# Sugar Species Model

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## General Description

The Sugar Species Models calculate thermo-physical properties of pure and technical sucrose solutions over the range of temperatures and concentrations found in the processing of sugar cane to sugar.

The correlations have been taken or adapted from public domain information. References and other relevant information are noted with the help for individual correlations. The calculated solution properties go smoothly to standard SysCAD water properties as solute concentrations go to zero. The correlations are self consistent and all functions are continuous and smooth over the entire range of applicability. The correlations are all based on Brix, Purity and Temperature where;

Brix The Brix includes all solutes in the liquid and is calculated as Brix = (total liquid mass - water mass). Any solutes may be included in the configuration file and used in the SysCAD model. Since the SysCAD sugar model only uses total liquid mass and water mass to calculate Brix, these will be implicitly included in the Brix and thus in the properties calculations.

Purity The purity is the mass of sucrose in solution divided by the total mass of solutes, Purity = Sucrose(aq)/Brix.

### Sugar Model Species

There is a set of species that have been developed for use with sugar solutions, although any species may be added. The species and descriptions are in the table below. There are some species which are comprised of pseudo elements which have been created in the SysCAD database.

 Sugar Species Species Formula Description Aqueous Species Aqueous Sucrose C22H22O11(aq) Sucrose in solution Reducing Sugars C6H12O6(aq) Generic formula for reducing sugars Soluble Ash SolAsh(aq) Soluble ash - remaining mass after solution is pyrolized. Modeled as pseudo element Sa with a molecular weight of 180. Soluble Protein SolProt(aq) Generic proteins in solution. Modeled as pseudo element Sp with a molecular weight of 180. Soluble Other SolOther(aq) Any other unidentified solutes. Modeled as pseudo element So with a molecular weight of 180. Solid Species Crystalline Sucrose C22H22O11(xt) Crystalline sucrose Amorphous Sucrose C22H22O11(am) Non-crystalline solid sucrose Reducing Sugars C6H12O6(s) Solid generic reducing sugars Soluble Ash SolAsh(s) Solid ash Soluble Protein SolProt(s) Solid proteins Soluble Other SolOther(s) Solid soluble other material Fibre C6H10O5(s) Plant Fibre - modeled as Cellulose Mud Solids MudSolids(s) Generic mud solids - composed of pseudo element inert solids, Is, with a molecular weight of 100.

Notes on individual species used on the sugar model.

Soluble Ash, Protein and Other The stoichiometry of these species is not defined and they are simply modeled as pseudo elements. The properties calculations for sucrose solutions depend only on the concentration sucrose and the purity not on detailed chemistry of the impurities. This means that detailed composition of the impurities is not required to describe the solution.

Fibre Fibre in the species model is Dried fibre (no bound water - basically just cellulose). It is reported as "dried" fibre to coincide with the way that measurements on sugar cane and bagasse are physically done. Any bound water is implicitly included in the calculation of bagasse properties (i.e. solids fraction, Brix). This description is consistent with standard practice in the sugar industry.

The chemical formula and properties are assumed to be those of cellulose and the calculation of fibre Cp is derived from published data on Cp of plant fibre.

Mud Solids Mud solids are defined as generic inert solids. They do no react so a more detailed description is not required. However, in the models where there is any solids separation, the mud solids and handling of the mud solids actually includes mud and any other solids that are not fibre and there is no reason that other solids cannot be added into the system if required.

### Sugar Model Properties

All of the properties have been adapted from the Sugar Technologists Handbook (8th edition, Bubnik et al, 1995) with the exception of boiling point elevation which uses a more recent reference. The properties have been developed in a format that is compatible with iterative numerical calculations. Some of the original correlations only covered certain parts of the temperature and concentration ranges. Where different correlations were given for different ranges, the original functions were used to generate a matrix of data and a single new function fit over the whole range using two or three dimensional curve fitting techniques. In some cases, the original functions were modified slightly to match values and slopes the range boundaries. In all cases there is only one correlation spanning the range of data so that they are smooth continuous functions to help insure numerical stability for iterative calculations.

The solution properties default back to pure water properties as solute concentration goes to zero. The pure sucrose solution properties include corrections to give technical solution properties when the purity is less than 100%. The corrections are in functional forms that disappear as purity goes to 100%. This gives a continuous set of properties over the whole range of concentrations and purities with a single function for both pure and technical solutions.

The pure water properties are the IAPWS95 properties for water and steam that are built into SysCAD. The water properties used are calculated for saturation conditions at the given temperature.

