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CONVERSION EFFICIENCY OF ORGANIC MATERIAL
TO METHANE
HELENICE O. FLORENTINO, ADRIANA F. V. BISCARO, JORGE DE LUCAS
JÚNIOR
Depto de Bioestatística IB, PG FCA, Depto de Engenharia Rural FCAV
UNESP
Depto de Bioestatística do Instituto de Biociências da Unesp, Botucatu SP
Brazil
Abstract: - The conversion of organic material to methane and carbon dioxide by
microbiological activity consists of consecutive, parallel, and independent reactions which make
up a very complex biological process. Microbial ecology studies of this digestion process have
shown that the conversion to biogas has six stages (polymer hydrolysis, fermentation of amino
acids and sugars, oxidation of acid and alcohol products from the previous phase, oxidation of
intermediary volatile acids, conversion of both acetate and hydrogen to methane). From this it is
possible to simulate the anaerobic process and predict biomass variation, and biogas production
and composition. This work studies mathematical models using Monod techniques and
predicting the efficiency of converting organic material to methane and carbon dioxide in
relation to retention time. We also propose a method to calculate optimum digestion efficiency
for total solids and volatiles. These techniques are proposed to help study methane production
efficiency in biodigesters.
Keywords: - Mathematical models, anaerobic digestion, treatment efficiency,
biodigester.
1 Introduction
From this, there is a growing
There is worldwide concern
need to understand techniques that
about renewable energy generation and
allow the rational use of available
environmental protection. These issues
energy, and to look for alternative
have much in common, because they
sources to oil in both energy production
deal with the increasing energy demand
from raw material and raw-material use
from several primary sources, favoring
in industries. In this way, biodigesters
the easiest extraction methods. In this
could have a very important role [1],
way oil, coal, and natural gas have
[2], [3], [7], [8], [9] and [11].
assumed the predominant role. They
Anaerobic digestion stands out
cause the highest environmental impact
from other microbiological sources of
when burnt or transformed.
energy; it is a fermentation process
where several bacteria species transform
and methane (CH4) in an anaerobic
organic material into a gaseous mixture,
biodigester.
biogas.
The
conversion
of
organic
There are studies in literature
material to methane and carbon dioxide
with mathematic techniques to help
by microbiological activity consists of
understand
which
consecutive, parallel, and independent
organic
reactions with a very large number of
material to methane and carbon dioxide
microorganisms involved in a very
which make use of mathematic models.
complex biological process. Microbial
These models can be used to predict
ecology studies of the digestion process
various parameters in the anaerobic
have shown that conversion to biogas
digestion
could
processes
microbiologically
convert
process
(retention
time,
be in
six
stages
(polymer
temperature, etc), which could help
hydrolysis, fermentation of amino acids
biodigester
and sugars, oxidation of acid and
efficiency
in
methane
production.
alcohol products from the previous
According to [13], anaerobic
phase,
oxidation
of
intermediary
biodigester mathematical models are
volatile acids, conversion of both
formulated
acetate and hydrogen to methane).
species
by
and
observing
bacteria
environments
and
Based on this, it is possible to simulate
extracting the main variables which
the anaerobic process and predict,
influence their growth or reduction.
biomass
These
production and composition. Some
models
describe
substrate
variation,
and
variation in a biodigester, in which it is
mathematical
assumed that bacteria growth depends
developed to simulate this conversion
on substrate quantity, and that substrate
process, but many use extensive and
consumption is viable.
complex experimental data making the
Merkel,
approximate
[12],
theoretical
estimated
values
models
have
biogas
been
models complex and difficult to use.
to
More simple models have been
calculate mass transfer by analyzing
found that can help in biodigestion
experimental data from a mathematical
projects,
model which described the anaerobic
optimization tool and helping in the
digestion process. The author discussed
analysis of experimental data. For this,
the controlling factors that influenced
the microorganisms can be divided into
mass transfer of carbon dioxide (CO2)
smaller groups, according to certain
serving
as
a
process
characteristics. Monad’s model has
often been used; it groups all the
anaerobic digestion processes into two
conversion processes, first, the biomass
2 The Anaerobic Digestion Process
The
conversion
of
organic
components are converted into volatile
material to methane and carbon dioxide
acids by a group of acetogenic bacteria,
by microbiological activities consists of
second, the acids produced by the first
consecutive, parallel, and independent
group are converted to methane and
reactions and involves a very large
carbon dioxide by another group of
group of microorganisms performing a
methanogenic bacteria, and the kinetics
very complex biological process. This
of anaerobic digestion are applied
conversion could be in six stages to
separately to each of these groups.
arrive at biogas (polymer hydrolysis,
Observing these kinetic parameters,
fermentation of amino acids and sugars,
mathematical modeling can be applied
oxidation of acid and alcohol products
to
from the previous phase, oxidation of
anaerobic
system
operation [4], [5] and [6].
design
and
intermediary volatile acids, conversion
of both acetate and hydrogen to
methane) as illustrated in Figure 1.
Complex organic
(carbohydrates, proteins, lipids)
Fermentative bacteria
(hydrolysis)
Simple organic
(sugars, amino acids, peptides)
Fermentative bacteria (Acidogenesis)
Organic acids
(acetic, propionic and butyric)
Acetogenous bacteria (Acetogenesis)
Acetogenous bacteria hydrogen producers
H2 + CO2
acetate
Acetogenous bacteria hydrogen consumers
Methanogenous bacteria
(Methanogenesis)
CH4 + CO2
Hydrogentrophic methanogenic bacteria
Acetoclastic methanogenic bacteria
Fig. 1 Metabolic sequence and microbial groups involved in anaerobic digestion
substrate concentration where  = m/2
2.1 Kinetics of Digestion
This section aims to determine
the
equations
microorganism
for
The combination of (1) and (2),
effluent
concentration
and
gives us an equation relating bacterial
growth with substrate use.
substrate concentration.
Bacterial
(g m-3).
growth
can
dX
S
 μm .
.X
dt
ks  S
be
expressed as a function of actual
(3)
bacteria concentration in the reactor at a
Considering the reduction in
particular moment in time. The gross
microorganisms due to the endogenous
growth rate of a bacteria population is a
metabolism, net microorganism growth
function of this number, mass or
rate can be expressed as:
concentration and a particular moment
in time. This rate could be expressed in
dX
S
 μm .
.X  k d X
dt
ks  S
where
the form of an equation (1).
kd
is
the
coefficient
(4)
of
endogenous respiration, d-1.
dX
 μX
dt
(1)
On the other hand, we remember
where, X is the concentration of
that the bacterial mass equilibrium
microorganisms in the reactor, SS or
equation is:
SSV g m-3;  is the specific growth rate,


