# Specific Surface Area (SSA)

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Related Links: Qualities Models, Precipitation3, Alumina 3 Bayer Species Model

## General Description

The Specific Surface Area (SSA) is used in the Precipitation1 or Precipitation3 model, a continuous stirred tank reactor with Gibbsite crystallisation precipitation that is used in the Alumina industry. However the SSA quality can be used in general in any project (ie not necessarily Alumina only).

The SSA data is described as follows:

The SAL - (Seed Surface Area Volume (m2/L) is a required variable in the Precipitation Model using the Yield Calculation method. It can be derived from SAM - (Seed Surface Area Mass (m2/g) or D - (seed particle size (mm), which is normally a derived value. However, the user may set the initial value of SAM or D entering the first precipitator to obtain the correct SAL, thus a correct yield in the precipitator.

#### Notes

• SAL is the Surface Area per unit volume of Liquor, not per volume of slurry. It is undefined (or comes out to be a large number) if there is no liquid present in the flow.
• SAM is the Surface Area per Mass of PSD solids

then

• Changing the SSA solids flow in a stream will change the SAL, but not the SAM.
• Adding other solids to a stream will not affect either parameter.

## Configuring SSA

In order for the SSA quality to be available in a project, it must included in the configuration file of the project.

Insert into Configuration file

Sort either by DLL or Group.

 DLL: SizeDst1.dll → Species Qualities → SpecificSurfaceArea or Group: General → Species Qualities → SpecificSurfaceArea

## Global SSA Configuration

In the Plant Model - Qualities Tab access window, View - Plant Model, the user defines:

1. the Mixing Rule: either to maintain particle count or maintain surface area when mixing two streams with different SSA. MaintainSurfaceArea is the default and recommended option.
2. the Global solids selection, to be applied to all SSA qualities within the project. If global is not selected, the user can instead allow the solid to be chosen Locally (ie. wherever the SSA quality is created or modified.) Global is the default and recommended option.

## Creating SSA in a Stream

Open a project which uses a configuration file with SSA configured (as described above).

Creating SSA in feeder or pipe (Note: this would usually be using a Bayer Species Model (See Generic Bayer Species Model or Alumina 3 Bayer Species Model):

• On the Feeder|Content OR Pipe|Qi tab page, under Qualities, click on the SzSSA.Action list box and select 'Create' (see Qualities Models - Fields and Actions for more information).
• A tab called 'SSA' (or 'DSSA' in SysCAD 9.3) will become visible.
• The user can select which species to base SSA calculations on when not using the global solids species selection.
• The user can enter the appropriate values for either SAM or D (Use the 'SetDiam' tickbox to toggle between these two options).

## Modify or Remove SSA

Once SSA has been created, it will perpetuate through all subsequent units. The SSA can be modified or the SSA quality can be removed altogether in the same way as other Qualities. Please refer to Qualities Models - Fields and Actions for more information.

NOTE: It is strongly recommended that the Remove feature is used in pipes exiting the process area where SSA is needed and used. It is inefficient to carry unused SSA data downstream, and it can interfere with convergence of recycle streams.

## SSA Data Sections

Tag / Symbol Input/ Calc Description
SSA Quality
Method Display Independent - when no PSD present and calculated from SAM; or FromPSD - when calculated from full PSD.
SetData Tickbox Allows the user to set values for SAM or Diameter (D).
SetDiam Tickbox Option when SetData is selected. Allows user to define SAM or D.
Solids List Solids Species that SSA calculations are based on. Result field if SSA solid component is set globaly in PlantModel. Otherwise, allows the user to select the solid component to base the SSA calculations on. Note: The selected solid flowrate must be non-zero for the propagation of the following parameters to downstream unit operations.
Solids.Qm Calc The amount of selected SSA solids species (eg: Al[OH]3) present.
SAM / SeedSurfaceAreaM Input Seed Surface Area, Mass basis (m²/g)
SAL / SeedSurfaceAreaL Calc Seed Surface Area, Volume basis (m²/L). That is total Liquid Volume basis at temperature.
#/s Calc Particle number per second.
#/L Calc Particle number per litre.
D / PartDiam Input Input when SetData and SetDiam is selected. Particle diameter.