NB Most of the correlations are valid for the processing of beet sugar although properties of very low purity solutions should be reviewed. Specific correlations for beet processing can be implemented on request.

### Crystalline Sucrose Density

The density of crystalline sucrose. Linearized relation adapted from original source.

$\text{Density Crystalline Sucrose, }\rho = \left(1590.43 -0.168201\times T(C) \right) \quad \left[kg/m^3 \right]$
NB Temperature in Centigrade. Range 0°C to 100°C.

Reference: Sugar Technologists Handbook, pp 116.

### Amorphous Sucrose Density

The correlation is adapted from crystalline solid correlation and scaled to match density for amorphous sucrose @ 15 C.

$\text{Density Amorphous Sucrose, }\rho = \left(1510.23 -0.168201\times T(C) \right) \quad \left[kg/m^3 \right]$
NB Temperature in Centigrade. Range 0°C to 100°C.

Reference: Sugar Technologists Handbook, pp 113.

### Sucrose Solution Density

The original correlations were used to give a matrix of density as a function of of temperature, Brix and purity. Then the difference between these data and pure water at the same temperature were calculated. A multi-dimensional curve fit was used to give a correlation for the difference as a function of temperature and dry substance (with a functional form that goes to zero as sugar concentration goes to zero). This difference can then be added to the density for pure water so that the density matches pure water exactly at zero concentration. This function matches tabulated data over the whole range very closely. NB this is specific to CANE sugar solutions - low purity BEET sugar solutions require slightly different correlations. Range 0°C to 150°C.

\begin{align} \text{Dry Substance, } W_{ds} & = \left( W_s/Purity \right)\\ \text{Density correction, } d\rho &= \left( a*W_{ds} +b*W_{ds}^2 + c*W_{ds}T + d*W_{ds}^2T + e*W_{ds}T^2 \right) \quad \left[kg/m^3\right] \end{align}

$\begin{array}{lll} \text{where T is in Centigrade and;}\\ a=3.87490374656497 &b=1.74007174938792*10^{-02} &c =-6.30477302750159*10^{-03}\\ d=1.83598990253782*10^{-05} &e=2.77577874108824*10^{-05} \end{array}$

\begin{align} \text{Solution Density, } \rho_{soln}=\rho_{water}\left(T,P_{sat}\right)+d\rho\left(T, W_s, Purity\right)\\ \text{Pure Water Density, } \rho_{water} \text{, comes from IFC97 water properties} \end{align}

Reference: Sugar Technologists Handbook, pp 164, 206. SRI reports.

### Sucrose Crystal Specific Heat

The specific heat of sucrose crystal.

$C_{P,crystal}= 1.1269 + 4.524*10^{-03}T + 6.24*10^{-06}T^2$
Where T is temperature in °C. Range 0°C to 100°C.

Reference: Sugar Technologists Handbook, pp 116.

### Sucrose Crystal Enthalpy

The enthalpy of sucrose crystal (this is the integral wrt temperature of specific heat). The enthalpy has been assigned a value of 0 kJ/kg at 0°C.

${{h}_{crystal}}={{h}_{0}}+1.1269*T+2.262*{{10}^{-03}}*{{T}^{2}}~+2.08*{{10}^{-06}}*{{T}^{3}}$

$\text{where T is in Centigrade}$

Reference: Sugar Technologists Handbook, pp 116.

### Sucrose Solution Specific Heat

The specific heat of pure and technical sucrose water solutions. The correlation is adapted from the Sugar Technologists Handbook. The correlation calculates a correction to the pure water specific heat as a function of purity (q %), temperature (T°C) and sucrose concentration (Ws %). This correction is then added to the specific heat for pure water to give the specific heat for the sucrose solution. The calculated specific heats match the tabulated data to within 1% over the whole range. The pure water specific heat is calculated using IAPWS_97 properties. Range 0°C to 140°C.

\begin{align} \ a_1 & = 0.0297\\ \ a_2 & = 4.6 \times 10^{-05}\\ \ a_3 & = 7.5 \times 10^{-05}\\ \end{align}

\begin{align} \text{Correction}\\ \Delta C_{p} & = -W_s \times \left( a_1 - a_2 \times q \right ) + \left (a_3 \times W_s \times T \right )\\ \end{align}

\begin{align} \text{Sucrose Solution Specific Heat, }C_{p, soln} & = C_{p,water} + \Delta C_{p} \\ \end{align}

Reference: Adapted from Sugar Technologists Handbook, pp 206.

