A New Approach to the Kinetic Study of Anaerobic

Biomass 23 (1990) 79-102

A N e w Approach to the Kinetic Study of Anaerobic Degradation of the Organic Fraction of Munic ipal Solid

Waste

Franco Cecchi, a Joan Mata Alvarez, b Pietro G. Traverso, a Franco Medici c& Guido Fazzini a

"Universit~ di Venezia, Dipartimento Scienze Ambientali, Calle Larga S Marta 2137, 1-30123 Venezia, Italy

bUniversitat de Barcelona, Departiment d'Enginyeria Quimica i Metallurgia, Mati i Franques 1/6pit, 08028 Barcelona, Spain

' Universit~ de L'Aquila, Dipartimento di Chimica Ingegneria Chimica e Materiali, Monteluco, 1-67100 L'Aquila, Italy

(Received 19 January 1989; revised version received 15 June 1989; accepted 17 August 1989)

ABSTRA CT

The kinetic models proposed by Monod, Chen and Hashimoto and Singh as well as those of a first order and diffusional type have been tested for fit as mathematical description~ to describe substrate utilization during anaerobic digestion of the organic fraction of source sorted municipal solid waste. A new model, described as step diffusional, is proposed and the results obtained with it are compared with those obtained using previ- ously published models. The new model is found to show a betterfit to the experimental result than those obtained with other models. The new model takes into account simple qualitative and quantitative chemical characteristics of the substrate to be digested. Although this new model is more complex than some others since it involves four kinetic constants, conceptually it is simple enough to find practical applications.

Key words: anaerobic digestion, municipal solid waste, kinetic models, degradation, organic fraction, mesophilic digestion.

N O T A T I O N

4a Kinetic constant represent ing the proport ional i ty constant be tween degradat ion rate and time for the methanogenic step (g C / m 3 per min 2)

79 Biomass 0144-4565/90/S03.50 - © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

80 17. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

4b

4c

GP HRT k

K

LF MSW K/ OF OLR P S Se

Si S. t UO

UI U2 V V,, Y Ycalc Ye×p Z

Kinetic constant representing the proportionality constant between degradation rate and time for the acidogenic step (g C/m 3 per min 2) Kinetic constant representing the proportionality constant between degradation rate and time for the hydrolytic step (g C/m 3 per min 2) Gas production Hydraulic retention time (days) Kinetic constant (day -~, first order model; (g C/m3) °5, diffusional model; m3/g VSS per day, Monod model) Chen and Hashimoto, kinetic constant (dimensionless) Saturation constant (g C/m 3) Lack of fit Municipal Solid Waste Feeding times per day Organic fraction Organic loading rate (kg TVS/m 3 per day) Times between one feed and the subsequent one (min) Substrate concentration in digester (g C/m 3) Substrate concentration in digester just before feeding (gC/m 3) Substrate concentration in digester after feeding (g C/m 3) Substrate concentration (g C/m 3) Time (day) Maximum degradation rate for methanogenesis (g C/m 3 . min) Maximum degradation rate for acidogenesis (g C/m 3 . min) Maximum degradation rate for hydrolysis (g C/m 3 . min) Digester volume (m 3 ) Volume fed to digester per time (m 3) Yield coefficient (g VSS/g C) Estimated degradation rate (g C/min) Experimental degradation rate (g C/min) Constant relating gas production at different temperatures (dimensionless)

#

]/k

m

Specific microorganism growth rate (day -1 ) Kinetic constant used in this study. It is equal to # m X / Y (g C/m 3 per day) Maximum specific microorganism growth rate (day- 1)

Anaerobic degradation of municipal solid waste 81

1 INTRODUCTION

Anaerobic digestion of the organic fraction (OF) of municipal solid waste (MSW) is a process which has received increased attention during the last few years. 1,2 In previous papers the potential of anaerobic digestion of OFMSW was assessed, using MSW from the north-east region of Italy. 3'4 The results suggested that the viability of such projects is increased where the organic content of the wastes is optimized by collecting the waste from specific sites. The potential of anaerobic digestion of OFMSW also increases in systems in which co-digestion of organic refuse and sewage sludge is carried out. 4 Conversion of the OF of MSW to methane provides some energy and can have a beneficial effect on the environment. The characteristics of the solid digestate are such that it can be disposed of on agricultural land, acting as a soil conditioner. 5