dX
S
V  Q X0  QX  V μ m
X  k d X 
dt
 ks  S

d; t is the time, d.
The growth rate (1), is used for
growth without substrate limitation.
[10], confirmed that the effect of a
limiting substrate or nutrient could be
adequately
expression,
defined
as
in
using
Monad’s
the
following
where, V is reactor volume, m3; Q is the
rate of in or outflow, m3 d-1; X0 and the
concentration of influent suspended
solids, mg L-1 or g m-3.
According to Tchobanoglous,
[10], ignoring influent microorganism
concentration and considering that there
equation:
S
μ  μm .
ks  S
(5)
was no accumulation in the steady state
(2)
where,  is the specific growth rate, d-1;
condition (dX/dt = 0, X0 = 0), equation
(5) could be written as:
Q
S
 μm .
 kd
V
ks  S
m is the maximum specific growth
rate, d-1; S is the concentration of
Using hydraulic retention time,
growth-limiting substrate, g m-3; ks is
the constant of saturation, defined as the
(6)
θ 
V
1
S
, we have:  μ m .
 k d (7)
Q
θ
ks  S
Using the maximum utilization rate
2.2 Anaerobic Digestion Efficiency
of substrate per unit of microorganism mass
In this section is presented the
(k), k 
μm
, where Y is the coefficient of
Y
cellular production, in gSSV (g(DQO))-1 in
equations (6) and (7) we have:
(8)
model
to
predict the efficiency of conversion for
organic material to biogas by anaerobic
that the anaerobic digestion is two
conversion processes, first the biomass
From (8) we have:
components are converted into volatile
(1  θ k d) ks
S
θ(Yk  k d)  1
is
mathematical
digestion, [4]. This author considered
1 kYS

