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A THEORETICAL MODEL OF NITRIFICATION IN FLOATING-BEAD FILTERS

by

William J. Golz

M.S. Thesis, Louisiana State University, 1997

ii

Copyright 1997

William Johnathan Golz

All rights reserved

W. J. Golz / M.S. Thesis, Louisiana State University, 1997

iii

Table of Contents

List of Tables ..............................................................................................................................v

List of Figures ............................................................................................................................vi

Abstract ....................................................................................................................................vii

Introduction.................................................................................................................................1

Objectives .............................................................................................................................3

Literature Review ........................................................................................................................4

Nitrification in Combined Systems.........................................................................................4

Experimental Studies.......................................................................................................5

Numerical Models...........................................................................................................8

Interspecific Competition in Multispecies Biofilms.........................................................10

Monod Kinetics.............................................................................................................13

Solids and Mean-Cell Residence Times................................................................................14

FBFs: Solids Capture and Biofiltration in RASs...................................................................15

Aquacultural Waste Production and Characteristics.......................................................15

Solids Decay.................................................................................................................16

Insitu Nitrification.........................................................................................................18

Floating-Bead Filters.....................................................................................................18

Summary: Potential Limitations on Oxygen Delivery and Transport .....................................19

Model Development...................................................................................................................23

Primary Solids ....................................................................................................................25

Biomass ..............................................................................................................................26

Total Solids.........................................................................................................................28

TAN ...................................................................................................................................28

BOD5 ..................................................................................................................................30

Dissolved Oxygen ...............................................................................................................30

Limits of the Model .............................................................................................................31

Model Calibration......................................................................................................................34

Calibration Against the BBF................................................................................................35

Calibration Against the PBF................................................................................................37

Summary ............................................................................................................................38

Results and Discussion ..............................................................................................................39

The Effects of Backwash Interval on Nitrification Rate in a Gently-Washed Filter................40

The Effects of Backwash Interval on Nitrification Rate in an Aggressively-Washed Filter.....41

Summary ............................................................................................................................43


iv

Conclusions...............................................................................................................................45

Solids Limitations ...............................................................................................................45

Backwash-Regime Limitations.............................................................................................45

Recommendations......................................................................................................................46

Model Improvements ...........................................................................................................46

Filter Improvements ............................................................................................................46

References.................................................................................................................................47

Appendixes

A. BBF-System Model Values ...........................................................................................51

B. PBF-System Model Values............................................................................................53

C. Model Excretion Rates, Waste Characteristics, and Kinetic Constants............................55

D. VisSimTM Model ...........................................................................................................57

E. Model Calibration Output .............................................................................................65


v

List of Tables

1. Definitions of variables........................................................................................................32

2. BBF calibration variables ....................................................................................................35

3. Comparison of predicted and experimental values for the BBF .............................................36

4. PBF calibration variables ....................................................................................................37

5. Comparison of predicted and experimental values for the PBF..............................................38


vi

List of Figures

1. Gently-washed BBF, during backwashing ..............................................................................2

2. Aggressively-washed PBF, during backwashing. ....................................................................2

3. Influence of backwash interval on nitrification rate in a BBF and a PBF.................................3

4. Effect of influent BOD5 on RBC NH4+-N removal..................................................................5

5. Effect of short-term DO and COD variations on NH4+-N removal in a trickling filter ..............6

6. Relationship of COD loading to removal rate .........................................................................7

7. Effect of COD removal on zero-order nitrification..................................................................7

8. Predicted species distributions for increasing acetate concentrations (1.5 mg/NH4+ -N/L) ........9

9. Modeled nitrification rate as a function of measured oxygen concentration............................10

10. Steady-state substrate profiles in a heterotrophic-autotrophic biofilm....................................11

11. Biofilm NH4+-N and NO3

--N profiles at low DO concentrations............................................11

12. Effect of increased glucose on biofilm DO and NH4+-N profiles............................................12

13. Critical depth as a function of biofilm thickness ...................................................................12

14. Density as a function of biofilm thickness ............................................................................12

15. Model mass-balance diagram showing major fluxes .............................................................24

16. KSO versus biomass respiration and flow rate .......................................................................39

17. Solids concentration and flow rate in the BBF......................................................................40

18. Modeled oxygen consumption in the BBF ............................................................................41

19. Modeled CA in the BBF .......................................................................................................41

20. Solids concentration and flow rate in the PBF ......................................................................42

21. Modeled oxygen consumption in the PBF.............................................................................42

22. Modeled CA in the PBF........................................................................................................43


vii

Abstract

Literature coefficients are used as the basis for a theoretical model that examines the major

factors that limit nitrification in a gently- and aggressively-washed floating-bead filter. Model

results are consistent with research, which indicated that nitrification can become limited by

oxygen delivery and transport as solids accumulate. The oxygen half-saturation constant (KSO) was

directly related (r2 = 0.95) to oxygen consumed during heterotrophic respiration and autotrophic

respiration for internally-loaded TAN, while it was inversely related to flow. KSO increased from

0.5-13 mg O2/L in the aggressively-washed filter, reflecting the comparatively-low solids

concentrations that resulted from a larger harvest fraction (hf = 0.57). KSO varied from 6.5-30 mg

O2/L in the gently-washed filter, because of the relatively-large solids concentrations that

accompanied a smaller harvest fraction (hf = 0.36). For the gently-washed filter (feed loading of

1.5-2 lbs/ft3/d), the model indicated that 80% of the initial biomass was retained in the filter

following backwashing. This large biofilm retention factor (BR) and the rapid increase in KSO

resulted in maximum nitrification (30.5 mg/ft2/d) occurring at an 8 hour backwash interval. In the

aggressively-washed filter (feed loading of 1.5 lbs/ft3/d), the model indicated that BR was 50%, and

the filter was initially biomass limited. The smaller value of BR and the slower growth of KSO may

explain why nitrification increased with backwash interval, reaching a maximum (31.6 mg/ft2/d) at

a backwash interval of 48 hours, before the solids-induced oxygen limitation inhibited nitrification.


1

Introduction

Our global population is growing at an unprecedented rate, putting increased pressure on

shrinking supplies of food and water. Worldwide demand for seafood already exceeds the

sustainable harvest from our natural waters, and flow-through aquaculture contributes to the

degradation of surface water (Miller 1990). These factors have led to a decade-long expansion of

research and commercial production in recirculating aquaculture systems (RASs). Average

production costs in RASs are currently $1.25 per pound, which is about double the $0.60 per

pound cost of producing fish in a pond culture (Losordo and Westerman 1991). Reducing

production costs is, therefore, crucial to the future of the recirculating aquaculture industry.

When fish are stocked at high densities in a closed system, the recirculated water must be

maintained by an appropriate treatment train or water quality will rapidly decline. Total ammonia

nitrogen (TAN) removal and solids capture are well documented as two of the major factors

limiting fish production in recirculating systems (Drennan et al. 1995, Owsley 1993). Floating-

bead filters (FBFs) perform nitrification in conjunction with solids capture, which may lead to

lower treatment costs by reducing the number of system components, thereby lowering overall

production costs. However, nitrification capacity controls FBF design, because of the toxicity of

TAN to the fish and the strict environmental requirements of the nitrifying bacteria (Malone et al.

1993).

The use of FBFs in a RAS began at Dworshak National Fish Hatchery, with a pneumatically-

washed filter (Cooley 1979). More recently, a hydraulically-washed filter was developed and tested

at Louisiana State University (LSU) (Wimberly 1990). In both filters, nitrification increased with

washing frequency, establishing the importance of reducing the time that solids are held in the

filter.

W. J. Golz / M.S. Thesis, Louisiana State University, 1997 2

The effect that solids have on

nitrification increases with solids

residence time (SRT), because

decay and particulate occlusion

increase as the solids accrete in

the filter bed. The optimum

backwash interval must,

therefore, minimize SRT while

providing a mean-cell residence

time (MCRT) that is sufficient

to support nitrification.

Influent

Effluent

Sludge withdrawal

Air inlet

Figure 1. Gently-washed BBF, during backwashing.

In terms of the SRT-MCRT relationship, all bead filters belong to one of two regimes: gently or

aggressively washed, and their differences impose important limitations on the selection of a

backwash interval.

The bubble-washed bead

filter (BBF), shown in Figure 1,

uses a pneumatic-hydraulic

washing mechanism, which

imparts a gentle wash,

minimizing biofilm detachment

during backwashing. The BBFs

low washing energy permits

solids removal with minimal

Sludge withdrawal

Effluent

Influent

Washing motor

Washing Props

Figure 2. Aggressively-washed PBF, during backwashing.

biofilm detachment, which means that SRT can be abbreviated without curtailing MCRT.

Conversely, the propeller-washed bead filter (PBF), shown in Figure 2, was designed to exert an


aggressive wash to overcome initial resistance to filter-bed expansion in heavily-loaded systems. In

the aggressively-washed PBFs, there is more biofilm detachment during backwashing, so SRT and

MCRT are more closely related, which subverts attempts to improve nitrification by reducing the

backwash interval (Malone et al. 1993).

As shown in Figure 3, the

BBF behaved like the earlier

pneumatically- and

hydraulically-washed filters, i. e.

decreasing the backwash

interval increased nitrification

(Sastry 1996). However, in the

PBFs, biofilm detachment

during backwashing appears to

be substantial, since nitrification

increases as the backwash

10.0

15.0

20.0

25.0

30.0

35.0

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Backwash Interval (days)

Are

al

Nit

rifi

cati

on

Ra

te (

mg

/ft2

-d)

BBFPBF

Figure 3. Influence of backwash interval on nitrification rate in a

BBF and a PBF (data from studies by Chitta 1993 and Sastry 1996).

interval is extended (see Figure 3, Chitta 1993). It is evident that backwash regime determines the

interval at which optimal nitrification will be achieved. However, the maximum TAN conversion

rate is nearly identical in both FBF backwash regimes, and it appears to be limited by solids-

loading effects.

Objectives

This work was initiated to: (1) use existing literature to develop a hypothesis of how solids

accumulation and differing biomass loss rates in gently- and aggressively-washed FBFs can affect

nitrification and (2) use a computer model based on literature coefficients to evaluate that

hypothesis.


4

Literature Review

This review discusses the potential theoretical limitations on nitrification in heavily-loaded

floating-bead filters. There has been no research on the specific mechanisms that limit nitrification

in FBFs. However, FBFs are combined reactors, performing nitrification and carbon oxidation

simultaneously like many wastewater treatment systems, for which there is research that explores

the limiting mechanisms (Beccari et al. 1992, Bovendeur et al. 1990, Manem and Rittmann 1992,

Shammas 1986, Siegrist and Gujer 1987, Zhang et al. 1995). Temperature and substrate

concentrations in a RAS, though, are maintained in a relatively narrow range, determined by the

requirements of the cultured species. Temperatures in a RAS are often between 20 and 30°C, and

substrate concentrations are generally about 0.5-1 mg TAN/L and 5 mg BOD5/L (Chitta 1993,

Sastry 1996). The temperatures in wastewater treatment applications can be more variable, the

substrate concentrations higher, and the physical configuration of the filters different.

Bead filters are unique systems, not only because of their operating regime but because they

capture solids, and FBFs can be described as fixed film in certain respects and like suspended

growth in others. However, the major processes that govern nitrification appear to be similar in all

combined systems. Irrespective of the system type or operating regime, an increase in carbon

concentration or a decrease in oxygen concentration is usually accompanied by decreased

nitrification (Beccari et al. 1992, Bovendeur et al. 1990, Manem and Rittmann 1992, Shammas

1986, Siegrist and Gujer 1987, Zhang et al. 1995). This review explores how a variety of reactor

types respond to different loading regimes and operating conditions.

Nitrification in Combined Systems

Nitrification and carbon oxidation are often combined, and empirical studies show that

nitrification usually declines when the carbon concentration is increased. Theoretical models and

direct observation of biofilm indicate that this decline probably results from the fact that

heterotrophic bacteria have higher growth rates than the autotrophic nitrifying species. This allows

the heterotrophs to overgrow and out-compete the nitrifiers for available oxygen (Beccari et al.

1992, Bovendeur et al. 1990, Shammas 1986, Siegrist and Gujer 1987, Zhang et al. 1995).


Experimental studies are necessary to predict the performance of a specific system that is

operated within a given operating regime because no general model exists that can reliably predict

the nitrification rate that will correspond to a given carbon concentration. This is because the

relationship of nitrification to carbon oxidation is complex, varying with filter type, loading regime,

and influent characteristics (Bovendeur et al. 1990, Figueroa and Silverstein 1992). This section

looks at studies of a rotating biological contactor (RBC) that was used to process domestic

wastewater and a trickling filter that was used in a RAS. Although their operating regimes were

very different, both systems demonstrated a linear decline in nitrification as C:N ratio increased.

Figueroa and Silverstein (1992) studied soluble and particulate carbon effects on nitrification

in a RBC with a media surface area of 125 ft2. The hydraulic loading rate was 2.4 gal/ft2/d,

ammonium chloride was held constant at 27 mg N/L (245 mg/ft2/d), and the influent temperature

was below the optima for nitrification at 11-14°C. Dissolved oxygen (DO) was held above 8 mg/L

in the influent and remained above 4 mg/L in the effluent. Alkalinity and pH were maintained in an

ideal range for nitrification, 180-270 mg CaCO3/L and 7.5-8.1, respectively. Five-day biochemical

oxygen demand (BOD5) was supplied in soluble form as molasses and in particulate form as

thickened domestic sludge (60% primary and 40% secondary). Soluble and particulate fractions of

BOD5 were varied

independently. The soluble plus

particulate BOD5 (tBOD5)

loading ranged from 12 to 82

mg/L. Data was collected only

after the system had reached

steady state, i.e. after

ammonium removal remained

constant for one week.

tBOD5 (mg/L)

NH

4+-N

R

emo

ved

(m

g/L

)

00

10

20

30

10 20 30 40 50 60 70 80 90 100

soluble

particulate

fitted line

No-N = 24.8- 0.223* tBOD5

Figure 4. Effect of influent BOD5 on RBC NH4

+-N removal.

(after Figueroa and Silverstein 1992).


Figure 4 shows that soluble and particulate BOD5 identically inhibited nitrification. As the

tBOD5 loading was increased from 12-82 mg/L (109-746 mg/ft2/d), ammonium removal declined

from 20-5 mg N/L (204-65 mg /ft2/d).

Bovendeur et al. (1990) explored how a short-term (3-4 hour) change in organic loading or DO

concentration affected nitrification in a trickling filter used in a RAS. During the study, water

temperature and pH were maintained at near-optimal conditions for nitrification, 25°C and 7.0-7.5,

respectively. Chemical oxygen demand (COD) was supplied as trout feed that had been partially

digested in an activated sludge reactor, resulting in an organic substrate with a BOD5:COD similar

to fecal solids. The steady-state loading rates were 84 mg NH4+-N/ft2/d, 465 mg COD/ft2/d, and 7

mg O2/L.

0

25

50

75

100

0 2 4 6 8 10

NH4

+-N Concentration (mg/L)

NH

4 +

-N R

emoval

Rat

e (m

g/f

t2/d

)

Low organic loading (93 mg COD/ft2/d)

DO = 7 mg/L

DO = 3 mg/L

0

25

50

75

100

0 2 4 6 8 10

NH4

+-N Concentration (mg/L)

NH

4+-N

Rem

oval

Rat

e (m

g/f

t2/d

)

High organic loading (1860 mg COD/ft2/d)

DO = 7 mg/L

DO = 3 mg/L

Figure 5. Effect of short-term DO and COD variations on NH4

+-N removal in a trickling filter.

(after Bovendeur et al. 1990).

Figure 5 shows how DO affected nitrification during low (93 mg/ft2/d) and high (1860

mg/ft2/d) COD loadings. Nitrification rate was approximately halved when DO was reduced from

7 to 3 mg O2/L, for both organic loadings. The nitrification rate exhibited a similar decrease when

the COD was increased from 93 to 1860 mg/ft2/d, at either DO concentration.


Figure 6 shows the best-fit

line of the COD removal rate, as

the loading was increased from

93 to 1860 mg/ft2/d. COD

removal was first order and the

relationship was the same

whether DO concentration was 3

or 7 mg O2/L.

Figure 7 depicts the decline

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

COD Loading Rate (mg/ft2 /d)

CO

D R

em

oval

Rat

e (m

g/f

t 2/d

)

Figure 6. Relationship of COD loading to removal rate


in nitrification as COD loading

was increased from 93 to 1860

mg/ft2/d. The rate of decline was

0.015 mg N/ft2/d per mg

COD/ft2/d removed. Based upon

an oxygen consumption ratio of

4.18 mg O2/mg N removed, the

reduction in oxygen consumed

for nitrification was -0.063

mg/ft2/d per mg COD/ft2/d

removed.

NH

4+-N

Rem

ov

al R

ate

(mg

/ft2

/d)

COD Removal Rate (mg/ft2/d)

0 500 1000 1500 2000 25000

25

50

75

100

DO = 7 mg/L

DO = 3 mg/L

Figure 7. Effect of COD removal on zero-order nitrification


All of the COD removed was not simultaneously oxidized, and a respirometric experiment

indicated that simultaneous carbon oxidation consumed 0.065 mg O2/mg COD removed. Because

the reduction in oxygen consumption for nitrification was similar to the increase in oxygen

consumption for COD removal, Bovendeur et al. concluded that for higher organic-loading rates

nitrification was limited by heterotrophic interference with oxygen penetration into the biofilm.


Numerical models are capable of theoretically predicting nitrification over a wide range of

operating conditions, and they describe the resistance to substrate transfer with Fick’s law or

Monod half-saturation constants (Beccari et al. 1992, Bhaskar and Bhamidimarri 1991, Gonzalez-

Martinez and Duque-Luciano 1992, Rittmann and Manem 1992, Siegrist and Gujer 1987,

Timberlake et al. 1988).

