Technical Support Document for the Evaluation of Aerobic Biological Treatment Units with Multiple Mixing Zones

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Technical Support Document for the Evaluation of
Aerobic Biological Treatment Units with Multiple Mixing Zones
I.

OVERVIEW AND PURPOSE
This document is intended to provide information to assist anyone who needs to evaluate

the performance of a biological treatment unit that does not meet the definition of an Aenhanced
biological treatment system or enhanced biological treatment process” (not considered a
"thoroughly mixed treatment unit") because of limitations in overall unit mixing. This document
is intended as support for evaluation of biological units with multiple mixing zones. The
evaluation of the biological treatment unit can be used for certain compliance demonstration
provisions in connection with Appendix C of 40 CFR part 63.

Potential users of this document

include owners and operators of sources who must demonstrate compliance with the requirements
for biological treatment units presented in Appendix C of 40 CFR part 63, as well as enforcement
personnel evaluating whether a specific biological treatment process meets the performance
criteria required for regulation compliance. It is therefore assumed that readers of this document
are familiar with the requirements of Appendix C of 40 CFR part 63, and consequently those
requirements are not restated in this document. Users of this information should be familiar with
conventional techniques for evaluating the extent of mixing in a biological treatment unit. This
information is intended for clarification purposes only, does not constitute final agency action, and
cannot be relied upon to create any rights enforceable by any party.
The purpose of this document is to provide technical support and procedures to determine
the performance of a biological treatment unit that does not meet the criteria for being considered
a “thoroughly mixed treatment unit” within the meaning of the enhanced biological treatment
process definition in 40 CFR 63.111. The objectives of these evaluation procedures are to
evaluate the performance of a unit that does not quickly disperse the entering wastewater and
recycled biomass throughout the unit due to the design and operation of the unit. The evaluation
of the effect of mixing limitations would provide an assessment of the volatilization of the
compounds of concern as well as the biodegradation rates of those compounds.
Several alternative approaches are presented for evaluating the performance of a biological

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treatment process that is not considered to be “thoroughly mixed”. All of these procedures are
considered to provide equally acceptable assessments and no one procedure is considered to take
precedence over another. In some cases, however, it is not possible to use some of the
procedures because of site specific conditions. These evaluation procedures have been designed
to allow, to the extent reasonable, the use of existing information and to minimize the amount of
new information that is required to evaluate the mixing characteristics of your system. After
implementing the procedures of choice, it is necessary for you to have defined zones that have
substantially uniform characteristics, especially the concentrations of volatile organic compounds.
It is therefore recommended that in those cases where sufficient information is not available to
successfully define zones using existing information, you should consider developing additional
information to define zones with substantially uniform characteristics.
Some of the guidance provided in this document may not be needed for each procedure
described in this document. For example, a laboratory based procedure may require uniform
dissolved oxygen concentrations within a zone, whereas the multiple zone concentration
measurement procedure may not require uniform dissolved oxygen concentrations. In other
methods that require a characterization of the biological process, the concentrations of dissolved
oxygen concentrations can be important.

II.

BACKGROUND
Guidance for the evaluation of whether a biological treatment unit is a “thoroughly mixed

treatment unit” is provided in the document Technical Support Document for Evaluation of
Thoroughly Mixed Biological Treatment Units (11/98). This document defines procedures that
may be used to divide a biological treatment unit into two or more mixing zones, with each mixing
zone potentially considered a “thoroughly mixed treatment unit”. The mixing zones approach
presented here is different from a tanks in series approach, because there is substantial exchange
of material among the different mixing zones. This exchange of material among the different
mixing zones is characterized by the concept of a recycle ratio that is applied to each of the
interacting zones. The more general computer modeling approach that accounts for exchange of

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material among the different mixing zones is described in section H. Tables 5 and 6 address
methods of estimating the extent of backmixing.

III.

DESIGN CHARACTERISTICS THAT INFLUENCE THE REQUIREMENTS FOR

MULTIPLE MIXING ZONES
This section describes the characteristics of units that are considered to contribute to
multiple mixing zones in biological treatment units. The presence of multiple mixing zones is of
concern because of the potential of volatilization as opposed to optimum biodegradation in some
of the entrance zones.
Biomass separation and agitation are two important characteristics that influence the
performance of a biological treatment system. The biomass characteristics can be different in the
different zones in a multiple zone system. The uniformity of the biomass characteristics can be
improved in a system that is designed or operated so that biomass separation occurs exterior to
the aeration system (e.g., secondary clarifier with return of separated biomass to the aeration
unit), with return of the separated biomass to the inlet of the system. In the design of the multiple
zone system, the unit may have segments that have little or no observable agitation (quiescent
zones in the air emission models), or segments with uneven liquid flow patterns, both in direction
and velocity. Even with the presence of relatively stagnant zones, there should be enough fluid
flow in each mixing zone to support the biomass suspension in the water column. Symptoms of a
failure to support biomass in the water column include biomass layers, low dissolved oxygen or
anaerobic decay at the base of the floor in these zones, and less overall biomass generation in the
system than is theoretically expected. If biomass is not removed from the system with a clarifier,
continued accumulation of the biomass in the system will require removal by dredging if the
biomass is not removed by degradation in the biomass layers. The presence of biomass settling
does not preclude the use of that section of the basin in the calculation of HAP removal, but the
presence of biomass settling is an indicator that sections of a basin with substantially different
biomass concentrations should be modeled as separate zones.

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Baffles reduce mixing in the unit as a whole and the presence of internal baffles suggests
deliberate control and restriction of mixing. Baffles can be intentionally included when designing
a system with multiple mixing zones. The absence of baffles does not indicate the absence of
multiple mixing zones.
One potential indicator of the need for the use of multiple mixing zones is a high length to
width ratio in the treatment unit. Mixing in biological treatment units depends on the length to
width ratio, the dispersion characteristics, and the retention time in the reactor. Long units are
more difficult to mix uniformly. Generally, a length to width ratio of four to one, or greater, is
considered a high ratio. Vivona (1983) states that plug flow sizing would be based on a length to
width ratio of 4:1 to 12:11 . The requirements for multiple mixing zones can be much less than
the requirements for plug flow design. In the technical approach described here, plug flow
characterization requires 10 well-mixed zones (10 zones), and the characterization for multiple
mixing zones is restricted to 2 to 5 zones. Additional information about well-mixed reactors,
multiple reactors in series, and plug flow is described in Levenspiel2, and Bailey and Ollis3.
Multiple mixing zones are used to characterize large aeration basins. These large basins
may be represented as a group of interacting zones. In a large aeration basin, these multiple zones
may be required to account for differences in the component concentrations, in the biomass
characteristics, and in the aeration characteristics.
Aeration that is greater near the inlet of the unit suggests a design for multiple mixing
zones that do not have the same conditions in each zone. The greater loading in the initial zone
could cause a greater oxygen demand near the inlet. This would imply that the inlet loading is not
distributed throughout the unit and significant volatilization may occur prior to efficient
biodegradation. The presence of non-uniform agitation and other characteristics such as
concentrations of chemicals and concentrations of biomass do not imply that the unit does not
meet the requirements for acceptable biodegradation performance, only that special procedures
should be followed to evaluate the biodegradation performance.

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Quiescent zones separating agitated zones may or may not be well-mixed . For
example, surface units may be considered well mixed and uniform within the agitation zone
around each surface aerator, but the aeration unit as a whole may not be well mixed throughout
the entire unit. In dividing a unit containing multiple aerators into mixing zones, the zone
definition should not be smaller than the zone around an aerator in a surface agitated basin that is
uniformly agitated with surface aerators. Units designed so that the wastewater flows sequentially
from one aeration unit to another may be considered as multiple mixing zones with one mixing
zone for each aerator in the path of wastewater flow through the unit. This flow in series may be
determined by inspection, or by tracer testing, or by design and operating characteristics.
Examples of design features that may result in poor biodegradation of the compounds in
the entering wastewater in the entrance zone of a multiple mixing zone unit include (1) the
absence of quick dispersion and thorough mixing and (2) the potential for significant
volatilization prior to biodegradation. These two factors are interrelated in that quick dispersion
and thorough mixing must occur prior to significant volatilization of the compounds of concern
for the system to achieve efficient destruction through biodegradation. Certain design
characteristics may lead to problems with respect to these factors. Some of these factors are
discussed in the following sections.
IV.

GENERAL PROCEDURES FOR EVALUATING THE MIXING CONDITION OF A

BIOLOGICAL TREATMENT UNIT

A.

