# Generic Bayer Species Model

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Related Links: Alumina3, Alumina 1 vs Alumina 3, Converting Alumina 1 to Alumina3

### 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: Recommended alternate Bayer Species Model is Alumina 3 Bayer Species Model

The Generic Bayer species model is used to calculate the properties of fluids within an Alumina project using equations defined in the public domain. These equations are documented in the Model Theory section given below.

General information regarding the Bayer species models, such as heats of reaction, volume displays, etc. is given in General Bayer Data.

All of the properties that are not explicitly calculated by this model are calculated using the Standard Species Model.

### Model Theory

The calculations for liquor and slurry densities, heat capacity and boiling point elevation are evaluated using the following formulae:

The variables used in the calculations are described below:

 A = Al2O3 concentration (g/L liquor) at the slurry temperature C = NaOH concentration, expressed as grams Na2CO3/L liquor @ the slurry temperature A25 = Al2O3 concentration (g/L liquor) at 25°C. C25 = NaOH concentration, expressed as grams Na2CO3/L liquor @ 25°C. T = Temperature in °C Tk = Temperature in K TNa = The sum of all sodium salts, caustic, carbonate, organics, NaCl, Na2SO4, all expressed as Na2CO3 @ 25°C. The engineering units for this is Concentration (mass/mass) wt%.
$\displaystyle{ \mathbf{\mathit{T_{Na}=\left([Na_2CO_3]+\left(\frac{[NaOH]}{2*MW(NaOH)}+\frac{[Na_2C_2O_4]}{MW(Na_2C_2O_4)}+\frac{[Na_{org}]}{MW(Na_2C_5O_7)}+\frac{[NaCl]}{2*MW(NaCl)}+\frac{[Na_2SO_4]}{MW(Na_2SO_4)}\right)*MW(Na_2CO_3)\right)*\frac{100}{L_m}}} }$
where: Lm - Liquor mass flow (engineering units need to be the same as individual salts in the equation.)

TAl2O3 = Total concentration (mass/mass) wt% of Alumina.

$\displaystyle{ \mathbf{\mathit{T_{Al203}=Al_20_3*\frac{100}{L_m}}} }$
where Lm - Liquor mass flow, engineering units used should be the same as for Al2O3 in the equation.

TOC25 = Total Organic carbon (Na2C5O7 + Na2C2O4) expressed as g/L Carbon @ 25°C;

#### Density Calculations

##### Liquid SG @ T1
$\displaystyle{ \mathbf{\mathit{LSG_T=LSG_{25}*\left\lfloor1-\left(0.0005021858*0.85\left(T-25\right)\right)-\left(0.0000011881*0.85\left(T-25 \right)^2\right)\right\rfloor}} }$
where: LSG25 -- liquid SG @ 25°C
##### Liquid SG @ 25°C1
$\displaystyle{ \mathbf{\mathit{LSG_{25}=\begin{matrix}&0.982+\left(0.01349855*T_{Na}\right)+\left(-0.00024948*T^2_{Na}\right)+\left(0.00000273*T^3_{Na}\right)\\ &+\left(0.00208035*T_{Al203}\right)+\left(0.00004113*T^2_{Al203}\right)+\left(-0.00000728*T^3_{Al203}\right)+\left(0.00033367*T_{Na}*T_{Al203}\right)\end{matrix}}} }$
where:
TNa Total concentration (mass/mass) wt% of Sodium, reported as Na2CO3.
TAl2O3 Total concentration (mass/mass) wt% of Alumina.
##### Slurry SG @ T
$\displaystyle{ \mathbf{\mathit{S_LSG=\frac{SolidsMass+LiquidsMass}{SlurryFlow}}} }$
$\displaystyle{ \mathbf{\mathit{SlurryFlow=\frac{SolidsMass}{SolidsSG}+\frac{LiquidsMass}{LSG_T}}} }$
##### Slurry SG @ 25°C
$\displaystyle{ \mathbf{\mathit{S_LSG_{25}=\frac{SolidsMass+LiquidsMass}{SlurryFlow\ 25^{\circ} C}}} }$
$\displaystyle{ \mathbf{\mathit{SlurryFlow=\frac{SolidsMass}{SolidsSG}+\frac{LiquidsMass}{LSG_{25}}}} }$