Manem and Rittmann (1992) developed a steady-state model to quantify interspecific

competition in a submerged heterotrophic-autotrophic biofilm. The model was based on a

completely-mixed biofilm system with Monod expressions for growth and substrate utilization, and

Fick’s first law was used to describe diffusion into the biofilm. In the experimental system used to

calibrate the model, steady-state conditions were 15°C, influent ammonium was 2.5 mg N/L, and

effluent DO was maintained above 2 mg/L. Influent acetate concentration was varied incrementally

from 0-10 mg C/L (COD of 0.8 mg O2/mg C, Sawyer et al. 1994). The experimental system’s

substrate variations were accurately predicted by the model, and COD:N ratios within the modeled

range of 0-3 resulted in a decrease in nitrification that lasted up to 70 days.

Figure 8 illustrates the predicted change in species distribution as the acetate concentration was

increased. The model predicted that increasing the carbon concentration would result in a thicker

biofilm, with heterotrophs dominating the outer surface and forcing the nitrifiers to exist more

deeply in the film. The experimental system showed that nitrification declined following an increase

in carbon concentration, although full nitrification was reestablished after 20-70 days of steady-

state operation. The initial increase in COD, from 0-0.8 mg/L, caused nitrification to decline by

about 70%. However, subsequent increases in COD, when there was an initial COD concentration

prior to the increase, the temporary decline in nitrification was about 20%.


Siegrist and Gujer (1987)

developed a model to describe

the effect of oxygen diffusion on

nitrification in homogeneous

autotrophic and double-layer

heterotrophic-autotrophic

biofilms. A diffusion coefficient,

determined empirically, was

used to describe mass transfer

into the biofilm, and Monod

expressions were used for

biomass growth and substrate

utilization.

The laboratory trickling

filter used to evaluate the model

was operated under a pure

oxygen environment at a

constant temperature of 20°C.

Homogeneous nitrifying biofilms

were cultured by varying

ammonium from 15-80 mg N/L

to maintain the desired biofilm

thickness. Initial experiments

were conducted on a 310 µm

single-layer homogeneous

nitrifying biofilm.

0 0.40.2 0.6 0.8 1.0

0

20

40

100

60

80

Attachment surface Biofilm-water interface

COD ~ 0.8 mg/L Biofilm thickness = 26 um

Inert Biomass

Autotrophs

Heterotrophs

Inert Biomass

Autotrophs

Heterotrophs

0.40.2 0.6 0.8 1.0

0

20

40

100

60

80

0

COD ~ 2.4 mg/L Biofilm thickness = 92 um

Inert Biomass

0.40.2 0.6 0.8 1.0

0

20

40

100

60

80

Biofilm Depth

0

COD ~ 8 mg/L Biofilm thickness = 433 um

Per

centa

ge

of

Eac

h S

pec

ies

Figure 8. Predicted species distributions for increasing acetate

concentrations (1.5 mg NH4

+-N/L) (after Rittmann and Manem

1992).


The final experiments were conducted on a double-layer biofilm: a 60 µm homogeneous nitrifying

biofilm that was overlaid with a 340 µm heterotrophic layer, which was cultured with acetate and

glucose while ammonium addition was temporarily stopped.

Figure 9 shows how the

predicted ammonium uptake rate

changed from half order in the

homogeneous nitrifying biofilm to

first order in the double-layer

biofilm. At an oxygen concentration

of 5 mg/L, the difference in

ammonium conversion rates was

dramatic: ammonium uptake was

nearly 50% of its maximum in the

Per

cent

of

Max

imum

NH

4

+-N

Upta

ke

Rat

e

Measured Bulk DO Concentration (mg/L)

Homogeneous Biofilm

dBionitrif = 310 ± 30 um

dBioheter = 0 um

Double Layer Biofilm

dBionitrif = 60 um

dBioheter = 340 um

0 5 10 15 20 25 30 35 40

0

20

40

60

80

100

Figure 9. Modeled nitrification rate as a function of measured

oxygen concentration (after Siegrist and Gujer 1987).

homogeneous biofilm but only 15% of the maximum in the double-layer biofilm. As shown in

Figure 9, neither biofilm was fully penetrated with oxygen below a concentration of 30 mg O2/L

(higher oxygen concentration did not increase the ammonium uptake rate).

Interspecific Competition in Multispecies Biofilms appears to be responsible for the decline

in nitrification when carbon concentration is increased (Bovendeur et al. 1990, Zhang et al. 1995).

Most heterotrophic species have a competitive advantage because they have growth rates and

cellular yields that are several times larger than those of the autotrophic nitrifiers (Figueroa and

Silverstein 1992, Metcalf and Eddy 1991). Therefore, when the carbon concentration is increased,

heterotrophs can form an overlying layer where they out-compete the nitrifiers for oxygen

(Bovendeur et al. 1990, Siegrist and Gujer 1987, Zhang et al. 1995). Micro-techniques allow

direct observation of a biofilm, and although they are not a predictive tool, they provide explicit

evidence of the limitation imposed on nitrifying bacteria by heterotrophic respiration.


Zhang et al. (1995) used microelectrode and micro-slicing techniques to observe the

competition for substrate and space in heterotrophic biofilms (HBs), heterotrophic-autotrophic

biofilms (HABs), and nitrifying biofilms (NBs). Steady-state conditions for the HAB were 5 mg

NH4+-N/L, 9 mg O2/L, and 10 mg glucose/L (COD of 0.32 mg O2/mg glucose, Sawyer et al.

1994).

Figure 10 shows the steady-

state oxygen, ammonium, and

nitrate profiles within the HAB.

Even though the biofilm was

fully penetrated by ammonium,

the nitrification rate changed at

a depth of 100µm (DO=0.4

mg/L). Nitrification ceased at

the effective oxygen penetration

depth (DO<0.1 mg/L) of 160

µm.

Distance (um)

Concentr

atio

n (

mg/L

)

-300 -200 -100 0 100 200 300 400

0

1

2

3

4

5

6

7

8

9

10

Med

ia

Wate

r In

terf

ace

NO3 -N

NH4 -N

O2

Figure 10. Steady-state substrate profiles in a heterotrophic-

autotrophic biofilm(after Zhang et al. 1995).

Figure 11 describes the

change in HAB ammonium

oxidation at low bulk DO

concentrations. While

ammonium oxidation continued,

it was inhibited at the lower

oxygen concentrations. At DO

concentrations of 2.3 and 0.5

mg/L, ammonium uptake ceased

at depths of 100 and 60 µm,

respectively.

Distance (um)

Conce

ntr

atio

n (

mg/L

)

-300 -200 -100 0 100 200 300 4000

1

2

3

4

5

6

7

8

9

10

Media

Wate

r In

terf

ace

O2 Concentration

in bulk solution (mg/L):

Curve 1: 2.3

2: 1.0

3: 0.5

1

2

3

NH4 -N

NO3 -N

Figure 11. Biofilm NH4

+-N and NO3

--N profiles at low DO

concentrations (after Zhang et al. 1995).


Figure 12 shows that an increase in

glucose had an effect similar to a

decrease in DO. The fact that elevated

glucose reduced oxygen penetration and

caused NH4+-N levels to rise indicates

that heterotrophic bacteria dominated

the biofilm surface, utilizing oxygen

before it could reach the underlying

nitrifiers. The species distribution lends

Distance (um)

Concen

trat

ion (

mg/L

)

-300 -200 -100 0 100 200 300 4000

1

2

3

4

5

6

7

8

9

10

Media

Wate

r In

terf

ace

NH4 -N

O2

1

32

6

5

4

Glucose conc. in

bulk soln. (mg/L):

Curves 1 & 4: 10

Curves 2 & 5: 20

Curves 3 & 6: 40

Figure 12. Effect of increased glucose on DO and NH4

+-N

profiles (after Zhang et al. 1995).

additional support to the belief that

there was significant autotrophic

oxygen limitation. A species count

indicated that the autotrophic

population density was 102 MPN/cm3 at

the water interface but increased to 104

MPN/cm3 at the attachment surface.

Figure 13 shows the mean oxygen

penetration for a composite of all

O2 P

enet

rati

on

Dep

th (

um

)

Biofilm thickness (um)

Pen

etra

tio

n D

epth

(%

)

500

450

400

350

300

250

200

150

100

50

0

100

90

80

70

60

50

40

30

20

10

500 1000 1500 2000 25000

Figure 13. Critical depth as a function of biofilm thickness

(after Zhang et al. 1995).

biofilms. For biofilm depths greater

than 750 µm, the critical thickness was

nearly constant at 300 µm.

Superimposing Figure 13 on Figure 14

will illustrate that oxygen penetration

and density are related: oxygen

penetration depth follows density, and

both are constant at any thickness

greater than 750 µm.

Bio

film

Densi

ty (

mg T

S/c

m3 b

iofi

lm)

Biofilm thickness (um)

0 500 1000 1500 2000 2500

0

20

40

60

80

100

120

Figure 14. Density as a function of biofilm thickness

(after Zhang et al. 1995).


Monod kinetics are widely used to describe substrate uptake during nitrification. Although

resistance to substrate transport is not explicitly included, it is implicitly expressed in the half-

saturation constants, which probably accounts for their large variability in literature (Beccari et al.

1992). Nitrification that is limited by ammonium and oxygen, and where oxygen diffusion is

impeded, can be described by the following expression (Beccari et al. 1992):

rk X S

K S

S

K Su n

n N N

SN N

O

SO O

= −+ +

η

Where: run is the TAN utilization rate (mass/volume-time);

kY

n

mn

N

=

µ

Where: kn is the maximum ammonium utilization rate (1/time);

µmn is maximum specific nitrifier growth rate (1/time); and

YN is the nitrifier yield coefficient (unitless).

XN is the nitrifying biomass concentration (mass/volume);

SN is the nitrogen concentration (mass/volume);

KSN is the nitrogen concentration at one half the maximum growth rate (mass/volume);

SO is the oxygen concentration (mass/volume);

η is the diffusional efficiency (unity is unimpeded diffusion) (unitless); and

KSO is the oxygen concentration at one half the maximum growth rate (mass/volume).

Beccari et al. (1992) used data from their own prior studies and literature values from typical

activated-sludge processes to model oxygen limitation in nitrifying biofloc. Monod expressions

were used to describe autotrophic growth and substrate uptake, and the experimentally-derived

effectiveness factor (η) described the ratio of actual to unimpeded oxygen transfer. Their central

goal was to offer an explanation for the large variation in literature values for KSO, by exploring

the widely-accepted assumption that internal resistance to oxygen transport is negligible.


For 40 µm diameter (φ) biofloc, a best fit of their experimental data resulted in a KSO of 0.83

mg O2/L. At φ=40 µm, and η was always >0.98 even when DO was 0.5 mg/L, meaning that

diffusional resistance was negligible. Similarly, when φ was in the range of 40-100 µm and DO

was ≥1.0 mg/L, η was always ≥0.90, so diffusional resistance remained small. However, as φ was

increased at ≥100 µm, η decreased rapidly, especially when DO was simultaneously lowered. They

concluded that internal diffusional resistance to oxygen transport could not be neglected, especially

when the biofloc diameter exceeded 100 µm.

Hanaki et al. (1990) studied how variations in COD and DO affected ammonia conversion in a

laboratory-scale suspended-growth reactor at a constant ammonia concentration of 80 mg N/L. In

a culture that was free of organic matter, the DO was lowered from 6 to 0.5 mg O2/L and the effect

on ammonia oxidation was negligible. However, nitrite oxidation was severely inhibited at 0.5 mg

O2/L, resulting in a reactor nitrite concentration of 60 mg N/L. In an organically-enriched culture,

where COD was 160 mg O2/L, ammonia conversion declined dramatically when DO was lowered

from 6 to 0.5 mg/L. In both cultures nitrite oxidation had a nearly-identical relationship to DO,

indicating that increased COD had a smaller impact than reduced DO concentration.

Solids and Mean-Cell Residence Times

When discussing suspended growth, MCRT and SRT are used equivocally, to describe the

average age of biomass in the reactor. In systems where nitrification and carbon oxidation are

combined, Metcalf and Eddy (1991) state that an MCRT in the range of 8-20 days can be required

for effective nitrification. Other authors report effective nitrification with MCRTs of 3-7 days

(Sharma and Ahlert 1977; Timberlake et al. 1988).

For floating-bead filters, SRT refers to the residence time of the interstitial solids, which

contain a large percentage of fecal matter, while MCRT describes the average age of the biomass.

Although differences between SRT and MCRT may be significant, only SRT has been previously

defined (Malone et al. 1993):

SRTh f

f b

=

1 1


Where: SRT is the residence time of the interstitial solids (time);

hf is the fraction of solids harvested during a backwash (unitless); and

1

fb

is the backwash interval (time).

Backwash interval is the primary means of managing SRT in bead filters, because the range

within which hf can be adjusted is limited by the filter’s mechanical design. The minimum harvest

fraction can be as low as 0.25 in gently-washed filters and the maximum as high as 0.75 in

aggressively-washed filters (Chitta 1993, Malone et al. 1993, Sastry 1996). In aggressively-

washed filters, the nitrification-rate trends suggest that MCRT is approximately equal to SRT,

while in gently-washed filters MCRT appears to be much greater than SRT.

FBFs: Solids Capture and Biofiltration in RASs

Solids and backwash regime both have important, and sometimes competing, effects on

nitrification in FBFs. Achieving an optimal backwash interval calls for limiting the solids loading

in the context of providing a sufficient MCRT for effective nitrification. This section discusses

these factors, by looking at the waste burden under which FBFs operate and the opposite way that

gently- and aggressively-washed filters respond to similar changes in backwash interval.

Aquacultural waste production and characteristics are functions of the cultured species’

excretions, which are related to the feed. In the short term, solids excretions are simply a

particulate load, but if they are allowed to remain in the system, their decay yields TAN and BOD5,

which results in an increase in bacterial biomass. Less than 0.5% of the feed given to the fish on a

daily basis will be converted to nitrifying biomass, although the heterotrophic yield can be as much

as 6% of the daily feed (Chen et al. 1991).

Wimberly (1990) reported excretion rates and waste characteristics for channel catfish that

were fed at a rate of 0.01 kg feed/kg fish/d. He observed VSS:TSS, BOD5:TSS, and TKN:TSS

ratios of 0.878, 0.385, and 0.0892, respectively. Mean values for solids excretion (ES), soluble

BOD5 (EB), and TAN excretion (EA) were 0.430 kg TSS/kg fed, 0.0504 kg BOD5/kg feed, and


0.0203 kg N/kg feed. The observed tBOD5 excretion was 0.216 kg BOD5/kg feed. It is notable that

the solids excretions have a BOD5:TKN ratio of about 4.3, while the soluble excretions have a

BOD5:TKN ratio of only about 3.

Several other authors who studied channel catfish reported values for ES (kg TSS/kg feed),

tBOD5 (kg BOD5/kg feed), and EA (kg N/kg feed): Page and Andrews (1973) reported ES as

0.180, BOD5 as 0.100, and EA as 0.021; Murphy and Lipper (1970) recorded a tBOD5 of 0.245;

Raune et al. (1977) observed ES, tBOD5 excretion, and EA as 0.692, 0.400, and 0.0462

respectively; Gordon (1974) reported ES as 0.393, tBOD5 excretion as 0.173, and EA as 0.0183.

Chen et al. (1991) studied the production and characteristics of sludge effluent from bead

filters that were used in a RAS that cultured channel catfish. Chen et al. (1991) observed a

BOD5:TSS ratios of 0.09-0.20 and TKN:TSS ratios of 0.038-0.061. The values observed by Chen

et al. (1991) result in BOD5:TKNs that vary from about 2.4 to 3.3. Ning (1995) collected data on

sludge effluent from bead filters used in a tilapia facility and reported mean TKN:TSS as 0.0449

and VSS:TSS as 0.880. Wang (1995) collected fresh fecal solids from tilapia and observed a

TKN:TSS of 0.0501.

Solids decay is usually treated as a first order reaction where the rate is considered constant

with time but variable with temperature (Corbitt 1990, Matsuda et al. 1988, Merritt 1983, Metcalf

and Eddy 1991, Viessman and Hammer 1985). However, there is research to indicate that decay

can be accurately represented by allowing the reaction rate (ks, 1/time) to vary not only with

temperature but with SRT (Rich 1982). In either case, solids decay is usually described by a

simple differential equation (Metcalf and Eddy 1991):

d

dtM k M

S S S( ) = −

Where: MS is the mass of biodegradable solids (mass)

Rich (1982) reviewed literature values for solids decay in batch reactors at 20°C. He cited

Goodman and Englande (1975) as having reported a kS of 0.48 SRT-0.415, and he plotted their


resulting curve against kS values from seven other studies: Adams 1974, Barnard 1978, Barnhart

1961, Reece et al. 1979, Reynolds 1973, Rich and White 1976, Smith et al. 1975. For a SRT

above 15 days, most kS values fell close to the curve. However, all kS values for SRTs below 10

days existed above the curve, indicating that Goodman and Englande’s expression underestimated

decay at the lower solids ages.

Matsuda et al. (1988) studied the behavior of nutrients during the aerobic digestion of waste-

activated sludge. Digestion was carried out over a 30 day period at 30°C. Parallel experiments that

employed both continuous and intermittent aeration yielded similar results, where the observed

VSS reduction rate was 0.15 d-1. Beginning solids content was about 6000 mg TSS/L and 5000 mg

VSS/L. After 20 days the sludge stabilized, with 40% of the TSS and 30% of the VSS remaining.

When digestion was begun, TKN was about 550 mg/L--90% existed in biomass and 10% in the

liquid phase. Liquid-phase nitrogen was mainly ammonium and nitrate, while organic nitrogen and

nitrite were negligible, suggesting that ammonification and nitrification were nearly instantaneous.

Final biomass nitrogen was 11%, comparing favorably to the 12.4% nitrogen content in C5H7NO2,

the common component formula for a bacterial cell (Metcalf and Eddy 1991).

Wang (1995) studied the decay of fecal matter from tilapia at an ambient laboratory

temperature of about 20°C and reported a kS of 0.12 d-1. Ning (1995) collected data on the decay

of sludge effluent from floating-bead filters used for tilapia grow out, which had an initial SRT of

5-7 days. He reported kS values, independent of sludge age, as 0.072, 0.049, and 0.04 d-1 at 30, 20,

and 10°C, respectively. These decay rates are somewhat lower than those for domestic primary

solids and sludge.

