Effects of dissolved oxygen and diffusion resistances on nitrification kinetics

Wat. Res. Vol. 26, No. 8, pp. 1099-1104, 1992 Printed in Great Britain. All rights reserved

0043-1354/92 $5.00+0.00 Copyright © 1992Pergamon Press Ltd

EFFECTS OF DISSOLVED OXYGEN A N D DIFFUSION RESISTANCES ON NITRIFICATION KINETICS M. BECCARI1 ~ , A. C. DI PINTO2~), R. RAMADOglz@ and M. C. TOMEI2 ~Dcpartment of Chemistry, University "La Sapienza', P. le A. Moro, 5, 00185 Rome and ZWater Research Institute, CNR, Via Reno 1, 00198 Rome, Italy (First received May 1991; accepted in revised form January 1992) Abatract--The effects of the dissolved oxygen concentration on biological nitrification in suspended biomass processes are investigated. A model of nitrification, in which the kinetics is expressed by considering both the intrinsic rate of ammonia oxidation and the diffusion rate of substrates inside the biological floe, is presented. The model is calibrated and validated utilizing experimental data of tests performed in conditions of oxygen limiting kinetics. Excellent agreement is found between experimental results and model predictions. Finally, the model is applied to evaluate the effectiveness factor, ~/, i.e. the ratio between the actual substrate removal rate and the intrinsic rate, as a function of the biofloc's diameter at different levels of dissolved oxygen concentration. The results obtained show that in nitrification processes, the effects related to oxygen internal diffusion resistances cannot be neglected in evaluating the overall kinetics. A marked decrease in the r/value is found at a biofloc diameter greater than 100/~m, particularly when the dissolved oxygen concentration is ~<2 mg 1-~. Key words--nitrification modelling, suspended biomass, intrinsic kinetics, internal diffusion resistance, effectiveness factor

NOMENCLATURE

INTRODUCTION AND OBJECTIVES

As = external area of the biofloc (L 2) B?/, = percent fraction of the bioflocs in the j class Cj = biofloc number of the j class D=diffusion coefficient of the considered substrate (ML-2T -I) DO ffi dissolved oxygen concentration (ML -3) = frequency of the j class = maximum specific consumption rate of ammonia substrate ( T - i ) Kss = saturation constant referring to the ammonia substrate (ML -3) Kso = saturation constant referring to the oxygen substrate (ML -I) N = ammonia nitrogen concentration (ML -3) NTB = total number of bioflocs r = generic biofloc radius (L) Re = external biofloc radius (L) Ri = inactive biofloc radius (L) S = substrate concentration (ML -3) Sb = substrate concentration in the liquid bulk phase (ML -3) Si = substrate concentration at r = Ri(ML -3) So = initial value of substrate concentration assumed in the integration procedure (ML -3) S s = substrate concentration at the liquid-biofloc interface (ML -3) Vb = mean volume of the bioflocs (L 3) VbS= mean volume of the bioflocs in the j class (L 3) W = substrate removal rate referring to a single biofloc (MT -I) X ffi biomass concentration (ML -3) ffi biofloc diameter (L) rl ffi effectiveness factor v = specific reaction rate referring to the unit volume of the biomass (ML-3T -I) p ffi biomass density (ML -3)

The effects of the dissolved oxygen c o n c e n t r a t i o n o n the biological nitrification process has been widely demonstrated by tests performed both with pure cultures and activated sludge from wastewater treatment plants. The conclusions of a review paper on this subject (Stentstrom a n d Poduska, 1980), referred to the following f u n d a m e n t a l aspects:

~

1099

- - t h e intrinsic rate of the process is expressed by a double substrate kinetic equation, i.e. the limiting effect of both a m m o n i a and oxygen must be considered: dN

N DO = k - X dt KsN + N Kso + D O

(l)

where N = a m m o n i a nitrogen concentration ( M L -3) X = biomass concentration ( M L -3) k=maximum specific c o n s u m p t i o n rate of a m m o n i a substrate ( T -~) KsN = saturation c o n s t a n t referring to the a m m o n i a substrate ( M L -3) D O = dissolved oxygen concentration ( M L -3) Kso = saturation constant referring to the oxygen substrate (ML=3). - - t h e total velocity o f the process depends o n the intrinsic kinetic [equation (1)] a n d o n the

