Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/watres
Modeling the behaviors of adsorption and biodegradation
in biological activated carbon filters
Chung-Huei Liang
a, Pen-Chi Chiang
a,, E-E Chang
baGraduate Institute of Environmental Engineering, National Taiwan University, No. 71, Chou-shan Road, Taipei 106, Taiwan b
Department of Medicine, Taipei Medical University, 250 Wu Hsing Street, Taipei 110, Taiwan
a r t i c l e
i n f o
Article history:
Received 27 December 2006 Received in revised form 9 May 2007
Accepted 15 May 2007 Available online 21 May 2007 Keywords:
Adsorption Biodegradation
Biological activated carbon (BAC) Granular activated carbon (GAC) Numerical model
a b s t r a c t
This investigation developed a non-steady-state numerical model to differentiate the adsorption and biodegradation quantities of a biological activated carbon (BAC) column. The mechanisms considered in this model are adsorption, biodegradation, convection and diffusion. Simulations were performed to evaluate the effects of the major parameters, the packing media size and the superficial velocity, on the adsorption and biodegradation performances for the removal of dissolved organic carbon based on dimensionless analysis.
The model predictions are in agreement with the experimental data by adjusting the liquid-film mass transfer coefficient (kbf), which has high correlation with the Stanton
number. The Freundlich isotherm constant (NF), together with the maximum specific
substrate utilization rate (kf) and the diffusion coefficient (Df), is the most sensitive variable
affecting the performance of the BAC. Decreasing the particle size results in more sub-strate diffusing across the biofilm, and increases the ratio of adsorption rather than biodegradation.
&2007 Elsevier Ltd. All rights reserved.
1.
Introduction
The biological activated carbon (BAC) process, which contains adsorption and biodegradation mechanisms, has been widely used in water and wastewater treatments for lowering the regeneration cost and prolonging the life of granular activated carbon (GAC) beds. Researchers and operators have been attempting to elucidate each mechanism for the purpose of
simulation and optimization. For biodegradation, Hozalski
et al. (1995)reported that the removal efficiency did not vary significantly under a certain empty-bed contact time (EBCT)
ranging between 4 and 20 min. Melin and Ødeggard (2000)
indicated that the optimum EBCT was approximately 20 min, since longer EBCT could not significantly increase the
removal efficiency.Rittmann et al. (2002)reported that EBCT
greater than 3.5 min had insignificant effects on dissolved
organic carbon (DOC) removal in pilot filters treating ozonated
groundwater.Li et al. (2006)reported that the optimum EBCT
was 15 min for an ozone-BAC process to treat raw waters. A well-validated mathematical model can provide valuable information to assess and predict the performance of BAC,
and some representative models are listed inTable 1(Chang
and Rittmann, 1987;Sakoda et al., 1996;Walker and Weath-erley, 1997;Abumaizar et al., 1997;Hozalski and Bouwer, 2001;
Badriyha et al., 2003).Chang and Rittmann (1987)developed a mathematical model that could quantify the extent of adsorption and biodegradation. One of its remarkable con-tributions is to illustrate and quantify the mass transfer of substrates diffusing through the biofilm, metabolized by microbes, and finally reaching the surface of GAC. The limitation is that it cannot be used under unsteady or
plug-flow conditions.Sakoda et al. (1996)suggested a theoretical
0043-1354/$ - see front matter & 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2007.05.024
Corresponding author. Tel.: +886 2 2362 2510; fax: +886 2 2366 1642. E-mail address:pcchiang@ntu.edu.tw (P.-C. Chiang).
