Bioresource Technology 94 (2004) 6981

Modeling solid waste decomposition

a,*
V.A. Vavilin , L.Ya. Lokshina a, J.P.Y. Jokela b, J.A. Rintala b

a
Water Problems Institute, Russian Academy of Sciences, Gubkina Street, bd. 3, Moscow 119991, Russian Federation
b
Department of Biological and Environmental Science, University of Jyvaskyla, P.O. Box 35, FIN-40351 Jyvaskyla, Finland
Received 6 July 2003; received in revised form 30 September 2003; accepted 28 October 2003

Abstract
The hydrolysis rate coecients of sorted municipal waste were evaluated from the biochemical methane potential tests using non-
linear regression. A distributed mathematical model of anaerobic digestion of rich (food) and lean (non-food) solid wastes with
greatly dierent rates of polymer hydrolysis/acidogenesis was developed to describe the balance between the rates of hydrolysis/
acidogenesis and methanogenesis. The model was calibrated using previously published experimental data [Biores. Technol. 52
(1995) 245] obtained upon various initial food waste loadings. Simulations of one- and two-stage digestion systems were carried out.
The results showed that initial spatial separation of food waste and inoculum enhances methane production and waste degradation
in a one-stage solid-bed digester at high waste loading. A negative eect of vigorously mixing at high waste loading reported in some
papers was discussed. It was hypothesized that the initiation methanogenic centers developing in time and expanding in space under
minimal mixing conditions might be a key factor for ecient anaerobic conversion of solid waste into methane.

2003 Elsevier Ltd. All rights reserved.

Keywords: Solids biodegradation; Hydrolysis kinetics; Food waste; One- and two-stage anaerobic digestion; Initiation methanogenic centers;
Distributed mathematical model

1. Introduction BH X
qH q
^m 1
K B BH K X X
A high concentration of food waste (FW) may pres-
where X volatile solid waste concentration, BH con-
ent a problem for eective waste biodegradation in
centration of hydrolytic (acidogenic) biomass, q ^m
landlls and bioreactors because of excessive volatile
maximum hydrolysis rate; KB equilibrium constant
fatty acids (VFAs) formation in the absence of active
equal to the ratio between the adsorption and desorp-
methanogenic populations (Barlaz et al., 1990). A sharp
tion rate constants; KX half-saturation coecient for
increase in VFAs and related decrease in pH is the major
the volatile solid waste concentration X .
factor limiting the onset of methanogenesis. In such
According to the model, microorganisms attached to
conditions, methanogenic bacteria require sites, which
a particle produce enzymes in the vicinity of this particle
will be protected from rapid acidogenesis. For that
beneting from soluble products released by the enzy-
purpose, an addition of lean solid waste will be favor-
matic reaction. A hydrolysis rate constant q ^m is re-
able for methanogenic microorganisms growth (Martin
ciprocal to the initial diameter of waste particles. It was
et al., 1997). In the laboratory reactors without leachate
shown (Vavilin et al., 1996) that the phenomenological
recirculation and pH adjustment it is quite dicult to
Contois model that uses a single parameter to represent
obtain reproducible signicant biogas yields (Martin,
saturation of both substrate and biomass is as good at
2001).
tting the data as the surface-related model
The surface-related hydrolysis kinetics model that
takes into account colonization of the waste particles by X =BH
qH qmH BH 2
hydrolytic bacteria has been developed (Vavilin et al., b X X =BH
K
1996).
where qmH maximum specic hydrolysis rate; K bX
half-saturation coecient for the ratio X =BH . The sur-
*
Corresponding author. Tel.: +7-95-135-4006; fax: +7-95-135-5415. face-related (1) and Contois (2) models have the same
E-mail address: vavilin@aqua.laser.ru (V.A. Vavilin). limiting cases:

0960-8524/$ - see front matter
2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.biortech.2003.10.034
70 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981

Nomenclature

A mass fraction of methane in biogas n number of experimental data

a, b, c, d combined parameters P methane volume released
aj parameter in initial food waste and VFA P0 initial methane volume
concentration distributions p number of parameters
B methanogenic biomass concentration r radial coordinate in cylindrical reactor
BH hydrolytic (acidogenic) biomass concentra- RH rate of VFA production by hydrolysis/acido-
tion genesis
bi parameter in initial non-food waste and bio- RM rate of VFA utilization by methanogenesis
mass concentration distributions S total volatile fatty acids (VFA) concentration
DB diusion coecient for biomass T time
DS diusion coecient for VFA W1 food waste (FW) concentration
dP =dT methane production rate W2 non-food waste concentration
FPE nal prediction-error criterion W0 initial waste concentration
f1 S, f2 S VFA inhibition functions for hydrolysis X volatile solid waste concentration
gS VFA inhibition function for methanogenesis Z vertical coordinate
Jh incoming VFA ow through the boundaries Y methanogenic biomass yield coecient
KB ratio between the adsorption and desorption YH hydrolytic (acidogenic) biomass yield coe-
rate constants cient
Kf 1 , Kf 2 inhibition constant of hydrolysis a conversion coecient of waste into methane
Kg inhibition constant of methanogenesis ci distribution coecients
KS half-saturation constant for VFA utilization qm maximum specic rate of VFA utilization
KX half-saturation coecient for the volatile so- q
^m maximum hydrolysis rate
lid waste concentration qmH maximum specic hydrolysis rate
bX
K half-saturation coecient for the ratio X =BH rZ initial food waste and VFA concentration
k1 , k2 rst-order hydrolysis rate constants distributions
kd specic biomass decay coecient v 1 , v2 stoichiometric coecients
L reactor length (height) wZ initial non-food waste and biomass concen-
mf 1 , mf 2 hydrolysis inhibition degree indexes tration distributions
mg methanogenesis inhibition degree index