Insitu nitrification is the percentage of TAN oxidation that takes place outside of the filter,

e.g. on tank and pipe walls. Malone et al. (1993) recommend a design value for insitu nitrification

in the range of 30-60%. Mia (1996) studied insitu nitrification in high-density RASs that used bead


filters for solids capture and biofiltration. He found that the insitu nitrification factor (IS) had an

inverse relationship to nitrification rate, with values ranging from 0.43 to 0.82 and averaging about

0.71.

Floating-bead filters respond differently to similar changes in backwash interval, based upon

their backwash regime. Gently-washed studies by Wimberly (1990) and Sastry (1996) showed that

decreasing the backwash interval enhanced nitrification. Notably, a point has not been found where

a further decrease in backwash interval fails to increase the nitrification rate. The relationship

between backwash interval and nitrification is reversed for aggressively-washed filters: Chitta

(1993) found that as the backwash interval was extended in a PBF nitrification initially increased

but eventually declined.

Wimberly (1990) evaluated a hydraulically-washed bead filter, which was used for solids

capture and biofiltration in a RAS. Reducing the backwash interval from 24 to 3 hours allowed an

increase in feed loading rate (FLR) from 0.3 to 1.6 lbs feed/ft3/d. This FLR corresponds to a TAN

loading of about 18-94 mg N/ft2/d (EA= 27,000 mg N/kg feed and media specific surface area=350

ft2/ft3) and a soluble COD loading of 33-174 mg COD/ft2/d (EB=50,400, Wimberly 1990;

BOD5:COD=0.6, Metcalf and Eddy 1991). For this reduction in backwash interval and increase in

FLR, CA increased from 7.66 to 32.4 mg N/ft2/d, and oxygen consumed for nitrification increased

from 18 to 52% of the total oxygen consumed during filtration.

Sastry (1996) looked at how variations in backwash interval affected nitrification in a BBF.

Reducing the backwash interval from 48 to 8 hours produced the following results: CA increased

from 17.2 to 30.5 mg N/ft2/d, which allowed FLR to be increased from 1.5-2 lbs feed/ft3/d (88-117

mg N/ft2/d and 164-218 mg COD/ft2/d). The hydraulic loading rate increased slightly from 28-31

gal/ft2/d. The total oxygen consumed in filtration (OCF) remained approximately constant (228-

214 mg O2/ft2/d) while oxygen consumed in nitrification (OCN=4.18 mg O2/mg N, Hochheimer

and Wheaton 1991) increased from 72-127 mg O2/ft2/d. SRT was reduced from 8 to 1.3 days. The


1.3 day SRT, corresponding to the higher nitrification rate, illustrates that MCRT is probably

much greater than SRT, since 1.3 days is well below the MCRT required for effective nitrification

(Metcalf and Eddy 1991, Sharma and Ahlert 1977; Timberlake et al. 1988).

Chitta (1993) explored the impact of backwash interval on CA in a PBF. The filter’s harvest

fraction was 0.57, the hydraulic loading rate averaged 42 gal/ft2/d, and FLR was held at 1.5 lb

feed/ft3/d (88 mg N/ft2/d and 164 mg COD/ft2/d). When the backwash interval was extended from

12 to 48 hours, CA more than doubled, from 15 to 31.6 mg N/ft2/d. OCF and OCN increased from

132-257 and 63-132 mg O2/ft2/d, respectively. When the backwash interval was extended to 3

days, OCF began to increase more slowly, reaching a maximum of about 296 mg O2/ft2/d while

OCN declined, leveling off at about 96 mg O2/ft2/d as CA declined to 23 mg/ft2/d.

Summary: Potential Limitations on Oxygen Delivery and Transport

The literature reviewed that discusses combined systems, other than FBFs, illustrates a

common trend that exists across a range of hydraulic-loading rates, substrate concentrations, and

operating conditions. That is, nitrification declines when the carbon concentration is increased or

when the oxygen concentration is lowered. Studies that look at both submerged and subaerial

fixed-film filters indicate that an increase in carbon concentration supports a proliferation of

heterotrophic bacteria, which, because of their higher growth rates, are able to overly and out-

compete the nitrifiers for oxygen (Bovendeur et al. 1990, Siegrist and Gujer 1987). A study that

used micro-techniques to observe competition in multispecies biofilms provided explicit evidence

that a biofilm surface can become dominated by heterotrophic bacteria, which exhaust oxygen

before it reaches the underlying nitrifying bacteria (Zhang et al. 1995).

Bead filters operate under a low bulk TAN loading, while solids are continuously augmented

by fecal matter and bacterial biomass. There is no doubt that the low-substrate regime and solids

accumulation complicate the comparison of FBFs to other filters. As solids accrete in the filter,

several important effects arise. Physical occlusion reduces the overall rate of bulk-substrate


delivery, and probably also results in an uneven distribution of substrate within the filter bed. In

addition, fecal matter and biomass probably agglomerate into macroparticles. These macroparticles

may have a large volume to surface area ratio, which reduces their diffusional efficiency (Metcalf

and Eddy 1991). In addition, they produce substrate internally during solids decay and

endogeneous metabolism (Matsuda et al. 1988, Sawyer et al. 1994). These factors may have a

significant impact on the uptake of externally-loaded TAN, especially after extended backwash

intervals.

Bulk-TAN delivery is obviously most efficient for the shortest backwash intervals, when the

biofilm is thinnest and the flow is most-evenly distributed within the filter (Malone et al. 1993).

The transfer of bulk TAN is probably impeded at high solids concentrations, when biomass and

fecal solids agglomerate (Malone et al. 1993). At higher solids loads, there is also an increase in

the amount of TAN produced during solids ammonification and heterotrophic metabolism

(Matsuda et al. 1988, Sawyer et al. 1994). The overall effect of aggregated macroparticles, where

diffusion is physically limited and substrate is produced internally, is probably profound. While the

diffusion of bulk TAN becomes increasingly limited, the TAN concentration within macroparticles

may approach or even exceed the bulk-TAN concentration, and thereby diffusion from the bulk

solution into the accreting macroparticles may slow, cease, or even reverse direction, diffusing

from the macroparticles into the bulk liquid. This would preclude any increase in the TAN

limitation. Additionally, it would mean that an increasing percentage of the oxygen reaching the

nitrifying bacteria would be used in oxidation of internally-generated TAN. This could be viewed

as a preferential oxidation of the internal load.

Heterotrophic respiration may also limit nitrification in FBFs, as it does in other filters

(Bovendeur et al. 1990, Zhang et al. 1995). Longer backwash intervals result in higher MCRTs

and larger solids concentrations, both of which may favor heterotrophs. Several of the studies

reviewed indicated that heterotrophs, by virtue of their higher growth rates, can overly nitrifying


bacteria and out-compete them for oxygen (Figueroa and Silverstein 1992, Manem and Rittmann

1992, Zhang et al. 1995). Longer backwash intervals probably encourage this layering, which is

favored by stasis, to develop more fully, and solids degradation may encourage increased

heterotrophic growth. Studies of aquacultural wastes indicate that the BOD5:TKN ratio of the

solids is higher than that of the soluble excretions (Chen 1991, Wimberly 1990), which would

elevate the soluble BOD5 as the solids decay, leading to an increased heterotrophic population.

Longer backwash intervals could, therefore, provide conditions favorable to heterotrophic growth

and over-layering, accentuating the oxygen limitation experienced by the nitrifying bacteria.

Solids accumulation apparently inhibits nitrification in FBFs through several separate, but

related, mechanisms. It is a simple matter to quantify the effects of a reduction in substrate delivery

due to declining flow. However, the effect of non-homogeneous flow and the diffusive

characteristics of large-thickness macroparticles, which generate substrate internally, are probably

worthy of further study.

Solids-loading effects become critical at different backwash intervals, depending on the type of

filter. Sastry’s study demonstrated that a gently-washed filter can have sufficient biomass for

effective nitrification at backwash intervals as short as 8 hours. This means that the solids load can

be mitigated by frequent washing, although the low harvest fraction allows the solids loading to

increase rather quickly when the backwash interval is extended. Flow rate declined at backwash

intervals greater than 8 hours, conducted at lower loading rates, while OCF remained

approximately constant and OCN declined. The increasing difference between OCF and OCN

probably reflects reduced oxygen delivery as well as increasing transport resistance. In an

aggressively-washed filter, Chitta observed an initial increase in nitrification as the backwash

interval was extended, indicating that filter was initially biomass limited. The larger harvest

fraction in this filter translated into lower solids loadings, extending the backwash interval at which

the solids loading became critical. However, a critical backwash interval was eventually reached,


where nitrification began to decline. The flow in Chitta’s study was maintained at a nearly-constant

rate, so the impact of solids on oxygen transport is clearly depicted by the relationship between

OCF and OCN, which increased together up to the critical interval. However, beyond the critical

backwash interval, OCF began to increase more slowly while OCN declined, probably reflecting a

decline in oxygen transport.


23

Model Development

The model discussed in this chapter was developed to illustrate how solids accumulation and

differing backwash regimes impact nitrification in FBFs. The model focuses on the effects of: (1)

the soluble substrate produced during solids degradation and (2) the different percentages of

biomass removed by each backwash regime. The model is based upon two related hypotheses that

derive from the discussion in the previous chapter.

The first hypothesis entails how nitrification becomes inhibited at longer backwash intervals by

the accumulation and decay of solids which produce soluble substrate. As solids accumulate, fecal

matter and biomass probably agglomerate, forming large macroparticles which obstruct flow in

local areas of the filter, severely limiting diffusion from the bulk liquid and producing soluble

substrate internally. The internal production of soluble substrate probably preempts autotrophic

TAN limitation, while simultaneously increasing oxygen demand and thereby accentuating the

oxygen limitation. The conditions that accompany longer backwash intervals favor heterotrophic

bacteria. The internally-loaded substrate may support an increase in the heterotrophic population,

and continuing static conditions probably foster the development of bacterial stratification, where

heterotrophs overly the nitrifying bacteria. The effects of diffusional limitation due to the formation

of macroparticles and increased heterotrophic competition for oxygen will be reflected by an

elevated KSO in the model (see Equation 5-a). KSO represents the concentration of oxygen required

for the nitrifying bacteria to achieve half their maximum growth rate (Metcalf and Eddy 1991).

Under ideal conditions, such as those for very short backwash intervals, KSO will be a relatively-

low baseline value, e.g. 0.4 (Beccari et al. 1992, Siegrist and Gujer 1987). However, impeded

oxygen transfer will increase the amount of bulk-liquid DO required to achieve half saturation

within the biofilm or biofloc (Beccari et al. 1992, Zhang et al. 1995).


The backwash interval that will most effectively mitigate the solids-induced oxygen limitation

depends upon the backwash regime of the filter. This gives rise to a second hypothesis involving

the amount of original biomass retained after a backwash and its relationship to MCRT. Gently-

washed filters appear to retain a relatively-large percentage of their original biomass following a

backwash (Sastry 1996, Wimberly 1990). This means that gently-washed filters, like BBFs, can be

washed more frequently, which reduces solids-loading effects without curtailing MCRT (Sastry

1996). In juxtaposition, aggressively-washed filters like the PBF remove a larger percentage of

solids and appear to retain a much-smaller percentage of their biomass following a backwash.

Therefore, the backwash interval must be extended to provide a sufficient MCRT for effective

nitrification, and nitrification declines due to the solids load only after a critical backwash interval

is reached (Chitta 1993). The difference in biomass retention between gently- and aggressively-

washed filters is represented in the model by a biofilm retention factor (BR, see Figure 13 and

Equation 6).

The model is based on the

following assumptions: (1) all

solids are captured in the filter,

which is a standard

approximation for FBFs and a

conservative assumption that

reflects a worst-case condition

with respect to solids

degradation (Chen et al. 1991);

(2) there is no uneaten feed,

which is an accepted protocol

for experimental RASs

Culture Tank

FBF

QR

8

8

RES, AT, OT, BT

VT

AB , OB , BB

VM

n

PS

hf + X h

f (1-B

R)

RDS SN RDS SB

RDS = PS SV ks + XH kd

Figure 15. Model mass-balance diagram showing major fluxes.


(Sastry 1996); (3) the FBF and culture-tank behave like completely-mixed reactors, which is

reasonable in the context of the high flow rates and the small differences between influent and

effluent concentrations in FBFs (see Figure 13, Malone et al. 1993, Metcalf and Eddy 1991).

Primary Solids

For the period between backwashes, the primary solids (PS) flux consists of excretions (RES)

accreting in the filter and being reduced by decay (RDP):

d

dtP R RS ES DP= − (1)

Where: RF

V EES

LR

M S=

2 2.(1-a)

R P S kDP S V S

= (1-b)

The feed applied per unit volume of filter media per day (FLR) and the media volume (VM) are given

by the system being modeled, and the TSS excretion per unit mass of feed (ES) does not vary

greatly for fish fed at normal rates, i.e. 1-2% (0.01-0.02 kg dry feed/kg body weight/d). The

VSS:TSS ratio (SV) and first-order solids-decay rate (ks) are, reportedly, relatively constant for the

temperatures and SRTs modeled (Metcalf and Eddy 1991, Ning 1995, Wang 1995).

The primary-solids harvest ([HS]) during backwashing is described by the fraction of solids

removed (hf). This is analogous to a Heaviside function, performed as a discreet adjustment at each

backwash interval (1/fb):

[ ] [ ]H P h Executed at eger multiples of t fS S f b

= ∗int (2)

The post-backwash primary-solids mass (P′S) is, therefore:

′ = −P P hS S f

( )1 (2-a)

The average age of primary solids (SRT) can be approximated by a function of backwash

interval and harvest fraction (Coffin 1993):


SRTh ff b

= ∗1 1

(3)

Research has shown that decreasing the backwash interval can enhance nitrification (Sastry 1996,

Wimberly 1990), and this is probably the result of a reduction in SRT, which is related to solids

concentration for a given FLR. However, the ability to minimize SRT is limited by the need to

provide a long enough biomass age to support nitrification.

Biomass

The net growth of heterotrophic bacteria (XH) is described by a Monod function where the

carbon substrate, expressed as oxygen uptake, is limiting:

d

dtX R R

H GH DH= − (4)

R

X B

K BGH

mh H B

SB B

=+

µ(4-a)

R k XDH d H

= (4-b)

RGH is the expression for heterotrophic growth, which depends upon their maximum growth rate

(µmh) and the BOD5 half-saturation constant (KSB). BOD5 removal is non-critical in FBF

performance, although it may limit nitrification through competition for oxygen, because

heterotrophic bacteria have relatively-large growth rates and utilize oxygen more efficiently than

the nitrifiers.

Net growth of nitrifying biomass (XN) that it is limited by TAN and DO can be described with

A Monod function (Beccari et al. 1992):

d

dtX R R

N GN DN= − (5)

Where: RX A

K A

O

K OGN

mn N B

SA B

B

SO B

=+

+

µ(5-a)

R k XDN d N

= (5-b)


It is unlikely that KSA increases in an absolute sense, with respect to backwash interval. Bulk-TAN

delivery is most efficient for the shortest backwash intervals, when the biofilm is thinnest and the

flow is most-evenly distributed (Malone et al. 1993). The delivery of bulk TAN and oxygen

probably becomes impeded when the backwash interval is extended, as biomass and fecal solids

agglomerate occluding areas of the filter bed. However, the concomitant increase in solids

ammonification and heterotrophic metabolism will elevate TAN production within the occluded

areas (Matsuda et al. 1988, Sawyer et al. 1994). This may lead to TAN concentrations within

localized occlusions that approach or even exceed the bulk concentration, changing the direction of

diffusion. Longer backwash intervals may also favor heterotrophic competition for oxygen, through

solids decay and the development of bacterial stratification. The combined effect of these

conditions is probably the evolution of an environment where oxygen limits nitrification, due to the

impeded mass transfer and the competition by heterotrophic bacteria, which is most pronounced

within macroparticles in the most occluded areas of the filter. Therefore, as backwash intervals are

extended, KSO should increase to reflect the increasing oxygen limit on nitrifier growth and TAN

uptake. The ability to decrease the backwash interval to minimize KSO effects, though, is limited by

a SRT-MCRT relationship, which is related to the biomass-harvesting characteristics of the filter.

Biomass harvest ([HX]) is similar to primary-solids removal ([Hs]), with the important

exception of a biofilm-retention factor (BR), which is introduced to account for the biomass

retained on the filter media during backwashing. Although the model was developed to look at the

effect of BR on nitrifiers, the harvest of heterotrophic and nitrifying biomass is, of necessity,

identical since the model does not impose a structure on relative biomass location.

[ ] ( ) [ ]H X h B Executed at eger multiples of t fX f R b

= − ∗1 int (6)

Post-backwash biomass (X′) is, therefore:

( ){ }′ = − −X X h Bf R

1 1 (6-a)


FBF research results indicate that BR is smaller in aggressively-washed filters, and increases as

washing energy decreases, e.g. in gently-washed filters (Chitta 1993, Sastry 1996, Wimberly

1990).

The average biomass age (MCRT) can be approximated with a function of solids residence

time and biofilm retention:

[ ]MCRTSRT

BB

R

R=

−

≤ <

10 1 (7)

Equation 7 illustrates the profound effect that biofilm retention has on partitioning MCRT and

SRT: As BR decreases, it becomes necessary to extend SRT to achieve a given MCRT, and

conversely, as BR increases, SRT can be reduced while a given MCRT is maintained.

Total Solids

Primary solids followed by heterotrophic biomass are the main constituents of the total solids

mass (MS) in the filter. The contribution of nitrifiers is negligible and is, therefore, excluded from

the expression:

M P XS S H= + (8)

Primary solids and biomass decay at different rates, although overall solids decay (RDS) is

largely determined by the decay of primary solids, since the percentage of heterotrophic bacteria is

relatively small at the backwash intervals modeled:

R R RDS DP DH

= + (9)

TAN

Biofilter TAN concentration (AB) is a function of substrate uptake (RUA), solids

ammonification (RDA), and mass exchange with the culture tank (RMA). These quantities become

concentrations relative to interstitial volume, the product of media volume (VM) and porosity (n):

( )d

dtA

R R R

VB

UA DA MA

M

=

− + +

n 28.3(10)


Where: RR

YUA

GN

N

= (10-a)

R R SDA DS N

= (10-b)

( )R Q A AMA R T B

= −5451 (10-c)

A completely-mixed reactor volume must encompass all of the biologically-active volume,

including liquid, biomass, and primary solids (Metcalf and Eddy 1991). Inert matter probably

causes some small reduction in filter-bed porosity (n), which is neglected in the model. RUA reflects

substrate uptake by bringing cellular yield (YN) into the growth term (Equation 5-a). RDA describes

ammonification during the decay of solids that have a given TKN:VSS ratio (SN). The mass

exchange rate of TAN, between the culture tank and the biofilter, depends on recycle flow rate

(QR) and the amount of external TAN load removed by the filter (AT-AB), where AT is the culture-

tank TAN concentration. RMA can be described as an apparent nitrification rate since it does not

include oxidation of the internally-loaded TAN that results from solids ammonification.