model for a BAC column, in which the mechanisms included dispersion, convection, biodegradation and adsorption. The primary assumption for simplifying is that the substrate concentration on the interface between the biofilm and the
GAC is identical to that in the bulk solution. However, this assumption implies that there is no concentration reduction within the biofilm; thus, that model is not fit for the condition
with thick biofilm. In1997, Walker and Weatherleyproposed a
Nomenclature
A
f surface area of a BAC granule (L2)b
tot total decay coefficient (1/T)d
p packing media diameter (L)D
f diffusivity in biofilm (L2/T)D
z dispersion coefficient in the liquid phase (L2/T)K
b half-velocity concentration in water (M/L3)k
b max. specific substrate utilization rate in water(M/CFU-T)
k
bf liquid-film mass transfer coefficient(dimension-less)
K
f half-velocity concentration in biofilm (M/L3)k
f max. specific substrate utilization rate in biofilm(M/CFU-T)
k
F Freundlich isotherm coefficients (dimensionless)K
L Langnuir isotherm coefficients (dimensionless)L
c column length (L)L
f length of the biofilm (L)m
g mass of a GAC granule (M)N
Da Damko¨hler number (dimensionless)N
F Freundlich isotherm coefficients (dimensionless)N
Re Reynolds number (dimensionless)N
Sh Sherwood number (dimensionless)N
St Stanton number (dimensionless)q
0 Langnuir isotherm coefficients (M/M)q
a adsorption capacity (M/M)r
f biofilm radius (L)r
g GAC granule radius (L)S
b substrate concentration in the liquid phase (M/L3)S
b0 influent concentration (M/L3)S
f substrate concentration in the biofilm (M/L3)V
g volume of a GAC granule (L3)x
distance along the BAC column (L)X
b cell density in the liquid phase (CFU/L3)X
f biofilm density (CFU/L3)Y
specific yield (CFU/M)v
s superficial velocity (L/T)Greek symbols
e
porosity (dimensionless)n
kinetic viscosity of the bulk solution (L2/T)r
g GAC granule apparent density (M/L3)Table 1 – Some of the representative BAC models
Reactor type
Mechanisms considereda
Kinetic condition Mass
transport descriptionb Solution method References Substrate in bulk phase Substrate in biofilm Biofilm amount Substrate in GAC Complex mixing A, B Non-steady monod Monod Non-steady Non-equilibrium
1, 2, 3, 4, 5 Analytical Chang and Rittmann
(1987)
Column A, B, C, D Non-steady no biodegradation
n.a.c Steady Equilibrium 1 Analytical Sakoda et
al. (1996)
Column A, B Uniform Monod
Monod Non-steady
n.a.c 1 Analytical Walker and
Weatherley (1997)
Column A, B, C Non-steady no biodegradation
Monod Steady Non-equilibrium 1, 5 Analytical Abumaizar et al. (1997) Column B, C, D Non-steady Monod Monod Non-steady
n.a.c 1, 2, 3 Numerical Hozalski
and Bouwer (2001) Column A, B, C, D Non-steady no biodegradation Monod Non-steady Non-equilibrium 1, 2, 3, 4, 5 Numerical Badriyha et al. (2003)
a A ¼ adsorption, B ¼ biodegradation, C ¼ convection, D ¼ dispersion.
b 1 ¼ bulk phase, 2 ¼ interface between bulk phase and biofilm, 3 ¼ biofilm, 4 ¼ interface between biofilm and GAC, 5 ¼ GAC. c Not analyzed in the article.
simplified predictive model for BAC fixed beds based on Monod kinetics. Their mathematical development is under the assumptions that the BAC system is a simple combination of adsorption and biodegradation, so that the model can be executed without the detailed analysis of diffusion and biodegradation in the biofilm. A detailed biofilter model was
reported byHozalski and Bouwer in 2001. In their model, the
length of the biofilm is controlled by biotic processes as well
as mass transfer dynamically. In 2003, Badriyha et al.
proposed a mathematical model for the design and the performance prediction of a bioadsorber reactor. Their governing equations contain the terms of adsorption, biode-gradation, convection and dispersion. Although it is able to solve the non-steady-state condition, the mass flux entering the biofilm from bulk solution will be restricted after the adsorption capacity is exhausted since the substrate concen-trations are assumed to be identical on the both sides of the adsorbent–biofilm interface.
This research developed a numerical model to simulate both adsorption and biodegradation quantities of a BAC column under a non-steady-state condition, so as to predict the effluent concentration, biomass profiles and the residual capacity of adsorption. The basic assumptions of our model are that (1) the granules used in BAC are spherical in shape, and the biofilm is homogeneous and the density of the biofilm is constant; (2) biodegradation reactions can be neglected in the pores of the granules, because the size of most meso- or
micro-pores (o0.05 mm) of GAC are less than the size of a
microbe; (3) desorption after the saturation of the GAC is not taken into consideration because this model focuses on the simulation of virgin GAC; (4) a peeled-off biofilm is neglected as the source of DOC; (5) there is no competition or inhibition between two substrates. We also performed a series of bench-scale continuous column tests for model calibration and validation, and assessed the effects of packing media size on adsorption and biodegradation performances with the di-mensionless analysis.
2.
Materials and method
2.1. Model developmentThe governing equation is based on mass balance for the substrate concentration in the liquid phase of the BAC column: qSb;i qt ¼Dz;i q2Sb;i qx2 vs qSb;i qx ð1 Þ Vg ZLf 0 kf;iXfSf;i Kf;iþSf;i 4pðrfþrgÞ2drf ð1 Þrgqqa;i qt kb;iXbSb;i Kb;iþSb;i , ð1Þ
where e is the bed porosity of the BAC column; Sb,i is the
substrate concentration in the liquid phase (M/L), and i ¼ 1, 2
denotes components 1 and 2, respectively; Dz,iis the
disper-sion coefficient in the liquid phase (L2/T), x is the distance
along the BAC column (L), nsis the superficial velocity (L/T); Vg
is the volume of a GAC granule (L3); L
f is the length of the
biofilm (L); kf,iis the maximum utilization rate in the biofilm
(M/T-cell); Xfis the cell density of the biofilm (cell/L3); Sf,iis the
substrate concentration in the biofilm (M/L3); Kf,iis the Monod
half-velocity coefficient in the biofilm (M/L3); rfand rgare the
radius of the biofilm and the GAC granule, respectively (L); rg
is the GAC granule density (M/L3); q
a,i is the adsorption
capacity (M/M); kb,iis the maximum utilization rate in the
liquid phase (M/T-cell); Xb is the cell density in the liquid
phase (cell/L3); and Kb,iis the Monod half-velocity coefficient
in the liquid phase (M/L3).