M. BEccAIoet al.

I100

diffusion rate of both substrates (ammonia and oxygen) inside the biological fioc. A contribution on this subject was given by Beccari et al. (1985) who performed a series of tests to define the effects of biofloc dimensions on nitrification kinetics. The results, interpreted by considering only the biochemical reaction as kinetically effective, show a significant effect of the biofloc diameter on the Kso value. This means that the parameter was not representative of the intrinsic kinetics but was a result of a "macrokinetic" determination including the quantitative effect of the oxygen transport phenomena. Consequently the frequently accepted hypothesis that internal diffusion resistance is negligible must be verified. This simplifying hypothesis possibly justifies the high variation of literature data about Kso from 0.4 to 2.0mgO21-' (Shah and Coulman, 1978; Stankewich, 1972; Nagel and Haworth, 1969; WPCFM, 1983). The objective of this paper is to formulate a model of the nitrification process in order to give a quantitative evaluation 9f the internal diffusion resistance related effects on the process kinetics. At the same time, the model will give information on the optimal value of the dissolved oxygen concentration to be assumed in different operating conditions.

MODELLING THE NITRIHCATION PROCESS Hypothesis In developing the model a number of fundamental hypotheses are needed, some based on theory, others required to simplify the solution. All the hypotheses considered are indicated in the following:

referring to an infinitesimal thickness layer, dr, of the biological floc. For spherical bioflocs the equation is:

~dr,]r+d, where r = generic biofloc radius (L) S = substrate concentration (ML -3) v = specific reaction rate referring to the unit volume of the biomass (ML-3T -I) D--diffusion coefficient of the considered substrate (L-2T - i). Substituting the Michaelis-Menten equation in (2), the following is obtained:

kpS

Dd(dS)

r2 dr r2--'~r =Ks..}_ S

(3)

where p = biomass density (ML-3). The boundary conditions are different, depending on whether penetration of the biofloc is full [Fig. l(a)] or partial [Fig. l(b)]. In the first case, in which the substrate concentration at the liquid-solid interface is known, the boundary conditions are:

S=Sb

atr=Re

dS/dr = 0

at r = 0

with R~ the external radius of the biofloc.

(1) steady-state conditions (2) uniform density of the biomass (3) bioflocs of spherical shape (4) kinetic, stoichiometric and diffusional parameters constant inside the biological flow (5) the external diffusional resistance is negligible, that is the liquid-biofloc interface substrate concentration (Ss) is the same as the concentration in the bulk phase (Sb) (6) the process kinetics is expressed by a Michaelis-Menten equation (7) only one substrate (oxygen, in the case considered) is both biokinetically and flux limiting. The verification procedure of the last hypothesis, that is the first step in the model application, is that proposed by Williamson and McCarty (1976).

Model description In the first phase of the calculations the evaluation of the limiting substrate profile inside the biological floc is obtained by integration of the second order differential equation resulting from the mass balance

I (a) l

Sb= S~

(b)

Sb= S

sij R, [

R. ] Fig. 1. Concentration profile of limiting substrate inside the biofloc in the case of full penetration (curve a) and that of partial penetration (curve b): Sb ffibulk liquid substrate concentration; S~--substrate concentration at r = ~ ; S, = fiquld-biofilm interface substrate concentration; R¢ = biofloc radius; Ri = inactive radius.

Nitrification modelling The second condition (dS/dr = 0 at r = 0) arises out of the necessity to have the diffusionai flux equal to 0 at the center of the biofloc (r = 0), which occurs only if the substrate concentration gradient in this position is 0. In the case of partial penetration of the biofloc, the substrate concentration (and consequently the diffusional fux) will be zero at an intermediate position within the biofloc (r = Ri), that is:

1lOl The initial value assumed for So is very small

(close to o) (4) numerical integration (Runge-Kutta method) until one of the two following conditons is satisfied [curves (1) in Fig. 2(a) and 2(b), respectively]:

S=Sb

at r
S
at r = Re.

or:

S=Sb

at

r=l~

dS/dr = 0 and

S --- 0

at r

~- R i .

