CHAPTER 6

Suspended Growth Models

Introduction

This chapter examines the suspended-growth models that are available in the different GPS-X libraries.  Each biological model available in GPS-X is implemented in many different unit process objects in both completely mixed and plug-flow formats. Regardless of the hydraulic implementation, the biological model is the same.

In this chapter, Common features of suspended growth models in GPS-X are first discussed before focusing between the models are first discussed before focusing on the distinct aspects of specific models.

Common Features

Modelling of Oxygen Transfer

The oxygen transfer model is based on theory presented in the USEPA Design Manual for Fine Pore Aeration Systems (USEPA, 1989) and Mueller et al. (2002).  The GPS-X aeration model is suitable for accurate design of diffused and surface mechanical aeration systems.

In GPS-X, oxygen transfer to the bulk liquid phase of a biological reactor is modelled using a dynamic mass balance written for dissolved oxygen gas.  For example, a dissolved oxygen mass balance around a completely stirred tank reactor (CSTR) is shown in Equation 6‑1.

Equation 6‑1

where:

          = reactor volume (m³)

= concentration of dissolved oxygen (DO) in the reactor (mg/L)

          = influent flow rate (m³/d)

= concentration of DO entering reactor (mg/L)

      = oxygen mass transfer coefficient at field conditions (1/day)

        = DO saturation concentration at field conditions (mg/L)

          = rate of use of DO by biomass (g/day), the respiration rate

The volume, flow rates, and reaction rates are known from specifications or other modelling equations leaving two terms that must be calculated to solve the dissolved oxygen mass balance over time for the concentration of DO in the reactor, C_L:

· DO saturation concentration at field conditions, ; and,

· Oxygen mass transfer coefficient at field conditions,

Calculation of DO Saturation Concentration at Field Conditions

The DO saturation concentration at field conditions is calculated as follows:

Equation 6‑2

where:

= temperature correction factor (-)

          = correction factor for salts, particulates and surface-active substances (-)

= pressure correction factor (-)

    = DO saturation concentration at 20°C and 1 atm (mg/L)

The correction factors are used to adjust the DO saturation concentration to account for the temperature of the liquid, the pressure at the submergence level of the diffusers, and the salts, precipitates, and surface-active substances found in the wastewater.

The temperature correction factor is calculated as follows:

Equation 6‑3

where:

       = surface DO saturation concentration at temperature of t and 1 atm (mg/L)

      = surface DO saturation concentration at 20°C and 1 atm (mg/L)

The surface DO saturation concentration at liquid temperature t and a pressure of 1 atm is obtained using a lookup table in GPS-X that is based on temperature.  The lookup table data were taken from Appendix C of the USEPA Design Manual – Fine Pore Aeration Systems (USEPA, 1989).  When the temperature falls between two data points in the table, GPS-X uses linear interpolation to determine the  value.  The value of  is 9.09 mg/L.

The correction factor for salts, particulates, and surface-active substances , is a parameter that must be measured or estimated for the wastewater of interest.  In GPS-X, a default value of 0.95 is used.

The pressure correction factor is calculated as shown below:

Equation 6‑4

where:

        = barometric pressure at elevation and air temperature (kPa)

         = standard barometric pressure (101.325 kPa)

        = vapour pressure of water at liquid temperature (kPa)

= effective pressure at depth of diffuser submergence

The barometric pressure at a given elevation and air temperature is calculated using the following formula taken from Appendix B-2 of Metcalf and Eddy (2003):

Equation 6‑5

where:

          = acceleration due to gravity (9.81 m/s²)

         = molecular weight of air (28.964 kg/kg-mole)

          = universal gas constant (8314 m/kg-mole K)

      = air temperature (K)

         = elevation at position i (m)

The vapour pressure of water at the liquid temperature is determined using the Antoine equation (Felder & Rosseau, 1986):

Equation 6‑6

where:

        = Antoine coefficients (found in System > Input Parameters >         Physical form in GPS-X under Physical Constants)

= wastewater temperature (°C)

The effective pressure at the depth of the diffuser submergence is calculated using the following formula:

Equation 6‑7

where:

                = the depth correction factor for oxygen saturation (m)

where  is determined by Equation 6‑8 or Equation 6‑9 depending on the type of diffuser being used:

Fine Pore and Jets

Equation 6‑8

Coarse Bubble

Equation 6‑9

where:

          = the depth of diffuser submergence

The DO saturation concentration at 20°C and 1 atm is calculated using Equation 6‑10:

Equation 6‑10

Oxygen Mass Transfer Coefficient at Field Conditions Calculation

The value of the oxygen mass transfer coefficient at field conditions, , specifies the amount of oxygen supplied to the aeration tank given the driving force , and the tank volume. GPS-X provides four ways for the user to specify the :

· If known, the user can directly supply the  at 20°C (no alpha, fouling, or temperature correction) for both diffused and mechanical aeration. GPS-X converts the  to field conditions.

· In the case of mechanical aerators, the user can supply an aeration power and mechanical aerator oxygen transfer rate from which GPS-X calculates the .

· In the case of diffused aeration, the user can supply an air flow rate (at either standard or field conditions) and a standard oxygen transfer efficiency (SOTE) from which GPS-X calculates the  at field conditions.

· The user can configure a DO controller which will manipulate the field  directly to match the desired DO concentration

The availability of these options depends on the selected aeration method.  For diffused aeration, the user can enter airflow, enter , or use a DO controller.  For mechanical aeration, the user can enter power, enter , or use a DO controller.  The four choices for specifying  are discussed in more detail in the following four sections.

Entering  Directly – Diffused Aeration

The  at field conditions is calculated using Equation 6.11:

Equation 6‑11

where:

            = mass transfer coefficient at temperature T in °C (1/day)

           = mass transfer coefficient at 20°C

                  = temperature correction factor (default value in GPS-X is 1.024)

                  = wastewater correction factor for

                 =diffuser fouling factor (default value in GPS-X is 1.0)

                 = wastewater temperature (°C)

The  correction factor can be specified along the length of the aeration tank in the case of a plug flow unit process.

GPS-X calculates other useful process variables from the standard and field  as detailed in the following sections:

Oxygen Transfer Rate (OTR) at Field Conditions in g/d

                                    The OTR at field conditions is calculated using Equation 6‑12

Equation 6‑12

Standard Oxygen Transfer Rate (SOTR) in g/d

                                    The SOTR is calculated using Equation 6‑13

Equation 6‑13

Airflow at Standard Conditions

Airflow rate under standard operating conditions is calculated using Equation 6‑14.

Equation 6‑14

where:

               = standard oxygen transfer efficiency (as a fraction)

                  = conversion factor to account for the density, molecular weight, and O₂ mole fraction of the standard air
(U.S. Standard = 277.6533841; European Standard = 300.495893)

In the case of user-defined standard air (see Entering Airflow section below), the airflow is calculated using Equation 6‑15.

Equation 6‑15

where:

            = mole fraction of O₂ in user-defined air   (mole/mole)

= molecular weight of O₂ (32 g/mole)

                = density of user-defined air (g/m³)

            = average molecular weight of user-defined air (g/mole)

The airflow at either U.S. or European standard conditions is converted to field conditions using the ideal gas law:

Equation 6‑16

where:

          = air temperature at standard conditions (°C)

                = air temperature at field conditions (°C)

Equation 6‑16 assumes that the field air has the same humidity as the standard air.  If the humidity of the field air is different than for the standard air, the user can multiply the GPS-X calculated field air by the ratio of the mole fraction of oxygen in the field air by the mole fraction of air in the standard air.

No conversion to field conditions is undertaken for user-defined standard air.

Entering  Directly – Mechanical Aeration

Mechanical surface aeration is calculated similarly to diffused; however, the fouling and depth correction factors are not required, and oxygen transfer is related to the mechanical power input.

For mechanical surface aeration, the DO saturation concentration at field conditions is calculated using Equation 6‑17, which is a modification of Equation 6‑2.

Equation 6‑17

as  = 1 in this case, the pressure correction factor is re-defined in Equation 6‑18.

Equation 6‑18

The  at field conditions is calculated using Equation 6‑19.

Equation 6‑19

The OTR is calculated using Equation 6‑20.

Equation 6‑20

The SOTR is calculated using Equation 6‑21:

Equation 6‑21

With value of SOTR, the mechanical power can be calculated using Equation 6‑22.

Equation 6‑22

where:

       = mechanical power (kW)

                      = mechanical aerator oxygen transfer rate (1.75 kg O₂/kW h)

                  = conversion factor (24,000)

The default α value for mechanical aeration in GPS-X is 0.9.

Entering Airflow

The airflow can be entered at either standard or field conditions.  At standard conditions, the user has three options:

1. U.S. Standard Conditions:

· Temperature = 20°C

· Pressure = 1 atm

· Relative humidity = 36%

2. European Standard Conditions:

· Temperature = 0°C

· Pressure = 1 atm

· Relative humidity = 0%

3. User-Defined Standard Conditions:

The user must specify the properties (mole fraction of O₂ in air, density, molecular weight, and exponent in blower power equation).  When using the user-defined standard conditions option, GPS-X uses a Henry’s law correction to adjust the value of .

Equation 6‑23

GPS-X converts the airflow to U.S. standard conditions and then calculates the SOTR using Equation 6‑13. The OTR is calculated using Equation 6‑24.

Equation 6‑24

The oxygen mass transfer coefficient at field conditions is calculated using Equation 6‑11. If the airflow is entered at U.S. or European standard conditions, the airflow at field conditions is calculated using Equation 6‑16.

Entering Mechanical Power

If mechanical power is entered, the SOTR in g/d is calculated using Equation 6‑21. The  at field conditions is then calculated using Equation 6‑19 and the OTR is calculated using Equation 6‑20.

DO Control

The user has the option of controlling the aeration supply to the reactor to maintain a specific dissolved oxygen setpoint. In this case the model will calculate the necessary oxygen mass transfer coefficient at field conditions to maintain the DO at the setpoint.

For diffused aeration with DO control, GPS-X uses Equation 6‑12, Equation 6‑13, and Equation 6‑14 to calculate the SOTR, OTR, and airflow.  For mechanical aeration with DO control, GPS-X uses Equation 6‑20, Equation 6‑21, and Equation 6‑22 to calculate the OTR, SOTR, and mechanical power.

Standard Oxygen Transfer Efficiency (SOTE)

The user has the option of using a constant SOTE or using a correlation in GPS-X to calculate the SOTE.  When using the constant SOTE option, the default value (0.3) represents a typical estimate of the efficiency for fine bubble diffusers submerged at 4.3 m (14 ft.).

Alternatively, GPS-X has SOTE correlations for fine bubble, coarse bubble, and jet diffusers. For fine bubble aeration, the SOTE correlations are based on a regression equation developed by Hur (1994) which is shown in Equation 6‑25.