Overview of procedure
This section presents a list of procedures that can be used to evaluate the mixing

conditions of a biological treatment unit that has multiple mixing zones. The overall performance
of the biological treatment unit is characterized by three factors: the fraction of the compounds
entering the unit that is biologically degraded, the fraction of the compounds that is emitted from
the unit as air emissions, and the fraction of the compounds that remains in the wastewater after
treatment in the unit. If the total removal by biodegradation is acceptably great for the entire

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treatment unit, the unit may be considered as an acceptable biological treatment process for the
purpose of regulatory compliance. In some cases, there may be very aggressive biodegradation
and low stripping in the first part of the biological treatment unit. If the required destruction of
compounds is achieved in that first part of the biological treatment unit, the characterization of the
other parts of the biological treatment unit would not be required. If you choose to only
characterize a section containing multiple zones of a large aeration basin, you should account for
the internal recycle effects at the end of the section, because there will be backflow from outside
the section back into the zone at the end of the section.
The first step is to subdivide the unit into a series of zones that have substantially uniform
characteristics within each zone, such as organic compound concentrations, dissolved oxygen
concentrations, and biomass concentrations. Then, the zone that can be considered as a wellmixed flow entrance zone is identified. If multiple inlets of wastewater are present, two or more
entrance zones may be present. Depending on the unit, an entrance zone could extend for as
much as one half the volume of the system. The procedures for evaluating the number of mixing
zones are described in Section C and these procedures can be summarized as identifying zones
that have uniform conditions and concentrations of components. The division of the system into
zones depends on the complexity of the system and the technical approach. If laboratory based
measurements of the biorate constant are used, it is important to match the dissolved oxygen and
other important variables in the laboratory with those same important variables in the full scale
system. With other procedures, the dissolved oxygen concentrations are less important. One of
the procedures relies primarily on evaluations of the concentrations of the compounds of interest
and the aeration characteristics: with that procedure, it is important to select zones with
substantially uniform compound concentration and agitation characteristics.
The second step is optional and can be used to reduce the resources required for
regulatory compliance if biological rate measurements are used to characterize the performance of
the system. If the emission potential for the well-mixed flow entrance zone is greater than or
equal to the other mixing zones, then only the first zone is evaluated and the performance of the

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other zones are assumed to be equal to the first zone. When the performance of the overall unit is
evaluated by this approach and determined to be acceptable by this method, then an evaluation of
the remaining zones are not required. The key to the confidence in this approach is the assurance
that the first zone does not have superior performance to the remaining zones (the ratio of
biological removal to air stripping is not greater in the first zone). Design factors that could
prevent the use of this optional procedure include more aggressive biodegradation in the initial
zone due to special biological activity from the recycled biomass, less aggressive aeration in the
initial zone, and deeper unit depth in the initial zone.
The third step in the evaluation process is to identify the number of mixing zones that are
needed to evaluate the system (2,3,4,5, or a maximum of 10) and proceed with the appropriate
form for the number of mixing zones. The number of mixing zones that are needed to evaluate
the system can be less than the total number of zones that are identified in step 1. Large aeration
basins can have more than two dozen surface aerators that could theoretically be considered as a
separate zone for each aerator, but due to the mixing characteristics, four or fewer zones could be
selected for evaluation purposes. In this case several aerators would be included in a single zone.
Procedures to identify the characteristics of mixing zones are described in Section C of this
document, and forms are provided to complete the appropriate calculations for this identification
of the number of mixing zones. The three procedures are design evaluation, tracer studies, and
inBbasin measurements. All of these procedures are considered to provide equally acceptable
assessments of the number of mixing zones and no one procedure is considered to take
precedence over another. Selection of the procedure will depend on the availability of
information, the relative ease of obtaining the necessary information, and/or personal preferences.
If there is a question about how many mixing zones that should be used for describing the
unit, use more zones rather than less. If additional zones are used to characterize a basin, the
recycle ratios should be appropriately adjusted. Some of the technical approaches do not require
the evaluation of recycle ratios.

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Under some special design conditions, the overall unit cannot be considered to be either
well-mixed, multiple-zones, or plug-flow. There are several different procedures for evaluating
units in this document and all of the procedures in this document may not apply to those systems
with specials designs, due to abnormal flow conditions, poor suspension of biomass,
uncharacterized dissolved oxygen gradients, or other special site-specific factors. For those
systems with special design conditions, the use of some of the procedures in this document may
require detailed modeling of the actual site based upon appropriate modeling techniques, using the
methods provided in this document as general guidance.

B.

Determination that the Unit is Not Well-Mixed
The first step in the general determination of the biological performance of a wastewater

treatment unit is to determine that the unit can not be considered as well-mixed. If an initial
evaluation of the procedures in the document Technical Support Document for Evaluation of
Thoroughly Mixed Biological Treatment Units indicates that the there is a likely probability
that the unit would not be considered well-mixed, then proceed to the evaluation of the multiple
mixing zones.

C.

Determination of the Number of Mixing Units

1. Initial mixing zone
When you break an unit into zones, one or more of the zones is an initial mixing zone.
You may determine that the unit has an initial mixing zone that can be considered as well-mixed
by design evaluations, by tracer testing, by concentration testing, or by initial inspection. If the
definition of the initial mixing zone cannot be considered as uniform or well-mixed, you should
redefine the initial mixing zone so that it can be considered to be substantially uniform in
conditions. Also, sampling of the initial mixing zones should be carried out in a central position in
these zones so that the measured concentrations are representative of the conditions throughout
the mixing zone.

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2. Number of mixing units from dispersion analysis
In the case of submerged aeration, if you have a spiral flow aeration systems you may use
Form 15 to estimate the dispersion coefficient by the method of Fugii or you should use the
default value of 0.068 m2/s (Chambers) for the other types of submerged aeration systems. Next,
use Form 16 to Calculate the value of u and L from the mean velocity and length of the aeration
unit; then, use those values to calculate the dispersion number (D/uL). Use Table 1 and Table 2
to select the number of mixing zones from the value of the dispersion number. The number of
units by this method is the equivalent number of tanks in series that will represent the
characteristics of the dispersion and may be somewhat conservative when compared to other
methods. The following equation describes dispersion in a closed system.4
σ2 = 2 (D/uL) - 2 (D/uL)2 (1 - e-uL/D)

Table 1 presents some of the calculated values of the dimensionless variance using the
above relationship.

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Table 1. Relationship between the dispersion number and the dimensionless variance.
σ2
0.9674836
0.9216251
0.8975636
0.8522453
0.8155969
0.7990033
0.7652601
0.6867261
0.654858
0.6159904
0.6026241
0.5676676
0.5198208
0.4992198
0.4769162
0.4264213
0.3772895
0.332554
0.240831
0.1958027
0.1638002

D/uL
10
4
3
2
1.55
1.4
1.16
0.8
0.7
0.6
0.57
0.5
0.42
0.39
0.36
0.3
0.25
0.21
0.14
0.11
0.09

The number of tanks in series model may be used for systems with either subsurface
aeration or surface aeration basins.
The dimensionless variance σ2 is then related to the number of tanks in series (no back
mixing) with an equivalent variance, where the number of mixing units5 equals the reciprocal of
the dimensionless variance, 1/σ2. The number of tanks in series that corresponds to the
dimensionless variance depends on the extent of back mixing. The amount of back mixing in the
tanks in series model is defined by the recycle ratio. The internal recycle ratio is the ratio of the
flow due to mixing in the unit toward the inlet to the flow in the wastewater plus any external
recycle. The recycle ratio in basins with surface aerators are estimated to be in the range of 2 to
4. The recycle ratio may be estimated from the local basin flow rates if they are available. If the

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backflow from zone N+1 to zone N is measured as 3 m3/s and the flow rate of the wastewater to
be treated plus the recycle flow is 1 m3/s, the recycle ratio is estimated as 3/1 or 3.

The recycle

ratio is used with a number of tanks in series to model the mixing characteristics of the actual unit.
Since the mixing characteristics of the actual unit are generally not identical to the theoretical
mixing characteristics of the tanks in series with recycle model, the success of the model in
describing the actual unit may depend on the selection of the number of zones and appropriate
values for the recycle ratio. The appropriate value of the recycle ratio may depend on the
selection of the zones. Information on the dispersion and flow in the system should be used to
estimate the value of the recycle ratio.
The internal recycle in the tanks in series model is the flow rate of tank N+1 back to tank N.
Figure 1 illustrates the model that was used to calculate the dimensionless variance for use in
Table 2. The values in Table 2 were calculated and rounded to two significant figures.

inlet

Figure 1. Tank in series model with
internal recycle.
tank
1

tank
2

internal recycle flow

tank
3

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Table 2. Calculated dimensionless variance numbers σ2 for various number of
tanks in series at specified internal recycle values
tanks
Internal recycle ratio
0
1
2
3
4
1
0.99
0.99
0.99
0.99
0.99
2
0.467
0.78
0.86
0.85
0.88
3
0.33
0.62
0.76
0.81
0.86
4
0.244
0.52
0.66
0.75
0.81
5
0.193
0.44
0.59
0.68
0.74
6
0.16
0.38
0.53
0.63
0.66
To use Table 2, identify the applicable column that corresponds to the recycle ratio identified for
the unit of interest. Look down the applicable column to locate the row containing the
dimensionless variance that was estimated. The corresponding number of tanks in series is listed
in the left column of that row. Linear interpolation may be used for Table 2.
Table 3 may be used for an assumed default recycle ratio of 3 for the biological treatment
system with estimated dispersion numbers.
Table 3. Default values for the number of mixing units based on estimated dispersion numbers.

