View source for Specific Surface Area (SSA)

[[Category:Size Distribution]] [[Category:Qualities]] [[Category:Alumina]]
{{Navigation|[[Models]]|[[Qualities Models]]}}
{{Qualities Header Table|currentpage=5}}

'''Related Links:''' [[Precipitation3]], [[Alumina 3 Bayer Species Model]]
----
{{TOC}}
== General Description ==

The Specific Surface Area (SSA) is used in the [[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 (i.e. not necessarily Alumina only).

The SSA data is described as follows:

The '''SAL - (Seed Surface Area Volume (m<sup>2</sup>/L)''' is a required variable in the [[Precipitation3|Precipitation Model]] using the Yield Calculation method. It can be derived from '''SAM - (Seed Surface Area Mass (m<sup>2</sup>/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 '''S'''urface '''A'''rea ''per unit volume of'' '''L'''''iquor'', 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 '''S'''urface '''A'''rea ''per'' '''M'''''ass 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.

{{Adding SubModel to a Project | DllName=SizeDst1 | DllSubGroup=Species Qualities | UnitOp=SpecificSurfaceArea | Group=General}}

== Global SSA Configuration ==

In the [[Plant Model#Qualities Tab|Plant Model - Qualities Tab]] access window, ''View - Plant Model'', the user defines:
# 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.
# 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 (i.e. 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 [[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#Quality Fields and Actions|Qualities Models - Fields and Actions]] for more information).
* A tab called 'DSSA' 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).

See [[Precipitation_Projects#Example_1:_Precipitation_Projects_using_Specific_Surface_Area_.28SSA.29_Yield_Method|example]] on how to set SSA in a project.  NOTE that is SetDiam tickbox is not selected, then SAM can be entered.

== DSSA Data Sections ==

{{DSSA Data Sections}}

== 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#Quality Fields and Actions|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 ==

{{SSA Data Sections}}

== SSA Calculations ==

The equations used in calculating '''SAL''' are:

# SAL = #/L * Pi * D * D
# #/L = 6.0 * 0.001 * Solids_Mass_Flow / (Pi * Solids_Density * D * D * D * Liquid_Volumetric_Flow)
# D = 3.0 / (500.0 * Solids_Density * SAM))
# #/s = 6.0 * Solids_Mass_Flow / (Pi * Solids_Density * D* D* D)
# SAM = 3 / (500 * Solids_Density * CalcD)
# 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 <tt>SetData</tt> 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.

:<math>SAM = \cfrac{\sum AG_i}{Solids Mass Flow}</math>
:<math>AG_i = 0.001 * \cfrac{3 * Species Particle Mass_i}{\rho_S * 0.5 * Geometric Mean Diameter_i}</math>

:<math>SAL = \cfrac{SAM * Solids Mass Flow}{Liquid Volumetric Flow}</math>

:<math>D = \cfrac{3}{500 * \rho_S * SAM}</math>

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)
* <math>\rho_S</math> 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|Plant Model - Qualities Tab]] (something has to give somewhere, you can't preserve everything).

'''MaintainParticleCount'''<br>
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'''<br>
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

== Hints and Comments ==

# It is IMPORTANT to note that the '''solid selected MUST''' be present in the stream (thus has a value) for the above to work properly.
# Once the SSA quality is created and used, the particle size information will be shown in all downstream pipes where the associated solid is present.
# If full stream [[Size Distribution (PSD)]] data is used, SSA is calculated from the PSD data. See [[Size Distribution (PSD)#Size Measurements Data Sections (MSz Tab)|Size Measurements Data Sections (MSz Tab)]] for description of PSD display of SSA, etc.