Precipitation Model

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General Description

IMPORTANT NOTE: Alumina1 models are not distributed and supported with SysCAD 9.3. SysCAD 9.3 version of Alumina1 is available on request for project conversion purposes.

NOTE: See also alternate Precipitator3 model which uses Alumina3 Species Model format.

The Precipitator is modelled as a continuous stirred tank reactor with Gibbsite crystallisation precipitation. The model may be configured either as a simple tank with reactions, or it may use a Yield Model to calculate the Gibbsite Precipitation.

If the Yield Model is chosen, the unit uses equations developed by S. Rosenberg and S. Healy[1] and Specific Surface Area (SSA). The model calculates yield, residence time, mass of occluded soda precipitated with the Alumina, and the caustic and Alumina concentrations in the tank. The Precipitator receives up to 20 feed streams and calculates a single product stream. The model does not take into account by-pass flow.

The user may also specify additional reactions using the Reaction Block.

The Precipitator will expect the feed to be of Bayer Liquor of Alumina1 Species Model format and will produce Gibbsite precipitant in the form of Al2O3.3H2O(s) and occluded soda in the form of Na2O(s).

Diagram

The diagram shows the default drawing of the Precipitator, with the required connecting streams.

The physical location of the connections is not important; the user may connect the streams to any position on the drawing. When the user inserts a Precipitator into a flowsheet, he may choose a different drawing from a pull down menu.

Inputs and Outputs

Label	Required Optional	Input Output	Number of Connections		Description
			Min	Max.
Feed	1 Required	In	1	20	The liquid or slurry inlet
Product	Required	Out	1	1	The product stream from the Precipitator.

Model Theory

Yield Method

Precipitation stage is modelled as a continuous stirred well-mixed tank reactor, assuming particle growth is the only mechanism for alumina precipitation; the rate equation is of the form:

[math]\displaystyle{ \mathbf{\mathit{\frac{dA}{dT}=k_G. SAL\left(\frac{A_o-A^*}{C}\right)^2}} }[/math] (Equation 1)

where kG is the Growth Rate Factor which takes the form of:

[math]\displaystyle{ \mathbf{\mathit{k_G=K. exp\left(\frac{-E}{RT}\right)}} }[/math]

Using equation 1, the Alumina balance over the Precipitator is given by:

[math]\displaystyle{ \mathbf{\mathit{Q_{in25}A_{in}-Q_{out25}A_{out}=k_G \times SAL \times V \left(\frac{A_o - A^*}{C}\right)^2}} }[/math] (Equation 2)

Where

Q	Mixture volumetric flowrate (m3/hr)
Ao	Alumina concentration leaving the precipitator (g/L)
A*	Saturated Alumina concentration (g/L)
C	Caustic concentration leaving the precipitator expressed in Na2CO3(g/L)
K	constant
E	Activation energy (J/mol)
R	Gas constant (J/mol.K)
T	Temperature (K)
SAL	Seed surface area (m2/L)
V	Tank volume (L)

The saturated Alumina concentration is calculated in the Bayer species model specified by the user. Please refer to the documentation for the relevant Bayer species model.

The relationship between the Outlet volumetric flow and the exiting Alumina concentration is given by the following equation:

[math]\displaystyle{ \mathbf{\mathit{Q_{out25}=\left( \frac{\alpha \rho_s - A_{in}}{\alpha \rho_s - A_{out}} \right) \times Q_{in25} }} }[/math] (Equation 3)

where

[math]\displaystyle{ \mathbf{\mathit{\alpha =\frac {MW_{Al_2O_3}}{MW_{Al_2O_3+3H_2O}} = \frac{102}{156} }} }[/math]

Yield Method 2003

This is basically the same as the normal Yield method, the only difference being different correlations for the Growth Rate constant are selectable, these are:

Method: White

[math]\displaystyle{ \mathbf{\mathit{k_G=1.96 \times 10^{10} exp\left(\frac{-7200}{T}\right)}} }[/math]

Method: Cresswell

[math]\displaystyle{ \mathbf{\mathit{k_G= \frac{15 \times exp\left[-7600 \left(\frac{1}{T}-\frac{1}{343.25}\right)\right]}{{\sqrt{\frac{C_o}{100}}}}}} }[/math]

Method: White and Bateman

[math]\displaystyle{ \mathbf{\mathit{k_G= \frac{7.4 \times 10^{12} \times exp\left(\frac{-8500}{T}\right)}{{\sqrt{C_o}}}}} }[/math]

NOTE: SAL - Seed surface area is measured in (m2/m3) in Yield Method 2003

Table 1 gives published values for E/R.

