Belt Filter

From SysCAD Documentation

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Contents 1 General Description 2 Diagram 3 Inputs and Outputs 4 Model Theory 4.1 Assumptions 4.2 Reference 5 Flowchart 6 Data Sections 6.1 Requirements 6.2 Results 6.3 WashLoss Section 7 Adding this Model to a Project

General Description

A Belt Filter is used for counter current filtration washing (CCFW). This technique enables the efficient recovery of the aqueous species in the feed liquor to the filtrate, with minimum losses to the liquor in the filter cake.

The techniques used to emulate the Belt filter with CCFW require the user to have data on filtration losses for Simple Filtration Washing (SFW), a wash loss curve.

Diagram

The diagram shows the default drawing of the Belt Filter, with all of the streams that are available for operation of the unit. The user does not have to connect streams to either the 'Wash Water' or 'Washings' connections.

If the user wants to use the Belt Filter model without washing (which is not recommended - rather use one of the other filter models available in SysCAD), do not connect the Wash Solution stream and specify washing stages = 0 and they may also leave the wash loss curve un-specified. The user must however still specify solids moisture.

The Belt Filter will operate without a connection to the Liquid Washings outlet. All of the wash solution from the belt filter will then report to the filtrate stream.

The physical location of the streams connecting to the Belt Filter is unimportant. The user may connect the streams to any position on the unit.

Inputs and Outputs

Label	Input / Output	No. of Connections		Description
		Min	Max
Feed	In	1	10	The slurry feed to the Belt Filter
Wash Solution	In	0	5	Wash water to the Belt Filter - optional
Liquid Filtrate	Out	1	1	Filtrate outlet from the unit
Solid Product (Cake)	Out	1	1	Solids outlet from the unit
Liquid Washings	Out	0	1	Washings outlet from the unit - optional

Model Theory

An example of a belt filter with five stages of counter current washing is shown in Figure 1 below:

Figure 1

The model will simulate any number of counter current washing steps, from 1 upwards. All of the wash water is assumed to be added to the final washing stage, with the filtrate from each stage being added as a wash to the previous stage. As the cake travels along the belt and is washed with progressively leaner wash liquor, it develops a concentration profile that varies from stage to stage. The average wash liquor concentrations and the cake concentration profile (for a given cake) are the same as those for a Simple Filtration Washing (SFW) system with the same wash liquor input.

For the belt filter with 5 stages shown in Figure 1 above, the concentration of the liquor remaining in the cake exiting the belt, c₅, can be calculated from:

c₅ = c₄ - N * (w₅ - w₀)

where

c_i - the average mass concentration in cake moisture discharged from the i^th stage

w_i - the average mass concentration of washings collected in the i^th stage

N - Mass Ratio of Wash Water used to the mass of liquor in the final cake

The equations required to calculate the intermediate cake moisture and washings concentrations, c_i and w_i, are described in the reference. All of these equations rely on both the value of N and the relationship between N and the fraction of liquor remaining in the cake.

An example of this relationship is shown in the Simple Filtration Washing (SFW) Wash Loss curve in Figure 2 below:

Figure 2

This curve can be obtained from pilot plant or full-scale operation, or if necessary it can be determined from a laboratory test that simulates the expected plant conditions.

(Please see Wash Loss Section, in the Data Sections for help on entering data for SFW Wash Loss curve)

The model uses the above curve to determine the displacement of original liquid from the cake at each stage on the belt filter. As the cake travels along the belt it is washed with less and less concentrated wash water. The liquid remaining in the cake that is discharged from the belt is mainly wash water.

The mass of wash water that is sent to the belt filter is re-used n times, where n is the number of stages of washing. The Simple Filtration Washing (SFW) loss, l_i, at each stage is:

l_i = f(i * N)

where f(i * N) - is obtained from the Wash Loss curve.

So, for the above example with 5 stages of washing, a mass ratio of wash water to cake moisture N = 1.5 the following SFW losses can be read from the Wash Loss curve in Figure 2:

Stage (i)	i * N	SFW Loss (f(iN))
1	1.5	0.2
2	3	0.085
3	4.5	0.022
4	6	0.008
5	7.5	0.003

NOTES:

1. The Wash Water to Final Cake moisture mass ratio, N, is displayed in the Belt Filter access window in SysCAD as WashRatio.

2. In the above example, with a Wash Water to Final Cake moisture ratio of 1.5, and 5 stages, the user must have a value for the Ratio (X-axis) of at least 7.5 for the simple wash loss curve. If the curve entered into SysCAD does not have a value for the Ratio of at least 7.5, e.g. the highest value was 5, then the model would give the user a warning: SFW wash loss 7.5 is out of user specified range of data points (0 to 5)

Assumptions

1. Ideal displacement washing is assumed, i.e. mass of liquid phase hold-up in the cake is constant throughout the washing process.
2. No solids are lost to the filtrate.

Reference

1. Tomiak, Predict performance of belt filter washing, Chemical Engineering Journal 19??

Note: The original paper uses volumetric concentrations to calculate the displacement of solutes from the solids moisture to the wash liquor. However, this assumes a constant liquor density, which is not always valid. Therefore, the model uses Mass concentrations, or ratios, to calculate the relative amounts of solutes in the exit streams from the belt filter.