The aim of the present work was to obtain kinetic information relating to substrate degradation in order to facilitate the design of fermenters to digest semi-solid wastes. In order to apply any kinetic model, two factors must be considered. The model must be complex enough to be realistic, but simple enough that fitted parameters can be easily interpreted and used for design purposes as well as being consistent with the observed experimental behaviour. However this is not an easy task. Due to the complexity of the biological processes associated with anaerobic digestion it is difficult to develop a detailed mathematical model reflect- ing the biological complexity. Hence, most models described in the liter- ature are simplifications. Here several kinetic models, which have been used to describe anaerobic digestion, are applied to the digestion of OFMSW in a semicontinuous system. The paper also proposes a new model which takes into account bo th the composition of the substrate and the characteristics of the various bacterial populations which catalyse the various partial processes leading to the overall degradation of the OFMSW.

2 MATERIALS AND METHODS

2.1 Experimental device

The experiments were carried out using a 3 m 3 working volume com- pletely stirred tank reactor maintained at the optimal mesophilic tem-

82 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

Represent a t Ivel

Treviaoeacity J I r-~ r s ° ~ e S ° r ' e d l ' r 0 F M SW I L ~ I , t

[Shredder ~--~ [~

Fig. 1.

M o i s t u r e ] A dJ ustementJ

F e e d s t o c k ,, Y

D i g e s t e r

A n a l y s e s

Gas Meter

~ E , flu-~nt S to~ck ~-~

Overall process and pilot plant flow-sheet.

perature range (35 _+ 2°C). A process flow-sheet of the pilot plant is shown in Fig. 1. The digester was fed 2-6 times a day (depending on the desired organic loading rate (OLR)), with 6% total solids (TS) substrate. The pressure of the gas was 150-180 mm water. Gas production was measured using a wet gas meter. The mixing device was an armed anchor stirrer rotating at 70 rpm. Other details of the pilot plant, feed composi- tion and process performance have been reported elsewhere)

2.2 Substrate

The digester was loaded with source separated OFMSW collected daily from a representative area in Treviso city. The waste was shredded and diluted before being stored in the feedstock tank. Substrate composition is shown in Table 1, which gives results of a detailed analysis of the OFMSW used in this work.

2.3 Analytical methods

Volatile fatty acids (VFA) were monitored using the gas chromato- graphic methods reported in Refs 6 and 7. Analysis of total alkalinity (pH end point 3"8), CO2 (Orsat method), pH and other parameters was as carried out using Standard Methods. 8 A complete description of the parameters measured can be found in Ref. 3.

3 RESULTS

The average values of the various parameters measured at four differing hydraulic retention times (HRT) are shown in Table 2, together with details of biogas production percentage composition. From the results of analysis of numerous samples taken along the axis of the reactor and from the effluent, it was possible to establish that the fluctuations in these

Anaerobic degradation of municipal solid waste 83

TABLE I Mean Values Obtained from Analysis of the Organic Fraction of Municipal Solid Waste Fed as Substrate to the Digester Used in the

Experiments Reported Here

TS 63"4 g/kg TVS 89"9 % TS SVS 28'6 % TVS TC 48"0 % TS SC 30"1%TC TCOD 91'2 % g/kg SCOD 30'0 % TCOD N 3"2 % TS P 0"4 % TS

Gas chromatograph analysis Methanol 31 g C/m 3 Ethanol 919 g C/m 3 Acetic acid 1 456 g C/m 3 Propionic acid 139 g C/m 3 Butyric acid 43 g C/m 3 /-Butyric acid 29 g C/m 3 Valeric acid 4.3 g C/m 3 i-Valeric acid 1.3 g C/m 3

TABLE 2 Characteristics of the Effluent from the Digester of Volume 3 m s

HR T (days)

25"0 17.8 13.6 8.9

OLR, kg TVS/m 3 per day 2.1 3.2 4.2 6.9 n (times/day) 2 3 4 6

TVS 16"3 18.2 18"8 22.7 TCOD 24.0 27.6 28-2 33.3 TC 11"3 12-6 12.0 14-8 SVS 1.2 1.6 1"5 2.1 SCOD 0"9 1.2 1.2 - - SC 0.8 0.8 0'9 2.2 Gas production (m3/day) 1.33 2.00 2.67 3.62 (% CH4) 63.0 61.5 62-5 56-0

Unless otherwise indicated, values are expressed in g/litre.