The boundary conditions (BC) of the dispersion–advection reaction equation are
BC 1 : Sb;i¼Sb0;i x ¼ 0; tX0, (2) BC 2 : qSb;i qx ¼0 x¼Lc , (3)
where Lcis the length of the BAC column (L).
The pathways of substrates after entering the biofilm are biodegradation and metabolism-independent processes such
as biosorption (Aksu and Tunc-, 2005). The non-steady-state
form of mass transfer and biodegradation reaction within biofilms, based on Fick’s law and Monod equation, can be expressed as qSf;i qt ¼Df;i q2Sf;i qr2 f kf;iSf;i Ks;iþSf;i Xf 0prfpLf, (4)
where Df,iis the diffusivity within the biofilm (L2/T). Eq. (4)
describes a non-steady-state biofilm condition, where diffu-sion and reaction are simultaneously occurring. One BC for Eq. (4) is that a diffusion layer exists between the bulk solution and the biofilm, and the BC can be simplified as Sf;i
r
f¼0¼kbf;iSb;i, (5)
where kbfis a factor to estimate the concentration reduction
within the diffusion layer.
Another BC for Eq. (4) describes the interface between the biofilm and the GAC surface based on the equilibrium of the
substrate. In the study conducted by Chang and Rittmann
(1987), they assumed that there existed an interface between the activated carbon and the biofilm, and used the Freundlich isotherm to describe the equilibrium at the interface. In this study, the Freundlich isotherm is also used to calculate the boundary concentration of the biofilm near the GAC side, which can be derived from the solid-phase concentration of the adsorbates. But for bi-component adsorbate cases, the Langmuir isotherm is used:
qa;i¼ q0KL;iCa;i 1 þ KL;jPCa;j
; j ¼ 1; 2, (6)
where q0is the unit-layer adsorption capacity (M/M); KL,iis
Langmuir coefficient (L3/M); and Ca,iis the substrate
concen-tration on the boundary of the biofilm (M/L3).
The calculation for the adsorption capacity is based on the fact that the substrate coming out from the biofilm is identical to that absorbed by a GAC:
4pr2 gDf;i qSf;i qrf rf¼Lf ¼qqa;i qt mg, (7)
where mgis the mass of a GAC granule (M).
The substrate diffusing into biofilm will be utilized by microbes for metabolism. In a control volume, the average
biodegradation rate can be derived by integrating the Monod reaction expression and the amount of biofilm volume:
ZLf 0 kfSf KfþSf Xf4pðrgþrfÞ2drf Ng; 0prfpLf, (8) Ng¼ DVð1 Þ Vg , (9)
where DV is a control volume unit of the BAC bed (L3) and N
gis
the number of BAC granules in a control volume.
Concerning the thickness of biofilm, the major enhancing factor is the reproduction of microbes, and the shrinking factors are the shear of water and the self-decay. Hence, biofilm thickness can be described as
qLf
qt ¼
YRLf
0 ððkiSf;iÞ=ðKs;iþSf;iÞXfÞ4pðrgþrfÞ2drf AfXf
btotLf,
0prfpLf, ð10Þ
where Y is true yield coefficient of biomass (CFU/M); Afis the
surface area of a BAC granule (L2); and b
totis the overall loss
rate of bacteria due to both decay and fluid shear (T1). In this research, the governing equation of the bacterial density in bulk solution can be simplified as an advection-reaction form, because dispersion and the effects of growth
and decay are insignificant in a macroscope (Hozalski and
Bouwer, 2001): qXb qt ¼ n qXb qx þ Ykb;iSb;iXb Kb;iþSb;i . (11)
The BCs of Eq. (11) are shown below:
BC 1 : Xb¼X0; x ¼ 0; tX0, (12) BC 2 : qXb qx ¼0 x¼L c . (13) 2.2. Numerical solution
The governing equation of the substrate concentration in bulk solution is a second-order partial differential equation, and can be numerically approximated by the Crank–Nicolson finite difference method, with the Crout factorization method solving a tridiagonal linear system. The initial condition is
Sbðx; tÞ ¼ 0; t ¼ 0, (14)
qaðtÞ ¼ 0; t ¼ 0. (15)
The non-steady-state substrate concentration within the biofilm is also numerically approximated by the Crank–Ni-colson finite difference method, and the initial condition is
Sfðrf;tÞ ¼ 0; t ¼ 0. (16)
The program was written in FORTRAN 90 developed by Microsoft PowerStation.
