each of the above Split Methods will be described separately below:

#### Mass Fraction

With this method the user can specify the mass fraction to either the Underflow or the Overflow on a total or by phase basis.

SplitTo Underflow The user specifies the mass fraction split to the Underflow stream.
Overflow The user specifies the mass fraction split to the Overflow stream.
SplitBy Total The user specifies the total mass fraction split to the defined stream.
Phase The user specifies the solid and liquid mass fraction splits to the defined stream.
FracToUF or FracToOF Input This is visible if SplitBy = Total. The user sets the total mass fraction split to the defined stream.
SolidsToUF or SolidsToOF Input This is visible if SplitBy = Phase. The user sets the solid mass fraction split to the defined stream.
LiquidsToUF or LiquidsToOF Input This is visible if SplitBy = Phase. The user sets the liquid mass fraction split to the defined stream.

#### Mass Flow

With this method the user can specify the mass flow to either the Underflow or the Overflow on a total or by phase basis.

SplitTo Underflow The user specifies the mass flow to the Underflow stream.
Overflow The user specifies the mass flow to the Overflow stream.
SplitBy Total The user specifies the total mass flow to the defined stream.
Phase The user specifies the solid mass flow and the liquid mass flow to the defined stream.
UF or OF.MassFlowReqd /
UF or OF.QmReqd
Input This is visible if SplitBy = Total. The user sets the total mass flow to the defined stream.
UF or OF.SolidMassFlowReqd /
UF or OF.SolidQmReqd
Input This is visible if SplitBy = Phase. The user sets the solid mass flow to the defined stream.
UF or OF.LiquidMassFlowReqd /
UF or OF.LiquidQmReqd
Input This is visible if SplitBy = Phase. The user sets the liquid mass flow to the defined stream.

#### Volume Fraction

With this method the user can specify the volume fraction to either the Underflow or the Overflow on a total or by phase basis.

SplitTo Underflow The user specifies the volume fraction split to the Underflow stream.
Overflow The user specifies the volume fraction split to the Overflow stream.
SplitBy Total The user specifies the total volume fraction split to the defined stream.
Phase The user specifies the solid and liquid volume fraction splits to the defined stream.
FracToUF or FracToOF Input This is visible if SplitBy = Total. The user sets the total volume fraction split to the defined stream.
SolidsToUF or SolidsToOF Input This is visible if SplitBy = Phase. The user sets the solid volume fraction split to the defined stream.
LiquidsToUF or LiquidsToOF Input This is visible if SplitBy = Phase. The user sets the liquid volume fraction split to the defined stream.

#### Volume Flow

With this method the user can specify the volume flow to either the Underflow or the Overflow on a total or by phase basis.

SplitTo Underflow The user specifies the volume flow to the Underflow stream.
Overflow The user specifies the volume flow to the Overflow stream.
SplitBy Total The user specifies the total volume flow to the defined stream.
Phase The user specifies the solid Volume flow and the liquid volume flow to the defined stream.
UF or OF.VolFlowReqd /
UF or OF .QvReqd
Input This is visible if SplitBy = Total. The user sets the total volume flow to the defined stream.
UF or OF.SolVolFlowReqd /
UF or OF.SolidQvReqd
Input This is visible if SplitBy = Phase. The user sets the solid volume flow to the defined stream.
UF or OF.LiqVolFlowReqd /
UF or OF.LiquidQvReqd
Input This is visible if SplitBy = Phase. The user sets the liquid volume flow to the defined stream.

#### Solid Separation

With this method the user can choose between setting the solids composition of the Overflow stream or defining the Underflow flowrate and then specifying the solids composition of the Underflow.

