# Sugar Crystalliser

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## General Description

The Sugar Crystallizer unit operation is available with the Sugar add-on.

The sugar crystallizer is used to precipitate aqueous sugar from molasses onto existing sugar crystals. The SysCAD sugar crystallizer unit operation can be used to represent a single channel, chamber, stage or pass in a larger sugar crystallizer. Multiple SysCAD crystallizer unit operations can linked together to create more complex crystallizer models as required.

Massecuite is fed into the crystallizer which may also have an additional molasses stream or dilution water fed it. The model also has optional connections for both cooling water and for heating water. An optional vent connection removes any vapors from the system. The residence time in the unit is defined by its geometry (volume) and the mass flow through the unit. There are different options to describe precipitation rate and a temperature profile may be imposed. There is a single product stream exiting from the unit.

A numerical solution is found by dividing the volume into a user specified number of independent segments. The process is modeled as a series of continuous well stirred tank reactors (CSTR). The flow into each segment is assumed to be perfectly mixed with the contents of the segment. Massecuite properties and precipitation rates are calculated at the outlet conditions from each segment.

A linear temperature profile for the unit may be specified. The outlet temperature may be specified either as a fixed temperature or as a temperature difference from the feed temeprature. The temperature is assumed to vary linearly from the feed temperature to the outlet temperature. If molasses or dilution is added at some point along the unit, then a new linear temperature profile is calculated from that point to give the target outlet temperature. The temperature profile may be specified even if there is no cooling or heating water to the unit. The amount of heating or cooling required to give the temperature profile is always calculated and displayed. If an optional heating or cooling stream is connected, this amount of heat will be removed or added from the appropriate stream and the heating or cooling outlet stream temperature will be adjusted accordingly. This allows crystallizer thermal demands to be accurately included in plant models.

A heat loss option is included that allows heat loss from the unit. Environmental heat loss is calculated and displayed for information and it is also included in the heating or cooling load calculations. The environmental heat loss is essentially a side calculation which is used to adjust the heating or cooling load to improve the accuracy of thermal modeling.

The number of sugar crystals is assumed to be constant through the unit and the precipitation of sugar is defined by the growth rate of those crystals. The crystal population is described by a mean equivalent diameter and a coefficient of variation. Growth rates are calculated in microns per hour. The change in the coefficient of variation through the process may be calculated as an option and dispersion may also be optionally included in the calculation.

There is an option for grid data display so that data for up to 256 points may be displayed. The actual number of increments allowed is limited to 2000 (this should be many more than is necessary - additional increments only serve to slow computation - somewhere around 30 to 50 segments should be about optimal). If there are more segments used than display points, the display points are evenly spaced.

## Input and Output Connections

A number of the inputs and outputs for the sugar crystallizer are optional. You connect the ones that you want to use depending on how you want the unit to operate.

 Label Required / Optional Input /Output Number of Connections Description Min Max. Feed Required In 1 5 Massecuite Feed to the Cystallizer. Molasses Optional In 0 1 Additional Molasses stream. DilnWater Optional In 0 1 Dilution Water stream to Crystallizer. CoolingIn Optional In 0 1 Cooling Water into Crystallizer. CoolingOut Optional In 0 1 Cooling Water out of Crystallizer. HeatingIn Optional In 0 1 Heating Water into Crystallizer. HeatingOut Optional In 0 1 Heating Water out of Crystallizer. Product Required Out 1 1 Massecuite stream out of Crystallizer. Vent Optional Out 0 1 Vent outlet containing all Vapors - NB required if there are vapors present.

## Behavior when Model is OFF

The sugar crystallizer may be turned Off by de-selecting the On tick box in the access window. When the unit is off the following behavior occurs:

• All input streams (Feed, Molasses and Dilution Water) are perfectly mixed and exit via the product stream. Energy is conserved and product temperature will be adjusted accordingly. NB any gases in any of the input streams will remain with those streams when the unit is off and are not sent to vent.
• There is no heat exchange and cooling and heating water exit at their respective inlet temperatures.