Dispersion number, D/uL

Number of mixing units

D/uL > 10

2

10 > D/uL > 1.4

3

1.4 > D/uL > 0.7

4

0.7 > D/uL > 0.5

5

0.5 > D/uL > 0.42

6

3. Number of mixing units from tracer analysis
You should only interpret the mixing characteristics of your unit by tracer analysis if you

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are experienced in tracer testing and understand the complexities of tracer interpretation. The
following discussion presents an overview of the use of tracer testing to characterize the mixing
characteristics of a unit.
When a sample of tracer is instantaneously added to the inlet pipe of a biological treatment unit,
the amount of tracer leaving the unit in the exit pipe is measured as a function of time. The tracer
measurements may be analyzed to determine the mean residence time and the standard deviation
of the distribution. The exit tracer concentration will increase with time, reach a peak or
maximum concentration, and then decay with time. Other observations of interest include the
time for the maximum in the peak and the absence of multiple peaks. You must correct the results
of the tracer analysis for recycle flow systems, because some of the exiting tracer will be returned
to the unit with the recycled sludge. If the hydraulic residence time (volume divided by inlet flow)
is approximately equal to the tracer residence time, this is an indication that the selection of tracer
was good and that the unit does not have significant bypassing and abnormal flow patterns6. The
ratio of the standard deviation to the mean residence time is the dimensionless variance. Look up
the equivalent number of mixing units from the measured dimensionless variance in Table 4 if
your unit has a recycle ratio of 2-4. The equations relating the dimensionless standard deviation
to the number of units are discussed in the previous section.
Table 4. Default values for the number of mixing units based on measured dimensionless variances
obtained from tracer testing. (Based upon a recycle ratio of 2-4)
dimensionless variance, σ2

Number of units

σ2> 1

2

1 > σ2 > 0.8

3

0.8 > σ2 > 0.66

4

0.66 > σ2 > 0.57

5

0.57 > σ2 > 0.53

6

0.53 > σ2 > 0.47

7

2

0.47 > σ > 0.41
2

0.35 > σ

8
10

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Tracer testing can provide information that may be helpful in evaluating the number of
tanks in series and the internal recycle ratios needed to use the tanks in series model with
backmixing. The peak or maximum tracer concentration discussed in the previous paragraph may
be used to characterize the unit. The dimensionless peak time is the time of maximum tracer
concentration at the exit of the unit divided by the hydraulic residence time of the unit. The
dimensionless peak concentration is the maximum tracer concentration at the exit of the unit
divided by the ratio of the amount of tracer to the volume of the unit. Tables 2, 5, and 6 may be
used to select the number of tanks and internal recycle ratios for unit evaluation.

Table 5. Dimensionless peak times at various internal recycle values
tanks
Internal recycle ratio
0
1
2
3
4
1
0.005
0.005
0.05
0.05
0.05
2
0.5
0.43
0.37
0.33
0.3
3
0.66
0.53
0.47
0.434
0.4
4
0.74
0.6
0.54
0.5
0.46
5
0.8
0.65
0.58
0.54
0.51
6
0.83
0.68
0.61
0.57
0.54
Table 6. Dimensionless peak concentrations at various internal recycle
values
tanks
Internal recycle ratio
0
1
2
3
4
1
0.997
0.997
0.997
0.997
0.997
2
0.740
0.550
0.440
0.363
0.309
3
0.819
0.627
0.517
0.442
0.386
4
0.907
0.68
0.573
0.498
0.443
5
0.991
0.730
0.618
0.543
0.487
6
1.07
0.777
0.656
0.580
0.524

4. Number of mixing units from design factors
Some units can have screens, baffles, and flow pattern designed to promote a controlled
path of wastewater through the unit, rather than general mixing. For those cases, it may be

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appropriate to separate the unit into zones based upon the physical construction of the unit. If the
unit contains nonuniform agitation or nonuniform aeration, zones should be selected that have
relatively uniform surface characteristics. The primary guidance for the selection of the number of
mixing zones in this case is that too many units will not adversely affect the results, but too few
can adversely affect the accuracy of the unit evaluation.

5. Number of mixing units from measurements of concentrations
The number of mixing units may be obtained from measurements of concentrations of volatile
compound concentrations at multiple locations in the unit. Zones are selected based upon these
concentrations and a zone does not need to have the same concentration throughout the zone.
Emissions from an area within the zone that are higher than the average for that zone can be offset
by lower emissions from other areas in that same zone that are lower than the average if the
concentrations in the zone are substantially uniform. In general, the division of the unit into more
zones will increase the accuracy of the estimated air emission rate from the unit, but this increase
may be very little for some systems. For systems with a continuous change in concentration
across the surface of the system, a 15% difference in the volatile compound concentrations from
the average value in a zone could be considered substantially uniform for the purpose of these
calculations (range of approximately 30% of the mean). A consideration of the impact of the
number of zones on the estimated fraction biodegraded and the estimated air emission rates can
help resolve issues in the determination of the number of zones. A larger difference from the
mean can be used if it can be shown that the zone size is sufficiently small such that numerical
errors introduced by the larger grid size are an acceptably low value.7 In some cases, errors in the
grid size are not important in the evaluation of a biotreatment unit:
•

the biodegradation removal effectiveness (fbio) is substantially greater than required for
regulatory compliance,

•

a decrease in the grid size has no significant impact on the biodegradation removal
effectiveness, and

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the biodegradation removal effectiveness is not sufficient for regulatory compliance and
additional accuracy would not change the evaluation.

In other cases, errors due to a larger grid size can be important in the evaluation of a
biotreatment unit: the biodegradation removal effectiveness (fbio)is neither significantly greater
than or significantly lower than the value required for regulatory compliance. In this case,
improved accuracy that is thought to be associated with a smaller grid size may be more effective
in resolving uncertainty in regulatory compliance issues.
For example, consider a biotreatment unit with a requirement that 90 percent of the inlet HAPs be
biodegraded (fbio). If data collected during an initial performance test show that the unit typically
achieves an fbio of 91 percent, the zone size should be selected such that the numerical error
introduced by using fewer zones is no more than 1 percentage point. However, if the initial
performance test data show that the unit typically achieves an fbio of, say, 97 percent, an
acceptable numerical error may be 2 to 3 percentage points.

D.

Determination of the Relative Performance of the Initial Mixing Unit

The second step is a determination of whether the initial mixing zone has an equal or
greater emission potential than the other zones. This step is optional and can be used to reduce
the resources required for regulatory compliance. If the emission potential for the well-mixed
flow entrance zone is greater than or equal to the other mixing zones, then only the first zone is
evaluated and the performance of the other zones are assumed to be equal to the first zone. When
the performance of the overall unit is evaluated by this approach and determined to be acceptable
by this method, then an evaluation of the remaining zones are not required. If the required
biodegradation is achieved in the initial mixing zone, an evaluation of the remaining zones is not
required.

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You must provide an assurance that the first zone does not have superior performance to
the remaining zones if you use this option. The first zone is generally the zone of the most
environmental concern since the concentrations are greater, the relative biorates are potentially
less, and mixing at the entrance is a potential problem. You should consider any design factors
that could prevent the use of this optional procedure. Other design factors could include a deeper
unit depth in the initial zone, the location of the inlet wastewater, and special mixing
characteristics near the wastewater conduit.
Another factor that could conceivably prevent the use of this option include more
aggressive biodegradation in the initial zone due to special biological activity from the recycled
biomass. It has been suggested that the biomass has a greater potential for active enzyme
formation and lower concentrations in the biomass, resulting in strong initial uptake of
concentrations by the biomass.
If there is less aggressive aeration in the initial zone than in other zones, the initial zone
could conceivably have a lower rate of stripping than in other zones. This could be especially
important for surface aerator units and for submerged aeration units with uneven aeration.

E.
Determination of the Overall Unit Performance from the Performance of the
Initial Mixing Unit

The fraction of the concentration loading that is removed as air emissions and as biological
products is estimated from the use of Form 3 using the measured biorate with the concentrations
of compound and biomass in zone 1 and the characteristics of zone 1. These same fractions are
then applied to each of the other zones in the biological treatment unit in sequence from zone 2 to
the last zone of the unit. The fractions of removal by biodegradation and air emissions are
estimated as follows:

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f e , i = f e ,1 f r ,i −1
f b , i = f b ,1 f r , i − 1
f r ,i = f r ,i −1 (1 − f e ,1 − f b ,1 )
The subscript i refers to the fraction in zone i, were i varies from 1 for the first zone to n
for the nth zone. If the biological treatment does not have an acceptable biological removal
effectiveness by this method, this does not mean that the unit is unacceptable. It does mean that
the unit is required to be evaluated by step 3 before it may be accepted as being biologically
effective.

F.

Determination of the Characteristics of the Mixing Units
1. Biological rates
The biological rates are measured in each mixing zone, where required for the procedures

in this document. In step 2 only the biological rate (as determined by the appropriate methods in
Appendix C of 40 CFR part 63) in the first mixing zone is required. If three or more mixing
zones are evaluated, the biological rates for three zones can be measured, and the results plotted
by the method of Lineweaver-Burk8, yielding a straight line with a slope that is related to the first
order rate constant and the intercept that is related to the zero order rate constant. The Monod
equation then may be used to estimate biorates in zones other than the three that were used to
measure biorates. For the purpose of the evaluation the actual biorate is used (gm/L-hr) for each
zone.

7/99

19

The following illustration indicates the Lineweaver-Burk method of plotting the Monod
rate data to obtain a straight line. Either the data from the correlating straight line may be used
for the estimate of the biorate, or the Monod parameters may be determined from the slope and
intercept. Formal statistics may be used to estimate the uncertainties in the values of the slope
and intercept obtained from this approach.

In some units, you will not be able to use the Monod equation to correlate your data
because your system may be more complex. For those systems a different correlation may be
used to estimate the biorates for some of the zones. The general guidance for this case is that
enough measurements must be carried out to establish an unambiguous correlation. Measurement
in the initial mixing zone is always required, and measurement of the last mixing zone is desirable,
unless the concentrations are too low for measurement. The user shall find a kinetic model to
extrapolate measured biorates to

1/rate

Lineweaver-Burk plot

zones that have concentrations

16000
14000
12000
10000
8000
6000
4000
2000
0

that are too low for biorate
measurement. The kinetic model
that is used should describe the
kinetics for the compound of
interest that was measured for
0

0.02

0.04

0.06
1/Concentration

0.08

0.1

0.12

those mixing zones with higher
concentrations.

