[14] Vlyssides, et al., 2009

Bioresource Technology 100 (2009) 4797–4806

Contents lists available at ScienceDirect

Bioresource Technology
journal homepage: www.elsevier.com/locate/biortech

An integrated mathematical model for co-composting of agricultural solid
wastes with industrial wastewater
A. Vlyssides *, S. Mai, E.M. Barampouti
National Technical University of Athens, School of Chemical Engineering, 9, Heroon Polytechniou St., Zografou, 15780 Athens, Greece

a r t i c l e

i n f o

Article history:
Received 6 February 2009
Received in revised form 5 May 2009
Accepted 5 May 2009
Available online 28 May 2009

Keywords:
Co-composting
Composting
Kinetics
Modelling
Olive mill waste

a b s t r a c t
An integrated model for the composting process was developed. The structure of the model is such that it
can be implemented in any mixture of different substrates, even in the case of co-composting of a solid
waste with industrial wastewater. This paper presents a mathematical formulation of the physicochemical and biological principles that govern the composting process. The model of the co-composting ecosystem included mass transfer, heat transfer and biological processes. The biological processes included
in the model were hydrolysis of particulate substrates, microbial growth and death. Two microbial populations (bacteria and fungi) were selected using Monod kinetics. Growth limiting functions of inhibitory
factors, moisture and dissolved oxygen were added in the Monod kinetics. The bacteria were considered
to utilise the easy biodegradable carbon hydrolysis product, fungi the difficult one, while both could
degrade the carbon of wastewater. The mass balances of the most important nutrients, nitrogen and
phosphorous, were also included in this approach. Model computer simulations provided results that fitted satisfactory the experimental data. Conclusively, the model could be a useful tool for the prediction of
the co-composting process performance in the future and could be used to assist in the operation of cocomposting plants.
Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction

From the standpoint of chemical engineering, composting is an
organic matter decomposition process under aerobic conditions.
During this process, bacteria, fungi and other microorganisms
transform the initial organic matter into a useful product called
compost. During composting, the biodegradable organic compounds are broken down whereas part of the remaining organic
material is converted into humic-like substances (Veeken et al.,
2000). This process consumes oxygen and emits carbon dioxide,
water vapor and heat resulting in a volume reduction of the waste
and pathogen destruction when a good control is performed (Keener, 1998). Because of its properties, the final compost obtained can
be used for many applications (Raviv, 2005; Stoffella and Kahn,
2001) such as soil amendment, organic fertilizer or raw material
for other industries. With the aim to enhance the composting process, increasing the degradation rate and the quality of the final
compost, several modifications have been made in the process;
such as the addition of biodegradable wastes to reach the optimum
C/N ratio of about 30 (Haug, 1993), that is co-composting, and the
addition of chemicals to increase the reaction rates and the composition of the compost (Bangar et al., 1988; Brown et al., 1998;
Sánchez-Arias et al., 2008).

* Corresponding author. Tel.: +30 2107723268; fax: +30 2107723269.
E-mail addresses: avlys@tee.gr (A. Vlyssides), mai@central.ntua.gr (S. Mai).

0960-8524/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.biortech.2009.05.005

Other parameters that control the composting procedure are:
the temperature of the process, the moisture of the bulking material and the nutrients (nitrogen and phosphorous) (Finstein et al.,
1985; Haug, 1980). For a continuous and stable process, the removed by degradation carbon as well as the moisture removed
by evaporation must be replaced. The use of a wastewater in order
to fill the water needs and partially or totally the carbon needs of a
continuously operating composting system can be an effective
technological solution. Also, possibly, an easy degradable and
nutrient rich bulking material could supplement a nutrient poor
wastewater of low degradable, due to inhibitory factors, organic
matter and vise versa (Vlyssides et al., 2003).
In order to reach the optimum results in the composting piles,
co-composting is widely used. Co-composting processes have been
reported for composting of agroindustrial wastes with wastewaters. For example, co-composting of exhausted grape marc with
different biowastes (Fernández et al., 2008), of winery and distillery wastes (Bustamante et al., 2008), of olive mill wastes and sewage sludge with industrial waste (Sánchez-Arias et al., 2008) has
been reported.
The inputs of every co-composting process are a liquid and a solid waste. At the end of a successful co-composting process, both
inputs would have been stabilised into a solid product that may

be used as a fertiliser. Thus, by appropriate control of the operational parameters, co-composting may be used for either the maximization of the solid waste treatment, or the maximization of the
wastewater treatment or for both.