### Sucrose Solution Enthalpy

The enthalpy of pure sucrose water solutions. The equation is the IAPWS_97 water enthalpy plus the sucrose correction for Cp integrated wrt to T. The values returned match the data in the table within 1% over the whole range. The correlation returns a correction to the water specific heat, water specific heat is calculated using IAPWS_97 properties. The enthalpy has been assigned a value of 0 kJ/kg at 0°C.

Correction for Solutes:

Sucrose Solution Enthalpy = ${{h}_{water}}\left( T,{{P}_{sat}} \right)+d{{h}_{Solutes}}$
Where:
$d{{h}_{Solutes}}=-W \times T\left( A_1-A_2 \times q \right)+A_3 \times W T^2$
$A_1 {{=}} 0.0297$
$A_2 {{=}} 4.6e-05$
$A_3 {{=}} 3.75e-05$
$T=temperature\left( {}^\circ C \right)$
$W={{W}_{s}} (\%)$
$q=Purity (\%)$

Reference: Adapted from Sugar Technologists Handbook, pp 168.

### Solubility Pure Sucrose Solutions

Sucrose solubility, WsSat(%), is the mass fraction of sucrose in solution at saturation for the given temperature and purity.

Pure solubility relation adapted from the correlations in the Sugar Tech Handbook 321/1, equations a and b. The equations were used to generate a data set from -13 to 145°C and a new curve was fit to this set of data to get a continuous function for pure sucrose over the full temperature range.

${{W}_{s}(\%)}={{C}_{0}}+\left( {{C}_{1}}*T \right)+\left( {{C}_{2}}*{{T}^{2}} \right)+\left( {{C}_{3}}*{{T}^{3}} \right)+\left( {{C}_{4}}*{{T}^{4}} \right)$

\begin{align} & \text{Where T is in Centigrade and;} \\ & \begin{matrix} {{C}_{0}}=64.35901\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ } & {{C}_{1}}=6.764212\text{E}-02 & {{C}_{2}}=2.788586\text{E}-03 \\ {{C}_{3}}=-2.295141\text{E}-05 & {{C}_{4}}=6.529764E-08 & {} \\ \end{matrix} \\ \end{align}

Reference: Adapted from the Sugar Technologists Handbook Table, pp 132,224.

### Solubility Technical Sucrose Solutions

Formulae for technical solutions are not given directly. Instead formulae for saturation coefficients, ysat, are given. The solubility of a pure sucrose solution at the given temperature is calculated and then multiplied by the saturation coefficient to correct for the effects of impurities. The saturation coefficient is a measure of the solubility of sucrose in a technical solution relative to the solubility in a pure solution at a given temperature. The saturation coefficient is defined as the ratio of the sucrose to water, (S/W), ratios in the technical and pure solutions;

${{y}_{sat}}=\frac{{{\left( {}^{S}\!\!\diagup\!\!{}_{W}\; \right)}_{sat,i}}}{{{\left( {}^{S}\!\!\diagup\!\!{}_{W}\; \right)}_{sat,p}}}$

The correlations for saturation coefficients are often themselves functions of the impurities to water ratio at saturation (for a given purity and temperature). These are generally not known before hand and are non-linear functions of impurities concentrations. Thus the calculation of solubility coefficients is an implicit calculation and requires an iterative solution. It is also worth noting here that BEET sugar and Cane sugar syrups have different solubilities because of difference in the types of impurities. Corrections for BEET sugar are given in Sugar technologists Handbook (pp 224, 342/1). Correlations for the effect of impurities at different temperatures and impurities concentrations were taken from SRI FORTRAN program. The saturation coefficient from the SRI program is given as a function of impurities to water ratio, (IW), temperature, T(C), and reducing sugar to ash ration (RS/Ash) as;

\begin{align} & A=0.01135+4.55*{{10}^{-4}}T \\ & B=0.6671+0.00208T-0.0656\left( RS/Ash \right) \\ & C=0.5425+0.00486T \\ & {{y}_{sat}}=\left( A*IW \right)+B+(1-B)\exp \left( -C*IW \right) \end{align}

The reducing sugar to ash ratio is limited to the range 0.3 to 3.0 with a default value of 1.0.

### Sucrose solubility coefficient

The ratio of the mass of Sucrose to that of water in an aqueous solution at saturation for the given temperature and purity.

