Sugar Dryer

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General Description

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

The sugar dryer is a counterflow dryer used to cool and dry sugar crystals in the final stage of processing. The dryer receives hot sugar crystal feed into one end. Air enters the other end of the dryer and flows in the opposite direction to the sugar.

The hot sugar crystal feed is coated with a film of molasses and as the sugar moves through the dryer heat is transferred from the sugar to the air and water evaporates from the sugar into the air. As water evaporates the concentration of sugar in the molasses film increases, the solubility of the sugar decreases and some of the aqueous sucrose in the film precipitates onto the existing sugar crystals. The change in the molasses film properties with increasing concentration due to evaporation and decreasing purity as sucrose precipitates affects the partial pressure of water and thus the evaporation rate of water from the film to the air and also the precipitation rate of sucrose from the film to the crystal. This is all taken into account in the model.

The model also has the option to add a water spray to the feed to allow adjustment of the final the moisture content of the sugar.

NB The model iteratively solves a finite element problem to find a solution. This is computationally expensive and can slow down the overall project so it is recommended that the dryer unit operation is only switched on after the rest of the circuit is solved.

Operation

The dryer is an inclined cylindrical kiln type dryer which rotates and generally include lifts which pick up sugar and drop it through the air stream to increase contact area with the gas stream. Air flow is normally ambient air which is drawn or forced through the dryer.

The sugar feed is high purity sugar crystals covered with a film of molasses. The mass fraction of molasses is in the order of several percent of the total mass and the moisture fraction in the order of one percent of the feed. The sugar particles are typically in the range of 0.5 to 1 mm. Although the sugar has a relatively high surface area per unit mass, only approximately 10% to 20% of the surface area is in active contact with the gas stream at any one time. The surface area of the sugar is calculated from diameter and coefficient of variation, the active area fraction is an input into the model.

Sugar in active contact with the air loses heat to the air through convective heat transfer and water via convective mass transfer (evaporation). The sugar crystal is pure (or almost pure) sucrose. The molasses film is an aqueous mixture of water, sucrose and impurities. As the molasses loses water, the sucrose concentration in the film increases and as the molasses loses heat, the sucrose solubility decreases. The molasses is generally close to saturation at the start of the drying process and with evaporation and cooling the molasses film becomes supersaturated in sucrose near the inlet of the dryer. Sucrose precipitation begins there and generally continues through the rest of the dryer process. As sucrose precipitates, the purity of the molasses decreases and as evaporation occurs the concentration of solutes increases which increases the boiling point elevation of the molasses film and slows evaporation.

Depending on the temperature and moisture of the feed sugar and the temperature and humidity of the air, water may be added to the feed sugar to control the final moisture content of the sugar to prevent over-drying.

The model also includes options for environmental heat loss from the dryer which may have a significant effect on the dryer operation. When the total heat loss rate is specified, the heat loss is divided uniformly between all of the segments and taken 50/50 from the sugar and the air in each segment. When heat loss to ambient method is selected, the heat losses from the air and sugar are based on the heat loss coefficient and the temperature difference from ambient at each segment.

Numerical Solution

The dryer model is solved by breaking it into a series of segments and solving the combined heat and mass transfer problem in each of the segments. A relaxation technique is used to solve the counter flow problem. Convergence is based on relative change between iterations. The number of segments is user selectable and up to 500 segments are allowed. However, there is generally no need for more than 50 segments and typically 30 to 50 is sufficient for accuracy.

There is an option to add damping. In general damping is not required and will slow down convergence. However, when temperature differences are large or heat transfer coefficients are very high then some damping may help (suggested values for damping are in the range of 0.1 to 0.25).

The dryer model solves a complete numerical finite element model at each iteration step. The model saves the last converged solution and uses that as its starting point so when there is no change from the last step, it will take only one step to converge and when there is only little change from the last step, convergence is usually fairly quick.

It is important to note that this model may consume a significant amount of computation time to solve at each step. Using a large number of segments may take some ten's of seconds or more to solve. There are some controls which can be used to optimize the solution speed. However, when the dryer unit is part of a larger process model it is possible that it can slow down the overall model. Given that this unit is generally at the end of the process and there is no recycle through it, a better approach may be to either use a small number of segments or to turn the unit off until the rest of the model is solved and then turn it back on - that way it will only need to solve once.

Input and Output Connections

A sugar stream and an air stream are required connections. The sugar stream must contain sugar crystal and have the specific surface area (SSA) quality present or an error is displayed. The sugar feed stream should not contain any gases. There are no specific checks built in for the air stream although it should contain only gases. The air stream may defined with water vapour and the pseudo-species Air or it may be defined in terms of the individual gas species. There may be up to five sugar feed streams. There is only one air stream connection allowed.