Unless kinetic equations simpler than the Michaelis--Menten are considered (zero or first order), the integration of (3) is possible only through numerical methods (Runge-Kutta, Hammings, etc.). In this case, independently of the method adopted, it is necessary to know the S concentration and the S gradient for the initial point. Therefore, in conformity with the boundary conditions, the integration must start from the center and continue, until the known value of Sb is attained. The integration procedure is presented in more detail in the following paragraph.

In the first case there is partial penetration of the biofloe [Fig. 2(a)] while in the second the penetration is complete [Fig. 2(b)] (5) in both cases the integration is repeated, varying the initial conditions. In the first case, the initial point is moved to progressively higher r values, Ri [obtaining the curves 2-n shown in Fig. 2(a)], until an Ri value is obtained for which the concentration at the biofloc-liquid interface (r -- Re) is equal to Sb. The initial conditions, for each step of integration, are: S = Si(~0)

Integration procedure

D, p, Re, Sb (3) definition of the initial conditions for the first integration cycle: S=S0

and

dS/dr=O

dS/dr - 0 at r = R i

In the second case, of full penetration, the initial value So at r = 0 is assumed to become progressively higher until the required condition at the interface (S = Sb) is reached: the curves in this case are shown in Fig. 2(b) (profiles 2-n).

The integration procedure is implemented in the following stages: (1) verification that the same substrate is both flux and biokinetically limiting using the Williamson and McCarty (1976) procedure (2) introduction of the input parameters: k, Ks,

and

Having evaluated the S gradient at the interface (dS/dr)r = Re, the substrate removal rate referred to a sin# biofloc, can be obtained from:

atr=0.

(a)

(b) Sb

i So o

Sb

So

r

Re Ri

I

,

Re

Fig. 2. Numerical solution procedure: (a) partial penetration of substrate and ( b ) full penetration of substrate. So = initial value of substrate concentration assumed in the integration procedure; Sb = bulk liquid substrate concentration; r -- generic biofloc radius; Re = biofloc radius; Ri ffi inactive radius.

1102

M. BECCARi et al.

where As = 4nR2~ is the external area of the biofloc. Finally, the effectiveness factor, r/, defined as the ratio between the actual substrate removal rate and the intrinsic rate, is given by:

NTB is the total number of bioflocs. Furthermore, NTB is given by:

VX/Vbp

NTB =

(9)

where

~l = W/[p4/3nR~k ~--~S J.

(5)

V = reactor volume ( L 3) biomass concentration (ML -3) p = biomass density (ML -3) Vb = Y.jFj Vbj is the mean volume of the bioflocs (where Fj and Vbj are respectively the frequency and the volume of the j class, i.e. parameters automatically evaluated by the particle counter).

X=

The effectiveness factor, r/, is the fundamental parameter employed in order to quantify the effects of internal diffusion resistance on the process kinetics. In fact, if the biofloc dimensions and the dissolved oxygen concentration in the bulk phase are known, the r/factor gives a measure of the intrinsic kinetics reduction exerted by the internal diffusion resistance.

In conclusion, in order to evaluate the oxygen consumption curves the following input data are required:

M O D E L CALIBRATION AND VALIDATION

The calibration and validation phases of the proposed model have been performed by utilizing experimental data obtained in previous batch tests (Beccari et al., 1985). A preliminary evaluation suggests that the batch test may be simulated as a sequence of steady-state stages provided that each one is characterized by a sufficiently short duration time, At (with reference to tested experimental conditions). In this short time the Sb value (substrate concentration in the bulk phase) and the substrate profile within the biofloc may be assumed to be constant. Moreover, because the tests were realized in conditions of oxygen limiting kinetics the equation (1) can be simplified as: dN DO X dt = k Kso + DO"

(6)

At the end of each test the biomass was characterized by a particle size analyser (PA-720 HIAC/ ROYCO), which gave a 23 dimensional class floc distribution function of the mean diameter of each class. In the tests 90% of the biofloc volume had a diameter in the range of 60-100 t~m with a mean value characterizing the distribution of 80/~m. The total bioconversion rate is the sum of the various contribuitons for all the classes expressed by: 23

v = ~ WjCj

(7)

j=l

where Wj is the bioconversion rate of a single biofloc belonging to the class j and Cj is the biofloc number of the j class. Cj is obtained from the following:

C: = B,voNTB

--Sb, oxygen concentration in the bulk phase at

t=O --k, Kso, kinetic intrinsic parameters --D, oxygen diffusion coefficient in the biofloc - - p , biomass density --X, biomass concentration --biomass dimensional distribution. The oxygen profile S(r) and the oxygen consumption rate Wj are evaluated at each time, t, for the single biofloc of the classj. The procedure is repeated for all 23 dimensional classes and, from (7), v, oxygen consumption rate in the whole reactor referring to the time step At is determined. Finally, from the oxygen mass balance, the new value of the oxygen concentration in the bulk phase is calculated and the procedure is repeated for the following At. The model calibration has been performed by considering the variability of k, Kso, D, p in the range of values shown in Table 1. The k and Kso data result from previous experimental tests performed using a 40/~m mean diameter biofloc [for this dimension, according to Shieh and La Motta (1979), it may be assumed that the effect of the internal diffusion resistances is negligible]. The diffusion (D) and the biomass density (p) data are taken from the literature. The best fit of the experimental data for the calibration test, as shown in Fig. 3, was obtained for the following values: k = 6.87 mg O2 mg SS- l d-i Kso = 0.83 mgO21 -l

(8)

D = 1.4 10-5cm2 s-l

where Bjvois the percent fraction of the bioflocs in the j class (evaluated by the particle size analyser) and

p = 50 mg cm- 3.

Table I. Calibration parameters and corresponding variability range

Parameter k Kso D p

Variability range

Units

Reference

6.87-7.18 0.46-0.83 0.5-2 30-77

mg 02 mg SS- ' d - ' m g O 21-' I 0 - s cm 2 s - ' mg crn -3

Beccari et al. (1985) Beccari et al. (1985) Matson and Charaklis (1976) Shieh and Keenan (1986)

Nitrification modelling

1103

14 12 `15

\ I 10

0

L °%'~°'•b°-~20 30

-J 40

I 50

F

t (rain) Fig. 3. Pattern of dissolved oxygenconcentration (Sb = DO) vs time: comparison between experimental data (O) and model simulation ( ). Test A, operating conditions: NI-I4-N= 100mgl-X; DO (at t =0)= 13.92mgl-t; mean diameter of bioflocs = 80.0# m; X = 117 rag SS lk = 6.87mgO2mgSS-t d-t; Kso=0.83mgO21-1; D = 1.4 x 10-Scm2s-J; p = 50mgcm -}.

n;

Sensitivity analysis referring to k, Ks• and p, in the range of values reported in Table 1, shows that these parameters poorly affect the effectiveness factor, ~/. On the contrary, the diffusion coefficient D has a significant influence on the ~/factor, as the variation of D from 0.5 to 2 x 10 -5 cm 2 s -~ gives a correspondent variation of r/from 0.91 to 0.98 at ~ ffi 80#m and from 0.73 to 0.93 at ~ = 140 ~tm. The set of parameters identified was used to validate the model by calculating the oxygen profile in a second test characterized by different operating conditions. The theoretical curves (Fig. 4)"are very close to experimental points. The very good agreement between the experimental values and the model predictions, confirming the hypothesis of simulating the batch test as a sequence of steady states, is also shown in Fig. 5(a) and (b) where the calculated DO concentrations are reported versus the correspondent experimental DO concentrations, respectively, for tests A

15

0

[

•

I

I

I

" "~ •'t

I

10

20

30

40

50

t (rain)

Fig. 4. Pattern of dissolved oxygenconcentration (Sb = DO ) vs time: comparison between the experimental data (@) and model simulation ( ). Tests B, operating conditions: NH4-N=I00mgI-m; DO (at tffi0)f18.34mgl-t; mean diameter of bioflocs = 81.4/~m; X ffi 110 mg SS l-t; k ffi6.87 mgO2mgSS-td-'; KSoffi0.83 mgO21-t; D = 1.4 x 10-Scrn2s-l; p -- 50mgcra -5. WR 26/8--G

0

8

5

5

~

10

o~ '10 E

i(o)

2

I

I

I

I

4

6

8

10

I '12

I '14

o 18

=~

•

I Ibl

o O 12

~

o

t

I

I

I

I

2

4

6

8

lo 12 '14 is m

Experimentol

volue

I

I

I

I

(rag Oa/I)