Culture-tank TAN concentration is a function of the culture species net excretions (R′EA) and

the rate of mass exchange with the culture tank:

( )d

dtA

R R

VT

EA MA

M

=′ −

n 28.3(11)

Where: ( )RF

V E IEA

LR

M A S'

.= −

2 21 (11-a)

R′EA varies with the amount of insitu (IS) nitrification that occurs outside the filter, i.e. in the tank

and on pipe walls (Mia 1996).

The apparent areal nitrification rate (CA) is the nitrification rate per total media-surface area,

which is a product of the media volume (VM) and its specific surface area (SA):

CR

V SA

MA

M A

= (12)


BOD5

The BOD5 equations introduced below are structurally identical to their TAN counterparts, as

previously discussed:

( )d

dtB

R R R

VB

UB DB MB

M

=

− + +

n 28.3(13)

Where: RR

YUB

GH

H

= (13-a)

R R SDB DS B

= (13-b)

( )R Q B BMB R T B

= −5451 (13-c)

d

dtB R R

T EB MB= ′ − (14)

Where: ( )RF

V E IEB

LR

M B S'

.= −

2 21 (14-a)

Insitu BOD5 removal and insitu nitrification appear to be similar, based upon BOD5 excretion

rates and substrate removal in the filter (Chitta 1993).

Dissolved Oxygen

The model assumes that DO in the culture tank (OT) is maintained at a constant level. The

biofilter DO (OB) is determined by oxygen use during the uptake of BOD5 (RUB) and TAN (RUOA),

and the mass exchange rate between the biofilter and tank (RMO):

( )d

dtO

R R R

VB

UB UOA MO

M

=

− − +

n 28.3(15)

Where: ( )R RUOA UA

= 418. (15-a)

( )R Q O OMO R T B

= −5451 (15-b)

BOD5 utilization is stated in terms of oxygen, so RUB is equivalent to the heterotrophic oxygen use.

Oxygen use for nitrification is 4.18 mg O2/mg TAN (Hochheimer and Wheaton 1991).


Oxygen consumed in filtration (OCF) is a measurable quantity, reported in many FBF studies

(Chitta 1993, Sastry 1996, Wimberly 1990). It expresses total oxygen use within the biofilter, for

oxidation of the external and internal loads:

OCFR

V S

MO

M A

= (16)

Oxygen consumed in apparent nitrification (OCN) is reported in most FBF studies. It is a

calculated quantity, based on a stoichiometric ratio, and accounts only for the oxygen used for

apparent, i.e. externally loaded, nitrification.

( )OCN CA

= 418. (17)

Oxygen consumption in total nitrification (OCNT) is derived from the model and expresses

oxygen use for nitrification of the aggregate, i.e. internal and external, TAN load:

OCNR

V ST

UOA

M A

= (18)

Limits of the Model

This model was developed to illustrate the major factors that may limit nitrification in bead

filters, and not as a predictive tool. A limit on the predictive application of the model, i.e. outside

the calibration boundaries, exists because the insitu nitrification that corresponds to a given

apparent nitrification rate must be based upon an experimental observation. Presently, though, this

is an irreconcilable necessity. Although the inverse empirical relationship between IS and CA is well

documented (Mia 1996), it is not theoretically defined, entailing system-specific parameters, that

are complicated by biofilm kinetics that are affected by turbulent pipe-flow regimes.

Table 1. Definitions of Variables

Var. Eq. No. Description Units

2.2 (1-a) Conversion from lbs of feed to kg feed lbs/kg

28.3 (10) Conversion from ft3 to L L/ft3

4.18 (15-a) Oxygen utilization ratio mg O2/mg N

5451 (10-c) Conversion from GPM to L/d L/d/GPM

µmh (3-a) Maximum heterotrophic specific-growth rate 1/d

µmn (5-a) Maximum nitrifier specific-growth rate 1/d

AB (5-a) Biofilter TAN concentration mg N/L


AT (10-c) Culture-tank TAN concentration mg N/L

BB (3-a) Biofilter BOD5 concentration mg BOD5/L

BR (6) Biofilm retention factor unitless

BT (13-c) Tank soluble BOD5 mg BOD5/L

CA (12) Apparent areal-nitrification rate mg N/ft2/d

EA (11-a) TAN excretion ratio mg N/kg feed

EB (13-a) Soluble BOD5 excretion ratio mg BOD5/kg feed

ES (1-a) Solids excretion ratio mg TSS/kg feed

fb (2) Backwash frequency 1/d

1/fb (3) Backwash Interval d

FLR (1-a) Feed loading rate lb feed/ft3/d

hf (2) Harvest fraction unitless

[HS] (2) Primary solids harvest mg

[HX] (6) Biomass harvest mg

IS (11-a) Insitu nitrification unitless

kd (3-b) Endogenous decay rate 1/d

ks (1-b) Specific solids decay rate 1/d

KSA (5-a) TAN half-saturation constant mg N/L

KSB (3-a) BOD5 half-saturation constant mg BOD5/L

KSO (5-a) Oxygen half-saturation constant mg O2/L

MCRT (7) Mean cell residence time d

MS (8) Total solids mg

n (10) Porosity unitless

OB (5-a) Biofilter oxygen concentration mg O2/L

OCF (16) Oxygen consumed in filtration mg O2/ft2 media/d

OCN (17) Oxygen consumed in apparent nitrification mg O2/ft2 media/d

OCNT (18) Oxygen consumed in true nitrification mg O2/ft2 media/d

OT (15-b) Culture-tank DO concentration mg O2/L

P’S (2-a) Post-backwash primary solids mg

PS (1) Primary solids mg TSS

QR (10-c) Recycle flow rate GPM

R′EA (11-a) Net TAN excretion mg N/d

R′EB (13-a) Net soluble BOD5 excretion mg BOD5/d

RDA (10-b) Solids ammonification rate mg N/d

RDB (13-b) BOD5 solubilization rate (from decay) mg BOD5/d

RDH (3-a) Heterotrophic decay rate mg VSS/d

RDN (5-b) Nitrifier decay rate mg VSS/d

RDP (1-b) Primary-solids decay rate mg VSS/d

RDS (9) Total solids decay rate mg/d

RES (1-a) Solids excretion rate mg TSS/d

RGH (3-a) Heterotrophic growth rate mg VSS/d

RGN (5-a) Nitrifier growth rate mg VSS/d

RMA (10-c) TAN mass exchange rate (apparent nitrification rate) mg N/d

RMB (13-c) Mass transfer of soluble BOD5 mg BOD5/d

RMO (15-b) Mass transfer of oxygen mg O2/d

table continued

Var. Eq. No. Description Units

RUA (10-a) TAN utilization rate mg N/d

RUB (13-a) BOD5 utilization rate mg BOD5/d

RUOA (15-a) Oxygen-utilization rate during nitrification mg O2/d

SA (12) Media specific-surface area ft2/ft3

SB (13-b) BOD5:VSS ratio mg BOD5/mg VSS

SN (10-b) TKN:VSS ratio mg N/mg VSS

SRT (3) Solids residence time d

SV (1-b) VSS:TSS ratio unitless


t (2) Time d

VM (1-a) Volume of filter media ft3

X (6) Biomass mg

X′ (6-a) Post-backwash biomass (heterotrophic or nitrifying) mg

XH (3) Heterotrophic biomass mg VSS

XN (5) Nitrifying biomass mg VSS

YH (13-a) Heterotrophic yield mg VSS/mg BOD5

YN (10-a) Nitrifier yield mg VSS/mg N


34

Model Calibration

The model developed in the previous chapter was calibrated to data from a BBF, representing

the gently-washed regime (Sastry 1996), and a PBF, exemplifying the aggressively-washed regime

(Chitta 1993). The BBF had 1 ft3 of media (Appendix A), so to allow the use of a single model, the

PBF data were normalized to 1 ft3 (Appendix B). The model was calibrated to three steady-state

backwash intervals for each system. The particular data sets, identified in each filter’s calibration

section, were chosen to reflect filter behavior at peak loading (1.5-2 lbs feed/ft3/d), near their

minimum and maximum recommended backwash intervals.

A calibration was sought that would provide an error of less than 5% for AT and AB, which are

reflected in CA. CA was most strongly affected by KSO, for all backwash intervals, and to BR for the

shortest intervals in each backwash regime. CA was less-strongly affected by OB, especially at

larger solids concentrations where the postulated oxygen limitation is greatest. OB was, therefore,

selected as a variable of secondary interest, as reflected in OCF. CA was not strongly affected by

variations in KSA, which is to be expected since AB increases with the solids concentration. (It is

quite possible that nitrifying bacteria preferentially utilize TAN that is produced by solids

ammonification and as a heterotrophic metabolite, although electron-donor proximity was not

addressed by this model because no structure was imposed on substrate production).

The model parameters can be divided into three classes. System constants are values imposed

on the model by the operational conditions of the experimental system and were not varied to

achieve calibration. These include the BBF and PBF system values--e.g. QR, VT, and OT

(Appendixes A and B). Aquacultural-waste excretion rates and characteristics, adopted from

average literature values, are also system constants (Appendix C).

Calibration constants were adjusted within literature norms to provide an initial calibration and

were fixed thereafter (Appendix C). The calibration constants included the Monod values for the

growth of heterotrophic and nitrifying bacteria, half saturation of BOD5 and TAN, and the specific

solids-decay rate. All of these values were held constant for both regimes, across all backwash

intervals. BR took on a single value specific to each filter type.


The final class are the calibration variables, IS and KSO. The value of IS was imposed by the

experiment, and increases as CA decreases (Chitta 1993, Mia 1996, Sastry 1996). The adjustment

of KSO was the final step in achieving a calibration for AB and AT. In the context of the literature

reviewed, the way that biomass and solids concentrations increase with a bead filter’s backwash

interval appear to favor oxygen limitation, which would be reflected in an increase in KSO (Beccari

et al. 1992, Bovendeur et al. 1990, Siegrist and Gujer 1987, Zhang et al. 1995).

The model was calibrated against experimental values measured just prior to a backwash. The

calibration output--for both filters at each backwash interval, beginning one time step after a

backwash and terminating one time step before the next backwash--is listed in Appendix E. The

model was implemented in VisSim, version 2.0 e, using a 4th order Runge-Kutta integration with

a time step of 1.25 x 10-4 days (Appendix D).

Calibration Against the BBF

The BBF system was operated at an alkalinity of 150-200 mg CaCO3/L, while DO levels in

the filter effluent were maintained above 2 mg/L (Sastry 1996). Flow rates declined as the

backwash interval was increased, and culture-tank DO varied over the backwash intervals. These

variations are reflected in the model, as listed in Appendix A. The three backwash intervals

selected for calibration were 0.33 day (FLR of 2 lbs feed/ft3/d), 1 day (FLR of 1.5 lbs feed/ft3/d), and

2 days (FLR of 1.5 lbs feed/ft3/d) (Appendix A).

Table 2. BBF calibration variables.

Description Variable 1/fb(days)

Units Calibr.

Value

Lit.

Range

Reference

Oxygen half saturation KSO 0.33 mg O2/L 6.5 0.4-30 Beccari et al. 1992,

Siegrist and Gujer 1987

“ “ 1 “ 17 “ “

“ “ 2 “ 30 “ “

Insitu nitrification IS 0.33 unitless 0.57 0.43-0.82 Mia 1996, Sastry 1996

“ “ 1 “ 0.58 “ “

“ “ 2 “ 0.65 “ “


Model prediction of TAN substrate levels and apparent nitrification at the 0.33 day backwash

interval determined the value of the biofilm retention factor as 0.8, i.e. 80% of the total biomass is

retained in the filter as biofilm or biofloc. For the 0.33-2 day increase in backwash interval, the

observed IS value increased from 0.57 to 0.65 (Table 2). To achieve a calibration, KSO was varied

from 6.5-30 mg O2/L (Table 2). Table 3 compares the model predictions with values observed in

the experimental system. The model provided a good replication of observed TAN substrate and

apparent nitrification. The only substantial error occurred in OCF, which was under-predicted by

12% at the 1 day backwash interval.

Table 3. Comparison of predicted and experimental values for the BBF.

1/fb(days)

FLR

(lbs/ft3/d)

Parameter Description Variable Units Model

Value

Exper.

Value

Error

0.33 2 Culture-tank TAN AT mg N/L 0.64 0.64 none

FBF effluent TAN AB mg N/L 0.38 0.38 none

Apparent nitrification rate CA mg N/ft2/d 30.2 30.5 < 5%

Oxygen consumed in filtration OCF mg O2/ft2/d 216 214 < 5%

1 1.5 Culture-tank TAN AT mg N/L 0.69 0.71 < 5%

FBF effluent TAN AB mg N/L 0.50 0.52 < 5%


Oxygen consumed in filtration OCF mg O2/ft2/d 199 226 12%

2 1.5 Culture-tank TAN AT mg N/L 0.72 0.72 none


Apparent nitrification rate CA mg N/ft2/d 18 17.2 < 5%



Calibration Against the PBF

The PBF system was operated at an alkalinity of 200 mg CaCO3/L and culture-tank DO levels

that averaged 6 mg/L (Chitta 1993). A FLR of 1.5 lbs feed/ft3/d was maintained throughout the

study, and the normalized flow rate across all backwash intervals was 9.32 GPM (Appendix B).

The three backwash intervals selected for calibration were 0.5, 1, and 2 days (Chitta 1993).

Table 4. PBF calibration variables

Description Variable 1/fb(days)

Units Calibr.

Value

Lit.

Range

Reference

Oxygen half saturation KSO 0.5 mg O2/L 0.5 0.4-30 Beccari et al. 1992,

Siegrist and Gujer 1987

“ 1 “ 5 “ “

“ 2 “ 13 “ “

Insitu nitrification IS 0.5 unitless 0.76 0.43-0.82 Chitta 1996, Mia 1996

“ 1 “ 0.68 “

“ 2 “ 0.47 “

The PBF biofilm retention factor was 0.5, which was determined by modeled TAN

concentrations and nitrification at the 0.5 day backwash interval. As shown in Table 4, to achieve a

calibration, KSO was varied from 0.5-13 mg O2/L, as the backwash interval was increased from

0.5-2 days. For the same backwash intervals, the observed IS values decreased from 0.76 to 0.47.

Table 5 compares the model output with the values observed in the experimental system. The

model predicted TAN substrate and apparent nitrification with an error of less than 5% across all

backwash intervals. The model’s prediction of solids concentration compares favorably with

limited backwash data from the experimental study. The only substantial error occurred in OCF,

which was under-predicted by 12% at the 0.5-day backwash interval and over-predicted by 8% at

the 2-day interval. However, as illustrated by Figure 14, the OCF error is not propagated in TAN

levels or apparent nitrification.


Table 5. Comparison of predicted and experimental values for the PBF.

1/fb(days)

Parameter Description Variable Units Model

Value

Exper.

Value

Error

0.5 Culture-tank TAN AT mg N/L 0.53 0.53 none

FBF effluent TAN AB mg N/L 0.44 0.44 none

Apparent nitrification rate CA mg N/ft2/d 15.3 15 < 5%


Percent solids SC % 2.6 2.6 N/A

1 Culture-tank TAN AT mg N/L 0.53 0.54 < 5%




Percent solids SC % 5 5.2 N/A

2 Culture-tank TAN AT mg N/L 0.72 0.72 none




Percent solids SC % 9.4 10.4 N/A

Summary

Model predictions are in good agreement with the observed data, indicating that the model

identifies the major factors that limit nitrification. The relationship of CA to KSO implies that

oxygen-transport resistance increases with the solids concentration, although this is probably due

to several factors. Oxygen availability probably becomes especially limited in areas of the bed

where macroparticles, consisting of an agglomeration of biomass and primary solids, locally

occlude areas of the filter bed. The model indicated that biomass retention was 80% (BR = 0.8) in

the gently-washed filter and 50% in the aggressively-washed filter, for an equivalent growth rate

(µmn). This supports the belief that there is less of an MCRT constraint in the gently-washed

regime than its aggressively-washed counterpart.


39

Results and Discussion

The increase in solids concentration that accompanies an extension of the backwash interval

can have two distinct, but related, effects on the availability of oxygen to the nitrifying biomass.

These effects are accounted for separately in the model. Reduced flow can cause a decrease in

oxygen delivery, and this is reflected in the mass balance. KSO is used to describe the bulk-liquid

DO concentration necessary to overcome every impediment to the transport of oxygen to the

nitrifiers. The model results indicated that the transport limitation, reflected in KSO, was minimal at

the shortest backwash intervals with the lowest solids concentrations. This limitation, though,

appears to increase with solids concentration, and this is represented in much larger values of KSO.

As Figure 16 shows, KSO is

directly related to VM SA (OCF-

OCN) and inversely related to

QR. This relationship cannot be

viewed simplistically because it

is probably the effect of several

complex and interrelated

causes. The term VM SA (OCF-

OCN) is the oxygen-

0

5

10

15

20

25

30

35

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

(OCF-OCN)

QR

KSO

(mg/L

)

Regression Line (r2 = 0.95)

Calibration Data

(mg/L)(VM SA)

Figure 16. KSO versus biomass respiration and flow rate.

consumption rate (mg O2/d) due to the removal of total BOD5 and internally-loaded TAN. This

may entail physical constraints on diffusion, heterotrophic competition for oxygen, and possibly

even preferential oxidation of the internally-loaded TAN. The macroparticles formed when biomass

and fecal matter agglomerate probably have a large surface area to volume ratio which slows

diffusion. The higher BOD5:TKN ratio of the fecal solids may induce additional heterotrophic

growth, and the static conditions that exist at long backwash intervals probably promote bacterial


stratification, where heterotrophs have an advantage in the competition for oxygen. Production of

TAN within macroparticles, and aggregates of these particles, may result in TAN levels that

approach or even exceed the TAN concentration in the bulk liquid. This could result in a condition

wherein all of the oxygen reaching the nitrifiers is used for oxidation of the internally-loaded TAN.

