dynamic transport and reaction

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Dynamic transport and reaction model for azo dye removal in a UAFB reactor

Linda V. Gonzalez-Gutierrez a,1, Hugo Jimenez-Islasb, Eleazar M. Escamilla-Silva b,*aCentro de Investigacion y Desarrollo Tecnologico en Electroqumica, Parque Tecnologico Queretaro Sanfandila, 76703 Sanfandila, Pedro Escobedo, Qro., Mexicob Instituto Tecnologico de Celaya, Departamento de Ingeniera Qu mica y Bioqu mica, Ave. Tecnologico y Antonio Garc a Cubas S/N, 38010 Celaya, Gto., Mexico

1. Introduction

The degradation of azo dyes from textile effluents has been the

objective of research for some years, due to the pollution problem

they generate. Physicochemical, advanced oxidative and biological

processes have been used in the removal of these compounds.

However, an efficient and cheap process to eliminate this

problem with low environmental impact is still unavailable.

Perhaps the biggest problem is that reactive dyes are highly water

soluble, due to the presence of sulfonated groups that are not

reduced under the ordinary wastewater treatment processes [1

3].

Anaerobic bioreactors have an important role in the treatment

of hazardous wastes, as they candegrade higher organic loads than

aerobic reactors. Fixed bed reactors can be either immersed bed

reactors, usually upflow, or trickle bed reactors, which are usually

downflow. The main characteristic of fixed bed reactors is that the

biomass forms a biofilm that covers a material that works as a

support or carrier for the growth and maintenance of the

microorganisms. Thus, the reactor efficiency is improved, because

the substratebiomass contact (effective surface area) is increased

and the process is more stable. The carrier is used to improve the

mechanical properties of the biomass and the cell retention, both

of which contribute to the degradation process[4,5].

A biofilm usually does not grow homogeneously on a support,

but rather forms clusters on the supports surface. The internal

structure of the biofilm depends on the superficial velocity of the

flow through the reactor, the mass transfer velocity and micro-

organism activity[6,7]. The degree of biomass formed affects the

hydrodynamic behavior of the reactor.

In the present work, an Upflow Fixed Bed Bioreactor (UAFB)

using activated carbon (AC) as a carrier was employed. It has been

proven that AC possesses good properties for biofilm growth and

the removal of diverse pollutants [37]. In addition, AC might

accelerate the degradation of azo dyes because of its redox

mediator function, due to the chemical groups on its surface [8].

DiIaconi etal. [9] proposed a mechanismfor biofilm growth: (1)

formation of a thin film covering the support by microorganisms,

(2) increase of the biofilm thickness, (3) breakage of the added

biofilmclusters andrelease of particles (biomass) due to theexcess

of growth, and (4)formation of a small pellet by detached particles.

In this type of reactors, it is common to have bioparticles (carrier

plus biofilm), some free cells, and biomass pellets as a function of

the superficial velocity in the reactor; the water flowing through

the bioreactor can reduce the drag by removing small biomass

pellets.

The mass transport through the bioparticles occurs during three

phases: diffusion of the dye molecule from the solution to the

biofilm, diffusionreaction through the biofilm, and adsorption

diffusion through the carbon surface.

One disadvantage of upflow fixed bed reactors is that the liquid

flow is non-ideal, and thus, the dispersion, backmixing, and by-

passing flows are considerable[10]. Therefore, it is important to

Process Biochemistry 45 (2010) 3038

A R T I C L E I N F O

Article history:

Received 9 October 2008

Received in revised form 21 July 2009

Accepted 24 July 2009

Keywords:

UAFB

Bioreactor

Azo dye

Activated carbon

Residence time distribution

Dynamic model

A B S T R A C T

An Upflow Anaerobic Fixed Bed (UAFB)reactor packed withactivated carbon was usedto removethe azo

dye Reactive red 272. The biomass grown on the activated carbon surface was composed of an adapted

consortium of microorganisms. Residence time distribution test indicated that the reactor was a plug

flow behavior.A dynamic mathematical model is presented for dye flux along the reactor andwithin the

bioparticles composed of two regions: activated carbon core and biofilm. The model considers that the

reactionis performed in the biofilm and in the liquid phase and includes dye transport by dispersionand

diffusion. The concentration profile within the bioparticles changes with reactor height and time as the

equilibriumis achieved. Changesin dye concentrations affect theconcentration profile in thereactorand

reduce the removal efficiency. The effectiveness factor depends on the reactor height and on the dye

concentration at the inlet.

2009 Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: +52 461 6117575; fax: +52 461 6117744.

E-mail address: [email protected] (E.M. Escamilla-Silva).1 Tel.: +52 442 2116034.

