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Development and calibration of a mathematical model for the simulation of the biofiltration process
Advances in Environmental Research 7 Ž2002. 11᎐33
Development and calibration of a mathematical model for the simulation of the biofiltration process P. Viotti a,U , B. Eramo b,1, M.R. Boni a,2 , A. Carucci c,3, M. Leccese a , S. Sbaffoni a a
Uni¨ ersity of Rome ‘La Sapienza’, Department of Hydraulics, Transportation and Roads, Via Eudossiana 18, 00184 Rome, Italy b A.C.E.A. ᎏ ATO 2 S.p.A., Piazzale Ostiense 20, 00100 Rome, Italy c Uni¨ ersity of Cagliari, Department of Geoengineering and En¨ ironmental Technologies, Piazza d’Armi, 09123 Cagliari, Italy Accepted 1 July 2001
Abstract Biofiltration is gradually gaining popularity among biological wastewater treatment processes, becoming a valid alternative to the more widespread activated sludge system. In order to understand better the operating conditions that influence the efficiency of such a process, a mathematical model has been developed. It allows the calculation of the COD and N-NHq 4 profiles along the filter height and inside the biofilm and simulates filter clogging due to the biomass growth. The model output has been verified through a series of sensitivity tests and its results have been calibrated considering the results of an experimental campaign conducted on the Biostyr 䊛 biofiltration unit of the Rome southern municipal wastewater treatment plant. Such a model can be used to understand better the influence of variation of the operating conditions on the efficiency of the biofiltration process, furthermore representing a valid predictive tool for the management of existing wastewater treatment plants and for the design of new ones. 䊚 2002 Elsevier Science Ltd. All rights reserved. Keywords: Biofilm kinetics; Biofiltration; COD removal; Mathematical model; Nitrification
1. Introduction Biofiltration is gradually gaining popularity among biological wastewater treatment processes, becoming a valid alternative to the more widespread activated
U
Corresponding author. Tel.: q39-064-4585512; fax: q39064-4585037. E-mail addresses: [email protected] ŽP. Viotti., [email protected] ŽM.R. Boni., [email protected] ŽA. Carucci.. 1 Tel.: q39-065-7993655. 2 Tel.: q39-064-4585506; fax: q39-064-4585037. 3 Tel.: q39-0706-755531; fax: q39-0706-755523.
sludge system ŽCanler and Perret, 1994.. The process is based on fixed film technology, requiring a granular medium Ž2᎐5 mm in size. as a support for the attachment of microorganisms ŽDiaco and Eramo, 1993a,b,c.. The small dimensions of the bioparticles results in a high arearvolume ratio, which allows high biomass concentrations using reactors substantially smaller than those required in the suspended-growth treatment processes. For this reason, biofiltration becomes more competitive when land availability represents a factor restricting the designer’s choices. Together with removing organic pollutants and converting ammonia-nitrogen into nitrate, the filter bed retains the solid particles suspended in the liquid and
1093-0191r02r$ - see front matter 䊚 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 0 9 3 - 0 1 9 1 Ž 0 1 . 0 0 1 0 6 - X
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P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
the biomass detached from the biofilm, thus producing a clarified effluent that does not need secondary settling. The retaining of the suspended solids results in gradual clogging of the filter medium. In order to loosen and remove the sludge deposited, the filter is backwashed using treated wastewater and air. The sludge is returned to the mechanical treatment units and extracted with the primary sludge. Moreover, up-flow biofiltration allows the reduction of odor emissions as the ambient air is in contact only with the oxygen-saturated, filtered water and the washing sludge remains in an enclosed tank away from any exposure to the atmosphere. This work presents the development of a mathematical model for simulation of the biofiltration process ŽSbaffoni, 2000.. It allows calculation of the concentration profiles of carbon and ammonia-nitrogen substrates along the bed and inside the biofilm, considering also the oxygen consumption in the latter case. Referring to the growth yield of both autotrophic and heterotrophic microorganisms, the biomass growth has also been simulated as well. It results in an increase in biofilm thickness, thus producing progressive clogging of the bed that makes the head loss rise. With the hypothesis of a linear relation between the medium permeability and the biofilm thickness, it is possible to compute the total head loss in the filter, once the biofilm thickness has been determined. The model is based on double-saturation Michaelis᎐Menten kinetics ŽMetcalf and Eddy, 1991. and considers the resistance to mass transport both within and outside the bioparticles. A monodimensional model of the reactor was used, taking into consideration convective transport and turbulent diffusion under steady-state conditions. The Biostyr 䊛 ŽHerbert, 1995. is a biological, aerated filter used for the removal of organic carbon and ammonia-nitrogen ŽFig. 1.. The flow of wastewater is upward; the support medium consists of expanded polystyrene Žbiostyrene. spheres, approximately 3 mm in size, with a specific weight of 0.04 trm3 Žpolystyrene is a granular, floating material.. The use of biostyrene provides a large surface area available for biomass
Fig. 1. Biostyr 䊛 filtering unit.
attachment, and consequently, significant treatment capability. The floating material is retained in the upper part of the structure by a slab fitted with nozzles. Air co-current to water supply is injected at the base of the bed. Construction characteristics of the filter are reported in Table 1.
2. Model layout The simulation of the biofiltration process may be divided into three consecutive steps ŽSbaffoni, 2000.: 䢇
䢇 䢇
Mass transport, diffusion and consumption of sub. strates ŽCOD, N-NHq 4 , O 2 in the biofilm; Filter flow model; and Biomass growth and head loss computation
The numerical model simulates a single filtration cycle by considering a sequence of discrete time intervals Ž30 min., each one assumed to occur under steady-state conditions. This implies that the substrate flux in the biofilm and the substrate profiles are assumed to be in steady-state conditions, while the biofilm grows and the thickness changes over time.
Table 1 Dimensional and construction characteristics Biofiltration units Width Length Total height Useful height of filtering material Useful volume of filtering material Filtering material type Filtering material size Specific weight of filtering material
16 8m 14 m 5.9 m 2.5 m 4480 m3 Polystyrene 3 Ž2᎐5. mm 0.04 Ž0.035᎐0.045. trm3
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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2.1. Mass transport, diffusion and consumption of substrates in the biofilm The model has been developed according to the following hypotheses ŽLa Motta and Mulcahy, 1978; Eramo and Gavasci, 1987; Eramo et al., 1993, 1994; Sbaffoni, 2000.: 1. The support medium particles are spherical; 2. The biofilm is homogeneous and uniform in thickness on a single bioparticle; 3. Mass transport is described by Fick’s law; 4. Biochemical reactions are described by doublesaturation Michaelis᎐Menten kinetics; and 5. There are pseudo steady-state conditions. Fig. 2. Bioparticle scheme.
Referring to a spherical coordinate system, with the r-axis starting from the bioparticle center and positive in the outward direction ŽFig. 2., mass balance equations applied on an elementary biofilm volume ŽFig. 3. for each substrate and for oxygen can be written as: Dsbc d dC C O r2 y k c bd ␣ s0 2 dr d r k q C k r sc sco q O
ž
/
/
s0
䢇
Ž 1b .
Dsbo d dO C O r2 y k o1 k c bd ␣ dr k sc q C k sco q O r2 dr
ž
/
N O Ž1 y ␣ . y k o2 k n bd s0 k sn q N k sno q O
Biofilm᎐support medium interface Ž r s rm .:
dN s0 dr
Ž 2b .
dO s0 dr
Ž 2c .
Liquid bulk᎐biofilm interface Ž r s rp .: Dsbc
dC s K cc Ž C b y C . dr
Ž 3a .
Dsbn
dN s K cn Ž Nb y N . dr
Ž 3b .
Dsbo
dO s K co Ž O b y O . dr
Ž 3c .
Ž 1c .
The boundary conditions for Eqs. Ž1a., Ž1b. and Ž1c. are: 䢇
Ž 2a .
Ž 1a .
Dsbn d dN N O Ž1 y ␣ . r2 y k n bd dr k sn q N k sno q O r2 dr
ž
dC s0 dr
Eqs. Ž2a., Ž2b. and Ž2c. express the fact that, due to the impermeability of the support medium surface, the
Fig. 3. Elementary volume of the biofilm.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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mass flow is equal to zero; Eqs. Ž3a., Ž3b. and Ž3c. express the equality between the flow of the substrates across the bioparticle surface for external mass transfer and the flow across the same surface for internal mass transfer. The external flow is proportional to the concentration gradient through the mass exchange coefficient K cc ; this parameter can be estimated with an empirical relation derived from a dimensional analysis ŽVan Loodsrecht, 1993.: 1.09 1r3 Sh s f Ž Re,Sc. s Re Sc 1r3
䢇
Ž 4a .
K ccdp where Sc s is the Schmidt number, Sh s is DL DL u d p the Sherwood number and Res is the Reynolds number. Eq. Ž4a. may be rearranged in order to calculate the value of K cc : K cc s
1.09 1r3 Re Sc 1r3
DL dp
dC U s0 dx
Ž 6a .
d NU s0 dx
Ž 6b .
dOU s0 dx
Ž 6c .
Liquid bulk᎐biofilm interface Ž xs 1.: dC U s Bcc Ž 1 y C U . dx
Ž 7a .
d NU s Bcn Ž 1 y N U . dx
Ž 7b .
dOU s Bco Ž 1 y OU . dx
Ž 7c .
Ž 4b .
2.2. Filter flow model Eqs. Ž1a., Ž1b. and Ž1c. may be expressed in dimensionless form Žwith respect to x, C U , N U and OU ., referring each substrate concentration Ž C, N, O . in the biofilm to the respective concentration in the liquid phase Ž C b , Nb , O b . and the r coordinate to the biofilm thickness Ž .: d dC U CU OU 2 Ž xq . 2 y ␣ Ž xq . 2 s 0 dx dx Yc q C U Yco q OU c Ž 5a . d d NU Ž xq . 2 y Ž1 y ␣ . dx dx = Ž xq .
2
NU OU 2 s 0 Yn q N U Yno q OU n
Ž 5b .
d dOU Ž xq . 2 y ␣ k o1 dx dx = Ž xq .
2
CU OU 2 U Yc q C Yco q OU co
y Ž 1 y ␣ . k o2 Ž xq .
2
NU OU 2 s 0 Yc q N U Yno q OU no Ž 5c .
The boundary conditions are: 䢇
Biofilm᎐support medium interface Ž xs 0.:
For simulation of the flow within the filter bed, it is necessary to introduce the following hypotheses ŽLa Motta and Mulcahy, 1978; Eramo and Gavasci, 1987; Eramo et al., 1993, 1994; Sbaffoni, 2000.: . are dissolved in the 1. Substrates ŽCOD, N-NHq 4 liquid phase and do not influence the fluid motion; 2. Biomass is attached to the support medium particles: the quantity of suspended biomass is negligible, and consequently no biodegradation occurs in the liquid phase; 3. Movement in the filter is monodimensional; 4. Liquid phase moves through the reactor by convection and turbulent diffusion; 5. The support medium characteristics are uniform through the bed height; 6. Initial porosity is assumed constant through the bed height; 7. There are pseudo steady-state conditions; 8. Removal kinetics of each substrate are limited by the concentration of the substrate itself and of oxygen; and 9. The dissolved oxygen concentration is assumed constant through the bed height. Such an assumption has proved to be close to reality, since measured values of DO concentrations were characterized by negligible variations. A Cartesian coordinate system is assumed, with the z-axis orthogonal to the cross-section of the filter bed and positive upwards ŽFig. 4..
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
d Nb s0 dz
Fig. 4. Bed scheme.