## Model Theory

### Environmental Heat Exchange Options

The sugar crystallizer may lose heat to the environment. The heat loss options are set from a drop down list and include;

1. None - No Heat Exchange occurs.
2. Fixed_Loss - A Heat Flow Rate to the Environment is specified by the user.
3. Ambient - A Heat Loss Constant is specified and heat loss is calculated as heat loss constant times the temperature difference between the product stream and ambient temperatures, Qloss = Constant * (Tprod - Tamb).

The Heat Flow is displayed for all options and heat flow from the crystallizer to the environment is positive in sign.

NB If a negative heat flow is reported, it indicates heat flow to the crystallizer from the environment.

### Physical Model

The crystallizer model follows the flow of massecuite through the crystallizer.

The only required input stream to the crystallizer is the Feed stream. The optional inputs include Molasses Addition, Dilution Water, Cooling Water and Heating Water streams.

The only required output stream is the product stream. However, when there are gases in any of the input streams a Vent stream is also required. The optional output streams are the Cooling Water and Heating Water outlet streams.

Geometry - The Crystallizer is modeled as a series of equal volume segments. For calculations the crystallizer is specified only by its volume and the number of segments it is divided into. The number of segments is user defined. Flow in the crystallizer is assumed to be plug flow and move from one segment to the next with no forward or backward mixing. The residence time in any segment is determined by the volume of the segment and the volumetric flow rate of massecuite (at the exit conditions). There is a Residence Time Efficiency parameter which effectively adjusts the working volume and can be used to account for the effects of by-passing or loss of working volume. The length of the unit may also be entered and a cross sectional area will be calculated from the length and volume and displayed. These data are not used for any calculations, but are displayed for information only. The X-distance is displayed in the grid data.

Shear - The shear rate is entered as a user defined input. The units of shear are per second.

Feed - All feed streams to the crystallizer are assumed to mix perfectly. The feed must be a sugar type stream, must contain some aqueous sucrose and must have some sugar crystal or a warning will be displayed.

Molasses Addition - A molasses stream may be added anywhere along the length of the crystallizer unit. The addition point is specified as percentage of the length or of the progress through the unit (i.e. 50% means molasses is added halfway through). When molasses is added, it is assumed to go into one segment (as defined by the length %) and mix perfectly with the contents of that segment. A molasses stream is not required. The molasses stream is not checked for composition and it may have solids content. The mass flow of molasses is shown in the grid display.

Dilution Addition - Dilution water may be added to the crystallizer. The dilution may be added either as a point addition (all into one segment and mixing perfectly with the contents) or it may be added as a spray across the whole unit. When it is added as a spray, it is assumed that an equal amount of spray is added to each segment and mixed perfectly with it contents. The addition of of dilution is optional and the composition of the dilution is not restricted to pure water (i.e. it could be a dilute molasses stream) and it may also contain solids. NB any solids in either the molasses or dilution streams are accounted for in the crystallizer calculations.

Temperature Profile - The crystallizer may be heated or cooled during operation and may also exchange heat with the environment. There is an option to impose a linear temperature profile through the unit. The product temperature is either set explicitly or set as a difference from the feed temperature. The temperature profile is assumed to change linearly from the inlet to the product. If a side stream comes in and changes the temperature of a segment when it mixes in, then the rate of temperature change is recalculated to give a linear drop from that point to the target temperature. when a spray is used for dilution, the required temperature drop is recalculated at each step. The plot below shows temperature profiles for a crystallizer with the same amount of cold dilution water being added as a spray and as a point source. The start and finish temperatures are the same, but the paths are somewhat different depending on how the water is added.