(i) exponential biomass growth (high value of the with leachate recirculation and pH adjustment, which
ratio of solid waste to biomass concentrations took into account the initial waste and biomass distri-
X =BH
K bX ) butions was developed to describe the balance between
qH  qmH BH 3 the rates of polymer hydrolysis/acidogenesis and meth-
bX ) anogenesis during the anaerobic conversion of organic
and (ii) rst-order kinetics (low value of X =BH  K
wastes in batch laboratory reactors (Vavilin et al.,
qmH
qH  X kX 4 2003a,b). This approach allows consideration of the
KbX bioreactor as an active or excitable medium that pro-
In the present work, the traditional rst-order and vokes concentration waves from some areas of metha-
Contois kinetics were used to describe the biochemical nogenic initiation to the total reactor volume. The
methane potential (BMP) tests for the dierent putres- model shows that mass-transfer-based acceleration of
cible fractions of municipal solid waste (PFMSW). methane production in the reactor is possible when the
The heterogeneous nature of the initial waste and intensity of volatile fatty acids (VFA) utilization in the
biomass distributions was taken into account in a two- methanogenic area is sucient for a complete digestion
particle model (Kalyuzhnyi et al., 2000; Veeken and of the incoming VFA. Otherwise, the initial methano-
Hamelers, 2000) based on the concept of acetogenesis genic area will be suppressed by increasing concentra-
and methanogenesis occurring in adjacent particles. tion of VFA.
However, this model based on ordinary dierential There are various methods used for the stabilization
equations could not describe non-synchronized pro- of PFMSW including the single and two-phase anaero-
cesses of waste conversion into biogas in the total di- bic digestion systems. In the single-phase system acid
gester volume. A distributed model of solid waste and methane-forming bacteria exist in the same bio-
anaerobic digestion in one-dimensional (1-D) bioreactor logical environment. By isolating the two key phases in
 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981 71

two separate reactors, a two-phase anaerobic digestion were operated at 37 C. FW was initially loaded in a
system was used to avert the imbalance between pro- solid bed at 20% TS (188 g VS/l). Experiments were
cesses of acidogenesis and methanogenesis. Lissens et al. performed at the dierent liquid ow rates.
(2001) compared the most common types of anaerobic
digesters for solid wastes. They concluded that batch 2.2. Simplied model of PFMSW conversion to methane
systems have the simplest design and are the least
expensive solid waste digesters. Two-stage systems are Assuming polymer hydrolysis is the rate-limiting step
more complex and more expensive systems; but these in methane production the simplied anaerobic diges-
systems are more stable. tion model of organic waste conversion to methane is
In the present work, the 1-D distributed model of written (Lokshina and Vavilin, 1999) as
anaerobic digestion of rich (FW) and lean (non-FW) dX
solid wastes with greatly dierent rates of hydrolysis/ qH X ; BH
dt
acidogenesis was developed and used for simulations of dBH dX
one- and two-stage anaerobic digestion systems. YH 5
dt dt
dP dX
a
dt dt
2. Methods where P methane volume released; qH X ; BH
specic rate of polymer hydrolysis; a conversion
2.1. Experimental coecient of waste into methane, YH hydrolytic (aci-
dogenic) biomass yield coecient. After integration
2.1.1. Grey waste assuming the Contois kinetics of hydrolysis (2), the
Jokela (2002) measured methane yield for grey waste following solution of the system (4) was obtained
(residual after source separation of PFMSW, metals, 0 1
paper, cardboard and glass). First, composition of the

1 B P  P0 C bX
K P  P0
grey waste was dened by a sorting test and the grey t B
ln 1 C  ln 1 
waste was sieved into undersized and oversized fractions YH qmH @ B0H A qmH aX0
a
produced at the waste management plant. The BMP YH
tests were done with the sorted components and with the 6
sieved fractions. Grey waste contained a high amount where X0 , B0H and P0 are the initial concentrations of
(41%-w/w) of biodegradable components included solid waste and hydrolytic biomass, and methane vol-
packaging, cartons and cardboard, newsprint and also ume. To evaluate the model parameters a non-linear
textiles and diapers. The BMP assays were carried out in regression applied to Eq. (6) can be used (Lokshina and
2 l glass vessels lled with dierent waste samples, for Vavilin, 1999):
237 days, at 35 C, in three replicates. The waste samples
were added into the vessels in amounts to provide 1.5 1 aB0H KbX
a ; b ; c ; d aX0 7
g VS/g VSinoculum , with an inoculum of 0.5 l of digested YH qmH YH qmH
mesophilic municipal sewage sludge from Nen ainniemi In the present study the best t curves with respect to the
sanitary treatment plant (Finland). Under anaerobic experimental data were obtained using the non-linear
conditions and in the presence of methanogenic mi- regression with the MarquardtLevenberg algorithm.
crobes, the grey waste components yielded high amounts This algorithm estimates values of model parameters by
of methane. minimizing the sum of squared dierences between ob-
served and predicted values. Dierent initial values of
2.1.2. Food waste the model parameters were tested to ensure that global
Cho et al. (1995) conducted BMP tests at various minima, rather than local minima, were obtained.
initial FW concentrations (2, 4, 10 and 50 g VS/l). The Although the integrated Contois model is the implicit
components of FW included boiled rice, cooked meat, expressions of methane volume (6), weighted least
fried eggs, bean sprouts, etc. All components were squares analysis can be employed to calculate approxi-
ground and freezedried. Prior to the BMP test, samples mate dierences in P values between model predictions
were analyzed for their volatile solid (VS) content. and data. The following sum of squared weighted errors
Anaerobic sludge from Taejon sanitary treatment plant was minimized:
(Korea) served as the inoculum. Xn
2
To increase solids reduction eciency, a two-stage SSWE wi tiobs  tipred  8
i1
anaerobic digestion system was used with the solid-bed
reactor for acid fermentation connected to the methane where is the time of the ith observation, tipred is the t
tiobs
fermenter (upow blanket lter) in series. Both reactors value predicted by the model for the measured P value, n
72 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981

