http://www.bioeng.ca/pdfs/journal/2009/c0807.pdf, 26/10/2010 jam 14.00 wib
Three-dimensional numerical simulation
model of
biogas production for anaerobic digesters
B. Wu1*, E.L. Bibeau2 and K.G. Gebremedhin3
1Philadelphia Mixing Solutions, Palmyra, PA 17078, USA; 2Department of Mechanical and
Manufacturing Engineering,
University of Manitoba, Winnipeg, Manitoba, R3T 5V6 Canada; and 3Department of Biological and
Environmental
Engineering, Cornell University, Ithaca, NY 14853, USA. *Email: bxwulk@hotmail.com
Wu, B., E.L. Bibeau and K.G. Gebremedhin. 2009. Threedimensional
numerical simulation model of biogas production for
anaerobic digesters. Canadian Biosystems Engineering/Le ge´nie
des biosyste`mes au Canada. x.1_x.1. A three-dimensional numerical
simulation model that predicts biogas production from a
plug-flow anaerobic digester is developed. The model is based on
the principles of conservation of mass, conservation of energy,
and species transport. A first-order kinetic model is used to
predict the forward reaction rate in the digestion process. A userdefined
function for computing the source terms of the reaction
rate in the species transport is developed. CFD (computational
fluid dynamics) simulations are conducted using Fluent 6.1 to
predict the temperature profiles and concentration distributions
in the digester. Model prediction is checked against measured
biogas production obtained from the literature. The predicted
and measured results agree within 5%. Biogas production
sensitivity to chemical reaction rates is numerically determined.
This simplified first-order kinetic model is part of an overall
effort to develop a three-dimensional numerical model that can
link digester-process controls, fluid flow conditions and anaerobic
digestion for different digester design, climatic conditions and
manure compositions. Keywords: numerical simulation,
anaerobic digester, chemical reaction, biogas production,
sensitivity analysis, renewable energy.
Une simulation utilisant un mode` le nume´rique en trois
dimensions est de´veloppe´e pour pre´dire la production de biogaz
d’un digesteur anae´robie. Le mode` le est fonde´ sur les principes de
la conservation de la masse, de l’e´nergie, et du transport des
espe`ces. Un mode` le de premier ordre cine´tique est utilise´ pour
pre´dire les vitesses de re´action pour le processus de digestion.
Une fonction est de´ finie pour calculer la vitesse de re´action des
l’espe` ce. Les simulations nume´riques sont effectue´es avec Fluent
6.1 pour pre´dire les profils de tempe´rature et de concentration
des espe`ces dans le digesteur. Les re´sultats du mode` le nume´rique
sont ve´ rifie´s en comparant la production de biogaz obtenu a`
partir de donnes disponible en litte´rature. La comparaissions des
re´sultants nume´rique avec les mesure ont une erreur the 5%.
L’impact de la sensibilite´ des re´actions chimiques a` la production
de biogaz est e´value´ . La simplification de premier ordre cine´tique
fait partie d’un effort visant a` de´velopper un mode` les nume´riques
en trois dimensions qui lie le processus de control dans les
digesteur anae´robie avec la dynamique des fluide et les conditions
de digestion anae´robie pour divers conception de digesteur,
conditions climatiques, et compositions de fumier.
Motscle´s: simulation nume´rique, digesteur anae´robique,
re´action chimique, production de biogaz, analyse de sensibilite´ ,
e´nergie renouvelable.
INTRODUCTION
Through anaerobic digestion, cow or swine manure can be
a source of energy. At the same time, the process reduces
the solid content of the material and produces less
offensive odors. Microorganisms break the organic compounds
into microbial biomass and other simpler compounds
eventually releasing water, carbon dioxide, and
methane. Biogas production using anaerobic digesters has
been experimentally and theoretically studied since the
early 1950s (Buswell and Mueller 1952), and modeling of
the process have evolved from simple models (Chen and
Hashimoto 1978; Hill 1982, 1983; Hashimoto 1983, 1984;
Safley and Westerman 1994; Toprak 1995; Vartak et al.
1999) to complex ones (Masse and Droste 2000; Batstone
et al. 2002; Minott 2002; Blumensaat and Keller 2005).
The simple models predict biogas by solving empirical
algebraic equations without considering the fundamental
biochemical reactions involved in the processes. In addition,
since the models are not general, they are good only
for the conditions they were based on. The complex
models, however, are general and include biochemical
reactions and contain more inputs. The inputs include:
hydraulic retention time (HRT), initial volatile solids (VS)
concentration, bacterial growth rate, digester volume, flow
rate of manure, and biochemical reactions. Out of the
complex models known to us, the ADM1 (Batstone et al.
2002) is the most comprehensive anaerobic digestion
model that includes multiple steps describing biochemical
and physico-chemistry processes.
Biogas production is sensitive to digester temperature,
pH of the liquid manure (Angelidaki and Ahring 1993;
Angelidaki et al. 1999; Keshtkar et al. 2003; Yilmaz and
Atalay 2003), and non-uniformity of flow of liquid
manure inside the digester (Fleming 2002; Vesvikar and
Al-Dahhan 2005). These parameters are time and spatially
dependent. All the biogas production models mentioned
previously but Minott (2002) are either algebraic or timedependent
differential equations without considering the
spatial coordinates.
With the simple models, biogas or methane prediction
is generally a function of manure temperature inside the
digester. For example, Chen and Hashimoto (1978)
predicted methane production rate as a function of volatile
Volume 51 2009 CANADIAN BIOSYSTEMS ENGINEERING 8.1
solids concentration, kinetic parameter, and specific
growth rate, which is dependent on manure temperature.
Hill (1982) used Chen and Hashimoto’s (1978) model and
performed a computer analysis of microbial kinetics of
methane fermentation and determined the maximum
volumetric methane production. Hashimoto (1983) studied
the effects of temperature (35 and 558C), volatile
solids concentration and hydraulic retention time on
methane production from swine manure, and developed
a mathematical formulation for calculating methane
production rate as a function of a kinetic parameter (K).
Later, Hashimoto (1984) experimentally determined the
kinetic parameter specific for swine manure. He concluded
that K increased exponentially as the volatile solids
concentration (S0) increased, and manure temperature
had no significant effect on K for S0 between 33.5 and 61.8
kg VS m_3.
Safley and Westerman (1994) studied methane yield in
a low-temperature digestion system. They reported a
linear relationship between methane yield and temperature.
In another study by Toprak (1995), however, a
power-law relationship between biogas production and air
temperature was reported. Vartak et al. (1999) experimentally
determined biogas production based on loading rate
of volatile solids at a specific low temperature (108C). In
addition to digestion temperature, pH of the liquid
manure is another important variable in biogas production.
Angelidaki and Ahring (1993) studied the effect of
pH and temperature on the growth rate of microorganisms
for thermophilic digestion of cattle manure. Later,
Angelidaki et al. (1999) extended their previous work to
develop a dynamic model involving co-digestion of
different types of wastes. Similarly, Keshtkar et al.
(2003) developed a mathematical model for anaerobic
digestion that describes the dynamic behavior of non-ideal
mixing of continuous flow reactors, and concluded that
methane yield was strongly dependent on pH of the
reactor and increased with increasing HRT. Yilmaz and
Atalay (2003) addressed the effect of various factors
including pH and alkalinity, temperature, nutrients, and
toxins on anaerobic bacteria behavior, and pointed out
that the optimum pH range for anaerobic digestion is
between 6.8 and 7.5, and the optimum temperature for
mesophilies appears to be around 358C.
The complex models are more general and include
more factors than the simple models. Masse and Droste
(2000) conducted a comprehensive literature review on
anaerobic digestion models and developed an improved
mathematical model for a sequencing batch-reactor process.
They expressed volumetric methane flow rate as a
function of volume of 1 mole of gas, volume of liquid in
the reactor, and biological activity.
Minott (2002) developed a model based on a moving
coordinate system that yields total biogas prediction for a
plug-flow digester. The model is a function of HRT, total
volatile solids, total substrate degradation, digester volume,
and operation temperature. Batstone et al. (2002)
developed a general anaerobic digestion model based on
biochemical processes (including acidogenesis from sugars,
amino acids, long-chain fatty acids, propionate,
butyrate and valerate, aceticlastic methanogenesis, and
hydrogenotrophic methanogenesis). This model contains
34 differential and algebraic equations and another 32
differential equations. The differential equations are functions
of time but are not functions of position. Blumensaat
and Keller (2005) did several modifications to the original
ADM1 model, which include: extension to a pilot-scale
digestion process, calibration to a two-stage thermophilic/
mesophilic process configuration, and for use with municipal
sewage sludge.
Several researchers (Fleming 2002; Vesvikar and AlDahhan 2005; Grebremedhin et al. 2005; Wu and Bibeau
2006; Wu and Chen 2008) studied heat transfer and fluid
flow in anaerobic digesters using CFD technique. Fleming
(2002) applied CFD to simulate 3-D flow patterns and
heat transfer inside a covered lagoon digester. He took the
simple kinetic model developed by Hill (1983), modified it
by incorporating CFD formulation to calculate biological
reaction rates and methane production rates. Vesvikar and
Al-Dahhan (2005) performed 3-D, steady-state, CFD
simulations to determine the flow patterns inside a digester
and to compute hydrodynamic parameters. Grebremedhin
et al. (2005) developed a CFD-based one-dimensional
comprehensive heat transfer model on plug-flow anaerobic
digesters. Later, Wu and Bibeau (2006) extended the 1D model developed by Gebremedhin et al. (2005) to a 3-D
heat transfer model on anaerobic digesters under cold
weather applications. Wu and Chen (2008) simulated 3-D
flow fields in lab-scale, scale-up, and pilot-scale anaerobic
digesters by assuming liquid manure as a non-Newtonian
flow, and proposed measures to reduce dead and low
velocity zones. These models did not include biochemical
reaction to predict biogas production.
To our knowledge, no three-dimensional numerical
simulation model that predicts biogas production from
anaerobic digestion systems that is based on fundamental
principles of biochemical processes exists. The goal of this
research is to fill that gap. The model is the first step in
developing an application tool that could be used to
evaluate the performance of plug-flow anaerobic digesters.
Extensive validation would, however, be required before
the model is used as an application tool.
Objectives
The specific objectives of the study are:
1. To develop a general 3-D model based on fundamental
principles of conservation of mass, conservation
of energy, and species transport that predicts
biogas production from plug-flow anaerobic digesters;
2. To simulate the temperature and concentration fields
in a digester by using Fluent CFD commercial
computer software;
3. To check model prediction against measured data
available in the literature; and
4. To conduct sensitivity analysis to determine the effect
of reaction rate on biogas production.
8.2 LE GE´ NIE DES BIOSYSTEMEZ AU CANADA WU ET AL.
MODELDEV ELOPMENT
Biogas production in an anaerobic digester is a chemical
reaction process, which is governed by conservations of
mass and momentum, turbulence, energy balance, species
transport, and chemical reactions. Because anaerobic
digestion is dependent on process flow parameters and
temperatures, prediction of temperature and flow variables
is critical to solve the species transport.
This model was developed based on the following
assumptions:
. Heat flow and species transport through the digester
are 3-D and steady.
. The model is limited to plug-flow anaerobic digesters
where fluid flow velocity is very low. Thus, momentum
and turbulence are considered to be negligible.
. Boundary conditions for the digester cover, walls, and
floor are assumed to be adiabatic (Wu and Bibeau
2006).
. Liquid manure is considered to be Newtonian.
. Manure temperature is kept constant at 328C before
species reaction.
. PH range is between 6.8 and 7.5 (Yilmaz and Atalay
2003).
. Species reaction takes place only in one step, i.e.,
reactants are directly converted into final product
without intermediate products.
. After reaction (C6H12O6) remains at 80%.
. The model is single phase, in which phase-interaction is
negligible, and thus, rise of biogas to the surface has no
effect on manure transport.
Mass conservation equation
The conservation of mass or continuity equation used is
expressed as:
@r
@t
_
@
@xi
(r ui)_0 (1)
Energy equation
The energy equation used is of the form (Patankar 1980):
@
@t
(rE)_
@
@xi
(ui(rE_p))
_
@
@xi
_
keff
@T
@xi
_X
j
hj J
0
j _uj(tij)eff
_
_Sh (2)
where the first three terms on the right-hand side of the
equal sign represent energy transfer due to conduction,
species diffusion, and viscous dissipation, respectively. Sh
includes heat of chemical reaction and any other volumetric
heat sources.
Species transport equations
The species transport equations for liquid manure can be
written in a general form as (Patankar 1980):
@
@t
(rYj)_
@
@xi
(r ui Yi)_
@
@xi
J_ i_Ri (3)
For mass diffusion in laminar flow, the diffusion flux, J_ i;
is computed as
J_ i_rDi;m
@Yi
@xi
(4)
Chemical reaction equations
The initial conversion of raw waste to soluble organics can
be expressed as (Chang 2004)
C6H13NO5_H2O_H_ 0 C6H12O6_NH_
4 (5)
In this study, methane production was simplified by
converting (C6H12O6) into CH4 and CO2 through chemical
reaction (Buswell and Mueller 1952) as
CnHaOb_
_
n_a
4
_b
2
_
H 2O
U
_n
2
_a
8
_b
4
_
CO2_
_n
2
_a
8
_b
4
_
CH4 (6)
where (CnHaOb) is organic matter, and a, b, and n are
dimensionless coefficients.
By substituting n_6, a_12 and b_6 into Eq. (10),
the chemical reaction of (C6H12O6) results in
C6H12O6_3CO2_3CH4 (7)
There are three species in the mixture. One species, Y1,
representing the reactant (C6H12O6) and the other two
species, Y2, and Y3, representing the simplified biogas
products, CO2 and CH4, respectively.
Modeling reaction rate
The reaction rate can be computed using the Arrhenius
expression as
Ri_Mw;i
X NR
r_1
Rˆi;r (8)
where, Rˆi;r is molar rate of creation or destruction of
species i in reaction r, which is calculated as:
Rˆi;r_(ni;r ƒ _ni;r ? )
_
kf ;r
YNr
j_1
[Cj;r]hj;r ?
_
(9)
Information for kf ;r is not available in the literature. In
this study, kf ;r is calculated by using first-order BOD
removal rate in an ideal plug-flow reactor (Metcalf and
Eddy 2003) as:
C
C0
_exp(_kf ;r _t) (10)
Volume 51 2009 CANADIAN BIOSYSTEMS ENGINEERING 8.3
where, C/C0 is percentage remaining of (C6H12O6). The
hydraulic retention time, t, is calculated as
t_L
n
(11)
where, the velocity of liquid manure, v, can be calculated
as
n_
V˙
A
(12)
Accordance to our assumption, if C/C0_80%, then,
kf,r_6.21_10_8(s_1).
CFD SIMULATION
The commercial CFD software Fluent 6.1 (Fluent 2005)
was used to model biogas production. The mesh of the
digester geometry was generated by using the Gambit
Software (Fluent 2005). The computational domain that
characterizes the liquid manure inside the digester consisted
of 31,480 hexahedral grids.
The modeling procedure includes the following steps:
1. Verify the grid.
2. Solve the 3-D, steady state, implicit, and pressurebased
model by activating the continuity, energy, and
species transport equations. The model accounts for
volumetric reactions, diffusion energy source and
finite-rate/eddy-dissipation.
3. Define material properties for (C6H12O6), CH4, and
CO2.
4. Define operational conditions by activating the
gravitational acceleration and keeping all other
default numbers.
5. Define boundary conditions by setting heat flux to be
zero at all solid walls. Also, set velocity_1.1_10_5
m/s (by solving Eq. 12), temperature_305 K, and
species mass fraction (C6H12O6) at the inlet_1.0 (no
chemical reaction takes place at the inlet). Also,
assume that flow at the outlet is fully developed.
6. Anaerobic digestion reaction rate, Ri, is calculated
from Eqs. (8 and 9) through user defined function in
Fluent.
Because flow of liquid manure in plug-flow digesters is
low, conservation of mass (Eq. 1), energy (Eq. 2) and the
species transport (Eq. 3) are solved without flow and
turbulence equations. First order upwind scheme was used
to discretize the governing equations and were solved
using the SIMPLE (semi-implicit method for pressurelinked
equations) algorithm (Patankar 1980).
RESULTS and DISCUSSIONS
Information obtained in the literature (Gebremedhin et al.
2004) for one specific plug-flow anaerobic digester was
used in the simulation to predict biogas production. The
data (Table 1) included: digester dimensions, manure flow
rate, hydraulic retention time and ambient temperature.
Biogas is assumed to be 60% methane with a density of
0.6679 kg/m3 (EPA 2005).
For the data given in Table 1, the model predicted
1,207 m3/day of biogas. The measured data for the same
digester (Gebremedhin et al. 2004) was 1,274 m 3/day,
which is within 5% of the predicted value. This is a onepoint
or one data check and cannot be considered a
validation. More data are necessary to establish the
statistical validation between the predicted and measured
results.
In the simulation, convergence occurred after 350
iterations as shown in Fig. 1. The two criteria set for
convergence were: (1) residual for species is less than 1_
10_3, and (2) residual for energy is less than 1_10_5. The
trend of the simulated results was steady and without any
oscillations, thus confirming convergence.
In this study, momentum and turbulence were not
considered in calculating biogas predictions because
velocity of liquid manure in a plug-flow digester is very
low. The model is based on the principles of conservation
of mass, conservation of energy, and species transport.
Three convergence curves _ one for energy, and two for
species transport are necessary, and the results of the
iterations are shown in Fig. 1. The two species are
(C6H12O6) and CO2. The sum of mass fractions of all
species is equal to one. For example, if there are N species
in the chemical reaction, the Nth mass fraction is determined
by [1_aN_1
i_1 Yi]: In this simulation, N_3 because
there are only three species. The third species is CH 4.
The range of molar concentrations for the three species
(C6H12O6), CH4 and CO2, are: 2.67_10_5 _ 3.80_
10_2, 8.72_10_6 _ 1.72_10_4, and 1.89_10_3 _
3.91_10_2 kmol/m3, respectively. The simulated
Table 1. Input information and comparison of measured and predicted results 1.
Digester dimension
Measured biogas
production (m3 day_1)
Simulated biogas
production (m3 day_1) Error (%)
Length (m) Width (m) Depth (m)
1274 1207 5
39.62 9.44 4.26
1Measured biogas production is from Gebremedhin et al. (2004)
Daily manure flow rate _38.336 m3 day_1.
HRT_3.6_106 s.
Retention temperature_328C.
8.4 LE GE´ NIE DES BIOSYSTEMEZ AU CANADA WU ET AL.
contours of the molar concentrations for the three species
are given in Figs. 2_4.
The concentration of organic material (C6H12O6) is