2. Submerged aeration rates
Determine the submerged aeration rates for each mixing zone. This procedure is especially
critical for systems that may have uneven aeration, either by design or by mechanical malfunction
(broken headers, clogged exits). This procedure is less critical if the submerged aeration rates are
generally uniform across the entire unit. The following two examples illustrate how the

7/99

20

submerged aeration characteristics can be used to define the mixing zones in the unit.
Example 1. The treatment unit is a long rectangular channel with two different aeration zones, a
higher initial aeration zone, and a lower secondary aeration zone. The unit was divided into four
mixing zones on the basis of concentration measurements along the length of the unit. The first
two mixing zones are characterized as higher aeration, and the last two mixing zones are
characterized with the lower aeration rates.
Example 2. The treatment unit is a circular tank with flow inlets and exits at opposite sides of the
tank. There is a broken header in the center of the tank with heavy aeration. The unit was
divided into three mixing zones on the basis of the observed surface disruption due the broken
header. The first and the last mixing zones are characterized with the design aeration rates as
confirmed by flow measurement, and the center mixing zones was characterized with the higher
aeration rates due to the broken header.
3. Mass transfer coefficients
You should select the number of mixing units to match the surface aeration pattern, for the
presence of non-uniform surface agitation. If there is a grouping of two or more aerators such
that their areas of agitation are sufficiently close together that the zone can be considered
thoroughly mixed, this grouping can be considered as a set. If an impoundment has 4 of these sets
of aerators between the entrance and the exit, four aeration zones could be an initial choice for
zones. For more complex situations, mixing zones with different mass transfer coefficients may
be required.
4. Biomass concentration
You should measure the biomass concentrations at several different places in each zone to
establish that the biomass can be considered to be uniformly distributed within each mixing zone.
If the system is operated with non-uniform biomass concentrations, non-uniform oxygen

7/99

21

concentrations, or non-uniform compound concentrations in a zone, all of the evaluation
procedures presented in this document should not be used , and appropriate site-specific methods
may be required for some of the evaluation procedures. For abnormal operation, the worst-case
measured conditions may be used with the guidance in this document to provide additional
assurance that the performance of the unit is acceptable. If this worst case option is used, enough
measurements should be taken to reasonably establish the worst case condition. Procedures that
rely only on measured concentrations and estimated mass transfer coefficients do not require
detailed measurements and characterizations of biomass concentrations and dissolved oxygen
concentrations.
5. Dissolved Oxygen Concentration
The same general considerations apply to measurements of dissolved oxygen as with
biomass, except that it is much easier to measure dissolved oxygen than biomass, since a dissolved
oxygen probe can provide instantaneous measurements. It is possible therefore to make many
dissolved oxygen measurements in a mixing zone demonstrating uniform conditions, and
therefore potentially reducing the number of biomass concentration measurements that may be
required. For effective aerobic biodegradation, the dissolved oxygen concentration will be
significantly less than equilibrium (generally less than 7 ppm) and greater than 1.5 ppm (very low
dissolved oxygen is an indication of less effective aerobic biodegradation. If the concentration of
dissolved oxygen in a zone is less than 1.5 ppmw, the kinetic characterization of the
biodegradation in that zone may indicate differences from the kinetic characterization in other
zones that have concentrations of dissolved oxygen that are greater than 1.5 ppmw. A minimum
dissolved oxygen concentration for aerated stabilization basins should be 0.5 ppmw. The actual
dissolved oxygen concentrations that are representative of each zone are used in any laboratory
measurements of biodegradation rates.

G.

Sampling Methods and Locations
In the initial characterization of the mixing characteristics of a unit, sampling of the water

7/99

22

in the unit is important for an accurate characterization. Some of the methods to characterize the
performance of the unit require the measurement of one or more component concentrations at
several sampling locations within the unit. The minimum number of sampling locations required to
characterize component concentrations within the unit includes (1) the inlet, (2) within unit near
the inlet, (3) the exit of the unit, and (4) within center of each mixing zone. Additional sampling
locations are initially required to establish the number of mixing zones and to establish that the
sampling location is characteristic of the zone. The inlet is sampled directly before entering the
particular unit, and the exit is sampled directly at the outfall of the particular unit. The inlet sample
may be collected upstream provided conveyance is by closed pipe and no additional streams are
added to the conveyance system.
The sample within the first mixing zone will be taken as described in the following: first
determine the physical dimensions of the first mixing zone. Sample within the center part of the
first mixing zone. Additional samples of the aeration unit contents nearer the inlet should also be
taken near the reactor inlet to confirm that the first mixing zone was appropriately chosen. The
success of sampling the unit with this method depends on an accurate sampling of the inlet stream
after it mixes with the aeration unit contents. Sampling in the unit should be conducted in the
flow path of the inlet stream after the inlet flow has an opportunity to mix with the unit contents.
The lesser value of either 2 the distance to the closest aerator, a distance of 10 times the
diameter of the wastewater inlet pipe , or 10 meters may be used as the maximum sampling
distance from the wastewater inlet.
Additional samples will be collected within each additional mixing zone as required by the
procedures, and as required for biological rate testing.

1. Collection and handling of samples.
Sufficient grab samples to characterize the concentrations of target compounds should be
collected from each of the following locations: (1) the influent to the biological treatment unit; (2)
the effluent from the biological treatment unit; (3) the inlet to the aeration unit within the

7/99

23

maximum sampling distance; and (4) near the center of each other relevant mixing zone. The
number of samples required to characterize the unit depends on the complexity of the unit and the
variability of the inlet waste concentrations and inlet flow concentrations. The relevant mixing
zone samples shall be taken anywhere practical within the center of the mixing zone avoiding
edge, bottom, or surface effects. When you sample to determine the number and location of the
zones, samples are taken in different regions of each zone to evaluate the variability. Note: these
samples may be collected by personnel from the sides of the aeration unit, with the assistance of
flotation devices, pumps, conduits, and other devices on the sampling equipment to obtain
samples that are representative of the center of the mixing zones. Measure the concentrations of
the compounds of interest, the biomass, and each characterization parameter (dissolved oxygen,
pH, COD) at each of these relevant locations. The aeration unit samples should be collected in
the upper part of the basin at a depth of at least 1.0 foot below the surface of the water. When a
set of samples is used to characterize the unit, all samples in the unit shall be collected during the
same 24 hour period. Each of the sets of samples1 should be collected to characterize the
sampling and unit variability. If more than 3 samples are to be collected for the purpose of zone
characterization, then the sample collecting should be carried out at approximately the same time.
If time delays are required because of the sampling methods, the sampling locations and times
should be scheduled to avoid a bias in the results due to systematic changes in concentrations. The
aeration unit samples should be collected during the same time periods that the influent and
effluent samples are collected. Under potentially changing conditions of treatment unit operation,
samples should be collected for enough days to establish that the operating conditions are stable
and that the measured samples are characteristic of those operating conditions.
One method for obtaining representative samples from the zones is to obtain grab samples
of the reactor contents removed by a recirculating conduit. Those grab samples should be
removed with a zero headspace device, especially if time composite samples are obtained.
Samples should be poured from the grab sampling device into sample bottles in a manner that will
1

More than 3 samples may be collected from any of the locations, if necessary.

7/99

24

minimize volatilization of organic compounds. Sufficient hydrochloric acid (HCl) shall be added
to each sample to reduce the pH to less than 2 to stop the biodegradation in the sample bottles,
unless it is demonstrated that a different pH range is effective for stopping biodegradation and
does not cause degradation products present at the lower pH level. The samples shall then be
refrigerated at 4o C until analysis.

2. Number of Samples.
When the coefficient of variance2 for sampling is large, it may be difficult to accurately
estimate the mean of the distribution. One method for improving the accuracy of the
determination of the mean is to increase the number of data points that is used in estimating the
mean of the distribution. The following list presents a recommended minimum number of
sequential data points that should be collected from the unit, based upon the measured coefficient
of variance.

Coefficient of variance

Minimum
number of data
points

10

3

15

4

20+

5

3. Measurement of concentrations of relevant compounds.
All sample preservation, storage, and analyses shall be performed in accordance with the
NPDES analytical procedures at 40 CFR part 136. You should only use methods that are suitable
for measuring the relevant compounds. All quality assurance/quality control requirements of the
applicable method shall be followed.

2

The coefficient of variance is the ratio of the standard deviation of the sample mean to the
sample mean, multiplied by 100.

7/99

25

4.
Estimation of zone concentrations with limited sampling
In the initial evaluation of the biological treatment unit, detailed sampling may be needed to
characterize the performance of the unit. In later evaluations it may not be necessary to collect
HAP samples from each zone in a multiple zone biological treatment unit in order to evaluate the
overall performance of unit. For example, under the Multiple Zone Concentration Measurement
Procedure (appendix C, part 63), the HAP concentration may be estimated for zones located
between zones with measured HAP concentration data. The initial unit investigation should
provide a sufficient database of measured concentrations in all zones of the treatment unit to
allow for interpolation for those zones that are between zones with measured HAP
concentrations. The database of HAP concentrations in each zone is developed during the initial
biological treatment unit characterization.