The inverse relationship between KSO and flow rate probably reflects flow distribution in the bed,

since the aggregation of macroparticles probably results in severe regional occlusions that impede

dispersion.

The Effects of Backwash Interval on Nitrification Rate in a Gently-Washed Filter

The gently-washed BBF exhibited a relatively-low harvest fraction (hf = 0.36), and the model

indicated that about 80% of the original biomass was retained following a backwash (BR = 0.8).

This results in comparatively-large solids and biomass concentrations. Therefore, optimal

nitrification occurs at the shortest backwash intervals. The low biomass-loss rate permits short

backwash intervals while the higher solids concentrations mean that frequent washing is necessary

to mitigate the solids-loading effects.

At an observed 8-hour

backwash interval and a feed

loading rate of 2 lbs/ft3/d, the

predicted MCRT was 4.6 days.

These conditions produced

good nitrification at a relatively

high flow rate and a low solids

concentration. However, even

at a lower loading (1.5 lbs

feed/ft3/d), backwash intervals

of 1 and 2 days resulted in

4

6

8

10

12

14

8 16 24 32 40 48

Backwash Interval (hours)

Soli

ds C

oncentr

ati

on

(%

)

6.7

6.8

6.9

7

7.1

7.2

7.3

7.4

7.5

Flo

w R

ate

(G

PM

)

Modeled SolidsObserved Flow

Figure 17. Solids concentration and flow rate in the BBF.


fairly large solids

concentrations and lowered

flow rates (Figure 17).

The decline in flow that

accompanied the higher solids

concentrations apparently

constrained OCF to a nearly

constant value because of the

limit on oxygen delivery

60

100

140

180

220

260

8 16 24 32 40 48

Backwash Interval (hours)O

xygen

Consu

mpti

on (m

g/ft2/d)

OCN

Heterotrophic Respiration

+

Autotrophic Respiration

for Internally-Loaded TAN

OCF

FLR = 1.5 lbs/ft3/dFLR = 2 lbs/ft

3/d

Figure 18. Modeled oxygen consumption in the BBF.

(Figure 18). The difference

between OCF and OCN, shown

in Figure 18, increases with

solids concentration. This

increasing difference reflects

the relationship illustrated in

Figure 16, which drives the

decline in apparent nitrification

shown in Figure 19.

14

18

22

26

30

34

8 16 24 32 40 48


CA

(mg/ft2/d)

Figure 19. Modeled CA in the BBF.

The Effects of Backwash Interval on Nitrification Rate in an Aggressively-Washed Filter

The PBF has a relatively-large harvest fraction (hf = 0.57), and the model indicated that

approximately 50% of the total biomass was retained following a backwash (BR = 0.5). The high

biomass-loss rate means that the backwash interval must be extended to provide a sufficient

MCRT for effective nitrification. However, the solids concentration for a given backwash interval

is small in comparison to the gently-washed filter, so the internal-loading effects grow more slowly.


For the observed feed

loading of 1.5 lbs/ft3/d, the

model indicates that the 12-

hour backwash interval resulted

in 2.6% solids with an MCRT

of 1.8 days, which corresponds

to a moderate nitrification rate

(15 mg/ft2/d). At a backwash

interval of 48 hours,

corresponding to the highest

2

4

6

8

10

12

14

12 24 36 48 60 72


Soli

ds C

oncentr

ati

on (%)

0

9.32

Flo

w R

ate

(GPM)

Observed Flow

Modeled Solids

Figure 20. Solids concentration and flow rate in the PBF.

nitrification rate (31.6

mg/ft2/d), the model predicted

an MCRT of 7 days and solids

at 9.4%. Although the feed

loading in the PBF and BBF

were comparable for backwash

intervals of 24 and 48 hours,

solids concentration was 28-

32% less in the PBF (Figures

16 and 19).

60

100

140

180

220

260

300

12 24 36 48 60 72


Ox

yg

en

Co

nsu

mp

tio

n (m

g/ft2/d)

OCF

OCN

Heterotrophic

Respiration

+

Autotrophic Respiration

for Internally-Loaded

TAN

Figure 21. Modeled oxygen consumption in the PBF.

The smaller solids concentration and constant flow rate extended the backwash interval at

which oxygen limitation began to depress nitrification in the PBF. As shown in Figure 21, OCF

and OCN increased with backwash interval as the biomass concentration grew. However, at a

backwash interval of just beyond 2 days, OCF appears to have become limited by oxygen delivery

and OCN began to decline, as oxygen transport became limited (Figures 16 and 21). The


increasing difference between

OCF and OCN, as backwash

interval was extended, indicates

that oxygen transport can limit

apparent nitrification even

when oxygen delivery is

maintained.

Figure 22 depicts the dual

constraint imposed on

12

16

20

24

28

32

12 24 36 48 60 72

Backwash Interval (hours)C

A

(mg/ft2/d)

Figure 22. Modeled CA in the PBF.

backwash interval in the PBF: nitrification initially improved when the backwash interval was

increased, when the filter was biomass limited. However, a critical backwash interval was

eventually reached, beyond which solids-loading effects depressed apparent nitrification.

Summary

The model illustrates that solids accumulation may depress apparent nitrification by restricting

the delivery and transport of oxygen to the nitrifying bacteria. The ability to control the solids

limitation through backwashing is, in large part, dependent on harvest fraction and biomass

retention, which are different for each backwash regime.

The model indicated that the gently-washed filter retained about 80% of the original biomass

following a backwash, so there was no MCRT limit for a backwash interval as low as 8 hours.

However, the filter removed only 36% of the solids during backwashing, so the solids

concentrations were relatively high at the longer backwash intervals, even though the feed-loading

rate was lower. Therefore, the primary criterion that should drive the selection of a backwash

interval in a gently-washed filter is the increase in apparent nitrification afforded by limiting the

solids loading.


Apparent nitrification initially increased in the aggressively-washed filter, when the backwash

interval was extended, although a critical backwash interval existed beyond which nitrification

became inhibited by the solids load. The model predicted that only about 50% of total biomass is

retained by the filter following a backwash. Therefore, the filter was biomass limited at shorter

backwash intervals, while the relatively large harvest fraction (hf = 0.57) resulted in a

proportionately-lower solids concentration. The relationship between harvest fraction and biomass

retention is complementary. The need to provide an extended backwash interval to overcome the

MCRT constraint was balanced by the fact that the solids-loading limitation increased gradually.

Both the biomass and the solids-loading limitation should be considered when devising an optimal

backwash interval for an aggressively-washed filter.


45

Conclusions

Solids Limitations

The experimental results, the literature reviewed, and the modeled filter behavior are consistent

with a hypothesis wherein solids accumulation depresses apparent nitrification through:

(1) A reduction in the mass-delivery rate of oxygen caused by decreased flow.

(2) The inhibition of oxygen transport due to:

a) decreased flow, which constrains dispersion;

b) heterotrophic competition for oxygen; and

c) the preferential oxidation of internally-loaded TAN.

Backwash-Regime Limitations

It is well documented that the backwash interval at which optimal nitrification occurs is

determined by backwash regime (Chitta 1993, Sastry 1995, Wimberly 1990). Model results

indicate that this optimum interval is determined by biomass retention and harvest fraction:

(3) The gently-washed filter exhibited:

a) a low harvest fraction (hf = 0.36), resulting in a rapid growth of solids

concentration; b) high biomass retention (BR = 0.8), with no MCRT limit at an 8 hour

interval; and

c) optimal nitrification at the shortest backwash interval studied.

(4) The aggressively-washed filter exhibited:

a) a high harvest fraction (hf = 0.57), with a gradual growth in solids concentration;

b) high biomass loss (BR = 0.5), with an initial MCRT limit; and

c) optimal nitrification at a critical backwash interval.


46

Recommendations

Model Improvements

The model’s predictive capability is limited by the relationship of insitu nitrification to

nitrification taking place in the filter:

(1) The relationship between insitu an in-filter nitrification should be defined to enable the

model to predict filter behavior outside of its calibration limits and

(2) The predictive model should be validated and, if necessary, recalibrated by comparing

model predictions to variations of the following parameters in an experimental system:

a) Oxygen;

b) Flow; and

c) Organic loading

Filter Improvements

The model and the literature indicate that an ideal nitrifying biofilter will have no organic or

particulate solids loading, high biomass retention, a large and sustainable flow rate, and a high

dissolved-oxygen concentration. The following design improvements should be studied collectively

(reasons):

(1) Increased harvest fraction (solids-loading reduction);

(2) Increased biomass retention (increased MCRT);

(3) Increased porosity (higher flow rates and more area for biomass growth);

(4) Increased oxygen concentrations (oxygen-limitation reduction); and

(5) Precise biofilm-thickness management (critical thickness of substrate penetration).


47

References

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Digester Design.” Wat. Res., 8:213-218. Cited by L. G. Rich (1982): p. 538.

Barnard, J. L. (1978) Private Communication. Cited by L. G. Rich (1982): p. 538.

Barnhart, E. L. (1961) “Application of Aerobic Digestion to Industrial Waste Treatment.”

Proceedings 16th Purdue Industrial Waste Conference:612-618. Cited by L. G. Rich (1982):

p. 538.

Beccari, M., A. C. Di Pinto, R. Ramadori, and M. C. Tomei (1992) “Effects of Dissolved Oxygen

and Diffusion Resistances on Nitrification Kinetics.” Wat. Res., 26:1099-1104.

Bhaskar, G. V. and S. M. Rao Bhamidimarri (1991) “Approximate Analytical Solutions for a

Biofilm Reactor Model with Monod Kinetics and Product Inhibition.” The Canadian Journal

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51

Appendix A

BBF-System Model Values


BBF Constant Values

Description Variable Value Units Reference

Culture-tank volume VT 429 Gal. Sastry 1996

Media specific-surface area SA 350 ft2/ft

3“

Harvest fraction hf 0.36 unitless Coffin 1993

BBF Values that Vary With Backwash Interval

1/fb(days)


0.33 Recycle flow rate QR 7.5 GPM Sastry 1996

Culture-tank DO OT 5.9 mg O2/L “

Feed loading rate FLR 2 lbs feed/ft3/d “

1 Recycle flow rate QR 7.1 GPM “


Feed loading rate FLR 1.5 lbs feed/ft3/d “

2 Recycle flow rate QR 6.7 GPM “




53

Appendix B

PBF-System Model Values


So that a single model could be developed, based on a filter with 1 ft3 of media, the

experimental PBF system was scaled up from its original size, by maintaining a constant dilution

factor, i.e. a specific exchange rate (Metcalf and Eddy 1991):

DQ

VB T

R

B T

,

,

=

Where: DB, T is the dilution factor for the biofilter or tank (1/min.);

QR is the recycle flow rate in the experimental system or model (GPM); and

VB, T is the biofilter-interstitial or tank volume in the experimental system or model (Gal.).

PBF Experimental-System Values


Operational flux rate N/A 5.33 GPM/ft2

Chitta 1993

Cross-sectional area of filter bed N/A 0.0873 ft2

“

Recycle flow rate QR 0.465 GPM “

Media volume VM 0.05

(0.374)

ft3

(Gal.)

“

Porosity n 0.35 unitless “

Biofilter interstitial volume VB 0.131 Gal. “

Biofilter dilution factor (spec. exch’g. rate) DB 3.55 min-1

Metcalf and Eddy 1991

Culture-tank volume VT 60 Gal. Chitta 1993

Tank dilution factor (spec. exch’g. rate) DT 0.00775 min-1

Metcalf and Eddy 1991

The model flow rate was determined by maintaining a constant biofilter dilution factor in the 1

ft3 media volume, which has an interstitial volume of 2.62 Gal. The model tank volume was then

calculated directly, based upon the model flow rate and the tank dilution factor. The calculated

flow rate and tank volume, along with the other system values used in the model, are listed in the

following table:

PBF System Values Used In the Model

Description Variable. Value Units Reference

Recycle flow rate QR 9.32 GPM Model scale

Culture-tank volume VT 1196 Gal. “

Harvest fraction hf 0.57 unitless Chitta 1993


Media specific-surface area SA 319 ft2/ft

3“

Culture-tank DO OT 6 mg O2/L “


55

Appendix C

Model Excretion Rates, Waste Characteristics, and Kinetic Constants


Excretion Rates and Waste Characteristics

Description Var. Units Calibr.

Value

Lit.

Range

Reference

BOD5:VS SB unitless 0.15 0.09-0.39 Chen 1991, Wimberly 1990

VS:TS SV “ 0.88 0.88 Ning 1995, Wimberly 1990

TKN:VS SN “ 0.05 0.038-0.089 Chen 1991, Wimberly 1990

Solids excretion ES kg TS/kg feed 0.43 0.18-0.69 Gordon 1974, Murphy & Lipper 1970,

Page & Andrews 1973, Raune et al.,

1977, Wimberly 1990

BOD5 excretion EB kg BOD5/kg feed 0.0504 0.0504 Wimberly 1990

TAN excretion EA kg N/kg feed 0.027 0.018-0.046 Gordon 1974, Murphy & Lipper 1970,

Page & Andrews 1973, Raune et al.,

1977, Wimberly 1990

Kinetic Constants

Description Var. Units Calibr.

Value

Lit.

Range

Reference

Prim. sld’s. spec. dc’y. rate ks d-1

0.1 0.07-0.12 Ning 1995, Wang 1995

Max. heter. growth rate µmh d-1

3 0.8-8 Metcalf and Eddy 1991

BOD5 half-sat. cons. KSB mg BOD5/L 30 25-100 “

Max. heter. yield YH mg VSS/mg BOD5 0.6 0.4-0.8 “

Max. nitrif. growth rate µmn d-1

2 0.3-3 Metcalf and Eddy 1991

TAN-N half-sat. cons. KSA mg N/L 0.7 0.2-5 “

Max. nitrif. yield YN mg VSS/mg N 0.2 0.1-0.3 “


57

Appendix D

VisSim Model


BBF: 8 Hour Backwash Interval

0.36 hf

Global Constants

0.333375 1/fb (d)

Qr (GPM) 7.5

Flr (lbs/ft^3-d) 2

429 Vt (Gal)

Br 0.8

350 Sa (ft^2/ft^3)

Is 0.57

Solids Graphs

ks (1/d) 0.1

BOD BOD Graphs

0.6 Yh (mg/mg)

30 Ksb (mg/L)

umh (1/d) 3

TAN GraphsTAN

0.2 Yn (mg/mg)

0.7 Ksa (mg/L)

umn (1/d) 2

Oxygen Graphs

6.5 Kso (mg/L)

Oxygen

Ot (mg/L) 5.9

Calibration Constants

(Ch'g. only w/ calibration)

System Constants

(Ch'g. w/ filter type)

System & Calibration Vars.

(Ch'g. w/ filter type & 1/fb )5.9

6.5

0.33

7.5

2

0.57

0.8

429

350

0.36

0.1

3

30

0.6

2

0.7

0.2

Solids

Data


0.36 hf

Global Constants

1 1/fb (d)

Qr (GPM) 7.1

Flr (lbs/ft^3-d) 1.5

429 Vt (Gal)

Br 0.8

350 Sa (ft^2/ft^3)

Is 0.58 Solids Graphs

ks (1/d) 0.1

BOD BOD Graphs

0.6 Yh (mg/mg)

30 Ksb (mg/L)

umh (1/d) 3

TAN GraphsTAN

0.2 Yn (mg/mg)

0.7 Ksa (mg/L)

umn (1/d) 2

Oxygen Graphs

17 Kso (mg/L)

Oxygen

Ot (mg/L) 4.8

0.2

0.7

2

0.6

30

3

0.1

0.36

350

429

0.8

0.58

1.5

7.1

1

17

4.8


(Ch'g. w/ filter type & 1/fb )

System Constants




Solids

Data



0.36 hf

Global Constants

2 1/fb (d)

Qr (GPM) 6.7


429 Vt (Gal)

Br 0.8

350 Sa (ft^2/ft^3)

Is 0.65 Solids Graphs

ks (1/d) 0.1

BOD BOD Graphs

0.6 Yh (mg/mg)

30 Ksb (mg/L)

umh (1/d) 3

TAN GraphsTAN

0.2 Yn (mg/mg)

0.7 Ksa (mg/L)

umn (1/d) 2

Oxygen Graphs

30 Kso (mg/L)

Oxygen

Ot (mg/L) 5.6



System Constants



(Ch'g. w/ filter type & 1/fb )5.6

30

2

6.7

1.5

0.65

0.8

429

350

0.36

0.1

3

30

0.6

2

0.7

0.2

Solids

Data

PBF: 12 Hour Backwash Interval

0.57 hf

Global Constants

0.5 1/fb (d)

Qr (GPM) 9.32


1196 Vt (Gal)

Br 0.5

319 Sa (ft^2/ft^3)

Is 0.76

Solids Graphs

ks (1/d) 0.1

BOD BOD Graphs

0.6 Yh (mg/mg)

30 Ksb (mg/L)

umh (1/d) 3

TAN GraphsTAN

0.2 Yn (mg/mg)

0.7 Ksa (mg/L)

umn (1/d) 2

Oxygen Graphs

0.5 Kso (mg/L)

Oxygen

Ot (mg/L) 6



System Constants



(Ch'g. w/ filter type & 1/fb )6

0.5

0.5

9.32

1.5

0.76

0.5

1196

319

0.57

0.1

3

30

0.6

2

0.7

0.2

Solids

Data



0.57 hf

Global Constants

1 1/fb (d)