The mass balance equations ŽFig. 5. are: u
dC b d2 C b y Dz q R vc s 0 dz d z2
Ž 8a .
d Nb d 2 Nb u y Dz q R vn s 0 dz d z2
Ž 8b .
These equations describe the change in concentration with filter height for each substrate. The boundary conditions for Eqs. Ž8a. and Ž8b. are: 䢇
d BU d 2 BU y Bo q R vc s 0 2 C dz bi z d
Ž 11a .
d 2⌳U d⌳U y Bo q R vn s 0 2 d N d bi
Ž 11b .
The boundary conditions are: 䢇
uNbd y Dz 䢇
dC b dz
d
d Nb dz
d
ž / s uC ž
bi
/ s uN
bi
Ž 9a .
Ž 9b .
End of the filter Ž zs H b .: dC b s0 dz
Ž 10b .
Eqs. Ž9a. and Ž9b. take into account the discontinuity in flow conditions, due to section widening and to the presence of bioparticles ŽChoi and Perlmutter, 1976.. The flow in the inlet tube Žconsidered in laminar conditions. is transformed in a fully developed turbulent flow caused by the enlargement of the section, in which both the convective and the dispersive transport are present. The mass balance equations wEqs. Ž8a. and Ž8b.x are solved according to these boundary conditions. To obtain Eqs. Ž8a. and Ž8b. in dimensionless form, it is necessary to refer each substrate concentration Ž C b , Nb . in the filter to the corresponding concentration at the filter inlet Ž C bi , Nbi . and the z coordinate to the height of the bed Ž H b .:
Base of the filter Ž zs 0.: uC bd y Dz
15
䢇
Ž 10a .
Base of the filter Ž s 0.: BU y Bo
d BU s1 d
Ž 12a .
⌳U s Bo
d⌳U s1 d
Ž 12b .
End of the filter Ž s 1.: d BU s0 d
Fig. 5. Elementary volume of the filtering bed.
Ž 13a .
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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d⌳U s0 d
Ž 13b .
2.2.1. Substrate consumption rates The substrate consumption rate is a function of the rate of the biological processes that take place inside the biofilm through the bed height. The mean values of the observed rate referred to the biofilm volume can be determined by integrating through the biofilm thickness: p
Hm ␣ k
c bd
R oc s
p
R on s
C O 4 r 2d r k sc q C k sco q O 4 r 3 y rm3 . 3 Ž p
Hm Ž1 y ␣ . k
n bd
Ž 14a .
4 r 3 y rm3 . 3 Ž p Ž 14b .
The observed velocity may be correlated to the intrinsic rate R I by the efficiency factor : Ž 15 .
where R I is the consumption rate corresponding to a constant concentration of the substrates through the biofilm and equal to the bulk concentrations: R Ic s ␣ k c bd
Cb Ob k sc q C b k sco q O b
R In s Ž 1 y ␣ . k n bd
Ž 16a .
Nb Ob k sn q Nb k sno q O b
Ž 16b .
It is possible to refer the substrate consumption rates to the volume of the filter by multiplying R o by the ratio VBrVL :
/
Ž 17a .
VB VM s n R In 1 y y VL Hb ⭈ A
/
Ž 17b .
R vn s R on
ž
kg VSS heterotrophs kg VSS heterotrophs q kg VSSautotrophs
Ž 18 .
It has generally been found that the fraction of nitrifying microorganisms is correlated to the CODrTKN ratio ŽMetcalf and Eddy, 1991.; the greater this ratio is, the smaller is the quantity of autotrophic biomass. In the lower part of the bed, where COD is much higher than TKN, the biofilm is almost entirely composed of heterotrophic bacteria, thus producing a high consumption of carbonaceous substrate. Consequently, the CODrTKN ratio decreases, allowing the growth of autotrophic biomass. ␣ must then result in a decreasing function; an s-shaped kind of function has been assumed: ␣ Ž z,t . s aq bey z
n
Ž 19.
where a, b, and n are constants to be estimated in the calibration phase. Given the value of the function ␣ for each z, the initial distribution of the two types of biomass through the bed height is determined. For each subsequent time interval, the relative value of ␣ Ž z . has to be estimated, considering the growth yield of the two classes of bacteria. Because the heterotrophs’ growth yield is higher than that of the autotrophs ŽMetcalf and Eddy, 1991., there is an increase in ␣ with time for each given z value ŽFig. 6.:
␣ Ž z,t . s
V VM R vc s R oc B s c R Ic 1 y y VL Hb ⭈ A
ž
Biological films are generally composed of a wide variety of microorganisms, but referring to their metabolism, they can be classified as heterotrophs and autotrophs; the heterotrophs are responsible for the COD removal, while the autotrophs operate the oxidation of ammonia-nitrogen to nitrate. To characterize the biofilm composition through the bed height, a function ␣ has been introduced; it can be defined as the fraction of heterotrophic microorganisms with respect to the total biomass ŽLeccese, 2000; Sbaffoni, 2000.:
␣Ž z. s
N O 4 r 2d r k sn q N k sno q O
R o s R I
2.2.2. Microbiological biofilm characterization
M bc Ž z,t . Ž M bc z,t . q M bn Ž z,t .
Ž 20 .
␣ Ž z,t q ⌬ t .
Eqs. Ž17a. and Ž17b. are to be used in the integration of Eqs. Ž11a. and Ž11b..
s
⌬ M bc Ž z,t q ⌬ t . rNp q M bc Ž z,t . Ž ⌬ M bc Ž z,t q ⌬ t . q ⌬ M bn Ž z,t q ⌬ t .. rNp q Ž M bc Ž z,t . q M bn Ž z,t ..
Ž 21 .
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
with: ⌬ M bc Ž z,t q ⌬ t . s yc ⭈ ⌬C ⭈ Q⭈ ⌬ t heterotrophic biomass increase
Ž 22.
⌬ M bn Ž z,t q ⌬ t . s yn ⭈ ⌬ N ⭈ Q⭈ ⌬ t
w N Ž z,t q dt . y N Ž z q d z,t q dt .x., referred to each elementary volume of the bed. Introducing the growth yield coefficients for heterotrophic and autotrophic microorganisms ŽHorn and Hempel, 1997., the biomass produced as a result of the utilization of the different substrates is: ⌬ Bc Ž z,t q dt . s ⌬C Ž z,t q dt . ⭈ Q⭈ ⌬ t ⭈ yc
autotrophic biomass increase
Ž kg VSS heterotrophs . ⌬ Bn Ž z,t q dt . s ⌬ N Ž z,t q dt . ⭈ Q⭈ ⌬ t ⭈ yn Ž kg VSSautotrophs .
heterotrophic biomass at Ž 24.
M bn Ž z,t . s Ž 1 y ␣ Ž z,t .. ⭈ bd ⭈ V1p Ž z,t . autotrophic biomass at time t
Ž 26.
Ž 23.
M bc Ž z,t . s ␣ Ž z,t . ⭈ bd ⭈ V1p Ž z,t . time t
17
Ž 27.
The total volume of biomass produced Žm3 . for a thickness d z of the filter is: ⌬V Ž z,t q dt .
Ž 25.
⌬C and ⌬ N represent the substrate consumption relative to each elementary volume of the bed.
2.3. Biomass growth and head loss computation A minimum value Ž min . is initially assigned to the biofilm thickness; this value may be either uniform or variable along the filter height. Thus, the concentration profiles of each substrate are obtained through Eqs. Ž11a. and Ž11b. and it is possible to calculate the substrate consumption Žkgrm3 . Ž ⌬C s w C Ž z,t q dt . y C Ž z q d z,t q dt .x and ⌬ N s
s
⌬ Bc Ž z,t q dt . q ⌬ Bn Ž z,t q dt . bd
Ž 28 .
To obtain the new biofilm thickness Ž t q dt . for each bioparticle, an iterative procedure is adopted; the volume increase ⌬V Ž t q dt . for each bioparticle is: ⌬V Ž t q dt . s
4 3 w rm q Ž t q dt .x 3
y w rm q Ž t .x
3
4
Ž 29 .
The total volume increase in an element of the bed
Fig. 6. Profile of the ␣ function along the bed height at different steps in a cycle.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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and on its variation along the height of the filter; it has been assumed that is a linear function of ŽFig. 8.: Ž z, . s max y Ž Ž z . y min Ž z .. ⭈ p
Ž 33 .
The head loss due to each element of the bed is: ⌬ hŽ z . s u ⭈ ⌬ z ⭈
1 g Ž z.
Ž 34 .
and the total head loss for the filter is: ⌬ h tot s
Fig. 7. Bioparticle disposition.
is calculated using the number Np of bioparticles present in that element: ⌬Vtot Ž t q dt . s ⌬V Ž t q dt . ⭈ Np
Np s
Ž dm q 2 .3
Ž 31 .
By applying the iterative procedure to Eqs. Ž28. and Ž30., the biofilm thickness increases, the filter starts to clog and the head losses rise. The filter may be considered a saturated system, and thus for the head loss computation, the one-dimensional Darcy equation is adopted ŽCharacklis and Marshall, 1989; Droste, 1997.: usK
⌬h ⌬h s g l l
Hb
u 1 ⭈ dz g Ž z.
Ž 35.
The suspended solids retention has not been considered in the head loss computation.
Ž 30 .
The disposition of the bioparticles is supposed to be cubic ŽFig. 7. Žthis configuration corresponds to the maximum value of the porosity ., and thus Np is: A⭈⌬ z
H0
Ž 32 .
The permeability depends on the biofilm thickness
3. Calculation procedure The equations are integrated using an implicit finite differences technique. Since Eqs. Ž5a., Ž5b. and Ž5c. and Eqs. Ž11a. and Ž11b. are non-linear, following the classical definition of a non-linear equation ŽSmith, 1985., calculation is carried out using an iterative method, which has been shown to have fast convergence, assigning to the terms causing non-linearity Žthese terms are the substrate concentrations in the denominator in Monod kinetics. initial values updated at every iteration by previously calculated ones. The calculation has been executed as follows ŽSbaffoni, 2000.: 1. Integration over the biofilm thickness to determine the concentration profiles of COD, N-NHq 4 and oxygen, and the efficiency factors Ž c and n .;
Fig. 8. Relation between the permeability and the biofilm thickness.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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Fig. 10. Subroutine for integration along the filter bed.
4. Sensitivity analysis
Fig. 9. Program flow chart.
2. Integration over the entire height of the filter bed using the values of c and n calculated above, to obtain the variation in substrate concentrations in the bed; 3. Computation of the increase in biofilm thickness, due to the biomass growth at different bed heights; 4. Calculation of the total head loss; and 5. Comparison between the calculated total head loss and the maximum acceptable one Ž130 mbar.. If the calculated value is lower than the maximum one, the time is increased by ⌬ t Ž30 min. and the calculation procedure is repeated, unless the maximum time is reached. Otherwise, filter clogging requires the interruption of the filtration phase to run the backwashing phase. The model was solved on a 233-MHz IBM-compatible PC. The running time depends on the maximum time that has been set and on the operating conditions, which may reduce the actual duration of the filtration cycle. Referring to a duration of 12 h, the program takes approximately 4 min to run. The flow charts depicting the program and the subroutines Žintegration along the bed and along the biofilm. are reported in Figs. 9᎐11.
The sensitivity analysis ŽSbaffoni, 2000. allows verification of the behavior of the model as a consequence of a variation of the input parameters Žthese variations represent any changes in the operating conditions of the filter.; for this purpose, a certain condition is assumed: this is called the reference situation, and the relative solution Žgiven by the numerical model. is compared with the different solutions obtained by vary-
Fig. 11. Subroutine for integration along the biofilm.
