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Effect of mass transport on BOD removal in trickling filters
Water Research Vol. 9, pp. 447 to 449. Pergamon Press 1975. Printed in Great Britain.
EFFECT OF MASS TRANSPORT O N BOD REMOVAL IN TRICKLING FILTERS NICHOLAS D. SYLVESTERand PUNYA PITAYAGULSARN Department of Chemical Engineering, University of Tulsa, Tulsa, Oklahoma 74104, U.S.A.
(Received 8 April 1974) Abstract--The effect of liquid-phase mass transport on BOD removal efficiency in a trickling filter is presented based on an analytical model of the process. It is shown graphically that liquid-phase mass transport resistances can significantly affect BOD removal for a given trickling filter. The applicability of the results presented to the analysis of experimental data and trickling filter design is discussed.
NOMENCLATURE
C
co De
Ez kT kL k~ k, Rp X U Z
reactant concentration, g-mole ccfeed reactant concentration, g-mole cc- i effective diffusivity in biomass cm 2 saxial dispersion coefficient, cm 2 s- i overall external mass transfer coefficient defined by equation (6) cm s- i liquid-side mass transfer coefficient, cm ssolid-liquid mass transfer coefficient, cm s- l intrinsic reaction rate constant, I spacking radius, cm conversion superficial velocity, cm saxial distance from filter inlet, cm
Greek letters Porosity in filtered bed biomass porosity defined by equation (2) 7 6 defined by equation (3) defined by equation (4) P (p defined by equation (5) 09 Z/Rp ~t
Dimensionless groups F URJD,, (1 -- ~) Np~ RpU/E: S 3(1 - ct)kr/U 2o (1 - ct)flk,R,/U 2a.2.3 defined by equations (7)-(10) INTRODUCTION
Previous approaches to the design of trickling filters have been based either upon the empirical work of Velz (1948) or others (Schulze, 1960; Sinkoff et al., 1959; Sullins and Galler, 1968), or the National Research Council formula (1946). A number of investigators have recognized the limitations of empirical design formulas and have approached the problem from a theoretical viewpoint. Atkinson et al. (1967, 1968a, 1968b, 1970, 1971) have formulated a compli447
cated reaction-diffusion model which takes into account all the processes mentioned above. This model, although requiring a numerical solution, does seem to describe the behaviour of the trickling filter. Maier et al. (1967) have used a similar approach. Kornegay and Andrews (1969) used a well mixed annular reactor; to eliminate external mass transfer effects to study the reaction kinetics. However, in actual operation, liquid phase resistance to mass transfer is important and may be a limiting factor. Mehta et al. (1972) developed a model for the case where oxygen transport was the limiting factor in the overall BOD reduction rate. In all the theoretical models mentioned above the need for considering external mass transport of oxygen and organics through the liquid phase to the biomass is apparent. It is the purpose of this note to present an analytical method which describes the effects of liquidphase mass transport on BOD removal in a trickling filter.
ANALYTICAL DEVELOPMENTS
The trickling filter is modeled as a fixed bed reactor with downflow of liquid. The reactants oxygen and organics must be transported to the biomass where a first order, irreversible, isothermal reaction occurs on the biomass surface. The analysis to be presented is analogous to that developed by Sylvester and Pitayagulsarn (1973) for three-phase, fixed-bed, catalytic reactors. The method developed was successfully applied to existing experimental data. The conversion, X, for an isothermal, first order chemical reaction in the trickling filter is given by equation (1) 1
-X
= - -Cc o = e X p [[ ~2/~=-UZ _ - _ (x ( y ) - 1)1
(1)
448
NICHOLASD. SYLVESTERand Pl. N'tA Pl I'AYA(iULSAI{N
where C is the effluent BOD, Co the feed BOD. and -,,=
4E:kr{3(l - 7)]6
I + ~w-\--~--!
