stratified mixed-culture biofilm model for anaerobic digestion

Stratified Mixed-Culture Biofilm Model for Anaerobic Digestion

M. Canovas-Diaz Department of Biochemistry, Faculty of Chemistry, University of Murcia, 30001 Murcia, Spain

J.A. Howell School of Chemical Engineering, University of Bath, Bath BA2 7A K United Kingdom

Accepted for publication August 20, 1987

Development of a novel two-layer anaerobic biofilm model is based on substrate utilization kinetics and mass transport. The model is applied to steady-state conditions for a fixed-film anaerobic reactor. The microbial film is considered to consist of two distinct biofilm layers, one adjacent to the second, with an acidogenic bacteria biofilm forming the outer layer and a methanogenic film the inner one. The model assumes that sugars are only metabolized by the first layer and converted into volatile fatty acids (VFA), while fatty acids are taken up only by the inner layer. The model is able to predict both substrate flux net uptake and methane production for steady-state conditions. The results of modeling agree with methane production experimental data published elsewhere. Further, the model shows why layered fixed- film reactors can withstand high and inhibitory concentrations of volatile fatty acids as well as severe overloading without failure.

INTRODUCTION

The utilization of biofilm processes for anaerobic waste- water treatment has become common practice because of the benefits offered by biofilms, such as active biomass is built up and maintained in the reactor attached to solid surfaces, there is limited solids production and those formed settle well, and they allow high volumetric organic loading rates and maintain reasonable effluent quality, even during shock loads. Three basic processes are involved in anaerobic digestion metabolism of sugars within biofilms: diffusion of sugars from the bulk liquid into the biofilm, transformation of the substrate through bacterial action into volatile fatty acids (VFA), and subsequent transformation of the VFA by hydrogen-producing bacteria to acetic acid and H,, which are the carbon and energy sources for methanogenic bacteria. As a result, methane gas is produced, and a valu- able energy source can be recovered from the water.

Biofilm models have usually dealt with steady-state conditions and considered one limiting substrate. '-' Concepts such as ideal thickness (equal to the penetration depth of the limiting substrate);' growth and decay of the microbial film;' deep, fully penetrated and shallow b i~f i lms;~ and biofilm at the steady state4 have been introduced. However, only some of the authors considered anaerobic processes ,, and only

recently have biofilm models distinguished between two populations (acidogenic and methanogenic bacteria).

The specific requirements of the model are that (a) the model has to be able to predict both sugar uptake and methane production at the steady state for any bulk liquid concentration and biofilm thickness, (b) it has to account for inhibition since methanogenic bacteria are affected by high concentrations of un-ionized VFA, 'O-I2,l4 and (c) it has to show why fixed-film reactors can withstand severe shock overloading of over 4 times the design load without failure, as has been observed by Kennedy and van den Berg."

This article presents a stratified biofilm model dealing with anaerobic metabolism in a fixed-film reactor and is compared to experimental results published elsewhere for a downflow fixed-film reactor treating deproteinized whey. l6

Steady-state conditions with a two-population anaerobic mixed culture are analyzed. Sugars, methane, and VFA were measured in terms of COD.

The model presented in this article is designed to show as clearly as possible the effects and advantages of a stratified ecology. The model has thus been deliberately simplified in other respects compared to the recent models of Dalla Torre and Stephanopoulos,'o%'' Paulotathis and Gossett,', and Droste and Kennedy.13

It does not, for example, consider different VFA separately; it does not consider hydrogen metabolism, pH- carbonate equilibrium chemistry, and the concomitant effects on substrate ionization; and it does not embed the film model within a complete reactor model. The film is analyzed locally and includes the effects of sugars and fatty acids with diffusional resistances in the film, two separated populations, and inhibition by fatty acids on methane formation.

THEORETICAL DEVELOPMENT

The overall processes are here simplified to two basic processes carried out by distinct population.

