CHAPTER 8
This chapter provides a description of the sedimentation and flotation models available in GPS-X.
Sedimentation Models
Sedimentation is one of the most important unit processes in activated sludge treatment plants. The sedimentation unit, whether it is a primary settler, secondary clarifier, or sludge thickener, provides two functions: clarification and thickening. The primary settlers and sludge thickeners are designed and operated to take advantage of the thickening process, while the secondary clarifiers are designed and operated to take advantage of the clarification process.
In GPS-X, the sedimentation models are either zero- (point) or one-dimensional (1d suffix), and either reactive (mantis, asm1...) or nonreactive (simple). The following models are available:
· Zero-dimensional, nonreactive: point
· One-dimensional, nonreactive: simple1d
· One-dimensional, reactive: mantis
In reactive models, biological reactions are included, and the model names are associated with the corresponding suspended-growth models, described in Chapter 6 (page 141). For example, the mantis sedimentation model uses the mantis suspended-growth model.
Empiric Models
The empiric model performs a mass and flow balance to determine the flow and concentration tor filtrate and solids streams. Where the users can specify 2 parameters out of the below 3 parameters:
· Underflow Rate
· Solids Capture (%)
· Underflow Solids Concentration
One-Dimensional Models
In the one-dimensional models, the settler is divided into a number of layers (10 by default) of equal thickness, as depicted in Figure 8‑1.
The following assumptions are made:
1. Incoming solids are distributed instantaneously and uniformly across the entire cross-sectional area of the feed layer.
2. Only vertical flow is considered.
Figure 8‑1 - One-Dimensional Sedimentation Model
The models are based on the solids flux concept: a mass balance is performed around each layer, providing for the simulation of the solids profile throughout the settling column under both steady-state and dynamic conditions.
Table 8‑1 shows the appropriate contribution of each layer of the settler to the mass balance. There are five different groups of layers, depending on their position relative to the feed point. This is shown schematically in Figure 8‑2.
The models are based on traditional solids flux analysis, but the solids flux in a particular layer is limited by what can be handled by the adjacent layer.
The solids flux due to bulk movement of the liquid is a straightforward calculation based on the solids concentration times the liquid bulk velocity, which is up or down depending on its position relative to the feed layer.
Table 8‑1 – Sedimentation Model: Input-Output Summary
Figure 8‑2 - Solids Balance Around the Settler Layers
The solids flux due to bulk movement of the liquid is a straightforward calculation based on the solids concentration times the liquid bulk velocity, which is up or down depending on its position relative to the feed layer.
The solids flux due to sedimentation is specified by a double exponential settling function, applicable to both hindered sedimentation and flocculant sedimentation conditions. The settling function, described by Takács et al. (1991), is given by:
Equation 8‑1
where:
vsj = the settling velocity in layer j (m/d)
vmax = the maximum Vesilind settling velocity (m/d)
rhin = hindered zone settling parameter (m3/gTSS)
rfloc = flocculant zone settling parameter (m3/gTSS)
Xjo = Xj – Xmin, where Xmin is the minimum attainable suspended solids concentration, Xj is the suspended solids concentration in layer j
The minimum attainable solids concentration in a layer, Xmin, is calculated as a fraction (non-settleable fraction or fns) of the influent solids concentration to the settler:
Equation 8‑2
It is subject to a maximum value specified by the user; the maximum non-settleable solidsor Xminmax. The settling velocity is lower bounded to zero, so that if the user specifies parameter values that would result in settling velocities becoming negative, a warning message is printed in the simulation Log window. The settling velocity is also subject to a maximum value specified by the user; the maximum settling velocityor vbnd.
The settling function is shown in Figure 8‑3. The four regions depicted in this figure are explained as follows: I) the settling velocity equals zero, as the solids attain the minimum attainable concentration; II) the settling velocity is dominated by the flocculating nature of the particles; thus the settling velocity is sensitive to the rfloc parameter; III) settling velocity has become independent of solids concentration (particles have reached their maximum size; and IV) settling velocity is affected by hindering and becomes dependent on the rhin parameter (the model reduces to the Vesilind equation).