2.3. Data analysis
The input parameters of this model were derived from our previous studies (Liang et al., 2003, 2004) and other research-ers’ work (Badriyha et al., 2003), listed inTable 2. In Scenario I, the target compound is an ozonation by-product, represented
as glyoxalic acid, which denotes a highly biodegradable but low absorbable substrate (Liang et al., 2003). In Scenario II, the target compounds are p-hydroxybenzoic acid and its ozona-tion intermediates, which represent the mixing of low biodegradable but highly absorbable (p-hydroxybenzoic acid) with highly biodegradable but low absorbable (ozonation intermediates) substrates (Liang et al., 2004). In scenario III, a pesticide alachlor is used as the target compound with
acetate to support the growth of microbes (Badriyha et al.,
2003).
Dimensionless parameters are calculated to determine the dynamics of the BAC reactor. In this study, the suggested dimensionless groups are
Reynolds number ¼ NRe¼ dpvs n , (17) Stanton number ¼ NSt¼kfcLc vsrg , (18) Sherwood number ¼ NSh¼ kfcrg Df , (19)
Damk €ohler number ¼ NDa¼
ðXfkf=KfÞr2g Df
, (20)
where n is the kinetic viscosity of the bulk solution (L2/T); d
pis
the diameter of the packing media (L); kfcis the liquid film
mass transfer coefficient in the column (L/T), and can be estimated by the dimensionless groups of Reynolds,
Sher-wood and Schmidt numbers (Wakao and Funazkri, 1978):
NSh¼2 þ 1:1 N1=2Re N 1=3
Sc. (21)
The Reynolds number represents the ratio between inertial force and viscous force; the Stanton number represents the ratio between liquid-film transfer and bulk transfer; the Sherwood number represents the ratio between liquid-film transfer and biofilm diffusive transfer; the Damko¨hler num-ber denotes the ratio between biodegradation rate and biofilm diffusive transport. A high Damko¨hler number indicates that the biodegradation rate exceeds the mass transfer rate within the biofilm, which implies that less substrate can transfer to the boundary of the GAC. It should be mentioned that these dimensionless groups are developed for scaling the reactor, and different reactors can be compared by each other through these dimensionless groups. In addition, certain operational parameters, such as the particle size of packing media and the superficial velocity of the influent, reasonably dominate the performance of a BAC column. Hence, we simulate the effects of the particle size on adsorption and biodegradation, and also attempt to formulate them according to dimensional groups.
3.
Results and discussion
3.1. Model calibrationThis model assumes that a diffusion layer exists between the bulk solution and the biofilm; thus, we introduce a liquid-film
mass transfer coefficient (kbf) to estimate the concentration
the experimental data. The best kbfvalue for simulation was
acquired by adjusting the output to the experimental data (Liang et al., 2004), and the results were represented quantitatively by the least-square value
Leastsquare value ¼1
N X all data points
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðCsim
eff CexpeffÞ2 ðCexpeffÞ2 v
u u
t . (22)
The average least-square value provides a quantitative comparison of the agreement between the simulation and the experimental data. As the average least-square value increases, the level of agreement between the two
simula-tions decreases. Meanwhile, a higher kbf permits a higher
driving force on the biofilm boundary, and makes the substrate concentration profile higher within the biofilm; as a consequence, the amounts of both biodegradation and adsorption increase at the same time.
Fig. 1 illustrates the correlation between the liquid-film mass transfer coefficient (kbf) and the Stanton number (NSt).
The Stanton number represents the ratio of the liquid-film transfer to the bulk transfer, and has inverse proportion to the particle size and the superficial velocity; that is, larger particle sizes or higher superficial velocities lead to a low liquid-film
mass transfer. Escudie´ et al. (2005) indicated that the
efficiency of the biological reactions was limited by the substrate transfer onto the biofilm. FromFig. 1, it is observed
Table 2 – Operation conditions and parameters used for model simulation
Parameter (symbol, unit) Scenario I (Liang et
al., 2004)
Scenario II (Liang et al., 2003)
Scenario III (Badriyha et al., 2003)
BAC filter and operation specifications
Target compound Glyoxalic acid p-hydroxy-benzoic acida Alachlor Column length (Lc, cm) 50 25 5b Column diameter (dc, cm) 5 5 1.25 Porosity (e) 0.4 0.4 0.4b Superficial velocity (vs, cm/h) 300 1200 972
GAC granule radius (rg, cm) 0.11 0.11 0.018
GAC granule apparent density (rg, g/cm3) 0.88 0.88 1.25
Temperature (1C) 25 25 25
Flow type Downflow Downflow Upflow
Recycle ratio 0 0 5
Substrate properties
Influent concentration (Sb0, mg/L) 0.4 (as DOC) 2.5 and 0.6 (as DOC) 0.8 (as alachlor)
Dispersion coefficient (Dz, cm2/h) 297 1296 154
Diffusivity in biofilm (Df, cm2/h) 2.9 102 2.3 102 1.3 102
Biokinetic and bioassay constants
Max. specific substrate utilization rate in water, biofilm (kband kf, mg/CFU-h)
1.7 1010 2.1 1011 0.66c
Half-velocity concentration in water, biofilm (Kband
Kf, mg/L)
0.1 10 60
Specific yield (Y, CFU/mg) 6.45 108 6.45 108 0.6c
Biofilm density (Xf, CFU/L) 5.0 1013 5.0 1013 35 (mg/cm3)
Total decay coefficient (btot, 1/day) 0.25 0.25 0.072
Adsorption constants
Freundlich isotherm coefficients (kF, NF) 14.1, 8.3 21.0, 3.7 102, 3.2
Langnuir isotherm coefficients (q0, KL) 18.9, 9.1 25.1, 11.1 102, 0.31
a With its ozonation intermediates; the properties of the intermediates set as Scenario I. b Assumption.
