# 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 RequiredOptional InputOutput 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:

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

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

$\mathbf{\mathit{k_G=K. exp\left(\frac{-E}{RT}\right)}}$

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

$\mathbf{\mathit{Q_{in25}A_{in}-Q_{out25}A_{out}=k_G \times SAL \times V \left(\frac{A_o - A^*}{C}\right)^2}}$ (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:

$\mathbf{\mathit{Q_{out25}=\left( \frac{\alpha \rho_s - A_{in}}{\alpha \rho_s - A_{out}} \right) \times Q_{in25} }}$ (Equation 3)

where

$\mathbf{\mathit{\alpha =\frac {MW_{Al_2O_3}}{MW_{Al_2O_3+3H_2O}} = \frac{102}{156} }}$

### 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

$\mathbf{\mathit{k_G=1.96 \times 10^{10} exp\left(\frac{-7200}{T}\right)}}$

Method: Cresswell

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

Method: White and Bateman

$\mathbf{\mathit{k_G= \frac{7.4 \times 10^{12} \times exp\left(\frac{-8500}{T}\right)}{{\sqrt{C_o}}}}}$

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:

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

Where

ksoda is the occluded soda factor, 0.00127
Esoda 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:

$\mathbf{\mathit{OccludedSoda = \frac{k_{soda}\left({A_o-A^*}\right)^2 \times \left(A_o - A_i \right)}{100} }}$

Where

ksoda = 1.58x10-4 for batch operation
ksoda = 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. StdHfFd@0 Calc The total heat values of the feed stream calculated using standard species model at 0dC. StdHfPr@0 Calc The total heat values of the product stream calculated using standard species model at 0dC. StdHOR@0 Calc Heat of reactions calculated using standard species model at 0dC. StdHfFd@T Calc The total heat values of the feed calculated using standard species model at Feed Temperature. StdHfPr@T Calc The total heat values of the product calculated using standard species model at Product Temperature. StdHOR@T Calc Heat of reactions calculated using standard species model at product temperature. MdlHfFd@0 Calc The total heat values of the feed stream calculated using Bayer species model at 0dC. MdlHfPr@0 Calc The total heat values of the product stream calculated using Bayer species model at 0dC. MdlHOR@0 Calc Heat of reactions calculated using Bayer species model at 0dC. MdlHfFd@T Calc The total heat values of the feed calculated using Bayer species model at Feed Temperature. MdlHfPr@T Calc The total heat values of the product calculated using Bayer species model at Product Temperature. MdlHOR@T Calc Heat of reactions calculated using Bayer species model at product temperature. UsedHOR@0 Calc The Heat of reactions @ 0dC used by the model calculations. UsedHOR@T 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.

### 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.