Equation 6‑25

where:

       = air flow per diffuser (scfm per diffuser)

       = diffuser density (diffusers/100ft²)

    = regression parameters

As shown, this equation depends on the depth of submergence of the diffusers, the diffuser density, and the airflow per diffuser.  Using this equation and the data found in Hur (1994), Hydromantis re-estimated the regression parameters to improve the fit of the regression. Separate regressions were performed for ceramic disc, ceramic dome, membrane disc, and membrane tube diffusers. The values of the regression coefficients can be found in the System > Input Parameters > Physical > More form.

There is also an option to use a user-defined SOTE correlation. The correlation has the same form as Equation 6‑25. The adjustable regression coefficients are found in the System > Input Parameters > Operational > More form of most biological objects.

Coarse Bubble and Jet SOTE

A separate SOTE correlation for coarse bubble and jet diffusers has been developed by Hydromantis based on data found in Mueller et al (2002) as shown in Equation 6‑26

Equation 6‑26

The SOTE for coarse bubble and jet diffusers is dependent upon the airflow per diffuser and the diffuser submergence.

In all the SOTE correlations, the airflow per diffuser has been limited to be within the ranges used for calibration.  The correlations are empirical and should not be extrapolated outside of the calibration range.  The ranges are used as follows:

Fine Bubble

Ceramic Disc:             

Ceramic Dome:           

Membrane Disc:          

Membrane Tube:         

Coarse Bubble

Jet

GPS-X applies a warning message to the log window if the airflow per diffuser is outside the ranges given above.

SOTE in Deep Tanks

The fine bubble SOTE correlation is modified for tanks deeper than 8 m.  Work by Pöpel and Wagner (1994) has shown that the SOTE does not continue to increase linearly with the depth of submergence beyond depths of approximately 8 m (see Figure 8 in Pöpel and Wagner (1994)).  At depths greater than 8 m the SOTE starts to level off so that the SOTE can never be greater than 100 %.

An extra quadratic term in diffuser submergence is added to Equation 6‑25 when the diffuser submergence is greater than 8 m, as shown in Equation 6‑27.

Equation 6‑27

The regression parameter  can be accessed in GPS-X in the Input Parameters > Operational > More form.  The parameter  was estimated by Hydromantis uses linear regression to fit Equation 6‑26 to the solid curve in Figure 8 of Pöpel and Wagner (1994).  To perform the regression, it was necessary to first adjust the airflow per diffuser and the diffuser density to match the SOTE of 20% at a depth of 5 m shown in Figure 8 of Pöpel and Wagner (1994).

The deep tank SOTE correlation is only applied for fine bubble diffusers.  It can be turned off by setting the parameter  to zero in GPS-X.

Blower Wire Power

The wire power in kW consumed by the blowers to deliver the required air is calculated in GPS-X using Equation 6‑28:

Equation 6‑28

where:

       = delivered power of blowers (kW)

          = overall efficiency of mechanical equipment (i.e., blowers, motors, coupling, and gearbox)

The overall efficiency of the mechanical equipment is entered into GPS-X in the Input Parameters > Operating Cost form of most biological objects. The delivered power of the blowers is calculated using the adiabatic compression equation (Mueller et al., (2002)):

Equation 6‑29

where:

         = mass flow rate of air

         = blower inlet air temperature (degrees K)

         =  where  is the heat capacity of air at constant pressure
(K = 0.283 for U.S Standard Air and K = 0.2857 for European Standard Air)

        = absolute pressure downstream of blower (discharge pressure in kPa)

         = absolute pressure upstream of blower (inlet pressure in kPa)

The discharge pressure of the blower is calculated as follows:

Equation 6‑30

where:

      = pressure drop in piping and diffuser downstream of blower (found in Input Parameters > Operating Cost form of most biological objects)

The inlet pressure is calculated as shown in Equation 6‑31

Equation 6‑31

where:

   = pressure drop in inlet filters and piping to blower (found in Input Parameters > Operating Cost form of most biological objects.)

Oxygen Transfer at Surface

A correlation relating the mean velocity gradient in a tank to the oxygen intrusion at the tank surface was adapted from Lahav et. al (2006).

Equation 6‑32

where:

            = Oxygen mass transfer coefficient at surface (1/d)

               = Geometry coefficient (m • s)

                       = Mean velocity gradient (1/s)

             = Water height in tank (m)

The value of the geometry coefficient depends on the shape of the tank and can be adjusted to calibrate the relationship between the mean velocity gradient and oxygen intrusion.

The surface oxygen transfer correlation is implemented in every biological tank with a surface open to the atmosphere in GPS-X. The correlation can be activated in the Oxygen Transfer at Surface section of the Input Parameters > Operational menu. Once activated, the mean velocity gradient and geometry coefficient can be adjusted if necessary. The option to set the  directly is also included.

The oxygen intrusion works on an either/or basis with each object’s aeration system. If non-passive aeration is active the oxygen transfer at the tank surface will be set to zero. If the object is not aerated the surface oxygen transfer correlation will govern the rate of oxygen transfer to the tank (assuming the correlation has been activated).

Alpha Correlation with Soluble Substrate COD

A correlation, shown in Equation 6‑33, relating the soluble substrate COD to the alpha factor for aeration was adapted from the work of Ahmed et al. (2021), shown in .

Equation 6‑33

where:

                 = aeration alpha factor in tank (-)

                 = maximum aeration alpha factor (default = 0.7 (-))

             = soluble substrate COD (mgCOD/L)

Figure 6‑1 – Aeration alpha factor correlation vs. soluble substrate COD concentration for different values of maximum alpha

The correlation is implemented in every aerated biological tank in GPS-X except the aerobic digester (due to high solids concentration the aerobic digester uses a correlation relating alpha to total suspended solids).

Dynamic alpha factor estimation using the soluble substrate COD is turned off by default and can be activated with a switch found in the Oxygen Transfer Settings section of the Input Parameters > Operational > Diffused Aeration menu. The maximum alpha factor that can be calculated by the correlation can also be specified in the same section of the Diffused Aeration menu.

Modelling of Temperature Dependent Kinetics

In general, the relationship between the growth kinetics and the temperature may be expressed using an asymmetrical bell-shaped curve.  The crest of the curve represents the maximum growth rate at optimum temperature.  The growth rate on either side of the crest decreases according to some appropriate growth rate-temperature relationship.

There are several models which may be applied to model the temperature dependent kinetics for biological reactions.  Depending on the structure of the model, the model may require estimation of model parameters which may be very different than the traditional temperature coefficient approach used in the wastewater engineering.  Generally, the Arrhenius equation is used to model the temperature effect on kinetic parameters in the range of 5℃ – 35℃.  This equation uses a temperature coefficient.  The values of temperature coefficients are well researched. Therefore, using any other model which deviates from this relationship will require recalculating of model parameters.  To model such a curve the following three parameter model was used.

1. Estimate the kinetic coefficient at the optimum temperature – The kinetic parameter values in GPS-X are listed at 20°C; therefore, this value is translated to a value at the optimum temperature using Equation 6‑34:

Equation 6‑34

where:

     = kinetic coefficient at  (time^-1)

       = kinetic coefficient at 20°C (time^-1)

      = optimum temperature at which the value of kinetic coefficients is maximum (°C)

         = Arrhenius coefficient for low temperature

        = Arrhenius coefficient for high temperature

2. Estimate the value of kinetic coefficient at a given temperature T by using Equation 6‑35:

Equation 6‑35

where:

        = kinetic coefficient at T (°C)

Based on the above relationships the temperature dependency of the kinetic coefficients can be expressed as shown in Figure 6‑2. For the low temperature range, the default GPS-X temperature coefficient values were used for all the kinetic parameters.  For the high temperature range temperature coefficient (), the default values of 1.15 and 1.25 were used for the growth rate of heterotrophic and autotrophic microorganisms, respectively.

Figure 6‑2 - Variation of Nitrifier Kinetic Parameter Value with Temperature

Temperature Modelling

The current GPS-X model uses a user-defined temperature in the biological unit processes. When using these models, it is assumed that the user has previous knowledge about the expected temperature in different biological reactors. Temperature in biological units is estimated based on the heat balance in the tank considering heat losses and gains.

A simple heat balance model as proposed by van der Graff (1976) and later validated by Gillot and Vanrolleghem (2003) is used to model the temperature change in a biological tank. The model was appropriately modified to account for the heat generation in denitrification and nitrifications reactions.

The equations described in Gillot and Vanrolleghem (2003) were developed for a completely mixed basin under steady state conditions. These equations were appropriately modified to model the temperature under dynamic conditions. The completely mixed hypothesis assumes that the water temperature is uniform over the basin and equals the outlet temperature. The energy balance over the reactor can be expressed with following equation.

Equation 6‑36

where:

= density of water (kg/m³)

      = the specific heat of water (J/kg/°C)

       = the wastewater flow rate (m³/s)

       = the influent temperature (°C)

      = the water temperature in reactor (°C)

       = enthalpy change due to heat transfer (J/s)

The  term includes the following terms:

· Convective and evaporative loss at the surface of the reactor due to aeration. ()

· Heat loss due to conduction across the reactor wall ()

· Heat input due to mechanical and blower energy ()

· Heat input due to biological heat production ()

The calculation method for each heat transfer term is shown in Table 6‑1.  The present model neglects the heat transfer due to solar radiation and long wave radiation. The surface convection and evaporation losses are lumped into the convection and evaporative heat transfer due to aeration.

Table 6‑1 – Heat Transfer Terms with Equations for Estimation

Heat Transfer Term	Equation Used for Estimation	Comment
		Convective and evaporative loss during aeration
		Heat transfer liquid/air contact wall Heat transfer liquid/soil contact wall
		Power input of surface aerator or blower
		Heat generation from the aerobic oxidation Heat generation from denitrification Heat generation from nitrification

The list of parameters used in the temperature estimation model is shown in Table 6‑2.

Table 6‑2 – Parameters for the Temperature Model

Parameter	Description	Unit	Value
	Heat coefficient	W/m^2/C	Subsurface aeration, Surface aeration,
A	Surface area of reactor	m^2	Variable
V	Volume of the reactor	m^3	Variable
	Air temperature	C	Variable
	Water temperature in reactor	C	Variable
	Heat transfer coefficient for liquid/air wall	W/m^2/C	1.0 (default)
	Liquid-air contact wall area	m^2	Variable
	Heat transfer coefficient for liquid/air wall	W/m^2/C	1.0 (default)
	Soil temperature	C	Variable
	Liquid-soil contact wall area	m^2	Variable
	Total aerator power	W	Variable
	Unit heat production during aerobic reaction	J/g O2 consumed	13985.0 (default)
	Unit heat production during denitrification	J/g NO3-N consumed	32000.0 (default)
	Unit heat production during nitrification	J/g NH4-N consumed	25000.0 (default)
	Oxygen uptake rate	g O2 consumed/s	Estimated by model
	denitrification rate	g NO3-N consumed/s	Estimated by model
	Ammonia oxidation rate	g NH3-N oxidized/s	Estimated by model

All the heat transfer terms are estimated, and the heat balance equation is solved for steady state and dynamic conditions. An iterative Newton-Raphson method is used to solve for temperature at steady state.