There is only one air flow and one sugar flow out of the dryer.

There is an option for a water addition stream to the sugar feed. Although it would normally be expected to be pure water, there are no restrictions on the added water composition other than it may not contain any vapours. It could contain aqueous sugar or impurities and can contain some solids. The added water is assumed to mix perfectly with the molasses film and any solutes or solids are included in the calculation of the solution.

 Label Required / Optional Input /Output Number of Connections Description Min Max. Feed Required In 1 5 Sugar Crystal Feed to the Dryer. Air Required In 1 1 Air Flow to the Dryer. Water Addition Optional In 0 1 Added Water Feed to the Dryer. Dried Sugar Out Required Out 1 1 Sugar out of the Dryer. Exhaust air Required Out 1 1 Air Flow out of the Dryer.

Behavior when Model is OFF

The sugar dryer may be turned Off by deselecting the On tick box in the access window. When the unit is off the following behavior occurs:

• All Feed material and any added water will flow through to the Product Sugar Stream with no changes or heat exchange.
• The air stream in will flow through unchanged with no heat exchange or mass transfer from the sugar stream.
• There is no environmental heat transfer.

NB any gases in either feed or wash water streams will remain with those streams when the unit is off.

Environmental Heat Exchange Options

The sugar dryer may lose heat to the environment. The heat loss is taken from both the air and sugar streams. How the loss is accounted for depends on the method chosen.

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. The heat loss is assumed to be taken evenly over all the segments the

loss is assumed to come evenly from both the sugar and the air streams. For example, if there are 50 segments, then the loss per segment is 1/50 of the total heat loss specified with 1/100 coming from each stream.

1. Ambient - An overall 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 loss is calculated individually for each segment and individually for the air and sugar streams. For example if there are 50 segments, then the heat loss from the sugar stream in segment(i) is; Qloss(i) = (0.5) * (1/50) * Constant * (Tsugar(i) - Tamb)

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

Model Theory

The model follows the flow of sugar and air through dryer stages.

Feed - All feed streams are assumed to mix perfectly. Any added water is assumed to mix perfectly with the molasses film on the sugar crystals. Sugar crystals are required to be present in the feed stream and the molasses film must be a Sugar type stream.

Air - The air stream in is characterized by its mass flow, temperature and water content.

Area - Each segment in the dryer has an active surface area for heat and mass transfer that is calculated from the solids mass flow rate, retention time in the dryer, the characteristic particle diameter, the coefficient of variation (CV) of size distribution of the feed crystal and the active surface area fraction. The active area fraction accounts for the fact that only a fraction of the sugar is exposed to the air stream at any one time and the rest is buried below the surface of the sugar. A typical active area for a dryer is in the order of 1,000 to 20,000 m^2. The total area is estimated as;

$Total Area= \frac{\left(RetentionTime \times Qm_{solids} \times 6.0 \times \left(1.0 + CV^2\right) \right)} {\left(Diameter \times Rho \times (1.0 + 3.0CV^2)\right)}$

And the active area per segment is;

$Area= \left(Total Area\right) \times \frac{\left(Active Area Fraction \right)} {\left(Number of Segments \right)}$

Heat Transfer

Convective heat transfer is calculated as;

$Q_{hex} = h \times Area \times \left( T_{slurry} - T_{gas} \right)$

The heat transfer coefficient, h, is a user input. Typical values of h for a sugar particles falling in a gas stream or in the order of 1 W/m^2.K to 10 W/m^2.K. The literature suggests a value of about 4 W/m^2.K for a typical application.

Evaporation

Mass transfer from the surface of the molasses film is a function of the saturation pressure of the water in the film, the partial pressure of the water in the air stream and the mass transfer coefficient, hm. The mass transfer coefficient may be estimated from the film coefficeint, h, using heat and mass transfer analogies.

$\frac{h}{h_m} = \frac{k}{D_{AB}Le^n}$

Where h is the heat transfer convection coefficient, hm is the mass transfer coefficient [m/s], k is thermal conductivity, DAB is the binary diffusivity and Le is the Lewis number - all evaluated at the film temperature. The mass transfer is then;

$Q_{m} = h_m \times Area \times \left( \rho_{slurry} - \rho_{gas} \right)$

where ρslurry is the saturation density of water vapor in the slurry and ρgas is the density of water vapor in the gas stream. The saturation pressure for water vapour over the high concentration, low purity molasses is given by;

