Modeling and experiments on the influence of biofilm size and mass transfer in a fluidized bed reactor for anaerobic digestion

PII: S0043-1354(97)00261-3

Wat. Res. Vol. 32, No. 3, pp. 657±668, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/98 $19.00 + 0.00

MODELING AND EXPERIMENTS ON THE INFLUENCE OF BIOFILM SIZE AND MASS TRANSFER IN A FLUIDIZED BED REACTOR FOR ANAEROBIC DIGESTION M M PIERRE BUFFIEÁRE1*, J. P. STEYER1* , C. FONADE2 and R. MOLETTA1*

Institut National de la Recherche Agronomique, Laboratoire de Biotechnologie de l'Environnement, Avenue des Etangs, 11100 Narbonne, France and 2Institut National des Sciences AppliqueÂes de Toulouse, Department de GeÂnie Biochimique et Alimentaire, Complexe Scienti®que de Rangueil, 31077 Toulouse Cedex, France

1

(First received July 1996; accepted in revised form August 1997) AbstractÐThe kinetics of ¯uidized bed bioparticles for glucose fermentation into methane is investigated. As bed strati®cation occurs, the behaviour of bio®lms is di€erent along the height of the column. The experimental part of this study concerns the characterization of bioparticles coming from di€erent heights of a pilot-scale reactor. Bio®lm sizes and activities are measured. Batch tests are achieved with glucose, acetate and propionate as carbon sources in order to estimate the speci®c activity of each trophic group. The experimental sections shows that, for thick bio®lms, the acidogenic activity is lower and the methanogenic activity is higher than for thin ®lms. The modelling part describes the relationship between mass transfer limitations (when several trophic groups are involved) and bio®lm size. The dynamic simulations gave a good ®t to the experimental batch tests. Both simulations and experiments indicates that the biomass composition of the bio®lm depends on bio®lm size. When bio®lm thickness increases, the amount of acidogens decreases and the amount of methanogens increases, mainly because acidogen growth is di€usion-limited. The biomass distribution in the bio®lm among each trophic group appeared to be a very important parameter. This shows that bed strati®cation has an in¯uence not only on the hydrodynamics of the ¯uidized layer but also on the kinetics of organic carbon elimination by methanogenic bio®lms. This phenomenon has to be taken into account for further modelling and design of ¯uidized bed fermenters. # 1998 Elsevier Science Ltd. All rights reserved Key wordsÐanaerobic digestion, ¯uidized bed strati®cation, bio®lm size, multi-species bio®lm model, bio®lm composition

NOMENCLATURE Ap=exchange area of the bioparticle (m2) AVS=attached volatile solids (kg.mÿ3) COD=chemical oxygen demand (kg.mÿ3) Cd=drag coecient dp=bioparticle diameter (m) ds=support particle diameter (m) Ds=di€usivity of component S in the bio®lm (m2.hÿ1) Dz=axial dispersion coecient (m2.hÿ1) g=normalized glucose concentration G=glucose concentration (kgCOD mÿ3) Ks=half-saturation constant in Monod model for component S (kgCOD mÿ3) Lf=bio®lm thickness (m m) MX=total amount of biomass (kg) NÇ s=¯ux of S at the liquid±bio®lm interface (kgS.hÿ1) OLR=organic loading rate (kgCOD.mÿ3.dÿ1) Qin=input ¯ow rate (m3.hÿ1) r=radial distance measured from bioparticle centre (m) rp=bioparticle radius (m) rs=support particle radius (m) Re=Reynolds number, Re ˆ r1 U1 dp =m1 RS=speci®c activity of S utilizing bacteria (kgCOD.kgVSSÿ1.hÿ1)

*Author to whom all correspondence should be addressed [Tel.: +33 (0)4 68-42-51-68, Fax: +33 (0)4 68-42-5160]. 657

S=concentration of component S (kgCOD.mÿ3) Sin=inlet concentration of S (kgCOD.mÿ3) TOC=total organic carbon (kg.mÿ3) Ul=liquid super®cial velocity (m.hÿ1) Ut=terminal velocity (m.hÿ1) v1S=reaction rate of S through reaction i(kgCOD.m3.hÿ1) Vb=bio®lm volume (m3) Vl=liquid phase volume (m3) Vp=bioparticle volume (m3) VFA=volatile fatty acids (kg.mÿ3) VSS=volatile suspended solids (kg.mÿ3) r ÿr x=rppÿrs dimensionless distance to the liquid±bio®lm interface XS=S-utilizing bacteria concentration (kgVSS.mÿ3) y0=ratio of clean particle radius to bio®lm thickness YXs/S=biomass yield factor for S-utilizing bacteria (kgVSS.kgCODÿ1) aiS=stoichiometric factors for component S in reaction i bi=dimensionless moduli (see text) nS=e€ectiveness factor for S-utilizing bacteria ml=liquid viscosity (kg.mÿ1.sÿ1) mS=speci®c growth rate for S-utilizing bacteria (hÿ1) mS,max=maximum speci®c growth rate for S-utilizing bacteria (hÿ1) rbf=wet density of the bio®lm (kg.mÿ3) rS=density of the clean particles (kg.mÿ3) rp=density of the bioparticles (kg.mÿ3) ÿ
12 dimensionless fA=fA ˆ Lf mA max
XA =DA
YXA=A
KA modulus ÿ B
12 fB=fB ˆ Lf mmax
XD =DB
YXB=B
KB dimensionless modulus ÿ
1 fG=fg ˆ Lf mG;m XG =DG YX=G KG 2 dimensionless modulus