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A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

Proper design and operation of the composting reactor is necessary to guarantee a good compost quality and the desired consumption of the raw materials (liquid and solid waste). To define
the optimal conditions, the dependence of the composting rate
on environmental conditions, i.e. composting kinetics should be
known (Hamelers, 2004). For this reason mathematical modelling
has been widely utilised in the description of the composting process. Mathematical models of the composting process have appeared in the literature since 1976, with more than 100 papers
addressing this topic published up to today. In addition, contributions from studies on liquid-phase aerobic digestion and the broader field of high solids aerobic degradation have provided models
with potential relevance to the understanding and prediction of
composting system behaviour (Mason, 2006). Nevertheless composting mathematical models that may use wastewater as an input
– substrate have not yet been addressed in the literature.
The present study is intended to present an integrated biochemical and physical model for such a co-composting process.
Taking into account the majority of the approaches of modelling
composting kinetics, the model developed would incorporate both
the theoretical knowledge (as represented by the basic parameters) as well as the information retained in the data (as represented

by identifiable combined parameters) (Hamelers, 2004).
2. Model theoretical principles
A volume unit (V) formed by a gaseous and a liquid phase was
considered, in which the solid particles were immersed or covered
by a water film (Fig. 1). Wastewater (WW), solid waste (PP) and air
(Air) were the inlet flows. The solid particles were considered
spherical and symmetrical with a given particle size distribution
(x fractions, each with diameter dx). All phases were regarded as
homogeneous and the particles size was supposed to be small en-

ough so that inner concentration or temperature gradients could
be neglected.
A schematic representation of all the processes included in the
model is shown in Fig. 1. The model contains 21 state variables corresponding to particulate, soluble and gas components, moisture,
temperature and flow rates (Table 1).
For the biological details of the composting process, much more
effort had to be made to find a suitable compromise which would
keep the model both practicable and realistic. The first problem

Table 1

Components of the model.
i,j

Symbol

Units

Description

1
2
3
4
5
6
7
8
9
10
11

12
13
14
15
16
17
18
19
20
21

Pb
Pdb
Pin
P
XB
XF
XD
Sb
Sdb

Sw
DO
nO2
nCO2
nH2 O
T
VL
VC
Vg
WW
Air
PP

gC
gC
g
g
gC
gC
gC

gC
gC
gC
g/L
mol
mol
mol
°C
L
L
L
g/h
L/h
g/h

Easy biodegradable carbon in particulate waste
Difficult biodegradable carbon in particulate waste
Inert organic material in particulate waste
Particulate waste
Bacteria

Fungi
Decayed biomass
Easy biodegradable carbon hydrolysis product
Difficult biodegradable carbon hydrolysis product
Soluble carbon of wastewater
Dissolved oxygen
Oxygen gas
Carbon dioxide gas
Water vapor
Temperature
Liquid phase
Co-composting mixture
Gas phase
Wastewater flow rate
Air flow rate
Solid waste flow rate

Fig. 1. Schematic representation of the considered processes.

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A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

that arose was the appropriate limitation of the number of substrate and biotic components. The components were classified in
a way that each substrate class could be treated like a homogeneous compound and each biotic class as a homogeneous population. Thus, a system of one defined substrate and one defined
consuming species could only give a very rough representation of
composting; it could not reflect the performance quantitatively,
including the speed of start and the duration of the process (Kaiser,
1996). Generally, the substrate range of composting includes components that vary considerably in degradability and structural
properties (bulk density). By comparing literature on composting
(Finstein et al., 1986; Biddlestone et al., 1987) and on natural degradation of organic matter (Knapp, 1985; Begon et al., 1990; Betts
et al., 1991), a natural classification within the substrate range of
typical raw materials of composting could be outlined as an easily
biodegradable fraction, a difficult biodegradable fraction and an inert (non-biodegradable) one (Haug, 1980; Kaiser, 1996). Thus, the
composting mass (P) was fractionated into easy biodegradable carbon (Pb), difficult biodegradable carbon (Pdb) and inert materials
(Pin).
Comparing literature, a natural classification of the microflora
range could be outlined. The main representatives of the regularly
aerobic degradation of plant materials are bacteria and fungi. So,
in this model two microbial populations, each with a particular
substrate specificity, were considered: bacteria (XB) and fungi
(XF) (Haug, 1980; Kaiser, 1996). The bacteria were considered to
utilise the easy biodegradable carbon hydrolysis product, fungi
the difficult one, while both could degrade the carbon of
wastewater.
The biological processes included in the model were hydrolysis
of particulate substrates, microbial growth and death (Fig. 1).
3. Hydrolysis

X

p  d2x  Nx

For j ¼ 5; i ¼ 1;