Figure 8‑3 – Settling Velocity vs. Concentration
Simple Models
In the simple1d sedimentation model, the only numerically integrated variable is the suspended solids concentration. This model can be used when biological reactions in the settler can be ignored. The concentrations of particulate state variables in the influent to the settler (heterotrophic organisms, etc.) are stored as fractions of the total suspended solids concentration entering the settler. Once the model completes the numerical integration of the suspended solids in the settler layers (at the end of each numerical integration time step), the concentrations of particulate state variables in the effluent, underflow (RAS), and pumped flow (WAS) are restored using those fractions. The concentrations of soluble state variables are not changed in the simple1d model.
WEF-TSS-SOL Models
The wef-tss-sol model is based of Tebutt and Christoulas (1975) and Wahlberg (2006) WERF study.
Surface overflow Rate
The surface overflow rate (SOR) of the clarifier can be expressed by the following equation:
Equation 8‑3
where:
SOR = surface overflow rate, m3/m2.d (gpd/sq ft)
Q = Flow to clarifier, m3/d (GPD)
A = surface area of clarifier, m2 (sq ft)
Non-Settleable Solids
User can specify one of the two setup methods for non-settleable solids:
1.
Set fraction -
, where:
Equation 8‑4
2.
Set concentration -
TSS Removal Efficiency
TSS removal efficiency can be calculated as:
Equation 8‑5
Equation 8‑6
Equation 8‑7
Where:
ETSSmax = maximum TSS removal efficiency
ETSS = TSS removal efficiency
λ = lambda value, settling parameter, m/d
TSS-SOR-SLE Models
Surface Overflow Rate
The surface overflow rate (SOR) of the clarifier can be calculated with Equation 8‑3 in the WEF-TSS-SOL Models section.
Surface Underflow Rate
The surface underflow rate (SUR) of the clarifier can be calculated with the following equation:
Equation 8‑8
Where:
SOR = surface underflow rate, m3/m2.d (gpd/sq ft)
QS = Sludge Flow, m3/d (GPD)
A = surface area of clarifier, m2 (sq ft)
Required Thickened Sludge Concentration
The required thickened sludge concentration to handle the SLR can be calculated with following equation:
Equation 8‑9
Where:
XTSS, required = surface underflow rate, m3/m2.d (gpd/sq ft)
Q = Flow to clarifier, m3/d (GPD)
QS = Sludge Flow, m3/d (GPD)
Xin = TSS to clarifier, mg/L
Thickening Factor
Thickening factor depends on the recycle rate can be calculated with the equation below:
Equation 8‑10
Where:
thickfactor = thickening factor
refsur = threshold underflow rate for no-thickening (m/d)
Expected Thickened Sludge Concentration
Expected thickened sludge concentration at given SVI and underflow can be calculated with the equation below:
Equation 8‑11
Where:
maxthickconc = expected thickened sludge TSS at given condition (mg/L)
SVI = Sludge Volume Index (mL/g)
Thickening Failure Exponent
Thickening failure exponent can be calculated with the equation below:
Equation 8‑12
Where:
expslr = thickening Failure Exponent
TSS removal efficiency
Non-settleable solids in effluent, will be
decided on whether entered
or fns*Xin is smaller. The
maximum TSS removal efficiency can be calculated with the equation
below:
Equation 8‑13
Equation 8‑14
Where:
clarifactor = clarification factor
Sludge Blanket Threshold Concentration
This variable is used to define the sludge blanket height for display purposes. If the concentration in a settler layer is above this threshold value (searching from top to bottom layer), then the sludge blanket is defined as the height of that layer.
Critical Sludge Blanket Level
This parameter is used to define the height of the sludge blanket in order for the dissolved oxygen in the underflow and pumped streams to be zero.
Soluble and Particulate Components
The soluble state variables in the nonreactive models are subject to a complete mix zone, unlike the particulate components, which move from layer to layer. If the user wishes to subject the soluble components to a number of tanks in series, then they must select a reactive type settler. In this case all of the state variables are transported from cell to cell according to the bulk fluid motion (but only the particulate components will be affected by a settling term). The feed layer then will become an important term in fixing the number of layers in series through which the soluble components will flow.
Correlation to Sludge Volume Index and Clarification
A feature of the sedimentation models in GPS-X (secondary clarifiers only) is the correlation provided between the settling parameters and Sludge Volume Index (SVI) measurements.
The SVI test characterizes the sedimentation, which occurs in the high solids concentration band of a clarifier. To specify the sedimentation characteristics over the full concentration spectrum, another parameter, the Clarification factor, is needed to specify the settling behavior in the flocculant or low solids concentration regions. This factor is a relative clarification index; a high number (1.0) indicates good clarification, and a low number (0.1) indicates poor clarification.