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658

ÿ
1 fp=fP ˆ Lf mPmax
XP =DP
YXP=P
KP 2 dimensionless modulus

INTRODUCTION

Fluidized bed bio®lm reactors o€er many advantages that make them suitable for many wastewater treatment applications (Shieh and Keenan, 1986). A large number of investigations report their eciency in many ®elds: anaerobic treatment (Jewell et al., 1981; Binot et al., 1983; Switzenbaum, 1983; Jeris, 1983; Iza et al., 1988; Heijnen et al., 1989), phenolic compounds degradation (Vidic and Suidan, 1992; He and Ping, 1994) and even simultaneous carbon and nitrogen removal (Fernandez-Polanco et al., 1994). In the ®eld of anaerobic treatment, they have proved their high COD removal capacity and stability (Bull et al., 1983; Ehlinger et al., 1994). Recent studies have been carried out to emphasize the role of bio®lm development in these reactors. First, biomass growth on the carrier a€ects the hydrodynamics of the bed by modifying its size and apparent density (Andrews and Tien, 1979; Shieh et al., 1981; Chang and Rittmann, 1994; Diez-Blanco et al., 1995). Second, following the start-up period of these reactors, many investigators report bed strati®cation, especially when a constant ¯uidization velocity is applied to beds of widely di€erent size of particles (Hermanowicz and Cheng, 1990; Miska and Svec, 1994; Ro and Neethling, 1994). Strati®cation is the arrangement of the bioparticles according to their terminal velocity. It is attributed to variations in bioparticle size and/or apparent density along the column height. This phenomenon occurs particularly when the carrier material is not of uniform size, or when bio®lm growth modi®es the apparent density of the particles (small carrier particles below 500 mm mean diameter). The alternate behaviour is the complete mixing of the solid, which is the tendency observed with carriers of uniform size. These two extreme cases have been well described by Andrews and Tien (1979). Another consequence of biomass growth is the modi®cation of the observed degradation kinetics. This phenomenon is mainly attributed to mass transfer. The diffusional resistance in the bio®lm has been generally well described and modelled (Atkinson et al., 1968; Rittmann and MacCarty, 1981), and experimental studies have con®rmed the importance of this phenomenon (Kitsos et al., 1992; Yu and Pinder, 1994). In the speci®c case of anaerobic treatment, the kinetics in free suspended cell systems has been extensively analysed (Dalla Torre and Stephanopoulos, 1986; Moletta et al., 1986; Denac et al., 1988; Costello et al., 1991). On the other hand, only few investigators have described the multispecies kinetics with mass transfer (Kissel et al., 1984; Wanner and Gujer, 1986; Rittmann and Manem, 1992; Bolte and Hill, 1993; BueÁre et al., 1995a). One of the interesting things of this approach lies in knowing exactly when mass trans-

fer a€ects the performance of the anaerobic treatment process. Furthermore, this would help to underline that di€erent kinetics may be observed along the column due to the existence of a gradient in bio®lm size. The objective of this study is to show that biomass hold-up is not the only operating parameter to be optimized in such a system. In the case of di€usion limited reactions, the e€ectiveness factor Z of the biocatalyst has also to be taken into account. As a consequence, the performance criterion for such reactor could be the ZX product (X being the biomass concentration), which gives an idea about the value of total active biomass. That is to say that bio®lm activity can be optimized with bio®lm size as operating parameter (He and Ping, 1994; Ruggeri et al., 1994). Another important point is the question of biomass composition in the bio®lm, which can be a€ected by growth e€ects such as di€usion limitations or by concentration gradients along the bed height. The purpose is to develop a dynamic model and to compare the simulations with batch experiments aiming at determining the kinetics of each reaction step, together with the sensitivity of the reaction rates to bio®lm size along the height of a ¯uidized bed reactor. The authors also intend to show that, in the present case, the ¯uidized bed reactor could be considered as a perfectly mixed system. Nevertheless, this does not mean that the biomass activity is the same along the column height. The objective is thus to demonstrate the need for a model that could take into account the di€erences between the bio®lms encountered in strati®ed anaerobic ¯uidized beds. This is performed by estimating the kinetic properties of three samples, taken out at di€erent bed heights of a pilot-scale reactor and characterized by a monosized bio®lm. The samples are analysed and their degradation capacities tested in laboratory-scale reactors. Values of speci®c activities of each trophic group are discussed. The results are then compared with the model predictions. KINETIC AND MASS TRANSFER MODELLING

The model developed here accounts for the ®ve main reactions occurring in the anaerobic digestion of glucose. It includes a bio®lm model, which describes the rate of substrate uptake for one individual bioparticle, and a mass balance on the whole reactor in order to link the bio®lm model to the overall performance of the system. Stoichiometric model It is recognized that the anaerobic digestion of wastewaters can be represented in a three-step processÐacidogenesis, acetogenesis and methanogenesis. The reaction pathway may thus be described by the following reactions (Denac et al.,

Anaerobic bio®lm model and experiments

1988): C6 H12 O6 !