#### Heat Capacity Calculations

##### Liquid Heat Capacity1
$\displaystyle{ \mathbf{\mathit{Cp_L=\begin{pmatrix}1.0275057375729-0.020113606661083*T_{Na2O}\\ +0.001081165172606*T^2_{Na2O}-0.000022606160779*T^3_{Na2O}\\ -0.004597725999883*T_{Al2O3}-0.000001053264708*T^2_{Al2O3}-0.00000218836287*T^3_{Al2O3}\end{pmatrix}*4.184}} }$
where $\displaystyle{ \mathbf{\mathit{T_{Na2O}=T_{Na}*\frac{MW(Na_2O)}{MW(Na_2CO_3)}}} }$

This is scaled for dilute liquors where $\displaystyle{ \mathit{T_{Na2O}} }$ as liquid weight % is less than 0.19.

##### Solids Heat Capacity

Solids Cp (Cps) is calculated from Cp values as given in the species database (ie using Standard Species Model).

##### Slurry Heat Capacity
$\displaystyle{ \mathbf{\mathit{Cp_{sL}=\frac{SolidsMass*Cp_s+LiquidsMass*Cp_L}{SolidsMass+LiquidsMass}}} }$

#### Boiling Point Elevation2

The Boiling Point Elevation method is selected globally from the Feeder unit operation as illustrated below. NOTE: The feeder must be using the Bayer species model.

##### Method 1: Dewey Equation
$\displaystyle{ \mathbf{\mathit{BPE=\begin{matrix}&0.00182+0.55379*\left(\frac{M}{10}\right)^7+0.004060625*M*T_L\\ &+\frac{1}{T_K}*\left(-286.66*M+29.919*M^2+0.6228*M^3\right)-0.032647*M*\left(M*\frac{T_K}{1000}\right)^2\\ &+\left(\frac{T_K}{1000}\right)^5*\left[5.9705*M-\left(0.57532*M^2\right)+\left(0.10417*M^3\right)\right] \end{matrix}}} }$
 Where M is the Total Molality of the solution, calculated using the following species: Al2O3, NaOH, Na2CO3, NaCl, Na2SO4, Na2C5O7 and Na2C2O4. Tk is the Saturated temperature for pure water at the stream Pressure.
$\displaystyle{ \mathbf{\mathit{BPE=\begin{matrix}&0.007642857+0.006184282*X+2.92857e^{-5}*T+0.00010957*X^2-3.80952e^{-8}*T^2\\ &+0.000208801.XT-8.61985e^{-10}*X^3-8.61985e^{-10}*T^3+1.7316e^{-10}*XT^2-2.49763e^{-7}*X^2T\end{matrix}}} }$
Where:-- X = Total Soda concentration expressed as g/L Na2O @ 25C; and
T = temperature in degree C.

NOTE: Constants in the above equation were determined by data fitting of published Adamson data.

#### Saturated Alumina Concentration3

$\displaystyle{ \mathbf{\mathit{A^{*} = \cfrac{0.96197 C_{25}} {1+\cfrac{ 10 ^{\left(\cfrac{\alpha_o \sqrt{I}} {1+ \sqrt{I}} \right)- \alpha_3 I - \alpha_4 I^{\frac{3}{2}} }} {{exp \left({\cfrac{\Delta G_{rxn}}{RT}}\right)}}}}} }$

Where a, a3, and a4 are constants (see table 1)
DGRXN is the Gibbs energy of dissolution (-30960 J/mol)
I is the ionic strength, calculated using the following equation:

$\displaystyle{ \mathbf{\mathit{I=0.01887C_{25}+\frac{k_1\left[NaCl\right]}{MW(NaCl)}+\frac{k_2\left[Na_2CO_3\right]}{MW(Na_2CO_3)}+\frac{k_3\left[Na_2SO_4 \right]}{MW(Na_2SO_4)}+k_40.01887*TOC_{25}}} }$
Where k1,k2, k3 and k4 are constants (see Table 1)
Concentration of salts and carbonate are @ 25 °C.