Contents lists available at ScienceDirect

Process Biochemistry

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / p r o c b i o

1359-5113/$ see front matter 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.procbio.2009.07.018
mailto:[email protected]://www.sciencedirect.com/science/journal/13595113http://dx.doi.org/10.1016/j.procbio.2009.07.018http://dx.doi.org/10.1016/j.procbio.2009.07.018http://www.sciencedirect.com/science/journal/13595113mailto:[email protected]


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conduct the hydraulic characterization of the reactor using a tracer

test. However, a plug flow is commonly considered to model the

reactor.

The modeling of such reactor allows the estimation of all its

important functional parameters, the optimization of the effi-

ciency, the prediction of its behavior, and the future scaling.

However, the scaling of a reactor from models made for laboratory

reactors is difficult; there are factors, such as the transport

between static and dynamic zones, which are negligible for small

reactors, but must be included in real reactor models. Therefore,

the main objective of this paper is to propose a mathematicaldynamic model for an upflow anaerobicbioreactor,UAFB,usingAC

as a carrier, that will result in improved biodegradation during the

removal of the azo dye reactive red 272 (Lanasol Red CE). The

mathematical model includes the following transport phenomena:

convection, dispersion, diffusion and mass transfer from one phase

to another along the reactor, and through the bioparticles, as well

as dye reduction reaction. We have tried to ensure our model

encompasses all the possible phenomena that occur in the reactor.

2. Materials and methods

2.1. Reactor assembling

A 3.71 L UAFB anaerobic upflow reactor madeof Pyrex glass with a fixed bed of

1.244L (43.75% ofits operationvolume)was used. Thereactoris depictedin Fig. 1

and its characteristics are shown inTable 1. At the beginning of the operation, anadsorption stage was performed to saturate the AC with the dye; thus ensuring

that any discolor of the solution was not simply due to adsorption on to AC. The

reactor was then inoculated by recirculating water containing 10% of an adapted

sludge representative of textile wastewater environment. The aim is to complete

azo dye reduction, especially reactive red 272, for a period of 15 days.

Subsequently, 11.586 mg biomass/g AC was adsorbed to form a biofilm on the

AC surface. The reactor was operated using synthetic wastewaters containing the

azo dye at different concentrations varying from 100 to 500 mg/L, as well as 1 g/L

of dextrose and yeast extract as carbon and nitrogen sources for the

microorganisms.

2.2. Residence time distribution

A lithium chloride solution was used as a tracer in order to determine the

hydraulic characteristics of the reactor and to obtain the residence time

distribution. Smith et al. [11] used LiCl as a tracer and recommended a

concentration of 5 mg Li+/L to avoid toxicity problems. We applied a 1-min pulse

of a 2000 mg/L LiCl solution. Dextrose and yeast extract (1 g/L) were used as

substrates during the test. Samples were taken from the reactor effluent every

30 min over 10 h (approximately 3 times the half-residence time ( RTm)). The Li

concentration was analyzed with an atomic adsorption spectrophotometer

(PerkinElmer model 2280).

The hydraulic residence time (HRT) should be better expressed as:

HRT

R10 tCC0dtR1

0 CC0dt (1)

whereCis the tracer concentration at a time tandC0is the tracer concentration at

t = 0. The parameters and non-dimensional numbers necessary to describe the

reactor as well as the axialdispersion and masstransfercoefficients werecalculatedaccording to the following equations.

Dispersion number (d) and Peclet number (Pe). These numbers indicate the

dispersion grade in the reactor. A Pe value above 1 indicates that convection is the

leading factorin the masstransport; for Pe values below 1, dispersion is the leading

factor. The numbers are given by[12]:

PeuL

D

1

d (2)

d1

2

s2DC

RTm

D

uL (3)

whereu is the superficial velocity in the reactor, L is the longitude, and D the axial

dispersion coefficient.

Dispersion coefficient (D). It can be calculated by the dispersion number or by

other correlations as the presented with the Reynolds number.

DduL 1:01nRe0:875 (4)

Here,n is the kinematic viscosity of the water in the reactor [12].