Summary of Aeration Input Parameters

This section discusses the aeration forms that are applicable to most biological objects.  The forms from the Completely-Mixed Tank are used as an example.

Physical

The Physical menu of the Suspend Growth model set-up can be accessed by right clicking on most biological models and selecting Input Parameters > Physical. Figure 6‑3 shows the GPS-X form that opens from the Completely-Mixed Tank process.

Figure 6‑3 – Physical Menu of the Completely-Mixed Tank Process

Dimensions

Maximum volume: the maximum volume of the reactor (which may be greater than the liquid volume if the tank is partially filled).

Tank Depth:  Depth of reactor (assuming constant surface area throughout depth).

Dimensions (More…)

The Dimensions More… menu can be accessed to set local conditions. The available parameters are shown in Figure 6‑4.

Local Environment Selection

Use local settings for O2 solubility and biological activity: Select whether local or global conditions are used for oxygen solubility.

Biological reactions:  Switch to turn biological reactions on/off

Gas-liquid transfer:  Switch to turn biological reactions on/off

Chemical reactions:  Switch to turn biological reactions on/off

Figure 6‑4 – Physical > Dimensions More… Menu

Oxygen Solubility (if individual settings are used)

Liquid temperature: Allows the user to specify the local wastewater temperature

Blower inlet air temperature: Allows user to specify the inlet air temperature for the blowers.

Elevation above sea level: Specifies the elevation above sea level.

Standard air conditions: If the aeration method is diffused, this switch selects which standard conditions are used to calculate the standard air flow used within GPS-X and displayed as an output. The available options are:

· U.S. (air temp 20C, 36% humidity)

· European (air temp 0C, 0% humidity)

· User-Defined

 If user-defined standard air is selected, the user must enter the properties of their air in the Properties of User-Defined Air sub-section.  The user-defined air option provides the user with a method of specifying pure oxygen

Properties of User-Defined Air

Mole fraction of oxygen in user-defined air: When user-defined standard air has been selected, this parameter specifies the oxygen mole fraction of the user-defined air.  The default value is 1 which is consistent with pure oxygen.

Density of user-defined air: When user-defined standard air has been selected, this parameter specifies the density of the user-defined air.  The default value is 1,429 mg/L which is consistent with pure oxygen.

Molecular weight of user-defined air: When user-defined standard air has been selected, this parameter specifies the molecular weight of the user-defined air.  The default value is 32 g/mole, which is consistent with pure oxygen.

Exponent in blower power equation: When user-defined standard air has been selected, this parameter specifies the value of exponent K in Equation 6‑28 for the user-defined air.  The default value is 0.284, which is consistent with pure oxygen.

Minimum K_La for Gases for Gas Release Under No Aeration

 These parameters can be used to set minimum gas transfer rates for non-aerated reactors (e.g. anoxic CSTR) to allow surface release of gases (e.g. CO₂, CH₄) from the liquid.  Note that surface intrusion of oxygen from mixing can be modelled using the Oxygen Transfer Settings.

Operational

The Operational menu of the Suspend Growth model can be accessed to perform aeration set-up in most biological models by right clicking on the object and selecting Input Parameters > Operational. Figure 6‑5 shows the GPS-X form that opens from the Completely-Mixed Tank process.

Figure 6‑5 – Operational Menu of the Completely-Mixed Tank Process

General Aeration Setup

Aeration method: Specifies the method used by the aeration system. Available options are:

· Diffused Air

· Mechanical (Surface Aeration)

Specify oxygen transfer by…: Specify the method of oxygen transfer. Available options are:

· Entering Airflow

· Entering Mechanical Power

· Using a DO Controller

· Entering

Entries that do not apply are greyed out. For example, you cannot specify the oxygen transfer by entering mechanical power if the aeration method is diffused.

Oxygen mass transfer coefficient (clean water): Clean water  at 20°C with no alpha or fouling factor correction.

General Aeration Setup > More…

The General Aeration Setup More… menu can be seen in Figure 6‑6.

Figure 6‑6 - General Aeration Setup > More... menu

Beta factor (for DO saturation): Specifies the DO saturation concentration correction factor for sales, particulates, and surface-active substances.  The default value is 0.95.

Temperature coefficient for : Specifies the temperature correction factor for ,  (default value is 1.024).

Diffused Aeration

This menu section is active when the Aeration method: Diffused Air and Specify oxygen transfer by…: Entering Mechanical Power options are selected.

Input air flow at…: Allows user to specify the conditions of the diffused air flow. Available options are:

· Standard Conditions

· Field Conditions

The user can select which standard conditions are used in the Input Parameters > Physical > More … if local conditions for O₂ solubility are used or in the System > Input Parameters > Physical form if global conditions for O₂ solubility are used.

Total air flow into aeration tank: the total amount of air being sent to the bioreactor, when the DO controller is not being used (for plug-flow tanks, this is the sum of all airflow in all zones in series).

Diffused Aeration > More…

The Diffused Aeration > More… menu can be seen in Figure 6‑7

Figure 6‑7 - Diffused Aeration > More... Menu

Diffuser Settings

Diffuser Type: Specifies the type of diffuser to be used.  This option is only active if diffused air has been selected.  GPS-X uses this selection to select the appropriate alpha value and to select the appropriate SOTE correlation (if applicable). Available diffuser types are:

· Fine Bubble

· Coarse Bubble

· Jet

Fine bubble diffuser head type: Used to specify the fine bubble diffuser head type when fine bubble diffused aeration has been specified and an SOTE correlation is being used. Available options are:

· Ceramic Disc

· Ceramic Dome

· Membrane Disc

· Membrane Tube

Height of diffuser from floor:  Vertical distance from floor to diffuser head.  Used in calculation of submergence for oxygen solubility.

Diffuser density: This menu allows the user to enter the diffuser density as diffusers/m², as well as specify the diffuser head surface area.  These parameters are used in the SOTE correlation described below.

Oxygen Transfer Settings

SOTE calculation Type: Specifies whether the SOTE is set by the user or calculated by a correlation.  The correlation used depends on the diffuser type selected.

Standard oxygen transfer efficiency per tank depth: When the SOTE type is set to constant, this value is used for the SOTE.  The SOTE is specified as % per unit depth.

SOTE regression coefficients: SOTE Regression parameters A₁ to A₆ used to determine SOTE when SOTE type is set to correlation.

Alpha factor: Specifies the value of the wastewater correction factor for the K_La. The default GPS-X settings are 0.6, 0.8 and 0.85 for fine bubble, coarse bubble, and jet, respectively.

Estimate dynamic alpha using soluble substrate COD: Specify if alpha should be calculated from the correlation relating soluble substrate COD to the alpha factor.

Maximum value for dynamic alpha: Maximum value of alpha that can be calculated by the soluble substrate COD to alpha factor correlation. Set to 0.7 in GPS-X by default.

Fouling Constant: Diffuser fouling factor. Default value is 1 (i.e., no fouling)

            Aeration Limits

Apply aeration Limits: Users can apply minimum and maximum airflow limits by turning on this feature.  

                                                Maximum airflow specification method: Airflow limits can be set via:

· By Diffuser – set min/max airflow rate per diffuser

· By Tank – set min/max airflow rate for entire tank (or for each tank in series, in the case of plug-flow units)

Airflow limits per diffuser:  minimum and maximum rates per diffuser for different diffuser types

Airflow limits per tank: minimum and maximum rates per tank (regardless of diffuser type)

Mechanical (Surface Aeration)

This menu section is active when the Aeration method: Mechanical (Surface Aeration) and Specify oxygen transfer by…: Entering Mechanical Power options are selected.

Aeration power: The rotor power applied to the mechanical aeration system.

Mechanical (Surface Aeration) > More…

The Mechanical (Surface Aeration) > More… menu can be seen in Figure 6‑8.

Figure 6‑8 – Mechanical (Surface Aeration) > More... Menu

            Aeration Limits

Minimum power per unit volume: minimum rotor power applied for mechanical aeration per unit volume of the reactor

Maximum power per unit volume: maximum rotor power applied for mechanical aeration per unit volume of the reactor

            Mechanical (Surface Aeration)

Mechanical aerator oxygen transfer rate: Specifies the mass of oxygen transferred to the liquid per unit of energy used by the mechanical aerator.

Alpha factor (mechanical aeration): Wastewater correction factor for mechanical .  The default value is 0.9.

Aeration Control

This menu section is active when the Specify oxygen transfer by…: Using a DO Controller option is selected.

DO setpoint:   Setpoint for the dissolved oxygen (DO) concentration in the reactor (or individual reactors, in the case of plug-flow tanks) when the DO control option is used.

Aeration Control > More…

                                    The Aeration Control > More… menu can be seen in Figure 6‑9.

For more information on controller setup, refer to CHAPTER 12 - Tools and Process Control Objects

Figure 6‑9 – Mechanical (Surface Aeration) > More... Menu

Oxygen Transfer at Surface

Estimate oxygen intrusion with correlation: ON/OFF button to turn on application of the oxygen intrusion function, as described in Oxygen Transfer at Surface.

Oxygen transfer coefficient at surface:   value for oxygen transfer at the liquid surface (used if correlation is turned off)

                                    Mean velocity gradient:  mixing input for oxygen intrusion correlation

Geometry factor: parameter for calibration of oxygen intrusion correlation for the tank geometry

Operating Cost

The Operating Cost menu of the Suspend Growth model can be accessed to define the operating cost of operating the process. The operating cost setup menu can be accessed for most biological models by right clicking on the object and selecting Input Parameters > Operating Cost. Figure 6‑10 shows the GPS-X form that opens from the Completely-Mixed Tank process.

Figure 6‑10 - Operating Cost Menu of the Completely-Mixed Tank Process

Blower Cost

Combined blower/motor efficiency:Specifies the overall efficiency of the mechanical aeration equipment (i.e., blowers, motors, coupling, and gear box).  The default value is 0.7 or 70 % efficiency.

Pressure drop in inlet filters and piping to blower: Specifies the pressure drop in the inlet filters and piping to the blowers for the purposes of calculating the wire power supplied to the mechanical aeration equipment.  The default value is 1 kPa.

Pressure drop in piping and diffuser downstream of blower:  Specifies the pressure drop in the piping and diffusers downstream of the blowers for the purposes of calculating the wire power supplied to the mechanical aeration equipment.  The default value is 7 kPa.