84 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

parameters were small presenting an acceptable range of experimental error. There was a close relationship between biogas production and organic loading rate. The possibility of using these parameters in digester control is discussed in Ref. 9. The methane content of the biogas fell at OLR 6.9 kg TVS/m 3 per day indicating that under these conditions the system was near its limits. The observed process efficiency was high, as previously reported? Previous results, 3 as well gts the results using substrate similar to that described in Table 1 together with the results shown in Table 2, indicate that the soluble fraction of the feed is digested, to a large extent, during the first hour after feeding and is almost completely degraded after 2-3 h in the digester. The contribution of the more easily hydrolysed fraction becomes important during the 5th and 6th hour, and thereafter the process is regulated by the rate of solubilization of the fractions which decompose more slowly. These differences in substrate utilization rate during the period between feeds constitute the basis for the proposed kinetic model developed below.

4 KINETIC STUDY

In a semicontinuous stirred tank digester, the profile of biogas produc- tion is a function of the feeding pattern. If substrate is fed at intervals of a given length p (min), the rate of biogas production will vary as shown in Fig. 2, reflecting changes in the organic matter concentration inside the digester. When a volume V 0 of fresh substrate is fed at a concentration S0, the same volume is withdrawn, with a concentration Se. At this time the substrate concentration in the digester can be calculated from the expression:

s,, v,, + se( v- v,,) S i- (1)

V

where Si is the substrate concentration after feeding the digester of working volume V. "~ The mean substrate flow rate is Vo/p (m3/min) and, as a consequence, the mean residence time will be:

HRT=pV/Vo (2)

During the period of time between one feed and the next, substrate concentration S in digester changes in accordance with the kinetics of the fermentation process:

dS/dt =S(k, t) (3)

Anaerobic degradation of municipal solid waste 8 5

e ~

Fig. 2. Profiles of biogas

i I r i i i I L i I

TIME

production in the semicontinuous or intermittently fed digester.

where k represents a vector containing the kinetic constants and t, the time. Limit conditions are, at t = O, S = S i and at t = 1/p, S = S e.

Several common kinetic models can be applied to mathematically describe the system. Some of these are considered here. These are: (a) first order; (b) Monod; (c) diffusional; (d) Chen and Hashimoto (Contois); (e) Singh and (f) step-diffusional proposed by the authors. The results are presented in the following sections.

4.1 First order model

This model considers the microorganisms as 'catalysts' and represents an overall mass transfer kinetic model for a 'catalysed' reaction. Although this is not a sophisticated model, it can provide a single and useful kinetic constant that will have applicability when dealing with complex systems, such as that involved in the fermentation of refuse. ~H4 The basic equation is:

d S /d t = - k S (4)

where k is the first order kinetic constant (time- ~).

86 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

4.2 Monod model

This model is most rigorously applicable to soluble substrates under conditions where the concentration of microorganisms involved can be evaluated. Lawrence and McCarty presented the basic equation: 15

dS k S X - ( 5 )

dt K ~ + S

which is normally used in combination with the growth rate equation. Lawrence extended the application of Monod kinetics to municipal sewage sludge, t6 This more complex waste made calculations somewhat more difficult, but, assuming methanogenesis to be the limiting step, the estimated constants gave good results. The Monod model has been applied to several wastes as has been pointed out by Chin ~7 and has been the basis of most anaerobic digestion models.

In the present case this type of model has been considered since the system is semicontinuous and hence the microorganism concentration may be considered constant. The time between one feed and the next one (6-12 h) is in fact insignificant when compared to the hydraulic and solids retention times which vary between 9 and 25 days.

4.3 Diffusional model

The combination of the Monod rate equation together with mass transfer limitation equations results in the following overall rate equation: ~8

dS /dt = - kS °5 (6)

where k is an apparent kinetic constant, ((g C/m3)°5).