Sherwood number (Sh) and mass transfer coefficient (km).Shwas calculated by the

Frossling correlation [13] that is applied to the mass transfer or flux around a

spherical particle. Thus, the following equation was used:

Sh2 0:6Re1=2Sc1=3 (5)

The mass transfer coefficient of the dye was estimated by the following equation:

km De fSh

dP(6)

where dp is theaverage particle diameter of the carbon particlesand biomassin the

bed. For this estimation, thedpvalue of the carbon particles at the beginning of the

study (1.03 mm) was used;s2DC

: variance, or a measure of the spread of the curve

(Fig. 2)

2.3. Kinetic model

The applied kinetic model to represent the dye biodegradation (reduction) was

derived according to experimental observations. The proposed model expresses a

change in reaction order and is given by Equation(7), where CA0 and CA are the

initial and at anytime azo dye concentrations,respectively,and k1 and k2 arethe 1st

and 2nd order specific reaction rates (h1, L/mg h). The deduction was explained in

a previous paper[14].

rA dCAdt

k1 CAk2CACA0CA (7)

2.4. Dimensionless numbers model

The dimensionless numbers that explain the transport process in the reactor

were obtained from the dimensionless analysis of the model. These numbers are

Biot number (Bi) that relates mass transfer to diffusivity, Fourier number (Fo) that

relates thediffusivity inthe reactionarea to thereactiontime, Wagnermodule(F

2

),

Fig. 1. Upflow Anaerobic Fixed Bed (UAFB) reactor.

Table 1

UAFB reactor characteristics.

Reactor volume, L 3.72

Work volume, L 3.3

Inside diameter, cm 6

Inside diameter of the settle, cm 9.5

Total longitude, cm 105.5

Initial and steady state porosity of the bed 0.53, 0.19

Fixed bed volume, L 1.244

Fixed bed longitude, cm 48

Superficial velocity (average), cm/min 0.52

Volumetric flow (average), mL/min 18

RTm(average), min 206.25

L.V. Gonzalez-Gutierrez et al. / Process Biochemistry 45 (2010) 3038 31


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used to generate Thiele number (F), which indicates whether diffusion modifiesthe reaction rate. From Thiele number, the effectiveness factor (h) is calculated,

which relates thereal reactionrate to thereactionratewithout diffusionresistance.

Thus, h expresses the influence of the diffusion on the reaction rate. Thiele number

is calculated by Eq.(8)(according to the proposed kinetic model there is a Thiele

number for the first-order term and other for the second-order term). The

effectiveness factor for the discolor rate of the dye by volume unit of bioparticleswas calculated using Eq.(9),according to the definition of volume average[14,15],

and using the proposed kinetic model expressed in Eq. (7). Here,RA is the average

reaction rate in the biofilm andRAjis the reaction rate in the bioparticle surface in

the liquidboundary; Fob is thecharacteristicFourier numberfor thebiofilm defined

in Eq.(19) in the next section.

F1 d

ffiffiffiffiffiffiffiffik1

Deb

s ; F2 d

ffiffiffiffiffiffiffiffiffiffiffiffiffik2CA0

Deb

s (8)

h4p

R10 RAj

2dj

43pRAj

3R1

0 RAj2

dj

RAj

3R1

0 F21 Fobvb F

22Fobvb vL vb

h ij

2dj

F21Fobvb F

22 Fobvb vL vb

h ij

RARAj

(9)

3. Results and discussion

3.1. Residence time distribution

The parameters and non-dimensional numbers that describe

the transport in the fixed bed reactor are given in Table 2. The

superficial velocity was calculated as uL Q=eLpR2i and theporosity of the bed eL was 0.19 at equilibrium.

The hydraulic behavior of the reactor was approximated to a

plug flow with axial dispersion; whenQwas increased, the reactor

was closer to an ideal plug flow behavior. This effect can be

attributed to the fine particles formed during the reaction time in

the interparticlespace in the reactor because these particles reduce

the bed porosity and as a result the by-pass fluxes. Kulkarni et al.

[15,16] have shown that the fine particles formed in packed bed

reactorsreduce the by-pass fluxbecause thereis a betterspreading

of the flux and, therefore, a reduced dispersion.

During residence time distribution tests biogas production

occurs, due to the digestion of dextrose in the synthetic waste-

water. However, the biogas production, with or without dye in the

water, is not sufficient to consider the reactor as a mixed tank.

Additionally, the rise of biogas through the bed is very slow and

generates a by-pass flow due to the trapped biogas bubbles. When

the superficial velocity in the reactor is increased, the bubbles are

pushed and can flow better, and the by-pass flux is reduced. Thus,

the reactor has a behavior that is closer to a plug flow[17,18].

TheHRTwas 1.61.8 times the RTmat low volumetric flows in

the reactor and 1.11.3 times at high volumetric flows.

The residence time distribution achieved for all the tests was

fitted by a statistical distribution of extreme value (FisherTippet),

given by Eq.(10). It is a frequency distribution function for slant

peaks.