high close to the inlet and low far from the inlet (Fig. 2).
The concentration remained unchanged after about onesixth
of the length from the inlet. This gradient is due to
the fact that influent to the grids near the inlet has higher
organic concentration. The distributions for CO2 and CH4
are similar (Figs. 3 and 4). The actual values of CH4 is,
however, higher than that of CO2 because CH4 is the main
product of the chemical reaction. Both concentrations
increased gradually from the inlet up to a point and then
remained unchanged thereafter.
The temperature profile in the digester is given in Fig.
5. The inlet temperature is 305 K (328C), which is the
assumed boundary-condition temperature, and the outlet
temperature is 311 K (388C). A temperature gradient
exists because of the chemical reaction taking place when
the reactants (organic material and water) are mixing. A
temperature difference of 58C exists between the inlet and
outlet. This could be because we made an assumption that
species reaction takes place only in one step and adiabatic
boundary conditions are assumed at the digester walls.
The assumption that species reaction is taking place only
in one step needs to be studied further.
Sensitivity analyses were conducted to determine the
effect of reaction rate (Ri and Rˆi;r in Eqs. 8 and 9,
respectively) on biogas production. The change in biogas
production is defined by the change in C/C0 (Eq. 10),
which is the percentage remaining of (C6H12O6). An
increase in C/C0 means that less of (C6H12O6) is reacting,
and consequently, less CH4 is produced.
The forward rate constant (kf,,r in Eq. 10) was
calculated for a given hydraulic retention time (t). For
t_3.6_106 s and C/C0_85%, the resulting kf,r_4.52_
10_8 s_1. An increase in C/C0 results in a decrease of the
forward reaction constant, which results in a decrease of
the reaction rate (Ri and Rˆi;r); and consequently, less
biogas is produced. For example, a 5% increase in C/C0
(from 80 to 85%) resulted in 43% decrease in biogas
production (from 1,207 to 689 m 3/day). It is apparent,
therefore, that the percentage of organic matter remaining
(e.g., C6H12O6) is critical for the volume of biogas
production. It should be noted that C/C0_80% is an
assumed quantity that need to be validated experimentally.
CONCLUSIONS
The following conclusions can be drawn from the study:
1. A three-dimensional numerical simulation model that
predicts biogas production from plug-flow anaerobic
digestion systems is developed. The model is based on
the principles of conservation of mass, conservation
of energy, species transport, and chemical reactions.
2. The model prediction is checked against one measured
data point available in the literature, and the
comparison is within 5%. More data are necessary to
Fig. 1. Residuals versus iterations in the simulation.
Fig. 2. Contours of simulated molar concentration of
C6H12O6 (kmol m_3).
Fig. 3. Contours of simulated molar concentration of CO2
(kmol m_3).
Fig. 4. Contours of simulated molar concentration of CH4
(kmol m_3).
Volume 51 2009 CANADIAN BIOSYSTEMS ENGINEERING 8.5
establish statistical validation of the model predictions.
3. Prediction of biogas production is very sensitive to
changes in chemical reaction rates. A 5% increase in
C/C0 resulted in 43% decrease in biogas production.
Chemical reaction rate is calculated from the percentage
remaining of organic materials and hydraulic
retention time.
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and Bioengineering 99: 700_711.
Yilmaz, A.H. and F.S. Atalay. 2003. Modeling of the
anaerobic decomposition of solid wastes. Energy
Sources 25: 1063_1072.
LIST of SYMBOLS
A influent area, m2 Sh source term, kg kJ m_3 s_1
ADM1 anaerobic digestion model 1 t time, s
BOD biological oxygen demand T temperature, 8C
BVS biodegradable volatile solides u, v velocity magnitude, m s_1
C concentration, mass/volume ui, uj velocity in tense form
methane, kmol m_3
/V˙ volumetric flow rate, m 3 s_1
CnHaOb organic matter, kmol m_3 VS volatile solides
CO2 carbon dioxide, kmol m_3 Y mass fraction, dimensionless
D diffusivity, m2 s_1 x, y, z Cartesian coordinates
E total energy, kJ
h species enthalpy, kJ Greek symbols
H2O water, kmol m_3 r density, kg m_3
HRT hydraulic retention time, day t hydraulic retention time, s
J diffusion flux, kg m_2 s_1 t shear stress, Pa
K kinetic parameter, dimensionless /ni;r ? ; ni;r ƒ stoichiometric coefficient, dimensionless
Keff effective heat conductivity, W m_1 8C_1
/h j;r ? forward rate exponent, dimensionless
kf,r forward reaction rate constant, s_1 Subscripts
L digester length, m i tense form
M molecular weight, kg kgmol_1 j species
N species m mixture
p pressure, Pa
R reaction rate, kg m_3 s_1
Volume
http://www.ruhr-uni-bochum.de/thermo/Forschung/pdf/IGRC_Full_Paper_Paris.pdf 4/11/2010 jam
12.00 wib
An Analysis of Available Mathematical Models
for Anaerobic Digestion of Organic Substances
for Production of Biogas
Main author
Mandy Gerber
Chair of Thermodynamics
Germany
m.gerber@thermo.rub.de
Co-author
Roland Span
Page 2 of 30
© Copyright 2008 IGRC2008
1. ABSTRACT
The interest in biogas plants to produce the renewable energy source “biogas” is
unbroken. The number of plants is increasing as well as the average plant size. A
trend of the last years is the growing interest in substituting natural gas by treated
biogas in natural gas networks. The option to convert biogas to (bio) natural gas
quality is primarily relevant for large-scale biogas plants. Due to increasing investment
and operating costs, the need for a fully developed design and optimised operation
increases for profitable operation of large-scale plants. The development of an
appropriate model for the complete process is an important step in this direction.
Crucial elements of a complete process model are detailed models for the upgrading
process and the anaerobic digestion.
Since nearly 40 years scientists have been developing models for anaerobic digestion
of organic substances. In the meantime there are dozens of approaches, but not
always with the same intention. Self-evidently, mathematical models are required:
- to comprehend and reproduce experiments,
- to apply experimental results to industrial plants for a better designing,
- to understand complex interrelationships of different process parameters and their
influence on the digestion, what might result in an optimised process,
- or just to analyse the biological, chemical and physical nature of the process.
The existing models vary with respect to their objectives and complexity. There are
comparatively simple models developed exclusively to calculate the maximum biogas
rate, which will theoretical be produced from organic substances. Another, also still
comparatively simple type of models for calculating a biogas rate includes degradation
or digestion rates, because not every component of the substrate is degradable at the
same conversion rate. Lignin, for instance, is degradable difficultly or only very slowly;
in contrast fat is degradable very well.
The application of these models does not allow for dynamic investigations. Therefore,
complex models were established including the kinetics of the growth of
microorganisms. If kinetics is taken into account, the activity of microorganisms and
consequently the biogas production rate can be investigated with appropriate models
for a variety of substrates, considering different charging mechanisms and intervals.
When using these models, the death rate and the wash-out of microorganisms can be
integrated as well.
Due to the close interconnection of the activity or rather the growth of microorganisms
to other process parameters, some models include modifications for investigating
dependencies, such as the influence of the process temperature, inhibition effects of
ammonia, hydrogen or substrate satiety. These aspects are particularly interesting for
the design and for an optimised operation management.
As mentioned before, the growth rate of microorganisms is depending on the quantity
and the composition of the substrate, but a lot of models are precisely adapted to a
special substrate or a small number of substrates. Therefore, a transfer of the model
to processes using different substrates is very difficult or even impossible without
experimental results. For investigations that are independent of the substrate type,
only models can be used, which consider the major organic components of the used
substrate – carbohydrates, fats and proteins.
Most of the available models allow for calculating both the biogas and the methane
production rate of the process. To design biogas plants and to evaluate the efficiency
of such plants both parameters are very important. However, there are also models,
which yield only one of these parameters. Some models are very special and aim
exclusively, e. g., at an evaluation of the influence of mixing on biogas production or
Page 3 of 30
© Copyright 2008 IGRC2008
economy, or at an investigation of flow characteristics in the fermenter or the
recirculation.
The process of biogas production contains several complex interconnections. The
multitude of parameters required to characterise the process complicates the
development of a well intelligible model. Often the transferability of the models to
problems in practice such as dimensioning and optimisation of biogas plants is limited.
The available models strongly differ with regard to their objectives, complexity and
transferability. This paper will give an overview of existing models, their application
and their capabilities and limits. Different models will be analysed and compared to
each other.
Page 4 of 30
© Copyright 2008 IGRC2008
CONTENTS
1. Abstract ................................................................................................. 2
2. Introduction........................................................................................... 5
3. Stages of Fermentation.......................................................................... 5
4. Models for Calculating Biogas Production .............................................. 7
5. Models with Reaction Kinetics................................................................ 8
5.1. Models for Growth Kinetics ..................................................................................9
5.1.1. Growth of Bacteria .......................................................................................9
5.1.2. Mathematical Models of Bacterial Growth ...................................................... 10
5.1.3. Influence of Inhibitors on Bacterial Growth .................................................... 13
5.1.4. Influence of pH on Bacterial Growth ............................................................. 17
5.1.5. Influence of Gas-Liquid Equilibrium on Bacterial Growth .................................. 18
5.1.6. Influence of Temperature on Bacterial Growth ............................................... 19
5.2. Kinetics of Substrate Degradation ...................................................................... 20
5.3. Kinetics of Product Formation ............................................................................ 22
6.
7.
8.
9.
Discussion............................................................................................ 23
Conclusion............................................................................................ 25
Acknowledgement................................................................................ 26
References ........................................................................................... 26
Page 5 of 30
© Copyright 2008 IGRC2008
2. INTRODUCTION
Models for describing a degradation process to produce biogas are required
1) to facilitate the understanding of the process,
2) to design new or enhance old biogas plants,
3) to compare and select appropriate substrates and substrate mixtures,
4) to compare and select appropriate process steps and components,
5) to optimise the operation of biogas plants,
6) for an ecological and economic analysis
Numerous models were developed in the last decades. In this paper a survey of
existing models, which are based on a biological and physico-chemical background, is
given.
3. STAGES OF FERMENTATION
The degradation of organic matter to biogas is a very complex process. Identified
subprocesses
of degradation are hydrolysis, acidogenesis, acetogenesis and
methanogenese (figure 1).
Hydrolysis
The main components of organic matter are carbohydrates, fats and proteins.
Microorganisms are not able to metabolise these biopolymers. Foremost biopolymers
have to be broken down in soluble polymers or monomers to pass the cell wall of
acidogenic bacteria. Therefore the acidogenic bacteria produce extracellular enzymes
such as cellobiase, amylase and lipase to hydrolyse biopolymers (Shin & Song, 1995).
This first step is called liquefaction or hydrolysis and is separated into three parts
(Gujer & Zehnder, 1983): Hydrolysis of proteins to simple amino acids, hydrolysis of
carbohydrates to simple sugars and hydrolysis of fats and oil to glycerol and fatty
acids. The hydrolysis rate depends on the biopolymer (to degrade glucose is, e.g.,
easier than to degrade lignin), on substrate concentration, on particle size, on the pH
value and on temperature (Veeken & Hamelers, 1999).
Acidogenesis
Acidogenesis includes the fermentation of amino acids and simple sugar as well as the
anaerobic oxidation of long chain fatty acids (LCFA) and alcohols by acid-forming
bacteria. Beside carbon dioxide, water and hydrogen primarily acetic, propionic,
butyric and valeric acid will be accumulate. Butyric and valeric acid are relevant
especially for protein-rich substances, because a number of amino acids will be
degraded to these fatty acids (Batstone et al., 2003).
Acid-forming bacteria are fast-growing bacteria with a minimum doubling time of
about 30 minutes. They prefer degradation to acetic acid, since this step results in the
highest energy yield for their growth. (Mosey, 1983)
Acetogenesis
Anaerobic oxidation of intermediates such as volatile fatty acids (primarily propionic
and butyric acid, except acetic acid) to acetic acid and hydrogen by acetogenic
bacteria is called acetogenesis. An accumulation of hydrogen has to be avoided due to
the inhibition of this sub-process by hydrogen. Therefore, hydrogen-utilising and
acetogenic bacteria live in agglomerates close together (Mosey, 1983).
Acetogenic bacteria grow rather slowly with a minimum doubling time of 1,5 to 4 days
even under optimum conditions such as a low concentration of dissolved hydrogen
(Lawrence & McCarty, 1969).
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© Copyright 2008 IGRC2008
Biogradable Organic Matter
Hydrolysis
(extracllular enzymes)
Amino Acids, Sugars Fatty Acids
Acidogenesis
(acidogenic bacteria)
Acetate
CH4, CO2
Methanogenesis
(mathane bacteria)
Acetogenesis
(acetogenic bacteria)
21%
100%
Proteins
Carbohydrates
Lipids
Complex Organic Matter
40% 5% 21%
46%
H2, CO2
Propionate, Butyrate, etc.
20% 34%
35% 12% 23% 11% 8% 11%
70% 30%
0%
?
Figure 1: Degradation process of complex organic components to biogas (Gujer &
Zehnder, 1983)
Methanogenesis
Methanogenesis indicates the methane production by methane bacteria out of acetate
and out of hydrogen and carbon dioxide. All methane bacteria so far studied utilise
hydrogen to reduce carbon dioxide to methane (Bryant, 1979). These hydrogenutilising
methane bacteria grow relatively fast with a minimum doubling time of about
6 hours (Mosey, 1983). Mosey (1983) called them the “autopilot” of the anaerobic
process, because they regulate the formation of volatile fatty acids (VFA).
The larger share of the methane (about 70%) is produced by acetoclastic methane
bacteria out of the methyl group of acetate (McCarty, 1964). Smith & Mah verified
1966 a share of 73% for the methane production out of acetic acid. Only few methane
bacteria groups are identified that catabolise acetate: Methanosarcina barkeri,
Methanococcus Mazei und Methanotrix soehngenii (Heukelekian & Heinemann, 1939).
These bacteria types generally control the pH value of the fermentation process by
removal of acetic acid and formation of carbon dioxide (alkalinity). Because of the low
energy yield of this reaction, acetoclastic bacteria grow very slowly with a minimum
doubling time of 2 to 3 days (Mosey, 1983).
All sub-processes are affected by ambient conditions such as temperature, pH value,
alkalinity, inhibitors, trace and toxic elements. Furthermore, all sub-processes are
linked to and influenced by each other. Most models for biogas production include all
sub-processes, although only the rate-limiting step is actually important for modelling
the process. To date, there are still discussions which step is the rate-limiting step.
According to Andrews (1969) the degradation of acetic acid to methane is ratelimiting.
According to Veeken & Hamelers (1999) hydrolysis is the rate-limiting step.
Page 7 of 30
© Copyright 2008 IGRC2008
Veeken & Hamelers validated their model of cumulative methane production
depending on a first-order hydrolysis rate constant with batch tests using various
organic wastes (leaves, bark, straw, grass, orange peeling, whole-wheat bread, filter
paper). Based on own batch tests, Converti et al. (1999) also found that the
hydrolysis of the lignocellulosic fraction of vegetable residues is always the ratelimiting
step. Rao & Singh (2004) described own batch tests with municipal garbage
using a first-order model based on the availability of substrate as the limiting factor.
Shin & Song (1995) tried to determine the rate-limiting step in a study with batch
tests. Using basic components of organic wastes, such as glucose and starch,
methanogenesis was the rate limiting step, due to easily degradable substrates
producing volatile fatty acids, which inhibit the methanogenesis. With various organic
wastes, such as food waste, paper or food packing waste, the hydrolysis and
acidogenesis regulate the degradation process. This result implies that the kind of
substrate plays a major role in identifying the rate limiting step.
Zuru et al. (2004) pursue the completely different approach of bubble formation and
bubble growth of the biogas in the liquid phase as the rate-limiting step.
Irrespective of the rate-limiting step, particularly in early modelling approaches,
authors took into account only two stages (acid-forming and methane-forming stage)
of the degradation process. Examples are the models of Hill & Barth (1974, 1977), of
Bala & Satter (1991) and of Jeyaseelan (1997). The model of Andrews (1968), which
was one of the first models at all, is considering only a one stage process. Over the
last decade the complexity of the models generally increased, due to the increasing
understanding and identification of important intermediates; examples are the models
of Batstone et al. (2002) and of Knobel & Lewis (2002).
4. MODELS FOR CALCULATING BIOGAS PRODUCTION
Simple ways to calculate the biogas production of organic matter are the models of
Buswell & Mueller (1952), Boyle (1976), Baserga (1998), Keymer & Schlicher (2003)
or Amon et al. (2007). These time independent models are based on data for basic
elements or components of organic matter and result only in values for the production
of methane and carbon dioxide. Since the models are time independent, no prediction
of required retention time, e. g., is possible.
Buswell & Mueller (1952)
If the chemical composition of organic matter is known, the methane and carbon
dioxide yield can be calculated with an uncertainty of about 5% using the simple
relation:

2 4 2 4 2 2 8 4 2 8 4 a b c
bcabcabc
C H O a H O CH CO (1)
The degradation of organic matter for the bacteria metabolism (synthesis of cell mass
and energy for growth and maintenance) is not included in this relation.
According to this relation, the methane fraction of degraded glucose is, e. g., 50 %:
6 12 6 4 2 C H O 3 CH 3 CO (2)
Other substrate components result in other methane fractions, as shown in table 1.
Boyle (1976):
Boyle modified the chemical reaction of Buswell & Mueller (1952) and included
nitrogen and sulphur to obtain the fraction of ammonia and hydrogen sulphur in the
produced biogas:
Page 8 of 30
© Copyright 2008 IGRC2008






2
4
232
3
4242
3
28484
3
28484
abcde
bcde
CHONSaHO
abcde
CH
abcde
CO d NH e H S
(3)
Baserga (1998)
Baserga classified organic matter of co-substrates in carbohydrates, fats and proteins
and defined gas yields and methane fractions for these three components separately.
Table 1: Gas yields and methane fractions of different organic components
(Baserga, 1998)
Gas yield (l/kg organic) CH4 (%)
Carbohydrates 790 50
Fats 1250 68
Proteins 700 71
As defined by Baserga (1998), co-substrates are organic substrates used in addition to
animal wastes.
Keymer & Schilcher (2003)
The approach of Keymer & Schilcher (2003) is based on the model of Baserga (1998)
and upgraded by a digestion rate depending on the kind of substrate. They supposed
the degradation of organic matter is similar to the process in a cattle craw. Empirically
determined digestion rates for a large number of animal feed depending on nutrient
fractions (crude protein XP, crude fat XL, crude fibre XF and N-free extracts XX) are
listed in an animal feed table (DLG, 1997) and used for prediction of the gas yield and
methane fraction.
Amon et al. (2007)
Similar to Keymer & Schilcher (2003), Amon et al. (2007) divided the organic matter
into four basic components (XF, XL, XF, XX). For estimating methane energy values
(MEV in l/kg volatile solids) of energy crops such as maize, cereals or grass a
coefficient of regression (x1 – x4) is considered, which was determined with batch tests
for various energy crops.
1 2 3 4 MEV x XP x XL x XF x XX (4)
5. MODELS WITH REACTION KINETICS
To investigate the kinetics of biogas production, the whole biogas process has to be
considered (except for black box models):
1) Growth of microorganisms,
2) degradation of substrate, and
3) formation of products.
According to the supply of substrate, processes can be divided into discontinuous and
continuous processes. Discontinuous batch processes are fed only once. Substrate
degradation and gas production change over the retention time, whereby growth
requirements for microorganisms change permanently. Continuous processes are
characterised by the fact that substrate continuously flows in and out of an open
system. A process with constant substrate flow and gas production is stationary
Page 9 of 30
© Copyright 2008 IGRC2008
(steady-state process). In this case, growth requirements for microorganisms are
constant over time.
The substrate balance of a continuous or a discontinuous process can be expressed
as:
/ /
o r dS dt D S D S dS dt
accumulation input output reaction
(5)
with the dilution rate D (flow per fermenter volume, in 1/h) and the substrate
concentration S. The reaction rate, which is directly proportional to product formation
and depending on the cell concentration, has to be determined. The kinetics of
bacterial growth provides the basis of the degradation process and is strongly
depending on growth requirements and the medium.
5.1. Models for Growth Kinetics
5.1.1. Growth of Bacteria
As for every living being, the life cycle of bacteria cultures is characterised by various
phases of growth as shown in figure 2. Regarding discontinuous batch processes, a
bacteria culture passes the phases (Monod, 1949):
Growth Rate
1) lag phase: zero,
2) acceleration phase: increases,
3) exponential phase: constant,
4) retardation phase: decreases,
5) stationary phase: null, and
6) phase of decline: negative.
Figure 2: Phases of growth of a
bacteria culture (Monod,
1949
In contrast to steady-state processes, bacteria cultures pass not only the stationary
phase, but also phase with notable active cell growth or death of cells, due to
permanent changing concentrations of nutrients and inhibitors. Because of this
continuous adaption, small time lags occur for discontinuous processes, which result in
measurable deviations of kinetic parameters (Wolf, 1991). Thus, kinetic parameters
for describing the growth of bacteria at discontinuous processes are not transferable
to continuous processes without control. This is a problem, because large-scale biogas
plants mainly use steady-state or rarely dynamic processes, while kinetic parameters
are mainly determined in small discontinuous batch processes.
The exact shape of the growth curve (figure 2) is depending on many factors, such as
ambient conditions, kind and concentration of substrate, bacteria type, physiological
conditions of inoculum and initial concentration of bacteria. Depending on life cycle
and growth conditions of a culture, the contact of bacteria cultures to a new medium
can lead to short or longer deceleration of growth. This phase is called lag phase and
is caused by a damage of cells through heat, rays or toxic chemicals. If the cells are
still viable in spite of damage, they need time for reparation. Also undamaged cells
can not resume cell growth immediately, if essential substances are absent and have
to be synthesised. If the new medium is similar to the medium used before, the lag
phase can be neglected. (Monod, 1949)
Page 10 of 30
© Copyright 2008 IGRC2008
The real growth takes place primarily at the exponential phase. During the exponential
phase, the rate of bacterial growth is constant. The transition between lag phase and
exponential phase is called acceleration phase. In this phase the growth rate
increases. However, in most cases the acceleration phase can be neglected.
The growth rate of the exponential phase changes only, if (Monod, 1949):
1) nutrients are exhausted,
2) toxic metabolic products are accumulated or
3) the ionic equilibrium and thus the pH value changes due to substrate degradation.
As result of these effects the retardation phase will start. The growth rate decreases
until the value zero is reached. During the stationary phase the number of cells
remains constant, but a lot of cell activities keep on going, such as energy
consumption due to metabolism or biosynthetic processes. Retardation and stationary
phase are usually short and therefore quite often hardly observable.
If the conditions of the medium or the growth conditions are not changed by others,
the microorganisms die with a death rate kd (in 1/h). Although the phase of decline
also behaves exponential, the rate is smaller than the one of the exponential phase.
Death biomass is assumed to decay into carbohydrates and protein and can be used
as new substrate (Angelidaki et al., 1999). This process is called disintegration.
The balance of bacteria cells can be expressed by:
/ o d dX dt D X D X μ X k X
accumulation input output growth death
(6)
with the cell concentration X (in g/l), the dilution rate D (in 1/h) and the specific
growth rate μ (in 1/h). The bacterial growth depends on the specific growth rate,
which cannot be infinite due to the limited availability of nutrients (substrate
concentration S in g/l) and other ambient conditions such as inhibitors (inhibitor
concentration I in g/l), pH value or temperature T.
S, I , pH, T
, (7)
A lot of mathematical models describing the limitation of the specific growth rate
depending on nutrients and other requirements were published in the last decades.
5.1.2. Mathematical Models of Bacterial Growth
The basis for modelling the kinetics of bacterial growth was derived by the two
German biochemists Michaelis and Menten. Their model, which was published as early
as 1913, describes the enzyme activity depending on substrate concentration. This
dependency can be transferred to bacterial growth, because the microbial growth is an
autocatalytic reaction, too. (Wolf, 1991)
But not until the 1940th Monod recognised the non-linear relation between specific
growth rate and limited substrate concentration, when he investigated the growth of
bacteria cultures and the parallelism to the Michaelis-Menten theory. For bacterial
growth, Monod formulated:

max
s
S
KS
(8)
According to this model, the specific growth rate increases strongly for low substrate
concentration and slowly for high substrate concentration, until a saturation of
bacteria is reached (see figure 3). This limit is the maximum specific growth rate μmax.
The Monod-constant Ks is the substrate concentration at 50% of the maximum specific
growth rate (μmax/2).
Page 11 of 30
© Copyright 2008 IGRC2008
substrate concentration
specific growth rate
Ks
μmax
μmax/2
max
S
μ=μ S
S+K
Figure 3: Specific growth rate depending on substrate concentration according to
Monod
The substrate concentration is the limiting factor. Limiting substrate is the component,
which limits the specific growth rate due to its concentration. The affinity of bacteria
to the limiting substrate is expressed by Ks (Monod, 1949). For S < Ks, the specific
growth rate is approximately linear. Ks is always greater than zero, thus S/(S+Ks) is
always less than 1 and therefore the specific growth rate is less than μmax. Unlike the
enzyme activity described by Michaelis-Menten, in fact μ(S) does not start at zero,
due to the degradation of substrate by bacteria for maintenance energy. Thus, the
growth cannot start until S reached a certain value (Fencl, 1966).
If the substrate is not the limited factor due to a high enough concentration, the
maximum specific growth rate can be reached. According to Grady (1969), the
maximum specific growth rate is unique for every bacteria culture.
The accuracy of the Monod model for pure cultures and simple substrates is very high
(Contois, 1959). The model is appropriate for homogenous cultures, but not for
heterogeneous cultures or complex substrates (te Boekhorst et al., 1981). Also Pfeffer
(1974), e.g., concluded that the Monod kinetic cannot be used to describe the
degradation of municipal wastes as a complex substrate. Furthermore, the lag phase
is not included in the Monod model.
For this reason quite a number of modifications were developed as shown in table 2.
The model of Moser (1958) describes growth which differs from the exponential
characteristic. Therefore, Moser (1958) upgraded the model of Monod with a
parameter n (usually n > 1) to integrate effects of adoption of microorganisms to
stationary processes by mutation. For n = 1 the specific growth rate becomes equal to
the Monod model.
Contois (1959) involved not only the substrate dependency, but also the cell
concentration to calculate the specific growth rate. Thus effects of inhibition and of
inoculum are directly included (Fujimoto, 1963), even though the lag phase is
neglected. This model yields good results both for discontinuous and continuous
processes, but its capability to model dynamic processes is strongly limited (Beba &
Atalay, 1986).
Powell (1967) included not only reaction kinetics, but also diffusion and permeation of
substrate through the cell wall with two additional parameters K and L. K describes
the kinetics of growth due to enzyme activity and the parameter L the diffusion and
permeability.
Page 12 of 30
© Copyright 2008 IGRC2008
Table 2: Models for bacterial growth
Author Model Eq.No
.
Monod, 1949 max
s
S
KS