ð1Þ

kh ¼ kh;T¼20 C ð1:066ðT20Þ  1:21ðT60Þ Þ

ð5Þ

4.1. Carbon mass balances
The kinetics of matter conversion was modelled according to
Monod kinetics.
As far as the microbial degradation of hydrolysed soluble products is concerned, bacteria were assumed to grow on the products
resulting from the degradation of easy biodegraded matter, while
fungi grew on the products resulting from the degradation of difficult biodegraded matter. Both microbial populations could degrade the carbon content of the wastewater. Thus, it is clear
that the carbon of the wastewater should be distributed both to
bacteria and fungi. It was assumed that this distribution takes
place proportionally to each species growth rate and concentration. In other words, the percentage of wastewater carbon available to bacteria is equal to an F ratio (Eq. (6))) and the rest
(1F) to fungi.

lB  X B
lB  X B þ lF  X F

ð6Þ

According to the assumptions mentioned above, the reaction
rates of substrate consumption are shown in the following
equations:

dSb
Sb
¼ lB  fmoist  kDOB  fin 
 XB
dt
ksb  V L þ Sb
dSdb
¼ lF  fmoist  kDOF  fin 
dt
ksdb
dSw
¼ lB  fmoist  kDOB  fin 
dt
ksBw
 lF  fmoist  kDOF

Sdb
 XF
 V L þ Sdb
F  Sw
XB
 V L þ F  Sw
ð1  FÞ  Sw
 fin 
 XF
ksFw  V L þ ð1  FÞ  Sw

ð7Þ
ð8Þ

ð9Þ

where lD is the maximum uptake rate for bacteria, lF the maximum
uptake rate for fungi, kSb the half-saturation concentration of bacteria for the easy biodegradable carbon hydrolysis product, kSdb the
half-saturation concentration of fungi for the difficult biodegradable
carbon hydrolysis product, kSBw the half-saturation concentration of
bacteria for the wastewater and kSFw the half-saturation concentration of fungi for the wastewater.
According to Haug (1980), the correction factor (fmoist) of the
maximum rate constant due to moisture content (moist) is described by the following equations:

For moist >¼ 40;

^j ¼ q  A  d
X
j

For moist < 40;

where qj are the densities of bacteria (j = 5) or fungi (j = 6) and d the
depth of minimum microbial layer.
In this context the hydrolysis rate function is equal to:

ð4Þ

4. Biomass growth

^ j covering the conThen, a saturation biomass concentration X
tact surface of the hydrolysed particles per unit volume is:

ð2Þ

j ¼ 6; i ¼ 2:

ð3Þ

where kh the hydrolysis constant.
The temperature dependence of the hydrolysis constant was
adopted from Haug (1980).

F¼

During hydrolysis the particulate substrates make contact with
hydrolytic microbial cells and the released enzymes. Two main
phases were taken into account for the description of the hydrolysis kinetics. The first phase is a bacterial colonization, during which
the hydrolytic bacteria cover the surface of solids. Bacteria on or
near the particle surface release enzymes and produce the monomers which can be utilised by the hydrolytic bacteria themselves,
as well as by other bacteria. When an available surface is covered
with bacteria the surface will be hydrolysed at a constant depth
per unit of time (second phase) (Vavilin and Rytov, 1996).
Hydrolysis of particulate matter was considered to be selectively performed by bacteria for easy biodegradable particulate
matter and by fungi for difficult particulate matter.
It was assumed that the hydrolysis rate was limited by a contact
area (A) between the particles of organic substrate and biomass,
and the diameter of the hydrolysed particle was much greater than
the depth of the bacterial layer. It was also assumed that the total
number (N) of the particles per unit volume did not change but
that the size of the particles decreased as a result of the hydrolysis.
With these assumptions the contact area per unit volume is written as:

A¼

dPi
^j
¼ khi  Pi if X j > X
dt
dPi
Xj
^j
if X j < X
¼ khi  Pi 
^j
dt
X


6:94
moist
f moist ¼ 1  17:3  1 
100

4:06
moist
f moist ¼ 20:6614 
100

ð10Þ
ð11Þ

The growth limiting function of dissolved oxygen (kDO) is given
by the following equation:

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A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

kDOj ¼

DO
kO2 j þ DO

ð12Þ

where kO2 is the oxygen saturation constant.
The temperature dependence of the oxygen saturation constant
was adopted from Haug (1980).

kO2 ¼ kO2 ;T¼20  1:12ðT20Þ

ð13Þ

Taking into consideration each time the composition of particulate
waste as well as the composition of the wastewater, inhibition factors could be included either for bacteria growth or for fungi. In this
model inhibition factors were considered to act according to the following equation:

fin ¼

kin
kin þ in

For i = 20, 21 and 22.
where ni;intake ; ni;exhaust are the in and out molar flows, respectively, ri the rate of production (or consumption) through biological
reactions.
Inflows are determined by the volumetric air flow and standard
air composition, while outflows are computed assuming ideal gas
behaviour and constant total pressure. The evolution of bioreaction
water is directly proportional to the evolution of CO2. According to
the oxidation equation of glucose.