Source	Date	E/R (Kelvin)
Misra and White	1970	7200±700
King	1973	6400±1500
Low	1975	7500±1500
Oberbey and Scott	1978	10000
Mordini and Cristol	1982	9500
White and Bateman	1988	8500±800
Audet and Larocque	1988+	9300±730

Occluded Soda

If the Yield method is used, Ohkawa, Tsuneizumi and Hirao [5] correlation defines the mass of soda precipitated with the Alumina as:

[math]\displaystyle{ \mathbf{\mathit{OccludedSoda = \frac{k_{soda}\left(\frac{A_o-A^*}{C_o}\right)^2 exp\left(\frac{E_{soda}}{T_K}\right) \times \left(A_o - A_i \right)}{100} }} }[/math]

Where

k_soda is the occluded soda factor, 0.00127

E_soda is a constant = 2535 K^-1.

If Yield Method 2003 is used, then an extra correlation is available. Sang [6], gives an expression in the form:

[math]\displaystyle{ \mathbf{\mathit{OccludedSoda = \frac{k_{soda}\left({A_o-A^*}\right)^2 \times \left(A_o - A_i \right)}{100} }} }[/math]

Where

k_soda = 1.58x10-4 for batch operation

k_soda = 4.74x10-4 for continuous operation

In both cases, the occluded soda produced by the precipitator model will be in the form of Na2O(s).

References

1. Rosenberg, S.P., Healy, S.J. “A Thermodynamic model for Gibbsite solubility in Bayer liquors”, Fourth International Alumina Quality workshop, June 1996, pp301-310.
2. White, L.T., Steemson, M., Milne, P. A Graphical Construction for Predicting the Yield from Continuous Precipitator Trains. Light Metals 1984, pp 223-236.
3. Cresswell, P.J., Harig, F.E., Johnston, R.R.M, Leigh, G.M. and Thurlby, J.A. Modelling alumina Trihydrate Precipitation - Prediction of Laboratory Kinetic and Size Data. 6th AusIMM Extractive Metallurgy Conference, Brisbane, 3rd-6th July 1994, pp325-332.
4. White, E.T. and Bateman, S.H. Effect of Concentration on the Growth Rate of Al(OH)3 Particles. Source Unknown.
5. Ohkawa, J,. Tsuneizumi, T., Hirao, T. “Technology of controlling soda pick-up in Alumina Trihydrate precipitation”. Light Metals 1984, pp 223-236.
6. Sang, J.V. Factors Affecting Residual Na2O in Precipitation Products. Source Unknown.

Data Sections

The default access window consists of two sections,

Summary of Data Sections

1. Precipitation tab - Contains general information relating to the unit.
2. RB - Optional tab, only visible if the Reactions are enabled in the Evaluation Block.
3. Info tab - Contains general settings for the unit and allows the user to include documentation about the unit and create Hyperlinks to external documents.
4. Links tab, contains a summary table for all the input and output streams.
5. Audit tab - Contains summary information required for Mass and Energy balance. See Model Examples for enthalpy calculation Examples.