2, -
(2)
1
3
)" = ~[x i).,,trlcoth\
Rp\ ( p c o t h ( R e \ (p) - 1 + t l I~ = krR/'D,,
(4)
~p = krfl/D ,,
(5)
1
kr
kL
+
1
=e
k,
~,'"
{7)
where Np, )°3 = T [ ( 1
+ 4 J . 2 / / N p e ) l'2 -
Nv,. : Rfl_//E:
{I 1)
S = 3tl - ~)kr, U
i12}
F = ['R/D,,{I - :~)
{131
2(, = (1 - :)[3krRjU
(14)
1]
18)
The term ,;o3may be regarded as a pseudo overall reaction rate and contains the effects of axial dispersion on 22, the overall reaction rate. which in turn contains the effects of liquid-phase mass transfer (S), biomass diffusion (F} and biomass reaction (2o). In the trickling filter model considered here the effects of biomass diffusion and axial dispersion are neglected in which case 2~ = 2o and 23 = 22 respectively. Thus only the effects of liquid-phase mass transport {parameter S} and biomass reaction rate (parameter 2o1 on BOD removal {conversion X) are shown. Figures I and 2 are a graphical representation of the effect of liquid-phase mass transport on BOD removal for various values of the reaction rate parameter if-o}
/>l
I0
f 04
0.2 01 004
.g
002 00I 0004 0.002
0001
10-3
10-3
(10)
(6)
where k L in the gas liquid mass transfer coefficient and k, is the liquid-solid mass transfer coefficient. Equation (I) describes the effects of axial dispersion, external diffusion, biomass diffusion and biomass reaction on BOD removal in a trickling filter. Equation (1) can be written in the following dimensionless form. 1 -X
(}.oF) - 1)]
and ,~ = Z R , , is the ratio of the filter depth to the media particle size. In these equations
and the overall external, mass transfer coefficient, kr is given by 1
(9t
1/5.~ + I ' S
10-2
IO-I
Ao Fig. I.
Effect of mass transport on BOD removal
449
3-3 t
I0
I
I0 -I
I0 -z
10-3
iO-4
IO I
tO-2 X
IO'~
IO-4
Fig. 2. a n d for various values of~o. S = z corresponds to no external mass transport resistance. It is clear from the figures that external mass transfer can have a significant effect on B O D removal under a given set of conditions. The figures have the potential of enabling one to determine the kinetic rate constant if the B O D removal a n d the external mass transfer effects are known. Alternately, if the kinetic rate constant a n d the mass transport coefficients are k n o w n the required trickling filter depth for a given B O D removal could be predicted. The obstacle to the use of the figures is the lack of experimental data on mass transfer coefficients a n d kinetic rate constants for trickling filters. It is hoped that this development will lead to further experimental study and i m p r o v e m e n t of the model presented. Ultimately a n improved design procedure for trickling filters should result.
Acknowledgement--The support of this work by NSF Grant GK-34764 is gratefully acknowledged.
REFERENCES
Atkinson B. et al. (1967) Trans. Inst. Chem. Enqrs. 45, T257. Atkinson B. and Daoud I. S. (1968a) Trans. lnstn. Chem. Engrs. 46, T 19. Atkinson B. and Daoud I. S. and Williams D. A. (1968b) Trans. Instn. Chem. Engrs. 46, T245. Atkinson B. and Daoud I. S. (1970) Trans. Instn. Chem. Engrs. 48, T245. Atkinson B. and Williams D. A. (1971) Trans. Instn. Chem. Enqrs. 49, 215. Kornegay B. H. and Andrews J. F. ((1969) FWPCA Grant WPO 1181. Maier W. J., Behn V. C. and Gates C. D. (1967) J. San. Engr. Div. ASCE, 93, 91. Mehta D. S., Davis H. H. and Kingsbury R. P. (1972) J. Sant. Eil#r. Div., ASCE, 98, 471. National Research Council (1946) Sewage Wks. J. 18, (5), 791. Schulze K. L. (1960) J. War Pollut. Control Fed. 32, 245. SinkoffM. D., Porges R. and McDermott J. H. (1959) J. San En.qr. Div. ASCE 85, SA6, 51. Sullins J. A. and Galler W. S. (1968) J. Wat. Pollut. Control Fed. 40, R303. Sylvester N. D. and Pitayagulsarn P. (1973) AIChE. J. 19, 640. Velz G. J. (1948) Sewaye Wks. J. 20(4), 607.