is the total number of experimental data, and wi is an methanogens. Volatile fatty acids (VFA), which are
appropriate weighting factor being the local slope of the transferred from the acidogenic to the methanogenic
methane production curve areas, serve as a precursor for methane production.
However, high VFA concentration inhibits both meth-
wi DP =Dt 9 anogenesis and hydrolysis/acidogenesis, which was taken
into account in the model.
Using this weighting factor the quantity wi tiobs  tipred in The following system of ve parabolic partial dier-
Eq. (8) is ential equations in which Z is the vertical coordinate of
the 1-D reactor 0 6 Z 6 L was considered:
DP obs
wi tiobs  tipred t  tipred  Piobs  Pipred 10 8
Dt i >
> oW1
>
> k1 W1 f1 S;
>
> oT
which is the error in the predicted Piobs . Thus, this ap- >
> oW2
>
>
proach provides an explicit approximate method to >
> k2 W2 f2 S;
>
> oT
minimize a dierence between the observed and pre- >
>
>
> oS o2 S
dicted values of P . >
< DS 2 v1 k1 W1 f1 S v2 k2 W2 f2 S
oT oZ
Using the traditional rst-order kinetics (4), the SB 13
>
> qm gS ;
cumulative methane volume is written as >
> K S
>
> S
>
>
>
> oB o2 B SB
P P0 aX0 1  ekt 11 >
>
> D B 2
Y qm gS  kd B;
> oT
> oZ KS S
>
>
To estimate the rst-order kinetic coecients the non- > oP
> SB
: A1  Y qm gS ;
linear regression was used. Assuming P0 0, there are oT KS S
four combined parameters (a; b; c; d) in the model (6)
and two parameters (aX0 ; k) in the model (11). It should Initial conditions:
be emphasized that during calibration of the integrated
Contois model (6), aX0 should be appointed larger than W1 Z; 0 r1 Z; W2 Z; 0 r2 Z;
14
the maximal experimental P value. SZ; 0 uZ; BZ; 0 wZ
All parameters were judged by diagnosis procedures
including Student-t, DurbanWatson (DWS), Kol- Boundary conditions:
mogorovSmirnov (NT) and constant variance (CVT)
tests. The Akaikes nal prediction-error criterion (FPE)
oS0; T oSL; T
reects the prediction-error variance that one could 0; 0 15
obtain, on the average, if the model were applied as a oZ oZ
predictor to data sets other than those used for the oB0; T oBL; T
identication (Ljung, 1987). The modied FPE criterion 0; 0 16
oZ oZ
was used to consider a relative error of prediction:

1 p=n 1 Xn
1 obs where W1  W1 Z; T P 0; W2  W2 Z; T P 0; S 
2
FPE P  Pipred =Piobs  12 SZ; T P 0; B  BZ; T P 0 are the solid wastes (two
1  p=n n i1 2 i
types), total VFA, and methanogenic biomass concen-
At the limited number of experimental data n, the FPE trations, respectively; dP =dT  dP =dT Z; T P 0 is the
criterion adds a penalty for complexity and tends to methane production rate; 0 6 T < 1 is time; k1 , k2 are
favor an accurate simple model with low number of the rst-order hydrolysis rate constants; qm is the max-
parameters p. imum specic rate of VFA utilization; kd is the specic
biomass decay coecient; v1 , v2 are stoichiometric
coecients; A 16=60 is the mass fraction of methane
2.3. Basic distributed model of anaerobic digestion in biogas; KS is the half-saturation constant for VFA
utilization; Y is the biomass yield coecient; DS and DB
A simplied kinetic scheme was used in the distributed are the diusion coecients for VFA and biomass,
1-D batch reactor model. Polymer hydrolysis/acido- respectively DS
DB . The traditional Monod func-
genesis and methanogenesis were included in the model tion and rst-order kinetics were used for VFA utiliza-
as the rate-limiting steps of the overall anaerobic diges- tion and polymer hydrolysis, respectively.
tion process. The rich (FW) and lean (non-FW) solid The dimensionless functions f S and gS describe
wastes were considered in the model. The lean waste, the VFA inhibition of hydrolysis (f1 S, f2 S) and
present for example in digested sludge or in seed (well methanogenesis gS, respectively. These functions can
decomposed refuse), is more favorable for survival of be written in the following explicit form:
 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981 73

1 the advection parts for VFAs and biomass concentra-

f1 S
mf 1 ;
I tions to describe a FW anaerobic digestion in the solid-
1 bed acidogenic reactor with water ow:
Kf 1
8
1 >
> oS o2 S oS SB
f2 S
mf 2 ; < DS 2  q v1 k1 W1 f1 S  qm gS ;
I 17 oT oZ oZ KS S
1 > oB 2
oB oB SB
Kf 2 >
: DB 2  qa Y qm gS  kd B;
1 oT oZ oZ KS S
gS
mg ; 18
I
1
Kg where q is the volumetric liquid ow rate per unit sur-
face area (specic liquid ow rate); a is the fraction of
where I S is the inhibiting concentration of VFA; biomass transferred by liquid ow. Because the liquid
Kf 1 > 0, Kf 2 > 0, Kg > 0 are the inhibition constants; was recycled in the two-stage system, the following
mf 1 P 1, mf 2 P 1 and mg P 1 are the corresponding boundary conditions for VFAs and biomass were used
inhibition degree indexes. Using the functions (17) it is in the acidogenic reactor:
possible to describe sharp or smooth inhibition of
oS0; T q
hydrolysis/acidogenesis and methanogenesis by VFA. S0; T  SL; T =p;
oZ DS
2.4. Batch reactor model of anaerobic digestion oSL; T
0 19
oZ
The uniform initial concentration distributions of oB0; T q
aB0; T  BL; T  p;
FW, VFA and biomass over the coordinate Z were used oZ DB
to calibrate the model (13) against the BMP experi- oBL; T
mental data. It was assumed that diusion was high 0 20
oZ
enough to average the parameter values through the
For simulations, a 0:1 and p 100 were used, and the
vertical coordinate. As a result, the model (13) trans-
uniform initial concentration distributions of FW, VFA
forms to the system of ordinary dierential equations.
and biomass through the vertical coordinate Z were
The second substrate (non-food waste) was assumed to
assumed.
be absent. A visual model calibration carried out using
previously published experimental data (Cho et al.,
2.6. One-stage solid-bed reactor model with non-uniform
1995) resulted in the following parameter values:
concentration distributions
k1 0:55 day1 ; v1 0:68; qm 1:1 day1 ;
The initial wastes (FW and non-FW), VFAs and
kd 0:001 day1 ; KS 0:5 g l1 ; Y 0:08 g1 ;
biomass distributions along the reactor height Z were
Kf 1 11:0 g l1 ; Kg 4:5 g l1 ; mf 1 7; mg 3: described using the following functions:
"
2 #!
In fact, the experimental data corresponded to the Z  a1
higher FW loading (10 and 50 g VS/l) were used for rZ c1 1  exp  0:5
c21
calibration, but the data with the lower loading (2 and 4 "
2 #!
g VS/l) were used for model verication. Evidently the Z  an
     1  exp  0:5 ; 21
set of coecients obtained as a result of model cali- c2n
bration was not unique. "
2 #!
Z  b1
wZ c3 1 c41 exp 0:5
2.5. Two-stage anaerobic digestion model c51
"
2 #!
To model the continuous-ow two-stage digestion Z  bm
     1 c4m exp 0:5 ;
system, both acidogenic and methanogenic reactors c5m
should be described. For simplicity and because of the 22
lack of sucient data, it was assumed that the euent
VFAs and biomass concentrations were reduced and
multiplied, respectively, by a factor of p in the methano- where c1 ; c21 ; c22 ; . . . ; c2n ; c3 ; c41 ; . . . ; c4m ; c51 ; c5m are the
genic reactor before coming back to the top of the aci- distribution coecients; n and m are the total number of
dogenic reactor. Also, a limitation of the value of biomass depression/peak zones of waste and biomass, respec-
concentration in the methanogenic reactor was assumed. tively. The functions (21) and (22) describe the case with
The second substrate (non-food waste) was assumed to multi-depression rZ : W1 ; S and multi-peak wZ :
be absent. The basic model (13) was modied by adding W2 ; B distributions along the reactor height Z for
74 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981