The HAP sample collected for the zone should be representative of the average concentration of
the zone. However, it is not necessary that the sample be collected at the center of the zone if it
has been demonstrated during the initial biological treatment unit characterization that the sample
location provides data that are representative of the zone. Any procedures used to correct the
data from the sample location to the average expected concentration of the zone should be
developed during the initial biological treatment unit characterization.
H.
Computer Models
Computer models may be used to perform the calculations required for step 3. As a requirement
for the use of the computer models for the site specific calculations, the following information
must be available:
C

an applicable set of site-specific rate data for each relevant compound correlated as Monod
constants;

C

a computer program that accounts for concentration variability of the biorate constant with
the Monod constants;

7/99
C

26

characterization of each mixing zone as a separate unit for modeling purposes, surface
agitation effects, submerged aeration, and other factors; and

C

evaluation of internal recirculation factors between each mixing zone for use in modeling
the recycle streams between each adjacent mixing zone.

The concentrations of the compounds in the mixing zones are available from measurements in the
mixing zones of the unit. Concentrations are estimated from the computer model accounting for
internal mixing and concentration effects on the biorate. The internal recycle rate and the Monod
constants are treated as adjustable parameters, and adjusted until the measured concentrations
match the estimated concentrations from the computer model. The computer estimation of the
biorates and the air stripping rates are then documented in Form 4, and the overall biological
removal effectiveness is evaluated.

I.
Applicable Multiple Mixing Zone Forms
Several forms are provided to assist in the organization of information that was used to estimate
the biodegradation rates within a multiple mixing zone unit.

1. Form 1. Data Form For The Estimation Of Multiple Zone Compound Fraction

Biodegraded And Air Emissions
Form 1 provides a summary of the unit performance (f bio and fe ) based upon measured biorates,
measured concentrations, and estimated mass transfer coefficients.

2. Form 2. Data Form For The Estimation Of The Biorate For Each Zone In The

Biological Treatment System
This form is used to list the measured biorates from multiple zones and the measured
concentrations in each zone. The bioremoval rate constant (sec-1) is calculated from the
concentrations and the measured biodegradation rates.

7/99

27

3. Form 3. Data Form For The Estimation Of The Biodegradation Rate For Each

Zone
This form is used to estimate the fraction biodegraded and the fraction air stripped in a specific
mixing zone of an unit. Form 3 compares the rate of biodegradation for a specific concentration
to the rate of stripping for that same concentration. The concentration that is in the zone will
depend on the recycle ratios, the number of zones, and other factors.

Form 4. Data Form For The Estimation Of Multiple Zone Compound
Concentrations (3 Zones)
Form 4 provides estimated concentrations from measured biorates and estimated internal recycle
rates. This form is used to estimate compound concentrations in the zones of units that are
characterized by three mixing zones with internal recycle between the units. This kinetic model is
different from reactors in series because of the internal recycle causing mixing of zone contents
among the three units. This form could be used to confirm the modeling approach or to
determine the internal recycling rates for modeling purposes.
5. Form 5. Data Form For The Estimation Of Multiple Zone Biodegradation From

Unit Concentrations
Form 5 provides a method to estimate the biodegradation rates of a unit based upon the measured
compound concentrations in each unit zone. This method can be useful for the situation in which
the compound concentrations are below the detection limits of the measurement method at the
exit and near the exit of the unit. The biodegradation rate is estimated as the difference in the
inlet loading rate and the sum of the exit removal rate and the air stripping rate. Either forms may
be completed or computer models (see Appendix C of 40 CFR part 63) may be used to estimate
the mass transfer coefficient in each zone and the actual concentrations in each zone are sampled
and measured. Because of uncertainties in the estimation of mass transfer coefficients, this
method should not be used when the air stripping rate can potentially account for more than 25
percent of the removal. In the case of steady operation with accurate inlet and outlet
concentrations and flows and estimated air stripping rates of a few percent, this method is thought

7/99

28

to provide an accurate estimate of the overall unit biodegradation rate.
V. EXAMPLE FOR THE USE OF MEASURED BIORATES
Example 1 using Form 1 is presented with the forms. This example illustrates how the
concentrations and measured biorates in the zones are used to estimate the fraction biodegraded
and the fraction of air emissions in the full unit.
Step 1. Identify the number of zones.
Information required by Form 1 is collected from the full-scale unit. Based on tracer testing, three
zones are identified for simulating the performance of the full-scale unit.
Step 2. Measure the concentrations in the zones.
Several concentrations are measured for various locations in the three zones that were identified
in Step 1. An average concentration for each zone was obtained for use in Form 1. Use the
actual measured concentrations, because the concentration in the recycle streams may not
necessarily exactly equal the exit concentration from the unit.

Step 3. Measure the biorate for each zones.
The average concentration in each zone was used for measuring the biorates in a bench scale
reactor. The biomass from the zone was used in the bench scale reactor. The reactor conditions
were adjusted to duplicate the actual zone conditions, including dissolved oxygen concentration,
waste concentrations, pH, and temperature.
Step 4. Complete Form 1.
Form 1 is completed and the following are calculated: the fraction biodegraded, the fraction of air
emissions, and the fraction remaining in the full unit.
Step 5. Review the results of Form 1.
The fraction predicted that is remaining in the full-scale unit (Form 1, line 23) is compared to the
calculated fraction remaining (Form 1, line 13). The concentration in the effluent is compared to
the concentration in the last zone. Based upon the data analysis of Form 1 it is concluded that
three zones are sufficient to model the full-scale system. If additional zones are needed, the
concentrations obtained in Step 2 are used to define additional zones.

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VI.

29

REFERENCES

1.

Vivona, "Designing Plug Flow Lagoons Using Two Stage Aeration", Poll.Eng., 15, p.2832 (1983)

2.

Levenspiel, Octave Chemical Reaction Engineering. Chapter 9. Non-Ideal Flow John
Wiley and Sons, Inc., New York, 1962.

3.

Bailey and Ollis, Biochemical Engineering Fundamentals, Chapter 9. Design and Analysis
of Biological Reactors. Second Edition, McGraw-Hill, Inc. New York, 1986.

4.

Levenspiel, Octave Chemical Reaction Engineering. P. 263 John Wiley and Sons,
Inc., New York, 1962.

5.

Levenspiel, Octave Chemical Reaction Engineering. P. 283 John Wiley and Sons,
Inc., New York, 1962.

6.

Levenspiel, Octave Chemical Reaction Engineering. John Wiley and Sons, Inc., New
York, 1962.

7.

Manson and Wallis, "Towards an Accurate Fate and Transport Model for Nonuniform
Surface Waters", Advances on Environmental Research, 1:1,p. 2, 1999.

8.

Bailey and Ollis, Biochemical Engineering Fundamentals, p 106. Second Edition,
McGraw-Hill, Inc. New York, 1986.

Form 1

DATA FORM FOR THE ESTIMATION OF MULTIPLE ZONE
COMPOUND FRACTION BIODEGRADED AND AIR EMISSIONS
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
Number of zones in the aerated biotreatment unit
VOLUME of full-scale system (cubic meters)
Average DEPTH of the full-scale system (meters)
FLOW RATE of wastewater treated in the unit (m3/s)
Recycle flow of wastewater added to the unit (m3/s)
ESTIMATE OF KL from Form 6 (m/s)
Concentration in the wastewater treated in the unit (mg/L)
Concentration in the recycle flow (mg/L)
Concentration in the effluent (mg/L).
TOTAL INLET FLOW (m3/s) Add the number on line 4 to the number on line 5
TOTAL RESIDENCE TIME (s) line 2 divided by line 10.
Residence time in each zone. (s) line 11 divided by line 1
fraction remaining (line 9 times line 10) divided by the sum of (line 7 times line
4) and (line 8 times line 5).
Stripping factor, (/s) line 6 divided by line 3.
Zone
number

BIORATE
Measured biorate for zone
(mg/L-s), Bi

Concentration for zone,
Ci (mg/L)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
AIR STRIPPING
line14 times Ci
(mg/L-s)

1
2
3
4
5
6
7
8
9
10
TOTALS sum for each zone.

15

16

REMOVAL FACTOR by air stripping (mg/L-s). Line 16.
17
REMOVAL FACTOR by biodegradation (mg/L-s). Line 15.
18
REMOVAL FACTOR for effluent (mg/L-s). Line 9 divided by line 12.
19
TOTAL of the three loss mechanisms. Add the numbers on lines 20,21,and 22.
20
Fraction biodegraded: Divide the number on line 18 by the number on line 20.
21
Fraction air emissions: Divide the number on line 17 by the number on line 20. 22
Fraction remaining in unit effluent: Divide line 19 by line 20.
23
Total: add the numbers on lines 21, 22, and 23. The sum should equal 1.0
24
note: as a quality control check, the number on line 23 should approximate the number on line 13.