The correlation equations are:
Equation 8‑15
Equation 8‑16
Equation 8‑17
where:
vmax = maximum Veslind settling velocity(m/d)
rhin = hindered zone settling parameter (m3/gTSS)
rfloc = flocculant zone settling parameter (m3/gTSS)
SVI = sludge volume index (mL/g)
clarify = clarification factor
fcorr1 - fcorr9 = SVI correlation coefficients
To use the correlation, the user must set the
parameter use SVI to estimate settling parametersto
ON. The Sludge Volume Index and Clarification
parameters can then be specified, and the settling parameters are
calculated automatically by GPS-X. The correlation coefficients can
be accessed in the
Options > General Data > System > Parameters >
Miscellaneous form.
Note: The default values of the correlation factors are for SVI. A correlation with SSVI has not been performed. The default values of the correlation coefficients are based on five sewage treatment plants.
Influent Flow Distribution
The sedimentation models will account for hydraulic effects caused by an increase in influent flow. Flow conditions are considered normal when the influent flow divided by the surface area is less than the quiescent zone maximum upflow velocity specified by the user. The load to the settler under normal flow conditions enters the settler at the feed layer. However, as the influent flow increases, the load to the settler is distributed to the layers below the feed point. When the upflow velocity in the settler surpasses the complete mix maximum upflow velocity specified by the user, the entire load enters the bottom of the settler.
When the upflow velocity is between the quiescent zone maximum upflow velocity and complete mix maximum upflow velocity, a smooth transition of feed distribution between the low loading case and the high loading case is generated. An average (medium) loading condition is initially calculated where the upflow velocity (vuavg) is the average of the quiescent zone maximum upflow velocity(vumin) and the complete mix maximum upflow velocity(vumax). At this hydraulic loading, the input distribution is equal to the feed layer and all layers below.
Smooth distribution is achieved by two linear interpolations. The first interpolation is between vumin and vuavg. At vumin, the influent fraction to the feed layer is 1.0 (all flow enters the feed layer), while at vuavg the influent fraction to the feed layer is 1.0 divided by the number of layers below the feed layer (including the feed layer itself). Once the influent fraction to the feed layer is calculated, the remaining flow is equally distributed to the layers below.
A similar algorithm will ensure smooth flow distribution above vuavg. The algorithm first calculates the feed fraction to the bottom layer. If vu is higher than vuavg, then the algorithm distributes the rest evenly.
This procedure of flow distribution is modelling the feed distribution to the settler by the influent baffle. The feed distribution is shown in Figure 8‑4.
During higher flows, the momentum of the incoming flow tends to carry the load further past the bottom edge of the influent baffle, effectively changing the feed point in the settler. The flow distribution aspect of the model captures this phenomenon.
Figure 8‑4 – Load Distribution into Settler
Types of Settlers/Clarifiers
There are four types of settler objects in GPS-X:
1. rectangular primary
2. circular primary
3. rectangular secondary
4. circular secondary
All of the settler objects contain the same settling model. The difference between primary and secondary clarifiers is the default settling parameters and the SVI correlation (SVI correlation is not used in the primary settlers).
The difference between the circular and rectangular configurations is restricted to the specification of the area and/or geometry of the tanks. The rectangular tanks require only a total surface area for input, whereas the circular tanks have several shapes available.
Circular Settler Configurations
There are 4 different circular settler shapes available in the circular primary and secondary settler objects, as shown in Figure 8‑5. The surface area of each layer is calculated from the clarifier type and dimensions specified by the user. For example, as shown in the figure, a clarifier with a conical shape will have a larger surface area in the upper layer and a smaller surface area in the bottom layer.
Figure 8‑5 – Circular Settler Shapes
Flotation Model
This section of the chapter describes the flotation model (simple1d) associated with the Dissolved Air Flotation (DAF) unit.
The flotation model is closely related to the one-dimensional sedimentation model. It is partly based on the double-exponential function, but the model is inverted to promote flotation of solids as opposed to sedimentation of solids. The flotation model includes a solids flux component to account for floating of solids. This floating component is primarily controlled by an air-to-solids ratio and a polymer dosage, specified by the user.
