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OXYGEN TRANSFER IN TRICKLING FILTERS

By Bruce E. Logan ~

ABSTRACT: Insufficient oxygen transfer can result in anaerobic biofilms and odor generation during biochemical oxygen demand (BOD) removal in trickling filters, and can limit ammonia oxidation in nitrifying trickling filters. Since oxygen transfer to biofilms in plastic media trickling filters occurs by diffusion of oxygen through thin fluid films, previous models used solutions based on penetration theory to calculate BOD removal. However, it is shown in this paper that penetration theory is not valid for typical hydraulic conditions in trickling filters since oxygen can diffuse through the fluid film and reach the biofilm surface. As a result, numerical solutions are required to solve the equations describing oxygen mass transport to the biofilm. Computer models are therefore used to calculate the maximum oxygen transfer during BOD and ammonia oxidation in plastic media trickling filters. These models can be used by design engineers to minimize conditions that may cause odor generation in trickling filters, and to provide an upper limit to the efficiency of nitrifying trickling filters.

INTRODUCTION

Trickling filters, or biotowers, continue to be an impor tant t rea tment technology for domest ic and industr ial wastewaters . Fur the rmore , the overall efficiency of biochemical oxygen demand (BOD) removal can be en- hanced when sludges from clarifiers are combined with tower effluent in a trickling filter/solids contact (TF/SC) process (Norris et al. 1982). Plastic media towers are also being increasingly used for nitrification of wastewaters (Parker et al. 1989b).

Early trickling filter design models for B O D removal , such as the Nat ional Research Council (NRC) and Velz equat ions, were based on the assumption that microbial kinetics l imited substrate removal (Logan et al. 1987b). In the last 20 -30 years, several models have challenged this assumption, show- ing that diffusion through the thin film, or mass transfer of substrate to the biofilm could be limiting B O D removal in trickling filters (Swilley and At - kinson 1963; Maier et al. 1967; Kissel 1986; Logan et al. 1987b). The most recent generat ion mass transfer models rely on numerical solutions of kinetic and transport equations (Logan et al. 1987b; Hinton 1989). The computer model developed by Logan et al. (1987b) successfully predic ted soluble B O D (SBOD) removal at several pilot- and full-scale t rea tment plants. The application of this model to trickling filter design has resolved several design issues. For example , kinetic models predict that for a given volume of plastic media, taller towers will remove a larger fraction of appl ied BOD. Similar calculations using mass transfer models , however , predict a very small increase in B O D removal using tal ler towers (Logan et al. 1987a). Al though it is now recognized that tower height has little effect on t rea tment efficiency, the continued use of kinetic models has required that kinetic "constants"

tEnvir. Engrg. Program, 206 Civ. Engrg. Building, Dept. of Chemical and Envir. Engrg., Univ. of Arizona, Tucson, AZ 85721.

Note. Discussion open until May 1, 1994. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on February 3, 1992. This paper is part of the Journal of Environmental Engineering, Vol. 119, No. 6, November/December, 1993. �9 ISSN 0733-9372/93/0006-1059/$1.00 + $.15 per page. Paper No. 3391.

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be adjusted as a function of tower height to correct the model (WEFManual of Practice 1992).

The calculation of oxygen transfer in a trickling filter (TF) used for either BOD removal or nitrification (nitrifying trickling filter [NTF]) is not adequately addressed in trickling filter design manuals and textbooks (WEF manual of practice 1992; Metcalf and Eddy 1991). The only model widely available to calculate oxygen transfer to plastic media TFs was developed by Mehta et al. (1972). The application of this model successfully accounted for BOD removal at three wastewater treatment plants. However, as will be shown below, Mehta's model was based on a solution of a transport equation (penetration theory) that is invalid for the operating conditions in most TFs and NTFs.

Oxygen transfer in TFs is an important design criterion since BOD removal in excess of oxygen availability to the biofilm can create anaerobic conditions and cause odors (Logan et al. 1989b), and in NTFs, can limit process efficiency (Parker et al. 1989a). Logan et al. (1987a) used a computer model to assess oxygen transfer to biofilms, and argued that since the observed rate of BOD removal exceeded the maximum rate of oxygen transport, it was unlikely that oxygen transfer would limit BOD removal in trickling filters treating domestic wastewater. However, it is apparent that the issue of oxygen transfer has not been adequately addressed (Hinton and Stensel 1989; Logan et al. 1989; Logan and Parker 1990).

There are two main objectives of the present study. The first is to show that calculations made by Mehta et al. (1972) cannot be used for calculating oxygen transfer to trickling filter biofilms despite claims and calculations by those authors. The second is to provide design procedures for calculating the maximum rate of oxygen transfer in TFs and NTFs. Establishing maximum rates will provide operators and engineers a basis for calculating the efficiency of treatment systems.