EFFECT OF MASS TRANSPORT O N BOD REMOVAL IN TRICKLING FILTERS NICHOLAS D. SYLVESTERand PUNYA PITAYAGULSARN Department of Chemical Engineering, University of Tulsa, Tulsa, Oklahoma 74104, U.S.A.
(Received 8 April 1974) Abstract--The effect of liquid-phase mass transport on BOD removal efficiency in a trickling filter is presented based on an analytical model of the process. It is shown graphically that liquid-phase mass transport resistances can significantly affect BOD removal for a given trickling filter. The applicability of the results presented to the analysis of experimental data and trickling filter design is discussed.
NOMENCLATURE
C
co De
Ez kT kL k~ k, Rp X U Z
reactant concentration, g-mole ccfeed reactant concentration, g-mole cc- i effective diffusivity in biomass cm 2 saxial dispersion coefficient, cm 2 s- i overall external mass transfer coefficient defined by equation (6) cm s- i liquid-side mass transfer coefficient, cm ssolid-liquid mass transfer coefficient, cm s- l intrinsic reaction rate constant, I spacking radius, cm conversion superficial velocity, cm saxial distance from filter inlet, cm
Greek letters Porosity in filtered bed biomass porosity defined by equation (2) 7 6 defined by equation (3) defined by equation (4) P (p defined by equation (5) 09 Z/Rp ~t
Dimensionless groups F URJD,, (1 -- ~) Np~ RpU/E: S 3(1 - ct)kr/U 2o (1 - ct)flk,R,/U 2a.2.3 defined by equations (7)-(10) INTRODUCTION
Previous approaches to the design of trickling filters have been based either upon the empirical work of Velz (1948) or others (Schulze, 1960; Sinkoff et al., 1959; Sullins and Galler, 1968), or the National Research Council formula (1946). A number of investigators have recognized the limitations of empirical design formulas and have approached the problem from a theoretical viewpoint. Atkinson et al. (1967, 1968a, 1968b, 1970, 1971) have formulated a compli447
cated reaction-diffusion model which takes into account all the processes mentioned above. This model, although requiring a numerical solution, does seem to describe the behaviour of the trickling filter. Maier et al. (1967) have used a similar approach. Kornegay and Andrews (1969) used a well mixed annular reactor; to eliminate external mass transfer effects to study the reaction kinetics. However, in actual operation, liquid phase resistance to mass transfer is important and may be a limiting factor. Mehta et al. (1972) developed a model for the case where oxygen transport was the limiting factor in the overall BOD reduction rate. In all the theoretical models mentioned above the need for considering external mass transport of oxygen and organics through the liquid phase to the biomass is apparent. It is the purpose of this note to present an analytical method which describes the effects of liquidphase mass transport on BOD removal in a trickling filter.
ANALYTICAL DEVELOPMENTS
The trickling filter is modeled as a fixed bed reactor with downflow of liquid. The reactants oxygen and organics must be transported to the biomass where a first order, irreversible, isothermal reaction occurs on the biomass surface. The analysis to be presented is analogous to that developed by Sylvester and Pitayagulsarn (1973) for three-phase, fixed-bed, catalytic reactors. The method developed was successfully applied to existing experimental data. The conversion, X, for an isothermal, first order chemical reaction in the trickling filter is given by equation (1) 1
-X
= - -Cc o = e X p [[ ~2/~=-UZ _ - _ (x ( y ) - 1)1
(1)
448
NICHOLASD. SYLVESTERand Pl. N'tA Pl I'AYA(iULSAI{N
where C is the effluent BOD, Co the feed BOD. and -,,=
4E:kr{3(l - 7)]6
I + ~w-\--~--!