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P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 12. COD concentration profiles in the filter: variation with fluid velocity.
Fig. 13. N-NHq 4 concentration profiles in the filter: variation with fluid velocity.
Fig. 14. COD concentration profiles in the filter: variation with DO concentration.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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Fig. 15. N-NHq 4 concentration profiles in the filter: variation with DO concentration.
ing the value of some input parameters. The following graphs have been obtained with the ␣ function: ␣ s exp ycos t ⭈
z Hb
ž /
n
Ž 36.
where cos t s 10y8 and n s 4. Figs. 12 and 13 show the influence of the flow velocity u on the concentration profiles of COD and N-NHq 4 ; in fact, with increasing u, the contact time between the wastewater and the bioparticles is reduced, producing lower treatment efficiency. Another important parameter is the concentration of dissolved oxygen in the filter bed, because it influences the removal efficiency, in particular Žas shown in Figs. 14 and 15. of the nitrification process, due to the greater sensitivity of autotrophic microorganisms to the
environmental parameters Ždissolved oxygen concentration, temperature, pH, etc... In the model, the oxygen concentration has been considered constant: indeed from the experimental campaign Ždescribed in the following section., strongly aerobic conditions were evident. The values adopted for the DO concentration in the sensitivity analysis are 2 Žthe typical value used in the activated sludge process., 1 Ža particularly low value. and 10 mgrl. These tests ŽFigs. 12᎐15. have been executed considering a single step; obviously, it is also possible to analyze the entire filtration cycle, following the evolution of the COD and N-NHq 4 concentration profiles over time. In this case, the increase in the head loss and the biofilm thickness may be studied. The concentration adopted for DO was 10 mgrl. In Figs. 16 and 17, the substrate concentration pro-
Fig. 16. COD concentration profiles in the bed: variation with time Ž yc s 0.45, yn s 0.2..
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P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Ž . Fig. 17. N-NHq 4 concentration profiles in the bed: variation with time yc s 0.45, yn s 0.2 .
Fig. 18. COD concentration profiles in the bed: variation with time Ž yc s 1.0, yn s 0.5..
Ž . Fig. 19. N-NHq 4 concentration profiles in the bed: variation with time yc s 1.0, yn s 0.5 .
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
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Fig. 20. COD concentration profiles in the biofilm: variation with bed height.
files in the bed at different steps of the cycle are shown, assuming the values of 0.45 for the heterotrophic biomass growth-yield coefficient and 0.2 for the autotrophic biomass. Figs. 18 and 19 represent the same profiles obtained with growth yield coefficients equal to 1.0 for the heterotrophs and 0.5 for the autotrophs. The cycle is interrupted at 510 min from the beginning of the cycle, rather than at 720 min. As a consequence of the higher growth yield coefficients adopted, the biofilm thickness increases more quickly, producing a rapid rise in the head loss; the filtration phase is stopped and the backwashing phase begins. The concentration profiles of the substrates in the biofilm are also obtained as an output of the numerical model; in Figs. 20 and 21, the concentration of COD
and DO in the biofilm at different heights of the bed are shown, respectively. Fig. 20 proves the effects of the ␣ function on COD removal; indeed, as the bed height rises, the carbonaceous substrate consumption rate decreases as a consequence of the lower quantity of heterotrophic biomass. Fig. 21 instead shows that at z s 0.001 m, the biofilm is fully penetrated by oxygen, because of the low con. sumption of substrate ŽCOD and N-NHq 4 at the bottom of the bed, while at z s 1 m, the biofilm is only partially penetrated. This is due to the simultaneous removal of COD and N-NHq 4 , with high consumption of oxygen Žespecially for the nitrification.. At z s 2 m, the oxygen concentration in the biofilm is almost constant, since at the end of the bed there is no removal of COD w ␣ Ž zs 2 m. s 0; only autotrophic biomass is pre-
Fig. 21. DO concentration profiles in the biofilm: variation with bed height.
24
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 22. COD concentrations during the day, 26 April 2000.
Ž sent. or of N-NHq 4 as shown in Fig. 15 with a concentration 10 mgrl of DO in the bed, the ammonia-nitrogen is entirely consumed at z s 2 m..
weekly collections, and samples were collected at eight different sections of a single filtration unit. The sections were located at the following points: 䢇
5. Experimental campaign
䢇 䢇
The numerical model was calibrated using experimental data obtained from a Biostyr 䊛 biofiltration unit at the Rome southern municipal wastewater treatment plant. Samples for the characterization of substrate concentration profiles were collected during March and April 2000. The sampling schedule consisted of two
Feed channel; Filtered water head; and Six sampling ports positioned every 50 cm along the bed height.
Samples were collected sequentially so as to follow the fluid motion through the filter. Withdrawals from the sampling ports along the bed were carried out considering the mean fluid velocity in order to take into account the water residence time in the filter.
Fig. 23. N-NHq 4 concentrations during the day, 26 April 2000.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
25
Table 2 Model parameters and relative references Parameter
Name
Axial dispersion coefficient Dynamic viscosity of the liquid phase Density of the liquid phase Žat 20⬚C. Glucose diffusivity in the liquid phase Ammonia-nitrogen diffusivity in the liquid phase Oxygen diffusivity in the liquid phase Biomass mean density Glucose diffusivity in the biofilm Ammonia-nitrogen diffusivity in the biofilm Oxygen diffusivity in the biofilm Half-saturation constant ŽCOD. Half-saturation constant ŽN-NH4 q. Half-saturation constant ŽO2 rCOD. Half-saturation constant ŽO2 rN-NH4q . Maximum rate coefficient ŽCOD. Maximum rate coefficient ŽN-NH4q .
DZ DSL C DSL N
Oxygen consumption for COD removal Oxygen consumption for N-NH4 q removal Heterotrophic biomass growth yield Autotrophic biomass growth yield
Model value y5
10 0.001005 998.2 6.7= 10y1 0 1.70= 10y9
DSL O bc DSBC DSBN
2.30= 10y9 60 3.35= 10y10 1.30= 10y9
DSBO ksc ksn ksco ksno kc kn
1.50= 10y9 0.05 0.001 0.0004 0.0004 5.78= 10y5 4.14= 10y5
ko1 ko2
1.07 4.57
yc yn
0.45 0.01
Ammonia-nitrogen, COD, nitrate, TSS, DO, pH and temperature were determined on each sample, according to standard analytical procedures. Head losses were also monitored during the sampling period.
6. Calibration phase In order to verify the ability of the numerical model to predict the results obtained from the samples collected at the Rome southern municipal wastewater treatment plant, the program was run using the operating conditions obtained in each sampling campaign
Units
Reference
2
m rs kgrm s kgrm3 m2 rs m2 rs
Characklis Characklis Characklis Characklis Characklis
m2 rs kgrm3 m2 rs m2 rs
Characklis and Marshall, 1989
and Marshall, 1989 and Marshall, 1989 and Marshall, 1989 and Marshall, 1989 and Marshall, 1989
Characklis and Marshall, 1989 Characklis and Marshall, 1989
m2 rs Characklis and Marshall, 1989 kg CODrm3 Metcalf and Eddy, 1991 kg N-NH4qrm3 Beccari et al., 1993 kg O2 rm3 kg O2 rm3 kg CODrkg VSS Metcalf and Eddy, 1991 kg N-NH4 q Beccari et al., 1993 rkg VSS kg O2 rkg COD Characklis and Marshall, 1989 kg O2 rkg N-NH4 q Metcalf and Eddy, 1991 kg VSSrkg CODr Beccari et al., 1993 kg VSS Beccari et al., 1993 rkg N-NH4q r
ŽLeccese, 2000. as input data Ždissolved oxygen, ammonia-nitrogen and COD concentrations, fluid velocity, water temperature and pH.. All of these parameters Žin particular ammonia-nitrogen and COD concentrations . obviously varied over time due to the well-known nonuniformity of wastewaters in sewage collectors. Figs. 22 and 23 show COD and ammonia-nitrogen concentrations in the plant inlet during the day, respectively. Parameters reported in Table 2 were obtained from the literature, while the parameters characterizing the functions ␣ Ž z ., Ž z . and Ž , z . have been calibrated in order to best fit the results of the simulation to those derived from the experimental campaign. Such a procedure allows us to associate with each of
Table 3 Parameters obtained through the calibration phase for the functions ␣ Ž z . and Ž z .
a b c d e f g h
03r28r2000
03r30r2000
04r04r2000
04r06r2000
04r11r2000
04r18r2000
04r20r2000
1.00= 10y1 9.00= 10y1 1.00= 10y1 1 4.7 1.00= 10y5 6.00= 10y5 1.00= 10y1 7 8.0
1.00= 10y1 9.00= 10y1 1.00= 10y11 4.98 7.00= 10y6 1.20= 10y4 1.00= 10y20 9.8
1.00= 10y1 9.00= 10y1 1.00= 10y9 4.15 1.00= 10y6 5.00= 10y5 1.00= 10y19 9.5
1.00= 10y1 9.00= 10y1 1.00= 10y10 4.7 5.00= 10y6 5.50= 10y5 1.00= 10y19 9.5
1.00= 10y1 9.00= 10y1 1.00= 10y11 4.98 5.00= 10y6 9.00= 10y5 1.00= 10y10 5.0
2.00= 10y1 8.00= 10y1 1.00= 10y9 3.85 2.00= 10y6 9.00= 10y5 1.00= 10y24 11.8
2.00= 10y1 8.00= 10y1 1.00= 10y9 3.85 1.00= 10y6 1.50= 10y4 1.00= 10y24 11.8
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
26
Table 4 Averaged parameters assumed in the functions ␣ Ž z ., Ž z . and Ž z . ␣Ž z.
Ž z.
Ž , z .
a
b
c
d
e
f
g
h
i
l
0.188
0.812
1 = 10y9
4.112
4.43= 10y6
8.79= 10y5
1 = 10y16
7.86
2.41= 10y8
2.09= 10y4
the aforesaid parameters a set of values ŽTable 3., used to fit each experimental curve. The functions obtained for the above-mentioned variables ␣ and , presented
in Figs. 24 and 25, have been averaged; the average functions have been adopted in further model applications. Figs. 26 and 27, which show the trend of ␣ and
Fig. 24. Heterotrophic biomass fraction distribution along the bed height.
Fig. 25. Biofilm thickness distribution along the bed height.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
27
Fig. 26. Assumed heterotrophic biomass fraction distribution along the bed height.
functions described later in the text, are obtained using the following expressions of ␣ , and : ␣ Ž z,t . s aq b⭈ exp yc ⭈
ž Hz /
d
Ž 37.
b
Ž z,t . s e q f ⭈ 1 y exp yg ⭈
z Hb
h
ž ž //
Ž Ž z . ,t . s i y 1 ⭈ w Ž z . y min Ž z .x
Ž 38 .
Ž 39.
where the different parameters assume the averaged values reported in Table 4. The values reported, obtained by averaging results from 10 experimental campaigns, may be used for analysis of the performance of similar biofiltration units in design problems, while if experimental data are available or can be obtained, a new calibration procedure can be useful to properly fit units already in operation. Eq. Ž38. shows the non-uniformity of the biofilm thickness distribution along the bed height: particularly, the thickness was assumed to be very small in the
Fig. 27. Assumed biofilm thickness distribution along the bed height.
28
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 28. COD concentration along the bed, 30 March 2000.
deepest layers Žapprox. 5 m. and to increase from the central part up to the top, where it reached approximately 90 m. Such a hypothesis is required in order to justify the slow consumption of the COD, confirmed from experimental results, in the lower part of the filter bed. Although this may seem anomalous, it can be explained by considering that, since the processrwash-
ing air is injected at the bottom of the filter bed, the lower layers are characterized by greater turbulence and irregularity in the water flow. Such flow conditions operate a strong shear stress on the bioparticles, thus hindering the biomass growth. The comparison between experimental data and the corresponding simulated profiles reported in Figs.