Qr (GPM) 9.32


1196 Vt (Gal)

Br 0.5

319 Sa (ft^2/ft^3)

Is 0.68

Solids Graphs

ks (1/d) 0.1

BOD BOD Graphs

0.6 Yh (mg/mg)

30 Ksb (mg/L)

umh (1/d) 3

TAN GraphsTAN

0.2 Yn (mg/mg)

0.7 Ksa (mg/L)

umn (1/d) 2

Oxygen Graphs

5 Kso (mg/L)

Oxygen

Ot (mg/L) 6



System Constants



(Ch'g. w/ filter type & 1/fb )6

5

1

9.32

1.5

0.68

0.5

1196

319

0.57

0.1

3

30

0.6

2

0.7

0.2

Solids

Data


0.57 hf

Global Constants

2 1/fb (d)

Qr (GPM) 9.32


1196 Vt (Gal)

Br 0.5

319 Sa (ft^2/ft^3)

Is 0.47

Solids GraphsSolids

ks (1/d) 0.1

BOD BOD Graphs

0.6 Yh (mg/mg)

30 Ksb (mg/L)

umh (1/d) 3

TAN GraphsTAN

0.2 Yn (mg/mg)

0.7 Ksa (mg/L)

umn (1/d) 2

Oxygen Graphs

13 Kso (mg/L)

Oxygen

Ot (mg/L) 6

0.2

0.7

2

0.6

30

3

0.1

0.57

319

1196

0.5

0.47

1.5

9.32

2

13

6


(Ch'g. w/ filter type & 1/fb )

System Constants




Data


Global Constants

$timeStep 0

Clock

Backwash Event 1/fb (d)

kd (1/d) 0.05

Rf (kg/d) *

0.453592

28.3168 Vb (L) *

0.35

1

Am (ft^2) *

Flr (lbs/ft^3-d)

Qr (L/d) *

Qr (GPM)

5451

Vt (L) *

Vt (Gal) 3.78541

Vm (ft^3)

Vm (ft^3)

Media Volume

Specific Surface Area

Void Ratio

ft^3 to L Conversion

Media Surface Area

Biofilter Interstitial Volume

Tank VolumeGallon to L Conversion

Lb to kg Conversion

Feed Rate

GPM to L/d ConversionFlow Rate

Endogeneous Decay Rate

Backwash Event Timer

Executes Backwash Event During One Time Step

Actuates Backwash Event at Time=1/fbBackwash Period

Geometric Constants

Rate Constants

Sa (ft^2/ft^3)

Vm (ft^3)

Dissolved Oxygen

/l

r

+

+

Kso (mg/L)

Ob (mg/L) Lso

OCF (mg/ft^2-d)

Ot (mg/L)

Ob (mg/L)

Qr (L/d)

+

-

*

/l

r

Am (ft^2) Rmo (mg/d)

Rub (mg/d)

Ruoa (mg/d)

Rmo (mg/d)

0

merge

b

t

f

0

>l

r

Vb (L) Ob (mg/L) /l

r

1/S

-

-

+

Rate Equation(s)

Oxygen Consumed in Filtration

Oxygen Limitation

Integrated Rate Equation(s)

Ruoa (mg/d) 4.18 *

Rua (mg/d)

OCNt (mg/ft^2-d) Oxygen Consumed in Nitrification (true)

OCN (mg/ft^2-d) *

4.18 Oxygen Consumed in Nitrification (apparent)Ca (mg/ft^2-d)

Am (ft^2) /l

r

Effluent DO


Solids

Rds (mg/d)

*

ks (1/d)

*

Rdb (mg/d)

*

Rda (mg/d)

+

+ Rdh (mg/d)

Backwash Event 1/S

b

r

Rdp (mg/d)

+

-

Ps (mg)

Res (mg/d)

Sv

Sb

Sn

Ps (mg)

Sn

Sb Sv 0.15

0.05

0.88

Local Constant(s)

Rate Equation(s)

Rds (mg/d) Soluble BOD5 production

Solids Decay

P's (mg)

430000 Es (mg/kg)

Total Solids


Post-Backwash Primary Solids

Ps (mg)

hf

+

-

*

1/Zb

x Clock

Ms (mg)

Vb (L) /l

r

*

Sc (%)

0.0001 Percent Solids Concentration

P's (mg)

1

Es (mg/kg) Solids Excretion*

Rf (kg/d) Res (mg/d)

Soluble TAN production

+

+

Xh (mg)

Ms (mg)

Rdp (mg/d)


BOD5

hf

1 +

-

*

1/Zb

x Clock

/l

r

+

+

Ksb (mg/L)

Bb (mg/L) Rub (mg/d)

Yh (mg/mg)

umh (1/d)

/l

r

*

R'gh (mg/d) -

+ *

kd (1/d)

50400

*

+

-

Qr (L/d)

Rdh (mg/d)

Br

Eb (mg/kg)

Bt (mg/L)

Bb (mg/L) Rmb (mg/d)

Xh (mg)

Xh (mg) X'h (mg)

Rgh (mg/d)

Local Constant(s)

Rate Equation(s)

Mass Transfer

Rmb (mg/d)

Vb (L) Bb (mg/L)

Bt (mg/L) Vt (L)

-

+ 1/S

1/S

-

+

+

Rub (mg/d)

Rdb (mg/d)

X'h (mg)

R'gh (mg/d)

Xh (mg) Backwash Event 1/S

b

r

Post-Backwash Biomass

Net Growth

BOD5 Utilization

Biofilter BOD5

Tank BOD5

Heterotrophic Biomass


R'eb (mg/d)

Net BOD5 ExcretionR'eb (mg/d) 1 +

-

*

Is

Reb (mg/d) Eb (mg/kg) *

Rf (kg/d)

/l

r

0

merge

b

t

f

0

>l

r

>l

r

0

merge

b

t

f

0

/l

r

*

+

- 1

BOD5 Excretion Ratio


TAN

kd (1/d) *

Lso

Rua (mg/d)

Yn (mg/mg)

umn (1/d)

*

/l

r

-

+

merge

b

t

f

>l

r

1 Lso

R'gn (mg/d)

Qr (L/d)

+

- *

27000

Rf (kg/d) *

Ea (mg/kg)

Local Constant(s)

Rate Equation(s)

Ea (mg/kg) Rea (mg/d)

Ab (mg/L) At (mg/L) Rma (mg/d) Mass Transfer

Xn (mg)

X'n (mg)

R'gn (mg/d)

Xn (mg) Backwash Event 1/S

b

r

Tank TAN

Biofilter TAN

Rma (mg/d)

R'ea (mg/d) >

l

r

0

merge

b

t

f

0

>l

r

0

merge

b

t

f

0

Rda (mg/d) Rua (mg/d) -

+

+

1/S

1/S -

+

Vt (L)

/l

r

/l

r At (mg/L)

Ab (mg/L) Vb (L)

Endogeneous Decay

Net Growth

Substrate Utilization


Nitrifying Biomass

TAN Excretion Ratio

Post-Backwash Biomass

Xn (mg)

Br

Clock 1/Z

b

x *

+

- 1

hf

Is

*

+

- 1

R'ea (mg/d)

Net TAN Excretion

*

+

-

X'n (mg)

1

0

Ab (mg/L)

Ksa (mg/L)

/l

r

+

+

merge

b

t

f

0

1

>l

r

Lsa

Lsa

Lsa

R'eb (mg/d) /

l

r BOD5:TANe

BOD5:TANt

R'eb (mg/d)

R'ea (mg/d)

+

+

+

+

Rda (mg/d)

Rdb (mg/d)

/l

r

TAN Limitation

Rma (mg/d)

Specific Areal NitrificationCa (mg/ft^2/d)

Am (ft^2) /l

r

/l

r

Ab (mg/L) At (mg/L) +

+

/l

r

2

C'a (L/ft^2/d)

Excretion BOD5:TAN

Total BOD5:TAN


65

Appendix E

Model Calibration Output



DO Solids BOD5 TAN BOD5:N

TAB OB OCF OCNT OCN SC PS XH XN BT BB R'EB RDB AT AB C'A CA R'EA RDA Total Excr.

(hrs) (mg/L) (mg/ft2/d) (%) (g) (mg/L) (g/d) (mg/L) (mg/ft2/d) (g/d)

0.0 4.16 204 138 125 2.74 221 50.3 8.40 3.48 3.01 19.7 3.30 0.639 0.382 58.6 29.9 10.50 1.10 1.97 1.87

0.2 4.15 204 138 125 2.77 224 50.4 8.41 3.49 3.01 19.7 3.34 0.639 0.383 58.6 29.9 10.50 1.11 1.98 1.87

0.4 4.15 204 139 125 2.80 227 50.5 8.43 3.49 3.01 19.7 3.38 0.639 0.383 58.6 30.0 10.50 1.13 1.98 1.87

0.6 4.15 205 139 125 2.84 230 50.6 8.45 3.49 3.01 19.7 3.42 0.639 0.383 58.6 30.0 10.50 1.14 1.98 1.87

0.8 4.15 205 139 125 2.87 234 50.7 8.46 3.49 3.01 19.7 3.46 0.640 0.383 58.7 30.0 10.50 1.15 1.98 1.87

1.0 4.14 205 139 125 2.90 237 50.8 8.48 3.49 3.01 19.7 3.50 0.640 0.383 58.7 30.0 10.50 1.17 1.98 1.87

1.2 4.14 206 140 125 2.93 240 50.9 8.49 3.49 3.01 19.7 3.55 0.640 0.383 58.7 30.0 10.50 1.18 1.98 1.87

1.4 4.14 206 140 126 2.96 243 51.0 8.51 3.49 3.01 19.7 3.59 0.640 0.383 58.7 30.0 10.50 1.20 1.98 1.87

1.6 4.13 206 140 126 3.00 246 51.1 8.53 3.49 3.01 19.7 3.63 0.640 0.383 58.7 30.0 10.50 1.21 1.98 1.87

1.8 4.13 207 140 126 3.03 249 51.2 8.54 3.49 3.01 19.7 3.67 0.640 0.383 58.7 30.0 10.50 1.22 1.99 1.87

2.0 4.13 207 140 126 3.06 252 51.3 8.56 3.49 3.01 19.7 3.71 0.640 0.383 58.7 30.1 10.50 1.24 1.99 1.87

2.2 4.12 207 141 126 3.09 255 51.4 8.57 3.49 3.01 19.7 3.75 0.640 0.383 58.7 30.1 10.50 1.25 1.99 1.87

2.4 4.12 208 141 126 3.12 258 51.4 8.59 3.49 3.01 19.7 3.79 0.641 0.383 58.8 30.1 10.50 1.27 1.99 1.87

2.6 4.12 208 141 126 3.16 261 51.5 8.61 3.49 3.01 19.7 3.84 0.641 0.383 58.8 30.1 10.50 1.28 1.99 1.87

2.8 4.12 208 141 126 3.19 264 51.6 8.62 3.49 3.01 19.7 3.88 0.641 0.383 58.8 30.1 10.50 1.29 1.99 1.87

3.0 4.11 209 141 126 3.22 267 51.7 8.64 3.49 3.01 19.7 3.92 0.641 0.383 58.8 30.1 10.50 1.31 1.99 1.87

3.2 4.11 209 142 126 3.25 271 51.8 8.66 3.49 3.01 19.7 3.96 0.641 0.383 58.8 30.1 10.50 1.32 1.99 1.87

3.4 4.11 209 142 126 3.28 274 51.9 8.67 3.49 3.01 19.7 4.00 0.641 0.383 58.8 30.1 10.50 1.33 1.99 1.87

3.6 4.11 210 142 126 3.32 277 52.0 8.69 3.49 3.01 19.7 4.04 0.641 0.383 58.9 30.1 10.50 1.35 2.00 1.87

3.8 4.10 210 142 126 3.35 280 52.1 8.70 3.49 3.01 19.7 4.08 0.640 0.383 58.9 30.1 10.50 1.36 2.00 1.87

4.0 4.10 210 142 126 3.38 283 52.2 8.72 3.49 3.01 19.7 4.12 0.640 0.383 58.9 30.1 10.5 1.38 2.00 1.87

4.2 4.10 211 143 126 3.41 286 52.3 8.74 3.49 3.01 19.7 4.17 0.640 0.382 58.9 30.1 10.5 1.39 2.00 1.87

4.4 4.10 211 143 126 3.44 289 52.4 8.75 3.49 3.01 19.7 4.21 0.640 0.382 58.9 30.1 10.5 1.40 2.00 1.87

4.6 4.09 211 143 126 3.48 292 52.5 8.77 3.49 3.01 19.7 4.25 0.640 0.382 59.0 30.1 10.5 1.42 2.00 1.87

4.8 4.09 212 143 126 3.51 295 52.6 8.79 3.49 3.01 19.7 4.29 0.640 0.382 59.0 30.1 10.5 1.43 2.00 1.87

5.0 4.09 212 143 126 3.54 298 52.7 8.80 3.49 3.01 19.7 4.33 0.640 0.382 59.0 30.2 10.5 1.44 2.00 1.87

5.2 4.08 212 143 126 3.57 301 52.8 8.82 3.49 3.01 19.7 4.37 0.640 0.382 59.0 30.2 10.5 1.46 2.00 1.87

5.4 4.08 212 144 126 3.60 304 52.9 8.83 3.49 3.01 19.7 4.41 0.640 0.382 59.0 30.2 10.5 1.47 2.01 1.87

5.6 4.08 213 144 126 3.63 307 53.0 8.85 3.49 3.01 19.7 4.45 0.640 0.382 59.1 30.2 10.5 1.48 2.01 1.87

5.8 4.08 213 144 126 3.67 310 53.1 8.87 3.49 3.01 19.7 4.49 0.640 0.381 59.1 30.2 10.5 1.50 2.01 1.87

6.0 4.07 213 144 126 3.70 313 53.2 8.88 3.49 3.01 19.7 4.53 0.640 0.381 59.1 30.2 10.5 1.51 2.01 1.87

6.2 4.07 214 144 126 3.73 316 53.3 8.90 3.49 3.01 19.7 4.57 0.639 0.381 59.1 30.2 10.5 1.53 2.01 1.87

6.4 4.07 214 145 126 3.76 319 53.4 8.92 3.49 3.01 19.7 4.62 0.639 0.381 59.1 30.2 10.5 1.54 2.01 1.87

6.6 4.07 214 145 126 3.79 322 53.5 8.93 3.49 3.00 19.7 4.66 0.639 0.381 59.2 30.2 10.5 1.55 2.01 1.87

6.8 4.06 215 145 126 3.82 325 53.6 8.95 3.49 3.00 19.7 4.70 0.639 0.381 59.2 30.2 10.5 1.57 2.01 1.87

7.0 4.06 215 145 126 3.86 328 53.7 8.97 3.49 3.00 19.7 4.74 0.639 0.380 59.2 30.2 10.5 1.58 2.01 1.87

7.2 4.06 215 145 126 3.89 331 53.8 8.98 3.49 3.00 19.7 4.78 0.639 0.380 59.2 30.2 10.5 1.59 2.02 1.87

7.4 4.06 215 145 126 3.92 334 53.9 9.00 3.49 3.00 19.7 4.82 0.639 0.380 59.3 30.2 10.5 1.61 2.02 1.87

7.6 4.05 216 146 126 3.95 337 54.0 9.02 3.49 3.00 19.7 4.86 0.638 0.380 59.3 30.2 10.5 1.62 2.02 1.87

7.8 4.05 216 146 126 3.98 340 54.1 9.03 3.49 3.00 19.7 4.90 0.638 0.380 59.3 30.2 10.5 1.63 2.02 1.87

8.0 4.05 216 146 126 4.01 343 54.2 9.05 3.49 3.00 19.7 4.93 0.638 0.380 59.3 30.2 10.5 1.64 2.02 1.87

Note: TAB is the time after backwash.

TAB=0.0: data values are reported at one time step (0.000125 d) after a backwash event.

TAB=1/fb: data values are reported at one time step (0.000125 d) before a backwash event.