4.4 Chen and Hashimoto model

The Chen and Hashimoto modeP 9 is a modification of that of Contois, adapted to the anaerobic digestion processes. 2° The Contois model is an expanded form of the Monod model which takes into account the fact that mass transfer limitations may cause the specific growth rate to vary with population density. Hence, the Contois model can be considered as a specialized case of that of Monod. The Contois model is normally applied directly to describe gas generation in terms of methane produced per kg of VS added, although the basic equation is as follows:

S/So (7) I~ =Pro K +(1 - K ) S / S o

Anaerobic degradation of municipal solid waste 87

where/~ is the specific growth rate ( t ime- 1). If the death and decay of microorganisms is neglected then microorganism balance can be described as:

d X /dt = /uX (8)

further, taking into account a yield coefficient ( Y ) gives:

dX/d t = Y d S / d t (9)

Finally combining these equations gives the following expression:

dS S/So - - = (10) dt K+(1 - K ) S / S o

where /~k is ItmX/Y, which remains constant so long as X remains constant. As mentioned previously, this approximates to the case for a semicontinuously operated digester. This hypothesis has been tested by the authors with data from publications including work on sewage sludge of O'Rourke, 2~ municipal refuse of Pfeffer ~1 and animal manure data of several authors, including their own.19

4.5 Singh model

A modified version of the first order kinetic model was proposed by Singh et aL :22

dS kS dt 1 +t (11)

The model was shown to be applicable to the anaerobic digestion of cattle waste.

4.6 Application of various models to the anaerobic digestion of OFMSW

All the models which have been described above were applied to data obtained from the digestion of OFMSW as described in the methods section with substrate degradation rates estimated from the values obtained for gas production. The rates of production of biogas were monitored after feeding, in all the conditions tested. The primary data was corrected for pressure and water content, and reduced to a standard temperature basis using the following equations: 23

GP at T - Z IT-351 (12) GP at 35

88 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

where Z is a constant and GP represents the gas production at a given temperature. A mean value of 1.051 for Z was determined from con- sideration of all the representative values. To facilitate the manipulation of data, biogas production rate is referred to as Total Carbon (TC)/min and concentrations are expressed as TC. The experimental points are shown in Fig. 3.

4 "O

¢.~ v

6

3

°% + O O A

o +++oCk +o+

A A Z~

++[3 +

O O O 0 ~ 0 +

[ ~ + ÷ + OO .4.

[] D

D + + []

D

+ +

D O [] D

' 2"00 ' ' ' 400 600 TIME (MIN)

Fig. 3. Variations in rate of biogas production during anaerobic digestion of OFMSW during the period between one feed and the next. The various symbols correspond to

data obtained at different organic loading rates.

Each set of data, corresponding to a given organic loading rate (OLR) has been fitted to the various kinetic models. Another set of data, combining all the data obtained, was also considered. These sets of data, describing the TC consumption rate and TC concentration, represent mean values, having been obtained by averaging a significant amount of experimental data.

Simple linearization techniques were applied, to fit the rate data. Fitted kinetics constants are shown in Table 3, which also indicates the lack of fit (LF) computed as:

L F = ( Yexp - Ycalc) 2 ( 1 3 )

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90 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

where Yexp represents the experimental degradation rate and Ycalc the estimated one obtained from the corresponding model equation.

Mean experimental points and fitted curves, obtained through iterative calculations, for all the studied models are shown in Fig. 4 for TC concentration profiles and in Fig. 5 for degradation rate profiles. The apparently better fit observed in Fig. 4 is a result of the fact that the relative variation of TC concentration is much lower than that of the biogas production rate.

As can be seen from the values of LF (Table 3), the best results were obtained with the Chen and Hashimoto model, followed by the Monod one. The fit to the first order model was not very good, which is somehow surprising, as it has been applied to this type of waste with fairly good results. ~- ~4 The diffusional model also showed a fairly poor fit whilst the Singh model was definitely not applicable. However, given its empirical nature, this result is not surprising.

Fig. 4.

I / I I I

2 O0 400 600

TIME (MIN)

Changes in the concentration of total carbon (TC) between one feed of

600

400

l.--

i 200 -

0 0

OFMSW and the next in a stirred digester. Points correspond to data obtained at different organic loading rates expressed as kg TVS per cubic meter digester volume per day of 2.1, 3-2, 4.2 and 6'9. Solid lines correspond to the fitted curves for the various models studied, as follows: 1, first order; 2, diffusional; 3, Monod; 4, Chen and

Hashimoto; 5, Singh.