Fig. 29. N-NHq 4 concentration along the bed, 30 March 2000.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
29
Fig. 30. COD concentration along the bed, 11 April 2000.
28᎐31 proves that the model output related to different operating conditions, even using averaged values for the parameters characterizing the biofilm behavior, fits well the real behavior of the examined biofilter. Figs. 28 and 29 refer to a single sampling, while Figs. 30 and
31 show the concentration profiles of the two substrates at two different times in a filtration cycle. ŽIt is worthwhile to note the great changes in the wastewater quality at the inlet.. The concentration trends of the two substrates along
Fig. 31. N-NHq 4 concentration along the bed, 11 April 2000.
30
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 32. Head loss trends with time: comparison between observed and simulated values, 30 March 2000.
the filter heights appear to be different in shape. This is mainly due to the function ␣ that greatly influences the model output, controlling the simultaneous removal of the substrates. Also, the increase in the fraction of heterotrophic microorganisms at each level with time correctly interprets the phenomenon generally
occurring as time elapses in a filtration cycle. Indeed, as a result of the faster growth of this group of bacteria, the efficiency of the COD removal increases, not being influenced by the increase in the inflow concentration. Figs. 32 and 33 show a comparison between the head
Fig. 33. Head loss trends with time: comparison between observed and simulated values, 11 April 2000.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
loss values derived from the on-line computerized control system of the Biostyr 䊛 and those calculated by the simulation program. For quantification of the errors, a polynomial regression curve of the second order has been adopted. The results presented show that the most important parameters are ␣ , and . Use of the numerical model is rather simple once these parameters are defined. The tests carried out have shown that the values suggested in the present paper can be used for operating conditions close to those encountered in wastewaters arriving at the treatment plant investigated. The only inputs then needed are the inlet conditions Žflow rate, temperature and pH. and the pollutant concentration involved in the treatment ŽCOD and ammonia-nitrogen removal..
7. Conclusions The numerical model developed has the aim of simulating: 䢇 䢇 䢇 䢇
COD removal; Ammonia-nitrogen removal; Biofilm growth; and Head loss trends.
The sensitivity analysis led to the determination of the parameters affecting the efficiency of the treatment process. Among those parameters, the most important are: 䢇 䢇
Fluid velocity; and Dissolved oxygen concentration.
Their control seems to be essential for proper process operation. The distribution of heterotrophic and autotrophic microorganisms, expressed by the function ␣ , influences the relative consumption of the two substrates. Also, the biofilm thickness profile along the bed height appears to be relevant for the model output. The experimental data collected have confirmed the assumption of s-shaped functions for both Ž z . and ␣ Ž z .. The model proposed for the simulation of the biofiltration process has proven to fit properly the experimental results derived from the sampling campaign conducted. Such a model can be used to better understand the influence of variations in operating conditions on the efficiency of the biofiltration process, representing furthermore a valid predictive tool for the management of existing wastewater treatment plants and for the design of new ones.
31
Appendix A: Nomenclature biofilter cross section Žm2 . C brC bi ; COD concentration in the liquid phase in dimensionless form Bcc : K cc rDsbc ; Biot modified number for COD B cn : K cn rDsbn ; Biot modified number for ammonia-nitrogen Bco : K co rDsbo ; Biot modified number for the oxygen Bo : DzrŽ uH b .; Bodenstein number C: COD concentration in the biofilm Žkgrm3 . CU : CrC b ; COD concentration in the biofilm in dimensionless form C b : COD concentration in the liquid phase Žkgrm3 . C bd : COD concentration at the internal points of the filter Žkgrm3 . C bi : COD concentration in the feed flow Žkgrm3 . D L : substrate molecular diffusion coefficient in the liquid phase Žm2rs. d m : support medium diameter Žm. d p: bioparticle diameter Žm. Dsbc : COD diffusion coefficient in the biofilm Žm2rs. Dsbn : ammonia-nitrogen diffusion coefficient in the biofilm Žm2rs. Dsbo : oxygen diffusion coefficient in the biofilm Žm2rs. Dz : axial dispersion coefficient Žm2rs. H b : height of the filter bed Žm. K: hydraulic conductivity Žmrs. kc: COD maximum utilization rate Žkgrkg s. K cc : COD mass exchange coefficient K cn : ammonia-nitrogen mass exchange coefficient K co : oxygen mass exchange coefficient k n: ammonia-nitrogen maximum utilization rate Žkgrkg s. k o1: oxygen specific consumption in the biofilm for COD degradation Žkg O 2rkg COD. k o2 : oxygen specific consumption in the biofilm for ammonia-nitrogen degradation Žkg O 2rkg N. NHq 4 k sc : COD half-saturation constant Žkgrm3 . k sco : oxygen half-saturation constant for COD removal Žkgrm3 . k sn : ammonia-nitrogen half-saturation constant Žkgrm3 . k sno : oxygen half-saturation constant for the ammonia-nitrogen removal Žkgrm3 . N: ammonia-nitrogen concentration in the biofilm Žkgrm3 . U N : NrNb ; ammonia-nitrogen concentration in the biofilm in dimensionless form Nb : ammonia-nitrogen concentration in the liquid phase Žkgrm3 . Nbd : ammonia-nitrogen concentration in the internal points of the filter Žkgrm3 . A: BU :
32
Nbi : O: OU : O b: O bi : p: Q: r: RI: R Ic : R In : rm : R o: R oc : R on : rp: R v: R vc : R vn : Sb: u: VB : VL : VM : x: Yc : yc : Yco : Yn : yn : Yno : z: ␣: : 2c : 2co : 2n :
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
ammonia-nitrogen concentration in the feed flow Žkgrm3 . oxygen concentration in the biofilm Žkgrm3 . OrO b ; oxygen concentration in the biofilm in dimensionless form oxygen concentration in the liquid phase Žkgrm3 . oxygen concentration in the feed flow Žkgrm3 . slope of the linear function s Ž Ž z .,t . Žm. flow rate Žm3rs. spatial coordinate in the biofilm Žm. intrinsic reaction rate for unit volume of the biofilm Žkgrm s. intrinsic reaction rate for unit volume of the biofilm for the COD Žkgrm s. intrinsic reaction rate for unit volume of the biofilm for the ammonia-nitrogen Žkgrm s. support medium radius Žm. observed reaction rate for unit volume of the biofilm Žkgrm s. observed reaction rate for unit volume of the biofilm for the COD Žkgrm s. observed reaction rate for unit volume of the biofilm for the ammonia-nitrogen Žkgrm s. bioparticles radius Žm. observed reaction rate for unit volume of the bed Žkgrm s. observed reaction rate for unit volume of the bed for the COD Žkgrm s. observed reaction rate for unit volume of the bed for ammonia-nitrogen Žkgrm s. generic substrate concentration in the liquid phase Žkgrm3 . QrA; fluid velocity Žmrs. biofilm volume Žm3 . bed volume Žm3 . support medium volume Žm3 . Ž r y rm .r; spatial coordinate in the biofilm in dimensionless form k scrC b growth yield coefficient for heterotrophic biomass Žkg VSS heterotrophicrkg COD. k scorO b k snrNb growth yield coefficient for autotrophic biomass Žkg VSSautotrophicrkg COD. k snorO b spatial coordinate in the filter bed Žm. heterotrophic biomass fraction in the biofilm porosity k c bd 2rŽ Dsbc C b .; Thiele modified module for the COD k c bd 2rŽ Dsbo O b .; Thiele modified module for the oxygen in the COD removal k n bd 2rŽ Dsbn Nb .; Thiele modified module for the ammonia-nitrogen
2no : ␥c : ␥co : ␥n : ␥no : : c : n : : : : bd : : : : : ⌳U :
k n bd 2rŽ Dsbo O b .; Thiele modified module for the oxygen in the ammonia-nitrogen removal k scrC bi k scorO bi k snrNbi k snorO bi efficiency factor efficiency factor for the COD efficiency factor for the ammonia-nitrogen permeability Žm2 . dynamic viscosity of the liquid phase Žkgrm s. density of the liquid phase Žkgrm3 . mean biomass concentration in the biofilm Žkgrm3 . biofilm thickness Žm. H bru d mr2 zrH b ; spatial coordinate in the bed in dimensionless form NbrNbi ; ammonia-nitrogen concentration in the bed in dimensionless form
References Beccari, M., Passino, R., Ramadori, R., Vismara, R., 1993. Rimozione di Azoto e Fosforo dai Liquami. Hoepli. Canler, J.P., Perret, J.M., 1994. Biological aerated filters: assessment of the process based on 12 sewage treatment plants. Water Sci. Technol. 29 Ž10᎐11., 13᎐22. Characklis, W.G., Marshall, K.C., 1989. Biofilms. Wiley Interscience. Choi, C.Y., Perlmutter, D.D., 1976. A unified treatment of the inlet-boundary condition for dispersive flow models’. Chem. Eng. Sci. 31, 250. Diaco L., Eramo B., 1993a. Adesione batterica e sviluppo di biofilm su superfici solide ŽI parte., Ingegneria sanitariaambientale, gennaio᎐febbraio. Diaco L., Eramo B., 1993b. Adesione batterica e sviluppo di biofilm su superfici solide ŽII parte., Ingegneria sanitariaambientale, marzo᎐aprile. Diaco L., Eramo B., 1993c. Modelli matematici di biofilm, Ingegneria sanitaria-ambientale, luglio᎐agosto. Droste, R.L., 1997. Theory and Practice of Water and Wastewater Treatment. Eramo B., Gavasci R., 1987. Reattori biologici a letto fluidizzato, Atti di Ingegneria sanitaria-ambientale. Eramo B., Gavasci R., Misiti A., 1993. Multisubstrate mathematical model for the simulation of the denitrification process in a fluidized bed biofilm reactor, Ingegneria sanitaria-ambientale, gennaio᎐febbraio, pp. 13᎐22. Eramo, B., Gavasci, R., Misiti, A., Viotti, P., 1994. Validation of a multisubstrate mathematical model for the simulation of the denitrification process in a fluidized bed biofilm reactor. Water Sci. Technol. 29 Ž10᎐11., 401᎐408. Herbert, S., 1995. Manuale di Funzionamento e Gestione dell’Im pianto di B iofiltrazione di R om a Sud. OTVrDTrMER.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33 Horn, H., Hempel, D.C., 1997. Growth and decay in an auto-rheterotrophic biofilm’. Water Res. 31 Ž9., 2243᎐2253. La Motta, E.J., Mulcahy, L.T., 1978. Mathematical Model of the Fluidized Bed Biofilm Reactor. Department of Civil Engineering, University of Massachusetts, Amherst. Report No Env E 59-78-2 Leccese, M., 2000. Modellizzazione del Processo di Biofiltrazione: Validazione Sperimentale e Applicazione al Caso dell’Impianto. ACEA di Roma Sud. Masters dissertation. Metcalf, A., Eddy, A., 1991. Wastewater Engineering: Treatment, Disposal, Reuse. McGraw Hill International. Sbaffoni, S., 2000. Modellizzazione del Processo di Biofiltrazione: Sviluppo del Codice Numerico e Analisi di Sensitivita. ` Masters dissertation. Smith, G.D., 1985. Numerical Solution of Partial Differential Equations: Finite Difference Methods. Clarendon Press, Oxford. Van Loodsrecht, M.C.M., 1993. Kinetics of Biofilm Systems. Department of Biochemical Engineering, Delft University of Technology.