659

Table 2. Chemical oxygen demand values of the reactants (from Denac et al., 1988)

aB1 CH3 …CH2 †2 COOH

By weight (kgCOD.kgÿ1)

‡aP1 CH3 CH2 COOH H ‡aA 1 CH3 COOH ‡ a1 H2

…1†

H CH3 …CH2 †2 COOH ‡ 2H2 O ! aA 2 CH3 COOH ‡ a2 H2 …2†

Glucose Butyric acid Propionic acid Acetic acid Hydrogen Methane Carbon dioxide

By mole (kgCOD.molÿ1)

1.07 1.82 1.51 1.07 8.0 4.0 0.0

192 160 112 64 16 64 0.0

CH3 CH2 COOH ‡ 2H2 O ! aA 3 CH3 COOH H ‡ aC 3 CO2 ‡ a3 H2 CH3 COOH ! CH4 ‡ CO2 4H2 ‡ CO2 ! CH4 ‡ 2H2 O

…3† …4† …5†

The stoichiometry of each reaction is given by the coecients listed in Table 1. These coecients correspond to the COD yields (COD mass of component S produced per unit mass of COD consumed from the limiting substrate during the reaction). Thus, the aij coecients in equations (1)±(5) can be expressed in COD according to the correspondence between the COD values of the reactants (Table 2).

  X Ds d 2 dS ˆ
vSi r r2 dr dr i With the boundary conditions 8 < for r ˆ rP ; S ˆ S0 : for r ˆ rs ; dS ˆ 0 dr

The second member of equation (6) is the sum of each rate of S uptake minus the sum of each rate of S production. Each reaction rate is supposed to follow a Monod model: vS ˆ

Bio®lm model The mathematical expressions are developed subject to the following assumptions: . homogeneous bio®lm of uniform thickness, which means that the species distribution is assumed to be the same at all locations in the bio®lm; . spherical support media of uniform size; . internal mass transfer described by Fick's ®rst law; . liquid phase perfectly mixed with homogeneous concentrations; . no external mass transfer limitations. This last assumption is based on the fact that the concentration drop in the liquid ®lm represents generally less than 8% of the concentration in the bulk liquid, as estimated by Shieh and Keenan (1986). Furthermore, Christiansen et al. (1995) found that the liquid ®lm di€usion in submerged bio®lters with biostyren spheres of 3 mm diameter could be ignored with super®cial velocity ranging from 1.3 to 11 m/h. The mass balance for a substrate S in the bio®lm may be expressed as follows (if pseudo steady-state is assumed):

…6†

mS;max SXS YXS=S KS ‡ S

in which Xs is the concentration of S-utilizing bacteria in the bio®lm calculated as the product of bio®lm density (kgAVS.mÿ3) by S-utilizing bacteria fraction. As the present model involves a large set of parameters, the authors do not expect here to determine exactly all of them. Moreover, the purpose is more to emphasize the in¯uence of mass transfer limitations rather than verifying a kinetic model for anaerobic digestion. This is the reason why it was decided to ®x the Monod kinetic parameters (speci®c growth rates, half saturation constant and growth yields) and to consider that they are known (see Table 3). Liquid phase mass balance In the liquid phase, the mass balance for one substrate S is represented by equation (7). This relation comes from the assumption that the liquid phase is perfectly mixed. In the pilot reactor, this assumption is justi®ed through the high values of recycle ratio (over 60) needed to maintain a ¯uidized state. Furthermore, concentration measure-

Table 1. Stoichiometry matrix expressed in COD

Reaction Reaction Reaction Reaction Reaction

1 2 3 4 5

Glucose

Butyrate

Propionate

Acetate

Hydrogen

CH4

ÿ1 ± ± ± ±

0.028 ÿ1 ± ± ±

0.144 0 ÿ1 ± ±

0.523 0.8 0.571 ÿ1 ±

0.305 0.2 0.429 0 ÿ1

0 0 0 1 1

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660

Table 3. Set of kinetics parameters used for the model (from Denac et al., 1988) Bacteria utilizing Glucose Butyrate Propionate Acetate Hydrogen

mmax (hÿ1)

Ks (kgCOD.mÿ3)