C6 H12 O6 þ 6O2 ! 6CO2 þ 6H2 O

1 mol of H2O evolves per mol of CO2, and 1 mol of O2 is consumed per mol of CO2 (respiration coefficient = 1) (Kaiser, 1996).
The rate of CO2 production due to biological reactions is equal to:

ð14Þ
rCO2 ¼ r H2 O ¼ r O2 ¼

where fin is the inhibition factor, kin inhibition coefficient and (in)
the concentration of inhibitor.
The microbial growth was described by the following equation:

X dSi
dX j
¼Y
 b  Xj
dt
dt

ð15Þ

where Y is the biomass yield coefficient and b the decay rate.

ð22Þ

X dSi
dnCO2
1
 ð1  YÞ 
¼
12
dt
dt

ð23Þ

For i = 8, 9 and 10.
For vapor mass balance the following assumptions were made:
(1) Intake air had a humidity f (kg H2O/m3 air).
(2) The exhaust gases were saturated in water and the saturation humidity (fs) was calculated according the following
equation (Vlyssides et al., 2003):

5. Nitrogen and phosphorous mass balances
In order to construct the mass balances for nitrogen and phosphorous, it was considered that these elements entered the system
from the hydrolysis process and from the wastewater, while they
were consumed through biomass yield. The nitrogen content of
bacteria (Nb), fungi (Nf), particulate matter (NP) and wastewater
(Nw) as well as the respective contents for phosphorous (Phb, Phf,
Php, Phw) were taken into account. The nitrogen mass balance
was described by the following equation:

X dPj
dN
dX B
dX F
¼ NP 
þ Nw  WW  Nb 
 Nf 
dt
dt
dt
dt

ð16Þ

For j = 1 and 2.
The phosphorous mass balance was considered by:

X dPj
dPh
dX B
dX F
¼ PhP
þ Phw  WW  Phb 
 Phf 
dt
dt
dt
dt

ð17Þ

For j = 1 and 2.

In order to describe the phenomena taking place in the gas
phase and consequently construct the mass balances, the term of
free air space (FAS) was introduced. FAS are defined as the ratio
of gas volume to the total volume of composting mixture (Haug,
1980).

V C  qP  V L
p

VC

ð24Þ

Taking into consideration the water produced from the biological reactions (Eq. (23)) and the saturation of exhaust gases in
water (Eq. (24)), the water mass balance is as follows:

dV L
 qw ¼ WW þ rH2 O  18  Air  ðf  fs Þ
dt

ð25Þ

where qw is the density of the liquid phase that is assumed water.
7. Energy balance
In order to construct the energy balance, it was taken into consideration that the heat flow in isobaric (constant pressure) processes is equal to the enthalpy change (Haug, 1980). The value of
specific heat at constant pressure varies depending on the component. The thermal balance is (Kaiser, 1996):

dQ dQ bio dQ ambient dQ intake dQ exhaust
¼

þ

dt
dt
dt
dt
dt

6. Gas phase

FAS ¼

fs ¼ 2; 40972  e0:029781ðT9=5þ32Þ  2; 22912  e0:02578ðT9=5þ32Þ

ð26Þ

where Q is the heat content of the composter, dQdtbio the evolution of
the heat loss by conduction from the
the bioreactions heat, dQ ambient
dt
intake
the heat flow via intake air and wastewater and
surface, dQ dt
dQ exhaust
the heat flow via exhaust air.
dt
The bioreactive evolution heat was considered directly proportional to the evolution of CO2 (5060 cal/gC) (Finstein et al., 1986),
thus

ð18Þ

where qp is the density of the particulate matter.
If co-composting process takes place in a reactor with a certain
volume as gas buffer (BF) the gas volume is calculated as:

V g ¼ BF þ FAS  V C

ð19Þ

Otherwise V g ¼ FAS  V C

ð20Þ

X dSi
dQ bio
¼ 5060 
dt
dt

ð27Þ

Heat loss by conduction from the surface is:

dQ ambient
¼ U  Ac  ðT  T a Þ
dt

ð28Þ

The molar balance equation for the components in the gas
phase is:

where U is the overall heat transfer coefficient of the surface, AC the
composter surface area and Ta the ambient temperature. The heat
flow via intake air is:

dni
¼ ni;intake  ni;exhaust þ V L  r i
dt

dQ intake
dAir
dWW
þ hintake;wastewater 
¼ hintake;air 
dt
dt
dt

ð21Þ

ð29Þ

A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

where h are the enthalpies of air streams and water, cp the specific
heat and
water vapor

hintake;air ¼ hintake

dry

þ hintake ¼ cvapor
 T intake  f þ cdry
p
p  T intake

ð30Þ

The heat flow via exhaust air is:

dQ exhaust
dV exhaust
¼ hexhaust 
dt
dt
water vapor
dry
where hexhaust ¼ hexhaust
þ hexhaust ¼ cvapor
 T  fs þ cdry
p
p T

ð31Þ
ð32Þ

4801

easy biodegradable carbon per g OSWR, 0.34 g difficult biodegradable carbon per g OSWR.
9.2. Olive mill wastewater
The water needs of co-composting process were fulfilled by olive mill wastewater (OMWW) produced in the same olive mill
plant in Crete, Greece. The composition of the OMWW, used for
all experiments is shown in Table 3. All parameters were analysed
according to standard methods (APHA, 1985).