A fixed temperature profile is used because heat transfer is difficult to calculate explicitly for these very viscous sugar-molasses slurry flows. However, the model does calculate the amount of heat that would be transferred to heating or cooling streams and the environment which allows modeling the impact of the crystallizer on plant energy demands. When heating or cooling streams are connected, the appropriate amount of heat is added or removed from the streams. NB the temperature profile is followed and the heat transfer is calculated even when there are no heating or cooling streams connected (see details below).

Environmental Heat Transfer - Environmental heat transfer is included in the model. It does not enter into the calculation of the temperature profile, but it is included in the heating and cooling load calculations.

Heating and Cooling Water - There are separate connections for cooling water in and out and for heating water in and out. If a cooling or heating stream in is connected, then a cooling or heating stream out must be connected or a warning is issued. The amount of energy absorbed or released to follow the temperature profile is calculated and then adjusted for any environmental heat transfer. If there is a net excess of heat, then this amount of heat is assumed to be removed by cooling water and if a cooling water stream is connected, then this amount of heat will be added to the cooling water so that it leaves hotter. Similarly, if there is a net deficit of heat, then it is assumed to be provided by heating water and if a hot water stream is connected, this amount of heat will be removed from the stream and it will leave colder. A warning is issued when there is insufficient water flow or when the water supply temperature is too hot or too cold for the required application.

Gases - Any gases present in any of the input streams are split off and go to the vent stream. If there is no vent attached, the gases are sent out with the product stream and a warning is displayed that there are gases present, but no vent.

### Crystallization Model

The crystallizer volume is divided into a series of equal volume segments. The segments are solved sequentially with any side streams coming in assumed to mix perfectly and the temperature of each segment matching the required temperature profile.

In general the contents of any segment will be supersaturated in sucrose and sucrose precipitation will occur onto the existing crystals. It is assumed that the supersaturation is low enough that there is no homogeneous nucleation and that there is no breakage, thus the number of sugar crystals is conserved. It is further assumed that the growth rate of the crystals is size independent.

The massecuite at any point is characterized by the molasses composition, the temperature, crystal mass fraction, crystal size and CV.

#### Particle Size Distribution

The particle size distribution of the sugar crystals throughout this process is characterized using a moment description. A normal distribution is assumed so that a volume equivalent size (diameter or U1) and a coefficient of variation (CV) are sufficient to fully describe the distribution. The second and third moments (area is proportional to the second moment and volume proportional to the third moment) may be found from:

$U1$

$U2 = U1^2 \left(1 + CV^2\right)$

$U3 = U1^3 \left(1 + 3 CV^2\right)$

#### Particle Growth

The segments are treated as a series non-nucleating crystallizers with size independent growth. When the segment residence time is small, the change in the moments between the inlet and outlet is given by;

• $\text{Growth, } GRDT=\left(\text{Growth Rate, }GR\right) \times \left(\text{time increment, } \Delta t\right)$
• $U1_o=U1_i+GRDT$
• $U2_o = U2_i + GRDT \left(2U1_i + P\right) + GRDT^2$
• $U3_o=U3_i + 3GRDT\left(U2_i + P\times U1_i\right) + 3GRDT^2\left(U1_i + P/2\right) + GRDT^3$

Where P in the above equations is the dispersion coefficient which accounts for the widening of distributions due to randomness in growth velocities. The dispersion (in units of microns) is calculated based on the impurities in the molasses and growth rate, GR, as;

• $\text{If } GR\lt 0 \text{, then }P_{}=-100$
• $\text{Else }P=Max\left\{100, \cfrac{10,000}{GR\times exp(0.92\, ItoW)}\right\}$

Where ItoW is the mass ratio of impurities to water in the syrup. The value of dispersion is limited to a maximum value of 100. The SysCAD crystallizer has a user selectable option to use dispersion or not (in which case P is set to 0).