0.05 0.0154 0.0129 0.01416 0.058

ments at several bed heights never showed any gradient across the column. VL

dS
S ˆ Qin …Sin ÿ S† ‡ N dt

…7†

The net ¯ux of S (NÇ s) has to be calculated using the di€usion and reaction multi-substrate model according to the following expression:
N S ˆ ÿDS AP dS …8† dr rˆrP It is noticed here that one needs to know the value of the derivative of S at the ¯uid±bio®lm interface. This is possible with a description of the concentration pro®les in the bio®lm, which is achieved through the derivation of the bio®lm model. It is also assumed here that the bio®lm size is uniform. One may notice that biomass growth on the carrier is not taken into account here. This rests on the fact that the batch experiments are performed within 40±80 h and that bio®lm growth is assumed negligible for such a short period of time compared to its original size. This assumption, though, could not be used for a longer period (e.g. prediction of biomass growth during the start-up). On the other hand, biomass growth is exactly counterbalanced by loss through friction for steady-state bio®lms and can also be neglected. The model presented here also assumes that the establishment of a concentration pro®le throughout the ®lm is straightforward when a change of concentration in the liquid phase occurs. Indeed, time does not explicitly appear in equation (6), which constitutes the pseudo-steady-state hypothesis. This is justi®ed by the fact that the concentrations in the liquid phase vary very slowly compared to the di€usion phenomenon. Model derivation The bio®lm model equation (equation (6)) written for each substrate constitutes a set of second-order di€erential equations with the two-points boundary value problem. This system is numerically solved with an iterative procedure using a ®nite di€erence method (BueÁre et al., 1995a). The numerical treatment is the following: . reduction of the system with dimensionless transformations; . discretization of the ®rst-order and second-order derivatives;

Y(kgVS kgCODÿ1)

0.140 0.500 0.800 0.237 0.0006

0.036 0.029 0.014 0.029 0.029

. resolution of the system with the Newton± Raphson second-order method. As an example, the glucose mass balance (only consumed) and the acetate mass balance (consumed and produced) reduce, respectively, to equation 9 and 10. The acetate mass balance is more complex because acetate is produced through glucose, propionate, and butyrate utilizing bacteria. d2 g 2 dg g ‡ ˆ f2g dx2 x ÿ y0 dx 1‡g

…9†

d2 a 2 da g b ‡
ˆ ÿ b1 f2G ÿ b2 f2B dx2 x ÿ y0 dx 1‡g 1‡b ÿ b3 f2P

p a ‡ f2A 1‡p 1‡a

…10†

where a, b, g and p are the normalized acetate, butyrate, glucose and propionate concentrations respectively, de®ned as the ratio between the concentration and the half saturation constant …g ˆ G=KG †; x ˆ rp ÿ r=rp ÿ rS is the dimensionless distance to the liquid±bio®lm interface: y0 ˆ rS =Lf is the dimensionless bio®lm size; - fa, fb, fg and fp are dimensionless moduli de®ned as  12 mG max
XG fG ˆ Lf DG
YXG=G
KG fB ˆ Lf



12



12

mBmax
XB DB
YXB=B
KB

fP ˆ Lf

mPmax
XP DP
YXP=P
KP

fA ˆ Lf

mA max
XA DA
YXA=A
KA

!12

and bi is the dimensionless moduli de®ned as a function of the stoichiometric coecient aji, di€usivity D and saturation constant K: b1 ˆ aA 1

K G DG
K A DA

b2 ˆ aA 2

K B DB
K A DA

b3 ˆ aA 3

KP DP
K A DA

The discretization with the central ®nite di€erence

Anaerobic bio®lm model and experiments

method leads to x0 ˆ 0; . . . ; xi ˆ i:Dx; . . . ; xn ˆ 1 ˆ nDx dgi gi‡1 ÿ giÿ1  dx 2Dx d2 gi gi‡1 ÿ 2gi ‡ giÿ1  dx2 Dx2 Applying these transformations to equation (9) for i = 1 to nÿ1 gives the system constituted by equation (11): gi‡1 ÿ 2gi ‡ giÿ1 2 gi‡1 ÿ giÿ1 ‡
Dx2 2Dx xi ÿ y0 ˆ f2g

gi 1 ‡ gi

for i ˆ 1 to n ÿ 1 …11†

The boundary conditions are 8 g0 ˆ normalized glucose concentration in the > > < bulk liquid (known) > gn ˆ gnÿ1 ; so that the flux at the solid± > : biofilm interface is zero equation (11) is the generic form of a set of (n ÿ 1) non-linear equations with (nÿ1) unknown variables. It is solved with the Newton±Raphson method. Furthermore, the dynamic model expressions (equation (7)) written for each of the ®ve substrates constitute a system of ®rst-order di€erential equations. This system is solved with the Runge± Kutta (fourth order) method with a ®xed-step procedure. Each calculation step needs a value of the ¯ux for every substrate; the resolution of the bio®lm concentration pro®les are then a subroutine for the calculation of the concentration in the liquid phase.