Fig. 5. Calculated DO concentration vs experimental values; ( ) regression line. (a) TeU A and (b) Test B. and B. The two series of data are well fitted (correlation coefficients equal to 0.99 for both cases) by straight lines of unitary slope and y-intercept equal 0. Only at very low oxygen concentrations are there small differences, which are probably due to the greater incidence of the numerical errors in this range of reduced concentration and related gradient values. By applying equations (4) and (5) with the set of parameters identified, the effectiveness factor t; was evaluated as a function of biofloc size ~ and dissolved oxygen concentration in the liquid phase bulk DO (Fig. 6). At ~ = 40 ~m, # is always >0.98 even when DO is low (0.5 mgl-]); this verifies the assumption that the effect of internal diffusional resistances is negligible at ~ 40/~m. When ~b is in the range 40-100ftm, r/is always >10.90 if DO is >11 mgl-t; consequently, also in these conditions, internal diffusional resistances can be reasonably neglected. However, experimental findings point out that a significant fraction of the biomass in the activated sludge plants may have a size of even several hundred /~m (Jenkins et al., 1986); to this regard, the model shows that a marked decrease in 17 begins to be observed at values of ~ higher than 100/~m, particularly when DO is < 2 mg I-L Consequently, in the activated sludge plants, where nitrification occurs, the effect related to internal diffusion resistances cannot be neglected in evaluating the overall kinetics.

1104

M. I~CCA~ et al. 1,0

ances cannot be neglected in evaluating the overall kinetics.

0.8

Acknowledgement--The authors wish to thank L. Bignami for his contribution in developing the computer program.

m,,w 0.6

mx m

e,~e.

REFERENCES

m"mm, ~ "mm,am"

0,4

"°'e m-.m..m.a m

0.2 I

I

I

1

I

~oo

2oo

3oo

4oo

5oo

~b(~,m)

Fig. 6. Effectiveness factor vs biofloc diameter: effect of dissolved oxygen concentration in the bulk phase. (a) DO = 4 m g l - [ ; (b) DO =2mgl-m; (c) DOff I mgl-~; and (d) DO-- 0.5 mg I-L CONCLUSIONS

The model developed in this paper provides a kinetic description of the nitrification process in suspended culture taking into account resistances related to oxygen diffusion inside the bioflocs and without the need to introduce a simplifying hypothesis concerning the reaction order in expressing the intrinsic kinetics. Excellent agreement was found between the experimental results and the model predictions. The model allows the effectiveness factor to be evaluated as a function o f the biofloc size and dissolved oxygen concentration in the liquid phase bulk. It shows that in the nitrification processes, the effect related to internal diffusional resist-

Beccari M., Franzini M. and Ramadori R. (1985) Effect of diffusion resistances on the kinetics of ammonia oxidation in suspended growth reactors. In Proc. Int. Workshop on Advanced Biological Processes, 28-30 November, National Research Council, Rome, Italy. Jenkins D., Richard M. G. and Daigger G. T. (1986) Manual on the Causes and Control of Activated Sludge Bulking and Foaming. Distributed by Ridgeline Press, Lafayette, Calif. Matson J. V. and Characklis W. G. (1976) Diffusion into microbial aggregates. War. Res. 10, 877-885. Nagel C. A. and Haworth J. G. (1969) Operational factors affecting nitrification in the activated sludge process. In 42nd Annual Conference WPCF, Dallas, Tex. Shah D. B. and Coulman G. A. (1978) Kinetics of nitrification and denitrification reactions. Biotechnal. Bioengng 20, 43-72. Shieh W. K. and Keenan J. (1986) Fluidized bed biofilm reactor for wastewater treatment. Adv. biochem. Engng Biotechnol. 33, 131-169. Shieh W. K. and La Motta E. J. (1979) Effect of initial substrate concentration on the rate of nitrification in a batch experiment. Biotechnol. Bioengng 21, 201-211. Stankewich M. J. (1972) Biological nitrification with the high purity oxygenation process. In Proc. Purdue Indust. Waste Conf. 27, 1-23. Stenstrom M. K. and Poduska R. A. (1980) The effect of dissolved oxygen concentration on nitrification. War. Res. 14, 643-649. Willimson K. and McCarty P. C. (1976) A model of substrate utilization by bacterial films. J. War. Pallut. Control Fed. 48, 9--23. WPCFM (Water Pollution Control Federation Manual) (1983) Nutrient Control. Manual of Practice, No. FD-7.