Precipitator Tab

Class: Precipitator

Tag / Symbol	Input / Calc	Description/Calculated Variables / Options
Common First Data Section
On	Tick Box	This can be used to take a precipitator off line. When a precipitator is not ON, the input stream will act as though it has bypassed the precipitator, thus no change will occur in this unit. This option is useful for feasibility studies of flowsheet configuration.
Reactions	List box	This can be used to switch on reactions in the unit. If this is On, RB becomes visible and may be configured. Note: The user does not have to configure a reaction file, even if this block is On.
Requirements:
V	Input	The volume of the unit
Method	Simple	The user does not use a yield model to calculate the amount of Gibbsite precipitated. The user may set a reaction in the Reaction Block to simulate the precipitation reaction. If no reactions are specified in the Reaction Block, then the model behaves like a perfectly mixed tank with no reactions.
	Yield Method	The unit uses the equations given above in the Yield Method in the Theory section to calculate the Yield of Gibbsite, based on the feed conditions. The user may also specify additional reactions in the Reaction Block.
	Yield Method 2003	The unit uses the equations given above in the Yield Method 2003 in the Theory section to calculate the Yield of Gibbsite, based on the feed conditions. The user may specify correlation used to calculate the Growth Rate Factor. This option also allows a second option for the soda precipitation.
E/R	Input	This variable is only visible if the Yield Method is chosen. The Activation Energy (E) divided by the Gas Constant (R). Published values are given in Table 1.
K	Input	This variable is only visible if the Yield Method is chosen. The Growth Rate Constant factor.
Ksoda	Input	The occluded soda factor. This variable is only visible if the Yield Method is chosen. The default value is 1.27*10-3.
GrowthMethod	List Box	Only available with the YieldMethod2003 option, allows the user to select which growth rate factor correlation is used.
The following is visible is the White Growth Method is selected.
E/R_White	Input	The Activation Energy (E) divided by the Gas Constant (R). Published values are given in Table 1.
K_White	Input	The Constant used in the Growth Rate Factor correlation.
gF_White	Input	This allows the user to tune the growth rate based on a factor.
The following is visible is the Cresswell Growth Method is selected.
E/R_Cresswell	Input	The Activation Energy (E) divided by the Gas Constant (R). Published values are given in Table 1.
Tref	Input	This is the reference temperature used in the Cresswell correlation, default is 343.25 K.
K_Cresswell	Input	The Constant used in the Growth Rate Factor correlation.
gF_Cresswell	Input	This allows the user to tune the growth rate based on a factor.
The following is visible is the WhiteBateman Growth Method is selected.
E/R_WhiteBateman	Input	The Activation Energy (E) divided by the Gas Constant (R). Published values are given in Table 1.
K_WhiteBateman	Input	The Constant used in the Growth Rate Factor correlation.
gF_WhiteBateman	Input	This allows the user to tune the growth rate based on a factor.
SodaPrecip Method	List Box	Only available with the YieldMethod2003 option, allows the user to select which soda precipitation correlation is used.
Ksoda_Sang	Input	The occluded soda factor. The default value is 4.74*10-4.
Ksoda_Ohkawa	Input	The occluded soda factor. The default value is 1.27*10-3.
ReactionHeatMethod	List Box	The Options available are: (1) Calculated - For correlation used to calculate the HOR, please refer to Heat of Dissolution of Gibbsite and Boehmite, (2) Override
HOR_a	Input	The user may specify a required heat of reaction for the Alumina precipitation reaction. Units for this coefficient is kJ/kg THA formed. This is an exothermic reaction.
HOR_b	Input	The user may specify a required heat of reaction for the Soda co-precipitation reaction.
ThermoLoss Method	List Box	The Options available are: (1) None, (2) TempDrop, (3) FixedLoss and (4) LossFraction
Temp_Drop	Input	The user may specify a temperature drop in the unit due to heat losses to ambient. This field is only available if TempDrop method is used.
		NOTE: Outlet T = Feed T – Temp_Drop + T Increase due to precipitation
ThermalLoss Rqd	Input	The user may specify a required heat loss value for the unit operation. This field is only available if FixedLoss method is used.
ThermalLoss Frac	Input	The user may specify a required heat loss as a fraction of the total heat content in the unit operation. This field is only available if LossFraction method is used.
Results Tank
Residence Time	Calc	The calculated residence time of the slurry in the unit.
Yield	Calc	The calculated Yield.
THAPrecip	Calc	The mass of Trihydrate Alumina precipitated in the unit.
OccludedSoda	Calc	The mass of Na2O precipitated in the unit as occluded soda.
Results
Qvi	Calc	Volumetric flowrate in.
Qvo	Calc	Volumetric flowrate out.
Ti	Calc	Temperature of stream in.
To	Calc	Temperature of stream out.
ACin	Calc	A/C ratio of stream in.
ACout	Calc	A/C ratio of stream out.
ASat	Calc	Alumina Saturation Value.
kG	Calc	Growth Rate factor.
GrowthRate	Calc	Growth Rate.
[email protected]	Calc	The total heat values of the feed stream calculated using standard species model at 0dC.
[email protected]	Calc	The total heat values of the product stream calculated using standard species model at 0dC.
[email protected]	Calc	Heat of reactions calculated using standard species model at 0dC.
[email protected]	Calc	The total heat values of the feed calculated using standard species model at Feed Temperature.
[email protected]	Calc	The total heat values of the product calculated using standard species model at Product Temperature.
[email protected]	Calc	Heat of reactions calculated using standard species model at product temperature.
[email protected]	Calc	The total heat values of the feed stream calculated using Bayer species model at 0dC.
[email protected]	Calc	The total heat values of the product stream calculated using Bayer species model at 0dC.
[email protected]	Calc	Heat of reactions calculated using Bayer species model at 0dC.
[email protected]	Calc	The total heat values of the feed calculated using Bayer species model at Feed Temperature.
[email protected]	Calc	The total heat values of the product calculated using Bayer species model at Product Temperature.
[email protected]	Calc	Heat of reactions calculated using Bayer species model at product temperature.
[email protected]	Calc	The Heat of reactions @ 0dC used by the model calculations.
[email protected]	Calc	The Heat of reactions @ temperature used by the model calculations.
Thermal Loss	Calc	The calculated heat loss.
ThermalTemp Drop	Calc	The calculated temperature drop based on the user specified heat loss method.
Di	Calc	The estimated average particle Diameter at the inlet conditions.
Do	Calc	The estimated average particle Diameter at the outlet conditions.
SALi	Calc	Seed Surface Area, Volume basis (m²/L) at the inlet conditions.
SALi	Calc	Seed Surface Area, Volume basis (m²/L) at the outlet conditions.
AOutEst	Calc	The estimated Alumina concentration of the outlet stream, used internally for precipitation tank calculation.