wastes, VFA, and biomass, which have the minimum Rich waste and VFA distributions:
and maximum at Z ai and Z bj , correspondingly.
c1 200 g l1 W1 ; c1 0:01 g l1 VFA;
The initial methane production was assumed to be zero.
According to the parameter values selected, the initial c21 c22 0:03L; a1 0:2L; a2 0:7L:
waste, VFA, and biomass concentrations were localized Lean waste and methanogenic biomass distributions:
in separate zones: maximum biomass and minimum
waste and VFA concentrations were placed at the same c3 0:1 g l1 W2 ; c3 1:0 g l1 Biomass;
points (n m 6 were used in Eqs. (21) and (22)): c41 c42 30 W2 ; c41 c42 200 Biomass;
Rich waste and VFA distributions: c51 c52 0:01L; b1 0:2L; b2 0:7L:
c1 340 g l1 W1 ; c1 0:01 g l1 VFA;
c21 c22    c26 0:03L;
a1 0:15L; a2 0:3L; a3 0:45L; 3. Results and discussion
a4 0:6L; a5 0:75L; a6 0:9L;
3.1. Polymer hydrolysis as the rate-limiting step during
Lean waste and methanogenic biomass distributions: grey waste anaerobic digestion
c3 0:1 g l1 W2 ; c3 1:0 g l1 Biomass;
The values of kinetic coecients obtained for various
c41 c42    c46 30 W2 ;
waste components are summarized in Tables 1 and 2.
c41 c42    c46 100 Biomass; For every value from replicated data of the various
c51 c52    c56 0:01L; waste components, the Contois model (6) was better
b1 0:15L; b2 0:3L; b3 0:45L; than the rst-order model (11). The last one could not t
the normality test (NT) and DWS statistic. In the
b4 0:6L; b5 0:75L; b6 0:9L:
beginning of the assay, the methane production was
For the lean waste (non-FW) the following model started within 3 days from all samples. The rst-order
coecients were appointed: hydrolysis kinetics overestimated methane volume at the
start and at the end of the process (ultimate methane
k2 0:055 day1 ; v2 0:5; Kf 2 11:0 g l1 ;
production) and underestimated a maximal rate of
Kg2 4:5 g l1 ; mf 2 7: methane production (Fig. 1). According to Eastman and
Ferguson (1981), the rst-order kinetics is an empirical
Assuming perfect mixing conditions along the X and Y -
expression that reects the cumulative eect of all
axis, volume units for all concentration variables were
microscopic processes. As it was written in the Intro-
used despite the 1-D character of the model.
duction, the phenomenological Contois kinetics, being a
2.7. Two-dimensional model of anaerobic digestion good approximation of a surface-related model, allows
description of the initial phase of microbial colonisation
Two-dimensional (2-D) reactor with cylindrical of a surface of solid waste as well as the phase of a solid
symmetry was considered: surface degradation. According to Vavilin et al. (1996),
8 two main phases should be taken into account for a
> oW1 description of the hydrolysis kinetics. The rst phase is a
>
> k1 W1 f1 S;
>
> oT
>
> bacterial colonization, during which the hydrolytic
>
> oW2
>
> k2 W2 f2 S; bacteria cover the surface of solids. Bacteria on or near
>
>
> oT
>
2
 the particle surface release enzymes and produce the
>
>
> oS D o S 1 o r oS
> v1 k1 W1 f1 S monomers, which can be utilized by the hydrolytic
>
> S
>
> oT oZ 2 r or or bacteria themselves as well as by the other bacteria. The
>
< SB daughter cells fall o into the liquid and then try to
v2 k2 W2 f2 S  qm gS ; 23
> K S attach to some new place on a particle surface. When an
>
>
2
 S
>
> oB oB 1 o oB available surface is covered with bacteria the surface will
>
> DB r
>
> be degraded at a constant depth per unit of time (second
> oT
> oZ 2 r or or
>
> phase).
>
> SB
>
> Y qm gS  kd B; For packaging and textile wastes, a scatter of exper-
>
> KS S
>
> imental data in replicates was signicant and the kinetic
>
> oP SB
>
: A1  Y qm gS ; coecients diered greatly. In a case, no big dierence
oT KS S between the Contois and rst-order models was ob-
where r is the radius and Z is the vertical coordinate of tained for averaged data (see FPE criterion in Tables 1
cylinder. Two peak/depression functions (21) and (22) and 2). Generally, it may be concluded that for grey
were used as the initial conditions: waste inoculated by digested sludge, polymer hydrolysis
 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981 75