8. Model evaluation
10. Experimental procedure
8.1. Materials and methods
8.1.1. Apparatus
In order to examine the model validity, a fully computerised
laboratory apparatus was designed and constructed (Fig. 2). The
programmable logic controller (PLC) used was Direct Logic 205.
The composter consists of a cylindrical double layered metal autoclave (10.058 L active volume) with a six wing anchor agitator. The
gas phase homogenization is achieved by continuous gas recycling.
A O2/CO2 gas analyzer (ADC 5000 Gas Analyzer) is included in the
gas-recycling line. During the bioreactions, oxygen is consumed
and carbon dioxide is produced, thus the oxygen partial pressure
tends to lower. The control of this parameter is performed by feeding dry atmospheric air according to the O2/CO2 gas analyzer’s
indications. Through a simple and fully handleable system the bioreactor may operate under constant pressure. The exhaust gasses
pass through a Wet Gas Meter (WGM) (Ritter Gas meter Drum type
TG01) and their moisture is removed by a water trap. Thus the carbon dioxide and the moisture of the gas phase can be estimated.
The wastewater is stored in a refrigerator (4 °C) in order to avoid
any undesirable biological degradation. The apparatus is able to
maintain constant moisture by wastewater addition through a Delta-T soil moisture sensor. The temperature inside the bioreactor
can be fully controlled through a Temperature Indicator Controller
(TIC) (SHIMADEN SR91 with a thermocouple PT100). The heating
of the reactor is achieved by the heating of the recycled gas. The
temperature of the recycled air is controlled under 80 °C. The bioreactor’s cooling is achieved by circulation of cool (4 °C) water between the layers of the reactor. Thus, due to the appropriate design
of this apparatus and its automations, temperature, oxygen partial
pressure and moisture could be kept constant to a predetermined
set point.
9. Raw materials
9.1. Olive stone wooden residue
Olive stone wooden residue (OSWR) was used as bulking material for the co-composting process. The OSWR samples were taken
from an olive mill plant in Crete, Greece. The main physical and
chemical characteristics of the OSWR used that were analysed
according to standard methods (APHA, 1985), are presented in
Table 2. The solid residues were classified by sieving (Fritsch,
ANALYSETTE 3 PRO) in order to estimate the initial particle size
distribution (Fig. 3). For the rest of the parameters like cellulose,
hemicellulose and lignin the methods of analysis that are cited in
Vlyssides et al. (1999) were used. In order to fractionate the composting particulate matter based on the model’s assumptions, cellulose and lignin (59.36% of TS) were considered as the difficult
biodegradable carbon, while proteins, sugars, fats and oils and
hemicellulose (28.41% of TS) as the easy biodegradable carbon
and the rest as inert matter (12.23% of TS). The same ratios were
adopted for carbon as well. Thus, this bulking material has 0.16 g