c Based on (mg-substrate/mg-biomass) or (mg-biomass/mg-substrate).
Stanton number, NSt (dimensionless) 0.00 0.02 0.04 0.06 0.08 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.035, 16.2, 4.4·10–6 (Badriyha et al., 2003) 0.3, 5.0, 8.1·10–6 (Liang et al., 2003) 0.3, 20, 8.1·10–6 (Liang et al., 2003) 0.3, 5.0, 1.0·10–5 (Liang et al., 2004) 0.3, 20, 1.0·10–5 (Liang et al., 2004) dp (cm), vs (cm/min), Df (cm2/s)
Liquid-film mass transfer coefficient, kbf (dimensionless) Fig. 1 – Correlation between the liquid-film mass transfer coefficient (kbf) and the Stanton number (NSt).
that the liquid-film mass transfer coefficient correlates with the Stanton number; that is, increasing the Stanton number can enhance the mass transfer from bulk solution into the biofilm.
3.2. Model verification
Fig. 2illustrates the adsorption capacities of the BAC granules according to our previous study (Scenario I) as well as the simulation results, which provide a criterion whether the
model fits the experimental data. InFig. 2, acceptable errors
exist between the model prediction and the experimental data; nonetheless, it implies that this model is a reasonable instrument for simulating the adsorption behavior of the BAC column.
Remarkable evidence is that the adsorbed DOC on BAC granules is less than that on GAC. During the simulation processes, the liquid-phase substrate concentration in the BAC column was lower than that in the GAC column because of the biological degradation; consequently, the equilibrium concentration of the BAC granules was lower than that of the GAC granules in the solid phase. In other words, the biodegradation mechanism can efficiently reduce the organic loading of the BAC granules.
To differentiate the quantities of adsorption and
biodegra-dation separately,Fig. 3a and bshows the cumulative removal
of p-hydroxybenzoic acid and the ozonation intermediates by the two mechanisms. Using the parameters of Scenario II, the simulation results are in accordance with the experimental data. As expected, the major mechanism for the removal of p-hydroxybenzoic acid is adsorption, and of the ozonation intermediates is biodegradation. The results of both experi-ment and simulation lead to a consensus that the BAC column cannot effectively remove the substrate until biode-gradation reaches the point of equilibrium. In this research,
biodegradation changed from an unsteady to a steady state after approximately 2–3 weeks of operation when the effluent concentrations varied within a narrow range.
In addition,Fig. 4denotes that our model is also validated
well by other researchers’ results (Badriyha et al., 2003). In their experimental system, some facts should be noted. First, they recycled the effluent back to the influent (recycle ratio ¼ 5), so that the influent concentration was amplified if the target compound existed in the effluent. Second, they added acetate in the feed solution to sustain the growth of microbes; that is, the behavior of biodegradation was
Cumulative removed p -hydroxybenzoic acid (g) Cumulative removed ozonation intermediates (g) 0 4 8 12 16 0 10 20 30 40 50 0 10 20 30 40 50 adsorption adsorption+biodegradation adsorption adsorption+biodegradation
}
}
simulation experiment adsorption adsorption+biodegradation adsorption adsorption+biodegradation}
}
simulation experiment 0 2 4 6 Time (day)Fig. 3 – Cumulative removal of DOC by adsorption and biodegradation: (a) p-hydroxybenzoic acid and (b) ozonation intermediates. 0 2 4 6 8 10 12 0 10 20 30 40 50 60 day L = 0 L = 20 L = 0 L = 20 (cm) experiment
}
simulation}
Dimensionless group NRe= 20.6 NSc= 864 NSh= 48.5 NSt= 3.3·10-2 NDa= 8.6·104 mg-organic carbon/g-BACFig. 2 – Organic carbon adsorbed on the GAC granules under various depths. Dimensionless effluent ( Si /S0 ) 0.0 1.0 0 20 Lf,Max = 4µm Lf,Max = 10µm Lf,Max = 2µm Experimental data Dimensionless group NRe = 2.1 NSc = 2034 NSh = 21.9 NSt = 3.8·10-2 NDa = 9.5·10-3 0.8 0.6 0.4 0.2 160 140 120 100 Time (day) 80 60 40
Fig. 4 – Simulation for the removal of alachlor (Badriyha et al., 2003).