## SSA Calculations

The equations used in calculating SAL are:

1. SAL = #/L * Pi * D * D
2. #/L = 6.0 * 0.001 * Solids_Mass_Flow / (Pi * Solids_Density * D * D * D * Liquid_Volumetric_Flow)
3. D = 3.0 / (500.0 * Solids_Density * SAM))
4. #/s = 6.0 * Solids_Mass_Flow / (Pi * Solids_Density * D* D* D)
5. SAM = 3 / (500 * Solids_Density * CalcD)
6. CalcD = Pow(6 * Solids_Mass_Flow / (Pi * Solids_Density * #/s), 1/3)

Combining (1) and (2) gives an alternative for SAL, which can be rearranged as below:

• SAL = 6.0 * 0.001 * Solids_Mass_Flow / (Solids_Density * D * Liquid_Volumetric_Flow)
• SAL = 3.0 * Solids_Mass_Flow / (500.0 * Solids_Density * D * Liquid_Volumetric_Flow)

Combining this with (5) for SAM gives

• SAL = SAM * Solids_Mass_Flow / Liquid_Volumetric_Flow

where

• Solids_Mass_Flow is the mass flow of the specified solids species (ignores other solids)
• Solids_Density is the density of the specified solids species (ignores other solids)
• Liquid_Volumetric_Flow is the total liquid phase volumetric flow rate at stream temperature

If the user ticked the SetData box and input value for SAM, SysCAD will use it to calculate the remaining variables; likewise, if the user input value for PartDiam (D), SysCAD will derive SAM using equation 3 and then calculate the remaining variables.

## SSA Calculations when PSD is present

When the SSA.Method is "FromPSD" because the PSD quality is present as well as the SSA quality, then SAM, SAL, Diameter, etc can be calculated from the full PSD of the selected solids species.

$SAM = \frac{\sum AG_i}{Solids Mass Flow}$
$AG_i = 0.001 * \frac{3 * Species Particle Mass_i}{\rho_S * 0.5 * Geometric Mean Diameter_i}$
$SAL = \frac{SAM * Solids Mass Flow}{Liquid Volumetric Flow}$
$D = \frac{3}{500 * \rho_S * SAM}$

where

• i is for each size interval for the specified solids species
• Solids_Mass_Flow is the mass flow of the specified solids species (ignores other solids)
• $\rho_S$ is the density of the specified solids species (ignores other solids)
• Liquid_Volumetric_Flow is the total liquid phase volumetric flow rate at stream temperature

NOTE:

• SAM and SAL are calculated based on specified solid species ONLY, unlike the calculation for SAM and SAL in PSD Quality on MSz page where ALL the solids species are used.
• The diameter D for SSA is just calculated to give the correct SAM assuming all the particles are the "same" size. It is not in any sense a mean of all the particle diameters or volumes.
• The Geometric Mean is used for calculating "average" diameter of size interval.

## Mixing Rule

The equations used when mixing streams with different SSA values is based on the user selected Mixing Rule. The MaintainParticleCount mixing rule has the effect of heavily weighting fine particles (since they are present in large numbers) - so mixing a stream of fines with a coarse stream gives a very inaccurate result. Therefore the MaintainSurfaceArea mixing rule is the default for new projects. The mixing of the two streams with different SSA's should preserve total surface area. The user can globally select which rule to use on the Plant Model - Qualities Tab (something has to give somewhere, you can't preserve everything).

MaintainParticleCount
Setting SAM of the mixed stream using the MaintainParticleCount mixing rule:

D = Pow(6 * (M1+M2) / (pi * Solids_Density * (N1+N2)), 1/3)
SAM = 3.0 / (500 * Solids_Density * D)


where M1 and M2 are the masses of the SSA species in the two streams and N1 and N2 are the particle count per second (#/s) in the two streams

MaintainSurfaceArea
Setting SAM of the mixed stream using the MaintainSurfaceArea mixing rule:

SAM = (M1*SAM1 + M2*SAM2)/(M1+M2)


where M1 and M2 are the masses of the SSA species in the two streams and SAM1 and SAM2 are Surface Area per Mass in the two streams