Generic Bayer Species 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: 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
T_k	=	Temperature in K
T_Na	=	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%.

[math]\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}}} }[/math]

where: L_m - Liquor mass flow (engineering units need to be the same as individual salts in the equation.)

T_Al2O3 = Total concentration (mass/mass) wt% of Alumina.

[math]\displaystyle{ \mathbf{\mathit{T_{Al203}=Al_20_3*\frac{100}{L_m}}} }[/math]

where L_m - 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

[math]\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}} }[/math]

where: LSG₂₅ -- liquid SG @ 25°C

Liquid SG @ 25°C¹

[math]\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}}} }[/math]

where:

T_Na Total concentration (mass/mass) wt% of Sodium, reported as Na₂CO₃.

T_Al2O3 Total concentration (mass/mass) wt% of Alumina.

Slurry SG @ T

[math]\displaystyle{ \mathbf{\mathit{S_LSG=\frac{SolidsMass+LiquidsMass}{SlurryFlow}}} }[/math]

[math]\displaystyle{ \mathbf{\mathit{SlurryFlow=\frac{SolidsMass}{SolidsSG}+\frac{LiquidsMass}{LSG_T}}} }[/math]

Slurry SG @ 25°C

[math]\displaystyle{ \mathbf{\mathit{S_LSG_{25}=\frac{SolidsMass+LiquidsMass}{SlurryFlow\ 25^{\circ} C}}} }[/math]

[math]\displaystyle{ \mathbf{\mathit{SlurryFlow=\frac{SolidsMass}{SolidsSG}+\frac{LiquidsMass}{LSG_{25}}}} }[/math]

Heat Capacity Calculations

Liquid Heat Capacity¹

[math]\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}} }[/math]

where [math]\displaystyle{ \mathbf{\mathit{T_{Na2O}=T_{Na}*\frac{MW(Na_2O)}{MW(Na_2CO_3)}}} }[/math]

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

Solids Heat Capacity

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

Slurry Heat Capacity

[math]\displaystyle{ \mathbf{\mathit{Cp_{sL}=\frac{SolidsMass*Cp_s+LiquidsMass*Cp_L}{SolidsMass+LiquidsMass}}} }[/math]

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

[math]\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}}} }[/math]

Where	M is the Total Molality of the solution, calculated using the following species:
	Al₂O₃, NaOH, Na₂CO₃, NaCl, Na₂SO₄, Na₂C₅O₇ and Na₂C₂O₄.
	T_k is the Saturated temperature for pure water at the stream Pressure.

Method 2: Adamson Equation

[math]\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}}} }[/math]

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

[math]\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)}}}}} }[/math]

Where a, a₃, and a₄ are constants (see table 1)

DG_RXN is the Gibbs energy of dissolution (-30960 J/mol)

I is the ionic strength, calculated using the following equation:

[math]\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}}} }[/math]

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)

[math]\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]}} }[/math]

Where Qv = Liquor Volume at 25 °C.

Qm_Na2CO3= 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:

The minimum density that can be returned is 700 kg/m³
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.
The maximum RP (A/C_Na₂O) that would be returned is 1.641 - this is the A/C value of NaAl[OH]₄ with no free caustic present.

References:

Molloy-Donaldson Model
Dewey, J.K.L. Boiling Point Rise of Bayer Liquors. Light Metals 1981. The Metallurgical Society of AIME pp 185 -- 197.
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.
BPE_Method	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.
DefnLiqMethod	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	Input(Based on DefLiqMethod selected)	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	Input (Based on DefLiqMethod selected)	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 T_Na 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.

Please refer to Hints and Comments of the Precipitation Model for more info.

Individual Component Volume Flow/Fraction Displays for Bayer streams

See General Bayer Data

Generic Bayer Species Model

Contents

General Description

Model Theory

Density Calculations

Liquid SG @ T¹

Liquid SG @ 25°C¹

Slurry SG @ T

Slurry SG @ 25°C

Heat Capacity Calculations

Liquid Heat Capacity¹

Solids Heat Capacity

Slurry Heat Capacity

Boiling Point Elevation²

Method 1: Dewey Equation

Method 2: Adamson Equation

Saturated Alumina Concentration³

Oxalate Equilibrium

Stream Property Limits

References:

Data Sections

Feeder Configuration Data

Liquid Specification

Solid Specification

Bayer Data

Individual Component Volume Flow/Fraction Displays for Bayer streams

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Generic Bayer Species Model

General Description

Model Theory

Density Calculations

Liquid SG @ T1

Liquid SG @ 25°C1

Slurry SG @ T

Slurry SG @ 25°C

Heat Capacity Calculations

Liquid Heat Capacity1

Solids Heat Capacity

Slurry Heat Capacity

Boiling Point Elevation2

Method 1: Dewey Equation

Method 2: Adamson Equation

Saturated Alumina Concentration3

Oxalate Equilibrium

Stream Property Limits

References:

Data Sections

Feeder Configuration Data

Liquid Specification

Solid Specification

Bayer Data

Individual Component Volume Flow/Fraction Displays for Bayer streams

Navigation menu

Search

Liquid SG @ T¹

Liquid SG @ 25°C¹

Liquid Heat Capacity¹

Boiling Point Elevation²

Saturated Alumina Concentration³