TI Acidogenesis sugars aVFA + (o,cells (1) bacteria

Biotechnology and Bioengineering, Vol. 32, Pp. 348-355 (1988) 0 1988 John Wiley & Sons, Inc. CCC 0006-35921881030348-08$04.00

'2

methanogenic bacteria

Methanogenesis VFA - PCH, + p2cells + ECO, ( 2 )

where a , p, p,, p,, and E are stoichiometric parameters and are considered positive nonzero constants. The net reaction rates of the two reactions are r , and r2, respectively. The overall system is the conversion of sugars into cells, VFA, CO,, and CH,. Assuming that the whole process occurs solely within a fixed film of microorganisms, the local rate of mass of sugar conversion per unit volume of film is r, ( r l ) and the rate of VFA formation in the first reaction is ar , . In the second process (methanogenesis) the rate of VFA removal per unit volume of viable organisms is r2. In this latter process methane is being produced at a rate of rM (Pr,). All rates are normalized and measured in mass of chemical oxygen demand (COD) per unit time per unit volume of film. (Thus, E = 0 , a + p, = 1 = P + p2). No attempt is made in the model to distinguish between the different sugars or fatty acids nor is hydrogen metabolism

I

Figure 1. respective,y,

Stratified biofilm: L , , L , , acidogenic and methanugenic layer,

considered. Therefore, the net rate of VFA consumption can be written as

fusion of substrate is equated to its removal by the micro- organism, leads to

or (3) d Z G r, = -arl + r,

D , 7 - r, = 0 dz

rM r, = -arc - - P (4)

Consider now a differentiated film with an outer acidogenic biofilm layer adjacent to an inner methanogenic one. Sugar is assumed to be transformed into VFA and acidogens by the first outer layer, and VFA are subsequently transformed into methanogens and methane gas by the second inner biofilm. The kinetics of VFA conversion will be assumed to be mainly zero order but is inhibited by VFA at high concentrations, and both zero- and first-order kinetics will be separately considered for sugar uptake. The use of an inhibition function enables the model to predict process failure at high concentrations of VFA.',

Here rI and rz may be expressed as

r l = r, = k , * X , or

where k , and k are, respectively, the zero- and first-order kinetic constants with respect to sugar uptake (M(C0D) * . TI, and T-I); k, and ki are the VFA uptake rate and inhibition constants, respectively (M * . T - ' , and M . L-3); and XI and X , are the COD mass volume densi- ties of acidogenic and methanogenic bacteria within the biofilm (considered constant at the steady state). Assuming that no reaction takes place in the liquid phase, the concentration profiles achieve steady state much faster than any local change in the bulk liquid concentration, and the liquid phase mass transfer is neglected with respect to solid phase diffusion.

Within each film the differential mass balance applied to the microbial mass in Figure 1, in which the molecular dif-

d2F dz

D , . , - r , = O (7)

where D , and D, are the effective molecular diffusion coefficients for sugars and VFA and G and F are the local sugar and VFA concentrations. Substituting r, and r, from equations (4) and (5) and considering the zero-order kinetics with respect to sugar uptake yields

d2G dz

D 1 7 = k , X ,

(9)

where a, the yield of VFA from the first step, is approximately unity at the steady state as little biomass is produced.

The preceding equations are general and can be applied to either film. In the outer film X , is zero and in the inner film XI is zero. With an outer film of thickness L , (for acidogenesis) and an inner film (for methanogenesis) of thickness L,, the differential equations have the following boundary conditions:

The surface is at the bulk liquid condition:

z = O G = G , F = F ,

There is continuity of concentration and flux through the interface between the films, but as no sugar uptake occurs in the second film, the gradient of sugars is already zero:

CANOVAS-DIAZ AND HOWELL: BlOFlLM MODEL FOR ANAEROBIC DIGESTION 349

There is no flux through the solid support:

This leads to a two-point boundary problem for each of the films. Alternatively, the problem can be tackled as that of a single film, where X I and X , are step functions of depth z .