Pt y0a expexpf1 f1 s 1f1

ttCw

(10)

where P(t) is the normalized tracer concentration,y0 represents the

distribution displacement (tracer concentration at time 0),ais the

amplitude of the distribution, and w the width of the peak. These

calculated parameters, the standard error and correlation coeffi-

cients are also given inTable 2.Fig. 2shows the distribution of the

residence time in the reactor for each test (P(t)) and the fitted with

described Extreme model equation(10).

Iliuta et al. [10] have stated that a long tail in the residence time

distribution can be caused by an axial dispersion in the dynamic

flow and by a mass transfer between the dynamic and static zones.

Also, when the packed bed of the reactor contains porous particles,

as in the present case, the alteration in the residence timedistribution can be attributed to an internal diffusion and a

reversible adsorption of the tracer. Although this alteration is

usually negligible, it does occur for the dye.

Thereactive red272 dyemolecule is reversibly and superficially

adsorbed on this biomass and the AC surface, albeit only poorly; it

has a limited adsorption capacity due to its molecular size and

characteristics. There is an equilibrium between adsorption,

reaction, and desorption. In our case, a constant saturation of

the bioparticles is considered, and the adsorption dynamics are

thus negligible.

Fig. 2. Experimental RTD with LiCl as pulse tracers applied to the reactor.

Table 2

Hydrodynamic, mass transfer and fitted extreme model Parameters for the UAFB reactor (L = fixed bed).

Parameter HRT1 HRT2 HRT3 HRT4 HRT5 HRT6

RTm(min) 57.264 66.203 66.203 42.412 42.412 42.412

uL (cm/s) 0.0735 0.0631 0.0631 0.0985 0.0985 0.0985

NReL 54.962 47.468 47.468 74.096 74.096 74.096

BoL 11029.2 9461.54 9461.54 14769.2 14769.2 14769.2

dL 2.864 2.255 2.407 2.332 1.208 0.413

DL(cm2/s) 10.026 6.828 7.287 11.022 5.709 1.953

PeL 0.349 0.443 0.415 0.429 0.828 2.420

ShL 45.403 42.246 42.246 52.283 52.283 52.283

kL(cm/s) 0.0176 0.0164 0.0164 0.0203 0.0203 0.0203

y0 0.0270 0.0470 0.0251 7.6 103 9.3 103 5.5 104

a 0.5697 0.6629 0.6175 0.8944 0.6959 1.0029

w 22.033 46.312 33.212 29.893 19.756 32.259

SEa 0.0255 0.0443 0.0325 0.0182 0.0226 0.0162

R2b 0.9945 0.9823 0.9920 0.9977 0.9966 0.9980

a Standard error of the fit.b

Multiple correlation coefficient

L.V. Gonzalez-Gutierrez et al. / Process Biochemistry 45 (2010) 303832


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3.2. Dynamic model: transport and reaction in the fixed bed

After calculating HRT and all the necessary parameters and

dimensionless numbers, a mathematical model was deduced and

executed to represent the transport and reaction of the dye in the

water upflow through the reactor (the clarifier zone is not

considered here due to the complexity of the process).

The dynamic model is based on the following assumptions:

1. The radial dispersion is negligible.

2. The reactor is divided into two zones: the fixed bed and the

clarifier (not considered). There is mass transfer between them.

3. The dispersion coefficient is constant in each zone.4. There is mass transfer between the water flowing through the

bed and the bioparticles.

5. The superficial velocity trough the bed is constant and

calculated as uL Q=eLpR2i.6. The dye can be reversibly adsorbed on the bioparticles.

7. The dye is diffused, adsorbed, and reacts in the biofilm. There is

also superficial diffusion in the activated carbon core macro-

pores because the molecular size (21 A) would limit the

micropore diffusion (pore average diameter: 23.3 A).

8. The particle is spherical and the biofilm is uniform and porous.

9. The biomass on the activated carbon core grows to a certainthickness. Afterwards, the biomass excess detaches and forms

small granules. Then, the biomass attached to the activated

carbon goes back to its normal or equilibrium thickness. Thus,

the biofilm thickness is dynamic. However, considering that

there is equilibrium between growth and detachment, an

average thickness value is used.

The modeldivides the bioparticle balance into twozones: zone I

represents the AC particles (core) and zone II the microorganism

biofilm surrounding the AC core. The reaction term is included in

two balance equations: in zone II of the bioparticles and in the

liquid balance, because as it is an extracellular process there are

free cells or small biomass granules in the flowing liquid. Fig. 3

depicts a graphical scheme of the model with CAL the liquid

concentration of the dye,CAPthe dye concentration in the AC core,

andCAbthe biofilm concentration.

The governing equations are:

(a) Balance for the liquid flow in the fixed bed.