METHODS

M e h t a M o d e l The calculation of oxygen to thin fluid films covering plastic media was

made by Mehta et al. (1972) using penetration theory, which is an analytical solution of gas absorption by a laminarly flowing film on a wetted-waU column. According to Mehta et al. (their Equation 8), the concentration profile of oxygen in the liquid film is:

Co(X , Z) __ ( 6 V o L ~1/2

c; ....................................... (:)

where Uavg = the average fluid velocity. Eq. (1) is incorrect, however, since it is dimensionally inconsistent: the left side of the equation is dimensionless, while the right side has dimensions of L 4 M-1. According to penetration theory, the correct concentration profile (Bird et al. 1960; Logan and Her- manowicz 1987) is:

Co(X , Z) - - C o , i n = erfc 1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) C~ - Co.i,, 4

L \ ~ a x / J

where the maximum velocity, v . . . . is equal to ( 3 / 2 ) V . v g , x = the distance

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from the air-liquid interface, and z = the distance of flow from the fluid entrance. The name given to this theory is derived from an assumption made to allow an analytical solution of the governing transport equation. The assumption is that the fluid velocity is constant, and equal to V=ax, if the gas absorbed by the fluid does not penetrate very far from the air-liquid interface. Therefore, penetration theory is only valid in the case of oxygen transfer into wetted films when oxygen penetration into the fluid is minimal. As will be shown below, this assumption is not valid for oxygen transfer to plastic media trickling filters.

Mehta et al. (1972) used penetration theory to derive an equation for oxygen transfer in terms of a mass transfer coefficient calculated (their equation 9) as:

/ x 1/2

k = \ ~ p L / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

where k = a mass transfer coefficient, Do = diffusivity of oxygen in the water, T = the hydraulic loading, p = the water density, ~ = the fluid film thickness, and L = the length of uninterrupted flow. Although (3) was derived in the original paper by Mehta et al. (1972) solutions of concentration profiles and mass transfer were readily available at the time in a standard mass transfer text (Bird et al. 1960).

The original expression used by Mehta et al. (1972) to calculate oxygen transfer into the liquid was not explicitly derived. In this paper the maximum overall rate of mass transfer to the biofilm, Ro, is calculated for the Mehta model using the definition of the mass transfer coefficient in (3); as:

( 6gl/3 ]l/2(DoL)l/2w2/3Ql/3(C~- Co,in) g 0 = ~K31/2,lTvl/31 . . . . . . . . . . . . . . . . . . (4 )

where g = the gravitational constant, v = the fluid viscosity, w = the width of a plate (or the wetted perimeter), Q = the applied flowrate, C~ = the saturation oxygen concentration, and Co,in = the bulk liquid concentration of oxygen entering the plate. The total oxygen transfer into the liquid can be calculated from the product of the number of modules, the surface area per module, and the oxygen flux. Eq. (4) provides the same solutions as those in Mehta et al. (1972) if it is assumed that C0,i, is zero at the entry to each module in a trickling filter.

Oxygen Transfer Model: BOD Removal in TFs Chemical transport in fluid films is calculated by numerically solving the

transport equation

OC D - - 02C - v (x ) __OC ~--7 = Ox ~ o z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5) where C = the concentration of the chemical, which can be oxygen, substrate, or ammonia, and v (x ) = the parabolic velocity profile in the liquid film. Details of the numerical approach have appeared elsewhere (Logan 1986; Logan et al. 1987b).

For substrate (BOD) removal, the three boundary conditions used in the original TF model (Logan et al. 1987b) were:

C, = Cs, in at z = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

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Fs = 0 a t x = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

Fs = (klsDs)v2C~ at x = 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)

where Fs = the substrate flux and kls = a first-order rate constant that was assumed to be a function of substrate diffusivity, according to the equation kas = 4"uDsEsn, where n = the number concentration of cells in the biofilm calculated from n = 3(1 - p)/(4~ra3). The diffusion coefficient is corrected for temperature by the usual assumption that D ~ / T is constant (Welty et al. 1976). The collector efficiency, EB, was determined to be 0.0035 from model calibration assuming values of 0.8 for the porosity, p, and 1 I~m for the cell radius, a. Using these values and equations, the third boundary condition becomes:

1/2

[ 3EB(1 - P) D, C~ at x = ~ . . . . . . . . . . . . . . . . . . . . . . . (9) Fs= L

The substrate flux, which is the sum of five different B O D components, is therefore based on a first-order kinetic model that has a rate constant that is a function of diffusivity to the first power, rather than the half power, as previously discussed (Logan 1986; Logan et al. 1987b; Logan et al. 1989). This dependence of the kinetic constant on the diffusion coefficient results in kinetic rate constants that decrease with increasing molecular weight. This result is reasonable since high molecular weight substrates must be hydrolyzed before incorporation into the cell. The kinetic model, which is based on mass transfer correlations, has also been used to demonstrate the effect of fluid motion on bacterial kinetics (Logan and Dettmer 1990; Logan and Kirchman 1991; Confer and Logan 1991).

Oxygen transfer is calculated using (5) and the boundary conditions:

C = Co.i, at z = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10)

C = C~ a t x = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

F0 = Fs (Fs-<F0 . . . . ) a t x = 8 . . . . . . . . . . . . . . . . . . . . . . . . (12a)

F0 = F0 . . . . (Fs > Fo . . . . ) at x = 8 . . . . . . . . . . . . . . . . . . . . . (12b)

where F0 and F0 . . . . are the actual and maximum oxygen fluxes into the biofilm. When Fs is less than the maximum rate of oxygen transfer into the biofilm, F0 is calculated from the total substrate flux by assuming a 1:1 ratio of substrate (as BOD) to oxygen. Previous investigations of heavily loaded trickling filters have shown that at most trickling filters treating domestic wastewater BOD removal can exceed the maximum oxygen transfer to a biofilm (Logan et al. 1987a). Therefore, if the amount of BOD removed in the biofilm is larger than the oxygen flux, the oxygen flux into the biofilm is calculated as the maximum oxygen flux using the oxygen gradient at the biofilm-liquid interface, or Fo(x = 8) = -Do(OCo/OX).