Table 1

a a3 a4 k1 k2 k3 k4
-9.2082 -0.8743 0.2149 0.9346 2.0526 2.1714 1.6734

#### Oxalate Equilibrium

Calculates the equilibrium concentration (g/l) of oxalate, based on stream properties.

(Equation from British Aluminium - Burnt Island)

$\displaystyle{ \mathbf{\mathit{OxEquil=7.62*Exp\left[0.012T-\left(\frac{MW(Na_2O)}{MW(Na_2CO_3)}\right)*\left(0.016*C_{25}+\frac{0.011*Qm_{Na_2CO_3}} {Qv}\right)\right]}} }$
Where Qv = Liquor Volume at 25 °C.
QmNa2CO3 = Mass flowrate of sodium carbonate
T = temperature in °C.

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#### Stream Property Limits

One limitation the Generic Bayer Species model (Alumina1) has is that under some (normally unrealistic) circumstances, the density equation can return very unrealistic values. This is because the Bayer species model uses dissolved alumina in terms of separate Al2O3(aq) and NaOH(aq) species, instead of the naturally occurring NaAl[OH]4 species (which is used Alumina3). In this form, it is possible for the user to mistakenly input stream composition containing Al2O3(aq) with no NaOH(aq). In this case, the A/C will be infinite and the density equation will return very incorrect value of 0 kg/m3.

To safe guard this situation, the Bayer stream property has been bound to the following limits:

1. The minimum density that can be returned is 700 kg/m3
2. The maximum A/C that would be returned is 0.96 - this is the A/C value of NaAl[OH]4 with no free caustic present.
3. The maximum RP (A/CNa2O) that would be returned is 1.641 - this is the A/C value of NaAl[OH]4 with no free caustic present.

### References:

1. Molloy-Donaldson Model
2. Dewey, J.K.L. Boiling Point Rise of Bayer Liquors. Light Metals 1981. The Metallurgical Society of AIME pp 185 -- 197.
3. Rosenberg S.P and Healy S.J. A Thermodynamic Model for Gibbsite Solubility in Bayer Liquors. Fourth International Alumina Quality Workshop. June 1996.

### Data Sections

The data will be displayed on the Qi and Qo pages of the Pipe access window, and under the Content page for units. Only the data that is calculated using the Bayer equations is shown below. The other data is discussed in the SysCAD Model help - Pipe Section.