33
subsoils and the atmosphere, and the numerical simulation of ecological systems. Biagio Eramo is Chief Executive of the ATO 2 firm that provides water supply and wastewater treatment in Rome. In the past he has carried out research activity on a pilot plant of a fluidized bed reactor. Maria Rosaria Boni is Associate Professor of Environmental Engineering at the University of Rome ‘La Sapienza’. She is mainly interested in research projects concerning the contamination of superficial and underground water and its treatments. Alessandra Carucci is Associate Professor of Environmental Engineering at the University of Cagliari. Her scientific activity concerns the areas of wastewater and municipal solid waste treatment.
Vitae
Michele Leccese has a Masters degree in Environmental Engineering.
Paolo Viotti is Associate Professor of Environmental Engineering at the University of Rome ‘La Sapienza’. His research topics mainly address pollutant transport in soils,
Silvia Sbaffoni has a Masters degree in Environmental Engineering.
Development and calibration of a mathematical model for the simulation of the biofiltration process P. Viotti a,U , B. Eramo b,1, M.R. Boni a,2 , A. Carucci c,3, M. Leccese a , S. Sbaffoni a a
Uni¨ ersity of Rome ‘La Sapienza’, Department of Hydraulics, Transportation and Roads, Via Eudossiana 18, 00184 Rome, Italy b A.C.E.A. ᎏ ATO 2 S.p.A., Piazzale Ostiense 20, 00100 Rome, Italy c Uni¨ ersity of Cagliari, Department of Geoengineering and En¨ ironmental Technologies, Piazza d’Armi, 09123 Cagliari, Italy Accepted 1 July 2001
Abstract Biofiltration is gradually gaining popularity among biological wastewater treatment processes, becoming a valid alternative to the more widespread activated sludge system. In order to understand better the operating conditions that influence the efficiency of such a process, a mathematical model has been developed. It allows the calculation of the COD and N-NHq 4 profiles along the filter height and inside the biofilm and simulates filter clogging due to the biomass growth. The model output has been verified through a series of sensitivity tests and its results have been calibrated considering the results of an experimental campaign conducted on the Biostyr 䊛 biofiltration unit of the Rome southern municipal wastewater treatment plant. Such a model can be used to understand better the influence of variation of the operating conditions on the efficiency of the biofiltration process, furthermore representing a valid predictive tool for the management of existing wastewater treatment plants and for the design of new ones. 䊚 2002 Elsevier Science Ltd. All rights reserved. Keywords: Biofilm kinetics; Biofiltration; COD removal; Mathematical model; Nitrification
1. Introduction Biofiltration is gradually gaining popularity among biological wastewater treatment processes, becoming a valid alternative to the more widespread activated
U
Corresponding author. Tel.: q39-064-4585512; fax: q39064-4585037. E-mail addresses: [email protected] ŽP. Viotti., [email protected] ŽM.R. Boni., [email protected] ŽA. Carucci.. 1 Tel.: q39-065-7993655. 2 Tel.: q39-064-4585506; fax: q39-064-4585037. 3 Tel.: q39-0706-755531; fax: q39-0706-755523.
sludge system ŽCanler and Perret, 1994.. The process is based on fixed film technology, requiring a granular medium Ž2᎐5 mm in size. as a support for the attachment of microorganisms ŽDiaco and Eramo, 1993a,b,c.. The small dimensions of the bioparticles results in a high arearvolume ratio, which allows high biomass concentrations using reactors substantially smaller than those required in the suspended-growth treatment processes. For this reason, biofiltration becomes more competitive when land availability represents a factor restricting the designer’s choices. Together with removing organic pollutants and converting ammonia-nitrogen into nitrate, the filter bed retains the solid particles suspended in the liquid and
1093-0191r02r$ - see front matter 䊚 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 0 9 3 - 0 1 9 1 Ž 0 1 . 0 0 1 0 6 - X
12
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
the biomass detached from the biofilm, thus producing a clarified effluent that does not need secondary settling. The retaining of the suspended solids results in gradual clogging of the filter medium. In order to loosen and remove the sludge deposited, the filter is backwashed using treated wastewater and air. The sludge is returned to the mechanical treatment units and extracted with the primary sludge. Moreover, up-flow biofiltration allows the reduction of odor emissions as the ambient air is in contact only with the oxygen-saturated, filtered water and the washing sludge remains in an enclosed tank away from any exposure to the atmosphere. This work presents the development of a mathematical model for simulation of the biofiltration process ŽSbaffoni, 2000.. It allows calculation of the concentration profiles of carbon and ammonia-nitrogen substrates along the bed and inside the biofilm, considering also the oxygen consumption in the latter case. Referring to the growth yield of both autotrophic and heterotrophic microorganisms, the biomass growth has also been simulated as well. It results in an increase in biofilm thickness, thus producing progressive clogging of the bed that makes the head loss rise. With the hypothesis of a linear relation between the medium permeability and the biofilm thickness, it is possible to compute the total head loss in the filter, once the biofilm thickness has been determined. The model is based on double-saturation Michaelis᎐Menten kinetics ŽMetcalf and Eddy, 1991. and considers the resistance to mass transport both within and outside the bioparticles. A monodimensional model of the reactor was used, taking into consideration convective transport and turbulent diffusion under steady-state conditions. The Biostyr 䊛 ŽHerbert, 1995. is a biological, aerated filter used for the removal of organic carbon and ammonia-nitrogen ŽFig. 1.. The flow of wastewater is upward; the support medium consists of expanded polystyrene Žbiostyrene. spheres, approximately 3 mm in size, with a specific weight of 0.04 trm3 Žpolystyrene is a granular, floating material.. The use of biostyrene provides a large surface area available for biomass
Fig. 1. Biostyr 䊛 filtering unit.
attachment, and consequently, significant treatment capability. The floating material is retained in the upper part of the structure by a slab fitted with nozzles. Air co-current to water supply is injected at the base of the bed. Construction characteristics of the filter are reported in Table 1.
2. Model layout The simulation of the biofiltration process may be divided into three consecutive steps ŽSbaffoni, 2000.: 䢇
䢇 䢇
Mass transport, diffusion and consumption of sub. strates ŽCOD, N-NHq 4 , O 2 in the biofilm; Filter flow model; and Biomass growth and head loss computation
The numerical model simulates a single filtration cycle by considering a sequence of discrete time intervals Ž30 min., each one assumed to occur under steady-state conditions. This implies that the substrate flux in the biofilm and the substrate profiles are assumed to be in steady-state conditions, while the biofilm grows and the thickness changes over time.
Table 1 Dimensional and construction characteristics Biofiltration units Width Length Total height Useful height of filtering material Useful volume of filtering material Filtering material type Filtering material size Specific weight of filtering material
16 8m 14 m 5.9 m 2.5 m 4480 m3 Polystyrene 3 Ž2᎐5. mm 0.04 Ž0.035᎐0.045. trm3
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
13
2.1. Mass transport, diffusion and consumption of substrates in the biofilm The model has been developed according to the following hypotheses ŽLa Motta and Mulcahy, 1978; Eramo and Gavasci, 1987; Eramo et al., 1993, 1994; Sbaffoni, 2000.: 1. The support medium particles are spherical; 2. The biofilm is homogeneous and uniform in thickness on a single bioparticle; 3. Mass transport is described by Fick’s law; 4. Biochemical reactions are described by doublesaturation Michaelis᎐Menten kinetics; and 5. There are pseudo steady-state conditions. Fig. 2. Bioparticle scheme.
Referring to a spherical coordinate system, with the r-axis starting from the bioparticle center and positive in the outward direction ŽFig. 2., mass balance equations applied on an elementary biofilm volume ŽFig. 3. for each substrate and for oxygen can be written as: Dsbc d dC C O r2 y k c bd ␣ s0 2 dr d r k q C k r sc sco q O
ž
/
/
s0
䢇
Ž 1b .
Dsbo d dO C O r2 y k o1 k c bd ␣ dr k sc q C k sco q O r2 dr
ž
/
N O Ž1 y ␣ . y k o2 k n bd s0 k sn q N k sno q O
Biofilm᎐support medium interface Ž r s rm .:
dN s0 dr
Ž 2b .
dO s0 dr
Ž 2c .
Liquid bulk᎐biofilm interface Ž r s rp .: Dsbc
dC s K cc Ž C b y C . dr
Ž 3a .
Dsbn
dN s K cn Ž Nb y N . dr
Ž 3b .
Dsbo
dO s K co Ž O b y O . dr
Ž 3c .
Ž 1c .
The boundary conditions for Eqs. Ž1a., Ž1b. and Ž1c. are: 䢇
Ž 2a .
Ž 1a .
Dsbn d dN N O Ž1 y ␣ . r2 y k n bd dr k sn q N k sno q O r2 dr
ž
dC s0 dr
Eqs. Ž2a., Ž2b. and Ž2c. express the fact that, due to the impermeability of the support medium surface, the
Fig. 3. Elementary volume of the biofilm.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
14
mass flow is equal to zero; Eqs. Ž3a., Ž3b. and Ž3c. express the equality between the flow of the substrates across the bioparticle surface for external mass transfer and the flow across the same surface for internal mass transfer. The external flow is proportional to the concentration gradient through the mass exchange coefficient K cc ; this parameter can be estimated with an empirical relation derived from a dimensional analysis ŽVan Loodsrecht, 1993.: 1.09 1r3 Sh s f Ž Re,Sc. s Re Sc 1r3
䢇
Ž 4a .
K ccdp where Sc s is the Schmidt number, Sh s is DL DL u d p the Sherwood number and Res is the Reynolds number. Eq. Ž4a. may be rearranged in order to calculate the value of K cc : K cc s
1.09 1r3 Re Sc 1r3
DL dp
dC U s0 dx
Ž 6a .
d NU s0 dx
Ž 6b .
dOU s0 dx
Ž 6c .
Liquid bulk᎐biofilm interface Ž xs 1.: dC U s Bcc Ž 1 y C U . dx
Ž 7a .
d NU s Bcn Ž 1 y N U . dx
Ž 7b .
dOU s Bco Ž 1 y OU . dx
Ž 7c .
Ž 4b .
2.2. Filter flow model Eqs. Ž1a., Ž1b. and Ž1c. may be expressed in dimensionless form Žwith respect to x, C U , N U and OU ., referring each substrate concentration Ž C, N, O . in the biofilm to the respective concentration in the liquid phase Ž C b , Nb , O b . and the r coordinate to the biofilm thickness Ž .: d dC U CU OU 2 Ž xq . 2 y ␣ Ž xq . 2 s 0 dx dx Yc q C U Yco q OU c Ž 5a . d d NU Ž xq . 2 y Ž1 y ␣ . dx dx = Ž xq .
2
NU OU 2 s 0 Yn q N U Yno q OU n
Ž 5b .
d dOU Ž xq . 2 y ␣ k o1 dx dx = Ž xq .
2
CU OU 2 U Yc q C Yco q OU co
y Ž 1 y ␣ . k o2 Ž xq .
2
NU OU 2 s 0 Yc q N U Yno q OU no Ž 5c .