MATERIALS AND METHODS

The pilot reactor is a ¯uidized bed of 1.5 m high and 15 litre of working volume (BueÁre et al., 1995b). Column diameter was 0.115 m. The input had a concentration of 20 kgCOD.mÿ3 and the organic loading rate after the colonization period ranged from 20 to 80 kgCOD.mÿ3.dÿ1 (input ¯ow rates ranged from 0.3 to 1.5 l hÿ1). The carrier material used was crushed pozzolana (volcanic rock with a density of 1990 kg.mÿ3). The ¯uidization velocity applied was 7.5 m.hÿ1 (¯ow rate 77 l hÿ1). The hydrodynamic properties of the ¯uidized bed has been extensively studied through pulse tracer analysis with lithium chloride as the

661

tracer. Mixing times and residence time distribution in the reactor were measured (BueÁre, 1996). The experiments were achieved with three laboratoryscale reactors (500 ml). Each one was carefully ®lled with bioparticles coming from a di€erent height of the pilot. The samples were taken at di€erent bed heights (0.4, 0.8 and 1.2 m, respectively) in order to get particles of di€erent characteristics. Several batch tests were then carried out with these samples without any biomass addition between the tests. All three reactors ran in parallel. First, glucose was used as substrate in order to determine the acidogenic activity for each bio®lm size. Then, propionate and acetate were used to study acetogenic and methanogenic activity, respectively. Butyrate tests were also performed, but the results appeared to be not consistent enough to be compared to the model. The reactors were three PVC columns of 3.6 cm internal diameter and 50 cm height. Each bed of bioparticles was ¯uidized up to 20±30% expansion by means of peristaltic pumps. The temperature was kept at 358C through water circulation in a water jacket. The reactors were supplied in batch mode with solutions of glucose, propionate, or acetate, together with nutrients. The substrate solutions were concentrated (50 gCOD lÿ1), so that substrate was provided within a small volume introduced with a 10-ml syringe. The ®rst sample (t0) was taken 15 min after the introduction of the substrate in order to make sure that the liquid phase was homogeneous. The composition of the solutions is detailed in Table 4. After introducing the substrate in the reactor, the evolution of concentrations were regularly measured. Glucose was measured with the dinitrosalycilic acid reduction method (Miller, 1959). Volatile fatty acids (VFA) were measured with a ¯ame ionization detector gas chromatograph Chrompack CP 9000, nitrogen being the carrier gas (335 kPa). The column was a semi-capillar Econocap FFAP (15 m length and 0.53 mm diameter). Injector and detector temperatures were 250 and 2758C, respectively. The temperature of the oven was programmed to rise from 80 to 1208C during the analysis, with an elevation of 108C minÿ1. The chromatograms were recorded and integrated with a Shimadzu CR3-A integrator. Total organic carbon (TOC) was measured with a Dohrmann DC 80 carbon analyser by UV-oxidation at low temperature. Lithium chloride concentrations were measured with a ¯ame photometer Ciba-Corning 410. Bioparticle measurements Each bioparticle sample was carefully analysed in order to determine its characteristics. The total attached volatile solids (AVS) of a known unexpanded volume were measured by the di€erence between the dry matter (after 24 h at 1058C) and the residual mass (after 4 h at 5508C). The average diameter of the biocovered and clean particles was also determined. The measurement was performed with an optical microscope and a Leitz-Wetzlar graduated slide. The average diameter (Sauter mean diameter) was calculated for approximately 100 particles for each sample. The measurements were done with clean and coated par-

Table 4. Nutrient solution characteristics (for 1 litre solution containing 20 g TOC) Mineral solution CaCl2.H2O NH4Cl K2HPO4 MgSO4.H2O Yeast extract Mineral solution

34.2 mg 2.076 mg 440 mg 255 mg 64 mg 10 ml

FeCl3.6H2O H3BO3 CuSO4.5H2O NaI MnCl2.4H2O Na2MoO4.2H2O ZnSO4,7H2O CoCl2.6H2O

Content for 1 litre 500 mg 50 mg 100 mg 10 mg 40 mg 20 mg 40 mg 50 mg

Pierre BueÁre et al.

662

ticles in order to estimate the bio®lm size as the semidi€erence between the average diameters: Lf ˆ dp ÿ ds =2. Determination of speci®c activities Each batch test was performed up to four times in each reactor in order to establish the repeatability of the results. The maximum speci®c activities towards each trophic group are measured with the initial slope of the batch curves. As the value of the slope dS/dt is known, the speci®c activity RS is estimated with the following expression: Rs ˆ VL


dS 1
dt MX

VL being the reactor volume (m3), S the substrate concentration (kg.mÿ3) and MX the total amount of biomass (kgVSS).

RESULTS AND DISCUSSION

Performances of the 15-litre reactor Mixing characteristics. Knowing if a concentration gradient in the reactor exists in the pilot reactor is of crucial interest as regards the problem. First of all, the very high recycling ratios used to maintain ¯uidization (recycle ¯ow 77 l hÿ1; maximal input ¯ow rate 1.5 l hÿ1) considerably attenuates the occurrence of a concentration pro®le through dilution e€ect. Moreover, the mixing pattern in a ¯uidized bed reactor can be described by a dispersed plug ¯ow model (Fan, 1989), and the values of the dispersion coecients are very important and a low Peclet number ÿcharacterized
by Pe ˆ U1 dp =Dz . This characteristic also leads to a better mixed system. In order to illustrate these properties, Fig. 1 represents the response to an injection of lithium chloride in a ¯uidized bed at low gas production. The injection was done at the bottom of the bed and the samples were taken above the bed. The liquid ¯ow was 77 l hÿ1 and the