Anaerobic degradation of municipal solid waste 91

When the values of the constants obtained are examined in more detail it can be seen that in some cases, for instance with the data f rom OLR 6-9 kgTVS/m 3 per day and that f rom the overall set, negative values are obtained for the Monod constants. This is possible as was pointed out by Roques et aL 24 These authors showed that the M o n o d model gives a saturation constant K s which is not a true constant but depends on the sludge age and the total amount of biomass contained in the reactor. Such factors can lead to anomalies during the estimation of Monod constants.

Compar ison between the constants for which a positive value were obtained here and those published in the literature, tS,t7,25,26 requires a knowledge of the active biomass concentrat ion inside the digester. This value was estimated in a previous paper, 27 and on this basis a mean value of 5.5 kgTVS/m 3 is taken here. This value is lower than the concentra- tion of volatile suspended solids in the mixed liquor (MLVSS), which can be estimated from the data shown in Table 2 to be around 1 6 kg/m 3. This difference results from the fact that only a fraction of the MLVSS is in fact active biomass. 28 The kinetic constants derived from the present work for the Monod model are compared in Table 4, which shows a reasonable agreement in general.

Table 4 also compares the values of the kinetic constants calculated from the Chen and Hashimoto model in the present work with those from the literature. For purposes of comparison /~k has to be trans- formed into/u m by multiplying/~k by Y/X. A value of Y=0.1 has been selected, on the basis of work carried out previously (Traverso & Cecchi). 27 Again, an estimated microorganism concentrat ion of X = 5-5 kgTVS/m 3 has been used. As shown in Table 4, the estimated maximum

TABLE 4 Comparison of Published Values of Various Kinetic Constants with those Obtained in the Present Study Assuming a Microorganism Concentration of 5-5 kgTVS/m 3 and a

Yield Coefficient of 0.1 kg VSS/kg C

Monod

OLR 4.2 3.2 2.1 Agardy z5 Lawrence 15 Chin 17 Chiu 26 k (g/g TVS per day) 3"9 5.5 11.4 1.1 4.7 3"1 13.8 K s(kg/m 3) 14.8 26-1 53.3 13.1 0"9 9-6 16.6

Chen and Hashimoto OLR 6"9 4-2 3"2 2'1 O'Rourke 2~ Pfeffer II kt,n (day- ~) 0"05 0-06 0.06 0'03 0"33 0"33 K 3.2 4.9 3-7 1.7 0.26 0"30

92 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

specific growth rate in the present case is lower than those reported from other work. Nevertheless, since ktm is numerically equal to the reciprocal of the minimum retention time, a better estimation of this parameter can be obtained. The estimated value of 16 days is, in fact, in agreement with the optimum retention time found (HRT = SRT = 14-15 days) for this digestion process? As far as the other kinetic constant (K) is concerned, this increases with the influent VS concentration. ~9 The concentration of biodegradable substrate used in this study is high enough to justify the larger value of K obtained in the present study. The first order kinetic constant estimated as k is around 3 day- ~. This value is larger than those reported by Pfeffer II (c. 0.15 day -l for MSW) or Gaddy L4 (0.45 day -I for corn stover). The higher value found here probably reflects the higher biodegradability of the OFMSW used as substrate. The first order model shows a rather poor fit since it does not represent the biogas production rate over the entire time period. Pfeffer t~ has already reported observations which show two distinct phases when the substrate concentration was plotted as a function of detention time. The biogas production profiles shown in Fig. 3, indicate that the rate of substrate varies, decreasing with time after feeding. This fact, together with further information as discussed in Section 3, led us to propose a new model to describe the anaerobic digestion process of complex mixed substrates such as OFMSW.

1,5.- ~

1.o ~ ' ~ , ~ , , , , ~ " ~,,

0.5 2

13 D ~+ 13 Q [] I

5 :-: [ ] m Z] [ ]

' 2 0 ( ) ' ' ' 400 600

TIME (MIN)

Fig. 5. Changes in the degradation rate of OFMSW between one feed and the next in a digester fed at different rates. OLRs and fitted curves are as detailed in Fig. 4.

Anaerobic degradation of municipal solid waste 93

5 PROPOSED STEP DIFFUSIONAL M O D E L

The approach adopted in construction of the step diffusional model is based on three particular considerations as follows:

(a) The observed changes in gas production rate between one feed and the next (see Fig. 3).