The maximum oxygen transfer can be computed by setting the B O D to be a very large number (i.e., 1,000 mg L-a) , and by summing the oxygen flux into the biofilm during the fluid flow along the plate. At the end of each module, or for cross-flow media at each mixing point, the fluid is assumed to be completely mixed and the dissolved oxygen concentration entering a successive plate is calculated from the average oxygen concentration leaving the previous plate. As a result, the steady state solution for

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(5) must be solved for each new entering fluid concentration and this calculation must be repeated for each successive module or plate. This can result in a substantial amount of computing time (several hours on a 80286 PC) for applied wastewaters with different dissolved oxygen concentrations.

Oxygen Transfer Model: Ammonia Oxidation in NTFs For nitrification, kinetic constants are well studied and the boundary

condition in (8) can be modified to reflect these kinetics. The rate of nitrification, dCN/dt, is:

dCu ~X dt YX/N

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 3 )

where CN = the ammonia concentration, X = the concentration of nitrifying microorganisms, and YX/N = a yield coefficient. The growth rate, I~, is usually assumed to follow Michaelis-Menten kinetics, and can be related to ammonia concentration from ~ = ~CN/(KN + CN). A simpler form, which yields a closed-form analytical solution to the flux, is to assume that first order kinetics for CN < 2KN, and zero-order kinetics for CN >- 2KN. With these assumptions, the ammonia flux (N-flux) can be calculated using standard solutions for CN < 2KN as:

( g X ,]1/2 FN = \K--7~m] D~N/2CN at x = 8 . . . . . . . . . . . . . . . . . . . . . . . . (14)

while the ammonia flux for CN -> 2KN is:

(20~X] 1/2 Fu = \Yx/N, I (DNCN) 1/2 a t x = 6 . . . . . . . . . . . . . . . . . . . . . . . . (15)

Oxygen transfer is calculated as above. By setting the ammonia concentration to be very high, the maximum oxygen transfer can be computed by summing the oxygen flux into the biofilm during the fluid flow along the plate at steady state. Since the oxygen concentrations vary from module to module, this calculation must be iterated, as just described, with successive modules in an NTF. The constants used in this model are summarized in Table 1.

TABLE 1. Parameters Used in Nitrifying Trickling Filter Model to Calculate Max- imum Rate of Oxygen Transport into Biofilm

Parameter Value (1) (2)

ON Do Ku T X YO/N Y~/N #

1.71 x 10 -s cm 2 s - ' 2.0 x 10 - S c m 2s 1

2.5 mg L -1 20~

40,000 mg-VSS L - '

4.33 mg-O2 mg-NHi -~ 0.02 mg-VSS mg-NH~-' 0.77 d -~

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RESULTS

Oxygen Transfer Using Mehta Model The limitations of the Mehta model are best illustrated using an example

calculation (example 1) from their original paper (Mehta et al. 1972). A 1.5-m2-by-5.5-m-deep (16-sq fl-by-18-fl) trickling filter containing 121 m g m -3 vertical flow media (VF121), which has a wetted perimeter of 1,127 cm per 60-cm-deep module, was loaded at 1.26 L m -g s -1 (1.85 gpm f t - : ) with wastewater containing 279 mg-BOD L-1. The effluent contained 92 mg-BOD L -1, achieving an overall removal of 187 mg-BOD L -1 (67%). Using (4), with D = 2.1 x 10 -5 cm 2 S - ] , V = 0.0089 cm 2 s -a, and C* = 8.54 mg L -1 at 25~ yields 16.2 g-O2 m -2 d -1 , o r a removal (without recycle) of 99.3 mg-BOD L - t. Since there was 50% recycle, the final effluent BOD would be 80 mg L -1 or 199 mg L -1 removed. Mehta et al. (1972) calculated 197 mg-BOD L -1 removed (71%) using their equation based on penetration theory.

The fact that predicted removal by Mehta et al. (1972) is close to the observed removal does not prove, by itself, that their model is valid. Closer examination of the results indicates that Mehta et al.'s method cannot be accepted. The dissolved oxygen concentration in the fluid film, nondimensionalized by the saturation oxygen concentration, is shown in Fig. I at three points along the length of flow through the plastic media module. The fluid

OF. 0"9i/'k" < 0.8- ' t r ,

0.7 Z O 0.6 I-" < 0.5 tr"

I.- 0.4- z LLI o 0.3- z 0 0.2- O 0 0.1- a 0

0

FIG. 1.

\ ,

"-%

"%

"" , , 11.3 cm

%,

1.63 cm

60 cm

i i ! i i i

20 40 60 80 100 120 DISTANCE INTO FLUID, p,m

140

Dissolved Oxygen Concentration Ratio (Co/C~) as Function of Distance into Fluid (from Air-Water Interface) Calculated Using Penetration Theory for Ver- tical-Flow (VF121) Media (1.26 L m -2 s -~, 25~ at Three Locations along 60-cm- Long Plate: z = 1.63, 11.3 and 60 cm

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film thickness, based on the above hydraulic loading, is 129 ixm. The concentration profile was calculated based on penetration theory using (2). After moving only 1.63 cm down the module, dissolved oxygen is 1% of C* halfway to the biofilm. According to penetration theory, however, oxygen cannot "penetrate" very far into the liquid, or the theory is not valid (Bird et al. 1960). Mehta et al. (1972) imply that their solution is valid as long as the oxygen concentration at the liquid-biofilm interface is not greater than 0.02 C*. However, this condition is met after fluid has reached 11.3 cm (Fig. 1). By the time the fluid has reached the end of the module (60 cm), the concentration at the liquid-biofilm interface is 0.4 C*, which is clearly greater than the range for which penetration theory could be con- sidered valid.