The boundary conditions are: 䢇
Biofilm᎐support medium interface Ž xs 0.:
For simulation of the flow within the filter bed, it is necessary to introduce the following hypotheses ŽLa Motta and Mulcahy, 1978; Eramo and Gavasci, 1987; Eramo et al., 1993, 1994; Sbaffoni, 2000.: . are dissolved in the 1. Substrates ŽCOD, N-NHq 4 liquid phase and do not influence the fluid motion; 2. Biomass is attached to the support medium particles: the quantity of suspended biomass is negligible, and consequently no biodegradation occurs in the liquid phase; 3. Movement in the filter is monodimensional; 4. Liquid phase moves through the reactor by convection and turbulent diffusion; 5. The support medium characteristics are uniform through the bed height; 6. Initial porosity is assumed constant through the bed height; 7. There are pseudo steady-state conditions; 8. Removal kinetics of each substrate are limited by the concentration of the substrate itself and of oxygen; and 9. The dissolved oxygen concentration is assumed constant through the bed height. Such an assumption has proved to be close to reality, since measured values of DO concentrations were characterized by negligible variations. A Cartesian coordinate system is assumed, with the z-axis orthogonal to the cross-section of the filter bed and positive upwards ŽFig. 4..
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
d Nb s0 dz
Fig. 4. Bed scheme.
The mass balance equations ŽFig. 5. are: u
dC b d2 C b y Dz q R vc s 0 dz d z2
Ž 8a .
d Nb d 2 Nb u y Dz q R vn s 0 dz d z2
Ž 8b .
These equations describe the change in concentration with filter height for each substrate. The boundary conditions for Eqs. Ž8a. and Ž8b. are: 䢇
d BU d 2 BU y Bo q R vc s 0 2 C dz bi z d
Ž 11a .
d 2⌳U d⌳U y Bo q R vn s 0 2 d N d bi
Ž 11b .
The boundary conditions are: 䢇
uNbd y Dz 䢇
dC b dz
d
d Nb dz
d
ž / s uC ž
bi
/ s uN
bi
Ž 9a .
Ž 9b .
End of the filter Ž zs H b .: dC b s0 dz
Ž 10b .
Eqs. Ž9a. and Ž9b. take into account the discontinuity in flow conditions, due to section widening and to the presence of bioparticles ŽChoi and Perlmutter, 1976.. The flow in the inlet tube Žconsidered in laminar conditions. is transformed in a fully developed turbulent flow caused by the enlargement of the section, in which both the convective and the dispersive transport are present. The mass balance equations wEqs. Ž8a. and Ž8b.x are solved according to these boundary conditions. To obtain Eqs. Ž8a. and Ž8b. in dimensionless form, it is necessary to refer each substrate concentration Ž C b , Nb . in the filter to the corresponding concentration at the filter inlet Ž C bi , Nbi . and the z coordinate to the height of the bed Ž H b .:
Base of the filter Ž zs 0.: uC bd y Dz
15
䢇
Ž 10a .
Base of the filter Ž s 0.: BU y Bo
d BU s1 d
Ž 12a .
⌳U s Bo
d⌳U s1 d
Ž 12b .
End of the filter Ž s 1.: d BU s0 d
Fig. 5. Elementary volume of the filtering bed.
Ž 13a .
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
16
d⌳U s0 d
Ž 13b .
2.2.1. Substrate consumption rates The substrate consumption rate is a function of the rate of the biological processes that take place inside the biofilm through the bed height. The mean values of the observed rate referred to the biofilm volume can be determined by integrating through the biofilm thickness: p
Hm ␣ k
c bd
R oc s
p
R on s
C O 4 r 2d r k sc q C k sco q O 4 r 3 y rm3 . 3 Ž p
Hm Ž1 y ␣ . k
n bd
Ž 14a .
4 r 3 y rm3 . 3 Ž p Ž 14b .
The observed velocity may be correlated to the intrinsic rate R I by the efficiency factor : Ž 15 .
where R I is the consumption rate corresponding to a constant concentration of the substrates through the biofilm and equal to the bulk concentrations: R Ic s ␣ k c bd
Cb Ob k sc q C b k sco q O b
R In s Ž 1 y ␣ . k n bd
Ž 16a .
Nb Ob k sn q Nb k sno q O b
Ž 16b .
It is possible to refer the substrate consumption rates to the volume of the filter by multiplying R o by the ratio VBrVL :
/
Ž 17a .
VB VM s n R In 1 y y VL Hb ⭈ A
/
Ž 17b .
R vn s R on
ž
kg VSS heterotrophs kg VSS heterotrophs q kg VSSautotrophs
Ž 18 .
It has generally been found that the fraction of nitrifying microorganisms is correlated to the CODrTKN ratio ŽMetcalf and Eddy, 1991.; the greater this ratio is, the smaller is the quantity of autotrophic biomass. In the lower part of the bed, where COD is much higher than TKN, the biofilm is almost entirely composed of heterotrophic bacteria, thus producing a high consumption of carbonaceous substrate. Consequently, the CODrTKN ratio decreases, allowing the growth of autotrophic biomass. ␣ must then result in a decreasing function; an s-shaped kind of function has been assumed: ␣ Ž z,t . s aq bey z
n
Ž 19.
where a, b, and n are constants to be estimated in the calibration phase. Given the value of the function ␣ for each z, the initial distribution of the two types of biomass through the bed height is determined. For each subsequent time interval, the relative value of ␣ Ž z . has to be estimated, considering the growth yield of the two classes of bacteria. Because the heterotrophs’ growth yield is higher than that of the autotrophs ŽMetcalf and Eddy, 1991., there is an increase in ␣ with time for each given z value ŽFig. 6.:
␣ Ž z,t . s
V VM R vc s R oc B s c R Ic 1 y y VL Hb ⭈ A
ž
Biological films are generally composed of a wide variety of microorganisms, but referring to their metabolism, they can be classified as heterotrophs and autotrophs; the heterotrophs are responsible for the COD removal, while the autotrophs operate the oxidation of ammonia-nitrogen to nitrate. To characterize the biofilm composition through the bed height, a function ␣ has been introduced; it can be defined as the fraction of heterotrophic microorganisms with respect to the total biomass ŽLeccese, 2000; Sbaffoni, 2000.:
␣Ž z. s
N O 4 r 2d r k sn q N k sno q O
R o s R I
2.2.2. Microbiological biofilm characterization
M bc Ž z,t . Ž M bc z,t . q M bn Ž z,t .
Ž 20 .
␣ Ž z,t q ⌬ t .
Eqs. Ž17a. and Ž17b. are to be used in the integration of Eqs. Ž11a. and Ž11b..
s
⌬ M bc Ž z,t q ⌬ t . rNp q M bc Ž z,t . Ž ⌬ M bc Ž z,t q ⌬ t . q ⌬ M bn Ž z,t q ⌬ t .. rNp q Ž M bc Ž z,t . q M bn Ž z,t ..
Ž 21 .
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
with: ⌬ M bc Ž z,t q ⌬ t . s yc ⭈ ⌬C ⭈ Q⭈ ⌬ t heterotrophic biomass increase
Ž 22.
⌬ M bn Ž z,t q ⌬ t . s yn ⭈ ⌬ N ⭈ Q⭈ ⌬ t
w N Ž z,t q dt . y N Ž z q d z,t q dt .x., referred to each elementary volume of the bed. Introducing the growth yield coefficients for heterotrophic and autotrophic microorganisms ŽHorn and Hempel, 1997., the biomass produced as a result of the utilization of the different substrates is: ⌬ Bc Ž z,t q dt . s ⌬C Ž z,t q dt . ⭈ Q⭈ ⌬ t ⭈ yc
autotrophic biomass increase
Ž kg VSS heterotrophs . ⌬ Bn Ž z,t q dt . s ⌬ N Ž z,t q dt . ⭈ Q⭈ ⌬ t ⭈ yn Ž kg VSSautotrophs .
heterotrophic biomass at Ž 24.
M bn Ž z,t . s Ž 1 y ␣ Ž z,t .. ⭈ bd ⭈ V1p Ž z,t . autotrophic biomass at time t
Ž 26.
Ž 23.
M bc Ž z,t . s ␣ Ž z,t . ⭈ bd ⭈ V1p Ž z,t . time t
17
Ž 27.
The total volume of biomass produced Žm3 . for a thickness d z of the filter is: ⌬V Ž z,t q dt .
Ž 25.
⌬C and ⌬ N represent the substrate consumption relative to each elementary volume of the bed.
2.3. Biomass growth and head loss computation A minimum value Ž min . is initially assigned to the biofilm thickness; this value may be either uniform or variable along the filter height. Thus, the concentration profiles of each substrate are obtained through Eqs. Ž11a. and Ž11b. and it is possible to calculate the substrate consumption Žkgrm3 . Ž ⌬C s w C Ž z,t q dt . y C Ž z q d z,t q dt .x and ⌬ N s
s
⌬ Bc Ž z,t q dt . q ⌬ Bn Ž z,t q dt . bd
Ž 28 .
To obtain the new biofilm thickness Ž t q dt . for each bioparticle, an iterative procedure is adopted; the volume increase ⌬V Ž t q dt . for each bioparticle is: ⌬V Ž t q dt . s
4 3 w rm q Ž t q dt .x 3
y w rm q Ž t .x
3
4
Ž 29 .
The total volume increase in an element of the bed
Fig. 6. Profile of the ␣ function along the bed height at different steps in a cycle.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
18
and on its variation along the height of the filter; it has been assumed that is a linear function of ŽFig. 8.: Ž z, . s max y Ž Ž z . y min Ž z .. ⭈ p
Ž 33 .
The head loss due to each element of the bed is: ⌬ hŽ z . s u ⭈ ⌬ z ⭈
1 g Ž z.
Ž 34 .
and the total head loss for the filter is: ⌬ h tot s
Fig. 7. Bioparticle disposition.
is calculated using the number Np of bioparticles present in that element: ⌬Vtot Ž t q dt . s ⌬V Ž t q dt . ⭈ Np
Np s
Ž dm q 2 .3
Ž 31 .
By applying the iterative procedure to Eqs. Ž28. and Ž30., the biofilm thickness increases, the filter starts to clog and the head losses rise. The filter may be considered a saturated system, and thus for the head loss computation, the one-dimensional Darcy equation is adopted ŽCharacklis and Marshall, 1989; Droste, 1997.: usK
⌬h ⌬h s g l l
Hb
u 1 ⭈ dz g Ž z.
Ž 35.
The suspended solids retention has not been considered in the head loss computation.
Ž 30 .
The disposition of the bioparticles is supposed to be cubic ŽFig. 7. Žthis configuration corresponds to the maximum value of the porosity ., and thus Np is: A⭈⌬ z
H0
Ž 32 .
The permeability depends on the biofilm thickness
3. Calculation procedure The equations are integrated using an implicit finite differences technique. Since Eqs. Ž5a., Ž5b. and Ž5c. and Eqs. Ž11a. and Ž11b. are non-linear, following the classical definition of a non-linear equation ŽSmith, 1985., calculation is carried out using an iterative method, which has been shown to have fast convergence, assigning to the terms causing non-linearity Žthese terms are the substrate concentrations in the denominator in Monod kinetics. initial values updated at every iteration by previously calculated ones. The calculation has been executed as follows ŽSbaffoni, 2000.: 1. Integration over the biofilm thickness to determine the concentration profiles of COD, N-NHq 4 and oxygen, and the efficiency factors Ž c and n .;
Fig. 8. Relation between the permeability and the biofilm thickness.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
19
Fig. 10. Subroutine for integration along the filter bed.
4. Sensitivity analysis
Fig. 9. Program flow chart.