(b) The nature and chemical characteristics of compounds present in the OFMSW, including the extent to which they are removed due to biological degradation. 29' 3o

(c) The metabolic characteristics of the different bacterial groups responsible for the degradation of the various compounds present in the feed (as discussed in more detail below), taking into account the complex scheme of carbon flow and interactions in the methanogenic syntrophic association. 3t

As far as soluble compounds are concerned on the basis of data in Tables 1 and 2, and previous results as reported in Ref. 3 it is assumed that almost 100% of the organic matter is digested. In contrast it is assumed that insoluble compounds in the OFMSW can be divided into three groups: 29 cellulose (32% TVS basis); hemicellulose (15% TVS basis) and lignin (15% TVS basis). As suggested by Ghosh, 3° these compounds, in mesophilic conditions, are removed by up to 32, 86 and 0% respectively. A complete materials balance is shown in Table 5. This is presented on the basis of carbon fed to digester and takes into account the analytical results shown in Table 1.

The degradation rate of each group of compounds is represented by a particular single straight line, which is reflected in the pattern of the

TABLE 5 Values for the Organic Matter Concentrations of the Main Groups of Compounds Found in the Digester after Feeding

with OFMSW

Acetate and the compounds (A) directly utilized by methanogenic bacteria (AcH, MeOH)

VFA> = C3 and EtOH (B)

Free organic matter (C)

Complex organic matter (D)

Non-biodegradable organic matter (E)

Total organic matter fed

28gC/m 3

21gC/m 3

124g C/m 3

255 g C/m 3

145 g C/m 3

573 g C/m 3

9 4 F . Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

experimental points shown in Fig. 3. These lines can be described by the following equations:

Compounds of group A:

dS/dt =(v 2 - 4a(S o - S)) 1/2 (14)

or,

or, integrating,

dS/dt =v o - 4at /2 (15)

S=So-v(,t +4at2/4 (16)

where S 0 represents the overall organic matter content of the substrate and v0 is the degradation rate at this point.

Compounds of group B:

The degradation of the rest of the soluble fraction may be described by taking a similar approach:

dS/dt =(v~ - 4b(S l - S)) '/2 (17)

or,

dS / d t = v 1 - 4b( t - t,)/2 (18) or, integrating,

S = S, - v , ( t - tf) + 4 b ( t - q)2/4 (19)

the last three equations apply for tl > t > t 2 where S 1 represents the resi- dual organic matter content of the substrate, once the easily degradable compounds (acetate, methanol, etc.) have been removed. At this point the degradation rate is v I which is indicated by an inflexion in the plot of rate against time at t = t I .

Compounds of group C:

The degradation of the rest of the organic matter, which is dependent on the hydrolysis of the polymeric components, can again be described by

approach. However, in this case the line has a

dS/dt =(v 2 - 4c(S 2 - - 8)) 1/2 (20)

following a similar different slope:

or,

dS /dt = v 2 - 4c( t - t2)/2 (21)

Anaerobic degradation of municipal solid waste 95

or, integrating,

S=S2-v2(t-t2) +4c(t-t2)2/4 (22)

These equations (20)-(22) apply for t2 < t < t 3 where S 2 represents the residual organic matter content of the substrate, once the soluble degradable compounds have been removed. At this point the degradation rate is v 2 producing an inflexion in the rate/time curve at t = t 2. At the end of this period, the degradation rate (denoted as v3) corresponds to the hydrolysis of compounds of group D, and remains practically constant as was reported previously. 32

6 DISCUSSION OF THE M O D E L

Once the model was established the biogas production data from the present experiments were treated in a similar way to the models discussed above and the various constants determined using a least squares method to obtain the fit. The results are presented in Table 6 and in Figs 6 and 7. On the basis of examination of the overall profile showing changes in the TC degradation rate several interpretations can be suggested. First of all, the value of v 0 can be considered as an estimation of the maximum acetate degradation rate. When the reactor is operated near its limits, at OLR = 6.9 kg TVS/m 3 per day, a plateau is formed (see the points indicated by a triangle in Fig. 3). This indicates that the microorganisms present in the reactor are unable to digest acetate or similar easily degradable compounds at a higher rate. Hence, this plateau is also an indication that v~ represents the maximum value for the

T A B L E 6 F i t t ed Kinet ic C o n s t a n t s O b t a i n e d for the Step Diffus ional Mode l , Inc lud ing Es t ima tes

of the Lack of F i t (LF)