@CAL@t

DL@2CAL

@Z2 uL

@CAL@Z

KmasbCALCAbjrRB k1CAL

k2CALCA0CAL (11)

This equation describes the dye convection, dispersion, and mass

transfer from the liquid phase to the biofilm surface and the

reaction. The initial and boundary conditions are:

t 0 CAL CA0

Z 0 CAL CA0

Z L f@CAL

@Z 0

(12)

(b) Balance for the bioparticles.

For the AC core:

@CA p@t De p

2

r

@CA p@r

@2CA p@r2

! (13)

This equation describes the dye convection and diffusion. The

initial and boundary conditions that express field equality at the

interface are:

t 0 CA p 0

r 0 @CA p

@r 0

r RC CA p CAb

(14)

For the biofilm (diffusion and reaction):

@CAb

@t D

eb

2

r

@CAb

@r

@2CAb

@r2 ! k

1C

ALk

2C

ALC

A0C

AL (15)

Fig. 3. Transport and reaction model in the UAFB, Reactor scheme.



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This equation describes the dye convection, diffusion,and reaction.

The initial and boundary conditions that express flux equality at

the interface and mass transfer from the bioparticles to the liquid

phase are:

t 0 CAb 0

r RC De p@CA p

@r Deb

@CAb@r

r RB Deb@CAb

@r KmCAbCAL

(16)

(c) Dimensionless model. The dimensionless governing equations

are given next.

For the liquid flow in the fixed bed:

@vL@t

dL@2vL

@z2

@vL@z

bmvL vb F21FobvL

F22FobvL1 vL (17)

t 0 vL 1

z 0 vL 1

z 1

@vL@& 0

(18)

Using the dimensionless numbers:

vL CALCA0

; z Z

Lf; t

t

tmL

tuLLf

; dL DLuLLf

1

PeL;

bmKmasbLf

uL

F21 d2k1

Deb; F22

d2k2CA0Deb

; Fob DebL f

d2uL

(19)

To include the two zones of the bioparticles to become

dimensionless, a parallel model was proposed. Thus, the AC core

and the biofilm are expressed as a single particle with adimensionless radius varying from 0 to 1 (see Fig. 4):

For the AC core:

@vp@t

Fop2

j

@vp@j

@2vp

@j2

! (20)

t 0 vp 1

j 0 @vp

@j 0

j 1 vp vb

(21)


vp CA pCA0

; Fop De pLf

R2CuL; t

t

tmL

tuLLf

(22)

For the biofilm:

@vb@t

Fob@2vb

@j2

2

j b

@vb@j

" # F2Fobvb

F2Fobvb vL vb (23)

t 0 vb 0;

j 0 @vb

@j ab

@vp@j

j 1 @vb

@j Bivb BivL

(24)


vb CAbCA0

; t t

tmL

tuLLf

; F21 d2k1

Deb;

F22 d2k2CA0

Deb; Fob

DebLf

d

2u

L

BiKmRB

Deb; a

DebDe p

; b RC

RBRC

RCd

: (25)

The reactor model, then, consists of three differential parabolic

equations. To solve the model, all the parameters are previously

calculated, and the spatial coordinates were discretized with

finite differences, following time integration with a 5th order

RungeKuttaFehlberg method. We coded this algorithm using

FORTRAN 90.

3.3. Model solution

We possessed the following data prior to solving of the model:

from the AC properties: rp= 0.435 g/cm3 (density), ep= 0.1392

(porosity), RC= 0.0515 cm (average particle radius), and for thereactor: LL= 48 cm (longitude), Ri= 3 cm (radius), eL= 0.19 (bed

porosity).

The dispersion coefficient (DL), the dispersion number (dL), the

Peclet number (Pe), the superficial velocity (uL), and the half

residence time (RTm), were estimated in the residence time

distribution analysis, as previously explained in the methodology

section.

The diffusion coefficient was calculated by the method of Hines

and Maddox [16], supposing a Knudsen diffusivity;the value of the

coefficient was changed in order to fit the model and to allow

comparison with values reported in the literature for other dyes.

The diffusivity in the biofilm was assumed to be 100 times greater

than the diffusivity in the AC core based on values reported for

similar dyes[5,16,18].The kinetic constants were estimated from experimental data

and fitted to model.

The mass transfer surface of the bioparticles was calculated by

Eq.(20)[19].

asb 6

db

6

dp 2g (26)

The parameters used to solve the mathematical model are given in

Table 3. In our case, the Thiele number of second order is applied

for an initial dye concentration of 250 mg/L. For 400 mg/L, it was

1.43 andfor 500 mg/L, it was 1.60. This indicatesthat when the dye

concentration is increasedin the reactor influent, the mass transfer

effects are also increased, particularly the resistance to the

diffusion. The dye removal is thus ceased.Fig. 4.Parallel, dimensionless model.