The relative change in crystal mass (which can be used to calculate the amount of sucrose precipitating out of solution) is given in terms of the third moment by;

• $\cfrac {Mass_o} {Mass_i}= \left( \cfrac {U3_o} {U3_i} - 1 \right)$

The CV at the segment outlet after growth can be calculated from the new first and second moments by;

• $CV=\cfrac{\left(U2_o - U1_o^2\right)^{0.5}}{U1_o}$

NB The SysCAD crystallizer has an option to allow CV to be held constant or to vary according to the above relation ( a new CV is calculated at based on the new U1 and U2 after growth).

The new syrup composition, crystal mass, CV and U1 are the starting input for the next segment.

There are three options for crystal growth - none, fixed growth rate and the SRI Growth Method.

### Particle Growth Models

#### None

There is no crystal growth and no change in composition except for mixing with any molasses or dilution side streams. The crystal size distribution is unchanged through the unit.

### Fixed Growth Rate

The growth rate of crystals is assumed to be a user input fixed rate with this option. Precipitation of sucrose in each segment will occur at the rate required to give the specified time rate of change in diameter regardless of any other parameters (such as supersaturation). Growth will continue until the molasses is depleted (or almost depleted) of sucrose. The crystal size distribution is described by the moment equations.

#### SRI Growth Model

The SRI model for growth rate uses the moment description and calculates a growth rate as a function of sucrose supersaturation in the molasses, mass transfer and diffusion rates. The SRI method calculates a minimum supersaturation for precipitation to occur. When supersaturation is greater than one and less than this minimum, there is no growth. This method also allows for dissolution of existing crystal when supersaturation is less than one.

The calculated growth rates with this model are strongly dependent on impurities concentrations. Temperature and supersaturation also have a strong influence. This model was developed to apply over a specific range of conditions and predicted growth rates outside of this range can be much larger than expected in reality. The model has an option to limit the maximum growth rate used in calculations. Typical values for crystallizer growth rates are about 2 um/h. The model default maximum value is 10 um/h and the upper limit to which this can be set is 50 um/h.

NOTE: Equations for the Growth model is only available via download from SysCAD Website for users with current maintenance contracts.

## Flow Chart

The process is shown schematically in the flow chart below for a crystallizer with n segments. The segments are numbered 1 to n. Molasses is shown entering at segment i and dilution at segment j, but in the model molasses and dilution may be added in any order and may also go to the same segment. Gases are sent to a vent and any cooling load, heating load or environmental heat loss is a side calculation.

## Data Section

### Sugar Crystallizer Access Page

Unit Type: SugarCrystalizer - The first tab page in the access window will have this name. Configuration, heat transfer and side stream connection inputs and results are displayed on this page.

Tag / Symbol
Input / Calc
Description
Common Data on First Tab Page

#### Requirements

On Tickbox Tickbox used to turn the unit ON or OFF (off behavior is described above).
TrackStatus Tickbox Option to display warnings.
ShowQFeed Tickbox Tickbox to display or hide Feed data tab.
ShowQProd Tickbox Tickbox to display or hide Product data tab.
Dimensions
VesselLength Input Length of Crystallizer (NB information only).
VesselVolume Input Volume of Crystallizer (NB required for residence time calculations).
CrossSectArea Display Cross Sectional Area of Crystallizer (NB for information only).
AvgShearRate Input Average Shear rate from paddles or agitators [1/s].
Segments for Numerical Solution
Segments Input Number of segments to use for solution (maximum = 2000).
IncrementLength Display Length of each segment.
ResidenceTimeEff Input Residence Time Efficiency - adjusts effective working volume.
IncResidenceTime Display Average residence time in each segment.
TotResidenceTime Display Total Residence time through unit.
Environmental Heat Loss
EnvLossMethod None No heat exchange with the environment.
FixedLoss User specified heat loss rate.
Ambient Heat loss determined as a constant times temperature difference from ambient. Qloss = EnvLossAmbient * (Tprod - Tamb)
EnvLossRqd Input The Required Heat Loss Rate - This is only visible if the FixedLoss Method is selected.
EnvLossAmbient Input The Heat Loss Rate Constant (kW/K) - This is only visible if the Ambient Method is selected.
EnvHeatLoss Display Heat flow to the environment (positive value is heat flow from crystallizer to Environment.).