$q_{sat}=(S/W)_{sat,p}$

### Sucrose Saturation Coefficient

The saturation coefficient is the ratio of the sugar to water mass ratio at saturation in a technical solution compared to that of a pure solution at the same temperature.

$y_{sat}=\frac{(S/W)_{sat,i}}{(S/W)_{sat,p}}$

### Sucrose Super Saturation

This is the ratio of the mass fraction of sugar in solution, Ws, compared to the mass of sugar in solution at equilibrium at the same temperature and purity. NB it is important to note that this is calculated at a constant purity as opposed to the Sucrose Supersaturation Coefficient which is calculated at constant I/W ratio.

$SSN=\frac{W_{s}}{W_{s,sat}}$

### Sucrose SuperSaturation Coefficient

The supersaturation coefficient is the ratio of the sugar to water mass ratio at saturation in a technical solution compared to that of a saturated technical solution at the same temperature and impurity to water ratio. NB this relation displays supersaturation in different terms than the above supersaturation measure - they are not equal. Both are useful but in different applications.

$y=\frac{(S/W)_{actual}}{(S/W)_{sat, constant(I/W)}}$

### Non-Sucrose to Water Ratio

This is the mass ratio of non-sucrose solutes (or impurities) in a solution to that of water. This is displayed both for the actual solution and for a saturated solution of the same temperature and purity.

$\left(I/W\right) and \left(I/W\right)_{sat}$

### Sucrose Solution Boiling Point Elevation

The original expression from Saska below calculates the boiling point elevation of pure and technical sucrose-water solutions as a function of Temperature T(C°), Sucrose Fraction WS(%), Purity q(%).

\begin{align} & BPE=a*{{\left( \frac{{{W}_{DS}}}{100-{{W}_{DS}}} \right)}^{b}}*{{\left( \frac{273+T}{100} \right)}^{b}}*{{\left( \frac{q}{100} \right)}^{d}} \\ & \text{where;} \\ & {{W}_{DS}}=\left( {}^{{{W}_{s}}}\!\!\diagup\!\!{}_{q}\; \right)\text{ and }\begin{matrix} a=0.166~ & b=1.1394 \\ c=1.9735 & d=0.1237 \\ \end{matrix} \end{align}

However, at very high concentrations (such as the molasses film in the drying process), the expression overestimates BPE. The revised expression below limits BPE rise at very high concentrations and is used in the model.

\begin{align} & BPE=a*{{\left( \frac{1.07*{{W}_{DS}}}{104.0-{{W}_{DS}}} \right)}^{b}}*{{\left( \frac{273+T}{100} \right)}^{c}}*{{\left( \frac{q}{100} \right)}^{d}} \\ & \text{where;} \\ & \begin{matrix} a=0.166~ & b=1.1394 \\ c=1.9735 & d=0.1237 \\ \end{matrix} \end{align}

Reference: M Saska, International Sugar Journal, 2002, 104, 1247, pp 500-507.

### Required Chemical Compounds

• H2O(l)
• C12H22O11(aq) - Sucrose in aqueous form
• C12H22O11(am) - Amorphous Sucrose in solid form
• C12H22O11(xt) - Crystalline Sucrose in solid form

## References

Most of the properties have been taken adapted from the Sugar Technologists Handbook (8th edition, Bubnik et al, 1995) with the exception of boiling point elevation which uses a more recent reference that is specific to CANE sugar solutions. A number of the solubility relations have been adapted from SRI work.

The solution properties have been developed so that they default back to pure water properties as sugar concentration goes to zero. The general approach was to use the Sugar Technologists Handbook functions to create a matrix of data over the range of interest and then calculate the difference between pure water properties and the sugar solution properties to give a matrix of corrections to water properties as a functions of temperature, sucrose concentration and purity. The functional forms were chosen so that the correction goes to zero as the sugar concentration goes to zero. This way the properties of solutions are continuous over the whole range of concentrations including down to zero.

The pure water properties have been taken from the IAPWS95 work on water and steam properties. These are generally acknowledged as the most accurate set of properties available and match the water and steam properties built into SysCAD. The water properties used are calculated for saturation conditions at the given temperature.

The pure sucrose solution properties include corrections to give technical solution properties when the purity is less than 100%. The corrections for technical sucrose solutions are in functional forms that disappear as purity goes to 100%. This gives a continuous set of properties over the whole range of concentrations and purities and a single function may be called for both pure and technical solutions. NB If no purity is entered, the default purity is 100%.