gas ¯ow rate was 6 l.hÿ1, which corresponds to a small COD loading (10 kgCOD.mÿ3.dÿ1). The plot shows that the complete mixing of the liquid phase is achieved after 6 min (normalized lithium concentration closed to 1). This mixing time has to be compared with the hydraulic retention time that is commonly applied to the pilot reactor (more than 3 h). This means that, in this particular case, the hydrodynamic phenomena are not in competition with the reactions because their dynamic is too rapid to have any in¯uence on the biological kinetics. As agitation due to the movement of the particles and to gas production increases considerably the degree of axial mixing in a ¯uidized bed fermenter, it can be considered as perfectly mixed as long as the recycling ratios are kept at a high level (over 10 at least). On the other hand, when the recycle ratio is low, the dynamics of mixing and reaction become closer and the perfect mixing hypothesis is more questionable. Reactor performance. The anaerobic ¯uidized bed reactor has been operated during more than 1 year. Figure 2 summarizes the evolution of the main parameters: total VFA, organic loading rate (OLR) and the carbon removal (based on TOC) during a 2-month period. The concentrations are measured at the outlet of the reactor. The organic loading rate is increased regularly from 30 to 75 kgCOD.mÿ3.dÿ1. One can observe a constant increase of the outlet VFA as the organic load is increased. It is attributed to the reduction of the hydraulic retention time during this period. Nevertheless, the carbon removal remains elevated (over 70%). The main VFA encountered during this period are acetate (av. 50215%), propionate (av. 35210%), the remaining being butyrate (10%) and valerate (5%). The maximal VFA concentrations encountered during this period were 5.4 kg.mÿ3. In

Fig. 1. Residence time distribution on an anaerobic ¯uidized bed bioreactor at low gas production.

Anaerobic bio®lm model and experiments

663

Fig. 2. Evolution of the organic loading rate, carbon removal and total volatile fatty acids concentrations during a 2-month period.

this case, the propionate concentration rose up to a value close to that of acetate (2.6 for acetate, 2.3 for propionate). Batch tests on the small reactors The experimental data for the batch tests are reported in Figs 3±5. It can be seen that the initial substrate consumption followed a straight line. This means that the value of the speci®c activity measured did not depend much on the initial con-

centration. Therefore, one can compare the di€erent values of the speci®c activities even if the initial concentrations of substrate in each reactor were not exactly the same. Characteristics of bioparticles The results obtained are presented in Table 5. It can be noticed that the carrier particle diameter is lower at the top of the reactor, in association with the largest bio®lm thickness. Bio®lm sizes are very

Fig. 3. Comparison of experimental glucose batch curves with the simulations.

Pierre BueÁre et al.

664

Fig. 4. Comparison of experimental propionate batch curves with the simulations.

Fig. 5. Comparison of experimental acetate batch curves with the simulations.

Table 5. Particle and biomass characteristics of the reactors Reactor 1 2 3

Sampling height (m) 0.4 0.8 1.2

Unexpanded volume (ml) 235 150 190

Mean bioparticle diameter (mm) 610 915 1057

Mean carrier diameter (mm) 365 254 194

Bio®lm thickness (mm) 120 330 430

AVS (kg.mÿ3 unexpanded bed) 20.2 49.1 49.4

Anaerobic bio®lm model and experiments

large at the top of the reactor (430 mm), while the clean support medium has a low diameter (200 mm). The bioparticles with such bio®lms almost look like UASB granules. On the other hand, the bottom particles have a smaller bio®lm growing on a higher diameter support. Furthermore, it is noticed that the biomass concentration does not increase much from 0.8 to 1.2 m height in the pilot. This strati®cation has to be related to the di€erences between the terminal velocities Ut of the particles, which are higher for the denser ones (important clean support diameter) even if their diameters are inferior to those of the lightest particles. Calculations of the terminal velocity Ut of the biocoated particles con®rmed that strati®cation is linked with an important decrease in the values of terminal velocity (see Table 6). Ut (equation (12) was estimated from the measured data (bio®lm thickness and carrier diameter) and from the value of the apparent density rp calculated from equation (13). Bio®lm wet density is taken equal to 1.1  1 4…rp ÿ r1 †gdp 2 Ut ˆ …12† 3r1 Cd with Cd ˆ

10 1

Re2t

rp ˆ rs

…for 0:4 < Ret < 500† ! ! ds3 ds3 ‡ rbf 1 ÿ 3 dp3 dp

…13†

In each of the reactors, glucose consumption is very quickly achieved (less than 3 h, Fig. 3). There is no signi®cant di€erence between the fermentation times, even if the total amount of biomass and the initial glucose concentrations are not the same in each reactor. It was observed that the measured glucose concentration never reaches zero. This is probably due to analytical problems in the dinitrosalycilic acid method, probably due to occasional presence of residual sugars coming from the bio®lm structure. This could a€ect the real values of the concentrations by a constant o€set, but does not modify the values of the speci®c activity. VFA degradation takes much longer (30 h or more, Figs 3 and 4). One can notice that the speci®c activity of glucose using bacteria RG of reactor 1 is higher Table 6. Estimation of terminal velocity of each bioparticle sample Reactor 1 2 3