Flowchart

Data Sections

The default sections and variable names are described in detail in the following tables. The default Belt Filter access window consists of 3 sections. This number may increase or decrease, based on user configuration.

1. The first section, which has the same name BeltFilt-1, contains general information relating to the unit
2. The second section, WashLoss, enables the user to enter the data for the simple filtration washing curve.
3. The Info section, contains general settings for the unit and allows the user to include documentation about the unit and create Hyperlinks to external documents. This is fully described in Common Data Sections.
4. Links tab, only visible in SysCAD 9.2, contains a summary table for all the input and output streams.
5. Audit tab - contains summary information required for Mass and Energy balance. See Model Examples for enthalpy calculation Examples.

Class: BeltFilt-1 - The first tab page in the access window will have this name.

Tag / Symbol	Input / Calc	Description/Calculated Variables / Options
Common First Data Section
Requirements
Stages	Input	The required number of washing stages on the belt filter. This can be any integer from 0 upwards.
RqdCakeMoist	Input	The required percentage liquid in the washed cake, the final cake moisture. This must be between 0.01% and 99%.
OperatingP... (available in SysCAD 9.2 or later)
Method	List	Atmospheric -- outlet streams will be at Atmospheric Pressure. The atmospheric pressure is calculated by SysCAD based on the user defined elevation (default elevation is at sea level = 101.325 kPa). The elevation can be changed on the Species tab page of the Plant Model.
		LowestFeed -- outlet streams will take the lowest pressure of the feeds.
		HighestFeed -- outlet streams will take the highest pressure of the feeds.
		RequiredP -- outlet streams will be at the user specified pressure.
Result	Display	The actual pressure used for the sum of the feeds which will also be the outlet pressure (unless further model options change the pressure).
TrackStatus	Tick Box	Enable warning messages if requirements are not met.
Results
WashRatio	Calc	The calculated wash ratio, N, on the Belt filter. Mass Ratio of Wash Water to Liquid in Cake.
WashEfficiency	Calc	The calculated wash efficiency of the Belt Filter.
FracFeedInCake	Calc	The fraction of feed liquor remaining in the cake from the Belt Filter.
CakeSolids	Calc	Displays the fraction of solids in the final Cake from the Belt Filter.
FiltSolids	Calc	Displays the fraction of solids in the filtrate from the Belt Filter.
CakeSolConc25	Calc	Displays the concentration of solids in the final Cake from the Belt Filter at 25 deg C.
FiltSolConc25	Calc	Displays the concentration of solids in the filtrate from the Belt Filter at 25 deg C.

WashLoss Section

The user types in the x and y values for the Simple Filtration Washing (SFW) wash loss curve. The user must go to the 'WashLoss' tab of the access window to enter this data. Figure 3 below shows an example of data entered for a SFW wash loss curve (this data corresponds to the curve shown in Figure 2 in the Theory section)

Figure 3

When the user first goes to this access window, the button next to Data Points will have a '+'. By clicking on this the fields for data entry will be visible and the user may then enter:

The number of points in the SFW wash loss curve, Length. In this example it is 9.

The actual data points for the curve.

Tag / Symbol	Input/ Calc	Options	Description
The black rectangle is for display purposes only. The user can configure the 'Information' data to display the wash loss curve.
Equation	Input	Data Only XYFunction	The data is entered in a csv file, or on this page, in two columns, x representing the wash ratio, and y for the simple filtration losses. The model interpolates linearly between the points and beyond the first and last points.
		Cubic-Spline	The data is entered in a csv file, or on this page, in two columns, x representing the wash ratio, and y for the simple filtration losses. The model fits a curve between the points, but beyond the first and last points it assumes a horizontal straight line relationship.
Equation	+ / -		This is used if the user wishes to use an equation. In this case the model only accepts a data function.
Information	+ / -		The user clicks on the + to obtain the following buttons, these allow the user to configure the display.
		Lin > Log X	Toggles between normal and log on the x scale
		Lin > Log Y	Toggles between normal and log on the Y scale
		Auto>Manual Scale Display	Toggles between automatic and manual display parameters. If the display is in auto mode, then the model sets the minimum and maximum display parameters. Changing to manual allows the user to set these parameters.
		Graph : Width and Height	These numbers determine the size of the graph on this page.
		Display Min	The minimum display point on the graph
		Display Max	The maximum display point on the graph
		Lower Boundary	The lower boundary of the actual data points, i.e. the lowest point to which the data may be extrapolated.
		Upper Boundary	The upper boundary of the actual data points, i.e. the highest point to which the data may be extrapolated.
Data Points	+ / -		The user clicks here to enter the data points.
		File	The user may type in the file and path if the points are stored in a csv file.
		Length	The number of data points. If the user wishes to type the data points directly into the model, then this value needs to be filled in. Once a number has been typed in, the X and Y columns will be visible with the required number of lines.
		Load Points	This will load the points from the file.
		Save Points	This will save the points into the file.
		Sort	This will sort the data points into ascending x values.

Adding this Model to a Project

Insert into Configuration file

Sort either by DLL or Group.

	DLL:	Separ1.dll	→	Units/Links	→	Separation: Belt Filter
or	Group:	Mass Separation	→	Units/Links	→	Separation: Belt Filter

See Project Configuration for more information on adding models to the configuration file.

Insert into Project

Insert Unit

→

Separation

→

Belt Filter

See Insert Unit for general information on inserting units.