Some of the original correlations only covered certain parts of the temperature and concentration ranges. Where different correlations were given for different ranges, the original functions were used to generate a matrix of data and a single new function fit over the whole range using two or three dimensional curve fitting software. In some cases, the original functions were modified slightly so that values and slopes matched at the range boundaries. In all cases there is only one correlation spanning the range of data so that they are smooth continuous functions to help insure numerical stability for iterative calculations.

## Data Sections

### Include Sugar Species Model in a Project

In Step 1 of Edit the configuration file, select the Sugar properties model from the list as show below:

In Step 2 of edit configuration file, make sure all the required compounds (under the Model Theory section) have been added to the species list.

Save the configuration file. Make a new project (or open an existing project) using this configuration file.

### Selecting Global Property Calculation Methods

 Tag / Symbol Input / Calc Description Menu Command View - Plant Model - Globals Tab - Bayer Properties: DensityMethod List Box 1) Standard. 2) Sugar1 SpecHMethod List Box 1) Standard. 2) Sugar1 BPEMethod List Box 1) Standard. 2) Sugar1 Sugar.ShowExtra Tick Box Selecting this will allow the user to view the Density, Cp and BPE calculated using the Sugar Properties model regardless of method chosen (above). Note these properties are for display purposes only, can be used to compare property calculation values between methods.

### Selecting a Sugar Species Model in a Feeder

The user must have a project that includes a Sugar species model in the configuration file. It is then possible to select the Sugar model. On the Feeder access window there is a field on the Contents Tab - 'Model (Reqd)' or 'Model (Inherit)' where the user may select the model, as shown below:

 Tag / Symbol Input / Calc Description Model Input Inherit - Model used follows upstream units. Standard - All the variables are calculated using the Mass Weighted Mean of the species. Sugar - Density, Specific Heat, Enthalpy, Solubility, Boiling Point Elevation, etc calculated using the equations defined for that sugar species model.

### Sugar Properties

NB These properties are for solutions only - these do not include any solid species in the calculations. For Bagasse where there is bound water associated with the fibre, the water must be taken into account in calculating properties such as Bagasse Brix (fibre is generally reported as dry fibre). For Massecuite where there is crystalline sucrose present, the general assumption is on the basis that is has been dissolved into solution. User calculations can be implemented in the configuration file #Calculation_Configuration to display properties referenced to Massecuite and Bagasse .

 Symbol Tag Input / Calc Description --- Sugar Properties --- Ws SucroseMassFraction Calc Mass Fraction of Sucrose in Solution. Wds BRIX Calc Mass fraction of total soluble solids in an aqueous sucrose solution or dry solids. Purity Purity Calc The mass ratio of sucrose to the total soluble solids in an aqueous sugar solution. WsSat SucroseSaturation Calc Sucrose Solubility - The mass fraction of a sucrose in a saturated solution at the given temperature and purity. SSN SucroseSuperSat Calc The mass ratio of sucrose in a solution to the mass of sucrose in a saturated solution at the same temperature and purity.[SuperSat=Ws/WsSat] SW SucroseWaterRatio Calc The mass ratio of sucrose to water in an aqueous sucrose solution. SWsat solubility coefficient Calc The mass ratio of sucrose to water in an aqueous sucrose solution at saturation for the given temperature and purity. SSNCoeff SuperSatCoeff Calc The ratio of the mass of sucrose to water in an aqueous sucrose solution to that of a saturated solution at the given temperature and impurities to water ratio. IW SatImpurityWater Calc The mass of non-sucrose solutes to water in an aqueous sucrose solution. IWsat solubility coefficient Calc The mass of non-sucrose solutes to water in an aqueous sucrose solution at the given temperature and purity. BPE BoilPtElev Calc Sucrose Solution Boiling Point Elevation --- Sugar Specific Properties --- (Visible only if the Sugar.ShowExtra tick box has been selected on View|PlantModel|Globals Tab. Sugar.LRho Display Only Shows the Liquor Density at Temperature calculated using the Sugar Property Correlation. Sugar.LmsCp@T Display Only Shows the Liquor Specific Heat at Temperature calculated using the Sugar Property Correlation. Sugar.LmsHs@T Display Only Shows the Liquor Enthalpy at Temperature calculated using the Sugar Property Correlation. Sugar.LmsBPE Display Only Shows the Liquor Boiling Point Elevation calculated using the Sugar Property Correlation.