The finding by Mehta et al. (1972) that BOD removal was similar to their calculated oxygen transfer does not require the system to be limited by oxygen. The use of other models, not based on oxygen-limited BOD removal, yields similar estimates of BOD removal. For example, the modified Velz model (WEF manual of practice 1992) yields 77% removal using a kinetic (k20) constant of 0.0014 (L m -2 S-1) ~ and a temperature correction factor of 1.035. Although the TF model of Logan et al. (1987b) was developed to predict SBOD removal, input of the total BOD into the model results in a predicted removal comparable to the BOD removal reported above. The TF model predicts an effluent BOD of 100 mg L -1, or 67% BOD removal, versus the observed effluent BOD of 92 mg L -1 (63% removal). Therefore, these other models provide reasonable predictions of tower performance without assuming that BOD removal is limited by oxygen transfer to the biofilm.

There are two other problems with using the Mehta model. First, fluid entering successive modules in a trickling filter will not be devoid of oxygen. The calculations by Mehta et al. (1972) calculations, however, assume that wastewater entering each module is devoid of oxygen. This assumption is inconsistent with their own calculation that wastewater leaving a trickling filter could contain an oxygen concentration of (5/8)C* even though the biofilm was limited by oxygen. The second limitation of the Mehta model is that it does not account for the fact that if fluid entering a module contains dissolved oxygen, an oxygen gradient will develop at the biofilm-liquid interface and will extend into the liquid. This has the effect of accelerating oxygen transport into the biofilm by increasing the oxygen gradient at the liquid-biofilm interface, and therefore, increasing the overall oxygen flux into the biofilm.

Oxygen Transfer Using Numerical Solution

Effect of Applied Dissolved Oxygen Concentration on Oxygen Transfer

The main differences between penetration theory and a numerical solution of oxygen transfer using the constituent transport equation is the ability in a numerical model to incorporate oxygen utilization by the biofilm and allow for a parabolic velocity profile. Shown in Fig. 2 are the DO profiles at a distance 30 cm and 60 cm along a typical 100 m 2 m -3 vertical flow media (VF100) loaded at 0.68 L m -2 s -1, calculated for the maximum rate of oxygen transfer in a TF. In one case [Fig. 2(a)] the influent stream is saturated with oxygen, while in the second case [Fig. 2(b)] the influent stream initially contains no dissolved oxygen. In both cases, the DO profiles

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O I Za [ C=.i,, = 8.8 mg/I

i

6o2~.., ", ...... \

O (A)

Qo 2'0 40 6'0 80 160 120 140 DISTANCE INTO FLUID, i~m

10 I o) l c..,, = o mg/I

4 \ "',,. 1.2 crd" .... " ' . . ""',~ 60 cm

0 \ ~. " .... Z \ "% "~ 0 " 0.6 era ..... " ....

0 2"

a (B)

0 0 2'0 4o 6o 8'0 160120140 DISTANCE INTO FLUID, i~rn

FIG. 2. Dissolved Oxygen Concentration as Function of Distance into Fluid from Air-Water Interface, Calculated Using TF Computer Model (VF100 Media, 0.8 L m-2 s -1, 20~ at Distances of Flow along Plate of 0.6, 1.2, and 60 cm: (a) Applied Wastewater is Saturated with Oxygen; and (b) Applied Wastewater is Devoid of Oxygen

at the end of the module are near ly identical. These profiles are shown in three dimensions along the length of flow in Fig. 3. It can be seen that the initial oxygen concentrat ion at the top of the tower has little effect on the total dissolved oxygen concentra t ion after the first module .

The total amount of oxygen transferred in a module of vertical-flow and cross-flow media is shown in Fig. 4 for three cases. The first two cases are as just presented, in which the fluid entering is saturated with oxygen or the fluid entering is devoid of oxygen. In the third case, the dissolved oxygen is entering at a steady state concentration, or an average concentration leaving modules

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ml

E Z

t

(

10

.-,t

~- B- Z

5"

(B)

FIG. 3. Three-Dimensional Profile of Dissolved Oxygen: (a) Applied Wastewater is Saturated with Oxygen; and (b) Applied Wastewater is Devoid of Oxygen; Air- Liquid Interface Is at Fluid Depth of 0; Fluid Enters Plate at z = 0, and Leaves at z = 1 (Distances in Fluid and along Plate are Nondimensionalized by Fluid Thick- ness and Plate Length); See Fig. 2 for Conditions

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"10

E

uJ

Z < 0E

Z uJ (.9

0

15'

10

5

VFIO0

Saturated

' \ \ ~ _ ~ d y State

" " " ' - . . . Devoid

(A) 0 0.0 015 110 11s 210 2.5

HYDRAULIC LOADING, L m ~ d "1

15"