#### Feeder Configuration Data

 Tag / Symbol Input / Calc Description Global Bayer Constants and Options: BPE_Method Dewey This is the original method implemented in SysCAD. This method becomes inaccurate in high caustic concentration range. Adamson This method is more accurate in the high caustic concentration range. See Boiling Point Elevation for equations used. BPE_Factor Input This field can be used as a "fudge factor" for the Boiling Point Elevation number, if the calculated value using the generic formula differs from actual expected value. Note: this will only adjust the value linearly. Rho_Factor Input This field can be used as a "fudge factor" for the Bayer Liquor Density number, if the calculated value using the generic formula differs from actual expected value. Note: this will only adjust the value linearly. H2OTestFrac0 Input This is used handle very dilute concentrations in the stream. If the Water Fraction in the stream is higher than this value, then the stream property will be calculated using the Standard Species Model. The maximum value for this is 99.99%. Bayer Liquor Design Values DefineLiquor Check Box If this box is checked, the Feeder will automatically calculate the make-up of the feed stream, based on the variables supplied below. DefnLiqMethod TotOrganics and Ratio Defines Organics using the Rqd_Organic and Rqd_OrgRatio fields. TOC and Oxalate Defines Organics using the Rqd_TOC and Rqd_Oxalate fields. Rqd_A/C Input The required ratio of A:C in the Feed stream, where A is the Al2O3 concentration (g/L liquor) and C is the NaOH concentration, expressed as grams Na2CO3/L liquor @ 25--C Rqd_C/S Input The required ratio of C:S in the Feed stream, where C is the NaOH concentration, expressed as grams Na2CO3/L liquor @ 25--C and S is the NaOH plus Na2CO3 concentration, expressed as grams Na2CO3/L liquor @ 25--C. Rqd_C Input The required value of C in the Feed stream, where C is the NaOH concentration, expressed as grams Na2CO3/L liquor @ 25--C. Rqd_SiO2 Input Required concentration of SiO2 in g/L @ 25--C Rqd_TOC Input(Based on DefLiqMethod selected) Required Total organic carbon concentration in the stream expressed as g/L carbon @ 25 °C. Rqd_Oxalate Required oxalate concentration in the stream expressed as g/L of Na2CO3 @ 25--C Rqd_Organic Input (Based on DefLiqMethod selected) Required organic [Na2C5O7(l) + Na2C2O4(l)] concentration in the stream expressed as grams of Na2CO3/L liquor @ 25--C. Rqd_OrgRatio Required ratio of Sodium Oxalate : Total organic in the stream. Where total organic is Rqd_Organic defined above. All concentrations are expressed as grams of Na2CO3/L liquor @ 25--C. Rqd_Na2SO4 Input Required concentration of Na2SO4 in g/L @ 25--C Rqd_NaCl Input Required concentration of NaCl in g/L @ 25--C SolidsFrac Input The fraction of solids in the feed. The proportion of the different solid species is maintained. If there are no solid species specified then THA is assumed.

The following points are essential to the user--s understanding of this feature:

##### Liquid Specification

The first eight of the above variables are used to define the percentages of the liquid species.

Note: The only liquid species that will be used in calculating the liquid make-up are:

H2O(l) - Water

Al2O3(l) - Alumina

NaOH - Caustic Soda

Na2CO3(l) - Sodium Carbonate

Na2SO4(l) - Sodium Sulphate

NaCl(l) - Sodium Chloride

SiO2(l) - Quartz

Organics:

Na2C2O4(l) - Sodium Oxalate

Na2C5O7(l) - Organic

##### Solid Specification

The last variable is used to specify the required solids fraction. In addition to this variable, the user must also specify the individual fractions of the solids required on the MF (Mass Fraction) page, as percentages of the SOLIDS flow, NOT as percentages of the entire flow.