The experiments were conducted in a semi-batch mode; the
OSWR (6 kg) was loaded in the beginning of each experiment. During the 20 days experiment, parameters such as wastewater addition, exhaust gas flow rate and composition were continuously
recorded, while total solids, carbon, nitrogen, phosphorous and
phenolic compounds in the liquid phase were measured daily. Several experiments were conducted for the model evaluation. In all
experiments temperature, oxygen partial pressure and moisture
were controlled in a given set point. For the evaluation experiment
that is presented in the paper, the set points were for temperature
70 °C, for oxygen partial pressure 17% and for moisture 40%. From
the model’s implementation under these conditions, a deficit of
nutrients (nitrogen and phosphorous) was estimated. Thus, in the
beginning of the experiment, adequate amount of these nutrients
(70 g N and 30 g P) was added as di-ammonium hydrogen phosphate and ammonium carbonate.
11. Model inputs
Three different categories of data are required in the model: initial values (substrate composition), kinetic and operational parameters. Default kinetic parameter values used in the model are listed
in Table 4. The values have been obtained after a literature review,
choosing values with physical and biological sense in the framework of the developed model.
It has been reported that the hydrolysis constant for the whole
process ranged from 0.00324 to 0.1798 h1 (Laspidou and Rittmann, 2001; Sole-Mauri et al., 2007; Tremier et al., 2005; Veeken
and Hamelers, 1999). Haug (1980) reported that the constant of
hydrolysis rate is a function of temperature and this proposal
was adopted in this model. For easy biodegradable carbon the value of Haug (1980) was selected, while kh db was selected in the
range of the reported values for the whole process considering difficult biodegradable fractions. The densities of bacteria and fungi
were adopted from Bakken and Olsen (1983) and were equal to
577 and 580 gC/L respectively. As far as the depth of minimum
microbial layer is concerned, it was supposed to be equal to
1.6  104mm and 8.3  104mm for bacteria and fungi respectively. For the bacteria, the maximum uptake rate and the half-saturation concentration were considered in accordance with
Vlyssides et al. (2009), where the biokinetic constants for aerobic
degradation of the olive mill wastewater were determined. The
respective values for fungi were selected from Sole-Mauri et al.
(2007).
For the aerobic degradation of OMWW, the inhibition of phenolic compounds is well established in literature (D’Adamo et al.,
1984; Liu et al., 2002). Thus, phenolic compounds were chosen to
act as an inhibitor factor. In the model’s implementation, phenolic
compounds were considered to inhibit just bacterial growth with
an inhibition constant equal to 373 mg/L (Vlyssides et al., 2009),
whereas fungal growth was not inhibited by any factor (in Eq.
(8), fin = 1). Phenolic compounds were considered to be degraded

4802

A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

Fig. 2. Experimental apparatus of co-composting.

just by fungi following the same kinetics as the difficult biodegradable carbon hydrolysis product Sdb. It was also considered that phenols were released during the hydrolysis of both fractions of OSWR.
During the model’s implementation, apart from the carbon mass
balance, the mass balance of the phenolic compounds was also accounted for in order to monitor the formulation of the inhibitor
factor. Thus, in the phenolic compounds mass balance, the
wastewater content in phenolic compounds and their release
and
rates
during
hydrolysis
(0.08 gCphenol/gCPbhydrolysed
0.04 gCphenol/gCPdbhydrolysed) were considered.
All microorganisms were supposed to have a biomass yield
coefficient (Y) of 0.246 gC/gC (Sole-Mauri et al., 2007; Stombaugh
and Nokes, 1996). Stombaugh and Nokes (1996) and Sole-Mauri
et al. (2007) have previously described the saturation constant values used for substrate and oxygen that have been adopted in this

model. For nitrogen and phosphorous mass balances certain inputs
were needed. According to Haug (1980), the chemical formula of
aerobic bacteria is C5H7O2N, while of fungi is C10H17O6N. Thus their
nitrogen content is 0.23 gN/gC and 0.12 gN/gC. Phosphorous
contents were considered equal to 0.069 gP/gC for bacteria
and 0.033 gP/gC for fungi. From Tables 2 and 3, it derived
that NP = 2  102 gN/gChydrolysed, Php = 9  104 gP/gChydrolysed,
Nw = 1.15  103 gN/g wastewater, Phw = 2.3  104 gP/g wastewater.
12. Results
The model has been successfully used to simulate the operation
of the reactor in the experiment. Using MATLAB (MathWorks), the
differential equations described above were solved and the

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A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806
Table 2
Physical and chemical characteristics of OSWR in dry base.

Table 3
Composition of olive mill wastewater (OMW) used in experiments.

Parameter

Characteristics

Value (mg L1)

pH
Total
Total
Total
Total

4.2
42,500
230
1150
14,250

Moisture (%)
Fats and oils (% of TS (total solids))
Nitrogen content substances (% of TS)
Total sugars (% of TS)
Cellulose (% of TS)
Hemicellulose (% of TS)
Ash (% of TS)
Ether extraction substances (% of TS)
Lignin (% of TS)
Kjeldahl nitrogen content (% of TS)
Phosphorous content as P2O5 (% of TS)
Potassium content as K2O (% of TS)
Calcium content as CaO (% of TS)
Total carbon content (% of TS)
Carbon/Nitrogen ratio
Carbon/Phosphorous ratio