Layout Wide Aeration Settings

When global conditions are being used for oxygen solubility or it is necessary to change global physical constants important to aeration, the relevant physical data is accessed by selecting System > Input Parameters > Physical Environment Settings.  The available parameters are shown in Figure 6‑11.

Figure 6‑11 – Layout Wide Physical Environments Settings

Oxygen Solubility (layout-wide settings)

Most of the parameters in this sub-section of the layout-wide physical form are duplicates of the local versions defined in Oxygen Solubility (if individual settings are used) with exception to:

Barometric pressure at sea level:  Specifies the pressure at sea level.  The default value is 1.0 atm or 101.325 kPa.

Properties of User-Defined Air

The parameters in this sub-section of the layout-wide physical form allow users to define global properties of user-defined air conditions. The parameters in this sub-section are duplicates of the local variables defined in Properties of User-Defined Air.

Properties of User-Defined Air > More

The Properties of User-Defined Air > More… menu can be seen in Figure 6‑12.

Figure 6‑12 - Properties of User-Defined Air > More Menu

Composition of Dry Air

Users can enter the mole fraction of gases to specify the composition of the user defined air source.

Physical Constants

Molecular weight of air (@ U.S. Standard Conditions):  Specifies the molecular weight of air at U.S. Standard Conditions which is used in Equation 6‑5 to calculate the barometric pressure at the elevation and air temperature specified.  GPS-X does its internal calculations in U.S. Standard Conditions.

Gas constant:  Specifies the value of the universal gas constant.

Antoine coefficient A1:  Coefficient A in the Antoine equation which is used to calculate the vapour pressure of water at a given water temperature.

Antoine coefficient A2:  Coefficient B in the Antoine equation which is used to calculate the vapour pressure of water at a given water temperature.

Antoine coefficient A3:  Coefficient C in the Antoine equation which is used to calculate the vapour pressure of water at a given water temperature.

Ratio of gas

These values are used to relate the mass transfer of oxygen (which is set by the user, manipulated via a DO controller, or calculated directly) to the mass transfer of the other gases in each GPS-X library.

Ammonia Stripping

Ammonia Stripping:  Switch to activate ammonia stripping

Ratio of  of NH₃ gas to  of O₂ gas:  parameter for relating ammonia stripping mass transfer coefficient to oxygen mass transfer

Ratio of mass of gas to state variable unit

These parameters relate the mass of the gas state variable to the corresponding mass of the liquid state variable for the gas.  For example, CH4 has units of gCH4 for gas, but gCOD for liquid, so a conversion of 0.25 is required to convert between them when calculating mass transfer.

Number of atoms per molecule of state variable unit

These parameters specify the number of atoms per unit of the corresponding state variable (e.g., oxygen state variable is O_2, so value is 2.0).

Aeration Output Variables

The aeration output variables can be accessed by right-clicking on most biological objects and selecting Output Variables > Oxygen Transfer.  For single tank objects, such as the Completely-Mixed Tank, the same form can be accessed by right-clicking on the overflow stream.  For muli-tank objects, such as the Plug-Flow Tank, the total airflow, SOTR, OTR, and mechanical power can be accessed by right-clicking on the overflow stream, navigating to the Output Variables option and selecting Total Air Flow, Total Oxygen Transfer, or Total Mechanical Power.

The output variables associated with the blower calculations can be accessed by right-clicking on the object (single-tank objects only) or the overflow stream and selecting Output Variables > Operating Cost.

MBR Aeration Model

In the Membrane Bioreactor (MBR) and Completely-Mixed MBR objects the biological air and cross-flow air in the membrane tanks are tracked separately.  The biological air is handled similarly as in the other objects in GPS-X with the exception that surface mechanical aeration is not an available option. 

Cross-flow air the MBR is assumed to be delivered using a coarse bubble aeration system. The inputs for the MBR cross-flow air system can be found by selecting Input Parameters > Operational Membrane under the Cross-Flow Air subsection, shown in Figure 6‑13. The user can enter the following variables for the crossflow air:

· Cross-flow air flow

· Alpha factor for cross-flow air

· Standard oxygen transfer efficiency (cross-flow)

The cross-flow air is assumed to be at the conditions specified for the biological air (i.e. Standard or Field).  Unlike other objects in GPS-X, the user can specify whether the air is at standard or field conditions even if the user is not entering the biological airflow.  GPS-X tracks the biological and cross-flow air separately but also calculates the total air flow, SOTR, and OTR delivered to the tank.

In the MBR objects, lower default alpha values are used to reflect the high MLSS concentrations typically found in MBRs.

Figure 6‑13 - Membrane Bioreactor Input Parameters > Operational - Membrane Menu

Air Delivery Head-loss Model

This model extends the capability of the standard aeration model in activated sludge unit process models to simulate the head-loss in the air delivery model, thus simulating the dynamic changes in the blower discharge pressure. The air delivery head loss model can be used to simulate the following losses in air delivery system:

1. Air diffuser

2. Air delivery pipes and fittings

3. Control valve

In the air delivery head loss model, the required air flow rate in each biological reactors (user specified or calculated by DO controller) are used to estimate head-losses in various components of the air delivery system.  To model the air delivery system, the model uses a predefined air delivery system as shown below. The model is based on the proposed model by Gray and Kestel, 2013 with some modifications.

Figure 6‑14 - Predefined air delivery system

The pressure loss calculations for the diffuser, air pipe and control valve are described in following sections.

Diffuser Headloss

The diffuser head loss is calculated based on a diffuser head loss curve. The default diffuser head loss curve in model is as shown in Figure 6‑15. Users can define headloss curves by providing several points specifying air flow rate per diffuser and the expected head loss. The air flow rate per diffuser is calculated based on the air flow rate requirement and the number of diffusers in each tank set by the user in the aeration menu. The user may use available diffuser head loss curves from the aeration system supplier.

Users may refer to the ASCE (1988) reference on Aeration for expected diffuser head loss for different diffuser systems.

Figure 6‑15 - Default curve for diffuser head loss

Air Delivery Pipe Head Loss

The head loss in a straight pipe is calculated using the following equation (Qasim, 1999).

Equation 6‑37

Where:

= Head loss (mH₂O)

= friction factor (-)

          = length of pipe (m)

         = pipe diameter (m)

= air flow rate (m³/min)

P          = Air supply pressure (atm)

          = Temperature in pipe (K)

The friction factor is calculated using the following equation:

Equation 6‑38

The temperature in pipe is estimated as below:

Equation 6‑39

Where:

= Ambient air temperature (K)

= Ambientbarometric pressure (atm)

Minor Fitting Losses

The minor fitting losses in the ell, tees and other fittings are estimated using the pipe head loss equation as above. The user is required to estimate the equivalent length of the fittings and input it into the model (Qasim, 1999).

The user may use the following equation to find the equivalent length of the fittings.

Equation 6‑40

Where:

          = Equivalent length of pip fitting (m)

= C value for equivalent pipe length (-)

         = Diameter of fitting (m)

The  values for the fitting are typically available from the manufacturer/supplier.

Valve Head loss

The head loss in a valve is estimated based on the following equation used by Gray and Kestel, (2013).

Equation 6‑41

Where:

          = Air flow rate (scfm)

= Inlet pressure (psia)

         = Outlet pressure(psia)

          = Temperature (K)

         = Specific gravity of air (-)

        = Valve flow coefficient (scfm/psia)

The specific gravity of air is estimated at the pressure and temperature of air in pipe as estimated for the pipe head loss. The valve flow coefficient depends on the valve position and the valve characteristics curve.  The model uses linear, equal percentage, hyperbolic, exponent, and square root valve characteristic curve equations to estimate the valve flow coefficient. Valve characteristic equations used are shown in Equation 6‑42 to Equation 6‑46.

Linear Valve Characteristic Equation

Equation 6‑42

Equal Percentage Valve Characteristic Equation

Equation 6‑43

Hyperbolic Valve Characteristic Equation

Equation 6‑44

Exponent Valve Characteristic Equation

Equation 6‑45

Square Root Valve Characteristic Equation

Equation 6‑46

Where:

= Valve flow coefficient (scfm/psia)

= valve flow coefficient at fully open valve (scfm/psia)

         = Valve position from 0 – 1 (-)

= Valve factor for the curve (-)

         = exponent (-)

For a given air flow rate in each reactor, the model estimates the head loss in diffusers, drop pipes and fittings and control valves. Based on the hydrostatic pressure and the calculated head losses, the pressure at point P₁ and P₂ (Figure 6‑14) are estimated. The pressure at point P₁ is balanced by manipulating the valve positions. Two algorithms of Most Open Valve (MOV) and Set Point Pressure are implemented. In MOV algorithm, the valve corresponding to the maximum head loss is opened until it is open to specified maximum and then the other valves are adjusted to achieve the same pressure as estimated by the MOV. In the Set Point Pressure method, all the valves are adjusted to achieve the set point blower pressure.

Activated Sludge Biological Models

State Variables

A few comments about the state variables used in each of these models is required. For all the models, the symbolic name of the state variables is prefixed with either an X for particulate component, S for soluble component, or in some cases a G for gaseous component. This designation follows the IWA (Henze et al., 1987a) convention, but is somewhat arbitrary because some soluble and particulate components are colloidal and will pass through a 0.45mm filter but will still be classified as part of a particulate component. For example, the slowly biodegradable material, designated xs, may include soluble and/or colloidal material. This approach greatly facilitates model development; however, it invariably introduces some error into the models. The issues of wastewater characterization are important, and the modeller should refer to the papers listed with the individual models discussed below.

Model Matrix

Most biological process models now follow a standard matrix format.  An example of this format is shown in Table 6‑3.

Table 6‑3 – Example Model Matrix (Wentzel et al., 1987a)

In this table, the components or state variables of the Monod-Herbert model (Herbert, 1958), designated by a variable with a subscript i, are numbered and listed across the top. Three state variables are defined (X_B, S_B and S₀), each having its own column.  Names and units for each state variable are provided in the bottom row of each of these columns. The important processes, designated p_j, in the system, which result in changes in the state variables, are shown in separate rows; the actual process rate (kinetic expression or rate equation) is shown in the rightmost column of each of these rows. All the necessary kinetic parameters are defined in the lower right-hand corner of the table.

The entries within the table are the stoichiometric parameters or relations, designated v_ij, used in defining the net process rate for a component. These parameters define the mass relationships between components and are defined in the lower-left hand corner of the table. If a process does not directly affect a component's rate, then the table cell will be empty (the entry is assumed to be zero in this case).

The net reaction rate of a component, designated r_i, is the sum of all the process rates, which cause a change in the mass of that component. The expression used to determine the net rate is listed in the table in the row labeled Observed Conversion Rates.  When the model is presented in matrix format, this equation has a simple visual interpretation. To determine the net rate of change for a component, first identify the column of the component of interest and move down that column until you find a table cell containing an entry. Multiply the table cell entry by the process rate shown in the rightmost column. The sum of these individual process rates is the net reaction rate. Do likewise for all remaining rows in the column, which contain stoichiometric parameters.