1.295 1.119 1.105

Table 7. Glucose, acetate and propionate speci®c activities (based on total attached volatile solids) and standard deviations Reactor

RG (kgCOD kgAVSÿ1 hÿ1)

RP (kgCOD kgAVSÿ1 hÿ1)

RA (kgCOD kgAVSÿ1 hÿ1)

1 (bottom) 2 (middle) 3 (top)

0.0914 20.015 0.0695 20.012 0.0489 20.008

8.2 22 10ÿ4 8.3 21.8 10ÿ4 5.7 21.6 10ÿ4

2.0 20.14 10ÿ3 4.8 20.25 10ÿ3 4.5 20.42 10ÿ3

than that of reactor 2 and 3 (see Table 3). The speci®c activity of glucotrophic bacteria seems then to be a€ected by bio®lm size. This result was observed repeatedly: even if the exact values of speci®c activities were di€erent for one batch test to the other for a speci®c reactor, the negative in¯uence of bio®lm size was always observed. Propionate uptake The acetogenic activity, Rp, of propionate utilizing bacteria shows a di€erent tendency than the glucotrophic species (see Table 7). The same relationship was not noticed between the values of speci®c activities using propionate as compared when using glucose. However, it seems that there is a di€erence between the three reactors even though they all use biomass coming from the same pilot. The activity in the third reactor is much lower than in the other ones. The authors do not have an explanation for this phenomenon. Anyhow, the values presented here are the average of three determinations. In addition, contrary to the batch tests run with glucose or acetate, the initial propionate uptake rates showed higher standard deviations, and clear conclusions cannot be drawn on activities because it varied from one test to another. Acetate uptake

Glucose uptake

Apparent density

665

Reynolds at terminal velocity 26 32.6 33.2

ÿ1

Ut (m h ) 124.0 102.7 90.4

Considering the values of speci®c activities RA in Table 7, acetate consumption rate is much lower in the ®rst reactor than in the other ones. This result has been con®rmed with several batch runs. In this case, bio®lm size does not seem to have an e€ect on reactors 2 and 3, but it seems to a€ect reactor 1. This may be attributed to a change in the amount of methanogens in the ®rst reactor. Discussion If the activity of the acidogenic bacteria is compared, a decrease in glucose fermentation activity from reactor 1 to reactor 3 is observed. It is possible to estimate the relative loss of glucotrophic activity along the bed height by dividing the values of RG obtained in reactors 2 and 3 by RG1, the value obtained in reactor 1 (see Table 8). This loss Table 8. Loss in glucose speci®c activities Reactor 1 2 3

Bio®lm size 122 331 430

RG/RG1 1 0.76 0.54

Pierre BueÁre et al.

666

suggests a decreasing fraction of acidogens along the bed height and is correlated with bio®lm size. The reason is that, in the present case, such a discrepancy cannot be attributed to the existence of concentration pro®les, since, as mentioned previously, the liquid phase is homogeneous in the pilot reactor. The kinetics of propionate utilizing bacteria do not reveal any mass transfer limitations problems if one looks at the values of speci®c activities RP. The di€erences encountered in the experimental values of speci®c activities does not allow the drawing of signi®cant conclusions. Nevertheless, it may be seen that the lowest average speci®c activity is encountered in the third reactor, as the two other values are approximately equal. This could be linked with the distribution of bacterial species in the bio®lm: it is possible that the total amount of propionate utilizing bacteria is inferior in the third reactor than in the two others. Concerning the uptake rate of acetate, it was seen in the previous section that the speci®c activity RA in reactor 1 was much lower than in the other ones. Indeed, the model predicts no signi®cant mass transfer problems in the three reactors. This result can be explained by a change in bio®lm composition with bio®lm size. If one considers the bio®lm development period and if one assumes that the glucotrophic bacteria are di€usion limited, it is clear that the inner regions of the deep bio®lms are not supposed to contain acidogens. That is to say that the amount of acidogens in thick ®lms is lower than in thin ones where glucose can reach the inner zones. Consequently, the amount of methanogens in thick ®lms is higher, which results in a better methanogenic activity. A similar phenomenon has been observed with UASB granules by Arcand et al. (1994): after sloughing the surface of the granules, the speci®c acidogenic activity decreases consequently and the methanogenic activity was not a€ected.