E o

10" LLI LL O9 Z < n" P" 5 Z LU (..9

0

X F 9 8 ~ a t e d

Devoid

(B) 0 o.o o'.s i'.o 1'.s

HYDRAULIC LOADING,

2',0 2.5

L m ~ d "1

FIG. 4. Effect of Influent Oxygen Concentration (Saturated, Steady-State, or De- void) on Total Amount of Oxygen Used by Biofilm in Single Module of: (a) VF100 Media; and (b) XF98 Media (20~

further down in the trickling filter. The steady-state concentration was determined by calculating the DO concentrations entering and leaving a series of modules until the DO concentrations leaving adjacent modules were identical. For example, at 0.68 L m -2 s-1 if the wastewater is initially devoid of oxygen, the effluent from the first module will contain 6.0 mg-O2 L-1, resulting in an overall aerobic removal of 7.7 mg-BOD L - ~. Wastewater leaving the second module will also contain 6.0 mg-O2 L 1. The overall aerobic removal in the second module is the steady-state removal of 9.6 mg-BOD L-~ module-~.

Effect of Kinetic Model on Maximum Oxygen Transfer The aforementioned numerical examples were calculated for oxygen

transport during BOD removal. If the influent concentration of oxygen is

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7 o 20 N

E t~

15

uJ U.

~. 10" < QC F-

Z 5- LU

>. X 0

"7, "O ? E

u.I ii r z < t~ I '- z ud

>- x 0

20

XF138

VF92

(A)

~ o'.5 1'.o 1'.5 2:o 2.5 HYDRAULIC LOADING, L m -z d "

15

10

XF138

" ' ~ VF100

~ ~ , 5-

VF~2

(B)

~ o:5 1:o 115 2:0 2.5 HYDRAULIC LOADING, L m "z d "1

"7 "o 20" N. E t~

15" I.I1.1 tL

z 10

I-- z ua 5- (..-3 >- x O

XF~ (NTF)

(C)

~ o~s 1'.o l:s 2:o zs HYDRAULIC LOADING, L m "z d "1

FIG. 5. Maximum Oxygen Transfer Rates for Different Plastic Media, Assuming Steady-State Removal Levels in Trickling Filter Using Different Models (20*(3): (a) Rates during SBOD Removal in Trickling Filter; (b) Rates in Nitrifying Trickling Filter; (c) Comparison of Two Media (XF98 and VFIO0) for TF and NTF Models

defined as the steady-state concentration, the maximum amount of oxygen transport into four different media can be calculated, as shown in Fig. 5(a). This oxygen flux can be compared with the maximum oxygen flux calculated using the nitrification model in Fig. 5(b). There is only a small difference

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"7, -O

E

15

~ XF 138

~ X F 9 8

1 0 - . " I~'VF10o L U o~ ~ ~

03LL .~ ~- . . . 1 ' ' ' ~

Z . . - . . . . . . V F 9 2 . . ~~176

~ o '~176 ~ ~ 1 7 6 I f " ..... ""

Z 5' U J

(.9 >. X O

0 ' 2'0 ' 0 10 3 0 4 0

T E M P E R A T U R E , ~ FIG. 6. Maximum Oxygen Transfer Rates for Different Plastic Media, Assuming Steady-State Removal Levels in a Trickling Filter as a Function of Temperature (0.68 L m -= s--l).

in maximum oxygen transfer determined using the two models [Fig. 5(c)]. This is due to the fact that very little oxygen is present at the biofilm surface (i.e., Fig. 3). In both cases, the oxygen flux is limited by oxygen transport through the thin film.

Effect of Temperature The maximum possible rate of oxygen transfer is not predicted to sub-

stantially change with changes in temperature. As shown in Fig. 6, the maximum rate of oxygen transfer increases only 14% for XF98 media, and 34% for VF100 media, between 10~ and 30~ using the BOD model. Similar changes are calculated for the nitrification model. The increase in oxygen transfer is due to an increase in oxygen diffusivity and a decrease in fluid film thickness. Although the detention time of fluid on media de- creases with increased temperature, this effect on the rate of oxygen transfer is calculated to be less important than changes in diffusion coefficients and fluid thickness.

ANALYSIS

Oxygen rapidly penetrates thin fluid films covering biofilms in plastic media trickling filters. In order to use penetration theory, oxygen should not penetrate far enough into the liquid to invalidate the assumption that the fluid velocity is constant and equal to the maximum velocity. However,

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oxygen from the air-liquid interface diffuses to the biofilm surface under typical hydraulic conditions in trickling filters. Therefore, the total oxygen flux cannot be calculated using the model by Mehta et al. (1972) based on penetration theory since the assumptions required for this analytical solution cannot be met in trickling filters. The Mehta model is also inaccurate since the oxygen concentration boundary layer above the biofilm will increase the oxygen gradient at the air-liquid surface, and this will accelerate oxygen transfer into the biofilm.

Numerical models, however, can be used to calculate the maximum oxygen flux to biofilms in plastic media trickling filters. Parker et al. (1989a) hypothesized that oxygen transfer limited the rate of ammonia oxidation in NTFs. Using the BOD-based oxygen transfer numerical model, they calculated the maximum amount of ammonia transformation from the maximum oxygen flux using a conversion factor of 4.3 g-NH3-N/g-O2. They found that observed nitrification rates at several treatment plants were within the range predicted based on oxygen-limited transfer. Parker et al. also suggested that maintaining thick nitrifying biofilms, through biofilm-control or periodic flooding, was critical for maintaining nitrification at the maximum rate. Much lower nitrification rates than the maximum have been observed due to biofilm consumption by predators, dry spots on media (incomplete wetting), and to excess BOD in the applied wastewater (Gujer and Boiler 1983; Logan and Parker 1990). In the latter instance, heterotrophs growing in the biofilm can be expected to grow faster and out-compete slower growing nitrifiers for oxygen in the biofilm.