2. Integration over the entire height of the filter bed using the values of c and n calculated above, to obtain the variation in substrate concentrations in the bed; 3. Computation of the increase in biofilm thickness, due to the biomass growth at different bed heights; 4. Calculation of the total head loss; and 5. Comparison between the calculated total head loss and the maximum acceptable one Ž130 mbar.. If the calculated value is lower than the maximum one, the time is increased by ⌬ t Ž30 min. and the calculation procedure is repeated, unless the maximum time is reached. Otherwise, filter clogging requires the interruption of the filtration phase to run the backwashing phase. The model was solved on a 233-MHz IBM-compatible PC. The running time depends on the maximum time that has been set and on the operating conditions, which may reduce the actual duration of the filtration cycle. Referring to a duration of 12 h, the program takes approximately 4 min to run. The flow charts depicting the program and the subroutines Žintegration along the bed and along the biofilm. are reported in Figs. 9᎐11.
The sensitivity analysis ŽSbaffoni, 2000. allows verification of the behavior of the model as a consequence of a variation of the input parameters Žthese variations represent any changes in the operating conditions of the filter.; for this purpose, a certain condition is assumed: this is called the reference situation, and the relative solution Žgiven by the numerical model. is compared with the different solutions obtained by vary-
Fig. 11. Subroutine for integration along the biofilm.
20
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 12. COD concentration profiles in the filter: variation with fluid velocity.
Fig. 13. N-NHq 4 concentration profiles in the filter: variation with fluid velocity.
Fig. 14. COD concentration profiles in the filter: variation with DO concentration.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
21
Fig. 15. N-NHq 4 concentration profiles in the filter: variation with DO concentration.
ing the value of some input parameters. The following graphs have been obtained with the ␣ function: ␣ s exp ycos t ⭈
z Hb
ž /
n
Ž 36.
where cos t s 10y8 and n s 4. Figs. 12 and 13 show the influence of the flow velocity u on the concentration profiles of COD and N-NHq 4 ; in fact, with increasing u, the contact time between the wastewater and the bioparticles is reduced, producing lower treatment efficiency. Another important parameter is the concentration of dissolved oxygen in the filter bed, because it influences the removal efficiency, in particular Žas shown in Figs. 14 and 15. of the nitrification process, due to the greater sensitivity of autotrophic microorganisms to the
environmental parameters Ždissolved oxygen concentration, temperature, pH, etc... In the model, the oxygen concentration has been considered constant: indeed from the experimental campaign Ždescribed in the following section., strongly aerobic conditions were evident. The values adopted for the DO concentration in the sensitivity analysis are 2 Žthe typical value used in the activated sludge process., 1 Ža particularly low value. and 10 mgrl. These tests ŽFigs. 12᎐15. have been executed considering a single step; obviously, it is also possible to analyze the entire filtration cycle, following the evolution of the COD and N-NHq 4 concentration profiles over time. In this case, the increase in the head loss and the biofilm thickness may be studied. The concentration adopted for DO was 10 mgrl. In Figs. 16 and 17, the substrate concentration pro-
Fig. 16. COD concentration profiles in the bed: variation with time Ž yc s 0.45, yn s 0.2..
22
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Ž . Fig. 17. N-NHq 4 concentration profiles in the bed: variation with time yc s 0.45, yn s 0.2 .
Fig. 18. COD concentration profiles in the bed: variation with time Ž yc s 1.0, yn s 0.5..
Ž . Fig. 19. N-NHq 4 concentration profiles in the bed: variation with time yc s 1.0, yn s 0.5 .
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
23
Fig. 20. COD concentration profiles in the biofilm: variation with bed height.
files in the bed at different steps of the cycle are shown, assuming the values of 0.45 for the heterotrophic biomass growth-yield coefficient and 0.2 for the autotrophic biomass. Figs. 18 and 19 represent the same profiles obtained with growth yield coefficients equal to 1.0 for the heterotrophs and 0.5 for the autotrophs. The cycle is interrupted at 510 min from the beginning of the cycle, rather than at 720 min. As a consequence of the higher growth yield coefficients adopted, the biofilm thickness increases more quickly, producing a rapid rise in the head loss; the filtration phase is stopped and the backwashing phase begins. The concentration profiles of the substrates in the biofilm are also obtained as an output of the numerical model; in Figs. 20 and 21, the concentration of COD
and DO in the biofilm at different heights of the bed are shown, respectively. Fig. 20 proves the effects of the ␣ function on COD removal; indeed, as the bed height rises, the carbonaceous substrate consumption rate decreases as a consequence of the lower quantity of heterotrophic biomass. Fig. 21 instead shows that at z s 0.001 m, the biofilm is fully penetrated by oxygen, because of the low con. sumption of substrate ŽCOD and N-NHq 4 at the bottom of the bed, while at z s 1 m, the biofilm is only partially penetrated. This is due to the simultaneous removal of COD and N-NHq 4 , with high consumption of oxygen Žespecially for the nitrification.. At z s 2 m, the oxygen concentration in the biofilm is almost constant, since at the end of the bed there is no removal of COD w ␣ Ž zs 2 m. s 0; only autotrophic biomass is pre-
Fig. 21. DO concentration profiles in the biofilm: variation with bed height.
24
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 22. COD concentrations during the day, 26 April 2000.
Ž sent. or of N-NHq 4 as shown in Fig. 15 with a concentration 10 mgrl of DO in the bed, the ammonia-nitrogen is entirely consumed at z s 2 m..
weekly collections, and samples were collected at eight different sections of a single filtration unit. The sections were located at the following points: 䢇
5. Experimental campaign
䢇 䢇
The numerical model was calibrated using experimental data obtained from a Biostyr 䊛 biofiltration unit at the Rome southern municipal wastewater treatment plant. Samples for the characterization of substrate concentration profiles were collected during March and April 2000. The sampling schedule consisted of two
Feed channel; Filtered water head; and Six sampling ports positioned every 50 cm along the bed height.
Samples were collected sequentially so as to follow the fluid motion through the filter. Withdrawals from the sampling ports along the bed were carried out considering the mean fluid velocity in order to take into account the water residence time in the filter.
Fig. 23. N-NHq 4 concentrations during the day, 26 April 2000.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
25
Table 2 Model parameters and relative references Parameter
Name
Axial dispersion coefficient Dynamic viscosity of the liquid phase Density of the liquid phase Žat 20⬚C. Glucose diffusivity in the liquid phase Ammonia-nitrogen diffusivity in the liquid phase Oxygen diffusivity in the liquid phase Biomass mean density Glucose diffusivity in the biofilm Ammonia-nitrogen diffusivity in the biofilm Oxygen diffusivity in the biofilm Half-saturation constant ŽCOD. Half-saturation constant ŽN-NH4 q. Half-saturation constant ŽO2 rCOD. Half-saturation constant ŽO2 rN-NH4q . Maximum rate coefficient ŽCOD. Maximum rate coefficient ŽN-NH4q .
DZ DSL C DSL N
Oxygen consumption for COD removal Oxygen consumption for N-NH4 q removal Heterotrophic biomass growth yield Autotrophic biomass growth yield
Model value y5
10 0.001005 998.2 6.7= 10y1 0 1.70= 10y9
DSL O bc DSBC DSBN
2.30= 10y9 60 3.35= 10y10 1.30= 10y9
DSBO ksc ksn ksco ksno kc kn
1.50= 10y9 0.05 0.001 0.0004 0.0004 5.78= 10y5 4.14= 10y5
ko1 ko2
1.07 4.57
yc yn
0.45 0.01
Ammonia-nitrogen, COD, nitrate, TSS, DO, pH and temperature were determined on each sample, according to standard analytical procedures. Head losses were also monitored during the sampling period.
6. Calibration phase In order to verify the ability of the numerical model to predict the results obtained from the samples collected at the Rome southern municipal wastewater treatment plant, the program was run using the operating conditions obtained in each sampling campaign
Units
Reference
2
m rs kgrm s kgrm3 m2 rs m2 rs
Characklis Characklis Characklis Characklis Characklis
m2 rs kgrm3 m2 rs m2 rs
Characklis and Marshall, 1989
and Marshall, 1989 and Marshall, 1989 and Marshall, 1989 and Marshall, 1989 and Marshall, 1989
Characklis and Marshall, 1989 Characklis and Marshall, 1989
m2 rs Characklis and Marshall, 1989 kg CODrm3 Metcalf and Eddy, 1991 kg N-NH4qrm3 Beccari et al., 1993 kg O2 rm3 kg O2 rm3 kg CODrkg VSS Metcalf and Eddy, 1991 kg N-NH4 q Beccari et al., 1993 rkg VSS kg O2 rkg COD Characklis and Marshall, 1989 kg O2 rkg N-NH4 q Metcalf and Eddy, 1991 kg VSSrkg CODr Beccari et al., 1993 kg VSS Beccari et al., 1993 rkg N-NH4q r
ŽLeccese, 2000. as input data Ždissolved oxygen, ammonia-nitrogen and COD concentrations, fluid velocity, water temperature and pH.. All of these parameters Žin particular ammonia-nitrogen and COD concentrations . obviously varied over time due to the well-known nonuniformity of wastewaters in sewage collectors. Figs. 22 and 23 show COD and ammonia-nitrogen concentrations in the plant inlet during the day, respectively. Parameters reported in Table 2 were obtained from the literature, while the parameters characterizing the functions ␣ Ž z ., Ž z . and Ž , z . have been calibrated in order to best fit the results of the simulation to those derived from the experimental campaign. Such a procedure allows us to associate with each of
Table 3 Parameters obtained through the calibration phase for the functions ␣ Ž z . and Ž z .
a b c d e f g h
03r28r2000
03r30r2000
04r04r2000
04r06r2000
04r11r2000
04r18r2000
04r20r2000
1.00= 10y1 9.00= 10y1 1.00= 10y1 1 4.7 1.00= 10y5 6.00= 10y5 1.00= 10y1 7 8.0
1.00= 10y1 9.00= 10y1 1.00= 10y11 4.98 7.00= 10y6 1.20= 10y4 1.00= 10y20 9.8
1.00= 10y1 9.00= 10y1 1.00= 10y9 4.15 1.00= 10y6 5.00= 10y5 1.00= 10y19 9.5
1.00= 10y1 9.00= 10y1 1.00= 10y10 4.7 5.00= 10y6 5.50= 10y5 1.00= 10y19 9.5
1.00= 10y1 9.00= 10y1 1.00= 10y11 4.98 5.00= 10y6 9.00= 10y5 1.00= 10y10 5.0
2.00= 10y1 8.00= 10y1 1.00= 10y9 3.85 2.00= 10y6 9.00= 10y5 1.00= 10y24 11.8
2.00= 10y1 8.00= 10y1 1.00= 10y9 3.85 1.00= 10y6 1.50= 10y4 1.00= 10y24 11.8
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
26
Table 4 Averaged parameters assumed in the functions ␣ Ž z ., Ž z . and Ž z . ␣Ž z.
Ž z.
Ž , z .
a
b
c
d
e
f
g
h
i
l
0.188
0.812
1 = 10y9
4.112
4.43= 10y6
8.79= 10y5
1 = 10y16
7.86
2.41= 10y8
2.09= 10y4
the aforesaid parameters a set of values ŽTable 3., used to fit each experimental curve. The functions obtained for the above-mentioned variables ␣ and , presented
in Figs. 24 and 25, have been averaged; the average functions have been adopted in further model applications. Figs. 26 and 27, which show the trend of ␣ and
Fig. 24. Heterotrophic biomass fraction distribution along the bed height.
Fig. 25. Biofilm thickness distribution along the bed height.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
27
Fig. 26. Assumed heterotrophic biomass fraction distribution along the bed height.
functions described later in the text, are obtained using the following expressions of ␣ , and : ␣ Ž z,t . s aq b⭈ exp yc ⭈
ž Hz /
d
Ž 37.
b
Ž z,t . s e q f ⭈ 1 y exp yg ⭈
z Hb
h
ž ž //
Ž Ž z . ,t . s i y 1 ⭈ w Ž z . y min Ž z .x
Ž 38 .