Table 1
Combined coecients of the integrated Contois model (6) and their standard errors obtained for various components of grey waste at X0 13:73
g VS/bottle
Waste aB0H =YH , mlCH4 /l qmH =YH , day1 Kb X =qmH , day a, mlCH4 /g1 VS FPE
Cardboard 179 8.9a 0.193 0.005a 2.89 0.066a 218.6 0.00a 0.0459b
1 155 9.1 0.203 0.006 3.77 0.067 175.6 0.00
2 218 8.5 0.156 0.003 1.62 0.059 235.2 0.00
3 30.3 2.9 0.536 0.016 4.84 0.05 245.2 0.00
Diapers 137 6.8a 0.159 0.004a 7.33 0.08a 206.1 0.00a 0.0602b
1 45.9 2.8 0.229 0.005 8.37 0.08 210.6 0.05
2 569 27 0.082 0.0027 5.78 0.09 220.8 0.02
3 127 5.3 0.121 0.002 5.37 0.07 186.6 0.00
Grey waste 4.708 0.615a 0.505 0.016a 6.89 0.077a 148.7 0.00a 0.0017b
1 2.98 0.43 0.537 0.017 7.56 0.08 154.0 0.00
2 21.05 1.43 0.303 0.007 4.201 0.338 147.1 0.00
3 3.87 0.56 0.545 0.018 7.66 0.08 144.8 0.00
Grey waste Uc 5.34 0.547a 0.462 0.011a 8.54 0.08a 220.7 0.03a 0.0329b
1 3.19 0.354 0.482 0.011 7.252 0.069 209.5 0.01
2 3.582 0.471 0.528 0.015 12.21 0.12 226.1 0.13
3 15.65 1.02 0.351 0.006 6.04 0.047 228.5 0.00
Grey waste Oc 29.9 2.15a 0.344 0.008a 8.89 0.066a 183.8 0.00a 0.0128b
1 27.0 1.75 0.348 0.007 8.46 0.006 225.5 0.02
2 32.3 2.07 0.288 0.006 7.94 0.07 175.3 0.00
3 93.5 5.87 0.233 0.007 7.55 0.07 150.6 0.00
Newsprints 99.5 11.7a 0.186 0.013a 3.50 0.114a 60.0 0.00a 0.0508b
1 95.6 10.1 0.128 0.008 1.51 0.107 48.9 0.00
2 125.2 15.5 0.183 0.014 4.25 0.126 61.7 0.00
3 34.9 6.34 0.449 0.034 5.41 0.1 69.5 0.00
Oce paper 154.9 6.5a 0.242 0.004a 5.23 0.053a 341.2 0.00a 0.0159b
1 267 10.2 0.205 0.004 3.44 0.047 351.1 0.01
2 245 8.75 0.177 0.003 2.74 0.048 313.3 0.00
3 124.4 4.95 0.223 0.004 6.68 0.052 359.4 0.02
Packaging 19.38 3.17a 0.711 0.035a 7.50 0.065a 166.3 0.00a 0.2453b
1 134.3 7.6 0.212 0.006 4.09 0.064 168.5 0.00
2 0.0216 0.055 2.73 0.761 7.29 0.118 52.9 0.00
3 6.23 2.05 1.178 0.085 7.02 0.08 277.3 0.01
Textile 46.8 3.1a 0.196 0.005a 6.77 0.08a 230.0 0.03a 0.2126b
1 45.5 3.8 0.129 0.005 3.37 0.108 108.1 0.06
2 83.3 4.4 0.193 0.004 8.37 0.09 344.4 0.09
3 87.6 5.4 0.155 0.004 4.63 0.06 238.3 0.01
a
Contois model parameters were obtained by weighted non-linear regression using averaged values of methane volume for denite time interval.
b
Modied FPE criterion (12) was calculated using all data including three replicates.
c
Grey waste U and O means the under-sized and oversized fractions of grey waste (Jokela, 2002). The undersized fraction was shredded to
maximum size of 200 mm and then sieved with a mesh size of 100 mm. The oversized fraction was further shredded to a maximum size of 50 mm.
Finally, all the samples were milled to a maximum particle size of 5 mm in a laboratory with a hammermill before the anaerobic incubation test.

was the rate-limiting step in methane production, and comparatively well, taking into account that a 25-fold
the high initial concentration of methanogenic micro- change of FW loading took place within the experi-
organisms in sludge promoted a balance between the mental period. Based on the model and experimental
rates of hydrolysis/acidogenesis and methanogenesis. data, we concluded that at an initial FW of 10 g VS/l
methanogenesis was suppressed by the high VFAs con-
3.2. A balance between the rates of polymer hydrolysis centration, but at the highest loading of 50 g VS/l both
and methanogenesis during food waste anaerobic digestion methanogenesis and hydrolysis were totally inhibited by
the very high VFA concentration (about 20 g/l, see Fig.
Simulations of BMP tests during FW anaerobic 3). According to the experimental data of FW degra-
digestion at various initial organic loading are shown in dation (Cho et al., 1995) used in our work, a drop in pH
Figs. 2 and 3. The model describes all experimental data to 4.0 corresponded to VFAs accumulation. In such
76 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981

Table 2 Grey Waste

Coecients and their standard errors obtained for various components 2500 First-order
of grey waste at X0 13:73 g VS/bottle by the rst-order model (11)

Methane production, ml
2000
Waste a, mlCH4 /g VS k, day1 FPE Contois
Cardboard 235.5 15.4 0.046 0.007 0.1484a 1500
1 189.4 15.2 0.0436 0.008
2 256.4 27.2 0.0388 0.009
1000
3 262.9 22 0.0563 0.011
Diapers 228.6 13.3 0.0246 0.003 0.2118a 500
1 233.8 23.2 0.0239 0.005
2 242.9 19.6 0.0280 0.005 0
3 209.0 23.4 0.0221 0.005 0 50 100 150 200 250
Time, days
Grey waste 163.4 9.8 0.0311 0.004 0.1943a
1 169.4 18.9 0.0296 0.007 Fig. 1. The integrated Contois and rst-order models prediction (lines)
2 162.4 18.2 0.0321 0.008 and experimental data (symbols) of methane production from grey
3 158.5 16.3 0.0317 0.007 waste for the triplicate data.
Grey waste U 245.2 15.3 0.0261 0.003 0.2270a
1 233.6 28.1 0.0262 0.007
2 247.7 25.7 0.0244 0.005
3 254.2 28.3 0.0278 0.007
Grey waste O 201.4 12.3 0.0308 0.004 0.1640a
1 248.3 23.3 0.0291 0.006
2 192.5 17.3 0.0297 0.006
3 163.8 11.9 0.0347 0.005
Newsprints 63.7 3.5 0.0568 0.007 0.1353a
1 56.7 4.7 0.0472 0.009
2 65.3 4.2 0.581 0.009
3 73.2 4.5 0.0637 0.009
Oce paper 372.9 20.6 0.0356 0.004 0.1313a
1 380.4 34.3 0.0421 0.008
2 342.4 33.9 0.0376 0.008
3 396.8 36.4 0.0288 0.006
Packagings 175.2 24.3 0.0560 0.018 0.2483a
1 182.1 14.5 0.0423 0.007
2 55.3 3.2 0.0687 0.009
3 290.0 20 0.0635 0.010
Textiles 257 30.8 0.0214 0.005 0.3021a
Fig. 2. Time proles of food waste, VFA and biomass concentrations
1 121.6 16.1 0.0206 0.006
during BMP tests and cumulative methane volume at the various waste
2 383.5 42.5 0.0214 0.005
loadings of 2 (1) and 4 g VS/l (2). Symbols: experimental data (Cho
3 267.9 31.6 0.0219 0.005
et al., 1995); lines: model prediction. Cumulative methane volume is
a
Modied FPE criterion was calculated using all data including 3 normalized to the initial solids mass.
replicates.