9
Moser, 1958
max
n
n
s
S
KS


10
Contois, 1959
1
cc
1
S
KXSKX
S

11
Powell, 1967
max max

max 2
114
2
KLSLS
LKLS



12
Chen & Hashimoto, 1978
max

/
1
i
i
SS
KS
K
S


13
Bergter, 1983
max 1 exp /
s
μStT
KS
14
Mitsdörffer, 1991
max
1
n
nn
bS
S
SKGS

15
Chen & Hashimoto (1978) modified a model from Contois (1959), where the cell
concentration, which depends on the level of substrate degradation, is included via the
relation between substrate concentration and initial substrate concentration Si.
Nevertheless, the integration of inhibition by substrate or products is limited (Hill,
1983). As a result, no prediction of process failures due to inhibition of
microorganisms is possible. Process failures due to wash-out effects can be predicted
(Hill, 1983).
The modified Monod model by Bergter (1983) considers deceleration during the lag
phase (see the exponential part of the mathematical model) with t for time and T for
lag time.
In the model of Mitsdörffer (1991), the specific growth rate depends beside other
parameters on the gas production Gs (in m³/kg organic dry matter). The parameter n
is 1,5 and indicates a higher substrate affinity, because mixed bacteria cultures need a
higher substrate transport compared to pure cultures.
Figure 4 shows the specific growth rate depending on substrate concentration as
calculated with a few of the discussed models. To simulate biogas production a model
has to be chosen, which fits well to the process data. A frequently used bacterial
growth model for biogas production is the model of Monod, which was used, e.g., by
Biswas et al. (2006) for batch processes, by Bryers (1985) for batch, steady-state and
dynamic processes, by Mosey (1983) for steady-state and dynamic processes, and by
Denac et al. (1988) and Simeonov et al. (1996) for dynamic processes.
The bacterial growth model of Contois is applied for example by Yilmaz & Atalay
(2003) for batch processes and by Chen & Hashimoto (1980) and Lo et al. (1981) for
steady-state processes. Chen & Hashimoto (1978) and Chen (1983) used their own
Page 13 of 30
© Copyright 2008 IGRC2008
model for steady-state processes. Hashimoto (1982) used the same model for batch
processes. Only Mitsdörffer (1991) applied his own model for steady-state processes.
specific growth rate
substrate concentration
Monod
Moser (n=2)
Powell (L/K=5)
maxWachstumsrate
μmax
Figure 4: Specific growth rate depending on substrate concentration according to the
models of Monod (1942), Moser (1958) and Powell (1967)
Unfortunately, it is difficult to describe biological processes with short and long
retention times or degradation of complex substrates using these models with only
one set of kinetic parameters. Therefore, so called first-order models were developed,
such as the model of Rao & Singh (2004), where the degradation of biodegradable
substrate only depends on a constant k (dS/dt = -k · S). These models are easy to
handle, but only accurate for confined requirements. They cannot be used for
predicting optimum conditions of maximum biological activity or process failures.
(Hashimoto et al., 1981) First-order kinetics were used in models of Angelidaki et al.
(1999), Batstone et al. (2002), Bryers (1985), Knobel & Lewis (2002), Siegrist et al.
(2002) for the hydrolytic step. Shin & Song (1995) used the first-order kinetics for
every step of the process.
5.1.3. Influence of Inhibitors on Bacterial Growth
Bacterial growth can be inhibited by certain substrate and product concentrations.
Both inhibition paths are based on very similar effects and are closely connected
especially for mixed bacteria cultures.
Substrate Inhibition
When the substrate concentration is increased, a maximum specific growth rate will be
reached at a certain concentration. A further increase of the substrate concentration
results in a decrease of the specific growth rate. This effect can be caused by a high
osmotic pressure of the medium or a specific toxicity of the substrate. A reduction of
the metabolic activity of a cell can lead to the following consequences (Edwards,
1970):
1) modified chemical potential of substrates, intermediates, or products,
2) altered permeability of cells,
3) changed activity of one or more enzymes
4) dissociation of one or more enzymes or metabolic aggregates,
5) affected enzyme synthesis by interaction with the genome or the transcription
process, or
6) affected functional activity of the cell.
A number of approaches developed to consider the effect of substrate inhibition on
microbial growth are listed in table 3.
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© Copyright 2008 IGRC2008
Table 3: Models for bacterial growth including the effect of substrate inhibition
Author Model Eq.No
.
Haldane, 1930
max
max 1 /
i
sisi
SSK
SKSKSKSK

16
Webb, 1963

max
 
2
1/
/
i
si
S SK
SKSK




17
Yano et al., 1966

max
1
1/
n
i
si
i
S
KSSK




18
Grant, 1967
max
1
iS K

19
Andrews, 1968
max 2 max
1
1s
s
ii
S
SKSSKSKK

20
Aiba et al., 1968
s
SSK
KS
max exp / i

21
Hill & Barth, 1977
,1 ,2
max 2
/ / sii
S
SKSKSIK

22
Han & Levenspiel,
1988

max * *
1
1/
n
m
s
SS
SSKSS


23
The model of Aiba et al. (1968) is an empirical correlation. Nevertheless, simulated
data with substrate inhibition agree well with empirical data from laboratory
experiments. Webb (1963) derived his model from enzyme kinetics and integrated an
allosteric effect with as reaction rate. The model of Haldane (1930) is also derived
from enzyme kinetics and is equivalent to the one by Webb (1963) for = 0.
Yano et al. (1966) generalised the approach of Haldane (1930), thus one enzyme is
able to accumulate several enzyme complexes. Transferred to bacterial growth this
means that n inhibitors are able to influence the specific growth rate. According to the
model of Grant (1979), the specific growth rate decreases almost linearly at high
concentrations of the substrate inhibitor.
The model of Andrews (1968) is based on Haldane (1930) for enzyme inhibition at
high substrate concentrations. Thus, the specific growth rate decreases when a
maximum tolerable substrate concentration is exceeded. Therefore, an inhibition term
is added to the model of Monod (1942). The inhibition constant Ki is the substrate
concentration, where bacteria growth is reduced to 50% of the maximum specific
growth rate due to substrate inhibition. Therefore, Ki is considerably higher than Ks.
The evaluation of these parameters is extensive.
A modification of the model of Andrews (1968) involving a second inhibitor was
developed by Hill & Barth (1977). As it is used in the model of Han & Levenspiel
(1988), S* is a critical inhibitor concentration, where growth stops. The parameters n
and m depend on the kind of inhibition (non-competetive, competetive or
Page 15 of 30
© Copyright 2008 IGRC2008
uncompetitive). The model is transferable to inhibition by product or cell
concentration. Further models were reported by Sinclair & Kristiansen (1993).
The selection of a model that is appropriate in the context of simulation of the whole
process of biogas production depends on the required accuracy and handling,
availability of the required data and constraints of the process. The models of Andrews
(e. g. by Hill, 1982, Angelidaki et al., 1999 and Moletta et al., 1986) and of Haldane
(e. g. by Angelidaki et al., 1999) were used in this context.
Product Inhibition
The effects of product inhibition are similar to those of substrate inhibition. Therefore,
some models can be used for both influences, e.g. the ones by Aiba et al. (1968) and
Han & Levenspiel (1988). In table 4 some of the existing models are listed. The
maximum specific growth rate is found at zero product concentration in these models.
Table 4: Models for bacterial growth including the effect of product inhibition
Author Model Eq.No
.
Ierusalimsky, 1967 max
p
sp
SK
KSKP


24
Holzberg et al.,
max 1 2 K P K 25
Aiba et al., 1968 max exp
1967
s
SKP
KS

26
Bazua & Wilke,
1977 max,P 0
s
S aP
KSbP



27
Ghose & Tyagi,
1979 max * 2 1
/ si
PS
PSKSK

28
Moser, 1981 und
Bergter, 1983 max
n
p
nm
sp
SK
KSKP


29
Dagley &
Hinshelwood, 1983
s
SKP
KS

30
Han & Levenspiel,
1 
1988

max * *
1
1/
n
m
s
PS
PSKPP


31
The most important inhibitors relevant for substrate and product inhibition of
anaerobic digestion are:
Fatty acids such as HAc (undissociated acetic acid), HPr (undissociated propionic acid),
HBt (undissociated butyric acid) and LCFA (long chain fatty acids) not only serve as
nutrient, but also reduce the pH value and thereby inhibit the process. Except LCFA,
they are commonly considered in models, sometimes as separate component, but also
summarised to VFA (volatile fatty acids) or VOA (volatile organic acids).
NH3 (undissociated ammonia) is most important for substrates with a high amount of
proteins, because these substrates are very azotic. NH3 particularly inhibits
acetotrophic methanogenesis and propionic acid degradation and is rarely considered
in models (e. g. in the model of Batstone et al., 2002 and Siegrist et al., 2002).
However, synthesis of biomass requires nitrogen from ammonia. Therefore, a too low
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© Copyright 2008 IGRC2008
nitrogen concentration limits the growth of microorganisms. (Angelidaki et al., 1999
and Batstone et al., 2002)
0.1 1 10 100
0
20
40
60
80
100
propionic acid
butyric acid
relative rates of acid formation
NADH/NAD+ ratio
acetic acid
0 200 400 600 800 1000
0
20
40
60
80
100
propionic acid
butyric acid
relative rates of acid formation
concentration of hydrogen in ppm
acetic acid
Figure 5: Relative rates of acidformation
from glucose at
different NADH/NAD+ ratios
(Mosey, 1983)
Figure 6: Relative rates of acidformation
from glucose
depending on hydrogen
concentration (Mosey,
1983)
0 200 400 600 800 1000
0.0
0.2
0.4
0.6
0.8
1.0
100
80
60
40
20
0
standardised methane production
undissociated hydrogen sulphur in mg/l
KH S=85 mg/l
inhibition in %
2
Figure 7: Methane production depending on undissociated hydrogen sulphur (Märkl &
Friedmann, 2006)
H2 (hydrogen) inhibits the degradation of propionic and butyric acid to acetic acid (see
figure 6). Some models for anaerobic digestion exist, which describe hydrogen
inhibition, see, e.g. Batstone et al. (2002), Knobel & Lewis (2002), Siegrist et al.
(2002) and Vavilin et al. (1994).
H2S (undissociated hydrogen sulphur) influences the ionic equilibrium and thus the pH
value (Märkl & Friedmann, 2006). Figure 7 shows the standardised methane
production depending on the concentration of undissociated hydrogen sulphur
according to Märkl & Friedmann (2006).
O2 (oxygen): Biogas production is very sensitive to O2. Even a short-time presence of
O2 can stop the degradation process (Märkl & Friedmann, 2006). The inhibition by
oxygen is not considered at all in the presented models.
NAD+/NADH: Degradation of glucose to fatty acids according to the Embden-Meyerhof
metabolic pathway depends on the availability of the carrier molecule NAD+/NADH
Page 17 of 30
© Copyright 2008 IGRC2008
(Nicotinamidadenindinukleotid, reduced: NADH, oxidised: NAD+). This coenzyme is
responsible for the degradation rate and the composition of produced fatty acids (see
figure 5). This inhibitor was integrated into a model by Mosey (1983), which is valid
for degradation of glucose to fatty acid by acid-forming bacteria and for degradation of
propionic and butyric acid to acetic acid by acetogenic bacteria (Mosey, 1983).
5.1.4. Influence of pH on Bacterial Growth
The pH value has a strong impact on the degradation process, see figure 8, and can
be integrated directly into a mathematical model such as in the models of Angelidaki
et al. (1993) and Knobel & Lewis (2002).
0.0
0.1
0.2
0.3
0.4
0 20 40 60 80 100 120
substrate concentration in mM/L
specific growth rate in 1/d
Figure 8: Maximum specific growth rate depending on substrate concentration for
different pH values (Andrews & Graef, 1971)
56789
0.0
0.2
0.4
0.6
0.8
1.0
NH3
NH4
+
HSH2S
CO3
2-
HCO3
-
Fraction of dissociated
and undissociated components
pH
CO2
Figure 9: Fraction of dissociated and undissociated ammonia, hydrogen sulphur and
carbon dioxide depending on the pH value (Märkl & Friedmann, 2006)
μmax = 0.4 1/d
Ks = 0.0333 mM/L
Ki = 0.667 mM/L
pH = 6.0
pH = 6.5
pH = 7.0
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© Copyright 2008 IGRC2008
In most cases the pH value is included in models via the ionic equilibrium, considering
the influence of the pH value on this equilibrium. According to a most commonly
accepted hypothesis, the cell wall is more permeable for undissociated molecules (Neal
et al., 1965).
At a pH value of 7 the highest amount of acetic acid is dissociated in biogas digestion.
But according to Märkl & Friedmann (2006), methane-forming bacteria can only use
undissociated acetic acid. Therefore, dissociation has to be considered for nutrients
such as acetic acid and for inhibitors such as acetic and propionic acids, LCFA, H 2, NH3
or H2S. The influence of the pH value on NH3, H2S and CO2 is shown in figure 9.
Furthermore, some components can buffer the pH value, whereby the pH value is not
changing immediately. This effect is called alkalinity. The most important buffer
systems are the CO2/carbonat system and the NH3/NH4
+ system.
From the ionic balance the concentration of H+ ions can be calculated (Märkl &
Friedmann, 2006):
22
33
23
24444
22
23
OH Ac HCO CO HS S
H PO HPO PO NH H Z




(32)
Z is the sum of further anion in the medium such as chloride, phosphate or sulphide,
and of further cations such as calcium, sodium or magnesium. From the ionic
equilibrium the pH value can be determined:
pH log10 H(33)
The integration of the pH value or the ionic equilibrium into models describing
bacterial growth is very clearly described by Märkl & Friedmann (2006). Using the
model of Ierusalimsky (1967), the specific growth rate can be derived as follows:
23
23
max
23
HPr H S NH
HAc HPr H S NH
HAc K K K
K HAcHPr K HS K NH K


(34)
Further models in table 5 are cited from Birjukow & Kantere (1985) and Sinclair &
Kristiansen (1993).
Table 5: Models describing the influence of the pH value on bacterial growth
Model Eq.No
. Model Eq.No
.
2
o12
H
H
K K pH K pH 35 max
K
KH

38

max
1 / 1 / H OH OH K OH K


36 max
OH
OH
K
K OH

39
max
max
1/
pH
KHKH


37
12
The ionic equilibrium is included for example in the models of Andrews & Graef
(1971), Angelidaki et al. (1999), Knobel & Lewis (2002) and Siegrist et al. (2002).
Page 19 of 30
© Copyright 2008 IGRC2008
5.1.5. Influence of Gas-Liquid Equilibrium on Bacterial Growth
In general, gas and liquid are assumed to be in equilibrium. For volatile components
such as CO2, H2, H2S and NH3 the partial pressure is determined by Henry’s Law
(Angelidaki et al., 1993). In most cases the solubility of CH4 is neglected, while the
solubility of CO2 is mostly considered. In this way, the gas-liquid equilibrium has an
influence on the composition of biogas and on the ionic equilibrium, and therefore on
the nutrient and inhibitor concentration. Andrews & Graef (1971), Angelidaki et al.
(1993), Batstone et al. (2002) and Siegrist et al. (2002) considered the gas-liquid
equilibrium in their models.
5.1.6. Influence of Temperature on Bacterial Growth
According to Ingraham (1962), temperature is the most important ambient condition
for bacterial growth. In principle the reaction rate in chemical processes increases with
temperature. This well known rule can be adapted to microbiological processes in
limited temperature ranges. Nevertheless, the integration of temperature
dependencies is poor for most models for biogas digestion. In most models, the
impact of temperature on anaerobic digestion is considered by the Arrhenius equation
(Moser, 1981 or Bergter, 1983):
k kmax exp Ea
RT