 kd
θ ks  S
Which
Jeyaseelan
the
(9)
equation
to
acids by a group of acetogenic bacteria,
second, these acids are converted to
methane and carbon dioxide by another
determine substrate concentration.
In function of substrate use, one
part is converted by new cells and the
other is oxidized into final inorganic
and organic products. The equation
which describes the solids balance is:
group of methanogenic bacteria. To
apply
the
model,
the
residue
is
considered as a mixture of carbohydrate
(C), protein (P), lipids (L) and a very
small proportion of other materials, and
are known the percentages of each of
dS
V  Q S0  QS  Vμ
dt
(10)
these components. These components
where, S0 is influent concentration of
biodegrade independently, without any
growth-limiting substrate, g m-3.
interactions within the intermediate
substrate
compounds, except in the second stage
concentration, as it does not accumulate in
where the combined volatile acids are
the steady state condition (dS/dt = 0), from
degraded to produce biogas. Figure 2
Ignoring
influent
 kYS 

 ks  S
(10) we have: So  S  θ
illustrates this conversion.
(11)
incorporating the new concepts to
From (7) and (11) we have:
 1

So  S  θkX
 kd 
 θμ m μ m 
consider carbohydrates, lipids, proteins,
(12)
From (12) we therefore have the
equation for effluent microorganism
(S0  S)Y
1  kd θ
and
the
organic
substances
substituted
i
(13)
other
separately, equations (9) and (13) are
X1  
concentration:
X
In the first phase of conversion,
by:
Yi (Soi  S1i )
i  C, L, P, O (14)
(1  θk di )
and S1   S1i
i
i  C, L, P, O
(15)
k si (1  θk di )
θ(Yi k i  k di )  1
Where S1i 
other organic compounds, the initial
concentrations can be expressed as parts
and the sub-index 1 indicates phase 1 of
of
the conversion process.
concentration.
The substrate in solution in the
the
total
influent
The
substrate
individual
concentrations are represented by:
S oi  c o a o a Si 100 , i  C, L, P, O
acid formation phase, represented by S1,
(18)
is the feed substrate for the methane
where, c0 is the influent residue
formation phase, and therefore, the final
concentration, %; a0 is the volatile
concentration of substrate in solution
solids concentration, %; asi is the ratio
and microorganism mass which forms
of component i/volatile solids;
the methane are given by the following
equations:
X2 
and
arrive at the mathematical model for
Y2 (S1  S 2 )
(1  θk d2 )
S2 
With these parameters, we can
(16)
digestion efficiency, or the percentage
of biogas produced based on total solids
k s2 (1  θk d2 )
θ(Y2 k 2  k d2 )  1
(E) and volatile solids (EV).
(17)
E
where sub-index 2 indicates phase 2 of
(c o a o 100  S2  X1  X 2 )
100 (19)
c o 10000
and
the process.
As the waste is composed of
EV  
carbohydrates, lipids, proteins, and
(c o a o 100  S2  X1  X 2 )
100 100
c o a o 10000
(20)
Organic Material
Carbohydrates
(C)
Lipids
(L)
Proteins
(P)
Other Organics
(O)
Phase 1
Bacteria
(X1)
Organic Acid
Others
Phase 2
Microorganisms
(X2)
Biogas
Fig. 2 The Conversion process using the Jeyaseelan mathematical model.
volatile solids can be estimated by
k si (1  θk di )
θ 
θ
i
i i  k di )  1
k / θ  k di k si
 lim  si
θ  
i (Yi k i  k di )  1/θ
equations (19) and (20). The object of