controlled by acetate as well as alachlor. Even though acetate did not influence the behavior of adsorption, it should be taken into consideration for biodegradation. The Stanton number and the Sherwood number of their experimental system are of the same order as our experimental system, but their Schmidt number is greater, which implies that viscous force has more influences on their system. The remarkable difference between the two systems is the Damko¨hler number; our Damko¨hler number is about seven orders (Scenario I) and four orders (Scenario II) higher than theirs, respectively. This is because they used a much finer GAC (0.035 cm in diameter) and the target compound alachlor is
less biodegradable (0.011 min1). As a result, the limiting
factor is the biodegradation rate rather than the biofilm mass transfer in their system.
3.3. Sensitivity analysis
The sensitivity analysis, which quantifies the magnitude of each variable affecting the simulation results, was executed by using the least-squares analysis to acquire quantitative comparisons between the baseline value and the output by increasing/decreasing the parameter. The baseline is the effluent concentration of Scenario I; meanwhile, the value of each parameter is increased 100% from its baseline value for one simulation and also decreased 50% from its baseline value for another simulation, and the results are listed in
Table 3. If the adjustment of an input parameter considerably increases the least-squares value, the model is sensitive to that parameter.
The Freundlich isotherm exponential term NFis one of the
most sensitive variables as indicated by the average least-squares value between the effluent substrate curves as shown inFig. 5a. The result is obvious because NF determines the
scale of adsorption exponentially, and results in a very large change in the simulated curve. Another remarkably sensitive variable is the maximum specific substrate utilization rate from Monod kinetics, since biodegradation is one of the key mechanisms of the BAC (Fig. 5b).
In the simulation process, the pathway of the substrates is to cross the biofilm and subsequently to be adsorbed by the activated carbon; this assumption leads to a result that the biofilm covering the BAC granules can be regarded as a resistance to the mass transfer of adsorption. As a
conse-quence, both the thickness and the diffusivity within the
biofilm (Df) determine the scale of the substrate mass flux
from bulk liquid transferring to the surface of the adsorbent.
Dfcan, moreover, influence the concentration profile within
Table 3 – The sensitivity analysis of the model input parameters
Parameter Increased
100%
Average least-squares value
Decreased 50% Average
least-squares value NF(8.3) 16.6 0.57 4.2 0.91 Df(2.9 102) 5.8 102 0.41 1.5 102 0.71 kf(1.7 1010) 3.4 1010 0.35 0.9 1010 0.71 kF(14.1) 28.2 0.13 7.1 0.45 btot(0.25) 0.5 0.34 0.13 0.17 Kf(0.1) 0.2 0.30 0.05 0.16 Y (6.45 108) 1.28 109 0.08 3.2 108 0.54 Xf(5.0 1013) 1.0 1014 0.13 2.5 1013 0.14 1.0 baseline increased 100% decreased 50% baseline increased decreased 0 10 20 30 40 baseline increased 100% decreased 50% 864, 25.2, 0.069, 8.6·104 NSc, NSh, NSt, NDa, (dimensionless) NSc, NSh, NSt, NDa, (dimensionless) Dimensionless effluent ( Si /S0 ) 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 100% 864, 25.2, 0.069, 1.7·105 50% 864, 25.2, 0.069, 4.3·104 864, 25.2, 0.069, 8.6·104 432, 20.5, 0.112, 4.3·104 1730, 31.2, 0.042, 1.7·105 Time (day)
Fig. 5 – Sensitivity analysis for the input parameters: (a)
Freundlich constant, NF; (b) maximum specific utilization
the biofilm, and consequently change the magnitude of the amount of biodegradation. In this model, shifting the value of
Df dramatically changes the simulation output (Fig. 5c). In
conclusion, the mass transfer within the biofilm also per-forms as an essential factor affecting the performance of BAC through both adsorption and biodegradation.
The simulation output is moderately sensitive to changes in the total decay coefficient (btot) and the Monod half-velocity
constant (Kf). The moderate impact of Kf is due to the
relatively low baseline value of the parameter of 0.1 mg/L relative to the initial substrate concentration of 0.4 mg/L. According to Monod kinetics, the influence of Kfon the overall
substrate degradation rate diminishes as the value of Kf
becomes insignificant relative to the range of substrate concentrations. As a result, the degradation reaction rate approaches zero order with respect to the substrate concen-tration.