One-Dimensional Model
The one-dimensional flotation model will predict the amount of solids removal achieved by the DAF unit. Solids are removed from the top of the unit in the float stream. Effluent is removed from the bottom of the DAF unit in the effluent stream. The one-dimensional flotation model is primarily based on the solids flux theory presented previously in this chapter, but it is modified to account for flotation as opposed to sedimentation. The major difference between the flotation and sedimentation models is the direction of solids flux and the parameters controlling it.
In the one-dimensional flotation model, the DAF unit is divided into a number of layers (10 by default) of equal thickness, depicted in Figure 8‑6.
The following assumptions are made:
1. Incoming solids are distributed instantaneously and uniformly across the entire cross-sectional area of the feed layer.
2. Only vertical flow is considered.
Figure 8‑6 - Layered Flotation Model
The model is based on the solids flux concept: a mass balance is performed around each layer, providing for the simulation of the solids profile throughout the DAF unit under both steady-state and dynamic conditions.
The model is based on traditional solids flux analysis, with an additional component for flotation. Model detail is provided in the previous section of this chapter devoted to one-dimensional sedimentation models.
The solids flux due to the bulk movement of the liquid is calculated by multiplying the solids concentration by the liquid bulk velocity (flow divided by area), which may be up or down depending on the position relative to the feed layer.
The solids flux due to flotation is specified by the same double exponential function used for sedimentation (Equation 8‑1). The parameters within Equation 8‑1 are altered to account for effects of flotation:
vsj = floating velocity in layer j (m/d)
vmax = floating velocity with optimal air-to-solids ration (m/d)
rhin = hindered zone floating parameter (m3/gTSS)
rflo = free floating zone floating parameter (m3/gTSS)
X jo = Xj – Xmin, where Xmin is the minimum attainable suspended solids concentration, Xj is the suspended solids concentration in layer j
The minimum attainable solids concentration in a layer, Xmin, is calculated as a fraction (non-floatable fraction of fns) of the influent solids concentration to the DAF unit:
Equation 8‑18
It is subject to a maximum value specified by the user, the maximum non-floatable solids or X minmax. The floating velocity is lower bounded to zero, so that if the user specifies parameter values that would result in floating velocities becoming negative, a warning message is printed in the simulation Log window. The floating velocity is also subject to a maximum value specified by the user, the maximum floating velocityor vbnd.
Model Parameters
This section of the chapter contains a description of the various model parameters and inputs that the user encounters when using the flotation model.
Physical
These menu items are found under the Parameters sub-menu item Physical. This input form contains the actual physical dimensions of the DAF unit being modelled, including the tank surface area, the maximum water level or height of the tank, and the location of the feed point relative to the bottom of the tank. The fourth item on the form allows the user to define the number of equivalent layers contained within the model. The physical parameter form is shown in Figure 8‑7.
Figure 8‑7 – Physical Parameters for the DAF Unit
Operational
The operational parameters for the DAF unit are located within the Parameters sub-menu item Operational. This input form contains the polymer dosage (g polymer/kg solids) and the air-to-solids ratio (g air/g solids) for daily operation of the DAF unit. The maximum float flow is an upper boundary limit for the amount of float that can be removed from the DAF unit. The operational input form is shown in Figure 8‑8.
Under the sub-heading other parameters, the optimal polymer dosage and optimal air-to-solids ratio are defined. These two values provide an estimate of the best expected solids condition. The optimal values may be expressed based on past operating experience with the actual DAF unit or may be provided through manufacturer literature. The dry material content of the float at the optimal polymer dosage is defined as a percentage. The dry material content of the float without polymer dosage is also defined. The model will use the range between these two values to predict the dry material content of the float under actual operating conditions.
Figure 8‑8 - Operational Parameters for the DAF Unit
Floatation
The Flotation parameters, shown in Figure 8‑9, are used to define the variables contained within the model (Equation 8.1). The maximum floating velocity provides an upper boundary limit for the model. The next variable is the expected floating velocity under the optimal air-to-solids ratio, as defined under the operational input form. The hindered zone and free floating zone floating parameters control the floating velocity defined in Equation 8‑1. There will likely be a fraction of solids, which cannot be removed by flotation. This fraction is characterized as the non‑floatable fractionand an upper boundary for this parameter as a concentration is set as the maximum non-floatable solids.
Figure 8‑9 – Flotation Parameters for the DAF Unit