0.0 3.13 185 123 96.5 5.47 437 105 16.2 1.69 1.30 14.4 6.56 0.690 0.482 39.4 23.1 7.72 2.19 2.12 1.87

0.6 3.13 185 122 95.9 5.54 443 106 16.3 1.68 1.29 14.4 6.64 0.685 0.478 39.5 23.0 7.72 2.21 2.12 1.87

1.2 3.13 184 122 95.4 5.60 450 106 16.3 1.67 1.28 14.4 6.73 0.681 0.474 39.5 22.8 7.72 2.24 2.12 1.87

1.8 3.14 184 122 94.9 5.67 456 106 16.3 1.66 1.28 14.4 6.81 0.677 0.471 39.6 22.7 7.72 2.27 2.12 1.87

2.4 3.14 184 122 94.5 5.74 462 106 16.3 1.66 1.28 14.4 6.90 0.673 0.469 39.6 22.6 7.72 2.30 2.13 1.87

3.0 3.14 184 122 94.1 5.80 469 106 16.4 1.65 1.27 14.4 6.98 0.671 0.467 39.6 22.5 7.72 2.33 2.13 1.87

3.6 3.14 184 122 93.8 5.87 475 107 16.4 1.65 1.27 14.4 7.07 0.668 0.465 39.6 22.4 7.72 2.36 2.13 1.87

4.2 3.14 184 122 93.5 5.93 481 107 16.4 1.65 1.27 14.4 7.15 0.666 0.464 39.5 22.4 7.72 2.38 2.13 1.87

4.8 3.14 184 122 93.2 6.00 487 107 16.5 1.65 1.27 14.4 7.23 0.665 0.463 39.5 22.3 7.72 2.41 2.14 1.87

5.4 3.13 184 122 92.9 6.06 494 107 16.5 1.64 1.27 14.4 7.32 0.664 0.463 39.5 22.2 7.72 2.44 2.14 1.87

6.0 3.13 184 122 92.7 6.13 500 107 16.5 1.64 1.27 14.4 7.40 0.663 0.463 39.4 22.2 7.72 2.47 2.14 1.87

6.6 3.13 185 122 92.5 6.19 506 108 16.6 1.64 1.27 14.4 7.49 0.662 0.462 39.3 22.1 7.72 2.50 2.14 1.87

7.2 3.13 185 122 92.3 6.25 512 108 16.6 1.64 1.27 14.4 7.57 0.662 0.463 39.3 22.1 7.72 2.52 2.15 1.87

7.8 3.12 185 123 92.1 6.32 518 108 16.6 1.65 1.28 14.4 7.65 0.662 0.463 39.2 22.0 7.72 2.55 2.15 1.87

8.4 3.12 186 123 92.0 6.38 525 108 16.7 1.65 1.28 14.4 7.73 0.662 0.463 39.1 22.0 7.72 2.58 2.15 1.87

9.0 3.12 186 123 91.9 6.45 531 108 16.7 1.65 1.28 14.4 7.82 0.663 0.464 39.0 22.0 7.72 2.61 2.15 1.87

9.6 3.11 187 123 91.7 6.51 537 108 16.7 1.65 1.28 14.4 7.90 0.663 0.465 38.9 22.0 7.72 2.63 2.16 1.87

10.2 3.11 187 123 91.6 6.57 543 109 16.7 1.65 1.28 14.4 7.98 0.664 0.465 38.8 21.9 7.72 2.66 2.16 1.87

10.8 3.11 188 124 91.5 6.64 549 109 16.8 1.65 1.28 14.4 8.06 0.664 0.466 38.7 21.9 7.72 2.69 2.16 1.87

11.4 3.10 188 124 91.5 6.70 555 109 16.8 1.66 1.29 14.4 8.15 0.665 0.467 38.6 21.9 7.72 2.72 2.16 1.87

12.0 3.10 188 124 91.4 6.77 561 109 16.8 1.66 1.29 14.4 8.23 0.666 0.468 38.6 21.9 7.72 2.74 2.16 1.87

12.6 3.09 189 124 91.3 6.83 567 109 16.9 1.66 1.29 14.4 8.31 0.667 0.470 38.5 21.9 7.72 2.77 2.17 1.87

13.2 3.09 189 125 91.3 6.89 573 110 16.9 1.66 1.29 14.4 8.39 0.668 0.471 38.3 21.8 7.72 2.80 2.17 1.87

13.8 3.08 190 125 91.2 6.96 579 110 16.9 1.66 1.30 14.4 8.47 0.669 0.472 38.2 21.8 7.72 2.82 2.17 1.87

14.4 3.08 190 125 91.2 7.02 586 110 17.0 1.67 1.30 14.4 8.55 0.671 0.473 38.1 21.8 7.72 2.85 2.17 1.87

15.0 3.07 191 126 91.1 7.08 592 110 17.0 1.67 1.30 14.4 8.63 0.672 0.475 38.0 21.8 7.72 2.88 2.18 1.87

15.6 3.07 191 126 91.1 7.14 598 111 17.0 1.67 1.30 14.4 8.72 0.673 0.476 37.9 21.8 7.72 2.91 2.18 1.87

16.2 3.06 192 126 91.1 7.21 604 111 17.1 1.67 1.30 14.4 8.80 0.675 0.478 37.8 21.8 7.72 2.93 2.18 1.87

16.8 3.06 193 126 91.1 7.27 609 111 17.1 1.68 1.31 14.4 8.88 0.676 0.479 37.7 21.8 7.72 2.96 2.18 1.87

17.4 3.06 193 127 91.0 7.33 615 111 17.1 1.68 1.31 14.4 8.96 0.677 0.480 37.6 21.8 7.72 2.99 2.18 1.87

18.0 3.05 194 127 91.0 7.39 621 111 17.1 1.68 1.31 14.4 9.04 0.679 0.482 37.5 21.8 7.72 3.01 2.19 1.87

18.6 3.05 194 127 91.0 7.46 627 112 17.2 1.68 1.31 14.4 9.12 0.680 0.483 37.4 21.8 7.72 3.04 2.19 1.87

19.2 3.04 195 128 91.0 7.52 633 112 17.2 1.68 1.32 14.4 9.20 0.682 0.485 37.3 21.8 7.72 3.07 2.19 1.87

19.8 3.04 195 128 91.0 7.58 639 112 17.2 1.69 1.32 14.4 9.28 0.683 0.487 37.2 21.8 7.72 3.09 2.19 1.87

20.4 3.03 196 128 91.0 7.64 645 112 17.3 1.69 1.32 14.4 9.36 0.685 0.488 37.1 21.8 7.72 3.12 2.19 1.87

21.0 3.03 196 129 90.9 7.70 651 112 17.3 1.69 1.32 14.4 9.44 0.686 0.490 37.0 21.8 7.72 3.15 2.20 1.87

21.6 3.02 197 129 90.9 7.76 657 113 17.3 1.69 1.32 14.4 9.51 0.688 0.491 36.9 21.8 7.72 3.17 2.20 1.87

22.2 3.02 197 129 90.9 7.82 663 113 17.4 1.69 1.33 14.4 9.59 0.690 0.493 36.8 21.8 7.72 3.20 2.20 1.87

22.8 3.01 198 129 90.9 7.89 669 113 17.4 1.70 1.33 14.4 9.67 0.691 0.494 36.7 21.8 7.72 3.22 2.20 1.87

23.4 3.01 198 130 90.9 7.95 674 113 17.4 1.70 1.33 14.4 9.75 0.693 0.496 36.6 21.8 7.72 3.25 2.20 1.87

24.0 3.00 199 130 90.9 8.01 680 113 17.5 1.70 1.33 14.4 9.83 0.694 0.498 36.5 21.8 7.72 3.28 2.20 1.87






0.0 3.65 204 133 88.3 9.2 744 171 24.3 1.27 0.897 12.0 11.1 0.713 0.511 34.5 21.1 6.43 3.70 2.28 1.87

1.2 3.68 200 131 85.9 9.4 755 171 24.3 1.23 0.875 12.0 11.3 0.687 0.490 34.9 20.5 6.43 3.75 2.28 1.87

2.4 3.71 198 129 83.7 9.5 767 172 24.4 1.21 0.863 12.0 11.4 0.666 0.474 35.1 20.0 6.43 3.80 2.29 1.87

3.6 3.72 196 128 82.0 9.6 778 172 24.4 1.19 0.857 12.0 11.6 0.651 0.463 35.2 19.6 6.43 3.85 2.29 1.87

4.8 3.73 195 127 80.5 9.7 789 172 24.5 1.19 0.854 12.0 11.7 0.639 0.455 35.2 19.3 6.43 3.90 2.30 1.87

6.0 3.73 195 127 79.4 9.8 800 173 24.5 1.18 0.855 12.0 11.9 0.631 0.449 35.2 19.0 6.43 3.95 2.30 1.87

7.2 3.73 195 126 78.5 9.9 811 173 24.6 1.18 0.856 12.0 12.0 0.626 0.446 35.0 18.8 6.43 4.00 2.30 1.87

8.4 3.73 195 126 77.8 10.0 822 173 24.6 1.19 0.859 12.0 12.2 0.622 0.444 34.9 18.6 6.43 4.05 2.31 1.87

9.6 3.73 195 126 77.2 10.2 833 173 24.6 1.19 0.862 12.0 12.3 0.621 0.444 34.7 18.5 6.43 4.10 2.31 1.87

10.8 3.72 196 126 76.8 10.3 844 174 24.7 1.19 0.865 12.0 12.5 0.620 0.444 34.5 18.4 6.43 4.15 2.31 1.87

12.0 3.72 197 127 76.4 10.4 855 174 24.7 1.19 0.869 12.0 12.6 0.621 0.445 34.3 18.3 6.43 4.20 2.31 1.87

13.2 3.71 197 127 76.2 10.5 866 174 24.8 1.20 0.872 12.0 12.7 0.622 0.447 34.1 18.2 6.43 4.25 2.32 1.87

14.4 3.70 198 127 76.0 10.6 877 175 24.8 1.20 0.876 12.0 12.9 0.624 0.449 33.9 18.2 6.43 4.29 2.32 1.87

15.6 3.69 199 128 75.9 10.7 887 175 24.9 1.21 0.879 12.0 13.0 0.626 0.452 33.7 18.2 6.43 4.34 2.32 1.87

16.8 3.69 200 128 75.7 10.8 898 175 24.9 1.21 0.883 12.0 13.2 0.628 0.455 33.5 18.1 6.43 4.39 2.33 1.87

18.0 3.68 201 129 75.7 10.9 909 176 25.0 1.21 0.887 12.0 13.3 0.631 0.458 33.2 18.1 6.43 4.44 2.33 1.87

19.2 3.67 202 129 75.6 11.1 919 176 25.0 1.22 0.890 12.0 13.5 0.634 0.461 33.0 18.1 6.43 4.49 2.33 1.87

20.4 3.66 203 130 75.5 11.2 930 176 25.0 1.22 0.894 12.0 13.6 0.637 0.464 32.8 18.1 6.43 4.53 2.34 1.87

21.6 3.65 203 130 75.5 11.3 941 177 25.1 1.22 0.897 12.0 13.7 0.641 0.468 32.6 18.1 6.43 4.58 2.34 1.87

22.8 3.64 204 131 75.5 11.4 951 177 25.1 1.23 0.900 12.0 13.9 0.644 0.471 32.4 18.1 6.43 4.63 2.34 1.87

24.0 3.63 205 131 75.4 11.5 961 177 25.2 1.23 0.904 12.0 14.0 0.648 0.475 32.2 18.1 6.43 4.67 2.34 1.87

25.2 3.62 206 132 75.4 11.6 972 178 25.2 1.23 0.907 12.0 14.2 0.651 0.478 32.0 18.0 6.43 4.72 2.35 1.87

26.4 3.62 207 132 75.4 11.7 982 178 25.3 1.24 0.910 12.0 14.3 0.655 0.482 31.8 18.0 6.43 4.77 2.35 1.87

27.6 3.61 208 133 75.4 11.8 992 178 25.3 1.24 0.914 12.0 14.4 0.658 0.485 31.6 18.0 6.43 4.81 2.35 1.87

28.8 3.60 209 133 75.4 11.9 1000 179 25.4 1.24 0.917 12.0 14.6 0.662 0.489 31.4 18.0 6.43 4.86 2.35 1.87

30.0 3.59 210 134 75.4 12.0 1010 179 25.4 1.25 0.920 12.0 14.7 0.665 0.493 31.2 18.0 6.43 4.90 2.36 1.87

31.2 3.58 211 135 75.4 12.1 1020 179 25.5 1.25 0.923 12.0 14.9 0.669 0.496 31.0 18.0 6.43 4.95 2.36 1.87

32.4 3.57 212 135 75.4 12.2 1030 180 25.5 1.25 0.926 12.0 15.0 0.673 0.500 30.8 18.0 6.43 4.99 2.36 1.87

33.6 3.56 213 136 75.4 12.3 1040 180 25.6 1.26 0.929 12.0 15.1 0.676 0.504 30.6 18.0 6.43 5.04 2.37 1.87

34.8 3.55 214 136 75.4 12.5 1050 180 25.6 1.26 0.932 12.0 15.3 0.680 0.507 30.4 18.0 6.43 5.09 2.37 1.87

36.0 3.54 215 137 75.4 12.6 1060 181 25.7 1.26 0.935 12.0 15.4 0.684 0.511 30.2 18.0 6.43 5.13 2.37 1.87

37.2 3.54 216 137 75.4 12.7 1070 181 25.7 1.26 0.937 12.0 15.5 0.687 0.515 30.0 18.0 6.43 5.17 2.37 1.87

38.4 3.53 216 138 75.4 12.8 1080 182 25.8 1.27 0.940 12.0 15.7 0.691 0.518 29.8 18.0 6.43 5.22 2.37 1.87

39.6 3.52 217 138 75.4 12.9 1090 182 25.8 1.27 0.943 12.0 15.8 0.695 0.522 29.6 18.0 6.43 5.26 2.38 1.87

40.8 3.51 218 139 75.4 13.0 1100 182 25.9 1.27 0.946 12.0 15.9 0.698 0.526 29.5 18.0 6.43 5.31 2.38 1.87

42.0 3.50 219 139 75.4 13.1 1110 183 25.9 1.27 0.948 12.0 16.1 0.702 0.529 29.3 18.0 6.43 5.35 2.38 1.87

43.2 3.49 220 140 75.4 13.2 1120 183 26.0 1.28 0.951 12.0 16.2 0.706 0.533 29.1 18.0 6.43 5.39 2.38 1.87

44.4 3.48 221 140 75.4 13.3 1130 183 26.0 1.28 0.953 12.0 16.3 0.709 0.537 28.9 18.0 6.43 5.44 2.39 1.87

45.6 3.47 222 141 75.4 13.4 1140 184 26.1 1.28 0.956 12.0 16.4 0.713 0.540 28.8 18.0 6.43 5.48 2.39 1.87

46.8 3.47 223 141 75.4 13.5 1150 184 26.1 1.29 0.958 12.0 16.6 0.717 0.544 28.6 18.0 6.43 5.52 2.39 1.87

48.0 3.46 224 142 75.4 13.6 1160 185 26.2 1.29 0.961 12.0 16.7 0.721 0.548 28.4 18.0 6.43 5.57 2.39 1.87






0.0 5.46 86 58.0 51.5 1.17 108 7.5 1.22 9.58 9.43 8.23 1.48 0.533 0.456 24.9 12.3 4.41 0.49 1.98 1.87

0.3 5.46 87 58.5 51.8 1.20 112 7.5 1.24 9.58 9.44 8.23 1.53 0.534 0.457 25.0 12.4 4.41 0.51 1.98 1.87

0.6 5.45 88 59.0 52.2 1.24 115 7.6 1.25 9.58 9.44 8.23 1.58 0.536 0.457 25.1 12.5 4.41 0.53 1.99 1.87

0.9 5.45 88 59.6 52.5 1.28 119 7.7 1.26 9.59 9.44 8.23 1.62 0.537 0.458 25.3 12.6 4.41 0.54 1.99 1.87

1.2 5.44 89 60.1 52.8 1.31 122 7.7 1.27 9.59 9.44 8.23 1.67 0.538 0.458 25.4 12.6 4.41 0.56 1.99 1.87

1.5 5.44 90 60.7 53.2 1.35 126 7.8 1.28 9.59 9.44 8.23 1.72 0.539 0.459 25.5 12.7 4.41 0.57 2.00 1.87

1.8 5.43 91 61.2 53.5 1.38 129 7.9 1.29 9.59 9.44 8.23 1.77 0.540 0.459 25.6 12.8 4.41 0.59 2.00 1.87

2.1 5.43 91 61.8 53.9 1.42 133 7.9 1.30 9.59 9.44 8.23 1.81 0.541 0.460 25.8 12.9 4.41 0.60 2.00 1.87

2.4 5.42 92 62.3 54.2 1.46 136 8.0 1.31 9.59 9.44 8.23 1.86 0.541 0.460 25.9 13.0 4.41 0.62 2.01 1.87

2.7 5.42 93 62.9 54.5 1.49 140 8.1 1.32 9.60 9.44 8.23 1.91 0.542 0.460 26.0 13.1 4.41 0.64 2.01 1.87

3.0 5.41 94 63.4 54.9 1.53 143 8.1 1.33 9.60 9.44 8.23 1.95 0.543 0.460 26.2 13.1 4.41 0.65 2.01 1.87

3.3 5.41 95 63.9 55.2 1.56 147 8.2 1.34 9.60 9.45 8.23 2.00 0.543 0.460 26.3 13.2 4.41 0.67 2.02 1.87

3.6 5.40 95 64.5 55.5 1.60 150 8.3 1.36 9.60 9.45 8.23 2.05 0.544 0.460 26.5 13.3 4.41 0.68 2.02 1.87

3.9 5.40 96 65.0 55.9 1.64 154 8.3 1.37 9.60 9.45 8.23 2.09 0.544 0.460 26.6 13.4 4.41 0.70 2.02 1.87

4.2 5.39 97 65.5 56.2 1.67 157 8.4 1.38 9.60 9.45 8.23 2.14 0.545 0.460 26.8 13.4 4.41 0.71 2.02 1.87

4.5 5.39 98 66.1 56.5 1.71 161 8.5 1.39 9.60 9.45 8.23 2.19 0.545 0.460 26.9 13.5 4.41 0.73 2.03 1.87

4.8 5.38 99 66.6 56.9 1.74 164 8.5 1.40 9.60 9.45 8.23 2.23 0.545 0.460 27.1 13.6 4.41 0.74 2.03 1.87

5.1 5.38 99 67.1 57.2 1.78 168 8.6 1.41 9.60 9.45 8.23 2.28 0.545 0.459 27.2 13.7 4.41 0.76 2.03 1.87

5.4 5.37 100 67.7 57.5 1.81 171 8.7 1.43 9.60 9.45 8.23 2.32 0.545 0.459 27.4 13.8 4.41 0.77 2.04 1.87

5.7 5.37 101 68.2 57.8 1.85 175 8.8 1.44 9.60 9.44 8.23 2.37 0.545 0.459 27.6 13.8 4.41 0.79 2.04 1.87

6.0 5.36 102 68.7 58.2 1.89 178 8.8 1.45 9.61 9.44 8.23 2.42 0.545 0.458 27.7 13.9 4.41 0.81 2.04 1.87

6.3 5.36 103 69.2 58.5 1.92 182 8.9 1.46 9.61 9.44 8.23 2.46 0.545 0.457 27.9 14.0 4.41 0.82 2.05 1.87

6.6 5.35 104 69.8 58.8 1.96 185 9.0 1.47 9.61 9.44 8.23 2.51 0.545 0.457 28.1 14.1 4.41 0.84 2.05 1.87

6.9 5.35 104 70.3 59.1 1.99 188 9.1 1.49 9.61 9.44 8.23 2.56 0.545 0.456 28.3 14.1 4.41 0.85 2.05 1.87

7.2 5.34 105 70.8 59.4 2.03 192 9.1 1.50 9.60 9.44 8.23 2.60 0.545 0.455 28.4 14.2 4.41 0.87 2.05 1.87

7.5 5.34 106 71.3 59.7 2.06 195 9.2 1.51 9.60 9.44 8.23 2.65 0.544 0.454 28.6 14.3 4.41 0.88 2.06 1.87

7.8 5.33 107 71.8 60.0 2.10 199 9.3 1.52 9.60 9.44 8.23 2.69 0.544 0.454 28.8 14.4 4.41 0.90 2.06 1.87

8.1 5.33 107 72.3 60.3 2.14 202 9.4 1.54 9.60 9.44 8.23 2.74 0.543 0.453 29.0 14.4 4.41 0.91 2.06 1.87