13.50 ± 0.52
1.85 ± 0.69
7.39 ± 0.037
2.13 ± 0.025
37.39 ± 0.438
17.04 ± 0.942
3.66 ± 0.225
8.61 ± 0.035
21.97 ± 0.45
1.093 ± 0.015
0.113 ± 0.008
0.83 ± 0.07
0.95 ± 0.092
56.13 ± 4.48
51.34 ± 4.52
1137 ± 99.11

response of the model was compared to the experimental data. Plots
of actual and simulated values are shown in Fig. 4. The wastewater
addition and exhaust gas flow which were parameters directly and
continuously recorded during the experiment were in good agreement with the predicted results. The wastewater addition was calculated from the implementation of the water mass balance that
was described by Eq. (25). This approach takes into account the
production of water from the biological reactions (Eq. (23)), the
saturation of exhaust gases in water as well as the progress of
the hydrolysis of particulate matter. The fact that the wastewater
addition predicted values follow the same exact pattern as the
measured values and present good numerical agreement indicates
that the model has managed to incorporate successfully all basic
processes (biological and physicochemical) involved in water consumption and production. As far as the exhaust gas flow rate is
concerned, given the good results that were obtained, the assumption that the liquid–gas phase transfer phenomena that were neglected did not reduce the credibility of the proposed model. The
good prediction of carbon dioxide flow indicates that the proposed
model describes adequately the biological activity.
Fig. 5 presents the nitrogen and phosphorous concentrations in
the liquid phase throughout the experiment. The consumption of
macronutrients was performed through biomass yield, while these
elements entered the system from the hydrolysis process and from
the wastewater. These results are also in good agreement with the
predicted values, reflecting the fact that the relative rates of all the
involved processes were sensibly assumed.

organic carbon
phosphorus
Kjeldahl nitrogen
phenolic compounds

The microorganisms performance is strongly related to the concentration of carbon and carbon dioxide production, as well as to
the concentration of the inhibitory factor (Figs. 4 and 5). Fig. 6 presents the biomass development of the different microbial populations considered in the model. This figure can provide useful
information for a better understanding of the data illustrated in
Figs. 4 and 5. Biomass from individual populations peaked at different times. Fungi were the first microorganisms to appear and grow,
since they were not inhibited by phenolic compounds. A lag phase
of approximately 72 h was observed before the growth of bacteria.
By the inhibitory factor’s depletion, bacteria became the predominant population. From Fig. 6, it is obvious that after a certain point
the biomass started to decrease, fact that indicates that the biomass that was produced was lower than the decayed one. The carbon dioxide production showed two main peaks, which reflect high
microbial activity. The first one can be attributed to the high availability of carbon from wastewater (initial value 42500 mg/L), while
the second one to the maximization of bacteria mass.
In Fig. 6 the reduction of the mass of bulking material (OSWR) is
presented. The model succeeded in predicting this mass reduction
during co-composting process and this is evidence that the phenomena of particulate matter’s hydrolysis were incorporated well
in the model. The results presented in this figure are in accordance
with literature since Hachicha et al. (2008) mention that a cocomposting mixture of olive cake (75%) and poultry manure
(25%) that was irrigated with olive mill wastewater presented a
44.4% organic mass loss after 27 days of co-composting in a
windrow. In the validation experiment the composting conditions
were fully controlled. Thus, a higher hydrolysis rate of the bulking
material was justifiable.
13. Discussion
Modelling the complex interaction between relevant and biochemical processes during co-composting represents a considerable challenge. The theory of co-composting is understood and
most of the forces involved are known, yet engineering of these

Fig. 3. Initial density distribution of OSWR.

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A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

Table 4
Default values for coefficients and parameters used in model evaluation.
Symbol
kh
kh

Name

b, T = 20 °C

db, T = 20 °C

lD

Units

Hydrolysis constant of easy biodegradable carbon in particulate
waste
Hydrolysis constant of difficult biodegradable carbon in particulate
waste
Maximum uptake rate for bacteria on Sb and Sw

d

0.0126 (Haug (1980))

d

1

0.00252 (Haug (1980))

ksb, kSBw

Maximum uptake rate for fungi on Sb and Sw
Half-saturation concentration of bacteria for Sb and Sw

mg C substrate/mgC
bacteriah1
mg C substrate/mgC fungih1
gC/L

kSdb, kSFw
kO2 ;B;T¼20
kO2 ;F;T¼20
bB
bF

Half-saturation concentration of fungi for Sdb and Sw
Oxygen saturation constant for bacteria
Oxygen saturation constant for fungi
Death constant for bacteria
Death constant for bacteria

gC/L
g/L
g/L
h1
h1

lF

Value

1

0.447/1.55 (Vlyssides et al. (2009))
0.122 (Sole-Mauri et al. (2007))
0.00289  1.07355(20T) (Vlyssides et al.
(2009))
0.195  1.07355(20T) (Haug (1980))
2  106 (Sole-Mauri et al. (2007))
7  106 (Sole-Mauri et al. (2007))
0.03 (Sole-Mauri et al. (2007))
0.01 (Sole-Mauri et al. (2007))

Fig. 4. Actual and simulated values of the instant wastewater addition, exhaust gas and carbon dioxide flow rates.