day1 (37 C). It was much higher than k1 values ob-

conditions, the methanogenic population becomes tained for grey waste components (Tables 1 and 2).
insucient to prevent VFAs accumulation causing the According to Veeken and Hamelers (2000), k1 values for
imbalance between processes of hydrolysis/acidogenesis biowaste components ranged from 0.003 to 0.15 day1
and methanogenesis. As was written above, the hydro- at 20 C to 0.240.47 day1 at 40 C.
lysis stage is microbial dependent; thus, a hydrolysis rate Simulations showed that methane production was
may be dependent on such factors as the product (VFA) enhanced in a batch reactor at a very high FW loading
concentration and pH level. The inhibiting VFAs con- of 20% TS (188 g VS/l) if a rather high initial biomass
centration of 20 g/l corresponded to Kf 1 11:0 g/l (see concentration of 80 g/l was used (Fig. 4). Such a system
Eq. (17)) at which the hydrolysis rate decreases two where the fermenting mass within the reactor is kept at a
times if mf 1 1. ten Brummeler et al. (1991) found that solids content in the range 2040% TS is called tradi-
hydrolysis of biowaste was severely inhibited under tionally as dry digestion system. To enhance solids
VFA concentration above 30 g/l. The rst-order kinetic reduction in full-scale one-stage solid-bed system a
coecient of FW hydrolysis was rather high: k1 0:55 leachate recirculation and a high percentage of micro-
 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981 77

Fig. 3. Time proles of food waste, VFA and biomass concentrations Fig. 5. Time proles of food waste, VFA and biomass concentrations
during BMP tests and cumulative methane volume at the various waste and cumulative methane volume in two-stage system at the high waste
loadings of 10 (3) and 50 g VS/l (4). Symbols: experimental data (Cho loading of 188 g VS/l and at the dierent liquid ow rate of 0.2 (1) and
et al., 1995); lines: model prediction. Cumulative methane volume is 0:05L day1 (2). Symbols: experimental data (Cho et al., 1995); dotted
normalized to the initial solids mass. lines: model predictions with uniform initial concentration distribu-
tions. Cumulative methane volume is normalized to the initial solids
mass.

lower liquid ow rate of 0:05L day1 . According to the

model, the higher the value of q, the more rapidly the
low VFAs and high methanogenic biomass concentra-
tion distributes over the spatial coordinate Z (results not
shown).
Six-peaks/depressions in the initial distribution of
methanogenic biomass and FW at the dierent values
of diusion coecients DS were used for the simulations
of one-stage digestion presented in Fig. 6. The FW
reduction and methane production were stimulated at
the signicantly lower initial averaged biomass concen-
tration of 18 g/l (compare Figs. 6 and 4) and at DS values
of 5 104 and 1 103 L2 day1 . At the highest DS value
of 2 103 L2 day1 both hydrolysis and methanogenesis
were totally inhibited. Fig. 7 shows concentration pro-
les along the coordinate Z at dierent time under the
Fig. 4. Simulated time proles of food waste, VFA and biomass highest methane production rate corresponding to
concentrations and cumulative methane volume in batch digester at
DS 1  103 L2 day1 . Initially, the methanogenic areas
the high waste loading of 188 g VS/l and at the initial biomass con-
centrations of 80 (1) and 50 g/l (2). Cumulative methane volume is coincided with the areas of initial distribution of lean
normalized to the initial solids mass. waste contained in digested sludge or seed.
Vavilin et al. (2002a,b) have formalized the condi-
tions of a mass transfer-based acceleration of methane
production, when the intensity of VFA utilization in a
bial seeding (up to 50%) are usually used (ten Brum-
methanogenic area H is sucient for the complete
meler, 2000).
conversion of the incoming VFA ow. The following
In the case of rich waste, a two-stage anaerobic
condition must hold for all values of T
digestion process is recommended (Mata-Alvarez et al.,
Z Z
2000). Fig. 5 shows the system dynamics in the two-stage
digestion system at the high FW loading of 188 g VS/l. JH RH Z; T dZ < RM Z; T dZ 24
H H
Methane production and FW reduction was obtained
during 30 days at the high liquid ow rate of 0:2L day1 . where RH vkWf S is the rate of VFA production by
The reaction time was increased signicantly at the hydrolysis/acidogenesis;
78 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981