(40)
with the rate constant k, the temperature T and the molar gas constant R. The
activation energy Ea and the maximum rate constant kmax have to be determined
empirically. This equation has been applied to various parameters, such as to the
specific growth rate (Siegrist et al. 2002, Sinechal et al., 1979), the maximum specific
growth rate (Hashimoto, 1982, Angelidaki et al., 1993), the saturation constant
(Siegrist et al., 2002), the hydrolysis rate, the death rate (McKinney, 1962, Siegrist et
al., 2002), the inhibition constants (Siegrist et al., 2002), the yield coefficient for
substrate to biomass (McKinney, 1962), the dissociation constant (Angelidaki et al.,
1993), the Henry-constant (Angelidaki et al., 1993) or to the self-ionisation of water
(Angelidaki et al., 1993). Most of these approaches are questionable from a theoretical
point of view, since the Arrhenius law is not valid for the corresponding parameters.
However, for an empirical description, the temperature dependence implied by
Arrhenius may be adapted.
15 20 25 30 35 40 45 50
0.2
0.4
0.6
0.8
1.0
1.2
maximum specific growth rate
temperature in °C
Figure 10: Maximum specific growth rate depending on temperature (Sinclair &
Kristiansen, 1993)
Page 20 of 30
© Copyright 2008 IGRC2008
A typical formulation adapting the Arrhenius law to the requirements of anaerobic
digestion processes was given, e.g., by Bergter (1983) and Sinclair & Kristiansen
(1993):
1 2
T k exp E k exp E
RT RT

max 1 2
(41)
where the first part describes the common increase of the reaction rate due to
temperature. The second part with typically higher activation energy describes the fast
decrease of the reaction rate above a certain temperature limit (rate of inactivation).
Figure 10 shows an example for the resulting temperature dependence of the
maximum growth rate.
If there is no causal correlation between temperature and kinetics, purely empirical
approaches can be used as listed in table 6.
Table 6: Numerical approaches for temperature depending parameters (Moser,
1981)
Trend Model Eq.No
.
linear
f T T 42
exponential
hyperbolic
f T expT 43
f T 
T




44
Hashimoto et al. (1981) used a simple linear approach to describe the temperature
dependence of the maximum specific growth rate between 20 and 60°C. Above 60°C
the maximum specific growth rate decreases considerably. McKinney (1962)
considered an exponential approach for the reaction rate between 5 and 35°C using
data for activated sludge to fit the parameters of the relation. A temperature increase
of 10 K doubled the reaction rate. Birjukow & Kantere (1985) published further
approaches describing the temperature dependence.
5.2. Kinetics of Substrate Degradation
Using an appropriate model for growth kinetics and including inhibition by substrate
and product concentrations, pH value, ionic equilibrium, gas-liquid equilibrium and
temperature if necessary, the bacterial growth can be mathematically described. The
result is the specific growth rate depending on the growth requirements and medium.
Based on the specific growth rate, the substrate degradation (dS/dt) r can be
calculated to complete the substrate balance expressed by equation (5), because
microorganisms need substrate:
1) to synthesise new cell material (dS/dt)x,
2) to produce products such as exoenzymes, acetic acid or methane (dS/dt) c, and
3) to supply required maintenance and growth energy (dS/dt) e.
The whole degradation of substrate can be considered the sum of these three terms:
rxec
dS dS dS dS
dt dt dt dt


(45)
Figure 11 shows the conversion of acetic acid to biogas by Methanosarcina Barkeri.
About 95% of the acetic acid is converted to biogas, only about 3% to cell material.
Page 21 of 30
© Copyright 2008 IGRC2008
About 2% of the substrate are needed for energy supply, whereby the bigger part of
energy related conversion results in biogas in the end.
Figure 11: Carbon balance of complete degradation of acetic acid to biogas by
Methanosarcina Barkeri (Wandrey & Aivasidis, 1983)
Synthesis of New Cell Material
To synthesise new cell material, microorganisms have to degrade substrate. The
substrate degradation to biomass can be described stoichiometrically. An example is
the relation used by Moletta et al. (1986) for acid-forming bacteria, which use glucose
as substrate:
C6H12O6 1.2 NH3 1.2 C5H7NO2 3.6 H2O (46)
According to this relation 1.2 mol acid-forming bacteria are formed by 1 mol glucose.
Considering the molar mass of glucose and biomass and assuming that the empirical
formula, C5H7NO2, represents 92% of the dry biomass, the yield coefficient of glucose
to acid-forming bacteria, Yx, is 0.82 g/g.
The empirical formula of biomass was published by Loehr (1974). Other representative
molecular structures are C75H105O30N15P (Loehr, 1974) or C5H9O3N (Mosey, 1983). The
chemical constitution of the formed biomass is not constant and varies with bacteria
group, growth phase and utilised substrate.
The substrate degradation due to biomass formation (dS/dt) x depends on the change
of cell concentration over time dX/dt and can be expressed as:
1
xxx
dS dX X
dt Y dt Y


(47)
Energy Supply of Bacteria
Bacteria need energy for their living to synthesise cell ingredients, which are degraded
continuously, or for osmotic activities to sustain the concentration gradient between
cell interior and exterior, see e.g. (Sinclair & Kristiansen, 1993) The energy demand
can be divided into growth energy and maintenance energy. The required energy is
provided by the substrate. However, the substrate limiting the growth is not
necessarily the same as the substrate limiting the energy supply (Stouthamer, 1976).
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The energy storage of a bacteria cell is ATP (Adenintriphosphat). Decomposition of
ATP in ADP (Adenindiphosphat) releases energy. For recycling of ADP to ATP energy is
required. During the degradation of one glucose molecule to three acetic acid
molecules, 6 molecules ATP will for example be produced (Moletta et al., 1986).
According to Stouthamer (1976), the maximum yield for cell production is 32 g
biomass per mol ATP. That means 0.938 g Glucose are required to synthesise 1 g
biomass. This coefficient is called growth energy rate Ksx.
The maintenance energy coefficient is specified by Moletta & Albagnac (1984) with
0.0169 mol ATP per g biomass and per hour. Assuming that degradation of 1 mol
Glucose to 3 mol acetic acid will result in 6 ATP, the maintenance energy rate Kmx is
12.1 g glucose per g active biomass and per day.
According to Moletta et al. (1986), the substrate degradation for energy supply can be
written as:
sx mx
es
dS K X K X S
dt K S

(48)
The first part on the right side is the substrate degradation for growth energy supply
and the second part on the right side is the substrate degradation for maintenance
energy supply.
Conversion of Substrate
The conversion of substrate to products can be considered stoichiometrical as well,
e. g. the degradation of acetic acid to methane:
3 4 2 CH COOH CH CO (49)
Thus, degradation of 1 mol acetic acid results in 1 mol methane. Using the molar mass
of acetic acid and methane, the yield coefficient of acetic acid to methane, Ys, is
0.27 g/g. Using the calculated yield coefficient, the substrate degradation due to
product formation can be determined as:
1
csp
dS dP
dt Y dt