#### Bayer Data

 Tag | Symbol Input or Calc Description [email protected] Calc The saturated temperature at the stream pressure [email protected] Calc The saturated pressure at the stream temperature BPE Calc The boiling point elevation at the stream composition and temperature. Bayer Liquor Values @ 25°C A | AluminaConc Calc Al2O3 concentration @ 25°C. (g/L liquor) C | CausticConc Calc NaOH concentration, expressed as grams Na2CO3/L liquor @ 25°C. S | SodaConc Calc NaOH plus Na2CO3 concentration, expressed as grams Na2CO3/L liquor @ 25°C. A/C Calc Ratio of A to C, see Stream Property Limits C/S Calc Ratio of C to S Cl/C Calc Ratio of Cl to C TOC Calc Total organic carbon concentration, as carbon equivalent. Grams of [Na2C5O7(l)*5 + Na2C2O4(l)*2] / L liquor @ 25°C. SodiumCarbConc Calc Sodium Carbonate concentration FC | FreeCaustic Calc Caustic Concentration excluding the amount assciated with A (Sodium Aluminate NaAl[OH]4), expressed as g/L of Na2CO3. SolidsConc25 Calc Expressed as grams of solids / L Slurry @ 25°C. Concentration @ 25°C, as Na2CO3 equivalent Organates Calc Grams of organic Na2C5O7(l) / L liquor @ 25°C. Oxalate Calc Grams of oxalate Na2C2O4(l) / L liquor @ 25°C. TotalOrg Calc Grams of [Na2C5O7(l) + Na2C2O4(l)] / L liquor @ 25°C. TOOC Calc Total organic carbon concentration as Na2CO3 equivalent. Grams of [Na2C5O7(l)*5 + Na2C2O4(l)*2] / L liquor @ 25°C NaCl Calc Grams of NaCl(l) / L liquor @ 25°C. Na2SO4 Calc Grams of Na2SO4(l) / L liquor @ 25°C. TotalNa Calc As per TNa Equation in Model Theory section, but expressed as g/L liquor @ 25°C. Other properties @ 25°C LVolFlow25 Calc Liquor Volumetric Flowrate @25°C. SLVolFlow25 Calc Slurry Volumetric Flowrate @25°C. LRho25 Calc The liquor density @ 25°C. see Stream Property Limits SLRho25 Calc The slurry density @ 25°C. Oxalate* Calc Grams of oxalate Na2C2O4(l) / L liquor @ 25°C. NaCl* Calc Grams of NaCl(l) / L liquor @ 25°C. Na2SO4* Calc Grams of Na2SO4(l) / L liquor @ 25°C. Bayer Liquor Values @ 25 °C, as Na2O Equivalent C_Na2O Calc NaOH concentration, expressed as grams Na2O/L liquor @ 25°C. S_Na2O Calc NaOH plus Na2CO3 concentration, expressed as grams Na2O/L liquor @ 25°C. TotalNa_Na2O Calc Total Sodium, expressed as grams Na2O/L Liquor @ 25°C. RP Calc Ratio of A : C expressed as Na2O. see Stream Property Limits Bayer Liquor Values @ Temperature [email protected] | AluminaConcT Calc Al2O3 concentration @ Temperature (g/L liquor) [email protected] | CausticConcT Calc NaOH concentration, expressed as grams Na2CO3/L liquor @ Temperature. [email protected] | SodaConcT Calc NaOH plus Na2CO3 concentration, expressed as grams Na2CO3/L Liquor @ Temperature. [email protected] Calc Total organic carbon concentration as Carbon equivalent. Grams of [Na2C5O7(l)*5 + Na2C2O4(l)*2] / L liquor @ Temperature. SolidsConcT Calc Expressed as grams of solids / L Slurry @ Temperature. BoilPtElev Calc The boiling point elevation. Bayer Liquor Precipitation Values @ Temperature* ASat | A_Saturation Calc The saturated Alumina concentration @ Temperature. A/CSat Calc The ratio of ASat : C @ Temperature. SSN_Ratio Calc The ratio of A : ASat @ Temperature. I | IonicStrength Calc The Ionic strength. See model theory under Alumina saturation for equation. OxalateEq Calc The Oxalate Equilibrium value. See Model Theory for equation. Alumina Particle Size Info (Under Tab SSA or MF if component list is short) Please see Specific Surface Area (SSA) Method Display SetData Tickbox Allows the user to set values for SAM Solids List Allows the user to select the solid component to base the calculation on. Note: The selected compound's flowrate must be none zero for the propagation of the following parameters to downstream unit operations. SAM | SeedSurfaceAreaM Input Seed Surface Area, Mass basis (m^2/g) SAL | SeedSurfaceAreaL Calc Seed Surface Area, Volume basis (m^2/L) #/s Calc Particle number per second #/L Calc Particle number per litre. D | PartDiam Input Particle diameter in μm. SolidsQm Calc The amount of solids (eg: Al2O3.3H2O) present.