$Z_1 = \frac{100\times(W/I)\times \left(100-Purity(\%)\right)}{50}$

$Z_2 = 0.01\times \left(51.2\times log_{10}\left( Z_1\right) - 25.0 \right)$

$P_{sat} = P_{sat,pure H_2O} \times Z_2$

If evaporation rates are high compared to the diffusion rate of water through the molasses, then the surface of the molasses coating the crystals may have less water water and a higher sugar content which will reduce the vapor pressure of water and slow the evaporation rate. To account for this there is an optional correction term in the evaporation rate calculation. The correction for segment i is of the form;

$C_1* \exp \left(\frac{-C_2 \times t_{res} \times i }{segments}\right)$

Where C1 is a constant (generally about 1), C2 is the diffusion rate of sucrose in water (~0.0035), tres is the residence time in the dryer and i is the segment number and segments is the total number of segments. This correction makes the evaporation rate taper off towards the end of the dryer. NB Setting C1 to 1 and C2 to zero will make the correction term equal to 1 and take it out of the calculations.

Crystallization

As the sugar cools and water evaporates, the molasses coating the sugar crystals will become supersaturated in sucrose and sucrose will precipitate onto the sugar crystals. The mass rate of precipitation is the growth rate times the area available for precipitation. The growth rates is given by;

$E_a = 15 - 0.2\times\left(T(K)-333.15\right)$

$FT = \frac{-E_a}{0.001987} \times\left(1/T(K)-1/333.15\right)$

$\text{Growth Rate (m/s)} = 0.00000206\times\left(SSN - 1.0046\right)\times\exp\left(FT - 1.75*I/W\right)\times GrowthFactor$

Where I/W is the impurity to water mass ratio, GrowthFactor is a tuning parameter (with a default value of 0.4) and the supersaturation, SSN, is given by;

$SSN = \frac{M_{sucrose}\times \left(100-PureSol(\%)\right)}{M_{water} \times PureSol(\%)\times\left(1.0-0.088I/W\right)}$

and PureSol(%) is the solubility of pure sucrose in water.

The area for precipitation in a segment is;

$Area=\frac{Qm_{sugar}\times t_{res} \times6\times\left(1+CV^2\right)}{\rho_{crystal}\times Dia_{crystal}}$

The precipitation rate is;

$Qm_{precip}= Area\times GrowthRate \times ResidenceTime$

Sugar Dryer Access Pages

SugarDryer

Unit Type: SugarDryer - The first tab page in the access window will have this name. User inputs and results are displayed on this page.

In general, the control inputs are defined in terms of parameters that are normally measured in sugar factories.

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 Option to Massecuite Feed Stream.
ShoqQProd Tickbox Option to display Dried Sugar Stream.

Numerical Solution

MaxIterations Input
Iterations Display Maximum number of iterations (suggest ~50)
Damping Input Damping factor (suggest ~ 0.2)
Tolerance Input Relative Tolerance for convergence (suggested range 5e-05 to 1e-06)
Segments Input Number of segments to use for numerical solution (suggest 30 to 50)

Display Segment Data

ShowSegmentData Tickbox Option to display a matrix of data for the solution
Segment.Total Display total number of segments.
Segment.display Input Number of segments to display (max = Segment.Total+2 or 256)

Residence Time

ResTime Input Total residence time in dryer
SegResTime Display Residence time in individual segments

Surface Area

TotArea Display Total calculated surface area of crystals
ActiveFrac Input Active fraction of surface area (exposed to gas stream)
ActiveArea Display Active surface area

Environmental Heat Loss

Method None No heat exchange with the environment.
Fixed_Loss User specified heat loss rate.
Ambient Heat loss determined as a constant times temperature difference from ambient. Qloss = ThermalLossAmbient * (Tprod - Tamb)
EnvLossRqd Input The Required Heat Loss Rate - This is only visible if the Fixed_Loss Method is selected.
EnvLossAmbient Input The Heat Loss Rate Constant (kW/K) - This is only visible if the Ambient Method is selected.
EnvHeatLoss Display This field displays heat flow to the environment (positive value is heat flow from Dryerto Environment.).

Air Stream In

AirInT Input Inlet Air Temperature.
AirInQm Input Inlet Air Mass Flow.
DryAirQm Input Inlet Air Dry Air Mass Flow.
MoistureQm Input Inlet Air Water Vapor Mass Flow.
AirInHumidity Input Inlet Air Relative Humidity.

Crystallization

The second tab page in the access window. Crystallization inputs, results and calculated data are displayed on this page.

Tag / Symbol
Input / Calc

Feed Crystal Diameter

DiamMethod Steam_DIA Crystal Diameter from Input Stream.
User_DIA User Specified Crystal Diameter.
InputDiameter Input User input crystal diameter (only displayed if User_DIA is selected).
StreamDiameterIn Display Feed stream crystal diameter.
StreamDiameterOut Display Product stream crystal diameter.