Stoichiometric Parameters

Two common stoichiometric parameters appearing in the biological models in this chapter are derived from their respective chemical equations. First is the nitrogen to oxygen stoichiometric parameter used in the denitrification equation. A value of 2.86 is used throughout the GPS-X libraries for all the biological models. This value is derived from the molecular ratios shown in Equation 6‑47:

Equation 6‑47

The ratio of mass oxygen produced per mass nitrogen gas produced is 160:56 or 2.86:1.  Similarly, the stoichiometric ratio of oxygen to nitrogen required for nitrification (used in many of the biological models) has a value of 4.57 which is derived from the molecular ratios shown in Equation 6‑48:

Equation 6‑48

The ratio of mass of oxygen to mass of nitrogen is 64:14 or 4.57:1.

Since these stoichiometric ratios cannot change, the values are hard-coded in GPS-X without user access.

Special Activated Sludge Units

Membrane Bioreactor (MBR)

The two membrane bioreactor objects in GPS-X (plug-flow and completely-mixed) are a combination of a suspended-growth activated sludge model, and a simple suspended solids separation filter.  They are available in all libraries, and with all biological models. The two MBR objects are shown in Figure 6‑16, with the connection points illustrated.

Figure 6‑16 - GPS-X Membrane Bioreactor Objects

General Model Structure

The structure of the MBR model combines a conventional activated sludge tank model (plug-flow or CSTR) with an in-tank solids separation filter, as shown in Figure 6‑17.  In the case of the plug-flow MBR, the filter is placed in the final tank (an optional internal recycle is shown for illustrative purposes).  Permeate flow is drawn through the filter at a rate determined by the filter model.

Figure 6‑17 - Membrane Bioreactor Model Structures

MBR Model Modes

The MBR models in GPS-X allow for three modes of operation. The mode of operation can be toggled in the Input Parameters > Model Options menu. The three modes can be set up using the Model Option settings summarized in Table 6‑4.

Table 6‑4 - Settings of MBR Operating Modes

Operation Mode	Backwash and TMP calculations	Volume Calculations
Simple	Do not calculate backwash or TMP	Fixed Volume
Intermediate	Calculate backwash and TMP	Fixed Volume
Advanced	Calculate backwash and TMP	Variable Volume

Simple Modeassumes that the filter is properly operated to maintain flux and does not consider the effects of trans-membrane pressure (TMP), cake formation, fouling, backwashing, and membrane resistance. The Intermediate model mode calculates the TMP, cake formation, fouling, backwashing, and membrane resistance based on the specified backwash rate and cleaning frequency, but the required permeate flux is calculated based on the influent flow and waste flow to ensure that the liquid volume in the last tank remains constant. The Advanced model mode is like the Intermediate model mode, however the liquid volume in the tank is variable and can increase or decrease based on the calculated permeate flux.  The user can control the liquid level using a feedback controller that manipulates the trans-membrane pressure. Table 6‑5 summarizes the differences between Simple Mode, Intermediate, and Advanced Mode.

Model Parameters – Physical

All physical and operational parameters relating to the specification and operation of the activated sludge reactors are identical to the CSTR and plug-flow tank objects (with one exception – mechanical aeration is not available).  The specification of the membrane filter physical characteristics is done in the Input Parameters > Physical – Membrane menu, as shown in Figure 6‑18.  All parameters except solids capture rate are ignored (and greyed-out on these menus) when the model is set to Simple Mode.

Table 6‑5 – MBR Model Modes

Operating Parameter	Operating Mode
	Simple	Intermediate	Advanced
Flow Balance and Reactor Volume	Model assumes flow in equals flow out, and there is no change in reactor volume.  All incoming flow is assumed to exit via the filter and waste flow stream	Required membrane flux is determined based on influent flow and waste flow to ensure the liquid volume in the reactor is constant	Membrane flux is determined from filter model.  Reactor volume increases and decreases depending on the difference between flow in and flow out.  A controller is provided to manage the tank level
Filter Operation	Filter operation is ignored	Users must specify TMP, backwash/relaxation cycles, and cross-flow aeration	same as intermediate
Cross-Flow Air	Filter-cake solids removal from cross‑flow aeration is ignored, but oxygen transfer from the cross‑flow air to the bulk liquid is calculated and included in the biological activity	Both solids removal and oxygen transfer are considered for cross-flow aeration	same as intermediate
Solids Capture	The solids capture rate determines what fraction of the mixed liquor solids remain in the reactor.  These solids remain suspended in the bulk liquid.	The solids capture rate determines what fraction of the mixed solids remains in the reactor.  These solids make up the filter cake, and can be returned to the bulk liquid through backwashing or cross‑flow aeration.	same as intermediate
Biological Activity	There is no difference in the biological model when using simple, intermediate, or advanced modes.

Figure 6‑18 – Physical – Membrane Forms

The GPS-X MBR model calculates the removal of solids due to the membrane using a mass balance and the solids capture rate (actually a fraction) specified in the
Input Parameters > Physical – Membrane form.  The default solids capture rate has been selected to provide a permeate TSS concentration of 1 mg/L or less for typical MBR MLSS concentrations (i.e., 8,000 to 12,000 mg/L).  A separate mass balance is applied to each particulate component in the biological model. 

In the simple mode, the permeate flow (and flux) is calculated using a volumetric balance and the specified influent and pumped flows.  In advanced mode, the permeate flux through the membrane is modelled using a resistance-in-series model (Choi et al., 2000) shown in Equation 6‑49.

Equation 6‑49

where:

           = Permeate flux (m/s)

        = Trans-membrane pressure (kPa)

          = Viscosity of water (Pa)

       = Intrinsic membrane resistance (m^-1)

        = Cake layer resistance (m^-1)

        = Fouling resistance (m^-1)

The trans-membrane pressure, ΔP, is specified in the Input Parameters > Operational – Membrane menu, as described in the following section. The viscosity of water is calculated using Equation 6‑50 (Günder, 2001):

Equation 6‑50

where:

          = Temperature (°C)

The intrinsic membrane resistance, R_m, is provided in the Input Parameters > Physical – Membrane menu.  The default value used is based on data provided by Chang et al. (1999).  In advanced mode, GPS-X tracks the formation of a cake layer on the surface of the membrane that resists the liquid flux across the membrane.  The cake layer is assumed to be homogeneous, and its thickness is calculated as shown below in Equation 6‑51 (Choi et al., 2000).

Equation 6‑51

where:

        = Cake layer thickness (m)

       = Dry mass of cake layer (kg)

= Density of a cake layer particle (kg/m³)

          = Porosity of cake layer (dimensionless)

       = Total membrane surface area (m²)

The dry mass of the cake layer (see Equation 6‑51) is calculated using the following dynamic mass balance on the cake layer:

Equation 6‑52

where:

= Permeate flow rate (m³/d)

       = Concentration of solids in bulk liquid phase within the MBR (kg/m³)

= Solids capture rate or fraction (dimensionless)

  = Backwash flow rate (m³/d)

= Mass of solids in cake layer (kg)

= Backwash solids removal rate (1/m³)

   = Crossflow or air scour flow rate (m³/d)

       = Total membrane surface area (m²)

= Cross-flow solids removal rate (kg/m)

= Half-saturation coefficient for cross-flow air (kg)

The cake layer mass balance considers the bulk convection of solids to the surface of the membrane, the solids removed due to backwashing, and the solids removed due to cross-flow aeration. Equation 6‑52 ignores the diffusion away from the cake layer into the bulk liquid as this term is assumed to be small compared to the other terms in the mass balance.  The half-saturation coefficient for cross-flow air and the switching function based on the mass of cake solids is used to smoothly stop the solids removal as the cake layer disappears.

The default density of a cake layer particle in Equation 6‑51is equal to the density of dry biofilm already used in the GPS-X fixed-film reactors.  The default porosity of the cake layer is given in the Input Parameters > Physical - Membrane > More… menu and is estimated using information given in Chang et al. (1999).  The membrane surface area is site-specific and should be selected to achieve a flux within the range normally recommended by the manufacturer (e.g. a typical range for hollow fiber membranes is 17 to 25 L/m²/h; see Wallis-Lage et al., 2005).

The backwash solids removal rate in Equation 6‑52 is specified in the Input Parameters > Physical – Membrane > More … form.  It is multiplied by the backwash flow and the cake solids mass to give the mass of solids removed from the filter cake per unit time.  The default backwash solids removal rate was calibrated using data from Garcia and Kanj (2002).  The default backwash flow is entered in the Input Parameters > Operational – Membrane form and is based on data provided by Garcia and Kanj (2002).

The cross-flow solids removal rate in Equation 6‑52 is the mass of solids removed from the filter cake, per unit of cross flow air, per unit surface area of the filter.  The default value is entered in the Input Parameters > Operational – Membrane > More …form and is calibrated based on data in Garcia and Kanj (2002).  The cross-flow airflow is entered in the Input Parameters > Operational – Membrane menu.  The default value gives airflow per surface area of 0.37 m³/m²/h (see Wallis Lage et al., 2005) for the default membrane surface area.  The cross‑flow airflow should be changed to reflect changes in the membrane surface area.

The cake layer resistance,  is calculated by combining Equation 6‑51 and the Kozeny-Carman equation for flow through porous passages as follows:

Equation 6‑53

where:

        = effective cake particle diameter (m)

The default effective cake particle diameter is given in the Input Parameters > Physical – Membrane > More… menu and is estimated using information given in Shin et al. (2002).

The fouling resistance is calculated as follows (adapted from Choi et al., 2000):

Equation 6‑54

where:

  = maximum fouling resistance (m^-1)

        = fouling rate constant (d^-1)

           = time since last recovery clean (d)

The maximum fouling resistance and fouling rate constant can be found in the Input Parameters > Physical – Membrane menu.  They are selected based on data in Merlo et al. (2000).  The model assumes that the fouling material is completely removed during a recovery clean so that the time for fouling starts after each recovery clean.

Model Parameters – Operational

The membrane operational parameters can be set in the Input Parameters > Operational – Membrane menu, shown in Figure 6‑19.

Figure 6‑19 – Membrane Operational Parameters Menu

The trans-membrane pressure from Equation 6‑49 is set in this menu, along with the MBR backwashing options (including the frequency, duration, and flow rate of the backwash).  Alternatively, the level controller can be used, which sets the backwash length to the amount of time required to refill the tank.  If the level controller is on and the tank is already full, no backwashing will take place.

A helpful warning alarm can be set in the Membrane Backwash > More… menu.  The warn if tank is overflowing or empty alarm will print information to the Command Window if the filter flow causes the final tank to overflow or become empty.

A membrane flux controller can be activated to maintain the trans-membrane pressure at the membrane flux setpoint using a built-in controller with the rate of pressure increase being the controller gain.

