# Sugar Vacuum Pan

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Sugar Properties Sugar Unit Models
Sugar Species Model Sugar Cane Shredder Sugar Crusher Sugar Crystalliser Sugar Dryer Sugar Fugal Sugar Juice Screen Sugar Mud Filter Sugar Vacuum Pan FFEvaporator 3

## General Description

The sugar vacuum pan is used to precipitate aqueous sugar onto existing sugar crystals in a continuous operation (as opposed to batch operation). The pan also includes the option for flashing off water vapour and for an internal heater.

Massecuite is fed into the vacuum pan (the pan allows for multiple feed streams to it). There is a single product stream exiting from the unit and an optional vapour stream out. Any vapours coming into the system and any flash steam generated leave via the vapour line connection. The model has optional connections to an internal condensing steam heater. Environmental heat loss options are included. There are different user selectable options to describe precipitation rate. Residence time in the unit is defined by its volume and the mass flow through the unit.

The number of sugar crystals is assumed to be constant through the unit and the precipitation of sugar is defined by the growth rate 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.

The operation of the unit is assumed to be steady state and modeled as a continuous well stirred tank reactor (CSTR) with a significant residence time and rapid mixing so that all processes are assumed to occur at exit conditions. A numerical solution that balances crystal growth, evaporation, heat transfer and environmental heat loss is found iteratively.

Multiple SysCAD vacuum pan unit operations can linked together to create more complex vacuum pan systems as required.

## Input and Output Connections

A number of the inputs and outputs for the sugar vacuum pan 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 Vacuum Pan. HeatingIn Optional In 0 1 Steam to Vacuum Pan Internal Heater. HeatingOut Optional In 0 1 Internal Heater Outlet Stream. Product Required Out 1 1 Massecuite Stream out of Vacuum Pan. Vapour Optional Out 0 1 Vapour Outlet Stream from Vacuum Pan containing all Vapors - NB required if there are vapors present.

## Behavior when Model is OFF

The sugar vacuum pan 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 feed streams are perfectly mixed and exit via the product stream. There is no heat exchange or environmental heat loss however, 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 the vapout outlet stream.
• There is no heat exchange and any heater input exits unchanged.

## Model Theory

### Physical Model

The only required input stream connection to the vacuum pan is the Feed stream (there may be up to 5 feed streams). The heater inlet stream connection is optional and only required if heater operation is enabled.

The pan output stream connection for the product stream is required. When there are gases in any of the feed streams or flashing is enabled on the pan side then a Vapor stream outlet connection is also required. The heater outlet stream connection is optional and only required if the heater operation is enabled.

Geometry - The vacuum pan geometry is specified completely by its working volume. This is the actual volume of massecuite contained within the unit and does not include head space for vapour or volume occupied by the heater.

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

Environmental Heat Transfer - Environmental heat transfer is included in the model. Any heat exchange with the environment is included in the energy balance calculations.

Heat Exchanger - There are optional connections for an indirect (non-contact), internal heater. If a heater inlet stream is connected then heater outlet stream must be connected or an error will be reported. There is a condensing heat exchange mode and a fixed heat transfer rate mode of operation. NB in the fixed heat transfer mode, A fixed quantity of heat is supplied to the pan side and there is no heat exchange between the heater stream and the sugar stream. The heater outlet conditions are exactly the same as the heater inlet.

Gases - Any gases present in any of the feed streams or any vapour flashed is split to the vapour outlet stream. If there is no vapour connection, the gases are sent out with the product stream and a warning is displayed. Gases may include non-condensible as well as water vapour.

Product Temperature - The vacuum pan may be heated or cooled during operation, may exchange heat with the environment and may flash off vapour during operation. In addition there is an enthalpy of crystallization associated with sucrose precipitation that will effect the final temperature. All of these effects are included in the energy balance and product temperature calculation.

### Environmental Heat Exchange Options

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

1. None - No Environmental 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 vacuum pan to the environment is positive in sign.

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

### Heat Exchanger Options

The heat exchanger has options for two modes of operation.

Condensing Steam The condensing steam mode assumes that steam will be supplied to the heat exchanger and that condensation will occur at the supply pressure (NB there is no internal pressure drop, however pressure drop may be added in the steam supply line if required). The heat exchanger is specified by the area, A, and overall heat transfer coefficient, U. Heat transfer is calculated as UA*delta T where delta T is the difference between the steam saturation temperature and the product temperature (the pan contents are assumed well mixed and at the product temperature). Steam will condense to balance the calculated transfer heat rate. The steam supply must contain some water vapour, but may be a two phase mixture (quality may be < 100%). The steam supply may not have any non-condensibles in it. A warning will be reported if there are non-condensibles or there is no steam. If the steam supply rate is greater than can be condensed for the given heat transfer area and coefficient, the heater outlet stream will be two phase (a warning will be issued if there is vapor in the heater outlet stream).