Outer Layer: Zero-Order Kinetics

tions can be reduced to For 0 < z < L , , X , = 0, the system of differential equa-

d2G k , XI - = a dz D ,

where a = -

d2F k , XI dz D2 - = -b where b = -

Both equations can be integrated analytically by using the boundary conditions [eq. (lo)] and defining g and f by

dG dF g = ! z f = - dz

and thus,

g = a(z - L , ) f = b(L , - z ) (14)

The flux of sugars entering the film (at z = 0) is given by go = -a,. The total sugar metabolized per unit area is k , X , L , . This equals (at steady state) the flux of sugar across the outer surface. The maximum flux can be shown to be

where go, is the sugar concentration gradient at the outer boundary of the layer with a corresponding maximum us- able thickness for the outer layer of

Zero-order kinetics cannot be exhibited in practice by layers thicker than L , ,.

For intrinsic zero-order kinetics and thin films the overall glucose uptake is proportional to the thickness of the acidogenic layer. At some critical thickness L , = L , , the glucose concentration will be zero, and the overall glucose flux will then be at its maximum. A thicker film would lead to the simple zero-order model predicting negative concentrations. Such a problem is avoided by appropriate checks in the relevant computer code.

Outer Layer: First-Order Kinetics

tions can be reduced to For 0 < z < L, , X 2 = 0, the system of differential equa-

d2G k X , G dz2 D I -- --

and defining g and f by equation (13), as for zero-order kinetics.

For intrinsic first-order kinetics the maximum uptake rate can only be exhibited by an infinitely thick acidogenic layer. Of this maximum uptake, 99% can be exhibited by a finite layer of thickness Llm.8

COD Conservation at the Steady State

At the steady state, if it is assumed that the net cell production is low, COD (sugars, VFA, and CH,) conservation requires that the boundary fluxes show no net COD flux as follows:

(19) go +fo + 1720 = 0

assuming thatf,, rn, < 0, i.e., there is a net production of VFA and methane. Here rn, is the flux of methane, andf, is the unconverted VFA flux leaving the film. Therefore,

lgol ’ If01 (20)

(This assumes thatf, < 0 or that the film is a net producer of VFA.)

The yield coefficient is defined as

overall CH, flux (21) = overall sugars flux

where y is the fraction of COD converted to methane in the system. Thus, m, can be written as

mo = Ygo ( 2 2 )

where y < 1 subject to the preceding assumption that the film is a net producer of VFA.

Boundary Conditions for Outer Layer (Zero- and First-Order Kinetics)

are thus The boundary conditions for a layer of thickness L , ,

z = 0 G = Gb F = Fb go = 0.99g0,

z = L I , G = O g = O f = h l F = F , ,

Equations (1 1) and (12) (zero-order kinetics) or (17) and (18) (first-order kinetics) can now be rewritten as four first-order differential equations and integrated using the first boundary condition as an initial condition until g = 0, when the second boundary condition requires that z = L , , and thus defines the interface between the layers. The second layer can now be examined.

350 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 32, JULY 1988

Inner Layer: Inhibitory Kinetics

layer is The only differential equation applicable to the inner

d2F - k2 x, - - d z 2 D2(1 + F / k , )

defining f = d F / d z , this may be numerically integrated as a pair of first-order differential equations with the initial boundary conditions

z = L , , F = FL, f = fL, (25)

until f = 0, when the second boundary condition [eq. (lo)] requires that

z = L, = L , , + L, (26)

The integration technique used was developed by Howell” and involves an implementation of imbedded fourth- and fifth-order Sarafayan algorithms due to Butcher. Here, k, was calculated from the concentration of VFA at which 50% inhibition of gas production was observed. l6 Suitable values of k , (or k for first-order kinetics), k,, and y were chosen so that the simulation matched observed values of bulk liquid concentration of sugars and VFA and methane production. ’‘ In order to compare the modeling results, the same biofilm model approach was applied to an unstratified biofilm in which acidogenic and methanogenic bacteria are considered to be uniformly mixed within the film.

RESULTS AND DISCUSSION

All the computations were for steady-state conditions in the biofilm. Even in a reactor where conditions are chang- ing, such as under overloading conditions,15 the dynamics of the biofilm are considered to be rapid enough that the steady-state solution will be reasonable. A series of such steady-state solutions can be used to represent the se- quence of changes during overloading.