OLR: 6"9 4"2 3.2 2"1 Global No. of points: 43 35 41 37 139

4 a 0 . 0 1 6 4 0 .0402 0 .01441 0 . 0 0 8 6 4 9 0 . 0 1 0 0 0 0 4 b 0 .00073 0 .0034 0"00310 0 - 0 0 3 9 5 7 0 . 0 0 3 6 2 0 4 c . . . . 0 . 0 0 1 0 5 0 0 . 0 0 5 0 4 9 LF 0 .1020 0 .2215 0-2155 0 . 3 3 8 6 9 9-778 v o 1.65 1.69 1-62 1.34 1.43 v I 1.09 1.16 1.10 1-09 0"98 v 2 - - - - - - 0.36 0 .40

96 F. Cecchi, J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

600

400

= 200

Fig. 6.

\

¢' + 0

o . ' - " , ~ + + ++ o<> Oo o oO []

i i i

20'0 460 600 TIME (MIN)

As Fig. 4, showing the goodness of fit of the proposed step diffusional model.

@

Fig. 7.

1,5.~

oo ~o~+ +

0.5 ~+ "~"~t+ ~ ++ + 0 O + 4" °

D n 0 121 0

i i i

20; 6o0 TIME (MIN)

As Fig. 5, showing the goodness of fit of the proposed step diffusional model.

Anaerobic degradation of municipal solid waste 97

acetogenesis step. Furthermore, a closer examination of the results from the individual experiments performed with a more concentrated feed, suggests that a plateau may also exist around v 2. This could indicate that v 2 is an estimate of the maximum value of acidogenesis. Finally, long- term experiments (profiles extending to 60 h after feeding) indicate clearly that v 3 represents a limit for the fermentation process. 32 No experimental evidence is available to positively connect v0 with the maximum rate of degradation of compounds such as acetate and methanol. However, from similar reasoning as used above for the other classes of metabolites, it can be suggested as a first approximation value.

The model proposed in eqns (14)-(22) has a strong diffusional character whilst the digester contains a considerable amount of non- soluble solids, which can act as a support for microorganisms, especially the methanogenic flora. Hence, diffusion of acetate seems to be the limit- ing step, represented by the slope 4a. Subsequent steps might be regulated by the diffusion of extracellular enzymes which must be excreted in order to hydrolyse the non-soluble compounds. It can be assumed that the amount of solids present in the digester give it some of the charac- teristics of a carrier digester. As a consequence, it is not surprising that diffusion can play an important role in modifying the kinetic results. Values of constants 4a, 4b and 4c are of the same order of magnitude as the constant k of the diffusional model tested here as shown in Table 3. The observed differences are due to the variations between the constants for the different steps of the degradation process, which also probably account for the lack of fit observed for the single diffusional step model.

The values obtained for the maximum degradation rate of the dif- ferent steps v0, vt, v 2 and v3 are shown in Fig. 8. The corresponding slopes 4a, 4b and 4c give rise to the values of t~ - t 3. Three zones, desig- nated as ZI , Z2 and Z3 can be represented where Z1 corresponds to biogas production controlled by the methanogenic-acetogenic step. The area of this zone gives an estimation of the amount of compounds which may be directly convertible to methane (compound of group A). Z2 corresponds to the acidogenic-acetogenic step control and its area is an estimation of the compounds listed under B and C in Table 5, (that is free organic matter, sugars and higher VFA, etc.). Finally, Z3 represents an estimate of the non-soluble compounds (group D), the solubilization of which represents a limiting step in biogas production. As shown in Table 7, analytical values and the estimates based on these kinetic relationships (Fig. 8) are comparable.

It has been assumed that a first approximation value of the maximum rate for the methanogenesis step is given by v 0 . In fact, if this is correlated with the active biomass concentration in the reactor (5"5 kgTVS/m3), a

98 F. Cecchi, J. M. Alvarez, P. G. Traverso, 17. Medici, G. Fazzini

,Vo;r0

L z 4a

~? V 1 ; T1 1.0

-~ 4b

0,5

Z3

~oo ' ~6o ' 600

TIRE (MtN)

Fig. 8. Illustration of the various components of the kinetic model fitted to a graphical representation of the change in degradation rate as a function of time between feeds for

the anaerobic digestion of OFMSW.

v2;r2 vs;r3

TABLE 7 A Comparison between the Values for the Concentrations of the Various Groups of Compounds Shown in Table 5 (expressed as g C/m 3) Obtained by Analysis with those