The cross-flow air used to clean the membranes is assumed to be delivered using a coarse-bubble aeration system.  The alpha factor for cross-flow air is based on total suspended solids concentrations of between 8,000 mg/L and 10,000 mg/L in the MBR.  The standard oxygen transfer efficiency (cross-flow) is based on a coarse bubble aeration system at submergence of 4.3 m (14 ft.).

The cleaning frequency sets how often physical/chemical cleaning is used to reset the membrane fouling resistance to zero.

Output Variables

Several membrane-specific output variables are available to be plotted. The Membrane Filter Variables menu is accessed from the overflow connection point (not the filter connection point) and is shown in Figure 6‑20.

The MBR Cake Variables menu, shown inFigure 6‑21, provides output variables for total cake mass and cake thickness.

Figure 6‑20 - Membrane Output Variables Menu

Figure 6‑21 - MBR Cake Variables Menu

Tips on Using the MBR Models

The following points are useful to keep in mind when setting up an MBR simulation:

· When modelling a recycle activated sludge (RAS) stream, the user can simply use the internal recycle feature (located in Operational – Tank > Internal Flow Distribution) and set the internal recycle from the final (membrane) tank to the desired tank.

· Use Simple Mode initially to establish the required operating conditions, such as MLSS, SRT, waste flow, etc.; and in cases where details on the maintenance of the permeate flux are not required.  If you are only interested in the biological treatment aspects of the system, use Simple Mode.  If you need to also simulate the physical aspects of the filter operation (i.e. different backwash cycles, TMP management, etc.), then Advanced Mode is required.

· When using Advanced Mode, pay close attention to the volume in the reactor(s), as it is easy to either drain or overfill the reactor that contains the membrane filter.

· If you wish to have a membrane “relaxation” period (rather than a backwash period), set the duration and frequency as normal, but set the backwash flow rate to zero.  This will cause the permeate flow to cease for the appropriate length of time, but there will be no backwash flow into the tank. This can be done in both the Intermediate and Advanced modes.

· There is no steady-state solution for the model in Advanced Mode. The discontinuous backwashing and cleaning cycles render the model without a true steady equilibrium state (similar to why the SBR object does not have a steady-state solution).  When using Advanced Mode, you may wish to run a long dynamic simulation (~100 days) to allow time for the system to reach a cyclic or periodic equilibrium.  As there is no backwashing or cleaning in Simple Mode, the steady-state solver can be used.

A summary of the default values of the GPS-X MBR model parameters are shown below in Table 6‑6:

Table 6‑6 – GPS-X MBR Model – Default Parameter Values

Model Parameter	Unit	Default Value	Comment/Reference
Solids capture rate	-	0.9999	Default value was selected to provide a permeate TSS concentration of 1 mg/L or less for typical MBR MLSS concentrations
Density of dry cake solids	kg/m^3	1,020	Hydromantis (2003)
Porosity of cake layer	-	0.15	Chang et al. (1999)
Solids backwash removal rate	1/m^3	100	Calibrated using data in Garcia and Kanj (2002)
Cross-flow solids removal rate	kg/m	200,000	Calibrated using data in Garcia and Kanj (2002)
Intrinsic membrane resistance	1/m	1.0e+11	Chang et al. (1999)
Maximum fouling resistance	-	1.0e+12	Calibrated using data in Merlo et al. (2000)
Fouling rate constant	1/d	0.005	Calibrated using data in Merlo et al. (2000)

Anaerobic Membrane Bioreactor (Manti2, Mantis2S and Mantis3 only)

Model Structure

The anaerobic MBR model in GPS-X combines the completely-mixed MBR (in simple mode) with the gas transfer and headspace model of the anaerobic digester object.  The result is a completely mixed membrane bioreactor with a closed headspace and gas production.  Unlike the completely-mixed MBR, there is no modelling of the cake formation on the membrane surface, backwashing of solids, or trans-membrane pressure calculations. 

The model assumes that the reactor is completely mixed with no aeration, and that filtrate flow from the MBR is equal to the influent flow minus the pumped flow.  It is assumed that the filter is not limiting to the flow (i.e., that whatever flow is calculated can pass through the filter unimpeded).  The solids captured by the filter are retained in the completely mixed bulk liquid.

The anaerobic MBR is only available in the Comprehensive (Mantis2), the Selenium and Sulphur (Mantis2S) and the Carbon Footprint (Mantis3) libraries.  The anaerobic biological and chemical reactions are identical to those used in the anaerobic digester and UASB models.

Model Input Parameters

The physical menu of the anaerobic MBR object is used to specify the dimensions of the liquid tank and the headspace.  In addition, the headspace total gas pressure, gas-liquid transfer constant, and membrane solids capture are specified here as well, as shown in Figure 6‑22.

Figure 6‑22 – Anaerobic MBR Physical Parameters Menu

In the Input Parameters > Operational menu, the only operational parameter to be considered is the pump flow rate from the pumped connection on the lower right-hand corner of the object.  A PID control loop is available to be configured as well.

The remainder of the menus are like those shown in other completely mixed biological reactors. 

Model Output Variables

The output variables available for the anaerobic MBR object are a combination of those from the conventional CSTR and the anaerobic digester.  The filtrate and pump connection points show flows, concentrations, and operating cost variables for the liquid streams.  The gas connection (at the top of the object) shows the gas flow and composition.

Sequencing Batch Reactor (SBR)

Common Features

The models associated with the sequencing batch reactor (SBR) object are combinations of suspended-growth and sedimentation models. The various aerated and mixed phases use a suspended-growth model, assuming a completely mixed hydraulic configuration, while the settling and decanting phases use a reactive sedimentation model. The models are combined to form the whole unit process model.

Modes of Operation

There are three different SBR objects in GPS-X:  the simple sequencing batch reactor (SBR) object, the Advanced SBR object, and the Manual SBR object.  All three objects have the same functionality, appearance, and choice of biological models.  They differ in the way the user specifies the operation of the SBR unit.

The simple and advanced SBR objects require the specification of the timing and flow rates to define the phases. The manual SBR object requires that the entire operational cycle be defined by the user, either by having the liquid flows, air flows, and mixing on interactive controllers, or as file inputs. The manual object is suited to operator training, while the simple and advanced objects are typical for an SBR application.

When using multiple, parallel SBRs, it may be desirable to stagger the cycle times of the units. For example, if two parallel SBRs are in use, each with a 6‑hour cycle time, it may be desired to shift one of the SBRs by 3 hours. If both have 3 hours of detention time, then a continuous influent could be switched between the two unit processes. To specify a timeshift for an SBR model using either the simple or advanced objects, the user enters the desired timeshift for the timeshift for simple and advanced cycles parameter. The timeshift parameter cannot be set to a value greater than the cycle time.

Simple SBR Cycle

The parameters used to specify the operational cycle (in the regular SBR object, not advanced or manual) are found in the Input Parameters > Operational – Cycle Settings menu.  These parameters include the duration of one complete cycle and associated seven separate phases, which have predefined functions. The parameters are shown in Figure 6‑23.

Figure 6‑23 - Regular SBR - Operation Cycle Parameters

                        The 7 fixed SBR phases are:

1. Mix (and fill):  The unit is modelled as a CSTR without aeration (i.e., air flow, power or  set to 0.0). This phase is usually the starting phase, used while the tank has just started filling with liquid. This phase represents the first of four mixing phases.

2. Aerate (and fill): The unit is modelled as a CSTR with aeration. This represents the second mixing phase and is used while the tank is filling after the aeration has been turned on.

3. Mix only: The unit is modelled as a CSTR without aeration. This represents the third mixing phase usually occurring sometime after the tank has finished filling. It is typically used as a denitrifying phase.

4. Aerate: The unit is modelled as a CSTR with aeration. This is the last mixing phase generally used to re-aerate the sludge so that it will settle properly.

5. Settle: The unit is modelled as a settler, with or without biological reactions, depending on the model selected. The mixing is turned off to allow the content of the tank to become quiescent and to promote settling.

6. Decant: The unit is modelled as a settler. During this phase, the user-specified decant flow is activated.

7. Desludge: The unit is modelled as a settler. This phase occurs at the end of the cycle, and the user-specified wastage flow is activated.

With the normal SBR object, the seven phases making up this cycle are fixed in sequence (the order is shown in the menu). The total length of all seven phases must not exceed the specified cycle time. If the total length of all seven phases adds up to less than the cycle time, the tank will be idle until the end of the cycle time. If it adds up to a value greater than the cycle time, the remaining time and/or phases beyond the cycle time will be ignored.  A phase can be disabled by setting its length to zero.

The decant flow rate (pumped flow parameter) and waste flow rate (underflow rate parameter) are entered in the InputParameters > Operational - Flow Control menu.

The influent flow to the SBR is taken from the upstream object (e.g., influent object) if the influent #1 pump label parameter is left blank in the Operational – Flow Control menu. The user must then make sure that the influent flow is synchronized with the SBR cycle (i.e., entering the SBR during the appropriate phase). Alternatively, in the Operational – Flow Control menu, you can enter a stream label for the influent #1 pump label parameter, a flow rate for the first influent flow parameter, and the SBR influent flow will be automatically taken from that stream during the appropriate phase within the cycle (automatic synchronization). The stream label must be associated with a pumped flow stream (`qcon' variable), for example an influent icon or pumped flow from a tank. The influent #2 pump label parameter is ignored in this cycle type.

Advanced SBR Cycle Settings

The SBR operational cycle parameters for the Advanced SBR model are shown in Figure 6‑24. The advanced SBR cycle is more general than the simple SBR model, allowing the user to define up to ten or more different phases. For each phase defined, the corresponding duration, mixing (either on or off), aeration (oxygen mass transfer coefficient), decant flow rate, and wastage flow rate can be specified. The order of the user-defined phases is fixed according to their order presented in the forms.

The influent flow to the SBR is taken from the upstream object (e.g. influent object) if the influent #1 pump labeland influent #2 pump labelparameters are left blank in the Input Parameters > Operational – Flow Control menu. The user must then make sure that the influent flow is synchronized with the SBR cycle (i.e. entering the SBR during the appropriate phase). Alternatively, you can enter stream labels for the influent #1 pump label, influent #2 pump label, influent #1 flow in phase and influent #2 in phase parameters in the Operational – Flow Control menu (Advanced section), and the SBR influent flow will be synchronized automatically.

The stream labels must be associated with pumped flow streams (`qcon...' variables), for example an influent icon or pumped flow from a tank. Most applications will only use one influent, but second influent was provided for cases where, for example, methanol is added.

Figure 6‑24 - Advanced SBR Operational Parameter

Manual SBR Model

If the manual SBR object is used, the user must set up all the important parameters such as air flow rate, mixing, decant flow rate, and waste flow rate on interactive controllers to change them as the simulation proceeds.