Although the profile of active biomass is a significant property of the biofilm, this model output is relatively
insensitive to the microbial density of the biofilm (Xf) and
the specific yield (Y). Generally, the biofilm is composed of
extracellular polymeric substances, inert biomass and active biomass, but only the last one can provide the capacity of
biodegradation. Zhang and Bishop (1994) indicated that on
the outer surface the viable biomass constituted nearly all the biofilm, while near the bottom the viable part was approxi-mately 30% of the total biomass. Another experimental study showed that the deep portion of the biofilm had a lower
live-cell ratio compared with the outer surface (Ohashi et al.,
1999). From the result of one-dimensional and multi-species
model simulation, it was concluded that active heterotrophic bacteria dominated near the outer surface of the biofilm, while inert biomass dominated near the attachment surface (Rittmann et al., 2002). In addition, the substrate-loading rate
can also affect the microstructure of biofilms. Wijeyekoon
et al. (2004)showed that increasing substrate concentrations produced more compact biofilms with lower porosity, and slowly growing biofilms having porous structures were found to have higher specific activities. According to the assumption of this model, the biofilm is homogeneous both in its structure and in its density because most of the biodegrada-tion parameters were derived from macroscale experiments.
NRe and NSh Removal efficiency (1-Si /S0 ) NSt and NDa (log scale) 0 10 20 30 40 0 0.5 –3 –2 –1 0 1 2 3 4 –3 –2 –1 0 1 2 3 4 0 20 40 60 80 Reynolds Sherwood Stanton Damköhler Biodegradation Adsorption Total 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 Particle size (diameter in cm)
0 0.1 0.2 0.3 0.4 0.5
Particle size (diameter in cm)
Fig. 6 – Simulations of various particle diameters for the removal of p-hydroxybenzoic acid. (a) and (c) Dimensionless groups
Nonetheless, such simplification is acceptable since this model is not very sensitive to the biofilm density, and the baseline value can tolerate a relatively uncertain range compared with the other parameters. Thus, the results of sensitivity analysis offer valuable information to operators to select the most significant parameters that determine the performance of the BAC.
3.4. Simulations for the removal efficiency of various particle sizes
To determine effects of particle size of the packing media on the removal efficiencies, a simulation procedure was com-puted to calculate the removal efficiency of adsorption and biodegradation of the BAC column. Apparently, decreas-ing the particle size results in raisdecreas-ing the efficiency of mass transfer as well as in enhancing the removal effici-encies of both adsorption and biodegradation. The case of
Scenario II with EBCT ¼ 5 and 1.25 min (vs¼5 and 20 cm/min,
respectively) was performed to assess the removal effici-ency of p-hydroxybenzoic acid operated at various particle sizes.
Fig. 6a and c shows the changes of dimensionless para-meters. It is obvious that Reynolds, Sherwood and Damko¨hler numbers increase as the particle size increases; at the same time, Stanton number decreases. As mentioned previously, a higher Stanton number represents a higher driving force for the mass transfer from bulk solution to biofilm. This phenomenon implies that the mass transfer within the biofilm is the limiting factor when the particle size increases.
Fig. 6b and dshows the simulated removal efficiencies of adsorption and biodegradation after biodegradation equili-brium. It is evident that decreasing particle size can improve the overall removal efficiency, especially for adsorption rather than for biodegradation. According to the definition of Damko¨hler number, a lower Damko¨hler number means a lower biodegradation rate or a higher transfer rate within the biofilm, which permits more substrate to cross the biofilm toward the adsorbent. As a consequence, the adsorption ratio rises as the particle size decreases. In addition, a higher superficial velocity reflects higher Reynolds and Sherwood numbers, but a lesser Stanton number on the contrary. Hence, the overall removal efficiency decreases as the superficial increases. Removal efficiency (1-Si /S0 ) NSt and NDa (lo g scale) 0 0 –2 –1 0 1 2 3 4 5 6 –3 –2 –1 0 1 2 3 4 5 6 0 NRe and NSh Reynolds Biodegradation Adsorption Total Sherwood Stanton Damköhler 40 30 20 10 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 80 60 40 20 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 Particle size (diameter in cm)
0 0.1 0.2 0.3 0.4 0.5
Particle size (diameter in cm)
Fig. 7 – Simulations of various particle diameters for the removal of ozonation intermediates. (a) and (c) Dimensionless
The same procedure was conducted to determine effects of particle size of the packing media on the removal efficiencies of the ozonation intermediates of p-hydroxybenzoic acid, and
the changes of dimensionless parameters are shown inFig. 7a
and c. It is also evident that Reynolds, Sherwood and Stanton numbers are the same as the simulation of p-hydroxybenzoic acid, but the only exception is the Damko¨hler number. In this case, the target compound is highly biodegradable but low absorbable, so that the Damko¨hler number in this case is greater than that in the p-hydroxybenzoic acid case.
According to the simulation above,Fig. 7b and dshows the
simulated removal efficiencies of adsorption and biodegrada-tion after biodegradabiodegrada-tion equilibrium. Decreasing particle size slightly improves the adsorption removal efficiency, and thus slightly increases the overall performance. Since the intrinsic property of ozonation intermediates is highly biodegradable but low absorbable, the magnitude of the improvement is limited.