tration increased rapidly in the areas where original FW

was degraded, however, methanogenic biomass, being
apart from active acidogenic zones, could utilize the
incoming VFAs. The maximum methane production
corresponded to the boundaries of these areas where the
VFAs concentration was not high enough to inhibit
methanogenesis (Fig. 7). The higher the diusion rate,
the more rapidly the initial methanogenic area expands
and this resulted in a higher methane production rate
(Fig. 6, curves 1 and 2). According to the model,
accelerated anaerobic digestion of FW in a one-stage
batch reactor without lechate recirculation was ob-
tained. However, at the highest diusion rate, metha-
nogenesis in the active methanogenic area was
suppressed, and evidently this caused a stop of metha-
nogenic area expansion (Fig. 8). Thus, the critical value
of VFA diusion coecient DS 2:0  103 L2 day1
above which a FW reduction became impossible was
Fig. 6. Simulated time proles of food waste, VFA and biomass
obtained. The lower L value (reactor height), the less the
concentrations averaged over the total reactor volume and methane
production rate in one-stage system at the high waste loading of 188 threshold maximal value of DS at which an accelerated
g VS/l and at the dierent diusion coecient values of 1 103 (1), FW digestion could be achieved. Taking into account
5 104 (2) and 2 103 L2 day1 (3). Non-uniform initial concentra- for a laboratory reactor the height of 20 and 10 cm, we
tion distributions were used. have DS of 9.3 106 and 2.3 106 cm2 s1 , respectively.
Fig. 9 shows a suppression of initial methanogenic area
by increasing concentration of VFA according to 2-D
distributed model simulations for a cylinder with height
0.1 m and the radius 0.028 m.
In experiments carried out in the batch one-phase
laboratory reactor, Veeken and Hamelers (2000) have
realized a spatial separation of waste and seed to show
an enhancement of biowaste degradation. Evidently, the
critical value of DS depends also on the other parameters
such as an eective distance between the areas of active

Fig. 7. Sequence of distributions of food waste, VFA, biomass con-

centrations and methane production rate throughout the coordinate Z
at 0 (0), 10 (1), 50 (2) days of incubation at the diusion coecient
value of 1 103 L2 day1 .

RM qm gS KSSBS is the rate of VFA consumption; JH

is the incoming VFA ow through the boundaries of
H-area due to diusion. In the opposite case, the acido-
genic area expands because of inhibition of methano-
genesis by the high incoming VFA concentration.
According to the model simulations presented in Figs. 6
Fig. 8. Sequence of distributions of food waste, VFA, biomass con-
and 7, during expansion of methanogenic areas the total centrations and methane production rate throughout the coordinate Z
methane production rate strongly depended on a VFAs at 0 (0), 10 (1), 50 (2) days of incubation at the diusion coecient
diusion. During the rst few days, the VFAs concen- value of 2 103 L2 day1 .
 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981 79

mixing improved digester performance. In a second

experiment, six digesters were operated under continu-
ous mixing and reduced mixing levels at various loading
rates and solids level. The continuously mixed digesters
exhibited unstable performance at the higher loading
rates with VFA accumulation. In a third experiment, it
was shown that an unstable, continuously mixed diges-
ter was quickly stabilized by reducing the mixing level.
Similar results were reported by Kim et al. (2002). They
showed that the non-mixed reactor conguration at
mesophilic and thermophilic temperatures removed
VFAs more eciently and produced more gas than
other reactor congurations. The non-mixed single-
stage reactors reached steady state in the shortest time
with relatively stable pH and low VFAs. Studying
anaerobic digesters fed swine waste, Angenent et al.
(2001) showed that gentle, intermittent mixing was
Fig. 9. Sequence of distributions of food waste, VFA, biomass and advantageous compared to gentle, continuous mixing.
methane production rate throughout the coordinate Z in 2-D reactor Following these experiments, let us assume that for
at 0 (0), 10 (1), 50 (2) days of incubation at the diusion coecient waste and inoculums randomly distributed over the
value of 5.6 104 m2 day1 .
reactor space, only part of the existing initial methano-
genic areas can survive and expand in space during
methanogenesis and acidogenesis, and also, according to waste digestion. We call it the initiation methanogenic
the condition (24), on a ratio between the rates of centers. The other part of the existing methanogenic
hydrolysis/acidogenesis and methanogenesis. The higher areas will be suppressed by incoming VFAs because of
the initial waste and lower the initial methanogenic diusion from acidogenic areas. To demonstrate it, the
biomass concentrations, the less the threshold maximal simulation at the highest diusion rate coecient of
value of DS . According to Martin et al. (1997), scale DS 2:0  103 L2 day1 was repeated assuming a
eects seem to be signicant for small laboratory reac- higher width of the central peak in initial biomass con-
tors without leachate recirculation and pH control. The centration distribution. In such conditions (Fig. 10),
rst-order hydrolysis kinetic constant k is reciprocal to only the central methanogenic area could survive and
the initial diameter of the waste particles. For labora- propagate (left and right directions) over the spatial
tory reactors, the waste particles are shredded and mil-
led. In this case because of the higher hydrolysis rate a
suppression of initial methanogenic areas is strength-
ened.

3.3. Mixing level and initiation centers for methanogenesis

Traditionally, the literature emphasizes the impor-

tance of adequate mixing to encourage the distribution
of enzymes and microorganisms throughout of digester
(Chapman, 1989). However, Stroot et al. (2001) studied
the feasibility of co-digestion of the organic fraction of
municipal solid waste, primary sludge, waste activated
sludge, and cattle manure in mesophilic laboratory-scale
digesters. Three types of experiments using mesophilic
(37 C), laboratory scale digesters were conducted. The
digesters were vigorously and continuously mixed on a
shaker table or minimally mixed (thoroughly shaken
by hand for 2 min each day) and operated in semi-
continuous mode with daily washing and feeding. In a
Fig. 10. Sequence of distributions of food waste, VFA, biomass con-
rst experiment four digesters were operated under
centrations and methane production rate throughout the coordinate Z
continuously mixed conditions. After two weeks, the at 0 (0), 10 (1), 50 (2) days of incubation at the diusion coecient
experiment was continued under minimally mixed con- value of 2 103 L2 day1 with higher width of c53 0:03L of the
ditions. Results demonstrated that reducing the level of central peak in initial biomass concentration distribution.
80 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981