Alternatively, the parameters can be set up as file inputs or controlled from custom code in the .usr file.

In the manual SBR model, there are no cycle settings as in the simple and advanced models.  The timing of mixing, aeration, and pumping must all be controlled directly.

The decant flow rate (pumped flow parameter) and waste flow rate (underflow rate parameter) can be entered in the Input Parameters > Operational - Flow Control menu, shown in Figure 6‑25.

The influent flow to the SBR is taken from the upstream object (e.g., influent object) if the influent #1 pump label parameter is left blank in the Operational - Flow Control menu. The user must then make sure that the influent flow is synchronized with the SBR cycle (i.e., entering the SBR during the appropriate phase). Alternatively, in the Operational - Flow Control menu, you can enter a stream label for the influent #1 pump label parameter, and the SBR influent flow will be automatically taken from that stream during the appropriate phase within the cycle (automatic synchronization).  The stream label must be associated with a pumped flow stream (`qcon' variable), for example an influent icon or pumped flow from a tank. The influent #2 pump label parameter is ignored in this cycle type.

Figure 6‑25 - Manual Cycle Operational Parameters

Oxidation Ditch

Setting the Recycle Flow

The oxidation ditch object operation as 16 CSTRs in series (a plug flow tank) with a large recycle from the last tank to the first.  The recycle can be specified in four different ways from the Input Parameters > Operational menu, using the ditch recirculation mode setting, shown in Figure 6‑26:

· Set ditch velocity – specify a constant surface velocity of the ditch flow

· Set constant ditch flowrate – rather than specifying velocity, set the flow

· Set proportional ditch flowrate – make the ditch flow proportional to the incoming flow to the oxidation ditch.  Typically, the ditch flow would be 50 to 200 times the incoming flow.

· Set constant outlet fraction – specify the fraction of the ditch flow that exits the ditch each time around.

Figure 6‑26 - Oxidation Ditch Recirculation Mode Settings

Special 2-D Greyscale Output Variables

The oxidation ditch has a series of special two-dimensional output variables that are designed to be displayed on 2-D greyscale outputs.  These variables are found in the Output Variables > 2-D Greyscale Ditch Output menu.  These graphs show a plan-view of the oxidation ditch, with first tank in the lower right-hand corner, and the effluent point in the upper-right hand corner (the actual influent point depends on the setting in the influent fractions menu).  The flow moves clockwise around each ditch.

Five different variables are available for output: 

· Dissolved oxygen (DO)

· Ammonia

· Nitrite

· Nitrate

· Oxygen uptake rate (OUR)

Figure 6‑27 shows an example of the 2-D greyscale DO graph for a typical oxidation ditch.

Figure 6‑27 - 2-D Greyscale Oxidation Ditch Output - Dissolved Oxygen

Steady State Convergence

Please note that due to the high recycle rate within the object (and subsequent short HRTs for each section of the ditch), the oxidation ditch model often will take longer than normal to converge to steady-state with the steady-state solver. You may find it necessary to increase the iteration termination criteria and/or the damping factor on final approach to achieve a reasonable solution. These variables can be accessed in the System > Input Parameters > Steady State Solver Settings menu.

If you are having difficulty with steady-state solutions, you can halt the steady-state solver at a higher iteration termination value and run a short dynamic simulation to test if the steady-state solver solution is adequate.  If the dynamic solution does not diverge appreciably from the steady-state conditions, then the higher iteration termination value is suitable.  If you have any questions or problems, please contact Hydromantis/Hatch for assistance.

Adapted Steady State Solver for Oxidation Ditch

It is notoriously difficult to achieve steady state convergence in oxidation ditch models, due to their large internal recirculation. To account for this, we have developed an adapted steady state solver, which can be found in the oxidation ditch Input Parameters > Operational > Ditch Flow Operation > More… menu, as seen in Figure 6‑28.

Figure 6‑28- Oxidation ditch adapted steady state solver.

Using the adapted solver may result in a slight sacrifice in the soluble concentration accuracy for the initial few days of the dynamic simulation but it greatly improves steady state convergence.

There are 3 parameters that can be adjusted to increase the accuracy of the solver:

1. Aeration Spread Factor: The aeration spread factor represents the extent to which the oxygen spreads around the ditch in regular dynamic operation. The closer to 1, the more spread the aeration is. The effects of using an aeration spread factor of 0 and 1 are shown in Figure 6‑29.

2. Influent weight: This weighting should be increased roughly proportional to the systems loading (i.e., influent BOD and ammonia). Increasing the influent weight may improve the accuracy of the steady state solver. The impact of increasing the Influent weight can be seen in Figure 6‑30.

3. SS to dynamic transition smoother: This feature will smooth the transition between the adapted steady state solver and the dynamic simulation in certain cases. It is typically most effective when “using a DO controller” is the oxygen transfer method. The impact of the SS to dynamic transition smoother variable is shown in Figure 6‑31.

Figure 6‑29 - The DO concentration for the steady state solution of the oxidation ditch when using an aeration spread factor of 0 (A) and 1 (B).

Figure 6‑30 - Impact of increasing the influent weight from 0 (A) to 4 (B) on the soluble nitrogen species profiles in the initial dynamic simulation.

Figure 6‑31 - Impact of having the SS to dynamic transition smoother off (A) and on (B) on the soluble nitrogen species profile.

The general strategy for oxidation ditch calibration using the adapted steady state solver is:

1. Start with an aeration spread factor of 1 and incrementally decrease it to minimize variability in the initial dynamic soluble effluent concentrations (ammonia, nitrate, sBOD, etc.). In some scenarios (i.e., high ditch velocity, small oxidation ditch, etc.) a spread factor of 1 may be ideal.

2. To further reduce the variability in the initial dynamic soluble effluent concentrations try increasing the influent weight.

3. Turn on the SS to dynamic transition smoother and observe the effect on the variability in the initial dynamic soluble effluent concentrations. If there is no noticeable effect, turn it off.

4. Fine tune the aeration spread factor and influent weight as necessary.

Continuous Flow Sequencing Reactor (CFSR)

Common Features

The models associated with the continuous flow sequencing reactor (CFSR) object operate as set of CSTRs in series (a plug flow tank) with a large recycle from the last tank in the series to the first tank.

The CFSR Recirculation mode can be specified using the recirculation mode field in the Input Parameters > Operational > Flow Operation menu, shown in Figure 6‑32.  The flow moves clockwise around the reactor, in ascending order of CSTR number. The CFSR has 5 different recirculation modes:

1. Set recirculation velocity – specify a constant surface velocity of CFSR flow

2. Set constant recirculation flowrate – rather than specifying velocity, set the flow

3. Set proportional recirculation flowrate – make the CFSR flow proportional to the incoming flow to the CFSR.

4. Set constant outlet fraction – specify the fraction of the flow that exits the CFSR each time around.

5. Set proportional to bridge – set the recirculation rate proportional to the rotational period of the aeration bridge (simulate rotating aeration bridge does not have to be on for this option to function)

Figure 6‑32 - Continuous Flow Sequencing Reactor Operational Menu

Rotating Aeration Bridge

The CFSR consists of a circular tank with an aeration grid suspended from a rotating bridge, though stationary aeration grids can be installed on the floor along the perimeter of the tank.

When modelling a rotating aeration bridge, users can specify the total air flow entering the CFSR through the rotating aeration bridge diffusers using the total air flow to rotating diffusers fieldin the Input parameters > Operational > Diffused Aeration submenu in Figure 6‑32. This air flow is moved around the CFSR from one CSTR cell to the next over the rotational period of aeration bridge specified in the Input parameters > Operational > Rotating Aeration Bridge submenu in Figure 6‑32. The rotational period of aeration bridge specifies the period of time required for the rotating diffusers to make one revolution around the tank

Conversely, when using stationary aeration grids, the total air flow can be specified using the total air flow to stationary diffusers field in the Input parameters > Operational > Diffused Aeration submenu in Figure 6‑32.

Controller Operation

The CFSR object specifies oxygen transfer by using either a DO controller option or entering airflow as the manipulated variable in place of  (similar to other DO controllers in GPS‑X). The PID DO controller manipulates  and back calculates the required airflow. For more information on setting up the PID controller, refer to CHAPTER 12.

The CFSR object contains a unique specify oxygen transfer by... option, the DO On/Off Controller is switching the airflow into the tank on and off depending on the specified DO high and low limits. How quickly action is taken by the controller (after the upper or lower limit is reached) is dependent on the controller’s specified sampling time.

The CFSR object in GPS-X contains three additional Aeration Controllers which can be paired with any of the specify oxygen transfer by... options: 

1. Aeration timer

2. Nitrate controller

3. Ammonia controller

These additional controllers can be seen in Figure 6‑33.  While the specify oxygen transfer by... controller options control only the DO concentration, the aeration controllers manage more complex aeration strategies in the tank.  During aerated phases of each of the aeration controllers, the selected specify oxygen transfer by... option manipulates the airflow according to the following strategies:

Figure 6‑33 - Continuously Flow Sequencing Reactor Additional Aeration Controllers

· Timer – The timer controller creates a fixed cycle of timed aerated and un-aerated phases.  The timer controller is configured by specifying the aeration start time, the aeration end time, and the length of the entire cycle, where the remaining time in the cycle is un-aerated.

· Ammonia controller – The ammonia controller controls airflow by turning on the air when the ammonia reaches the ammonia high limit in anoxic phase and turns off the air when the ammonia reaches the ammonia low limit in oxic phase.

· Nitrate controller – The nitrate controller consists of three phases: Oxic, anoxic, and anaerobic:

o Oxic – During the oxic phase, the aeration system in the CFSR is on.  Aeration in the tank continues until the nitrate high limit in oxic phase, nitrate concentration, is reached.  Upon reaching the specified upper concentration limit, the controller switches to the anoxic phase.

o Anoxic – During the anoxic phase, the aeration system in the CFSR is off.  The anoxic phase continues until the nitrate low limit in anoxic phase is reached.  Upon reaching the specified low concentration, the controller switches to the anaerobic phase.  If the average nitrate removal rate across the CFSR drops below the minimum nitrate removal rate in anoxic phase before reaching the low nitrate concentration, the controller will end the anoxic phase and return directly to the oxic phase without executing the anaerobic phase.

o Anaerobic – The anaerobic phase is a time phase of specified duration, commencing at the completion of the anoxic phase.  During the anaerobic phase, the aeration system in the CFSR is off.  Once the length of time specified in the anaerobic phase length has passed, the controller will return to the oxic phase.

Steady State Convergence

Please note that due to the high recycle rate within the object (and subsequent short HRTs for each section of the reactor), the CFSR model often will take longer or fail to converge to steady-state with the steady-state solver. You may find it necessary to increase the iteration termination criteria and/or the damping factor on final approach to achieve a reasonable solution. These variables can be accessed in the System > Input Parameters > Steady State Solver Settings menu.