Figure 2 represents an operating film with the stratified layers. Sugar is diffusing into the outer layer and is being metabolized to fatty acids. The outer layer is thin so that not all of the sugar is metabolized (the sugars have accu- mulated without metabolism in the inner layer until the steady-state concentration is reached). The fatty acids formed diffuse from the outer layer in two directions, into the inner film where they are metabolized to methane and out into the bulk liquid. In a well-operated film most of the sugars are converted to methane, but only a very small proportion finish as fatty acids and leave the film to accumulate in the bulk liquid (Fig. 3). In a single-layer mixed population film, (Fig. 4), the fatty acids will tend to accumulate to high concentrations within the film and will tend to have a net outward diffusion with relatively low per- centage of conversion to methane. The bilayer film, on the other hand, may exhibit a near zero gradient at the outer surface, even though there is much conversion of sugars to VFA, as is shown in Figure 3.

0 . 5 1 1.5 BIOFILM THICKNESSES (MM)

Figure 2. Stratified biofilm model. Concentration profiles at steady state (Gb = 4.5 g sugars/L, Fb = 1.8 g VFA/L as COD, experimental and computational overall methane yield, y = 0.96 and y = 0.94, respectively). Zero-order kinetics sugars uptake.

BIOFILM THICKNESSES (MM)

Figure 3. Stratified biofilm model. Concentration profiles at steady state (Gb = 4.5 g sugars/L, Fb = 1.5 g VFA/L as COD, experimental and computational overall methane yield, y = 0.97). Zero-order kinetics sugars uptake rate.

6 4 i

3 1 1 I I n . a 0 . 3 0.6 Ij . 4

BIOFlLM T H I C K N E S S IMM)

Figure 4. Unstratified biofilm model. Concentration profiles at steady state (Gb = 5.5 g sugars/L, Fb = 2 g VFA/L as COD, experimental and computational overall methane yield, y = 0.97 and y = 0.32, respectively). Zero-order kinetics sugars uptake rate.

CANOVAS-DIAZ AND HOWELL: BIOFILM MODEL FOR ANAEROBIC DIGESTION 351

If VFA production is high due to very high sugar concentration in the bulk liquid, the single-layer film will rapidly develop inhibitory concentrations of VFA deep within the film (Fig. 5), while by maintaining the barrier to diffusion in the stratified film, the inner layer may still experience the lower noninhibitory concentration, and methane production can be maintained (Fig. 6). It is possible that outward diffusion of VFA may be marked, and it may well accumulate in the bulk liquid (Fig. 7).

If the concentration of VFA in the bulk is now high (Fig. 8) and the concentration of the sugar begins to be reduced, a net inward diffusion of VFA can occur, but still due to the noninhibitory concentration experienced by the methanogens they continue to function well, VFA is metabolized, and the net bulk concentration is reduced to nor- mal levels once more.

Figure 9 shows how very severe overloading by increas- ing the bulk sugar concentration (Gb) can result in lower methane yields. It is also interesting to note that thick outer films may produce excess fatty acids, leading to lower methane yields as the excess VFA diffuses out of the film.

I I

2b SIY;pR$ I 1

0 4 , I 0.0 0.2 0.1 0.8 0 1 1.D

EIOFILM T H I C K N E S S E S I M M )

Figure 7. Stratified biofilm model. Concentration profiles at steady state. (G, = 8 g sugars/L, F, = 2 g VFA/L as COD, experimental and computational overall methane yield, y = 0.95). Zero-order kinetics sugars uptake rate

10 I

* I

L

" 0.0 0.4 0.8 1 . 2

BlOFILM THICKNESS (MM)

Figure 5. Unstratified biofilm model. Concentration profiles at steady state (Gb = 14 g sugars/L, F, = 5 g VFA/L as COD, experimental overall methane yield, y = 0.89, and computational, y = 0.33). First-order kinetics sugars uptake rate.

* - , . , . . . . . . . I

0.6 1 , 2 1 ,8 BlOFlLM THICKNESSES (MM)

Figure 6. Stratified biofilm model. Concentration profiles during overloading at steady state. (G, = 11 g sugars/L, Fb = 8 g VFA/L as COD, experimental and computational overall methane yield, y = 0.8). First- order kinetics sugars uptake rate.