Feed Size Distribution CV

CrystalCVin Input User input crystal CV.
CrystalCVout Display Product stream crystal CV.

Crystal Growth Factor

GrwthFactor Input Scaling factor for crystal growth rate (nominal value 0.4).

Crystallization

AvgGrowthRate Display Average crystal linear growth rate through the dryer.
AvgPrecipRate Display Average sucrose precipitation rate through the dryer.

Evaporation

DiffusionLimit TickBox Use diffusion limited model for evaporation rate.
Evap_Diff_Factor1 Input Diffusion limited evaporation factor 1 (default = 1.0).
Evap_Diff_Factor2 Input Diffusion limited evaporation factor 2 (default = 3.5e-03)
AvgEvapRate Display Average water evaporation rate through the dryer.

WaterQm Display Added water mass flow rate.

Feed

FeedT Display Feed Temperature.
FeedQm Display Feed total mass flow.
FeedCrystal Display Feed sucrose crystal mass flow.
FeedMoisture Display Feed moisture (not including water addition).

Feed Molasses

FeedMolasses Display Feed Molasses mass flow.
FeedWs Display Feed Molasses sucrose mass fraction.
FeedBrix Display Feed Molasses Brix.
FeedPurity Display Feed Molasses Purity.
FeedItoWratio Display Feed Molasses Impurities/Water mass ratio.
FeedSSN Display Feed Molasses supersaturation.

Total Moisture

TotalMoisture Display Total feed moisture into dryer including water addition.

Product

ProdT Display Prod Sugar Temperature.
ProdQm Display Prod total mass flow.
ProdCrystal Display Prod sucrose crystal mass flow.
ProdMoisture Display Prod moisture.

ProductMolasses

ProdMolasses Display Product Molasses mass flow.
ProdWs Display Product Molasses sucrose mass fraction.
ProdBrix Display Product Molasses Brix.
ProdPurity Display Product Molasses Purity.
ProdItoWratio Display Product Molasses Impurities/Water mass ratio.
ProdSSN Display Product Molasses supersaturation.

Data Access Page

Data for various points through the drier may be displayed on this page. The data display is turned on or off in the first tab (see display segment data above). The data is displayed in a matrix format with the headings below arrayed across the top of the page.

It is possible to display up to the number of segments plus 2 data points through the dryer. Fewer points may be selected. The data displayed for any segment are the exit conditions for the sugar and air streams from that segment.

Segment 0 is is the inlet condition for the sugar feed and exit condition for the air stream.

Segment n+1 is the inlet condition for the air stream and exit condition for the product sugar.

Segments 1 through n are data for the segments. The points displayed depend in the specified number of points to display. These would normally be the inlet and exit points plus evenly spaced segments in between.

NB if the number of data points to display is changed, SysCAD must be run for at least one iteration to refresh the display values.

Tag / Symbol
Input / Calc
Description

Product Crystal

Display Display Display point number.
Segment Display Segment number.
Time Display Feed time in dryer from start.
Tslurry Display Feed slurry temperature.
QmXtal Display Sucrose crystal mass flow rate.
QmFilm Display Molasses film mass flow rate.
Moist Display Sugar slurry moisture.
Wds Display Molasses film sucrose mass fraction.
Purity Display Molasses film purity.
SSN Display Molasses film supersaturation.
QmPrcp Display Molasses to crystal sucrose precipitation rate.
XtalDia Display Sugar crystal diameter.
QmEvap Display Evaporation rate.
BPE Display Molasses film boiling point elevation.
PPsat Display Molasses film water saturation partial pressure.
Qhex Display Heat transfer rate.
Tgas Display Air Stream temperature.
hm Display Mass transfer coefficient.
QmVapor Display Air Stream water vapor mass flow.
Humidity Display Air Stream relative humidity.

Warnings

 Warning Message Comments Invalid Feed - check streams Missing Sugar Feed or Drying Air. Feed has no SSA - turn on SSA Sugar Feed must have SSA property, may need to turn on SSA. No Crystal in Feed - Check Stream Compositions There must be sucrose crystal in the Dryer feed stream. Feed is not a Sugar Species model The feed stream must be a sugar stream. Model not Converged - mismatched mass flows? increase damping, more/less iteration steps Model has not converged, check operating conditions, number of segments and damping.

Adding this Model to a Project

Insert into Configuration file

Sort either by DLL or Group.

DLL:

SugarUnits.dll

Sugar: Sugar Dryer

or

Group:

Sugar