The kinetic model used to calculate the substrate flux into the biofilm has little effect on the maximum rate of oxygen transfer to the biofilm. It was shown using two different kinetic models (Fig. 5) that similar maximum rates of oxygen transfer (within _+ 10%) into the biofilm were predicted by both models. Therefore, the diffusion of oxygen through the liquid limits the maximum amount of oxygen transfer. The actual rate of oxygen transfer can be less than the maximum for several reasons. First, a reduction in biofilm kinetics would decrease oxygen utilization to less than the maximum rate. Kinetic rates typically halve with a 10~ decrease in temperature. In pilot- and full-scale NTFs, Parker et al. (1986b) cites a 50% increase in average nitrification rates in an NTF over a temperature range of 10-20~ The NTF model just presented, however, predicts only a 15% increase in the maximum rate with temperature. The increased rate of nitrification documented by Parker et al. (1989b) is likely not only a result of the decreased activity of the biofilm at lower temperatures, but could also be a function of factors not investigated such as changes in biofilm thickness, wastewater composition (i.e., BOD loads), and media wetting.

Recently, other investigators (Hinton 1989; Hinton and Stensel 1991) have suggested that the fluid interruptions in TFs occur not through stream intersection in cross-flow media, but through fluid disruptions by drops generated by stalactites formed by microorganisms. The number and im- portance of these stalactites is hypothesized to vary with media, plant lo- cation, wastewater composition, and probably numerous other factors. In Hinton's model, fluid interruptions are modeled to have the same effect as those included in the above analysis. However, stalactites were only observed in TFs, and it is not known if thinner biofilms obtained in NTFs would similarly generate stalactites. Until methods become available to predict, a priori, the number of interruptions per module generated by stalactites, it is likely that the calculations presented above in this paper will

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continue to be useful for design and for increasing our understanding of oxygen transfer in TFs and NTFs.

Using the numerical model just presented, the effect of a variable number of interruptions on oxygen transfer can be determined. For the conditions of 0.68 L m -2 s -1, no recycle, and 20~ the maximum oxygen transfer was calculated for a hypothetical module of media having a constant specific surface area of 100 m 2 m -3. As shown in Fig. 7, oxygen transfer increases from 10.0 g-O2 m -2 d -1 for no interruptions, to 12.6 g-O2 m -2 d -1 with nine interruptions. This translates to an increase in removal of 10.5 mg- BOD L -1 to 13.3 mg-BOD L -1 per module. Therefore, a large number of interruptions could substantially increase oxygen transfer.

Another factor that limits high oxygen transfer rates in trickling filters is incomplete wetting of media. For example, in a pilot study using XF138 media, Parker et al. (1989) estimated that since 71 -99% of the maximum ammonia transformation was obtained, 1 - 2 9 % of the media was incom- pletely wet. Although these estimates are useful measures of efficiency, oxygen transfer is not a linear function of surface area as implied in the calculation. For example, at 0.68 L m -2 s -~ (1 gpm ft 2) a module of 98 m 2 m -3 cross-flow media has a maximum transfer aerobic removal of BOD of 18.2 mg L - L At 50% wetting, the change would be 9.2 mg L -1. This is only 8% larger, however, than the rate estimated as 50% of the oxygen rate at 0.68 L m -2 s -1 (9.10 mg L-~).

"T,

E E~

15

10' LU LL CO Z <: rr"

!,- 5 Z LU (.9

0

01 2 3 4 5 6 7 9 NUMBER OF INTERRUPTIONS

FIG. 7. Effect of Variable Number of Fluid Interruptions on Maximum Rate of Oxygen Transfer in Module of Plastic Media (0.68 L m -2 s - I , 100 m 2 m -3, 20~ Entering Wastewater Is Saturated with Oxygen)

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DESIGN CALCULATION

Trickling filters should be designed to maximize SBOD removal and to avoid problems with generation of odors by anaerobic processes. It has been demonstrated in previous examples (Logan et al. 1987a) that SBOD removal can exceed oxygen transfer if a sufficient pool of alternate electron acceptors are available in the wastewater (Logan et al. 1989). As a result, the deter- mination of oxygen transfer and SBOD removal is a two-step design process. First, SBOD removed should be claculated by assuming the oxygen transfer does not limit SBOD removal. This can be done using the TF model, as described by Logan et al. (1987a), based on (5)-(7) and (9). Second, the maximum rate of oxygen transfer can be calculated using the equations just presented, which can be computed using a model calculating the maximum rate of oxygen transfer (TFO), based on (5) and (10)-(12). These models are available from the writer as either complete FORTRAN programs or in a condensed version that completes calculations in several seconds, as opposed to several hours required in the original models.

As a design example, consider a 20-ft (10-module) trickling filter com- posed of XF98 media, loaded at 0.68 L m -2 s-1 and operating at 20~ with no recycle, with an influent SBOD of 100 mg L -1, and with wastewater entering the tower saturated with oxygen. Using the TF model, the effluent SBOD would be 26.6 mg L -1 (73.4% removal), with 13.2 mg L -1 of a SBOD removed in the first module. For the same conditions, oxygen transfer is sufficient to remove 12.0 mg-SBOD L-1 aerobically in the first module (assuming the wastewater entering the tower is saturated with oxygen). Therefore, the trickling filter would remove 1.2 mg-SBOD L-1 anaerobi- cally.