Ž 39.
where the different parameters assume the averaged values reported in Table 4. The values reported, obtained by averaging results from 10 experimental campaigns, may be used for analysis of the performance of similar biofiltration units in design problems, while if experimental data are available or can be obtained, a new calibration procedure can be useful to properly fit units already in operation. Eq. Ž38. shows the non-uniformity of the biofilm thickness distribution along the bed height: particularly, the thickness was assumed to be very small in the
Fig. 27. Assumed biofilm thickness distribution along the bed height.
28
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 28. COD concentration along the bed, 30 March 2000.
deepest layers Žapprox. 5 m. and to increase from the central part up to the top, where it reached approximately 90 m. Such a hypothesis is required in order to justify the slow consumption of the COD, confirmed from experimental results, in the lower part of the filter bed. Although this may seem anomalous, it can be explained by considering that, since the processrwash-
ing air is injected at the bottom of the filter bed, the lower layers are characterized by greater turbulence and irregularity in the water flow. Such flow conditions operate a strong shear stress on the bioparticles, thus hindering the biomass growth. The comparison between experimental data and the corresponding simulated profiles reported in Figs.
Fig. 29. N-NHq 4 concentration along the bed, 30 March 2000.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
29
Fig. 30. COD concentration along the bed, 11 April 2000.
28᎐31 proves that the model output related to different operating conditions, even using averaged values for the parameters characterizing the biofilm behavior, fits well the real behavior of the examined biofilter. Figs. 28 and 29 refer to a single sampling, while Figs. 30 and
31 show the concentration profiles of the two substrates at two different times in a filtration cycle. ŽIt is worthwhile to note the great changes in the wastewater quality at the inlet.. The concentration trends of the two substrates along
Fig. 31. N-NHq 4 concentration along the bed, 11 April 2000.
30
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
Fig. 32. Head loss trends with time: comparison between observed and simulated values, 30 March 2000.
the filter heights appear to be different in shape. This is mainly due to the function ␣ that greatly influences the model output, controlling the simultaneous removal of the substrates. Also, the increase in the fraction of heterotrophic microorganisms at each level with time correctly interprets the phenomenon generally
occurring as time elapses in a filtration cycle. Indeed, as a result of the faster growth of this group of bacteria, the efficiency of the COD removal increases, not being influenced by the increase in the inflow concentration. Figs. 32 and 33 show a comparison between the head
Fig. 33. Head loss trends with time: comparison between observed and simulated values, 11 April 2000.
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
loss values derived from the on-line computerized control system of the Biostyr 䊛 and those calculated by the simulation program. For quantification of the errors, a polynomial regression curve of the second order has been adopted. The results presented show that the most important parameters are ␣ , and . Use of the numerical model is rather simple once these parameters are defined. The tests carried out have shown that the values suggested in the present paper can be used for operating conditions close to those encountered in wastewaters arriving at the treatment plant investigated. The only inputs then needed are the inlet conditions Žflow rate, temperature and pH. and the pollutant concentration involved in the treatment ŽCOD and ammonia-nitrogen removal..
7. Conclusions The numerical model developed has the aim of simulating: 䢇 䢇 䢇 䢇
COD removal; Ammonia-nitrogen removal; Biofilm growth; and Head loss trends.
The sensitivity analysis led to the determination of the parameters affecting the efficiency of the treatment process. Among those parameters, the most important are: 䢇 䢇
Fluid velocity; and Dissolved oxygen concentration.
Their control seems to be essential for proper process operation. The distribution of heterotrophic and autotrophic microorganisms, expressed by the function ␣ , influences the relative consumption of the two substrates. Also, the biofilm thickness profile along the bed height appears to be relevant for the model output. The experimental data collected have confirmed the assumption of s-shaped functions for both Ž z . and ␣ Ž z .. The model proposed for the simulation of the biofiltration process has proven to fit properly the experimental results derived from the sampling campaign conducted. Such a model can be used to better understand the influence of variations in operating conditions on the efficiency of the biofiltration process, representing furthermore a valid predictive tool for the management of existing wastewater treatment plants and for the design of new ones.
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Appendix A: Nomenclature biofilter cross section Žm2 . C brC bi ; COD concentration in the liquid phase in dimensionless form Bcc : K cc rDsbc ; Biot modified number for COD B cn : K cn rDsbn ; Biot modified number for ammonia-nitrogen Bco : K co rDsbo ; Biot modified number for the oxygen Bo : DzrŽ uH b .; Bodenstein number C: COD concentration in the biofilm Žkgrm3 . CU : CrC b ; COD concentration in the biofilm in dimensionless form C b : COD concentration in the liquid phase Žkgrm3 . C bd : COD concentration at the internal points of the filter Žkgrm3 . C bi : COD concentration in the feed flow Žkgrm3 . D L : substrate molecular diffusion coefficient in the liquid phase Žm2rs. d m : support medium diameter Žm. d p: bioparticle diameter Žm. Dsbc : COD diffusion coefficient in the biofilm Žm2rs. Dsbn : ammonia-nitrogen diffusion coefficient in the biofilm Žm2rs. Dsbo : oxygen diffusion coefficient in the biofilm Žm2rs. Dz : axial dispersion coefficient Žm2rs. H b : height of the filter bed Žm. K: hydraulic conductivity Žmrs. kc: COD maximum utilization rate Žkgrkg s. K cc : COD mass exchange coefficient K cn : ammonia-nitrogen mass exchange coefficient K co : oxygen mass exchange coefficient k n: ammonia-nitrogen maximum utilization rate Žkgrkg s. k o1: oxygen specific consumption in the biofilm for COD degradation Žkg O 2rkg COD. k o2 : oxygen specific consumption in the biofilm for ammonia-nitrogen degradation Žkg O 2rkg N. NHq 4 k sc : COD half-saturation constant Žkgrm3 . k sco : oxygen half-saturation constant for COD removal Žkgrm3 . k sn : ammonia-nitrogen half-saturation constant Žkgrm3 . k sno : oxygen half-saturation constant for the ammonia-nitrogen removal Žkgrm3 . N: ammonia-nitrogen concentration in the biofilm Žkgrm3 . U N : NrNb ; ammonia-nitrogen concentration in the biofilm in dimensionless form Nb : ammonia-nitrogen concentration in the liquid phase Žkgrm3 . Nbd : ammonia-nitrogen concentration in the internal points of the filter Žkgrm3 . A: BU :
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Nbi : O: OU : O b: O bi : p: Q: r: RI: R Ic : R In : rm : R o: R oc : R on : rp: R v: R vc : R vn : Sb: u: VB : VL : VM : x: Yc : yc : Yco : Yn : yn : Yno : z: ␣: : 2c : 2co : 2n :
P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33
ammonia-nitrogen concentration in the feed flow Žkgrm3 . oxygen concentration in the biofilm Žkgrm3 . OrO b ; oxygen concentration in the biofilm in dimensionless form oxygen concentration in the liquid phase Žkgrm3 . oxygen concentration in the feed flow Žkgrm3 . slope of the linear function s Ž Ž z .,t . Žm. flow rate Žm3rs. spatial coordinate in the biofilm Žm. intrinsic reaction rate for unit volume of the biofilm Žkgrm s. intrinsic reaction rate for unit volume of the biofilm for the COD Žkgrm s. intrinsic reaction rate for unit volume of the biofilm for the ammonia-nitrogen Žkgrm s. support medium radius Žm. observed reaction rate for unit volume of the biofilm Žkgrm s. observed reaction rate for unit volume of the biofilm for the COD Žkgrm s. observed reaction rate for unit volume of the biofilm for the ammonia-nitrogen Žkgrm s. bioparticles radius Žm. observed reaction rate for unit volume of the bed Žkgrm s. observed reaction rate for unit volume of the bed for the COD Žkgrm s. observed reaction rate for unit volume of the bed for ammonia-nitrogen Žkgrm s. generic substrate concentration in the liquid phase Žkgrm3 . QrA; fluid velocity Žmrs. biofilm volume Žm3 . bed volume Žm3 . support medium volume Žm3 . Ž r y rm .r; spatial coordinate in the biofilm in dimensionless form k scrC b growth yield coefficient for heterotrophic biomass Žkg VSS heterotrophicrkg COD. k scorO b k snrNb growth yield coefficient for autotrophic biomass Žkg VSSautotrophicrkg COD. k snorO b spatial coordinate in the filter bed Žm. heterotrophic biomass fraction in the biofilm porosity k c bd 2rŽ Dsbc C b .; Thiele modified module for the COD k c bd 2rŽ Dsbo O b .; Thiele modified module for the oxygen in the COD removal k n bd 2rŽ Dsbn Nb .; Thiele modified module for the ammonia-nitrogen
2no : ␥c : ␥co : ␥n : ␥no : : c : n : : : : bd : : : : : ⌳U :
k n bd 2rŽ Dsbo O b .; Thiele modified module for the oxygen in the ammonia-nitrogen removal k scrC bi k scorO bi k snrNbi k snorO bi efficiency factor efficiency factor for the COD efficiency factor for the ammonia-nitrogen permeability Žm2 . dynamic viscosity of the liquid phase Žkgrm s. density of the liquid phase Žkgrm3 . mean biomass concentration in the biofilm Žkgrm3 . biofilm thickness Žm. H bru d mr2 zrH b ; spatial coordinate in the bed in dimensionless form NbrNbi ; ammonia-nitrogen concentration in the bed in dimensionless form
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P. Viotti et al. r Ad¨ ances in En¨ ironmental Research 7 (2002) 11᎐33 Horn, H., Hempel, D.C., 1997. Growth and decay in an auto-rheterotrophic biofilm’. Water Res. 31 Ž9., 2243᎐2253. La Motta, E.J., Mulcahy, L.T., 1978. Mathematical Model of the Fluidized Bed Biofilm Reactor. Department of Civil Engineering, University of Massachusetts, Amherst. Report No Env E 59-78-2 Leccese, M., 2000. Modellizzazione del Processo di Biofiltrazione: Validazione Sperimentale e Applicazione al Caso dell’Impianto. ACEA di Roma Sud. Masters dissertation. Metcalf, A., Eddy, A., 1991. Wastewater Engineering: Treatment, Disposal, Reuse. McGraw Hill International. Sbaffoni, S., 2000. Modellizzazione del Processo di Biofiltrazione: Sviluppo del Codice Numerico e Analisi di Sensitivita. ` Masters dissertation. Smith, G.D., 1985. Numerical Solution of Partial Differential Equations: Finite Difference Methods. Clarendon Press, Oxford. Van Loodsrecht, M.C.M., 1993. Kinetics of Biofilm Systems. Department of Biochemical Engineering, Delft University of Technology.
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subsoils and the atmosphere, and the numerical simulation of ecological systems. Biagio Eramo is Chief Executive of the ATO 2 firm that provides water supply and wastewater treatment in Rome. In the past he has carried out research activity on a pilot plant of a fluidized bed reactor. Maria Rosaria Boni is Associate Professor of Environmental Engineering at the University of Rome ‘La Sapienza’. She is mainly interested in research projects concerning the contamination of superficial and underground water and its treatments. Alessandra Carucci is Associate Professor of Environmental Engineering at the University of Cagliari. Her scientific activity concerns the areas of wastewater and municipal solid waste treatment.
Vitae
Michele Leccese has a Masters degree in Environmental Engineering.
Paolo Viotti is Associate Professor of Environmental Engineering at the University of Rome ‘La Sapienza’. His research topics mainly address pollutant transport in soils,
Silvia Sbaffoni has a Masters degree in Environmental Engineering.