3 Digestion Efficiency Optimization
According to Jeyaseelan , [4],
digestion efficiency based on total and
lim S1  lim
i
this section is to find the optimum value
of E and EV in function of retention
time θ , or to determine the retention
time
that
efficiency,
maximizes
k di k si
(Yi k i  k di )
Then:
lim S1  
θ
i
digestion
E  E( ) . For this the
θ
Maximize E (θ)
(21)
subject to :
{S1  0, S 2  0, X 1  0, X 2  0, θ  0}
Efficiency
E
in
terms
of
retention time has the following curve:
k si k di
i  C, L, P, O. (22)
(Yi k i  k di )
In the same way with S2 we have:
lim S2 
following model is proposed:
 θ(Y k
k s2 k d2
(Y2 k 2  k d2 )
(23)
For X1 and X2 we have:
lim X1  lim
θ 
θ

i
Yi (S 0i  S1i )
 0 (24)
(1  θk di )
and
Y2 (S1  S 2 )
 0 (25)
θ   (1  θk )
d2
lim X 2  lim
θ  
From (22), (23), (24) and (25)
we have:
 (d)
k d2 k s2
Y2 k 2  k d2 (26)
c o 100
c o a o 100 
Fig. 3 Curve for digestion efficiency in
E max  lim E(θ) 
terms of hydraulic retention time ().
θ  
In the same way, for the
As can be seen in Figure 3,
digestion efficiency increases according
digestion efficiency of volatile solids,
the maximum is given by:
to a horizontal asymptote, or tending to
a
value
Emax,
which
could
be
k d2 k s2
Y2 k 2  k d2
100
c o a o 100
c o a o 100 
E v max  lim E v () 
θ 
determined solving the limit:
E max  lim E(θ)
θ  
Thus
maximum
an
upper
anaerobic
limit
(27)
for
digestion
To analytically determine the
efficiency was determined. However
limit of E, we calculated the following
this needs a very high retention time
limits:
which is not viable in practice; this
value can be used as an analysis
parameter of efficiency and retention
time control.
References:
[1] Chanakya, H.N.; Venkatsubramaniyam,
R.;
Modak,
J.
Fermentation and methanogenic
4 Acknowledgements
The authors are grateful to
characteristics of leafy biomass
(grant
feed stocks in a solid phase
numbers 557-01-DCP, 250/04-DFP and
biogas fermentor, Bioresearch
030/2004-PROINTER/PROPP) for their
Technology, v. 62, 1997, p.71-
support.
78.
FUNDUNESP
and
PROPP
[2] Groscurt, H.M.; Almeida, A.;
Bauen, A.; Costa, F.B. Total
5 Conclusions
Mathematical
anaerobic
system
modeling
projects
in
and
operations is a valuable prediction tool.
It contributes to the understanding
inherent phenomena in the process and
The model proposed by [4] to
estimate the efficiency of anaerobic
digestion in the conversion of organic
material to biogas is simple and easy to
influence
of
hydraulic
retention time on anaerobic digestion
efficiency is a limiting factor, because
depending on treatment and residue
type, a long retention time is not viable.
The optimization model proposed here
is a good tool to help in the analysis of
confidence
Union, Energy, v. 25, 2000,
p.1081-1095.
[3] Hall, D.O. Biomass energy in
of the future, Forest Ecology
and Management, v. 91, 1997,
p.17-45.
[4] Jeyaseelan,
S.,
Mathematical
calculate.
efficiency,
selected regions of the European
industrialized countries-a view
helps in the practical limitations.
The
costs and benefits of biomass in
giving
to
the
establish
hydraulic retention time.
operator
the
best
A
Simple
Model
for
Anaerobic Digestion Process.
Wat. Sci. Tech. V 35(8), 1997,
pp. 185-191.
[5] Lasdon,
L.
S.
Optimization
theory for large systems, New
York: Macmillan, 1970.
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Linear
and
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Martinhão, N. Dinâmica
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