(50)
Vavilin et al. (1994), e. g., specified representative molecular composition of proteins
(C16H30O8N4, 404 g/mol), lipids (C47H96O9, 804 g/mol) and carbohydrates (C6H12O6,
180 g/mol). Using these molecular compositions, a stoichiometric consideration of the
hydrolysis step becomes possible, too.
Further stoichiometrical approaches can be found in models by Moletta et al. (1986),
Mosey (1983), Angelidaki et al. (1999), Bryers (1985), Hill (1982), Siegrist et al.
(2002) or very detailed at Knobel & Lewis (2002).
5.3. Kinetics of Product Formation
The end product of the considered fermentation process is biogas. Nevertheless, also
a lot of intermediates are very important products. The kinetics of product formation
can be calculated based on the kinetics of substrate degradation and of bacterial
growth, respectively. Gaden (1959) investigated fermentation processes and classified
products into three types:
Type I: products, which result from primary energy metabolism,
Type II: products, which result from energy metabolism indirectly, and
Type III: products, which obviously do not result from energy metabolism.
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Common classifications of products became more detailed today, but using the
classification of Gaden (1959), the kinetics of product formation is well distinguishable
(Sinclair & Kristiansen, 1993).
Type I: the product is produced at the same time as substrate is degraded; an
example is the fermentation of alcohol (see figure 12).
p1 p1
dP Y X Y dX
dt dt
(51)
Type II: the product is produced at side reactions or following interactions of direct
metabolic products; an example is the fermentation of glucose to lactic acid
(Luedeking & Piret, 1959). Therefore, the product formation is delayed and two
maxima appear in substrate degradation and bacterial growth.
p1 p2 p1 p2
dP Y X Y X Y dX Y X
dt dt
(52)
Type III: formation of complex molecules (biosynthesis), such as the formation of
antibiotics. Energy metabolism is practically complete while the complex product
accumulates.
p2
dP Y X
dt
(53)
To model biogas productions primarily type I is usually be used, e. g., by Andrews &
Graef (1971), Bryers (1985), Denac et al. (1988) and Sinechal et al. (1979).
substrate concentration
specific growth rate
XSP
substrate concentration substrate concentration
Figure 12: Substrate degradation, bacteria growth and product formation at different
fermentation types (Gaden, 1959)
6. DISCUSSION
To model the whole biogas digestion process based on biological and physico-chemical
background, the kinetics of bacterial growth, substrate degradation and product
formation have to be considered. The corresponding approaches differ depending on
the requirements and the authors.
The objective of this work is the identification of an appropriate model for describing
the process of biogas digestion. Therefore, 22 existing models for anaerobic digestion
in biogas production, in completely stirred tank reactors (CSTR), were analysed with
regard to:
1) included parameters,
2) complexity / handling,
3) scope of application, e.g., process type, kind of substrate, substrate concentration,
temperature range, and
Typ I Typ II Typ III
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© Copyright 2008 IGRC2008
4) accuracy.
Included parameters: The included parameters are summarised in table 7. Parameters
here mean influence factors, which were considered, such as inhibitors, temperature
and pH value. Rarely included parameters are:
1) the temperature, even though this parameter is supposed to be the most important
ambient condition,
2) the pH value and gas-liquid equilibrium, though both factors can inhibit the
process,
3) the lag phase, though this phase is important for the adaption to new substrate or
generally for the dynamic behaviour of processes,
4) the decay rate, even though this rate reduces the amount of active biomass and
therefore the substrate degradation and product formation, and
5) the inhibition by some components such as NH3, LCFA or H2.
For some investigations, the impact of these parameters is insignificant, e.g. to study
processes at constant temperature. Therefore, at first the requirements to model a
process have to be defined. The effect of neglecting these parameters on the process
model has to be proven carefully.
Complexity / handling: Also mentioned in table 7 are the considered bacteria groups
and reactions. The amount of considered bacteria groups, reactions and included
parameters affects the complexity of the model. Numerous considered bacteria groups
and reactions as well as many included parameters increase the complexity. There are
two examples to give an impression:
Converti et al (1999) developed a very simple model to describe batch processes. The
methane production is directly ascertainable from the initial substrate concentration by
a first-order kinetics model depending on time. The cell concentration of bacteria is
assumed to be constant due to their very slow growth. If the cell concentration and
the methane yield on substrate are known, only a kinetic constant k has to be fitted to
experimental data. This model is not complex, very simple to handle and appropriate
to get results in a short time. Influences of ambient conditions and other requirements
except substrate concentration cannot be studied.
The Anaerobic Digestion Model No. 1 (ADM1) of the IWA Anaerobic Digestion
Modelling Task Group (Batstone et al, 2002) includes 8 bacteria groups and 11
reactions. Death rate, disintegration and hydrolysis were considered as well as the
influence of the pH value, ionic equilibrium and gas-liquid equilibrium. Only the
influence of temperature and the yield on substrate to maintenance energy are
neglected. This model is one of the most comprehensive ones and very complex. In
the model, 32 dynamic state concentration variables were used, which increases the
effort of validation enormously. The handling of the numerous differential equations is
time consuming and sophisticated, but enables the design of large-scale plants, the
investigation of optimisation and operation of plants as well as the prediction of
process failure.
Scope of application: Table 7 also contains the process type and the substrate, which
was used in laboratory or large-scale plants to fit the model parameters. Desirable is a
general model, which is applicable for every kind of substrate and for every process
type. Quite often models are adapted using experimental data from batch processes.
In these cases special care is needed when applying these models to steady-state or
dynamic processes. Also the transferability of models to other substrates has still to
be proven, because the kinetic parameters mainly depend on substrate.
Since the majority of models does not include the dependency on temperature, their
application is limited to certain temperatures. Biswas et al. (2006) used data of batch
processes at 40°C, Garcia-Ochoa et al. (1999) at 35°C and Rao & Singh (2004) at 25
Page 25 of 30
© Copyright 2008 IGRC2008
and 29°C, e.g. The applicability of these models at different temperatures is
questionable.
Table 7: Selected models of anaerobic digestion to produce biogas and most
important parameters included in the models (only completely stirred tank
reactors, a – not clear, BVS – biodegradable volatile solids, CH –
carbohydrates, HS – undissociated substrate concentration, VFA – volatile
fatty acids, VS – volatile solids, XL – crude lipids, XP – crude proteins)
Growth Kinetics (A - Andrews, CH Chen & Hashimoto, FO - firstorder,
H - Haldane, M - Monod)
Adapted Substrate
Process Type
Input
Output
Substrate Inhibition
Yield of Substrate to Product
Yield of Substrate to Biomass
Yield of Substrate to Energy
Death Rate
Disintegration
Hydrolysis
Stoichometric Equations / Stages
Bacteria Groups or Stages
Temperature
pH or Ionic Equilibrium
Gas-Liquid Equilibrium
Andrews & Graef,
1971
A sewage water steady-state,
dyn
HS (HAc, HPr
or HBt)
CH4, CO2 HS (HAc, HPr
or HBt)
x x - - - - 1 1- x x
Angelidaki et al,
1999
FO, M, A, H organic waste dyn CH, XL, XP CH4, CO2,
H2S
HAc, LCFA,
NH3
x x - x x x 10 8x x x
Bala & Satter,
1991
A swine waste dyn BVS CH4 VFA x x - x - - 2 2- - Batstone et al,
2002
FO, M
inhibited
n.s. steady-state,
dyn
COD CH4, CO2,
H2, H2Od
H2, NH3 x x - x x x 11 8- x x
Biswas et al, 2006 M municipal
waste
Batch CH, XL, XP CH4, CO2 - x - - - - - 5 2- - Bryers, 1985 FO, M various Batch, dyn,
steady-state
BVS CH4, CO2, H2- x x - x - x 6 3- x x
Carr & O'Donell,
1977
A, FO lag
term
nutrient
medium
dyn HS (HAc, HPr
or HBt)
CH4, CO2 HS (HAc, HPr
or HBt)
x x - x - - 1 1- x x
Chen & Hashimoto,
1978
CH various steady-state COD or VS CH4 - x x - - - - 1 1- - Converti et al,
1999
FO vegetable
refuses
Batch COD CH4 - x - - - - x 1 1- - Costello et al,
1991a
M inhibited,
komp.,
nonkomp. glucose dyn
soluble
glucose
CH4, CO2,
H2, H2O
H2/NDAH,
VOA x x x x - - 15 6- x x
Denac et al, 1988 M molasses
wastewater
dyn COD CH4, CO2 - x x - x - - 5 5- - Garcia-Ochoa et al,
1999 FO cattle manure Batch COD, VFA CH4 - x x x - - x 6 2- - Hill, 1982 A animal waste steady-state,
dyn
soluble
organics
CH4, CO2 VFA x x - x - x 7 5x - Knobel & Lewis,
2002
FO, M, M
inhibited
wastewater Batch, dyn,
steady-state
CH, XL, XP CH4, CO2,
H2, H2S
H2, undiss.
VFA, H2S
x x - x - x 17 12- x x
Moletta et al, 1986 A various Batch glucose
equivalent
CH4 VFA x x x x - - 2 2- x Mosey, 1983 M glucose steady-state,
dyn
glucose CH4, CO2 NADH x x x x - - 7 4- x Rao & Singh, 2004 FO municipal
waste
Batch BVS gas
production
- x - - - - xa 1- - - Shin & Song, 1995 FO various Batch COD CH4 - x - - - - x 2 2- - Siegrist et al, 2002 FO, M
inhibited
sewage sludge dyn COD CH4, CO2, H2NH3, HAc, H2 x x - x - x 7 6x x x
Simeonov et al,
1996
M animal waste dyn soluble
organics
spec. prod.
rate
- x x x x - x 3 2- - Sinechal et al,
1979
M, A algae semicontinuous
BVS CH4 HPr, HBt x x - x - - 2 2 x - Vavilin et al, 1994 FO, Moser or
Ma
food industry
wastewater
Batch CH, XL, XP,
others
CH4, CO2,
H2S, H2
H2, NH3,
H2S, HPr
x x - x x x 13 7x x -
Accuracy: In most cases deviations between simulated data and data, which were
produced experimentally in laboratory or in large-scale biogas plants, were not stated
directly. Thus, the accuracy of the selected models cannot be compared easily.
All models are fitted to very different requirements and data bases. In general,
objectives and requirements have to be defined (such as medium, accuracy, process
type, etc.) to select an appropriate model. Extending the applicability and accuracy of
a model, results in an increasing number of involved parameters and an elaborate
validation. In any case, compromises have to be accepted.
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© Copyright 2008 IGRC2008
7. CONCLUSION
A large number of existing models for biogas production were analysed and compared.
The work has been focussed on selecting, enhancing or redeveloping an appropriate
model for the degradation process, independent of process type and kind of substrate.
Some of the more general approaches are promising, but for a final selection an
evaluation of accuracy is needed.
Therefore, a few models will be simulated and fitted to a set of experimental data. The
fitting of models requires accurate experimental data with a large amount of
parameters. The data will be taken from literature, which is implemented in our
database or from own empirical data produced in laboratory, test facilities or largescale
plants. In order to compare the accuracy of the models, they will all be fitted to
the same set of data.
8. ACKNOWLEDGEMENT
The work presented in this paper was carried out as part of the “competence centre
thermodynamics of gases” initiative jointly financed by E.ON Ruhrgas and by the
Ministry of Innovation, Science, Research and Technology of North Rhine-Westphalia.
The corresponding financial support is gratefully acknowledged.
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http://digilib.its.ac.id/bookmark/6036/DAQ, 04/11/2010 jam 12.30 wib
PERANCANGAN SIMULATOR SISTEM PENGENDALIAN PH PADA BIOREAKTOR
ANAEROB BERBASIS FUZZY LOGIC CONTROLLER
THE DESIGN OF pH CONTROL SYSTEM FOR ANAEROBIC DIGESTER SIMULATOR
BASED ON FUZZY LOGIC CONTROLLER
Created by :
Rahmawati, Nila ( 2404100098 )
Subject:
Alt. Subject :
Keyword:
Teknik pengawasan otomatis
Automatic control
Anaerobic digester
Labview
DAQ
[ Description ]
Bioreaktor anaerob sangat efektif untuk mengolah limbah organik dan menghasilkan biogas
sebagai sumber energi alternatif. Mikroorganisme dalam bioreaktor hanya dapat tumbuh
secara optimal dalam range pH 6.7�7.4. Untuk itu, dirancang simulator sistem pengendalian
pH berbasis Fuzzy Logic Controller menggunakan software LaBVIEW yang dilengkapi data
akuisisi (DAQ) agar dapat merespon gangguan dari eksternal. Kontroler ini memanipulasi
sinyal error (selisih antara pH terukur dengan set point) untuk mengatur aliran Bikarbonat (B)
dan Dilution/pengenceran (D). Sistem openloop hanya mampu menerima uji step masukan
substrat S2 maksimum 15.9, lebih dari itu terjadi wash out, dengan pH 6.98 dan
menghasilkan biogas 3.6x10-3 liter/jam. Sedangkan sistem closeloop dapat menerima uji step
masukan substrat S2 hingga 34.0, dengan pH 6.96 dan biogas yang dihasilkan jauh lebih
besar, yaitu 18x10-3 liter/jam. Dari hasil pengujian dengan pemberian gangguan dari
eksternal untuk sistem closeloop yang dilengkapi DAQ, diperoleh saat tegangan adaptor 3.00
Volt analogi dengan substrat S2 13.54, sehingga dapat dikatakan bahwa bioreaktor dapat
merespon gangguan dari eksternal, dimana tegangan dari adaptor tersebut merupakan
representasi dari gangguan substrat S2.
Alt. Description
Anaerobic digester is very effective to process organic waste and producing biogas as an
alternative energy source. Microorganism in bioreactor is only able to grow optimally in pH
range 6.7-7.4. Therefor, it is designed a simulator of pH control system based on Fuzzy Logic
Controller using LabVIEW software completed Data acquisition (DAQ) in order to respon
external noise. This controller manipulate error signal (difference between measured pH and
the set point) to control the flow of bicarbonate (B) and Dillution (D). Openloop system is
only able to accept input of step test of substrate S2 15.9 maximum, if it�s more than that
point, it will wash out. In that maximum point, it is 6.98 pH and producing 3.6x10-3
liters/hours. While closeloop system is able to accept input of step test of substrate S2 until
34.0, with 6.96 pH and much more biogas, i.e. 18x10-3 liters/hours. From testing result with
external noise for closeloop system completed DAQ, it is gained when the adaptor voltage of
3.00 Volt analogized with substrate S2 of 13.54, so it can be said that bioreactor is able to
respon the external noise, where the voltage of the adaptor represents the noise of substrate
S2.
Contributor :
1. Dr. Ir. Totok Soehartanto, DEA.
Date Create : 10/12/2009
: Text
Type
: Pdf
Format
: Indonesian
Language
: ITS-Undergraduate-3100009036146
Identifier
Collection ID : 3100009036146
Call Number : RSF 629.801 511 313 Rah p
Source :
Undergraduate theses of Physic Engineering, RSF 629.801 511 313 Rah p, 2009
Coverage :
ITS Community Only
Rights :
Copyright @2009 by ITS Library. This p ublication is protected by copyright and permission
should be obtained from the ITS Library prior to any prohibited reproduction, storage in a
retrievel system, or transmission in any form or by any means, electronic, mechanical,
photocopying, recording, or likewise. For information regarding permission(s), write to ITS
Library
http://www.engr.colostate.edu/~meroney/PapersPDF/CEP08-09-2.pdf download 04/11/2010
jam 14.11 wib
Civil and Environmental Engineering Department, Colorado State University,
Fort Collins, CO 80523, robert.meroney@colostate.edu
1
1
2
3
CFD Simulation of Mechanical 4 Draft Tube
5 Mixing in Anaerobic Digester Tanks
6
17 Robert N. Meroney, Ph.D., P.E. Colorado
8
9 prepared for
10 WATER RESEARCH
11 Journal of the International Water Association (IWA)
12
13 August 2008
14
15
16
17 Key words
18 anaerobic digesters, high-rate digesters, jet mixing, mechanical draft-tube mixing,
19 continuous stirred tank reactors (CSTR), computational fluid dynamics (CFD), stabilization,
2 Civil and Environmental Engineering Department, Colorado State University,
Fort Collins, CO 80523, robert.meroney@colostate.edu
2
CFD Simulation of Mechanical 1 Draft-tube
2 Mixing in Anaerobic Digester Tanks
3
4 2Robert N. Meroney, Ph.D., P.E. Colorado
5 ABSTRACT: Computational Fluid Dynamics (CFD) was used to simulate the
mixing
6 characteristics of four different anaerobic digester tanks (13.7, 21.3, 30.5, and 33.5
m)
7 equipped with single and multiple draft impeller tube mixers. Rates of mixing of
step and
8 slug injection of tracers were calculated from which digester volume turnover time
(DVTT),
9 mixture diffusion time (MDT), and hydraulic retention time (HRT) could be
calculated.
10 Washout characteristics were compared to analytic formulae to estimate any
presence of
11 partial mixing, dead volume, short-circuiting, plug or piston flow.
12
13 1.0 INTRODUCTION
1
14 The intent of anaerobic digestion is the destruction of volatile solids by
microorganisms in
15 the absence of oxygen. Digestion rates are primarily functions of a) solid retention
time, b)
hydraulic retention time, c) temperature ~ 95oF, and d) mixing. 16 Environmental
engineers
17 generally agree that the key to good continuous-stirred-tank-reactor
(CSTR)
anaerobic digester operation is mixing. Mixing 18 produces uniformity by
reducing
19 thermal stratification, dispersing the substrate for better contact between
reactants,
20 and reduces scum buildup in the digester. If mixing is inadequate, the
efficiency of
digestion is reduced.2, 4, 6, 13 21
22 Several “rules-of-thumb” are common among digester designers to size
23 anaerobic digestion systems, these include:
24 - Digester Volume Turnover Time (DVTT) = (Tank volume/Pump Capacity),
25 - Hydraulic Retention Time (HRT) = (Tank volume/Sludge volume input rate),