COMPARISON OF THE BATCH EXPERIMENTS WITH MODEL PREDICTIONS

Active biomass density Like many investigators, the present authors did not make the di€erence between the attached solid and the biomass at ®rst. Therefore, they took par-

ameters estimated from chemostat experiments in the literature (Denac et al., 1988). However, it has been shown more recently that a large amount of inactive organic material contributes to the measured volatile suspended solids (VSS) in bio®lm systems (Kuba et al., 1990; Furumai et al., 1991; Imai et al., 1994). In order to take this factor into account, the active biomass density was introduced as a parameter of the model. This variable does not correspond exactly to the bio®lm dry density, whose role and nature has been well investigated by Ro and Neethling (1991). However, active biomass density is not easy to correlate with bio®lm size or structure, because it seems to depend on several factors such as bio®lm size and liquid velocities (Araki and Harada, 1994). Biomass composition It is very dicult to estimate the biomass distribution between the di€erent species in an anaerobic digestion consortium. Moreover, as seen previously, it seems that this composition in biomass is not the same for all bio®lms, even in an identical reactor. Consequently, two sets of simulations were run: in the ®rst set, the biomass distribution is considered to be equal in every bio®lm (run 1). The biomass composition taken in the present simulation are averaged from several studies: the modelling work of Mosey (1983) and Dalla Torre and Stephanopoulos (1986) and the experimental investigation of Sanchez et al. (1994). In the second one, the average composition of bio®lm in acidogens decreases with bio®lm size as methanogen amount increases (run 2). This adjustment of parameters have been done with a trial-and-error method in order to ®t the data. The values of the biomass used for the two runs are presented in Table 9. Simulation results The simulation of acidogenic activity is of the same order of magnitude as the experimental data (Fig. 3a±c). It is noticed that the second run of simulations allows a better description of the kinetics, especially for the third reactor (large bio®lm, Fig. 3c). Nevertheless, there is no signi®cant di€erence between run 1 and 2 for the ®rst and second reactor. Propionate uptake is well represented by the model at least for the ®rst 40 h of simulation (Fig. 4a±c). The two simulation runs are close to

Table 9. Biomass distribution (%) for each simulation run Bacteria utilising Glucose Butyrate Propionate Acetate Hydrogen

Run 1 Reactor 1,2,3:

Run 2 Reactor 1:

Run 2 Reactor 2:

Run 2 Reactor 3:

65 2.5 2.0 7.0 23.5

72 2.5 2.0 5.1 18.4

58.5 2.5 2.0 8.4 28.6

49 2.5 1.9 9.7 36.9

Anaerobic bio®lm model and experiments

one another because the amount of propionate utilizing bacteria taken from the literature (run 1) gave satisfactory results. Therefore, those values were not much changed. Nevertheless, a deviation between simulations and experiments can be observed after 40 h. Acetate degradation is well described by the model (Fig. 5a±c). However, it can be noticed that acetate degradation in the second reactor is always overestimated even in the second run (Fig. 5b). From a global point of view, good behaviour of the present model is noticed when compared to experimental data, but a closer adequation can be seen with the second set of simulations (i.e. acidogens decreasing and methanogens increasing with bio®lm size). This is not completely surprising since acidogens cannot develop in the inner part of large bio®lms because of mass transfer limitations of glucose. Indeed, the biomass distribution among di€erent species in a heterogeneous bio®lm is an important state parameter for a general model, even if the exact value of this distribution is not easy to estimate. Another important point is the validity of the assumption of homogeneous biomass distribution throughout the bio®lm, which is here very questionable. Many investigators used a spatial layering to describe multispecies bio®lms (Wanner and Gujer, 1986; Rittmann and Manem, 1992). In UASB granules, a layered structure has been observed (MacLeod et al., 1990) and the populations of the outer regions seem to have a higher acidogenic activity (Arcand et al., 1994). This result is not con®rmed for ¯uidized bed particles, but a certain part of spatial layering could explain the di€erences observed here.

CONCLUSIONS

1. The experiments shown in this paper demonstrate that bed strati®cation due to mechanical e€ects occurs in a ¯uidized bed using particles of di€erent size. Smaller particles with thicker bio®lms accumulate at the top of the reactor. 2. The speci®c activity of the bio®lm seems to be a function of the bed height. In deep ®lms (top of the bed), the glucotrophic activity clearly decreases, as the methanogenic activity increases. This indicates a change in the bio®lm composition with bed height. These variations are attributed to bio®lm size, because the liquid phase of the pilot was always kept homogeneously mixed. The fundamental reason of this di€erence could be glucose di€usion limitations in the deep ®lms, which could be responsible of a limited development of acidogens. 3. The model developed here shows good abilities for the description of bio®lms with the combined e€ect of di€usion and biological kinetics. The

667

crucial point appeared to be the biomass distribution between each trophic group. The model required an adaptation of the biomass distribution depending on the bio®lm size in order to ®t the data. This indicates clearly that biomass composition of the bio®lm is not constant in a given reactor and may be a€ected by spatial variations. These variations can be attributed here only to a di€erent arrangement of the species according to bio®lm size. It could also be a consequence of concentration gradients. Further modelling and experiments are needed to give precisions about the variation in biomass composition with bio®lm size, including perhaps layered bio®lm approaches. Such explicit models could then be used for the design and optimization of anaerobic ¯uidized bed units or any other bio®lm systems involving heterogeneous populations of micro-organisms for carbon or nitrogen removal.

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