Fig. 5. Actual and simulated values of soluble carbon, phenolic compounds and nutrients (nitrogen and phosphorous) concentrations in the liquid phase.

systems is still conducted using ‘‘handbooks” approach with limited knowledge of how to control these forces to achieve the final
end product. Composting kinetics modeling is a scientific topic

well established in literature, whereas co-composting kinetics
has not yet been cited (Haug, 1980; Kaiser, 1996; Mason and Milke,
2005; Sole-Mauri et al., 2007).

A. Vlyssides et al. / Bioresource Technology 100 (2009) 4797–4806

4805

Fig. 6. Actual and simulated values of the mass of bulking material (OSWR) and representation of biomass development of the different microbial populations (bacteria and
fungi).

Composting kinetic models are generally inductive models. The
inductive approach seems to have reached its practical limit. The
deductive approach seems therefore an additional fruitful direction
to investigate composting kinetics. Care should however be taken
not to develop models with non-identifiable parameters, as deductive models of complex systems like composting contain many
parameters. To prevent this situation it is proposed that a model
should be constructed with combined parameters, i.e. fewer
parameters that are identifiable however still a clear relationship
with the basic parameters has. The advantage of this approach is
that it enables to use information from existing knowledge (as represented by the basic parameters) with the information retained in
the data (as represented by the identifiable combined parameters)
(Hamelers, 2004). Thus, taking into consideration the mathematical models of composting process, their performance and limitations, a new model describing the co-composting process was
proposed.
It is known that simplifications of the whole process as a nonbiological process described by a first order kinetics or considerations of it as a ‘‘single organism and substrate” system didn’t
manage to fully describe composting process. It was not until Kaiser (1996) and Sole-Mauri et al. (2007) that the active biomass was
divided into different populations, each specialized in certain categories of substrate available in the liquid phase. Kaiser (1996) proposed that the first trophic level was described as a consumption of
four substrates by a four-component microflora, while Sole-Mauri
et al. (2007) proposed an even more complicated system with six
polymeric substrates, which were hydrolysed and consumed by
six microbial populations. Each population had particular substrate
specificity. In an innovative approach, the present model combined
the fractionation of the compostable waste into only three fractions and the introduction of hydrolysis for each fraction according
to the two-phase model for hydrolysis kinetics (Vavilin and Rytov,
1996). Another innovative point in the proposed model was that
the wastewater carbon content could be consumed by both microbial populations. As in other works, biomass growth was modelled
by multiple Monod kinetics for organic substrate and oxygen. In
the model presented here, growth limitation due to inhibitory factors was implemented by including a term in the general growth
kinetic expression. In the model evaluation, this parameter turned
to be crucial. The mass balances of the most important nutrients,
nitrogen and phosphorous, were included in this approach. They
were considered to be immobilized due to microbial growth, while

they were released in the liquid phase through hydrolysis of the
particulate matter and wastewater addition. The principle of mass
and energy conservation represented another cornerstone of the
model.
Simulations generated with the new model fitted the experimental measurements on the time-course exhaust-gas flow and
composition, as well as wastewater addition. The description of
the biological reactions as well as the liquid–gas equilibrium was
adequate enough to represent the co-composting process. The
reduction of particulate waste mass was in good agreement with
the model predictions, enforcing the assumption for hydrolysis
kinetics. Furthermore, the microbial community dynamics were
depicted in the simulated results and followed the pattern proposed in composting systems (Sole-Mauri et al., 2007). The biomass yield and hydrolysis rates were also validated given the
successful representation of the macronutrients concentration
throughout the experiment. From the validation experiment, it
was revealed the selection of the inhibitory factor was crucial. A
possible omission would lead to devious results that would underestimate the credibility of the model. It of vital importance for a
sound implementation of the model to be familiarized either
experimentally or from literature with the biological kinetic
parameters of the raw materials of the co-composting system.
Generally, the simulation results justified the classification of substrate range and microbial range as well as the model’s assumptions on substrate utilisation.
14. Conclusions
An integrated model for the co-composting of solid wastes with
industrial wastewater was developed. The model of co-composting
ecosystem included mass transfer, heat transfer and biological processes. Two microbial populations (bacteria and fungi) were selected using Monod kinetics. The mass balances of the most
important nutrients, nitrogen and phosphorous, were also included
in this approach. Model computer simulations provided results
that fitted satisfactory the experimental data. In summary, the
model represents a valuable tool that will contribute to the understanding of the complex biological and physicochemical interactions of co-composting and will be essential for the design and
operation of co-composting units in compliance with strict market
demands and tight environmental legislation. Further research is
directed to calibrate and validate the model in an even wider range

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of operational conditions and raw materials. For an even more
integrated composting model, the gas–liquid transfer coefficients
should be incorporated in the model. A biomass growth limiting
factor that would take into account the macronutrients availability
should also be incorporated in order to predict the performance of
the biological system in case of nutrients depletion.
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