Form 2

DATA FORM FOR THE ESTIMATION OF THE BIORATE
FOR EACH ZONE IN THE ACTIVATED SLUDGE SYSTEM
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
The number of defined zones in the activated sludge system.
1
BIORATE DATA FOR EACH DEFINED ZONE (Form 3)
BIORATE (mg/L-s) Measured biorate for zone 1.
2
BIORATE (mg/L-s) Measured biorate for zone 2.
3
BIORATE (mg/L-s) Measured biorate for zone 3.
4
BIORATE (mg/L-s) Measured biorate for zone 4.
5
BIORATE (mg/L-s) Measured biorate for zone 5.
6
CONCENTRATION FOR EACH DEFINED ZONE
CONCENTRATION (mg/L) for zone 1.
7
CONCENTRATION (mg/L) for zone 2.
8
CONCENTRATION (mg/L) for zone 3.
9
CONCENTRATION (mg/L) for zone 4.
10
CONCENTRATION (mg/L) for zone 5.
11
CALCULATED BIOREMOVAL RATE CONSTANT FOR EACH DEFINED
BIOREMOVAL RATE (/s) for zone 1, line 2 divided by line 7.
12
BIOREMOVAL RATE (/s) for zone 2, line 3 divided by line 8.
13
BIOREMOVAL RATE (/s) for zone 3, line 4 divided by line 9.
14
BIOREMOVAL RATE (/s) for zone 4, line 5 divided by line 10.
15
BIOREMOVAL RATE (/s) for zone 5, line 6 divided by line 11.
16

Form 3

DATA FORM FOR THE ESTIMATION OF
THE BIODEGRADATION RATE FOR EACH ZONE
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
ESTIMATE OF K1 in the zone from Form 8 line 11, Form 9 line 15, Form 10
line 15, Form 11 line 13, or Form12 line 9. (L/g bio-hr)
BIOMASS (g/L) This is the dried solids that are obtained from the mixed liquor
suspended solids in the full-scale bioreactor.
VOLUME of zone (cubic meters)
AREA of the liquid surface of the zone (square meters)
ESTIMATE OF KL from Form 6 (m/s)
FLOW RATE of waste treated in the zone (m3/s)
CALCULATIONS FROM ESTIMATES OF K1 AND KL
BIORATE (m3/s) Multiply the numbers on lines 1, 2, and 3 together and divide
the results by 3600. Enter the results here.
AIR STRIPPING (m3/s). Multiply the numbers on lines 4 and 5 together. Enter
the results here.
EFFLUENT DISCHARGE (m3/s). Enter the number on line 6 here.
TOTAL of the three loss mechanisms. Add the numbers on lines 7, 8, and 9.
Enter the results here.
Fraction biodegraded: Divide the number on line 7 by the number on line 10 and
enter the results here.
Fraction air emissions: Divide the number on line 8 by the number on line 10
and enter the results here.
Fraction remaining after zone treatment: Divide the number on line 9 by the
number on line 10 and enter the results here.
Total: add the numbers on lines 11, 12, and 13. The sum should equal 1.0

1
2
3
4
5
6

7
8
9
10
11
12
13
14

Form 4

DATA FORM FOR THE ESTIMATION OF MULTIPLE ZONE
COMPOUND CONCENTRATIONS (3 ZONES)
Total inlet flow (m3/s)
Total number of zones
Internal recycle ratio
Total unit volume (m3)
Zone volume (m3)
Flow factor B, line 1 times line 3
Flow factor A, line 6 plus line 1
Inlet adjusted concentration (waste plus recycle)
Flow factor E, line 8 times line 1
Ratio of exit concentration to Zone 3 concentration

1
2
3
4
5
6
7
8
9
10

biorate (/s)

air stripping
(/s)

A(i)

B(i)

removal factor
(m3/s)
C(i)=(ai + bi)
times line 5

Zone 1
Zone 2
Zone 3

Calculation exit concentration, C(3) = E / [-D(1)B/A - (B+D(2))D(1)D(3)/A/A - B D(3)/A]
Calculation concentration ZONE 2, C(2) = C(3) D(3) /A
Calculation concentration ZONE 1, C(1) = [E + C(2) B]/D(1)
Calculation exit concentration, C(4) = number on line 10 times the number on line 11

D(i)
ci plus line 7

Form 5

DATA FORM FOR THE ESTIMATION OF MULTIPLE ZONE
BIODEGRADATION FROM UNIT CONCENTRATIONS
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
Number of zones in the biological treatment unit
VOLUME of full-scale system (cubic meters)
Average DEPTH of the full-scale system (meters)
Flow rate of wastewater treated in the unit (m3/s)
Recycle flow of wastewater added to the unit, if any (m3/s)
Concentration in the wastewater treated in the unit (mg/L)
Concentration in the recycle flow, if any (mg/L)
Concentration in the effluent (mg/L).
TOTAL INLET FLOW (m3/s) line 4 plus the number on line 5
TOTAL RESIDENCE TIME (s) line 2 divided by line 9.
TOTAL AREA OF IMPOUNDMENT (m2) line 2 divided by line 3

Zone
number

Concentration
for zone, Ci
(mg/L)

1
2
3
4
5
6
7
8
9
10
TOTALS sum for each zone.

1
2
3
4
5
6
7
8
9
10
11

Estimate of KL in
Area of the
the zone (m/s)
zone, A (m2)
from Form 6

12

AIR STRIPPING
KL A Ci (g/s)

13

Removal by air stripping (g/s). Line 13.
Loading in effluent (g/s). Line 8 times line 9.
Total loading (g/s). (Line 5 * line 7) + (line 4* line 6).
Removal by biodegradation (g/s) Line 16 minus (line 14 + line 15).
Fraction biodegraded: Divide line 17 by line 16..
Fraction air emissions: Divide line 14 by line 16.
Fraction remaining in unit effluent: Divide line 15 by line 16.

(identical to Form XIII Appendix C to Part 63)

14
15
16
17
18
19
20

Form 6

PROCEDURES FORM FOR THE
ESTIMATION OF THE KL FROM UNIT SPECIFICATIONS
NAME OF THE FACILITY for site specific biorate determination
NAME OF UNIT for site specific biorate determination
NAME OF COMPOUND
HENRY'S LAW constant for the compound (mole fraction in gas per mole
fraction in water at 25 degrees Celsius)
IDENTIFY THE TYPE OF UNIT (check one box below)
Quiescent impoundment
Surface agitated impoundment
Surface agitated impoundment with submerged air
Unit agitated by submerged aeration gas
EPA Method 304A, Covered unit, UNOX system, or bench scale reactor

1
2
3
4
5

PROCEDURES BASED UPON THE TYPE OF UNIT
1. Use the quiescent impoundment model to determine KL. Use Kq as KL as determined from
Form 7.
2. Use the quiescent impoundment model to determine KL for the quiescent zone, Form 7. Use the
aerated impoundment model to determine KL for the agitated surface, Form 13.
3. Use the quiescent impoundment model to determine Kq for the quiescent zone, Form 7. Use the
aerated impoundment model to determine KL for the agitated surface, Form 13.
The total system KL is the sum of the KL from Form 13 and the equivalent KL f
4. Use the aerated impoundment model to determine KL if the surface is agitated. Use the quiescent
impoundment model if the surface is not agitated. KL includes the effect of volatilization in the air
discharge. See section 5.6.1 in the AIR EMISSIONS MODELS FOR WASTE AND WASTEWATER
(EPA -453/R-94-080A).
5. KL for the surface is assumed to equal zero. Determine equivalent KL based upon air discharge.
Use Form 9 for EPA Method 304A or if the concentration in the vent is not measured.
Use Form 10 if the concentration in the vent is measured.

Estimate of KL obtained from above procedures (m/s)

(identical to Form II, Appendix C to Part 63)

6

Form 7

FORM FOR CALCULATING THE MASS TRANSFER COEFFICIENT
FOR A QUIESCENT SURFACE IMPOUNDMENT
FACILITY NAME for site specific biorate determination
COMPOUND for site specific biorate determination

1
2

Input values
Enter the following:
F - Impoundment fetch (m)
D - Impoundment depth (m)
U10 - Windspeed 10 m above liquid surface (m/s)
Dw - Diffusivity of compound in water (cm2/s)
Dether - Diffusivity of ether in water (cm2/s)
µG - Viscosity of air, (g/cm-s)
G - Density of air, (g/cm3)
Da - Diffusivity of compound in air, (cm2/s)
A - Area of impoundment, (m2)
H - Henry's law constant, (atm-m3/g mol)
R - Universal gas constant, (atm-m3/g mol. K)
µL - Viscosity of water, (g/cm-s)
L - Density of liquid, (g/cm3)
T - Impoundment temperature, ( C)

3
4
5
6
7
8
9
10
11
12
13
14
15
16

Calculate the following:
Calculate F/D:

A.

17

Calculate the liquid phase mass transfer coefficient, kL, using one of the
following procedures, (m/s)
Where F/D < 14 and U10 > 3.25 m/s, use the following procedure from
1 MacKay and Yeun:
Calculate the Schmidt number on the liquid side, ScL, as follows:
ScL = µL/ (L x Dw)

18

Calculate the friction velocity, U*, as follows, (m/s):
U* = 0.01 x U10(6.1 + 0.63 U10)^0.5

19

Where U* is > 0.3, calculate kL as follows:
kL = (1.0 x 10^-6) + (0.00341)U* x ScL^-0.5

20

Where U* is < 0.3, calculate kL as follows:
kL = (1.0 x 10^-6) + (0.0144)(U*)^2.2 x ScL^-0.5

21

For all other values of F/D and U10, calculate kL using the following
2 procedure from Springer:

(identical to Form VII, Appendix C to Part 63)

1 of 2

Form 7

B.