#### Temperature Profile

TempProfileMethod None Product and all Segment Temperatures equal to Feed Temperature.
Fixed_Delta_T User specified temperature change between feed and product (Tprod - Tfeed).
Set_Product_T User specified product temperature.
DeltaT_Rqd Input The Required temperature change (only visible if the Fixed_Delta_T Method is selected).
DeltaTemperature Display Temperature change between Feed and Product (Tprod - Tfeed).
FeedTemperature Display Feed Temperature to Crystallizer.
Product_T_Rqd Input User specified product temperature (only visible if the Set_Product_T Method is selected).
ProductTemperature Display Product temperature from crystallizer.

These are the calculated loads required to match the specified temperature profile.

TotalHeatXfer Display Total heat transfer from crystallizer.
EnvironHeatLoss Display Heat loss to environment.
CoolingWaterQm Display Cooling water Mass flow in.
CoolingWaterTin Display Cooling water temperature in.
CoolingWaterTout Display Cooling water temperature out.
HeatingWaterQm Display Heating water mass flow.
HeatingWaterTin Display Heating water temperature in.
HeatingWaterTout Display Heating water temperature out.

MolassesAddX Input Location for molasses addition input as percent of length through the crystallizer.
MolassesAddL Display X location of molasses input.
MolassesQm Display Mass flow of molasses added.
MolassesT Display Temperature of molasses added.
MolassesBrix Display Brix of molasses added.
MolassesPurity Display Purity of molasses added.

Spray Tickbox When ticked ON Dilution is added as an even spray over the whole length of the crystallizer.
DilutionAddX Input Location of dilution addition as percent of length through the crystallizer (not displayed when Spray is selected).
DilutionAddL Display X location of dilution input (not displayed when Spray is selected).
DilutionAddi Display Segment number of dilution addition (not displayed when Spray is selected).
DilutionQm Display Mass flow of dilution added.
DilutionT Display Temperature of dilution added.
DilutionBrix Display Brix of dilution added.
DilutionPurity Display Purity of dilution added.

### Crystallization Access Page

The second tab has the name Crystallization and has inputs and results for the crystal growth process.

Tag / Symbol
Input / Calc
Description

#### Feed Crystal diameter

DiaMethod Stream_DIA Use diameter from feed stream.
User_DIA User specified diameter.
InputDiameter Input User specified crystal diameter of feed (only displayed when User_DIA is selected).
StreamDiameterIn Display Crystal diameter of feed.
StreamDiameterOut Display Crystal diameter of Product.

#### Feed Size Distribution CV

CrystalCVin Input CV of feed crystal size distribution
CrystalCVout Display CV of product crystal size distribution
UseDispersion TickBox Option to use dispersion in growth equations.

#### Crystal Growth Model

DiaMethod None No crystallization.
Fixed_Growth_Rate User specified fixed precipitation rate.
SRI_Growth SRI Growth Rate Model.
FxdPrecipRate Input User specified crystal growth rate (only displayed when Fixed_Growth_Rate Method is selected).
GRM Input User specified growth constant for SRI method, default value is 1.09 (only displayed when SRI_Growth Method is selected).
MaxGR Input User specified maximum growth rate for SRI method, default value is 10 um/h (only displayed when SRI_Growth Method is selected).

#### Crystallization

AvgGrowthRate Display Average crystal growth rate through the crystallizer.
AvgPrecipRate Display Average mass precipitation rate through the crystallizer.

#### Feed Massecuite

FeedQm Display Total Feed mass flow rate.
FeedCrystalFrac Display Feed Crystal mass fraction.
FeedMassecuiteVisc Display Feed Massecuite viscosity.