Fixed Heat Transfer Rate In this mode the heat transfer rate to the pan contents is user specified and the pan energy balance is based on this. It is important to note that there is NO heat exchange with the heater stream. The heat exchanger inlet and outlet streams are not required for this mode and may be omitted from the model. If the streams are connected, any flow to the heater will exit at the same conditions. It is recommended that if a model is going to be used in this mode, the heater inlet and outlet connections are left out to avoid confusion.

### Size Distribution

In general the contents of the pan 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'.

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 the third) may be found from:

• $U1$
• $U2 = U1^2 \left(1 + CV^2\right)$
• $U3 = U1^3 \left(1 + 3 CV^2\right)$

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

Particle Growth - Particle growth is modelled as non-nucleating with size independent growth. The change between inlet and outlet is given by;

• $\text{Growth, } GRDT=\left(\text{Growth Rate, }GR\right) \times \left(\text{time increment, } \Delta t\right)$
• $U1_{out}=U1_{in}+GRDT$
• $U2_{out} = U2_{in} + GRDT \left(2U1_{in} + P\right) + GRDT^2$
• $U3_{out}=U3_{in} + 3GRDT\left(U2_{in} + P\times U1_{in}\right) + 3GRDT^2\left(U1_{in} + P/2\right) + GRDT^3$

Dispersion - 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 syrup 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 vacuum pan has a user selectable option to use dispersion or not (in which case P is set to 0).

Mass Change - The relative change in crystal mass (which is also equal to the amount of sucrose precipitating out of solution) is given in terms of the third moment by;

• $\Delta \text {mass}= \left( \cfrac {U3_{out}} {U3_{in}} - 1 \right)$

CV Change - The CV at the outlet can be calculated from the first and second moments at the outlet by;

• $CV=\cfrac{\left(U2_{out} - U1_{out}^2\right)^{0.5}}{U1_{out}}$

NB The SysCAD vacuum pan has an option to allow CV to be held constant or to vary according to the above relation.

There are four options for crystal growth - none, fixed mass rate, fixed linear growth rate and the SRI Method {need a reference for this}.

### Precipitation Models

There are four different options for growth models listed below.

There are two options (fixed mass rate and fixed linear growth) which allow the amount of crystal growth to be fixed regardless of any other parameters such syrup compositions or supersaturation. These are useful modes for tuning operation to an existing plant. However, caution should be used since specifying excessive rates may deplete the syrup of sucrose and give a product which is undersaturated - which is physically unrealistic. A warning is displayed if the product stream is undersaturated.

#### None

There is no crystal growth. However, environmental heat transfer may still occur, the heat exchanger may operate and flashing may occur (NB the syrup composition may change if flashing occurs).

#### Fixed Mass Rate

The sucrose precipitation rate is a user input fixed rate. Precipitation of sucrose occurs at the specified rate regardless of any other parameters (such as supersaturation). Growth will continue until the syrup is nearly depleted of sucrose. The crystal size distribution is described by the moment equations.

#### Fixed Linear Growth

The linear growth of crystals is a user input fixed amount. Precipitation of sucrose occurs to give the specified change in diameter regardless of any other parameters (such as supersaturation). Growth occurs to the specified diameter or until the syrup is nearly depleted of sucrose. The crystal size distribution is described by the moment equations.

#### Fixed Growth Rate

The linear growth rate of crystals is a fixed user input. Precipitation of sucrose occurs at a rate corresponding to the growth rate regardless of any other parameters (such as supersaturation). Growth will occur at the specified rate or until the syrup is nearly depleted of sucrose. The crystal size distribution is described by the moment equations. NB it is possible to use an external calculation of growth rate using a user defined General Controller and write the growth rate value to this input thus allowing the user to define and test various growth rate equations.

#### SRI Growth Model

The SRI model for growth calculates a growth rate as a function of sucrose supersaturation in the syrup, sucrose concentration and temperature. The SRI method also calculates a minimum supersaturation for precipitation to occur. When supersaturation less than this minimum, there is no growth even if supersaturation is greater than one. Dissolution of existing crystal is not considered in the vacuum pan model.