SolidsSeparMethod OF Solids Fraction The user specifies the solids mass fraction in the Overflow stream.
OF Solids Conc The user specifies the solids concentration in the Overflow stream.
OF Solids Conc25 The user specifies the solids concentration at 25°C in the Overflow stream.
Recovery to UF The user specifies the solids recovery to the Underflow stream, i.e. how much of the solids in the unit reports to the Underflow stream.
UF MassFlow The user specifies the total mass flow of the Underflow stream.
UF VolumeFlow The user specifies the total volume flow of the Underflow stream.
Solids Density Each solid species is split between the Overflow and Underflow streams based on the user specified SolidsCutDensity. This option is new to Build 136.
Solids PSD The user then specifies one of the SolidMethods for defining a partition curve which then separates the solids based on PSD data in the feed. This option is new to Build 135.
OFSolidFracReqd Input This is visible if SolidsSeparMethod = OF Solids Fraction. The user sets the solids mass fraction in the Overflow stream.
OFSolidConcReqd Input This is visible if SolidsSeparMethod = OF Solids Conc. The user sets the solids concentration in the Overflow stream.
OFSolidConc25Reqd Input This is visible if SolidsSeparMethod = OF Solids Conc25. The user sets the solids concentration at 25°C in the Overflow stream.
SolidsToUFReqd Input This is visible if SolidsSeparMethod = Recovery to UF. The user sets the mass fraction of solids in the unit that must report to the Underflow stream.
UFQmReqd Input This is visible if SolidsSeparMethod = UF MassFlow. The user sets the total mass flow of the Underflow stream.
UFQvReqd Input This is visible if SolidsSeparMethod = UF VolumeFlow. The user sets the total volume flow of the Underflow stream.
CutDensityMethod This is visible if SolidsSeparMethod = Solids Density.
Simple If the density of a solid species is greater than the SolidsCutDensity then it is all sent to the Underflow stream, otherwise it is all sent to the Overflow stream.
Erf An error function is used to determine the split of each solid species between the Overflow and Underflow streams based on the species density, SolidsCutDensity and Sharpness.
SolidsCutDensity Input This is visible if SolidsSeparMethod = Solids Density. The user sets the solids cut density which is used to determine how much of each solid species to send to the Overflow and Underflow streams.
Sharpness Input This is visible if SolidsSeparMethod = Solids Density and CutDensityMethod = Erf.
SolidMethod, etc Input This and related inputs and results are visible if SolidsSeparMethod = Solids PSD. See partition curve methods described in Screen2.
UFSolidsMethod UF Solids Fraction The user specifies the solids mass fraction in the Underflow stream.
UF Solids Conc The user specifies the Solids concentration in the Underflow stream.
UF Solids Conc25 The user specifies the Solids concentration in the Underflow stream at 25°C.
UF Density The user specifies the density of the Underflow stream.
UFSolidFracReqd Input This is visible if UFSolidsMethod = UF Solids Fraction. The user sets the solids mass fraction in the Underflow stream.
UFSolidConcReqd Input This is visible if UFSolidsMethod = UF Solids Conc. The user sets the solids concentration in the Underflow stream.
UFSolidConc25Reqd Input This is visible if UFSolidsMethod = UF Solids Conc25. The user sets the solids concentration at 25°C in the Underflow stream.
UFRhoReqd Input This is visible if UFSolidsMethod = UF Density. The user sets the density of the Underflow stream.

VapourToUF Input The user may set the fraction of vapour entrainment to the Underflow stream. This will only be relevant IF the user has set the vapour entrainment values on the first tab to a value greater than zero.

#### Selected Solid Species Calculation Method

With this method the user may specify fractions of any number of solid species to bypass to either the Underflow or Overflow streams, or the user may specify the bypass to both Over and Under flow streams. Please see the examples in Model Theory.