26 - Unit Power (UP) = (Pump horsepower/Tank volume/1000), and
27 - RMS Velocity Gradient (VGT or G) = (Pump power/Tank volume/Sludge
viscosity).
3 Solid Retention Time (SRT), in days, is equal to the mass of solids in the
digester divided by the solids removed; however, for digestion systems without
recycle,
SRT and HRT are equal.
3
DVTT is a measure of anticipated mixing capacity of the digester, HRT 1 is an
indicator of
the mean reaction time32 , whereas UP and G quantify pump capacity and normalize
mixing
3 intensity based on the flow properties of the sludge. Desirable magnitudes of
DVTT, HRT,
UP and G are typically about 0.5-1 hr, 15-30 days, 0.2-0.3 Hp/1000 ft3, and 50-85 s14 ,
respectively.1,13 5
6 But once a system is designed, some confirmation of system mixing efficiency is
7 often sought. In the past this has been determined by full-scale tracer methods
which can
8 be quite time-consuming and require internal placement of instrumentation and
expensive
9 test apparatus. The experimental procedures require seeding a slug of inlet sludge
with
10 tracers (Eg. lithium chloride) and inferring sludge residence time from
measurements of
11 the “wash out” of tracer concentrations within the tank and at the outlet over
extended
12 times (up to 90 days). The final results are expressed in terms of measured
Mixing
13 Dispersion Time (MDT, the time for the slug to mix uniformly throughout the tank
such that
14 the outlet tracer concentrations reach a maximum), a measured Hydraulic
Retention Time
15 (HRT, associated with the time constant for the exponential decay of outlet tracer
16 concentrations), and the Active Volume (AV, ratio of nominal tank volume minus
dead or
17 inactive volume to nominal tank volume). AV is normally implied from tracer
washout tests
by comparing actual decay of tracers at the digester exit to analytic or ideal decay
rates.3, 18
4, 10, 11, 17 19
20 Today modern Computational Fluid Dynamics (CFD) software permits the
21 confirmation of mixing efficiencies for different digester configurations before
construction,
4
hence, eliminating the need for expensive post-construction field tests.8,9,14,15,17 1
Furthermore, this approach eliminates the painful realization a system 2 is inefficient
after
3 installation. CFD visualization and analysis also provide an opportunity to examine
4 alternative inlet, outlet and pump configurations. Visualization of fluid velocity
vectors,
5 streamlines and particle trajectories can help the user understand the mixing
processes,
6 and it can identify possible problems in advance. This paper will examine the
mixing
7 characteristics of four different size digester tanks equipped with alternate
arrangements
8 of external and internal draft tube mechanical mixers using CFD simulation
methods.
9 Resultant tank mixing behavior has been compared with analytic integral models
which
10 allow for the effects of partial mixing, dead volumes, short-circuiting, and piston
flow.
11 2.0 COMPUTATIONAL MODEL
12 A CFD solution of mixing in such mixed tanks requires specification of the tank
geometry,
13 inlet, outlet, boundary and initial conditions. The solution requires the
simultaneous CFD
14 solution of the discretized mass, momentum, and energy equations.
15 2.1 Flow Domain and Boundary Conditions The flow domain consisted of a
cylindrical
16 tank of a given diameter and height, inlet and outlet pipes, and impeller driven
draft tubes
17 placed around the perimeter or within the tank. No-slip boundary conditions were
imposed
18 on all wall surfaces. At the inlet a constant flow rate was specified, and the outlet
was
19 treated as a mass flow boundary. Pumps in the draft tubes were simulated as
virtual fan
20 areas across which a pressure rise of ~6500 pascals was adjusted until a desired
draft 21 tube flow rate was obtained.
22 2.2 Computer Code The commercial CFD code Fluent, version 6.3, developed by
23 Fluent/ANSYS was used for all calculations. The code uses a finite volume
method based
5
on discretization of the governing differential 1 equations.
2 2.3 Turbulence Model The standard _-_ turbulence model was used for all
calculations
3 with standard wall function approximations near walls; hence, additional transport
4 equations for turbulent kinetic energy (_) and eddy dissipation (_) were solved for
these
5 quantities. The standard _-_ model has been successfully used by many
researchers for
similar mixing problems.8, 9, 15 6 When draft-tube Reynolds number exceeded 10,000
previous calculations agreed well with experiments.15 7 In the current analysis the
8 minimum draft-tube Reynolds numbers always exceeded 285,000.
9 2.4 Computational Grids The geometry of the tank was modeled in GAMBIT which
10 discretized the domain into an unstructured array of tetrahedral mesh elements.
Total cells
11 ranged between 775,000 to 1,640,000. Elements were concentrated in regions of
walls,
12 inside draft tubes, and near flow inlet and flow outlet to preserve details of velocity
shear
13 and increased turbulence.
14 2.5 Solver A 3-D, implicit, pressure based, segregated, steady solver algorithm
was
15 used for predicting the velocity and turbulence fields, and a time dependent mode
was
16 used for predicting sludge concentrations. The SIMPLE pressure-velocity
coupling method
17 was specified, and second-order upwind discretization molecules were used for
all
18 discretized terms. Under-relaxation factors were 0.3, 1.0, 1.0, 0.7, 0.8, and 0.8 for
19 pressure, density, body forces, momentum, kinetic energy, and dissipation,
respectively.
20 The solution strategy for the large tanks was to initially solve for the steady-state
flow
21 circulation produced by the draft tubes and inlet flow, and then introduce a step
change in
22 inlet concentration or introduce a slug of tracer at time zero in a time dependent
evaluation
23 of mixing. During the solution for mixing, solutions for the flow field were held
constant.
6
The inlet sludge was assumed diluted such that the density of the 1 solid-water
suspension
2 and its absolute viscosity approximate the characteristics of water. Low shear
3 measurements of actual sludge suggest higher apparent viscosities are possible
due to
4 non-Newtonian effects, but given the property uncertainties many researchers use
the
lower viscosity of water when active mixing occurs.5, 12 5
6 2.6 Convergence Criteria The method to judge convergence was to monitor the
7 magnitude of scaled residuals. Residuals are defined as the imbalance in each
8 conservation equation following each iteration. The solutions were said to have
converged
when the scaled residuals go below values of 10-49 .
10 3.0 SMALL TANK VALIDATION EXERCISE
11 In 1959 Cholette and Cloutier derived integral models which described the time
dependent
12 tank mixing in idealized reactors when influenced by imperfections in the mixing
process.3, 4 13 They created algebraic expressions which included the deleterious
effects of
14 partial mixing, short-circuiting of inlet flow directly to the outlet, the effects of plug
(or
15 piston) flow which ejects unmixed fluid from the outlet, and the impact of dead or
non16
participant regions on the outlet concentrations. Later Wolf and Resnick proposed a
generalized washout equation based on these ideas,17 17 where
18
19 Eq (1)
20
21
22
23
7
One should note that with so many variables, it is sometimes difficult 1 to
differentiate
2 between effects of dead space, d, measurement error, r, and partial mixing, a,
when f ~ p
3 are nearly zero, especially when mixing efficiency is near ideal. Indeed, it is not
unusual
4 for curve fitting to produce small but negative dead space volumes, which is
obviously not
5 physical. Alternatively dad zones can be found by calculating the fractional volume
of the
6 cells with very low liquid velocities. Veviskar and Al-Dahhan suggested that regions
with
7 velocities less than 5% of the maximum velocities could be considered stagnant or
inactive
regions.14 8 One advantage of this method is it does not permit negative dead
volumes, but
9 a disadvantage is that it does not relate directly to the washout equation.
10 A small tank experiment was performed by Cholette and Cloutier to examine the
influence of partial mixing and short-circuiting on tank mixing.3 11 They introduced
fresh water
12 into a tank filled with a 1/20 N solution of NaCl in the configuration shown in
Figure 2. After
13 running the agitator for some time at a fixed speed to allow the mixing pattern to
fully
14 develop, fresh water was introduced suddenly at a rate of 4.35 liters/min (1.15
gpm).
15 Hydraulic retention time (HRT) for this experiment was 1.56 hrs. They measured
outlet
16 concentrations every five minutes and plotted them versus time on semilogarithmic paper.
17 Axis intercepts and line slopes were fit to the data to define coefficients related to
partial
18 mixing, a, and short-circuit behavior, f, in Equation 1. Mixing intensity was
qualitatively
19 parameterized by the rotation rate of the mixer. At zero mixer rotation the flow
was driven
20 by only the inlet jet such that mixing parameters were f = 0.23 and a = 0.38, and
when
21 mixer operated at full speed mixing parameters approached f = 0.0 and a = 1.0.
22 A CFD model of the Cholette and Cloutier apparatus was constructed to validate
the
23 methodology described in Section 2.0. The domain was filled with 381,000
tetrahedral
8
cells adapted for greatest resolution near the upper surface of the fluid and 1 around
the inlet
2 jet and outlet pipe. The inlet to the outlet pipe was positioned to two locations
below the
3 fluid surface (_z = 0.65 and 1.30 cm) since exact location was not provided by the
authors.
4 Calculations did not show any significant differences in results. Cases were also
simulated
5 for both laminar and turbulent mixing for the fan off case, again differences were
small.
6 The turbulence model used was the realizable kappa-epsilon model. The model
was run
7 with a pressure-based implicit unsteady solver, and residuals were set at 0.001 for
flow
8 quantities and 0.0001 for concentrations. The mixing turbine was simulated by
specifying
a circular fan area of 25 cm2 9 with a pressure drop of _p = 345 pascals, and
tangential swirl
speed of 30.5 cm/sec. The tank was filled with salt-water of density 1027 kg/m3 10
(sg =
11 1.00292) and fresh water was injected of density 998 kg/m (sg = 1.00). Outlet and
tank
12 average salt-water concentrations were tabulated versus time. Results are
reported in
13 Figure 3 for the cases with no fan mixing and strong fan mixing.
14 When fresh water is introduced into the mildly turbulent salt-water filled tank, the
15 mixing is inhibited by the vertical density gradient induced by the two fluids. The
fresh
16 water rises directly to the surface spreads radially, and almost immediately is
entrained into
17 the outlet producing significant short-circuit behavior (Figure 4a). The stratification
inhibits
18 vertical mixing such that particle tracks are limited to the upper 1/3 of the tank.
(Figure 5a).
19 The integral parameters, a and f equal 0.65 and 0.25, respectively. This
corresponds to
20 behavior Cholette and Cloutier reported of 0.63±0.05 and 0.20±0.05 for a turbine
rotating
21 at 140 rpm. When the numerical fan was set to enhance mixing (_p=345 pascals,
Vtangentia l 22 = 30.5 cm/s), density stratification was eliminated, the outflow removed
fluid mixed
23 over the entire tank volume (Figure 5b), and particle tracks filled the entire volume
before
9
exiting through the outflow pipe (Figure 5b). The resultant integral 1 parameters, a
and f
2 equal 1.0 and 0.0 respectively. These equal the values found by Cholette and
Cloutier
3 when their turbine rotation exceeded 215 rpm. Not ice in Figure 3 that the out let
concentration ratio Cso/CoCFD is contiguous with Ctank/CoCFD 4 which indicates the
outflow is
5 releasing fully mixed tank fluids. Parameters calculated for various fan mixing
intensities
6 are shown in Figure 6.
7 A caveat should be mentioned concerning the comparisons of actual tank mixing
8 performance in the Cholette and Cloutier experiment with the analytic model found
in
9 Equation 1. Detailed mixing deviates from the simplified idealized assumptions
inherent
10 in this equation. As noted in Figure 3 short-circuiting takes finite time to exhibit its
11 influence, and the initial inhibition to mixing due to stratification decreases as time
12 proceeds which results in the increase in magnitude of the partial mixing
parameter, a, with
13 time.
14 3.0 FULL SIZE TANK ANALYSIS AND RESULTS
15 Mixing during unit operations can be achieved by impellers, introduction of gas
jets, or the
16 use of mechanical draft-tube mixing. During draft-tube mixing part of the liquid
from the
17 tank is re-circulated into the tank at high velocities through draft tubes with the
help of
18 pumps and nozzles. The resulting fluid jet entrains surrounding fluid and creates
a flow
19 pattern that circulates radially and circumferentially about the tank from top to
bottom.
20 Draft tubes are categorized as external (EDT) when the pump is outside the tank
and
21 internal (IDT) when the pump and tube are within the tank volume. Tube nozzles
are
22 generally directed at an angle to the radius to improve mixing efficiency.
23
10
Recently, Wasewar and Sarathi used CFD modeling to determine 1 optimum nozzle
geometries.15 2 They also reviewed some nine previous studies that used cfd codes
to
3 evaluate nozzle mixed tanks. They used the commercial CFD code Fluent 6.2, with
4 50,000-80,000 tetrahedral cells over the calculation domain, the SIMPLE and PISO
5 algorithms for steady and transient pressure-velocity coupling, the segregated
solver
6 algorithm, and the standard kappa-epsilon turbulence model. They concluded their
CFD
7 simulations faithfully reproduced experimental measurements for cases where the
draft8
tube Reynolds number exceeded 10,000. Since their calculations were limited to
tanks
9 approximately 0.5 m diameter and 0.5 m high with jet diameters of 0.01 m, it was
10 considered worthwhile to present calculations here that considered full size tanks
in actual
11 application configurations.
12 A set of four different tank and draft tube geometries were examined to provide a
13 range of performance data concerning full size tanks with different draft tube
14 arrangements. The geometry, pump and flow characteristics, and performance
parameters are displayed in Figure 7 and Table 1. Tank volumes range from 1k to
10k m3 15
16 (293 k to 265 M gallon) capacity, draft tubes numbered 1, 4 and 5 in various EDT
and IDT
arrangements, and nominal draft tube flow rates varied from 28 to 47 m 3 17 /min/tube
(7,500
18 to12,500 gpm/tube) with sludge inlet/outlet rates set to 0.38 cubic m/min (100
gpm).
19 Sludge exited the tank from a pipe located at tip of the conical bottoms. In all
cases
20 studied draft tube jet Reynolds numbers exceeded 285,000.
21 3.1 Model 1: 30.5 m Diameter Tank with 4 External Draft Tubes This tank was
designed
22 to produce a nominal HRT = 15.2 days. The sludge was introduced into the tank
at a level
23 1.5 m below the fluid surface midway between two adjacent EDT positions
through a 25.4
11
cm diameter pipe mounted on the side wall. Inlets and outlets to 1 the draft tubes
were
oriented at 45o 2 to produce a clockwise flow when viewed from above. Mixing was
tested
3 after the tank system reached a steady state condition, a constant magnitude of
tracer was
4 added to the inlet pipe and the subsequent mixing and exit of the tracer from the
outlet was
5 recorded.
Plots of velocity magnitude, V, and turbulence intensity, TI = (ui’2)½ /Vref6 , across the
7 tank diameter at five depths are shown in Figure 8. The draft tube jets induce a
rotational
8 circulation that is constant with depth, zero at tank center and maximum near the
tank walls
9 (Figure 9). Turbulence is maximum in the high shear regions surrounding the jets
and
10 close to the walls, and turbulence persists across the tank center (Figure 10).
Paired
11 Figures 11 & 12 and 13 & 14, display the pathlines and particle tracks following
tracers
12 emitted from the sludge inlet and draft tube fans, respectively. Pathlines follow
circular
13 paths associated with the average fluid velocity motion, whereas particle tracks
display
14 erratic mixing about the pathlines resulting from local turbulence disturbances.
Mixing
15 occurs as a result of fluid dispersion associated with the particle tracks. Mixing
associated
16 with the EDT nozzles distributes circumferentially, fluid from top to bottom, and
from tank
17 center to walls very effectively. Multiple draft tubes help turn the fluid over as they
18 withdraw fluid from the tank top and reintroduce it at the tank bottom. A mixing
particle
19 traverses the tank many times before it is removed at the oulet at the bottom of
the tank
20 cone.
21 To evaluate the Hydraulic Retention Time and the efficiency of the mixing
geometry
22 a constant quantity of tracer was introduced at the sludge inlet starting at time
zero.
23 Figures 15, 16, and 17 display the progressive growth of mixing at three typical
times as
12
the tracer spread across the tank. Initially the tracer plume grows along 1 the wall in
a cigar
2 shaped plume, but then tracer is drawn out of the plume and reintroduced by the
nozzles
3 near the tank bottom, which produces four additional circular plumes. These
plumes
4 eventually coalesce, mix, and the level of concentration increases dynamically.
Since, the
5 tank outlet is at the bottom of the tank cone, concentrations tend to appear
symmetric
6 about the tank center. Concentrations surfaces are progressively drawn downward
and
7 swept from the outlet until the tank (at long times) is completely filled with the
tracer at its
8 inlet concentration.
9 The time variation of tracer concentration at the sludge outlet relative to sludge
inlet,
CSO/CSI 10 CFD, was recorded during the computations and is plotted in Figure 18.
The same