Hints and Comments

General Configuration Hints:

1. The species model, which the Precipitator uses, is important for the calculations. The feed streams to the precipitator must be configured with a Bayer species model for the calculations to be valid.
2. The user may find it more efficient not to use the Yield model when first setting up a complex Alumina Flowsheet, but to set reaction extents for the Gibbsite and soda precipitation. Once the flowsheet is controlled and the Alumina and Caustic concentrations around the plant are close to the expected values, the Yield model may be implemented.
3. If using the yield method, the feed to the first precipitator in a precipitation train (either fresh or recycle) should contain some seed. Using the SetData method can modify the seed surface Area. See below for Hints on Setting the Alumina Particle Size Information.
4. Compound Al2O3.3H20(s) must be present as this is the solid precipitated by the Yield model.
5. Compound Na2O(s) must be present as this is the Occluded soda.
6. The user may set the volume of the Precipitator (V) to 0.0 to effectively remove it from the circuit. NOTE: this can now be done using the On tick box.

Hints on Setting the Alumina Particle Size Information:

The seed surface area or particle size information can be set in the FEEDER - Content or PIPE – Qi or Qo (if it is the recycle) entering the precipitator model, if required. Please refer to section Specific Surface Area (SSA) for the steps required.

The SAL - Seed Surface Area Volume (m2/L) is a required variable in the Precipitator 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 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.

To do so, the FEEDER or PIPE must be using the Bayer Species Model, under the section "SSA" located on the Content or Qi tab page respectively; the user MUST tick the SetData box and enter the appropriate values, and either SAM or D is needed. (See Bayer Data)

The equations used in calculating SAL are:

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

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.

The setting of SAM is only for initialization purposes; therefore it is usually set at the stream entering the first precipitator, whether it is a fresh feed or a recycle stream. Once the SetSAM method is used, the particle size information will be shown in all downstream pipes.

NOTE: It is IMPORTANT to note that solid Al2O3.3H2O (THA) MUST be present in the stream for the above to work properly.