The total amount of SBOD removed in the top module can be reduced by providing wastewater recycle. If the SBOD can be decreased to 90 mg L-1, SBOD removal in the first module would be nearly equal to the total oxygen flux. Choosing a recycle ratio of 0.1 (0.75 L m-2 s-1 total hydraulic load) produces an effluent SBOD of 27.3 mg L - l ; for a primary clarifier BOD of 100 mg L -1, this produces an applied SBOD of 92.7 mg L -~, and a removal of 11.3 mg L-~ of SBOD in the first module. Assuming the tower effluent contains 6.2 mg L -~ of dissolved oxygen would produce a total applied wastewater containing 8.6 mg L-1. The TFO calculation indicates that a total of 11.0 mg L -~ could be removed aerobically. Since this is reasonably close to the calculated removal of SBOD, this should be sufficient oxygen transfer for the design calculation.

As long as oxygen transfer exceeds SBOD removal in the top module, oxygen transfer will be sufficient for lower modules in the tower. SBOD concentrations above 90 mg L -~ could either result in anaerobic removal of SBOD or, if no alternate electron acceptors were present in the wastewater, a decrease in SBOD removal. In addition, a series of calculations should be performed assuming other recycle ratios and primary clarifier dissolved oxygen concentrations to produce a reasonable range of performance within the expected design conditions of flow, temperature and SBOD concentrations. These calculations do not include oxygen demands associ- ated with particulate BOD, and it may be necessary to estimate this organic load on total oxygen consumption in the trickling filter.

It should not be concluded, without calculations, that because vertical- flow media are calculated to have a lower oxygen transfer efficiency than cross-flow media, that anaerobic removal of organic matter is more likely than with cross-flow media. Vertical-flow media are also predicted to remove

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SBOD less efficiently than XF media, thus necessitating a similar set of design calculations for VF media.

CONCLUSIONS

Although penetrat ion theory cannot be used to predict B O D removal in trickling filters, existing numerical models can be used to predict oxygen transfer to biofilms in plastic media trickling filters. The aforement ioned examples demonstrate that biofilm kinetics and tempera ture will have small effects on the max imum rate of B O D removal and nitrification, but that surface area (wettability and development of thick biofilms) and fluid disruptions can have large effects on trickling filter performance. Through the application of the trickling filter computer models, hydraulic loading and recycle rates can be chosen that eliminate conditions that may result in organics removal by anaerobic processes or conditions that limit trickling filter performance.

ACKNOWLEDGMENTS

This research was funded by National Science Foundation Grant No. BCS 8912893.

APPENDIX I. REFERENCES

Bird, R. B., Stewart, W. E., and Lightfoot, E. N. (1960). Transport phenomena. John Wiley and Sons, New York, N.Y.

Confer, D. R., and Logan, B. E. (1991). "Increased bacterial uptake of macro- molecular substrates with fluid shear." Appl. Environ. Microbiology, 57(11), 3093- 3100.

Gujer, W., and Boiler, M. (1983). "Operating experience with plastic media tertiary trickling filters for nitrification." Design and operation of large wastewater treatment plants. Bonder Ende and H. B. Tenchs, eds., Pergammon Press, Oxford, England.

Hinton, S. W. (1989). "A mechanistic model for the trickling filter process which considers the effects of both substrate and oxygen availability on substrate uptake kinetics," PhD thesis, University of Washington, Seattle, Wash.

Hinton, S. W., and Stensel, H. D. (1989). Discussion of "A fundamental model for trickling filter process design," by B. E. Logan, S. W. Hermanowicz, and D. S. Parker. J. Water Pollution Control Federation, 61(3), 363-364.

Hinton, S. W., and Stensel, H. D. (1991). Experimental observations of trickling filter hydraulics. Water Res., 25(11), 1389-1398.

Kissel, J. C. (1986). "Modeling mass transfer in biological wastewater treatment processes." Water Sci. Technol., 18, 35-45.

Logan, B. E. (1986). "Mass transfer models for microorganisms in aggregates and biofilms," PhD thesis, University of California, Berkeley, Calif.

Logan, B. E., and Dettmer, J. W. (1990). "Increased mass transfer to microorganisms with fluid motion." Biotechnol. Bioeng., 35(11), 1135-1144.

Logan, B. E., and Hermanowicz, S. W. (1987). "Application of the penetration theory to oxygen transfer to biofilms." BiotechnoL Bioeng., 29(6), 762-766.

Logan, B. E., Hermanowicz, W. W., and Parker, D. S. (1987a). "Engineering implications of a new trickling filter model." J. Water Pollution and Control Fed- eration, 59(12), 1017-1028.

Logan, B. E., Hermanowicz, S. W., and Parker, D. S. (1987b). "A fundamental model for trickling filter process design." J. Water Pollution Control Federation, 59(12), 1029-1042.

Logan, B. E., Hermanowicz, S. W., and Parker, D. S. (1989). Reply to Discussion of S. W. Hinton and H, D. Stensel. J. Water Pollution Control Federation, 61(3), 364-366.

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Logan, B. E., and Kirchman, D. K. (1991). "Increased uptake of dissolved organics by marine bacteria as a function of fluid motion. Marine Biology, 111(1), 175- 181.