Where U10 is < 3.25 m/s, calculate kL as follows:
kL = 2.78 x 10^-6(Dw/Dether)^(2/3)

22

Where U10 is > 3.25 and 14 < F/D < 51.2, Calculate kL as follows:
kL = [2.605 x 10^-9(F/D) + 1.277 x 10^-7] U10^2 (Dw/Dether)^(2/3)

23

Where U10 > 3.25 m/s and F/D > 51.2, calculate kL as follows:
kL = (2.611 x 10-7)U10^2 (Dw/Dether)^(2/3)

24

Calculate the gas phase mass transfer coefficient, kG, using the following
procedure from MacKay and Matsasugu, (m/s):
Calculate the Schmidt number on the gas side, ScG, as follows: ScG =µG/
(G x Da)

25

Calculate the effective diameter of the impoundment, de, as follows, (m):
de = (4A/3.14 )^0.5

26

Calculate kG as follows, (m/s): kG = 0.00482 U10^0.78 ScG^-0.67 de^-0.11 27
C.

Calculate the partition coefficient, Keq, as follows: Keq = H/[R(T+273)]

28

D.

Calculate the overall mass transfer coefficient, Kq, as follows, (m/s):
1/Kq = 1/kL + 1/(Keq x kG)

29

Where the total impoundment surface is quiescent:
KL = Kq

30

Where a portion of the impoundment surface is turbulent, continue with
Form 13.

(identical to Form VII, Appendix C to Part 63)

2 of 2

Form 8

DATA FORM FOR THE ESTIMATION OF
THE EPA METHOD 304B FIRST ORDER BIORATE CONSTANT
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
INLET CONCENTRATION used in EPA METHOD 304B
EXIT CONCENTRATION measured by EPA METHOD 304B
BIOMASS (g/L) This is the dried solids that are obtained from the mixed liquor
suspended solids in the bench scale bioreactor.
TEMPERATURE OF BIOREACTOR (deg. C)
VOLUME of EPA METHOD 304B bench scale bioreactor (L)
FLOW RATE of waste treated in the bench scale bioreactor (L/hr)
CALCULATIONS FROM EPA METHOD 304B DATA MEASUREMENTS
RESIDENCE TIME (hr) Divide the number on line 5 by the number on line 6 and
enter the results here.
Concentration Decrease (g/m3). Subtract the number on line 2 from the number on
line 1 and enter the results here.
BIORATE (g/m3-hr). Divide the number on line 8 by the number on line 7 and enter
the results here.
Product of concentration and biomass. Multiply the number on line 2 by the number
on line 3 and enter the results here.
BIORATE K1 (L/g MLVSS-hr) Divide the number on line 9 by the number on line
10 and enter the results here.
Temperature adjustment. Subtract 25 deg. C from the number on line 4 and enter the
results here.
Temperature adjustment factor. 1.046 is the default temperature adjustment factor.
Enter the temperature adjustment factor here.
Biorate temperature ratio. Raise the number on line 13 to the power of the number on
line 12.
BIORATE K1 at 25 deg. C (L/g MLVSS-hr) Divide the number on line 11 by the
number on line 14 and enter the results here.

(identical to Form I, Appendix C to Part 63)

1
2

3
4
5
6

7

8

9

10

11

12

13

14

15

Form 9

DATA FORM FOR THE ESTIMATION OF K1 FOR EPA METHOD 304A
OR FROM A COVERED, VENTED BIODEGRADATION UNIT.
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
BIOMASS (g MLVSS/L) This is the dried solids that are obtained from the mixed
liquor suspended solids in the unit.
VENT RATE of total gas leaving the unit (G, m3/s)
TEMPERATURE of the liquid in the unit (deg. C)
INLET CONCENTRATION of compound (g/m3 or ppmw)
EXIT CONCENTRATION of compound (g/m3 or ppmw)
ESTIMATE OF Henry's law constant (H, g/m3 in gas / g/m3 in liquid). Obtained
from Form IX
AREA OF REACTOR (m2)
VOLUME OF REACTOR (m3)
FLOW RATE of waste treated in the unit (m3/s)
CALCULATION OF THE ESTIMATE OF K1
TOTAL REMOVAL (g/s) Subtract the number on line 5 from the number on line
4 and multiply the result by the number on line 9. Enter the results here.
[H G] ESTIMATE (m3/s) Multiply the number on line 2 by the number on line
6. Enter the results here.
[K1 B V + H G] (m3/s) Divide the number on line 10 by the number on line 5.
Enter the results here.
[K1 B V] ESTIMATE (m3/s) Subtract the number on line 11 from the number
on line 12. Enter the results here.
If the number on line 11 is greater than the number on line 13, this procedure cannot
be used to demonstrate that the compound is biodegradable. Do not complete lines
14 and 15.
Product of B and V. Multiply the number on line 1 by the number on line 8 and
enter the results here.
K1 ESTIMATE (L/g MLVSS-hr) Divide the number on line 13 by the number
on line 14 and multiply by 3600 s/hr. Enter the results here.
EQUIVALENT KL. Divide the number on line 11 by the number on line 7. Enter
the results on line 16.

(identical to Form V, Appendix C to Part 63)

1
2
3
4
5
6
7
8
9

10
11
12
13

14
15
16

Form 10

DATA FORM FOR THE CALCULATION OF K1 FROM A COVERED,
VENTED BIODEGRADATION UNIT. THE VENT CONCENTRATION IS MEASURED.
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
BIOMASS (g/L) This is the dried solids that are obtained from the mixed liquor
suspended solids in the unit.
1
VENT RATE of total gas leaving the unit (G, m3/s)
2
TEMPERATURE of the liquid in the unit (deg. C)
3
INLET CONCENTRATION of compound (Ci, g/m3 or ppmw)
4
EXIT CONCENTRATION of compound (Ce, g/m3 or ppmw)
5
VENT CONCENTRATION of compound (Cv, g/m3)
6
AREA OF REACTOR SURFACE (m2)
7
VOLUME OF REACTOR (m3)
8
FLOW RATE of waste treated in the unit (m3/s)
9
CALCULATION OF THE ESTIMATE OF K1
TOTAL REMOVAL (g/s) Subtract the number on line 5 from the number on line 4
and multiply the results by the number on line 9. Enter the results here.
10
[ G Cv/Ce] ESTIMATE (m3/s) Multiply the number on line 2 by the number on
line 6 and divide by the number on line 5. Enter the results here.
11
[K1 B V + G Cv/Ce] (m3/s) Divide the number on line 10 by the number on line
5. Enter the results here.
12
[K1 B V] ESTIMATE (m3/s) Subtract the number on line 11 from the number
on line 12. Enter the results here.
13
If the number on line 11 is greater than the number on line 13, this procedure cannot
be used to demonstrate that the compound is biodegradable. Do not complete lines 14
and 15.
Product of B and V. Multiply the number on line 1 by the number on line 8 and enter
the results here.
14
K1 ESTIMATE (L/g MLVSS-hr) Divide the number on line 13 by the number on
line 14 and multiply by 3600 s/hr. Enter the results here.
15
EQUIVALENT KL. Divide the number on line 11 by the number on line 7. Enter the
results here.
16

(identical to Form Va, Appendix C to Page 63)

Form 11

DATA FORM FOR THE ESTIMATION OF K1
FROM FULL SCALE UNIT DATA WITH BIODEGRADATION
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
BIOMASS (g/L) This is the dried solids that are obtained from the mixed liquor
suspended solids in the full-scale bioreactor.
VOLUME of full-scale system (cubic meters)
AREA of the liquid surface of the full-scale system (square meters)
INLET CONCENTRATION of compound (g/m3 or ppmw)
EXIT CONCENTRATION of compound (g/m3 or ppmw)
ESTIMATE OF KL from Form 6 (m/s)
FLOW RATE of waste treated in the full-scale bioreactor (m3/s)
CALCULATION OF THE ESTIMATE OF K1 FROM FIELD DATA
REMOVAL WITH BIODEGRADATION (g/s) Subtract the number on line 5
from the number on line 4 and multiply the results by the number on line 7. Enter
the results here.
[KL A] ESTIMATE (m3/s) Multiply the number on line 3 by the number on line
6. Enter the results here.
[K1 B V + KL A] (m3/s) Divide the number on line 8 by the number on line 5.
Enter the results here.
[K1 B V] ESTIMATE (m3/s) Subtract the number on line 9 from the number
on line 10. Enter the results here.
Product of B and V. Multiply the number on line 1 by the number on line 2 and
enter the results here.
K1 ESTIMATE (L/gbio-hr) Divide the number on line 11 by the number on line
12 and multiply by 3600 s/hr. Enter the results here.

(identical to Form VI, Appendix C to Part 63)

1
2
3
4
5
6
7

8

9

10

11

12

13

Form 12

DATA FORM FOR THE CALCULATION OF BATCH RATES
AND THE DETERMINATION OF THE MONOD CONSTANTS
COMPOUND for site specific biorate determination
Stripping rate constant (/hr) Form XI, line 11
Enter the batch test Biomass concentration (g/L) on line 2.
Headspace correction factor. For a Sealed Batch test use Form X line 12 or
1.00 for an Aerated Batch test.
A
B
C
D
E
F
concentration S
(mg/L)

time (hr)

Ratio of
Log Mean S for
rate to S
Rate for interval
(mg/L-hr) (ai-ai+1)/ interval (mg/L) (ai(/hr)
(bi+1-bi)
ai+1)/ ln(ai/ai+1)
(C/D)

Adjusted rate (/hr)
(E-line 1)

1
2
3
G
Reciprocal of adj.
rate (hr) (1/F)

Continue table on attached sheet as needed. Plot values in column G on y axis, values in column
D on x axis. Extrapolate the trend of data points to the y intercept (S=0). Attach the plot to the
form.