8.4 5.32 108 72.8 60.6 2.17 206 9.4 1.55 9.60 9.44 8.23 2.79 0.543 0.452 29.2 14.5 4.41 0.93 2.06 1.87

8.7 5.32 109 73.3 60.9 2.21 209 9.5 1.56 9.60 9.43 8.23 2.83 0.542 0.451 29.4 14.6 4.41 0.94 2.07 1.87

9.0 5.31 110 73.8 61.2 2.24 213 9.6 1.58 9.60 9.43 8.23 2.88 0.541 0.449 29.6 14.6 4.41 0.96 2.07 1.87

9.3 5.31 111 74.3 61.5 2.28 216 9.7 1.59 9.60 9.43 8.23 2.92 0.541 0.448 29.8 14.7 4.41 0.97 2.07 1.87

9.6 5.30 111 74.8 61.8 2.31 219 9.8 1.60 9.60 9.43 8.23 2.97 0.540 0.447 30.0 14.8 4.41 0.99 2.07 1.87

9.9 5.30 112 75.2 62.1 2.35 223 9.8 1.62 9.60 9.42 8.23 3.01 0.539 0.446 30.2 14.9 4.41 1.01 2.08 1.87

10.2 5.29 113 75.7 62.3 2.38 226 9.9 1.63 9.60 9.42 8.23 3.06 0.538 0.444 30.4 14.9 4.41 1.02 2.08 1.87

10.5 5.29 114 76.2 62.6 2.42 230 10.0 1.64 9.59 9.42 8.23 3.11 0.537 0.443 30.6 15.0 4.41 1.04 2.08 1.87

10.8 5.28 115 76.7 62.9 2.45 233 10.1 1.66 9.59 9.42 8.23 3.15 0.536 0.441 30.8 15.0 4.41 1.05 2.09 1.87

11.1 5.28 115 77.1 63.2 2.49 236 10.2 1.67 9.59 9.41 8.23 3.20 0.535 0.440 31.0 15.1 4.41 1.07 2.09 1.87

11.4 5.27 116 77.6 63.4 2.52 240 10.3 1.68 9.59 9.41 8.23 3.24 0.534 0.438 31.2 15.2 4.41 1.08 2.09 1.87

11.7 5.27 117 78.0 63.7 2.56 243 10.4 1.70 9.59 9.41 8.23 3.29 0.532 0.437 31.4 15.2 4.41 1.10 2.09 1.87

12.0 5.26 118 78.5 63.9 2.59 247 10.4 1.71 9.58 9.40 8.23 3.33 0.531 0.435 31.7 15.3 4.41 1.11 2.10 1.87






0.0 5.22 124 83 70.2 2.25 202 20.5 3.25 4.60 4.40 11.0 2.82 0.532 0.427 35.0 16.8 5.88 0.94 2.02 1.87

0.6 5.22 125 83 70.7 2.32 209 20.7 3.28 4.60 4.40 11.0 2.92 0.535 0.429 35.1 16.9 5.88 0.97 2.03 1.87

1.2 5.21 126 84 71.2 2.39 216 20.9 3.31 4.61 4.40 11.0 3.01 0.538 0.431 35.2 17.0 5.88 1.00 2.03 1.87

1.8 5.20 127 85 71.6 2.46 223 21.0 3.34 4.61 4.40 11.0 3.10 0.540 0.433 35.2 17.1 5.88 1.03 2.04 1.87

2.4 5.19 129 86 72.1 2.53 230 21.2 3.37 4.61 4.41 11.0 3.19 0.542 0.434 35.3 17.2 5.88 1.06 2.04 1.87

3.0 5.19 130 87 72.5 2.60 236 21.4 3.39 4.62 4.41 11.0 3.28 0.544 0.435 35.4 17.3 5.88 1.09 2.04 1.87

3.6 5.18 131 88 72.9 2.67 243 21.6 3.42 4.62 4.41 11.0 3.37 0.546 0.437 35.5 17.5 5.88 1.12 2.05 1.87

4.2 5.17 132 88 73.3 2.74 250 21.7 3.45 4.62 4.41 11.0 3.46 0.548 0.438 35.6 17.6 5.88 1.15 2.05 1.87

4.8 5.16 133 89 73.8 2.81 257 21.9 3.48 4.62 4.42 11.0 3.55 0.549 0.438 35.7 17.6 5.88 1.18 2.06 1.87

5.4 5.16 135 90 74.1 2.88 264 22.1 3.51 4.63 4.42 11.0 3.64 0.551 0.439 35.9 17.7 5.88 1.22 2.06 1.87

6.0 5.15 136 91 74.5 2.95 270 22.3 3.54 4.63 4.42 11.0 3.73 0.552 0.440 36.0 17.8 5.88 1.25 2.07 1.87

6.6 5.14 137 92 74.9 3.02 277 22.5 3.57 4.63 4.42 11.0 3.82 0.553 0.440 36.1 17.9 5.88 1.28 2.07 1.87

7.2 5.13 138 92 75.3 3.09 284 22.7 3.60 4.63 4.42 11.0 3.91 0.553 0.440 36.2 18.0 5.88 1.31 2.07 1.87

7.8 5.13 139 93 75.6 3.16 290 22.9 3.63 4.63 4.42 11.0 4.00 0.554 0.441 36.4 18.1 5.88 1.33 2.08 1.87

8.4 5.12 140 94 76.0 3.23 297 23.1 3.67 4.64 4.42 11.0 4.09 0.555 0.441 36.5 18.2 5.88 1.36 2.08 1.87

9.0 5.11 141 95 76.3 3.30 304 23.3 3.70 4.64 4.42 11.0 4.18 0.555 0.440 36.7 18.3 5.88 1.39 2.08 1.87

9.6 5.11 143 95 76.6 3.37 310 23.4 3.73 4.64 4.43 11.0 4.27 0.555 0.440 36.8 18.3 5.88 1.42 2.09 1.87

10.2 5.10 144 96 76.9 3.44 317 23.6 3.76 4.64 4.43 11.0 4.36 0.555 0.440 37.0 18.4 5.88 1.45 2.09 1.87

10.8 5.09 145 97 77.2 3.51 324 23.8 3.79 4.64 4.43 11.0 4.45 0.555 0.439 37.2 18.5 5.88 1.48 2.10 1.87

11.4 5.09 146 97 77.5 3.57 330 24.0 3.82 4.64 4.43 11.0 4.54 0.555 0.439 37.3 18.5 5.88 1.51 2.10 1.87

12.0 5.08 147 98 77.8 3.64 337 24.2 3.86 4.64 4.42 11.0 4.63 0.555 0.438 37.5 18.6 5.88 1.54 2.10 1.87

12.6 5.07 148 99 78.1 3.71 343 24.5 3.89 4.64 4.42 11.0 4.71 0.555 0.437 37.7 18.7 5.88 1.57 2.11 1.87

13.2 5.07 149 99 78.3 3.78 350 24.7 3.92 4.64 4.42 11.0 4.80 0.554 0.436 37.8 18.7 5.88 1.60 2.11 1.87

13.8 5.06 150 100 78.6 3.85 356 24.9 3.96 4.64 4.42 11.0 4.89 0.553 0.435 38.0 18.8 5.88 1.63 2.11 1.87

14.4 5.05 151 101 78.8 3.91 363 25.1 3.99 4.64 4.42 11.0 4.98 0.553 0.434 38.2 18.9 5.88 1.66 2.12 1.87

15.0 5.05 152 101 79.1 3.98 369 25.3 4.02 4.64 4.42 11.0 5.07 0.552 0.433 38.4 18.9 5.88 1.69 2.12 1.87

15.6 5.04 153 102 79.3 4.05 376 25.5 4.06 4.64 4.42 11.0 5.15 0.551 0.432 38.6 19.0 5.88 1.72 2.12 1.87

16.2 5.03 154 102 79.5 4.12 382 25.7 4.09 4.64 4.41 11.0 5.24 0.550 0.431 38.8 19.0 5.88 1.75 2.13 1.87

16.8 5.03 155 103 79.7 4.19 389 25.9 4.12 4.63 4.41 11.0 5.33 0.549 0.429 39.0 19.1 5.88 1.78 2.13 1.87

17.4 5.02 156 104 79.9 4.25 395 26.1 4.16 4.63 4.41 11.0 5.41 0.548 0.428 39.2 19.1 5.88 1.80 2.13 1.87

18.0 5.01 157 104 80.1 4.32 402 26.4 4.19 4.63 4.41 11.0 5.50 0.547 0.426 39.4 19.2 5.88 1.83 2.14 1.87

18.6 5.01 158 105 80.2 4.39 408 26.6 4.23 4.63 4.40 11.0 5.59 0.545 0.425 39.6 19.2 5.88 1.86 2.14 1.87

19.2 5.00 159 105 80.4 4.45 415 26.8 4.26 4.62 4.40 11.0 5.67 0.544 0.423 39.8 19.2 5.88 1.89 2.14 1.87

19.8 5.00 160 106 80.6 4.52 421 27.0 4.30 4.62 4.40 11.0 5.76 0.542 0.421 40.0 19.3 5.88 1.92 2.15 1.87

20.4 4.99 161 106 80.7 4.59 427 27.3 4.33 4.62 4.39 11.0 5.85 0.541 0.420 40.2 19.3 5.88 1.95 2.15 1.87

21.0 4.99 162 107 80.9 4.65 434 27.5 4.37 4.62 4.39 11.0 5.93 0.539 0.418 40.4 19.3 5.88 1.98 2.15 1.87

21.6 4.98 163 107 81.0 4.72 440 27.7 4.40 4.61 4.38 11.0 6.02 0.538 0.416 40.6 19.4 5.88 2.01 2.16 1.87

22.2 4.97 164 108 81.1 4.79 446 27.9 4.44 4.61 4.38 11.0 6.10 0.536 0.414 40.9 19.4 5.88 2.03 2.16 1.87

22.8 4.97 164 108 81.2 4.85 453 28.2 4.47 4.60 4.37 11.0 6.19 0.534 0.412 41.1 19.4 5.88 2.06 2.16 1.87

23.4 4.96 165 109 81.3 4.92 459 28.4 4.51 4.60 4.37 11.0 6.27 0.532 0.410 41.3 19.5 5.88 2.09 2.16 1.87

24.0 4.96 166 109 81.4 4.98 465 28.7 4.55 4.60 4.36 11.0 6.36 0.531 0.408 41.5 19.5 5.88 2.12 2.17 1.87






0.0 4.67 212 142 119 4.30 364 62.3 9.8 2.64 2.31 18.2 5.3 0.688 0.508 47.7 28.5 9.74 1.76 2.04 1.87

1.2 4.65 215 144 120 4.44 377 62.8 9.9 2.65 2.32 18.2 5.5 0.694 0.514 47.6 28.8 9.74 1.82 2.05 1.87

2.4 4.64 217 146 121 4.58 390 63.3 9.9 2.66 2.33 18.2 5.6 0.700 0.518 47.6 29.0 9.74 1.88 2.05 1.87

3.6 4.62 219 147 122 4.71 403 63.8 10.0 2.67 2.33 18.2 5.8 0.705 0.522 47.5 29.2 9.74 1.93 2.05 1.87

4.8 4.61 222 149 123 4.85 416 64.4 10.1 2.68 2.34 18.2 6.0 0.710 0.525 47.5 29.3 9.74 1.99 2.06 1.87

6.0 4.59 224 150 123 4.98 429 64.9 10.2 2.69 2.35 18.2 6.1 0.714 0.528 47.5 29.5 9.74 2.05 2.06 1.87

7.2 4.58 226 152 124 5.11 441 65.5 10.3 2.70 2.36 18.2 6.3 0.717 0.531 47.5 29.6 9.74 2.11 2.07 1.87

8.4 4.57 228 153 125 5.25 454 66.0 10.4 2.71 2.36 18.2 6.5 0.720 0.533 47.6 29.8 9.74 2.16 2.07 1.87

9.6 4.55 230 154 125 5.38 467 66.6 10.5 2.71 2.37 18.2 6.7 0.722 0.534 47.6 29.9 9.74 2.22 2.08 1.87

10.8 4.54 232 155 126 5.51 479 67.1 10.6 2.72 2.37 18.2 6.8 0.724 0.536 47.7 30.0 9.74 2.28 2.08 1.87

12.0 4.53 234 157 126 5.64 492 67.7 10.7 2.72 2.37 18.2 7.0 0.726 0.536 47.8 30.1 9.74 2.33 2.09 1.87

13.2 4.52 236 158 126 5.78 504 68.3 10.8 2.73 2.37 18.2 7.2 0.727 0.537 47.9 30.2 9.74 2.39 2.09 1.87

14.4 4.51 238 159 127 5.91 517 68.9 10.8 2.73 2.38 18.2 7.3 0.728 0.537 48.0 30.3 9.74 2.45 2.09 1.87

15.6 4.49 240 160 127 6.04 529 69.5 10.9 2.73 2.38 18.2 7.5 0.728 0.537 48.1 30.4 9.74 2.50 2.10 1.87

16.8 4.48 242 161 127 6.17 541 70.1 11.0 2.73 2.38 18.2 7.7 0.728 0.537 48.2 30.5 9.74 2.56 2.10 1.87

18.0 4.47 243 162 128 6.30 553 70.7 11.1 2.73 2.38 18.2 7.8 0.728 0.537 48.3 30.6 9.74 2.61 2.11 1.87

19.2 4.46 245 163 128 6.42 566 71.3 11.2 2.74 2.38 18.2 8.0 0.728 0.536 48.5 30.6 9.74 2.67 2.11 1.87

20.4 4.45 247 164 128 6.55 578 71.9 11.3 2.73 2.38 18.2 8.2 0.728 0.535 48.6 30.7 9.74 2.72 2.11 1.87

21.6 4.44 248 165 129 6.68 590 72.5 11.4 2.73 2.38 18.2 8.3 0.727 0.534 48.8 30.7 9.74 2.78 2.12 1.87

22.8 4.43 250 166 129 6.81 602 73.1 11.5 2.73 2.37 18.2 8.5 0.726 0.533 48.9 30.8 9.74 2.83 2.12 1.87

24.0 4.42 251 167 129 6.94 614 73.7 11.6 2.73 2.37 18.2 8.7 0.725 0.531 49.1 30.8 9.74 2.88 2.13 1.87

25.2 4.41 253 168 129 7.06 626 74.4 11.7 2.73 2.37 18.2 8.8 0.724 0.530 49.3 30.9 9.74 2.94 2.13 1.87

26.4 4.40 254 168 129 7.19 637 75.0 11.8 2.73 2.36 18.2 9.0 0.723 0.528 49.4 30.9 9.74 2.99 2.13 1.87

27.6 4.39 256 169 129 7.31 649 75.6 11.9 2.72 2.36 18.2 9.1 0.721 0.527 49.6 31.0 9.74 3.05 2.14 1.87

28.8 4.39 257 170 130 7.44 661 76.3 12.0 2.72 2.36 18.2 9.3 0.720 0.525 49.8 31.0 9.74 3.10 2.14 1.87

30.0 4.38 259 171 130 7.56 673 76.9 12.1 2.72 2.35 18.2 9.5 0.718 0.523 50.0 31.0 9.74 3.15 2.14 1.87

31.2 4.37 260 172 130 7.69 684 77.6 12.2 2.71 2.35 18.2 9.6 0.716 0.521 50.2 31.0 9.74 3.20 2.15 1.87

32.4 4.36 261 173 130 7.81 696 78.2 12.3 2.71 2.34 18.2 9.8 0.714 0.519 50.4 31.1 9.74 3.26 2.15 1.87

33.6 4.35 263 173 130 7.93 707 78.9 12.4 2.71 2.34 18.2 9.9 0.712 0.517 50.6 31.1 9.74 3.31 2.15 1.87

34.8 4.34 264 174 130 8.06 719 79.5 12.5 2.70 2.33 18.2 10.1 0.710 0.515 50.8 31.1 9.74 3.36 2.16 1.87

36.0 4.33 265 175 130 8.18 730 80.2 12.6 2.70 2.33 18.2 10.2 0.708 0.513 51.0 31.1 9.74 3.41 2.16 1.87

37.2 4.33 267 176 130 8.30 742 80.9 12.7 2.69 2.32 18.2 10.4 0.706 0.511 51.2 31.1 9.74 3.47 2.16 1.87

38.4 4.32 268 176 130 8.42 753 81.5 12.8 2.69 2.32 18.2 10.6 0.704 0.509 51.4 31.1 9.74 3.52 2.17 1.87

39.6 4.31 269 177 130 8.54 764 82.2 12.9 2.68 2.31 18.2 10.7 0.702 0.506 51.6 31.2 9.74 3.57 2.17 1.87

40.8 4.30 270 178 130 8.66 776 82.9 13.0 2.67 2.31 18.2 10.9 0.700 0.504 51.8 31.2 9.74 3.62 2.17 1.87

42.0 4.30 272 178 130 8.78 787 83.6 13.1 2.67 2.30 18.2 11.0 0.697 0.502 52.0 31.2 9.74 3.67 2.18 1.87

43.2 4.29 273 179 130 8.90 798 84.2 13.2 2.66 2.29 18.2 11.2 0.695 0.499 52.2 31.2 9.74 3.72 2.18 1.87

44.4 4.28 274 180 130 9.02 809 84.9 13.3 2.66 2.29 18.2 11.3 0.693 0.497 52.4 31.2 9.74 3.77 2.18 1.87

45.6 4.27 275 180 130 9.14 820 85.6 13.4 2.65 2.28 18.2 11.5 0.691 0.495 52.6 31.2 9.74 3.82 2.19 1.87

46.8 4.27 276 181 130 9.26 831 86.3 13.5 2.64 2.27 18.2 11.6 0.688 0.493 52.8 31.2 9.74 3.87 2.19 1.87

48.0 4.26 278 182 130 9.37 842 87.0 13.7 2.64 2.27 18.2 11.8 0.686 0.490 53.0 31.2 9.74 3.92 2.19 1.87

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A THEORETICAL MODEL OF NITRIFICATION IN FLOATING-BEAD FILTERSnsgl.gso.uri.edu/lsu/lsux97004.pdf · A THEORETICAL MODEL OF NITRIFICATION IN FLOATING-BEAD FILTERS by ... pound cost