The growth rate in microns per hour is given by:

• $G=A \times C_{suc} \times \left( SS-SS_{limit} \right) \exp\left[\cfrac{-E_a}{R} \left( \cfrac{1}{T(K)}-\cfrac{1}{333.16}\right) -\left( B \cfrac{I}{W}\right)\right]$
Where:
$SS = \text{The sucrose supersaturation (calculated from the sugar properties model).}$
$SS_{limit} = \text{The minimum supersaturation for crystal growth to occur is calculated from the equation;}$
$SS_{limit} =1.057+\left(0.036\, ItoW\right)-\left(0.0012\, T(^oC)\right)$
$C_{Suc} =\text{The molar concentration of sucrose in the syrup.}$
$\left(\frac{I}{W}\right) = \text{The mass ratio of impurities to water in the syrup.}$
$R =\text{Gas constant, 8.3143 kJ/mol.K}$
$E_a =\text{Activation Energy}$
$E_a =\left(112977.4 - 836.87\, T(^oC)\right)\text{kJ/mol}$
$A =\text{Growth rate constant.}$
$B =\text{Growth rate constant.}$
$\text{For High Grade Boilings: A = 520 B = 0.94}$
$\text{For Low Grade Boilings: A = 900 B = 1.20}$

### Numerical Solution

The solution is found by iterating until the predicted growth rate at product conditions, the amount of sucrose precipitated and the energy balance (outlet temperature) all match.

The feed conditions are used as initial guess for product conditions. Growth and heat transfer rates, flashing, CV and P are calculated rate and used to give a new estimate for product conditions. The measured error for convergence is the sum of the relative errors between successive estimates of precipitation rate, CV, P and energy. The calculation is repeated until a solution is found.

For the most complex situation with environmental heat transfer, condensing steam heater and detailed growth models, the solution may require some damping to be used in the model. The default damping is set at 50% which should be good for most circumstance. The damping setting is hidden by default, but can be exposed with the "All fields" button.

The model "remembers" the last converged values and uses these to start the next iteration so the initial guess should be close which speeds convergence.

## Flow Chart

The process is shown schematically in the flow chart below for the vacuum pan. Feed streams are mixed going in and product slurry (all liquids and solids) exit via the product stream and all gases (flash vapour plus any gases in the feed streams) exit via the vapour stream. Heat is exchanged indirectly with steam or hot water streams and the environment.

## Data Sections

### VacuumPan

Unit Type: VacuumPan - The first tab page in the access window will have this name. Configuration and 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). TackStatus 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. ShowQVap Tickbox Tickbox to display or hide Vapour data tab. Environmental Heat Loss EnvLossMethod None No heat exchange with the environment. FixedLoss User specified environmental heat loss rate. Ambient Heat loss determined as a constant times temperature difference from ambient. Qloss = EnvLossCoeff * (Tprod - Tamb) EnvLossRqd Input The Required Heat Loss Rate - This is only visible if the FixedLoss Method is selected. EnvLossCoeff Input The Heat Loss Rate Constant (kW/K) - This is only visible if the Ambient Method is selected. Heat Exchanger Connection HeatExchanger None Heat exchanger not connected. HEX_Connected Heat Exchanger is connected (Heat exchange options are configured on another tab). Flashing Option Flashing None Flashing does not occur on Pan Side. Target Pressure Pan contents may flash to specified pressure. FlashVapourQm Display Mass Flow Rate of Flashed Vapour (flash data only visible if the Flashing Method is selected). PanPressureTarget Input Target Flash Pressure for Pan. PanPressure Display Actual Pan Pressure (target may not be achievable). Thermal Balance EnvHeatLoss Display Heat flow to the Environment (positive value is heat flow from Vacuum Panto Environment.). HeaterThermalGain Display Heat flow from the heater to the Vacuum Pan is positive). NetThermalGain Display Net Thermal Gain between heat transfer from the heater and loss to the environment (positive is net gain to the pan contents). Dimensions PanVol Input Working Volume of Vacuum Pan.