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Fig. 5 shows the concentration profile along the reactor at

different dye concentrations of the reactor inflow,and Fig. 6 shows

the concentration profile within the bioparticles (AC core plus

biofilm) for an initial concentration of 250 mg/L.

It can be seen in Fig. 6 that the particles close to the reactor

influent (z= 0.045) containhigher dye concentrations than the onesin the effluent zone, whose concentration is close to the dye effluent

concentration. The concentration profile in the bioparticles changes

with time as the bioparticles are saturated and reach equilibrium.

However, a curvedprofile indicative of the reaction is observed in the

biofilm zone. Indeed, when the bioparticles are close to the effluent,the profile flattens and the concentration is approximately uniform

within the bioparticles. This is due to the lower dye concentration in

that zone and therefore the reaction velocity is slower.

The RTm in the reactor does not have much influence on the

removal of thedye according to theresults predictedby themodel.

Fig. 7 shows the concentrationprofile along the reactor at different

RTm conditions (see Table 4) andusing an inflow dye concentration

of 250 mg/L. It is apparent that there is no noticeable effect on the

concentration profile as RTm is incremented. However, the

concentration profile in the bioparticles is altered in a different

way by changes in RTm.Fig. 8shows that asRTmis increased, the

bioparticles aresaturated faster. This is due to an increased contact

time for adsorption and reaction and to an improved mass transfer

between the liquid phase and the bioparticles.Asa result, the RTm in thereactoraffects only the mass transport

rate in the reactor but not the biodegradation reaction. Thus, it

does not have an influence on the concentration profile along the

reactor and consequently on the removal efficiency. Therefore,

analyzing the profiles depicted inFig. 5, the main factor affecting

the removal efficiency is the inflow dye concentration.

Similar results were obtained by other authors. Spigno et al.

[20] presented a mathematical model for the steady state

degradation of phenol along a biofilter reactor and obtained a

concentration profile for phenol reduction at two differentconcentrations. They found the same profile for both concentra-

tions, with a greater reduction in phenol at lower concentrations.

Mammarella and Rubiolo [21] could predict the concentration

profile for lactose hydrolysis in an immobilized enzyme packed

bed reactor under different operating conditions. They obtained an

asymptotic profile for lactose conversion along the reactor height

and a much higher conversion at the lowest volumetric flow

(100 mL/h). On the contrary, in our case the volumetric flow has

much influence. Those authors do not include the dynamic of the

pollutant inside the bioparticles, as is shown in this work.

Leitao and Rodrigues[22,23]reported on the influence of the

biofilm thickness on the removal of a substrate when the support

carrier material is, and is not, an adsorbent. They obtained the

concentration profile within the bioparticles but in the absence ofreaction. The profiles showed saturation of the bioparticles with

time, and the concentration increased as the biofilm thickness

Fig. 5. Predicted concentration profile along the reactor. CA0in mg/L.

Table 3

Parameters used in model solution.

DL (cm2/min) 423.4 Wa1

a 1.061

u (cm/min) 3.786 Wa1b 1.276

Km(cm/min) 0.984 F1c 1.030

Dep(cm2/min) 2.58 105 F2

d 1.130

Deb(cm2/min) 2.58 103 b 2

k1(min1) 3.046 a 100

k2(L/mg min) 1.47 102 Bi 34.27

asb(cm2/cm3) 36.81 Bm 459.22

Fop 0.091 dL 2.33Fob 36.404

a,bWagner number.c,dThiele number (1.08 average).

Fig. 6. Predicted concentration profile in the bioparticle at different tand zin the bed. Radius in cm.



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increased. However, it was notobserved in the reaction zone in the

biofilm as it was in our case. Leitao and Rodrigues [23] proposed an

intraparticle model for biofilms on a carrier material including the

convective flow inside the particle. They obtained the concentra-

tion profile and biofilm thickness as a function of time. They

concluded that bioreactors have to be operated under conditions

that allow the liquid movement to occur in the void space of the

biofilm in order to improve mass transfer and, as a result, the

efficiency of the process.

In biofilms the hydrodynamics and kinetics of the system are

related to the fact that most biofilm reactions are diffusion limited.

Therefore the shape of the concentration profiles is determined bydiffusivity and convection [23,24]. We hypothesize that the biofilm

is a continuous phase, even though it is not as biofilms are formed

by clusters, void spaces, and channels. Thus, the convection in the

system is important and the measured diffusion coefficients are

always approximations. This is shown in Fig. 8 as RTm in thereactor

affects the mass transfer and, as a result, the concentration profile

in the bioparticles.