2, -
(2)
1
3
)" = ~[x i).,,trlcoth\
Rp\ ( p c o t h ( R e \ (p) - 1 + t l I~ = krR/'D,,
(4)
~p = krfl/D ,,
(5)
1
kr
kL
+
1
=e
k,
~,'"
{7)
where Np, )°3 = T [ ( 1
+ 4 J . 2 / / N p e ) l'2 -
Nv,. : Rfl_//E:
{I 1)
S = 3tl - ~)kr, U
i12}
F = ['R/D,,{I - :~)
{131
2(, = (1 - :)[3krRjU
(14)
1]
18)
The term ,;o3may be regarded as a pseudo overall reaction rate and contains the effects of axial dispersion on 22, the overall reaction rate. which in turn contains the effects of liquid-phase mass transfer (S), biomass diffusion (F} and biomass reaction (2o). In the trickling filter model considered here the effects of biomass diffusion and axial dispersion are neglected in which case 2~ = 2o and 23 = 22 respectively. Thus only the effects of liquid-phase mass transport {parameter S} and biomass reaction rate (parameter 2o1 on BOD removal {conversion X) are shown. Figures I and 2 are a graphical representation of the effect of liquid-phase mass transport on BOD removal for various values of the reaction rate parameter if-o}
/>l
I0
f 04
0.2 01 004
.g
002 00I 0004 0.002
0001
10-3
10-3
(10)
(6)
where k L in the gas liquid mass transfer coefficient and k, is the liquid-solid mass transfer coefficient. Equation (I) describes the effects of axial dispersion, external diffusion, biomass diffusion and biomass reaction on BOD removal in a trickling filter. Equation (1) can be written in the following dimensionless form. 1 -X
(}.oF) - 1)]
and ,~ = Z R , , is the ratio of the filter depth to the media particle size. In these equations
and the overall external, mass transfer coefficient, kr is given by 1
(9t
1/5.~ + I ' S
10-2
IO-I
Ao Fig. I.
Effect of mass transport on BOD removal
449
3-3 t
I0
I
I0 -I
I0 -z
10-3
iO-4
IO I
tO-2 X
IO'~
IO-4
Fig. 2. a n d for various values of~o. S = z corresponds to no external mass transport resistance. It is clear from the figures that external mass transfer can have a significant effect on B O D removal under a given set of conditions. The figures have the potential of enabling one to determine the kinetic rate constant if the B O D removal a n d the external mass transfer effects are known. Alternately, if the kinetic rate constant a n d the mass transport coefficients are k n o w n the required trickling filter depth for a given B O D removal could be predicted. The obstacle to the use of the figures is the lack of experimental data on mass transfer coefficients a n d kinetic rate constants for trickling filters. It is hoped that this development will lead to further experimental study and i m p r o v e m e n t of the model presented. Ultimately a n improved design procedure for trickling filters should result.
Acknowledgement--The support of this work by NSF Grant GK-34764 is gratefully acknowledged.
REFERENCES
Atkinson B. et al. (1967) Trans. Inst. Chem. Enqrs. 45, T257. Atkinson B. and Daoud I. S. (1968a) Trans. lnstn. Chem. Engrs. 46, T 19. Atkinson B. and Daoud I. S. and Williams D. A. (1968b) Trans. Instn. Chem. Engrs. 46, T245. Atkinson B. and Daoud I. S. (1970) Trans. Instn. Chem. Engrs. 48, T245. Atkinson B. and Williams D. A. (1971) Trans. Instn. Chem. Enqrs. 49, 215. Kornegay B. H. and Andrews J. F. ((1969) FWPCA Grant WPO 1181. Maier W. J., Behn V. C. and Gates C. D. (1967) J. San. Engr. Div. ASCE, 93, 91. Mehta D. S., Davis H. H. and Kingsbury R. P. (1972) J. Sant. Eil#r. Div., ASCE, 98, 471. National Research Council (1946) Sewage Wks. J. 18, (5), 791. Schulze K. L. (1960) J. War Pollut. Control Fed. 32, 245. SinkoffM. D., Porges R. and McDermott J. H. (1959) J. San En.qr. Div. ASCE 85, SA6, 51. Sullins J. A. and Galler W. S. (1968) J. Wat. Pollut. Control Fed. 40, R303. Sylvester N. D. and Pitayagulsarn P. (1973) AIChE. J. 19, 640. Velz G. J. (1948) Sewaye Wks. J. 20(4), 607.