4.
Conclusions
This model provides a good approximation of the experimental data by adjusting the liquid-film mass transfer coefficients. A
higher kbf reflects a higher driving force on the biofilm
boundary, and results in a higher substrate concentration profile within the biofilm. Furthermore, the liquid-film mass transfer coefficient has a certain correlation to the Stanton number; that is, increasing Stanton number can improve the mass transfer from bulk solution into the biofilm.
The Freundlich isotherm exponential term NFand the
maxi-mum specific substrate utilization rate from Monod kinetics are two of the most sensitive variables. The mass transfer within the biofilm is another essential factor influencing the
perfor-mance of BAC. Because Df can shift the concentration profile
within the biofilm as well as the boundary concentration for adsorption, it thus dominates the magnitude of both adsorption and biodegradation. The model output is relatively insensitive to the microbial density of the biofilm and to the specific yield; that is, the baseline value can tolerate a relatively uncertain range compared to the other parameters.
Reynolds number, together with Sherwood and Damko¨hler numbers, increases as the particle size increases, and results in the mass transfer within the biofilm being the limiting factor of the performance of a BAC column. On the contrary, decreasing the particle size, the condition of lower Damko¨hler number, leads to a lower biodegradation rate or a higher transfer rate within the biofilm. Therefore, more substrate diffuses across the biofilm, which increases the ratio of adsorption rather than biodegradation.
R E FE RE N C E S
Abumaizar, R.J., Smith, E.H., Kocher, W., 1997. Analytical model of dual-media biofilter for removal of organic air pollutants. J. Environ. Eng. ASCE 123 (6), 606–614.
Aksu, Z., Tunc-, O¨., 2005. Application of biosorption for penicillin G removal: comparison with activated carbon. Process. Biochem. 40 (2), 831–847.
Badriyha, B.N., Ravindran, V., Den, W., Pirbazari, M., 2003. Bioadsorber efficiency, design, and performance forecasting for alachlor removal. Water Res. 37 (17), 4051–4072.
Chang, H.T., Rittmann, B.E., 1987. Mathematical modeling of biofilm on activated carbon. Environ. Sci. Technol. 21 (3), 273–280.
Escudie´, R., Conte, T., Steyer, J.P., Delgene`s, J.P., 2005. Hydrody-namic and biokinetic models of an anaerobic fix-bed reactor. Process. Biochem. 40 (7), 2311–2323.
Hozalski, R.M., Bouwer, E.J., 2001. Non-steady state simulation of BOM removal in drinking water biofilters: model development. Water Res. 35 (1), 198–210.
Hozalski, R.M., Goel, S., Bouwer, E.J., 1995. TOC removal in biological filters. J. Am. Water Works Assoc. 87 (12), 40–54. Li, L., Zhu, W., Zhang, P., Zhang, Q., Zhang, Z., 2006. AC/O3-BAC
processes for removing refractory and hazardous pollutants in raw water. J. Hazard. Mater. 135 (1-3), 129–133.
Liang, C.H., Chiang, P.C., Chang, E.E., 2003. Systematic approach to quantify adsorption and biodegradation in biological activated carbon. Ozone Sci. Eng. 25 (5), 351–361.
Liang, C.H., Chiang, P.C., Chang, E.E., 2004. Quantitative elucida-tion of the effect of EBCT on adsorpelucida-tion and biodegradaelucida-tion of biological activated carbon filters. J. Chin. Inst. Chem. Eng. 35 (2), 1–9.
Melin, E.S., Ødeggard, H., 2000. The effect of biofilter rate on the removal of organic ozonation by-product. Water Res. 34 (18), 4464–4476.
Ohashi, A., Koyama, T., Syutsubo, K., Harada, H., 1999. A novel method for evaluation of biofilm tensile strength resisting to erosion. Water Sci. Technol. 39 (7), 261–268.
Rittmann, B.E., Stilwell, D., Garside, J.C., Amy, G.L., Spangenberg, C., Kalinsky, A., Akiyoshi, E., 2002. Treatment of a colored groundwater by ozone-biofiltration: pilot study and modeling interpretation. Water Res. 36 (13), 3387–3397.
Sakoda, A., Wang, J., Suzuki, M., 1996. Microbial activity in biological activated carbon bed by pulse responses. Water Sci. Technol. 34 (5-6), 222–231.
Wakao, N., Funazkri, T., 1978. Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds. Chem. Eng. Sci. 33, 1375–1384.
Walker, G.M., Weatherley, L.R., 1997. A simplified predictive model for biologically activated carbon fixed beds. Process. Biochem. 32 (4), 327–335.
Wijeyekoon, S., Miho, T., Satoh, H., Matsuo, T., 2004. Effects of substrate loading rate on biofilm structure. Water Res. 38 (10), 2479–2488.
Zhang, T.C., Bishop, P.L., 1994. Density, porosity and pore structure of biofilms. Water Res. 28 (10), 2267–2277.