coordinate Z. The other initial methanogenic areas were and microbial community structure. In: Velsen, V., Verstraete, W.
suppressed by high VFAs value (compare Fig. 8 with (Eds.), Proc. 9th World Congress Anaerobic Digestion 2001,
Antwerpen, Belgium, 26 September 2001. Belgian Technological
c53 0:01L and Fig. 10 with c53 0:03L). The maximum Institute, Part 1, pp. 267274.
methane production was dened by the boundaries of Barlaz, M.A., Ham, R.K., Schaefer, D.M., 1990. Methane production
the central area where the VFAs concentration was not from municipal refuse: a review of enhancement techniques and
high enough to inhibit methanogenesis. All in all, under microbial dynamics. Crit. Rev. Environ. Control 19, 557
vigorously mixing most of the initial methanogenic areas 584.
Chapman, D., 1989. Mixing in anaerobic digesters: state of the art. In:
may be reduced in size averaged over the reactor vol- Cheremisino, P. (Ed.), Encyclopedia of Environmental Control
ume, and nally dissipated. In opposite, at the non- Technology, vol. 3. Gulf Publishing Company, Houston, pp. 325
mixing or minimal mixing regimes the most initial 354.
methanogenic areas could survive and expand over the Cho, J.K., Park, S.Ch., Chang, H.N., 1995. Biochemical methane
reactor volume becoming the initiation methanogenic potential and solid state anaerobic digestion of Korean food
wastes. Biores. Technol. 52, 245253.
centers. Eastman, J.A., Ferguson, J.F., 1981. Solubilisation of particulate
organic carbon during the acid phase of anaerobic digestion.
JWPCF 53, 352366.
4. Conclusions Jokela, J., 2002. Landll Operation and Waste Management Proce-
dures in the Reduction of Methane and Leachate Pollutant
Emissions from Municipal Solid Waste Landlls. Dissertation.
The Contois model tted the data on grey waste University of Jyvaskyla, Finland.
decomposition signicantly better than did traditional Kalyuzhnyi, S., Veeken, A.H.M., Hamelers, B.V.M., 2000. Two-
rst-order kinetics. A distributed model of anaerobic particle model of anaerobic solid state fermentation. Water Sci.
digestion of rich (FW) and lean (non-FW) solid wastes Technol. 41 (3), 4350.
with denitely dierent rates of polymer hydrolysis was Kim, M., Ahn, Y., Speece, R.E., 2002. Comparative process stability
and eciency of anaerobic digestion; mesophilic vs. thermophilic.
developed. The model simulations showed that an initial Water Res. 36, 43694385.
spatial separation of FW and inoculum enhanced Lissens, G., Vandervivere, P., De Baere, L., Biey, E.M., Verstraete,
methane production and waste degradation in a one- W., 2001. Solid waste digesters: process performance and practice
stage solid-bed digester at high waste loading at rather for municipal solid waste digestion. Water Sci. Technol. 44 (8), 91
low initial methanogenic biomass concentration, if 102.
Ljung, L., 1987. System Identication: Theory for User. Prentice-Hall,
VFAs coming into the initial methanogenic areas by Inc., NJ.
diusion were consumed eciently. If acidogenic and Lokshina, L.Ya., Vavilin, V.A., 1999. Kinetic analysis of the key stages
methanogenic phases were imbalanced, the volatile fatty of low temperature methanogenesis. Ecol. Modell. 117, 285303.
acids (VFA) accumulated. This inhibited not only Martin, D.J., 2001. The site of reaction in solid-state digestion. A new
methanogenesis: the nal stage of the process, but also hypothesis. Trans. I. Chem. E. 79 (B), 2937.
Martin, D.J., Plotts, L.G.A., Reeves, A., 1997. Small-scale simula-
hydrolysis: the primary stage of the process. For waste tion of waste degradation in landlls. Biotech. Lett. 19, 683685.
and inoculum randomly distributed over bioreactor Mata-Alvarez, J., Mace, S., Llabres, P., 2000. Anaerobic digestion of
space, only a part of the existing initial areas of meth- organic solid wastes. An overview of research achievements and
anogenesis are not decayed. Excessive VFA diusion perspectives. Biores. Technol. 74, 316.
into the initial areas of methanogenesis, where concen- Stroot, P.G., McMahon, K.D., Mackie, R.I., Raskin, L., 2001.
Anaerobic codigestion of municipal solid waste and biosolids
tration of microorganisms is low, suppresses micro- under various mixing conditionsI. Digester performance. Water
organism growth. Thus, a negative eect of vigorously Res. 35, 18041816.
mixing observed earlier in experiments may be inter- ten Brummeler, E., 2000. Full-scale experience with BIOCELL-
preted as a signicant reduction of a number of possible process. Water Sci. Technol. 41 (3), 299304.
initiation methanogenic centers. ten Brummeler, E., Horbach, H.C.J.M, Koster, I.W., 1991. Dry
anaerobic batch digestion of the organic fraction of municipal solid
waste. J. Chem. Tech. Biotechnol. 50, 191209.
Vavilin, V.A., Rytov, S.V., Lokshina, L.Ya., 1996. A description of
Acknowledgements hydrolysis kinetics in anaerobic degradation of particulate organic
matter. Biores. Technol. 56, 229237.
Vavilin, V.A., Shchelkanov, M.Yu., Rytov, S.V., 2002a. Eect of mass
This work was supported by Copernicus-2 Grant
transfer on concentration wave propagation during anaerobic
under reference ICA2-CT-2001-10001. L.Ya. Lokshina digestion of solid waste. Water Res. 36, 24052409.
was supported by Science Support Foundation for Vavilin, V.A., Shchelkanov, M.Yu., Lokshina, L.Ya., Rytov, S.V.,
Talanted Young Russian Researchers. Jokela, J., Salminen, E., Rintala, J., 2002b. A comparative analysis
of a balance between the rates of polymer hydrolysis and
acetoclastic methanogenesis during anaerobic digestion of solid
waste. Water Sci. Technol. 45 (10), 249254.
References Vavilin, V.A., Rytov, S.V., Lokshina, L.Y., Pavlostathis, S.G., Barlaz,
M.A., 2003a. A distributed model of solid waste anaerobic
Angenent, L.T., Sung, S., Raskin, L., 2001. Mixing intensity in digestion: eect of leachate recurculation and pH adjustment.
anaerobic sequencing batch reactors aects reactor performance Biotechnol. Bioeng. 81, 6673.
 V.A. Vavilin et al. / Bioresource Technology 94 (2004) 6981 81

Vavilin, V.A., Rytov, S.V., Pavlostathis, S.G., Jokela, J., Rintala, Veeken, A.H.M., Hamelers, B.V.M., 2000. Eect of substrate-seed
J., 2003b. A distributed model of solid waste anaerobic diges- mixing and leachate recirculation on solid-state digestion of
tion: sensitivity analysis. Water Sci. Technol. 48 (4), 147154. biowaste. Water Sci. Technol. 41 (3), 255262.