The effect of the bed height with a constant inlet dye

concentration of 250 mg/L is shown inFig. 9. It can be seen that

the dimensionless dye concentration is reduced as the longitude of

the bed height (Lf) is increased. This indicates higher removal

efficiency. A higherLfimplies more bioparticles and more time for

the degradation reaction. However, most of the reduction of the

dye is carried out in the lower third of the bed longitude.

3.4. Effectiveness factor

The effectiveness factor (h) was calculated at different azo dyeconcentrations with the reactor influent varying from 100 to

500 mg/L, and at RTm between 54.3 and 226.2 min. Each

calculation was carried out using the predicted dimensionless

concentrationvaluein the biofilmand in theliquid, andsolving the

model for a t= 2. The results indicate that theaverage reaction ratein the biofilm and at the biofilm surface is different at different

reactor heights. Thus, the effectiveness factor is changed.

Furthermore, the effectiveness factor depends mainly on the azo

dye concentration[25,26].Table 5shows the results for different

dye concentrations andTable 6for different RTm.

The change of the reaction rate as a function of the reactor

height can be explained by the higher amount of active biomass at

the inlet, i.e., at the bottom of the reactor. In this zone, dye and

substrate concentrations (dextrose and yeast extract) are alwayshigher and in consequence there is always a major reaction

activity. Thus,most of thedegradationof the dye takes place in this

zone as shown inFig. 6.

Fig. 7. Predicted concentration profile along the reactor at different RTm.

Table 4

Parameters used in model solution at different RTm.

RTm(min) 226.195 81.429 75.398 67.859 54.287

Q(cm3/min) 6.000 16.67 18.00 20.00 25.00

u (cm/min) 1.117 3.102 3.351 3.723 4.654

Km(cm/min) 0.695 0.913 0.939 0.978 1.083

dL 7.899 2.843 2.633 2.370 1.896

bm 1099.8 519.7 495.1 464.4 411.5

Fop 0.308 0.111 0.103 0.093 0.074

Fob 123.4 44.42 41.13 37.02 29.62

Bi 24.21 31.78 32.70 34.07 37.75The rest of the parameters remain the same as in Table 4.

Fig. 8.Predicted concentration profile in the bioparticle at differentRTm. Radius in

cm.t= 2 andz= 0.045 (close to the influent) in the bed.

Table 5

Effectiveness factor values at different dye concentration.

CA0, mg/L z vL vbjj1 RAjj1 RA h

100 0.0455 0.8382 0.8244 31.6271 23.8782 0.7550

0.13 64 0.596 2 0.58 62 22 .5320 17.2 755 0.76 67

0.5000 0.1705 0.1675 6.4614 5.0965 0.7888

1.0000 0.0593 0.0578 2.2318 1.7972 0.8053

Average 0.7789

250 0.0455 0.8612 0.8482 32.2433 22.3889 0.6944

0.13 64 0.659 3 0.64 90 24 .7535 17.7 281 0.71 620.5000 0.3038 0.2988 11.4687 8.6993 0.7585

1.0000 0.1977 0.1922 7.3753 5.7812 0.7839

Average 0.7382

400 0.0455 0.8828 0.8705 32.8209 20.9943 0.6397

0.13 64 0.7207 0.71 02 26 .8769 17.8 430 0.66 39

0.5000 0.4708 0.46 35 17 .6518 12.4 575 0.705 7

1.0000 0.412 3 0.4012 15 .1619 11.084 0 0.73 10

Average 0.6851

500 0.0455 0.8942 0.8823 33.1018 18.3187 0.5534

0.13 64 0.752 9 0.74 24 27 .9572 14.7 441 0.52 74

0.5000 0.5572 0.5490 20.7897 8.7838 0.4225

1.0000 0.5211 0.5077 18.9753 7.2410 0.3816

Average 0.4712

Fig. 9.Predicted concentration profile along the reactor, increasing the reactor bed

height (Lf). CA0= 250 mg/L at the inlet.



8/9

The calculated effectiveness factor decreased from 0.78 to 0.47

when the dye concentration was increased from 100 to 500 mg/L,

proving that when the dye concentration is increased the diffusion

of the dye through the biofilmhas a major influence on thereaction

rate. This is reflected by a reduction of the removal efficiency.

On the contrary, changes in RTm in the reactor at a constant

inflow dye concentration did not influence the value of theeffectiveness factor. Indeed, the effectiveness factor varied

between 0.74 and 0.73 when RTm was decreased from 226.2 to

54.3 min. These values indicate that there is a slight effect of dye

diffusion on the reaction rate when RTmis changed.