plot also includes the CFD calculated tank average concentrations, Ctank/CSI 11 CFD.
The line
Ctank/CSI 12 Analytic is calculated from the expression, /
........(2). HRT
exp
CCt
Tank SI 
This expression lies directly over the Ctank/CSI 13 values computed by CFD, which
confirms that
14 the calculation obeys the species conservation equation. The fit of this equation
to the
15 data also provides the value for tank Model 1 of HRT = 17.88. As noted in Table
1, the
16 nominal value of HRT for the actual CFD calculated conditions was 17.7, which
agrees
17 closely to the CFD generated value.
18 If the mixing was ideal (instantaneous mixing of the tracer over the entire tank)
then
the sludge outlet concentration would also follow this line. Note that C SO/CSI 19 CFD
initially
20 lags the idealized mixing curve. This may be due to a number of real phenomena
21 discussed earlier in Section 3.0, and considered in the analytic expression
Equation 1. For
22 the Model 1 tank the deviation reflects the finite mixing rate and finite travel time
for the
23 tracer between the sludge inlet and the sludge outlet. As a result initial fluid
passing out
13
of the tank is fluid displaced out by inlet fluid in a piston or plug-flow 1 manner.
Equation 1
with the coefficients p = 0.0007 and a = 0.9993 is shown as curve CSO/CSI 2 Piston &
Partial
3 Mix. Alternatively, one might identify deviations from ideal performance as a dead
volume
4 issue; and, using the method of fractional volumes with velocities less than 5% of
the
5 maximum as suggested by Veviskar and Al-Dahhan, one obtains d ~ 0.0008 from
the CFD
predicted velocity fields.15 6 This tank design produces excellent fluid mixing, and the
7 deviation of the coefficients from 0 and 1.0, respectively, are insignificant.
8 3.2 Model 2: 13.7 m Diameter Tank with 1 External Draft Tube This much smaller
9 tank was designed to produce a nominal HRT = 2.03 days. It has a single EDT, but
10 sludge inlet flow rate and draft tube dimensions were identical to Model 1. The
asymmetric
11 location of a single draft tube may be expected to produce non-symmetric flow
patterns.
12 Nonetheless, the central bottom exit and the round tank tend to center the flow
patterns
13 (See Figures 19, 20 and 21). However, as shown in Figure 21, a slightly less
mixed region
14 hangs above the outlet, and higher tracer concentrations exit the outflow before
this region
15 is fully assimilated into the tank. The effect of this “cloud” of less-well-mixed fluid
is to
16 produce a fit for Equation 1 with coefficients p = 0.008 and a = 0.992 as shown in
Figure
17 22. These deviations from 0 and 1 are also small, and can effectively be ignored.
The
18 calculated HRT value equals 2.04 days, which compares well with the nominal
value of
19 2.03 days.
20 3.3 Model 3: 21.3 m Diameter Tank with 3 External and 1 Internal Draft Tubes
21 This tank is larger than Model 1, has five rather than four draft tubes, and all
tubes are
22 internally mounted. The four outer IDT tubes draw fluid inward radially at the tank
top and
jet the fluid out near the bottom at a 45o 23 angle which induces clockwise rotation.
The
14
center IDT sucks fluid radially inward from the bottom of the tank and 1 ejects it
radially
2 outward at the top. Thus, fluid which might initially tend to exit the tank in an
untimely
3 manner is drawn back into the mixing merry-go-round. Figures 23, 24, and 25
display the
4 time varying concentration surfaces for Model 3. Figure 26 reports the time varying
5 behavior of the outlet concentrations. The predicted magnitude of HRT =18.4 days
exactly
6 equals the nominal value based on tank volume and sludge inlet flow rate. The
best fit
7 coefficient values for Equation 1 were p = 0.0013 and a = 0.9987. Thus, there is
8 essentially zero dead volume and the fractional active volume is one.
9 3.4 Model 4: 33.5 m Diameter Tank with 4 Internal Draft Tubes Finally, we
examined
10 a medium size tank part way between the tank diameters of Model 1 and 4, but
with three
11 EDT tubes and one central IDT. Again the EDT tubes draw off surface fluid and
reinject
12 it at the tank bottom, and the central IDT lifts bottom fluid up to spread it outward
radially
13 at the tank top. Figures 27, 28, and 29 display the developing concentration
surfaces with
14 time. In the later mixing stages the surfaces seem to burst upwards and outwards
around
15 the central IDT like a flower in bloom. The CFD calculated HRT value equals 4.98
days,
16 versus the nominal value of 5.0 days. Equation 1 coefficients were p = 0.004 and
a=
17 0.996 (Figure 30).
18 4.0 SUMMARY OF PERFORMANCE OF DIFFERENT TANK
CONFIGURATIONS
19 Exploration of the small mixing tank studied by Cholette and Cloutier provided an
20 opportunity to explore the nuances of CFD simulation of mixing phenomena in
CSTR
21 systems. It was noted that tank mixing may deviate from ideal behavior for a
variety of
22 reasons associated with placement of inlets, outlets, stratification, and tank
geometry. The
23 presence of even a slight amount of density difference between the mixing fluids
(SG =
15
1.0029 vs 1.000) was determined to strongly influence the progression 1 of mixing.
2 Uncertainties about the actual test configuration and measurement methods can
also
3 influence how well CFD simulations and experimental data agree. The CFD
simulations
4 of the Cholette and Cloutier tank reproduced the gross characteristics of lowturbulence
5 and fan-mixed circulations; however, the agreement was not exact, and this author
doubts
6 if agreement can be improved given missing details about experimental uncertainty
and
7 nuances of the tank geometry (exact outlet placement, mixer characteristics).
8 Nonetheless, the exercise provided the tools and confidence to explore full-scale
anaerobic
9 digester tank conigurations.
10 Four likely configurations of mixing tanks were examined. The tanks varied in
size,
11 combinations of EDT and IDT mixers, and draft tube configurations. These tanks
nominal
12 characteristics fall within the range recommended by ASCE and WEF design
manuals.
13 A summary of tank performance is available in Table 2. Nominal and calculated
HRT
14 values were in good agreement. All the tank configurations considered produced
excellent
15 mixing without any evidence of short-circuiting, dead volumes, significant partial
mixing, or
16 plug flow. The analysis was performed using conventional and typical CFD
software,
17 readily available to the practicing engineer, and its completion was significantly
more
18 efficient than post-construction field tests.
19
20 ACKNOWLEDGMENTS: I would like to acknowledge the very helpful discussions
with
21 Jeff Wight, Olympus Technologies, Inc., Eugene, Oregon about anaerobic
digester design
22 and operating characteristics and with Dr. David Hendricks, Professor Emeritus,
Civil and
23 Environmental Engineering, Colorado State University on anaerobic digester
physics,
24 mixing theory, and digester performance.
25
16
1 5.0 REFERENCES:
2 1. Bargaman, R.D. (Chairman) (1968) Anaerobic Sludge Digestion, Manual of
Practice
3 No. 16, Manuals of Water Pollution Control Practice, Water Pollution Control
4 Federation, Washington D.C., 76 pp.
5 2. Butt, J. B. (1980), Reaction Kinetics and Reactor Design, Prentice Hall, Inc.,
6 Englewood Cliffs, New Jersey, 431 pp.
7 3. Cholette, A. and Cloutier, L., (1959) , Mixing Efficiency Determinations for
8 Continuous Flow Systems, The Canadian Journal of Chemical Engineering, June
9 1959, Vol. 37, No. 3, pp. 105-112.
10 4. Cholette, A., Blanchet, J., and Cloutier, L. (1960), Performance of Flow
Reactors
11 at Various Levels of Mixing, The Canadian Journal of Chemical Engineering, Vol,
12 38, 1-18.
13 5. Cooper, A.B. and Tekippe, R.J. (1982), Current Anaerobic Digester Mixing
Practices, 55th 14 Annual Water Pollution Control Federation Conference, St. Louis,
15 Missouri, 24 pp.
16 6. Hendricks, D. (2006), Water Treatment Unit Processes: Physical and
Chemical,
17 CRC Publishers, 1266 pp.
7. Levenspiel, O. (1999), Chemical Reaction Engineering, 3rd 18 Edition, John Wiley
&
19 Sons, New York, pp.
20 8. Littleton, H.X., Daigger, G.T. and Strom, P.F. (2007), Application of
Computational
21 Fluid Dynamics to Closed-Loop Bioreactors: 1. Characterization and Simulation of
22 Fluid-Flow Pattern and Oxygen Transfer, Water Environment Research, Vol. 79,
No.
23 6, 600-612.
17
9. Littleton, H.X., Daigger, G.T. and Strom, P.F. (2007), Application 1 of
Computational
2 Fluid Dynamics to Closed-Loop Bioreactors: II. Simulation of Biological
Phosphorus
3 Removal Using Computational Fluid Dynamics, Water Environment Research, Vol.
4 79, No. 6, 613-624.
5 10. Monteith, H.D. and Stephenson, J.P. (1981), Mixing efficiencies in full-scale
6 anaerobic digesters by tracer methods, Journal of WPCF, Vol. 53, NO. 1, 78-84.
7 11. Olivet, D., Valls, J., Gordillo, M.A., Freixo, A. And Sanchez, A. (2005),
Application
8 of residence time distribution technique to the study of the hydrodynamic behavior
9 of a full-scale wastewater treatment plant plug-flow bioreactor, J. Chem. Technol.
10 Biotechnol., Vol. 80, 425-432.
11 12. Schlicht, A.C. (1999), Digester Mixing Systems: Can you properly mix with too
little
12 power?, Walker Process Equipment, Aurora, IL, 6 pp.
13 www.walker-process.com/pdf/99_DIGMIX.pdf
14 13. Vesilind, P.A. (Editor) (2003), Wastewater Treatment Plant Design, Water
15 Environment Federation, Alexandria, VA, pp.
16 14. Vesvikar, M.S. and Al-Dahhan, M. (2005), Flow Pattern Visualization in a
Mimic
17 Anaerobic Digester Using CFD, Biotechnology and Bioengineering, Vol. 89, No.
6,
18 719-732.
19 15. Wasewar, K. L. and Sarathi, J.V. (2008), CFD Modeling and Simulation of Jet
Mixed
20 Tanks, Engineering Applications of Computational Fluid Mechanics, Vol. 2, No. 2,
21 pp. 155-171.
22 16. Water Environmental Federation (WEF) and American Society of Civil
Engineers
23 (ASCE) (1998), Design of Municipal Wastewater Treatment Plants, ASCE Manual
18
and Report on Engineering Practice No. 76, 4th edition, or 1 (Water Environmental
2 Federation Manual of Practice No. 8, Alexandria, Va), in Vol. 3: Solids Processing
3 and Disposal, Chapter 22, Stabilization, pp. 22-1 to 226.
4 17. Wolf, D. And Resnick, W. (1963), Residence Time Distribution in Real
Systems,
5 I & EC Fundamentals, Vol. 2, No. 4, 287-293.
6
19
1 FIGURE TITLES:
2 1. Schematic of idealized mixing processes including effects of partial mixing, short-circuiting, piston
3 flow, and dead volume. Symbols are defined with the generalized mixing relation, Section 3.0.
4 2. Experimental mixing apparatus (Cholette and Cloutier, 1959)3
5 3. CFD simulation of Cholette and Cloutier tank mixing experiment. Two cases a) mild tank
turbulence
6 present initially and b) intense fan mixing present during test.
4a. Fluid density (kg/m 37 ) for low mixing case at t = 506 sec.
4b. Fluid density (kg/m 38 ) for high mixing case at t = 5355 sec.
9 5a. Particle tracks for low mix case, colored by residence time (sec) at t = 506 sec.
10 5b. Particle tracks for high mix case, colored by residence time (sec) at t = 5355 sec.
11 6. Parameters for mixing model (Equation 1) fit to Cholette & Cloutier, 1959, experiment, and their
12 comparison to CFD simulations.
13 7. Geometry and draft tube configuration for full size model tanks studied.
14 8. Radial velocity and turbulent Intensity profiles at various levels within the Model No. 1
Anaerobic
15 Digester.
16 9. Velocity magnitude contours within Model 1.
17 10. Turbulence intensity contours within Model 1.
18 11. Pathlines emitted from sludge inlet after t = 15 min for Model 1.
19 12. Particle tracks emitted from sludge inlet after t = 15 min for Model 1.
20 13. Pathlines emited from draft tube pump after t = 15 min for Model 1.
21 14. Particle tracks emitted from draft tube pump after t = 15 min for Model 1.
22 15. Concentration surfaces after mixing for 15 min. Release of tracer from sludge inlet, Model 1.
23 16. Concentration surfaces after mixing for 25 min. Release of tracer from sludge inlet, Model 1.
24 17. Concentration surfaces after mixing for 50 min. Release of tracer from sludge inlet, Model 1.
18. Concentration changes as a result of a step addition of tracer, _o 25 = 0.05 at sludge inlet, Model
1, p
26 = 1 - a = 0.0007.
27 19. Concentration surfaces after mixing for 2 min. Release of tracer from sludge inlet, Model 2.
20
20. Concentration surfaces after mixing for 27 min. Release of tracer from sludge 1 inlet, Model 2.
2 21. Concentration surfaces after mixing for 43 min. Release of tracer from sludge inlet, Model 2
22. Concentration changes as a result of a step addition of tracer, _o 3 = 0.05 at sludge inlet, Model 2,
p
4 = 1 - a = 0.008
5 23. Concentration surfaces after mixing for 17 min. Release of tracer from sludge inlet, Model 3.
6 24. Concentration surfaces after mixing for 60 min. Release of tracer from sludge inlet, Model 3.
7 25. Concentration surfaces after mixing for 246 min. Release of tracer from sludge inlet, Model 3.
26. Concentration changes as a result of a step addition of tracer, _o 8 = 1.00 at sludge inlet, Model 3,
p
9 = 1 - a = 0.0013.
10 27. Concentration surfaces after mixing for 1.7 min. Release of tracer from sludge inlet, Model 4.
11 28. Concentration surfaces after mixing for 27 min. Release of tracer from sludge inlet, Model 4.
12 29. Concentration surfaces after mixing for 34 min. Release of tracer from sludge inlet, Model 4.
30. Concentration changes as a result of a step addition of tracer, _o 13 = 1.00 at sludge inlet, Model
4, p
14 = 1 - a = 0.004.
15
16
21
Table 1: Anaerobic Tank Models Examined During 1 CFD Simulations
Unit Power = Power-to-Volume Ratio = PMixers 2 / V
Digester Volume Turnover Rate, DVTT = V / QPMixers 3
RMS Velocity Gradient, G = (PMixers / V / μ)½ 4
Hydraulic Retention Time, HRT = V / Q Sludge In 5
6
7
8 Note: The U.S. EPA and the ASCE Manual and Report on Engineering Practice No. 76
recommends a
minimum Unit Power for mixing anaerobic sludge digesters of 5.2 W/m 3 ( 0.2 Hp/1000 ft39 ) of sludge
volume,
a volume turnover rate, DVTT, of 30 to 45 minutes, and a velocity gradient, G, of 50 sec-1 10 or more.
HRT =
SRT ranges from 15 to 30 days.11 16
12
22
Table 2: Characteristics of Anaerobic Tank Models Examined During 1 CFD
Simulations
2
3
4
23
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Figure 1: Schematic of idealized mixing processes including effects of
partial mixing, short-circuiting, piston flow, and dead volume. Symbols
are defined with the generalized mixing relation, Section 3.0.
Figure 2: Experimental mixing apparatus (Cholette and
Cloutier, 1959)3
24
Figure 4a: Fluid density (kg/m3) for low
mixing case at t = 506 sec.
Figure 3: CFD simulation of Cholette and Cloutier tank mixing
experiment. Two cases a) mild tank turbulence present initially
and b) intense fan mixing present during test.
Figure 4b: Fluid density (kg/m3) for high
mixing case at t = 5355 sec.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
25
Figure 5a: Particle tracks for low mix case,
colored by residence time (sec) at t = 506
sec.
Figure 5b: Particle tracks for high mix case,
colored by residence time (sec) at t = 5355
sec.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Figure 6: Parameters for mixing model (Equation 1) fit to
Cholette & Cloutier, 1959, experiment, and their comparison to
CFD simulations.
26
1
2
Model 3 1
4
5
6
7
8 Model 2
9
10
11
12
13
14 Model 3
15
16
17
18
19
20 Model 4
21
22
23 Figure 7: Geometry and draft tube configuration for full size model tanks studied.
27
Figure 9: Velocity magnitude contours
within Model 1.
1
2
3
4
5
6
7
8
Figure 8: Radial velocity and turbulent Intensity profiles at various levels 9 within the
Model
10 No. 1 Anaerobic Digester.
11 :
12
13
14
15
16
17
18
19
20
21
22
23
24
Figure 10: Turbulent intensity contours
within Model 1.
Figure 12: Particle tracks emitted from
sludge inlet after t = 15 min for Model 1.
Figure 11: Pathlines emitted from sludge
inlet after t = 15 min for Model 1.
28
Figure 13: Pathlines emitted from draft
tube pump after t = 15 min for Model 1.
Figure 14: Particle tracks emitted from draft
tube pump after t = 15 min for Model 1.
Figure 15: Concentration surfaces after
mixing for 15 min. Release of tracer from
sludge inlet, Model 1.
Figure 17: Concentration surfaces after
mixing for 50 min. Release of tracer from
sludge inlet, Model 1.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Figure 16: Concentration surfaces after
mixing for 25 min. Release of tracer from
sludge inlet, Model 1.
Figure 18: Concentration changes as a result
of a step addition of tracer, _o = 0.05 at
sludge inlet, Model 1, p = 1 - a = 0.0007.
29
Figure 19: Concentration surfaces after
mixing for 2 min. Release of tracer from
sludge inlet, Model 2.
Figure 20: Concentration surfaces after
mixing for 27 min. Release of tracer from
sludge inlet, Model 2.
Figure 21: Concentration surfaces after
mixing for 43min. Release of tracer
from sludge inlet, Model 2.
Figure 22: Concentration changes as a
result of a step addition of tracer, _o =
0.05 at sludge inlet, Model 2, p = 1 - a =
0.008
Figure 23: Concentration surfaces after
mixing for 17 min. Release of tracer
from sludge inlet, Model 3.
Figure 24: Concentration surfaces after
mixing for 60 min. Release of tracer
from sludge inlet, Model 3.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
30
Figure 26: Concentration changes as a
result of a step addition of tracer, _o =
1.00 at sludge inlet, Model 3, p = 1 - a =
0.0013.
Figure 25: Concentration surfaces after
mixing for 246 min. Release of tracer from
sludge inlet, Model 3.
Figure 28: Concentration surfaces after
mixing for 27 min. Release of tracer
from sludge inlet, Model 4.
Figure 27: Concentration surfaces after
mixing for 1.7 min. Release of tracer from
sludge inlet, Model 4.
Figure 29: Concentration surfaces after
mixing for 34 min, Model 4.
Figure 30: Concentration changes as a
result of a step addition of tracer, _o =
1.00 at sludge inlet, Model 4, p = 1 - a =
0.004.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23