If you are having difficulty with steady-state solutions, you can halt the steady-state solver at a higher iteration termination value and run a short dynamic simulation to test if the steady-state solver solution is adequate. If the dynamic solution does not diverge appreciably from the steady-state conditions, then the higher iteration termination value is suitable. If you have any questions or problems, please contact Hydromantis/Hatch for assistance.

High Purity Oxygen (HPO) System

The high purity oxygen (HPO) activated sludge object works the same way as a plug-flow tank object, except that the aeration system uses a HPO gas feed instead of regular air.  In addition, the entire plug flow system is capped, and each reactor has a headspace.  The headspaces are connected, to allow downstream flow.  The flow of gas downstream equalizes the pressure of the headspaces in all reactors and is determined from the gas input and venting flows. Figure 6‑34 shows the physical configuration of the HPO system

The flow of gas and flow of water are modelled separately.  The exchange of O₂ gas, N₂ gas and CO₂ gas at the air/water interface is determined using Henry’s Law, corrected for temperature and headspace pressure.

The regular biological models have been supplemented in the HPO object with stoichiometry to calculate CO₂ gas generation.  As the gas travels downstream, O₂ is transferred into the liquid and consumed by the biological activity.  N₂ and CO₂ are generated and equilibrated with the gas concentrations in each headspace.  Consequently, the composition of the gas (fraction of the gas that is O₂, N₂ and CO₂) can be displayed for each reactor in the plug-flow system.  Output variables for the gas composition can be found in the Output Variables > HPO Headspace menu.

Figure 6‑34 - Schematic of High Purity Oxygen (HPO) System

As the HPO system is capped, and CO₂ gas is contained in the headspace at concentrations often much higher than atmospheric values, HPO systems may have an atypical pH.  The GPS-X HPO object contains a pH calculator that determines the pH in the liquid for each reactor.  For details on the pH model, refer CHAPTER 1.  It is important to properly specify the anion and cation concentrations in the tank to achieve a calibrated pH calculation.

The pH that is determined for each reactor can be set to inhibit biological growth, using the pH inhibition settings in the Physicalparameters more… button.  The pH inhibition is set to OFF by default.

The growth of biomass is multiplied by a pH inhibition factor, taken from Grady and Lim (1980), which is bounded between zero and one.  This creates a linear decline between pH = 7.2 and pH ≈ 6.1.

Equation 6‑55

Open Basin HPO (MANTIS2LIB, MANTIS2SLIB and MANTIS3LIB only)

The open basin HPO unit process models the gas-liquid transfer processes for a pure oxygen fed activated sludge process. The open basin systems are considered to provide good oxygen transfer efficiency while allowing better exchange of CO₂. The better exchange of CO₂ prevents excessive drop in pH. The open basin HPO model has the following features:

· A gas-liquid transfer model based on feed gas and outlet gas composition

· Temperature estimation model based on energy balance

· High temperature and kinetic parameter relationship

Typical outputs from the energy balance model and the oxygen transfer model are shown in Figure 6‑35 and Figure 6‑36.

Figure 6‑35 - Typical Outputs from the Open Basin HPO Energy Balance Model for Temperature Estimation

Figure 6‑36 - Typical Outputs for the Open Basin HPO Oxygen Transfer Rate

Modelling of Gas Transfer in Open Basin HPO

The gas transfer to the bulk liquid phase of a biological reactor is modelled using a dynamic mass balance written for each dissolved gas (Hydromantis, 2011).  For example, refer to Equation 6‑1, which defines a dissolved oxygen mass balance around CSTR.

Calculation of DO Saturation Concentration at Field Conditions

The DO saturation concentration at field conditions is calculated as follows:

Equation 6‑56

where:

          =  mol fraction of oxygen in the headspace (-)

The correction factors are used to adjust the DO saturation concentration to account for the temperature of the liquid, the pressure at the submergence level of the diffusers, and the salts, precipitates, and surface-active substances found in the wastewater.

The temperature and pressure correction factors are calculated as shown in Equation 6‑3 and Equation 6‑18 respectively:

Referring to Equation 6‑10, the DO saturation concentration at 20 C and 1 atm is calculated as:

Where the depth correction factor for oxygen saturation is calculated using Equation 6‑57.

Equation 6‑57

The η for each gas is estimated using Equation 6‑58:

Equation 6‑58

where:

= average mole fraction of oxygen in bubble (-)

    = mole fraction of oxygen in air (-)

The average mole fraction of oxygen in the bubble is estimated using Equation 6‑59.

Equation 6‑59

where:

     = mole fraction of oxygen in feed gas (-)

       = mole fraction of oxygen in out gas (-)

= weight factor for averaging (-, default values is 1.0)

By substituting Equation 6‑10 in Equation 6‑56, the final expression for the DO saturation concentration at field conditions is defined in Equation 6‑60.

Equation 6‑60

Oxygen Mass Transfer Coefficient at Field Conditions Calculations

GPS-X provides four different ways to specify the user inputs to estimate gas-liquid transfer in the open basin HPO system.

1. Direct specification of the clean water at  at 20°C

2. Specifying the gas flow rate at standard condition of 1 atm pressure and 20°C temperature

3. Specify the wire point input of the oxygenator

4. Use a DO controller

In each of the above, the user has the option of specifying SOTE.  The default value for SOTE for high purity oxygen is considered to be 90%.

Entering  Directly

Estimate  at field conditions

The  at field conditions is calculated using Equation 6‑11:.

Estimate Oxygen Transfer Rate (OTR) at Field Conditions in g/d

The OTR at field conditions is calculated using Equation 6‑12.

Estimate Standard Oxygen Transfer Rate (SOTR) in g/d

The SOTR is calculated using Equation 6‑13.

Airflow at Standard Conditions in m³/d

The airflow at standard conditions is calculated using Equation 6‑15:

Estimate Airflow rate at Field Conditions

The airflow at standard conditions is converted to field conditions using the ideal gas law defined in Equation 6‑61.

Equation 6‑61

where:

                = HPO Feed pressure (kPa)

Estimate the SAE

The SAE is estimated based on the correlation provided by Praxair, shown in Equation 6‑62.  The expression is valid for SOTE in the range of 86% to 100%.  If the user specified SOTE is less than 80%, then SAE is bounded at 7.11 kg/kWh.

Equation 6‑62

where:

SAE      = Specific aerator energy (wire), kgO₂/kW-hr

The mechanical power requirement is estimated using Equation 6‑63.

Equation 6‑63

where:

 = motor efficiency

Entering Airflow

The gas flow rate is entered at a given standard condition of 1 atm and 20°C.

Standard Oxygen Transfer Rate (SOTE) in g/d

The SOTR is calculated using Equation 6‑64:

Equation 6‑64

where:

                 = density of feed gas (g/m³)

              = average molecular weight of gas (g/mole gas)

Estimate OTR

The OTR is calculated using Equation 6‑24:

Estimate  at Standard Condition

The  at standard conditions is calculated rearranging Equation 6‑13 to Equation 6‑65.

Equation 6‑65

Estimate  at Field Condition

The  at field conditions is calculated rearranging Equation 6‑12 to Equation 6‑66.

Equation 6‑66

Airflow at Standard Conditions in m³/d

The airflow at standard conditions is calculated using Equation 6‑67:

Equation 6‑67

Estimate Airflow Rate at Field Conditions

The airflow at standard conditions is converted to field conditions using the ideal gas law, shown in Equation 6‑61.

Estimate the SAE

The SAE is estimated based on the correlation provided by Praxair, shown in Equation 6‑62. The expression is valid for SOTE in the range of 86% to 100%. If the user specified SOTE is less than 80% then the SAE is bounded at 7.11 kg/kWh.

The mechanical power requirement is estimated using the following expression shown in Equation 6‑63.

Entering Oxygenator Power

Estimate the SAE

The SAE is estimated based on the correlation provided by Praxair, shown in Equation 6‑62. The expression is valid for SOTE in the range of 86% to 100%. If the user specified SOTE is less than 80% then the SAE is bounded at 7.11 kg/kWh.

Estimate the SOTR

The SOTR is estimated by rearranging Equation 6‑63 to get Equation 6‑68:

Equation 6‑68

Estimate OTR

The OTR is calculated using Equation 6‑24:

Estimate  at Standard Condition

The  at standard conditions is calculated using Equation 6‑65.

Estimate  at Field Condition

The  at field conditions is calculated using Equation 6‑66.

Airflow at Standard Conditions

The airflow at standard conditions is calculated using Equation 6‑67:

Estimate Airflow rate at Field Conditions

The airflow at standard conditions is converted to field conditions using the ideal gas law, shown in Equation 6‑61.

DO Control

Estimate  at field condition

The  at field conditions is calculated by the controller

Estimate  at standard condition

The  at standard conditions is calculated rearranging Equation 6‑19 to Equation 6‑69.

Equation 6‑69

The

Estimate Oxygen Transfer Rate (OTR) at Field Conditions in g/d

The OTR at field conditions is calculated using Equation 6‑12.

Estimate Standard Oxygen Transfer Rate (SOTR) in g/d

The SOTR is calculated using Equation 6‑13.

Airflow at Standard Conditions in m3d

The airflow at standard conditions is calculated using Equation 6‑67:

Estimate Airflow rate at Field Conditions

The airflow at standard conditions is converted to field conditions using the ideal gas law, shown in Equation 6‑61.

Estimate the SAE

The SAE is estimated based on the correlation provided by Praxair, shown in Equation 6‑62. The expression is valid for SOTE in the range of 86% to 100%. If the user specified SOTE is less than 80% then the SAE is bounded at 7.11 kg/kWh.

Estimate the SOTR

The SOTR is estimated using Equation 6‑68:

Estimation of Effluent Gas Composition

The open basin HPO considers the gas-liquid transfer of O₂, CO₂, N₂, H₂ and CH₄ in Mantis2 model. In the Mantis3 model, gas liquid transfer of N₂O is also modeled. The partial pressure of each gas at the surface of the tank is estimated by assuming a virtual gas headspace having a volume equivalent to the volume of the gas holdup in the tank. The virtual head space thus represents the volume in the tank occupied by the bubbles.

The volume of the virtual headspace is estimated by using Equation 6‑70:

Equation 6‑70

The

where:

        = volume of headspace (m³)

              = volume of liquid in tank (m³)

            = gas holdup in tank (-)

The partial pressure of each gas in the headspace is then integrated using Equation 6‑71:

Equation 6‑71

where:

                   = partial pressure of i gas, atm

               = total pressure of the gas in headspace (atm)

                   = gas transfer rate for i gas, mole/m³/d

              = volume of liquid, m³

     = molar volume of gas at standard condition

                  = partial pressure of feed gas, atm

              = feed gas flow rate, m³/d

                = outlet gas flow rate, m³/d

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