Logan, B. E., and Parker, D. S. (1990). Discussion of "Nitrification performance of a pilot scale trickling filter," by H. A. Gullicks and J. L. Cleasby. Res. J. Water Pollution Control Federation, 62(7), 933-936.

Logan, B. E., Parker, D. S., and Arnold, R. G. (1990). "02 limitations in CH4- and NH4-utilizing biofilms." Proc. 1990 ASCE Conf. in Envir. Engrg., ASCE, Apr. 8-11, 31-38.

Maier, W. J., Behn, V. C., and Gates, C. D. (1967). "Simulation of the trickling filter process." J. Sanit. Engrg. Div., ASCE, 93(4), 91-112.

Mehta, D. S., Davis, H. H., and Kingsbury, R. P. (1972). "Oxygen theory in biological treatment plant design." J. Sanit. Engrg. Div., ASCE, 98(3), 471-489.

Norris, D. P., Parker, D. S., Daniels, M. L., and Owens, E. L. (1982). "Production of high quality trickling filter effluent without tertiary treatment." J. Water Pol- lution Control Federation, 54(7), 1087-1098.

Parker, D., Lutz, M., Dahl, R., and Bernkopf, S. (1989a). "Enhancing reaction rates in nitrifying trickling filters through biofilm control." J. Water Pollution Control Federation, 61(5), 618-631.

Parker, D. S., Lutz, M. P., and Pratt, A. M. (1989b). "New trickling filter appli- cations in the U.S." Proc. Conf. on Tech. Advances in Biofilm Reactors, Inter- national Association of Water Pollution Research and Control, Apr. 4-6.

Swilley, E. L., and Atkinson, B. (1963). "A mathematical model for a trickling filter." Proc. 18th Ind. Waste Conf., Purdue, Ind., 18, 706-732.

WEF manual of practice, No. 8. (1992). "Suspended-growth biological treatment." Design of municipal wastewater treatment plants, Water Environment Federation, Alexandria, Va.

Welty, J. R., Wicks, C. E., and Wilson, R. E. (1976). Fundamentals of momentum, heat and mass transfer. 2nd ed., John Wiley and Sons, New York, N.Y.

APPENDIX II. NOTATION

The following symbols are used in this paper:

a = radius of cell in biofilm (L); C = concentration of a substance (substrate, oxygen or nitrogen) in

fluid (M L-3) ; CN = concentration of ammonia (as nitrogen) in fluid (M L-3) , Co = concentration of dissolved oxygen in fluid (M L-3) ;

Co,in = bulk concentration of dissolved oxygen entering plate (M L 3); Co .... = bulk concentration of dissolved oxygen leaving plate (M L-3) ;

C~' = concentration of dissolved oxygen in fluid in equilibrium with air (M L - 3);

Cs = concentration of substrate in fluid (M L-3) ; Cs.in = bulk concentration of substrate entering plate (M L-3) ;

D = diffusion coefficient of substance in water (L a T- l ) ; DN = diffusion coefficient of ammonia in water (L 2 T-1); Do = diffusion coefficient of oxygen in water (L 2 T- l ) ; D, = diffusion coefficient of substrate in water (L ~ T- l ) ; FN = ammonia flux (M L -2 T - l ) ; Fo --- oxygen flux (M L -z T-X); Fs = substrate flux (M L -2 T 1); g = gravitational constant of acceleration (L T-2); k = mass transfer coefficient describing oxygen transfer into thin

fluid film under laminar flow conditions (L T- l ) ;

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k~, = first order rate constant describing rate of substrate utilization by biofilm (T- 1);

kN = first-order rate constant describing rate of ammonia utilization by nitrifying microorganisms in biofilm (T- t ) ;

L = length of uninterrupted travel of laminar fluid flowing over biofilm in trickling filter (L);

n = number concentration of cells in biofilm (L-3); p = porosity of biofilm; Q = hydraulic flow rate of liquid applied to trickling filter (L 3 T-a);

R0 = maximum rate of oxygen transfer to laminarly flowing fluid (M T- l ) ;

SBOD = soluble biochemical oxygen demand (M L-3); T = temperature (~ t = time (T);

VF = abbreviation for vertical-flow media, where number indicates specific surface area of media;

vavg = average velocity of water in thin fluid film (L T- l ) ; v,,ax = maximum velocity of water in thin fluid film, equal to 3 Vavg/2

(L T - l ) ;

v(x) = velocity of water in thin fluid film as function of distance into fluid (L T- l ) ;

w = width of wetted plate, i.e., wetted perimeter (L); X = concentration of nitrifying microorganisms in biofilm (M L-3) ;

XF = abbreviation for cross-flow media, where number indicates specific surface area of media;

x = distance into fluid film from air-water interface (L); Yx/v = yield coefficient for mass of cells produced per mass of ammonia

as nitrogen; z = distance from entrance of plate in direction of flow (L);

= thickness of the thin fluid film covering biofilm on trickling filter media (L);

~t = maximum growth rate of microorganisms (T-~); Ix = specific growth rate of nitrifying microorganisms (T- l ) ;

~z s = dynamic viscosity of fluid (M L -a T 1); v = kinematic viscosity of fluid (L 2 T- 1); P = water density (M L3); and

= hydraulic loading rate per wetted perimeter, which can be calculated from ~ = 82pg/(3v) (L 2 T-a).

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