(identical to Form XII, Appendix C to Part 63)

1 of 2

Form 12

Slope of line near intercept (hr-L/mg)
Y intercept from plot (hr)
First order rate constant K1 (or Qm/Ks, L/g-hr). The number 1.00 divided
by the products of the values on line 5, line 2, and line 3.
Zero order rate constant (Qm, /hr). The number 1.00 divided by the products
of the values on line 4, line 2, and line 3.
Concentration applicable to full-scale unit. Enter on line 8.
Effective biorate K1 ESTIMATE (L/g bio-hr)*

4
5
6
7
8
9

*Match the concentration on line 8 to the values in Column D and look up the equivalent rate in
Column F. Divide the result with both the biomass concentration (line 2) and the headspace
correction factor (line 3). Enter this value on line 9. Do not use this method to estimate K1 for
line 9 in the data qualtiy is poor in Column F. The number on line 9 is multiplied by the biomass
and the system concentration to estimate the full scale biorate. Alternatively, the Monod model
parameteers may be used.

(identical to Form XII, Appendix C to Part 63)

2 of 2

Form 13

DATA FORM FOR CALCULATING THE
MASS TRANSFER COEFFICIENT FOR AN AERATED SURFACE IMPOUNDMENT
Facility Name:
Waste Stream Compound:
Enter the following:
J - Oxygen transfer rating of surface aerator, (lb O2/hr-hp)
POWR - Total power to aerators, (hp)
T - Water temperature, ( C)
Ot - Oxygen transfer correction factor
MWL - Molecular weight of liquid
area per agitator (M2)
At - Turbulent surface area of impoundment, (ft2)
(If unknown, use values from Table 1)
A - Total surface area of impoundment, (ft2)
rho L - Density of liquid, (lb/ft3)
Dw - Diffusivity of constituent in water, (cm2/s)
Do - Diffusivity of oxygen in water, (cm2/s)
d - Impeller diameter, (cm)
w - Rotational speed of impeller, (rad/s)
a - Density of air, (gm/cm3)
N - Number of aerators
gc - Gravitation constant, (lbm-ft/s2/lbf)
d* - Impeller diameter, (ft)
Da - Diffusivity of constituent in air, (cm2/s)
MWa - Molecular weight of air
R - Universal gas constant, (atm-m3/g mol. C)
H = Henry's law constant, (atm-m3/g mol)
Calculate the following:

A.

Calculate the liquid phase mass transfer coefficient, kL, using the following
Equation from Thibodeaux:,
kL =[8.22 x 10^-9 J (POWR)(1.024)^(T-20) Ot 10^6 MWL/(At x rhoL/62.37)]
(Dw/Do)^0.5, (m/s)

B.

Calculate the gas phase mass transfer coefficient, kG, using the following
procedure from Reinhardt:,
Calculate the viscosity of air, µa, as follows, (g/cm.s):
µa = 4.568 x 10^-7 T + 1.7209 x 10^-4
Calculate the Reynold's number as follows:
Re = d^2 w a/µa
Calculate power to impeller, PI, as follows, (ft.lbf/s):
PI = 0.85 (POWR) 550/N

(identical to Form VIII, Appendix C to Part 63)

1 of 3

Form 13

Calculate the power number, p, as follows:
p = PI gc/( rho d*^5 w^3)
Calculate the Schmidt number, ScG, as follows:
ScG = µa/ (a x Da)
Calculate the Fronde number, Fr, as follows:
Fr = d* x w^2 /gc

C.

D.

Calculate kG as follows:
kG = 1.35 x 10^-7 Re^1.42 p^0.4 ScG^0.5 Fr^-0.21 Da MWa/d, (m/s)
if quiescent gas phase mass transfer coefficient is used, enter here else use
above line.
Calculate the partition coefficient, Keq, as follows:
Keq = H/[R(T+273)]
Calculate the overall turbulent mass transfer coefficient, Kt, as follows, (m/s):
1/Kt = 1/kL + 1/(Keq x kG)

E.

Calculate the quiescent mass transfer coefficient, Kq, for the impoundment using
Form 7 line 29.

F.

Calculate the overall mass transfer coefficient, KL, for the impoundment as
follows: KL = (A-At)/A*Kq + At*Kt/A

(identical to Form VIII, Appendix C to Part 63)

2 of 3

Form 13 Table 1

PROCEDURES FORM FOR THE ESTIMATION OF THE KL FROM WATER8 a.b
Motor
horsepower,
Effective
V, Agitated
aV, Area per
hp
depth,
ft
volume,
ft3
volume
ft2/ft3
At, Turbulent area,
5
7.5
10
15
20
25
30
40
50
60
75
100

ft2
177
201
227
284
346
415
491
661
855
1075
1452
2206

m2
16.4
18.7
21
26.4
32.1
38.6
45.7
61.4
79.5
100
135
205

10
10
10.5
11
11.5
12
12
13
14
15
16
18

1,767
2010
2383
3119
3983
4986
5890
8587
11970
16130
23240
39710

0.1002
0.1000
0.0953
0.0911
0.0869
0.0832
0.0834
0.0770
0.0714
0.0666
0.0625
0.0556

a Data for a high speed (1,200) rpm) aerator with 60 cm propeller diameter (d).
b This table provides information potentially useful for the value of At.

3 of 3

Form 14

DATA FORM FOR THE ESTIMATION OF THE HENRY'S LAW CONSTANT
FOR A COMPOUND IN THE BIOLOGICAL TREATMENT UNIT
NAME OF THE FACILITY for site specific biorate determination
COMPOUND for site specific biorate determination
LISTED HENRY'S LAW VALUE AT 25 degrees Celsius. (ratio of mol fraction in
gas to mole fraction in water at one atmosphere)
1
TEMPERATURE of the liquid in the unit (deg.C)
2
CALCULATION OF K
Temperature adjusted Henry's law value (equals the value on line 1 if the
temperature on line 2 is 25)
3
Discuss the basis of the temperature adjustment.

Temperature in degrees Kelvin. Add 273.16 to the number on line 2. Enter the
results here.
Temperature ratio. Divide 273.16 by the number on line 4. Enter the results here.
Henry's Law adjustment factor. Multiply the number on line 5 by 0.804 and enter
the results here.
Henry's Law value (g/m3 gas per g/m3 liquid) Multiply the number on line 3 by the
number on line 6 and divide the results by 1000. Enter the results here.
Henry's Law value (atm m3 per mol ) Divide the number on line 3 by 55555 and
enter the results here.

4
5
6
7
8

Form 15

Form for the Estimation of Eddy Diffusivity with Submerged Aeration
Reference Fujie, 1983. Only use this form for spiral circulation due to aeration.
Sprial circulation is usually found only in municipal plants. For more
information, consult a reference book such as Metcalf and Eddy or WEF
Aeration Manual.
H
W

L
Q
h
A

Name of site
depth of unit (m)
width of unit (m) (area/diameter for circular tanks)
LENGTH [L] distance from inlet to reactor exit. (m) Represents the
mean path of actual flow from inlet to exit. Can use diameter for
circular tank. If the flow is across the width of a rectangular unit,
enter the width here.
Flow rate water (m3/s)
diffuser depth (m)
Aeration rate per tank (m3 air/m3 liquid per h), volumetric rate of air
divided by the volume of the unit.
for fine bubble system enter 1 on line 8.

1
2

3
4
5
6
7

CALCULATION OF EDDY DIFFUSIVITY
Ugc
theta
m
a
Uts
Utsc
lamda
Ut
E
D

sup.air feed rate (cm/s) A*H/36
h*100*Ugc*(h/H)^0.5*(H/W)^0.333
value from Table I.1 (see below)
value from Table I.1 (see below)
a*(theta^m) (cm/s)
Uts/100*3600 (m/h)
0.0115*(1+H/L)^(-3)*Ugc^-0.34
Q*3600/W/H
diffusivity (m2/h) lamda*Utsc*(H+W)
(m2/s) E/3600

8
9
10
11
12
13
14
15
16
17

theta<=20
theta>20
theta<=20
theta>20

Table I.1
m
0.64
0.46
0.78
0.56

a
7
12
3.5
4.9

fine
coarse

1

Form 16

DATA FORM FOR THE CALCULATION OF THE DISPERSION NUMBER
FROM A SUBMERGED AERATION UNIT
NAME OF THE FACILITY for site specific dispersion number
determination
VOLUME OF REACTOR (m3)
FLOW RATE of wastewater treated in the unit (m3/s)
FLOW RATE OF RECYCLE (m3/s)
LENGTH [L] distance from inlet to reactor exit. (m) Represents the
mean path of actual flow from inlet to exit. Can use diameter for
circular tank. If the flow is across the width of a rectangular unit, enter
the width here.
EDDY DIFFUSIVITY [D] from Form 1 line 17 if spiral agitation or
default value of 0.068 (m2/s)

1
2
3

4
5

CALCULATION OF THE DISPERSION NUMBER
TOTAL INLET FLOW (m3/s) Add the number on line 2 to the number
on line 3. Enter the results here.
RETENTION TIME IN THE REACTOR (s) Divide the number on line
1 by the number on line 6. Enter the results hers.
MEAN VELOCITY [U] (m/s) Divide the number on line 4 by the
number on line 7. Enter the results here.
DISPERSION NUMBER [D/UL] Divide the number on line 5 by the
product of the number on line 8 and the number on line 4. Enter the
results here.

6
7
8

9