#### Feed Molasses

FeedT Display Feed Temperature.
FeedWs Display Feed Molasses sucrose fraction.
FeedBrix Display Feed Molasses Brix.
FeedPurity Display Feed Molasses purity.
FeedItoWratio Display Feed Molasses Impurities to Water mass ratio.
FeedMolassesVisc Display Feed Molasses viscosity.
FeedSSN Display Feed Molasses sucrose supersaturation.

#### Product Massecuite

ProdQm Display Total Product mass flow rate.
ProdCrystalFrac Display Product Crystal mass fraction.
ProdMassecuiteVisc Display Product Massecuite viscosity.

#### Product Molasses

ProdT Display Product temperature.
ProdWs Display Product Molasses sucrose fraction.
ProdBrix Display Product Molasses Brix.
ProdPurity Display Product Molasses purity.
ProdItoWratio Display Product Molasses impurities to water mass ratio.
ProdMolassesVisc Display Product Molasses viscosity.
ProdSSN Display Product molasses sucrose supersaturation.

#### Vent Mass Flow

VentQm Display Mass flow of Gases to Vent connection.

#### Display Segment Data

ShowSegmentData TickBox Option to display a data grid - when ON adds Data tab for grid data display.
Segment.Total Display Number of segments used for numerical solution.
Segment.Display Input Number of data points to display - maximum is 256 and must be < (Segment.Total + 1). When display number is less than total. not all data points are displayed.

### Data Access Page

When the tick box ShowSegementData is selected a tab named Data appears and displays a matrix of results for segments through the process. Data is displayed sequentially in columns with feed at the top and product at the bottom. The data are for the exit properties of the segments.

 Column Heading Data Display Display name - part of full tag address for the data. Segment Segment number being displayed in the row. Time Residence time through to (and including in) the displayed segment. Temperature Temperature in the segment. MolPurity Molasses purity in the segment. XtalFrac Crystal mass fraction of the segment. Diameter Crystal diameter in the segment. MolVisc Molasses (liquid only) viscosity in the segment. MassVisc Massecuite (slurry) viscosity in the segment. MolAdded Running total mass of molasses added up to and including the segment. DilnAdded Running total mass of dilution added up to and including the segment. GrwthRate Crystal growth rate in the segment. SSN Sucrose supersaturation in the segment. SSlim Limiting supersaturation for crystal growth in the segment. Brix Brix of the molasses in the segment. ItoW Impurities to Water Mass ratio of the molasses in the segment. Distance Distance from feed inlet to the segment. CV CV of the crystal in the segment. Dispersion Dispersion factor used in calculations in the segment.

### Warnings

 Warning Message Comments Vapor in Feed or Side Streams and NO Vent Connected When vapors are present in any input stream a vent stream must be connected. No Sucrose(aq) in Feed - Check Stream Compositions The feed stream must contain some aqueous sucrose. No Crystal in Feed - Check Stream Compositions The feed stream must contain some solid sugar crystal. Feed is not a Sugar Species model The feed stream must be a sugar stream. Cooling Water Connection Missing Cooling water connection with no cooling water connection out. Heating Water Connection Missing Heating water connection with no heating water connection out. Insufficient Cooling Water Qm for Required Heat Load Cooling water is too warm or there is insufficient flow to carry away the required heat load. Insufficient Heating Water Qm for Required Heat Load Heating water is too cool or there is insufficient flow to supply the required heat load. Crystallizer Volume Incorrectly Specified Volume should be greater than 0.1 cubic meters. Crystallizer Length Incorrectly Specified Length should be greater than 0.1 meters.

## Adding this Model to a Project

Insert into Configuration file

Sort either by DLL or Group.

 DLL: SugarUnits.dll → Units/Links → Sugar: Sugar Crystallizer or Group: Sugar → Units/Links → Sugar: Sugar Crystallizer