Estimated from the Kinetic Relationships Expressed by the Step Diffusional Model

Group Analytical value Kinetic estimate Zone

A 28 19 Z1 B + C 145 137 Z2 D 255 265 Z3

The zones (Z1-Z3) correspond to those shown in Fig. 9.

specific acetic removal rate can be estimated at around 0-4 g C/g VSS per day. This is slightly smaller than other reported values, as shown in Table 8. This table also summarizes some reported maximum removal rates for glucose and sucrose. 33-36 These compounds are included in the second group (B), hence it would be expected that v~ should be close to these values, which is in fact the case. Finally, a comparison is also made in respect of the hydrolysis rate. However, here it is found that the results obtained in this work are significantly lower than that published previ- ously. 36

A n a e r o b i c degrada t i on o f m u n i c i p a l so l id was te 99

TABLE 8 Comparison of the Maximum Utilization Values for Different Substrates Obtained from

this Study (v0, v I and v2) with Values Published by Various Authors as Indicated

Acetic acid 1.4 g/g VSS per day Kennedy et al. 33 4-7 g/g VSS per day Lawrence and McCarty ~5 2"4-4-8 g/g VSS per day van den Berg 34 0-40 This study

Glucose 0"75 g/g VSS per day Anderson et aL 35

Sucrose 0"93 g/g VSS per day Kennedy et al. 33

0-4-0.8 g/g VSS per day Switzenbaum and Jewel136

0"26 g/g VSS per day This study

Cellulose 2.3 g/g VSS per day Golueke 37 0-10 g/g VSS per day This study

The values are corrected for variations in units and normalized for a microorganism concentration of 5"5 gTVS/litre.

In compar i son with the other models , the one p roposed here fits the experimental data bet ter because of the step approach adopted . Al though this approach results in the need to use more constants the mode l is still simple enough for practical purposes . In fact, the com- plexity of the mode l reflects the complexity of substrate, so that if it is applied, for instance, to a substrate containing only cellulosic material, only one step has to be considered. In such a case the maximal substrate utilization may not always be achieved for the soluble compounds . T he true mode l constants are 4a, 4 b and 4c, that is the slopes of the degrada- tion rate versus time. The values of v0, vl and u 2 will depend on the substrate composi t ion. W h e n the reactor was fed with pr imary sewage sludge, 4 the slopes reflecting the obse rved rates of biogas product ion were very close to those observed in this study, although the values of the actual rates of degradat ion varied as shown in Table 9.

TABLE 9 Comparison of the Kinetic Constants Calculated for the Step Diffusional Model using Data from this Study with Data Obtained from the Digestion of Primary Sewage Sludge

4a 4b 4c 13 o lfl i u 2

This study 0.010 0"003 0.005 1.34 0.98 0.40 Ref. 4 0.012 0.006 0.003 -- 0.67 0.21

100 F. CecchL J. M. Alvarez, P. G. Traverso, F. Medici, G. Fazzini

7 CONCLUSIONS

Of the previously published models tested in this work using OFMSW digested in a 3 m 3 semicontinuous stirred tank digester, Chen and Hashimoto's model as well as the classical Monod model gave the best fit. The first order model showed a poor fit, a surprising result since it was proposed for high solids systems. In order to get a better representa- tion of the degradation process for complex wastes, a new model which took into account the different steps of the anaerobic process was investigated. The model emphasizes the characteristics of diffusional limitations in the process likely to take place when treating wastes with a high content of suspended solids. The values of the kinetic constants obtained from this model were of the same order of magnitude as reported values, when the mass transfer limitations are taken into account. The model presented here gives somewhat better results than the other models investigated in terms of a better fit resulting from a new approach taking into account substrate composition. Although it is more complex than some other models, conceptually it is simple enough to be used in practice, showing greater flexibility, enabling it to be adopted to describe a larger range of substrates. However, more experimental work needs to be done, particularly with different types of MSW (e.g. mechanical classified), in order to fully validate the model under a wider range of conditions and substrates.

A C K N O W L E D G E M E N T S

The authors thank J. Coombs for his useful suggestions, the Instituto Trevigiano di Ricerca Scientifica of Treviso City for its interest and support, and acknowledge Nato grant no. 178/87 which has facilitated communication between the authors.

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