### Crystallization Access Page

The second tab has the name Precip 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. UserDiameter Input User specified crystal diameter of feed (only displayed when User_DIA is selected). StreamDiaIn Display Crystal Diameter of Feed. StreamDiaUsed Display Crystal Diameter Used in Calculations. StreamDiaOut Display Crystal Diameter of Product. Size Distribution CV AdjustCV TickBox Option to adjust CV during crystal growth. UseDispersion TickBox Option to use Dispersion in growth equations. CrystalCVin Input User input CV of feed crystal size distribution. CrystalCVout Display CV of product crystal size distribution. Dispersion Display Dispersion of product crystal size distribution [um]. Crystal Growth Method GrowthMethod None No crystallization. Fixed Precip Rate User Specified Fixed Precipitation Mass Rate. Fixed Linear Growth User specified Fixed Linear Crystal Growth. Fixed Growth Rate User specified Crystal Growth Rate (um/h). SRI Growth Model SRI Growth Rate Model. FxdPrecipRate Input User Specified Mass Precipitation Rate [t/h]. FxdGrowth Input User Specified Crystal Linear Growth [um]. FxdGrowthRate Input User Specified Crystal Linear Growth [um/h]. I/W Display Impurities to Water Mass Ratio. Grwth_Const_A Input User specified Growth Constant (see above for default values). Grwth_Const_B Input User specified Growth Constant (see above for default values). Precipitation ResidenceTime Display Residence time in the vacuum pan. PrecipRate Display Rate of Sucrose Mass Precipitation [t/h]. GrowthRate Display Rate of linear Crystal Growth [um/h]. Growth Display Crystal Linear Dimension change [um]. Yield Display Mass of Sugar precipitated per unit volume of feed liquid. Feed Massecuite Feed.Qm Display Feed Mass flow into pan. Feed.T Display Feed temperature to the pan. Feed.MassBrix Display Feed Massecuite Brix. Feed.MassPurity Display Feed Massecuite Purity. Feed.SolidsConc Display Feed Solids Mass Fraction. Feed Molasses Feed.MolBrix Display Feed Molasses Brix (Wds). Feed.MolPurity Display Feed Molasses Purity (q). Feed.MolPol Display Feed Molasses POL (Ws). Product Massecuite Prod.Qm Display Product Mass flow from pan. Prod.T Display Product temperature to the pan. Prod.MassBrix Display Product Massecuite Brix. Prod.MassPurity Display Product Massecuite Purity. Prod.SolidsConc Display Product Solids Mass Fraction. Prod.SolidsMax Display Maximum Product Solids (?? - reference and more explanation). Prod.CrystalCF Display Crystal Content Factor (CCF). Product Molasses Prod.MolBrix Display Product Molasses Brix (Wds). Prod.MolPurity Display Product Molasses Purity (q). Prod.MolPol Display Product Molasses POL (Ws). Prod.MolSSN Display Product Molasses Supersaturation (SSN). Vapour Flow Flash.Qm Display Vapour Flash Rate. Vapour.Qm Display Vapour mass flow out of pan (includes flash vapor plus any gases in feed streams). Convergence Information Iterations Display Iterations to convergence. Normally hidden. Damping Input Numerical solution Damping Factor (0% to 95%, default = 50%). Damping may be helpful at high precipitation rates. Normally hidden.

### Heater Access Page

The third tab shows the Heater Access Page when the heater connections are enabled.

 Tag / Symbol Input / Calc Description Heater On Heater.On TickBox Option to turnheater on or off. When off, no heat transfer and heater flow out equals flow in. Heater Operation HeaterMethod Fixed.dQ Fixed, user specified heat flow. CondSteam Condensing Steam. dQtarget Input Target Heat Transfer Rate. HeatingRate Display Actual Heating Rate. Heat Exchanger HX.Area Input Heat exchanger area. HX.HTC Input Heat exchanger overall heat transfer coefficient. Hx.UA Display Effective UA. Hx.deltaT Display Delta T for heat transfer. Hx.TheoDuty Display Theoretical heat exchanger duty. Hx.ActualDuty Display Actual heat exchanger duty. Heater Flows HeaterTin Display Heater temperature in. HeaterTout Display Heater temperature out. HeaterQm Display Heater mass flow. HeaterQvIn Display Heater volume flow in. HeaterQvOut Display Heater volume flow out.

### Warnings

 Warning Message Comments No Incoming Flow No Feed flow to pan. No Sucrose(aq) in Feed - Check Stream Compositions No Aqueous Sucrose in feed. No Sucrose Crystal in Feed - Check Stream Compositions No sucrose crystal in feed. Feed is not a Sugar Species Model Feed is not a sugar species model. No Diameter info in Feed Stream: using user input Model expecting diameter information in feed stream but none there. Using User input instead. No Convergence of model: try increased damping Model may require increased damping for convergence. Excess Steam Flow for Heat Load - vapour in heater outlet In fixed heat transfer mode, there is too much steam supplied the required heat and vapor in the outlet . Missing Connections to Condensing Heater Both inlet and outlet must be connected. Incorrect Heater connections Both inlet and outlet must be connected - one is missing. Gases in Feed Flow and no Vapor Connection Out Feed to pan contains gases and there is no vapour outlet connection. Non-Condensibles in Flow to Heater - none expected Heater inlet flow contains non-condensibles. No steam in Flow to Heater - some expected In Condensing mode, the heater supply must contain some steam. SSN < 1 in product stream - check precip rates Product supersaturation less than one, more sucrose precipitated than should be possible (this can happen with fixed mass or growth).

## Adding this Model to a Project

Insert into Configuration file

Sort either by DLL or Group.

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