G I ---- 1 I

I 0

BIOFILM THICKNESSES IMM)

Figure 8. Stratified biofilm model. Concentration profiles at steady state. (Gb = 4 g sugars/L, Fb = 6.5 g VFA/L as COD, experimental and computational overall methane yield, y = 0.88). Zero-order kinetics sugars uptake rate.

2 4 I 1

BlOFlLM THICKNESSES (m)

Figure 9. Stratified biofilm model. Concentration profiles at steady state during overloading (G, = 20 g sugars/L, F, = 6.5 g VFA/L as COD, experimental and computational overall methane yield, y = 0.4). Zero-order kinetics sugars uptake.


In order to test the model, it was compared with experimental data from a 50-L downflow fixed-film reactor fed with deproteinized cheese whey (DPW).I9 This whey is particle free and contains nearly all of its COD as lactose, which is broken down to glucose and galactose, both of which were metabolized by the mixed culture of acidogens to a mixture of acetic, propionic, and butyric acids. Total COD was measured conventionally, and the individual acid concentrations were monitored by gas liquid chromatogra- phy, converted to COD, and subtracted from the total to give the COD of the sugars. The organisms were grown initially on fatty acids to form the inner layer before switch- ing to DPW to develop the full film. The measurements reported here were taken at steady state, approximately 2 months after start-up. The film thickness was uncon- trolled and varied over the length of the reactor between 1 and 2 mm. A high recycle rate meant that the concentrations were approximately uniform over the reactor so thickness variation might have been related to hydrody- namics, a factor not yet quantified with respect to film thickness control, although it was mentioned by Howell and Atkinson.'

The vessel contained support surfaces in the form of needled polyester fabric tubes -25 mm diameter. Loading rates were on the order of 6-10 kg/m3 d and resulted in 85-95% COD removal. There was 5 m3/m3 d gas produced containing 65% methane. There was total agreement between the experimental and computational overall methane yield ( y) for the stratified model (Table I), whereas the unstratified model could not be adjusted to match the experimental values irrespective of the kinetic coefficients used in the simulation (Table I). For the results shown in Table I the unstratified model was simulated using the same kinetic coefficients as used for the stratified model. The method of calculation provided the film thickness from the external bulk concentrations and the kinetic coefficients. Moreover, the COD conversion to methane for the stratified model was approximately the same as the experimental value. The unstratified model not only gave a lower conversion value (30-35%) but also implied that 65-70% of the COD was converted to additional biomass. Low

biomass production is a feature of anaerobic digestion,20 while an unstratified film would appear to produce consid- erable biomass, unlike the stratified ecology reactor. l 6 The biofilm thicknesses computed for both models were within the observed range (1-2 mm).

The computations predict inhibition (which occurred ex- perimentally at a threshold of 6.5 g/L VFA as COD) due to higher VFA levels within the film than predicted exter- nally. An unstratified biofilm reactor would not be ex- pected to exhibit the stability to shock loadings that was observed.16 Thus, the outer layer acts as a protective barrier against inhibitory compounds (VFA, toxic compounds) and makes the stratified ecology system more stable than other anaerobic reactors.

Figure 10 illustrates steady-state biofilm thicknesses calculated at a variety of bulk liquid conditions of sugars and VFA (zero-order kinetics). Both biofilms were grown lin- early and independent of bulk sugars concentration. At high sugars concentrations the rate of sugars removal depends only on the specific surface area in the reactor as

0,o 0.2 0.4 0.6 0.8 1 . 0 L2 (MM)

Figure 10. Stratified biofilm model. Biofilm growth at different steady- state conditions. (Gb and Fb ranging from 2 to 11 and 0.25 to 6.5 g/L sugars and VFA as COD, respectively.) Zero-order kinetics sugars uptake rate.

Table I. and unstratified models.