Method None There is no overriding of solid species to the Underflow or Overflow streams.
Bypass to Underflow The user may specify the fractions of one or more Solid species that bypass to the Underflow stream.
Bypass to Overflow The user may specify the fractions of one or more Solid species that bypass to the Overflow stream.
Bypass to Both The user may specify the fractions of one or more Solid species that bypass the Solid-Liquid calculation block and is then split between the Over and Under flow streams. This method is only available in Build 135 and later.
ByPassSeparCalcs Tick Box If this is enabled then the unit will NOT include the bypassed species fraction in the solid/liquid separation calculations. If it is not ticked, then the unit will include the fraction of bypassed species in the solid/liquid separation calculations. Please see the examples in Model Theory for clarification.
Count Input The number of solid species for which the user wishes to configure bypasses. This may be up to 10 species.
Solids Species Overall Bypass to Underflow, Overflow or Both
Speciesx Species List The user may select a species from a drop down list of all of the Solid species in the project.
BypassFracx Input The user sets that fraction of species x that must bypass to the Underflow or Overflow streams OR that must bypass Both.
Example 1: The user chooses Bypass to Overflow, with Count = 1, Species1 = B(s) and BypassFrac1 = 10%, then 10% of B(s) will bypass the solids separation step and will report to the Overflow stream. 90% of B(s) will be involved in the solid-liquid calculation.
Example 2: The user chooses Bypass to Both, with Count = 1, Species1 = B(s), BypassFrac1 = 100% and FracToOF1 = 10%. ALL of B(s) will bypass the solids separation step, 10% of B(s) and will report to the Overflow stream and the remaining 90% will report to the Underflow stream.
FracToOFx Input This field is only visible if the user selects Bypass to Both. The user sets that fraction of species x that must bypass to the Overflow streams.
For example: The user chooses Bypass to Both, with Count = 1, Species1 = C(s), FracToOf1 = 100% and FracToOF1 = 50%. ALL of the C(s) will bypass the solids separation step, 50% of C(s) and will report to the Overflow stream and 50% will report to the Underflow stream.

#### Results

Temperature / T Display The temperature of mixture in the solid liquid separator.
MassFlow / Qm Display The total mass flow to the Underflow and Overflow streams.
VapourMassFlow / VQm Display The total flow of vapour to the Underflow and Overflow streams. (This does NOT include the vapour to the Vent)
UF.BypassMassFlow / UF.BypassQm Display The mass flow of the material that bypasses the underflow.
OF.BypassMassFlow / OF.BypassQm Display The mass flow of the material that bypasses the overflow.
BypassMassFlow / BypassQm Display The mass flow of the solids in the unit that bypasses the separation section.
UF.SolidsTakeoffQm Display Only visible for Classifying Precipitator. The solids mass flow takeoff from the underflow for recycle.
UF.SolidsTakeoffFrac Display Only visible for Classifying Precipitator. The mass fraction of solids in the underflow that reports to takeoff for recycle.
UF.FinalSf Display Only visible for Classifying Precipitator. The final underflow solids mass fraction after removal of solids takeoff.

#### Slurry Separation Results (Excluding Bypass)

UFSolidsRecovery Display The fraction of feed solids sent to the underflow.
UFLiquidRecovery Display The fraction of feed liquid sent to the underflow.
The following table displays the flows and compositions of the Underflow and Overflow streams. Note: These are for slurry only, vapours are excluded.
MassFlow / Qm Display The total mass flow in each of the Underflow and Overflow streams.
VolFlow / Qv Display The total volume flow in each of the Underflow and Overflow streams.
SolidMassFlow / SQm Display The solids mass flow in each of the Underflow and Overflow streams.
LiquidMassFlow / LQm Display The liquid mass flow in each of the Underflow and Overflow streams.
SolidFrac / Sf Display The solid fraction in each of the Underflow and Overflow streams.
Density / Rho Display The total density of each of the Underflow and Overflow streams.
SolidConc Display The solid concentration (mass of solids/density of slurry) in each of the Underflow and Overflow streams.
SolidConc25 Display The solid concentration at 25°C (mass of solids/density of slurry at 25°C) in each of the Underflow and Overflow streams.