3.5. Conclusions

The proposed mathematical model for a UAFB bioreactor was

able to predict the concentration profiles along the reactor and

within the bioparticles (carbon core and biofilm) for the

biodegradation of a reactive red azo dye, using a kinetic model

with a change in the reaction order. The profiles at different inflow

dye concentrations showed an asymptotic curve with a major

reactionactivity in the lowerzone of the reactor. The concentrationdecrease was reduced as the inflow dye concentration was

augmented. Nevertheless, the RTm has little influence on the

concentration profile along the reactor. In addition, the model

predicts a larger removal rate as the longitude of the bed is

increased for a same inlet dye concentration.

The profiles within the bioparticles illustrate the saturation of

the particle and reflect the zone of reaction in the biofilm.

Differences in the concentration values with respect to the reaction

zone along thereactorcould be observed.The saturation rate of the

bioparticles changed with the RTm. With longerperiods of time, the

mass transfer was improved and the bioparticles were saturated

faster without affecting the reaction.

The calculation of the effectiveness factor showed that the

reaction rate changed with respect to the position at the height of

the reactor and was function of the dye diffusion when the

concentration was increased.

The reported dynamic model could predict the dye and COD

removal rate in a UAFB reactor by specifying its characteristics,dye

inflow concentration, and residence time.

Acknowledgments

This research was funded by Fondos Mixtos - Consejo Nacional

de Ciencia y Tecnologa del Estado de Guanajuato (Project: 31756).

SAGARPA-CONACYT (200-C01-77).

Table 6

Effectiveness factor values at different RTm. CA0=250mg/L.

TRm, min z vL vbjj1 RAjj1 RA h

226 .195 0.0455 0.85 72 0.839 0 1 07 .432 4 7 4.77 56 0.69 60

0.136 4 0.65 08 0.636 5 81 .897 0 5 8.84 57 0.71 85

0.5000 0.29 36 0.286 8 37 .238 3 2 8.32 66 0.76 07

1.0000 0.19 09 0.184 3 23 .933 7 1 8.79 67 0.78 54

Average 0.7402

81.429 0.0455 0.8599 0.8459 39.1935 27.2297 0.69480.136 4 0.65 66 0.645 5 30.01 68 2 1.51 63 0.71 68

0.5000 0.3005 0.295 1 13 .8205 10.49 18 0.75 91

1.0000 0.1954 0.1897 8.8786 6.9636 0.7843

Average 0.7388

75.398 0.0455 0.8606 0.8469 36.3521 25.2495 0.6946

0.136 4 0.65 79 0.647 1 27 .874 5 1 9.97 29 0.71 65

0.5000 0.3021 0.2969 12.8735 9.7693 0.7589

1.0000 0.1966 0.1909 8.2768 6.4899 0.7841

Average 0.7385

67.859 0.0455 0.8611 0.8480 32.7804 22.7622 0.6944

0.136 4 0.65 91 0.648 7 25 .161 6 1 8.0212 0.71 62

0.5000 0.3036 0.2985 11.6521 8.8388 0.7586

1.0000 0.1975 0.1920 7.4926 5.8734 0.7839

Average 0.7383

54.287 0.0455 0.8625 0.8506 26.3450 18.2815 0.6939

0.136 4 0.66 21 0.652 6 20.2734 1 4.5050 0.71 55

0.5000 0.3071 0.3025 9.4520 7.1630 0.7578

1.0000 0.2000 0.1948 6.0808 4.7634 0.7834

Average 0.7376

Appendix A. Nomenclature

asb specific surface of the particles, cm2/cm3

Bi Biot number

C, CA dye or tracer concentration, mg/L

C0, CA0 initial tracer, dye concentration, mg/L

Cm average concentration, mg/L

d dispersion number

D axial dispersion coefficient, cm2/s

De effective diffusivity coefficient, cm2/s

Fo characteristic Fourier number

HRT hydraulic residence time

Km mass transfer coefficient, cm/s

k1 1st order specific reaction rate, h1

k2 2nd order specific reaction rate, L/mg h

Lf reactor bed height, cm

Q volumetric flow

rA reaction rate, mg/L h

RB bioparticle radius, cm

RC AC core radius, cm

Ri reactor internal radius, cm

S crosswise area to the flux, cm2

t time

tm, RTm half-residence time

VP pore volume

u superficial velocity

Greek symbols

r density, g/cm3

e porosity

d biofilm thickness

z dimensionless longitude

j dimensionless particle radius

v dimensionless concentration

t dimensionless time

Wa Wagner number

F Thiele number

bm dimensionless parameter

a dimensionless parameter

b dimensionless parameter

Subindex

b biofilm

L fixed bed

p AC particle

1 for the first-order term

2 for the second-order term



9/9

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