Comparative study between experimental and computational results for both stratified

Zero-order kinetics First-order kinetics Experimental

values Unstratified Unstratified Stratified Stratified

Sugars (g COD/L) 4.5 4.5 4.5 4.5 4.5 VFA (g COD/L) 1.5 1.5 1.5 1.5 1.5 Y Conversion of sugars

0.97 0.38 0.33 0.97 0.97

to CHI (%) 89 35 30 92 92 Biofilm thickness, (mm) 1-2 1-1.2 0.8-1.2 1-1.4 0.9-1.2

CANOVAS-DIAZ AND HOWELL: BIOFILM MODEL FOR ANAEROBIC DIGESTION 353

well as on the outer biofilm thickness. In Figure 11, the same plot for first-order kinetics is shown. In this case, at a very low concentration of sugars, the acidogenic biofilm grows faster than the methanogenic one. As the concentration of sugars increases, so does the flux of VFA converted to biomass, and, therefore, the methanogenic biofilm grows faster. In this case, the rate of sugars removal no longer depends only on L , and surface area but also on G, .

Figure 12 shows a drop of overall methane yield as the bulk liquid concentration of the sugars increases during overloading at different steady states. If biofilm growth stops, conversion of sugars will not be complete, the result of overloading being a drop of the overall methane yield. On the other hand, should both biofilms be able to grow, the overall methane yield would remain constant after an initial drop. This is usually the case as the system moves from a pseudo-steady-state toward the maximum one. Young and McCarty’ observed that the effluent COD concentration generally reached new equilibrium levels approximately 2 days after a change in the loading. Under these conditions in the bulk liquid, methanogenesis therein would be totally inhibited. Oakley et showed evidence of a double or layered biofilm by using scanning electron mi- croscopy techniques to study the biofilm development within an anaerobic fluidized-bed reactor.

f

- 1

o . o o l I I I 1 0 .0 0.2 0.4 0.6 0 .8 1.0

L2 (MM)

Figure 11. Stratified biofilm model. Biofilm growth at different steady- state conditions. (G, and Fb ranging from 2 to 11 and 0.25 to 6.5 g/L sugars and VFA as COD, respectively.) First-order kinetics sugars uptake.

100 I

GB (G/L)

Figure 12. Variation of overall methane yield with sugars (G,) bulk liquid concentration at different steady state conditions (L I , acidogenic biofilm thickness at steady state.)

Although further research is required on the dynamics of the stratified ecology biofilm, its steady-state analysis has given further understanding of the anaerobic biofilm reactor.

CONCLUSIONS

The stratified ecology biofilm model is able to predict both the substrate flux concentration and biofilm thicknesses of a downflow anaerobic fixed-film reactor at the steady state. The modeling results demonstrated good agreement with the methane production experimental data. The model shows why a stratified fixed-film reactor can withstand a high concentration of VFA as well as severe overloading without failure. It also demonstrates the clear advantages of stratified ecology in promoting high methane yields.

NOMENCLATURE

defined in eq. (11) defined in eq. (12) molecular diffusion coefficients (L2 . T-I) initial VFA flux at the surface volatile fatty acid concentration (g L-’) volatile fatty acid concentration (g L-I) in bulk liquid sugar flux, sugar flux at the surface, and the maximum sugar flux at the surface of the biofilm, respectively sugar concentration (g L-’) sugar concentration (g L-’) in the bulk liquid first-order kinetic constant ( T I ) zero-order kinetic constant ( M . L-’ . T - ] ) volatile fatty acid uptake constant (M . L-’ . T - ’ ) volatile fatty acid inhibition constant (M . L-’) acidogenic biofilm thickness (mm) methanogenic biofilm thickness (mm) maximum acidogenic biofilm thickness (mm) total film thickness (mm) initial methane flux rate of sugar removal ( M . L - ~ . T - ’ ) rate of VFA removal (M . L-’ . T I ) net rate of VFA removal (M . L-’ . T I ) rate of sugar removal ( M . L-’ . T I ) rate of CHI production (M . L - 2 . T-I ) distance through biofilm (L) fraction of acidogenic and methanogenic bacteria in the film overall methane yield (dimensionless) chemical oxygen demand volatile fatty acids

Greek letters

a, p. (ol, (oz, E stoichiometric coefficients

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CANOVAS-DIAZ AND HOWELL: BlOFlLM MODEL FOR ANAEROBIC DIGESTION 355

stratified mixed-culture biofilm model for anaerobic digestion

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