2
Microbial Metabolism
Yves Comeau
2.1
INTRODUCTION
Wastewater originates from residences, institutions,
offices and industries, and can be diluted with storm
water, groundwater and surface water. Not treating
wastewater before its discharge into receiving water
bodies results in environmental and human health
effects such as the generation of odours, the depletion of
dissolved oxygen and the release of nutrients, toxic
contaminants and pathogens.
biodegradable or non-biodegradable organic matter,
some of which can be toxic, and nutrients including the
macronutrients nitrogen and phosphorus.
While source reduction of contaminants should be
encouraged, wastewater treatment by physical, chemical
or biological processes remains necessary to minimize
the potential impacts of wastewater discharge and to
favour the production of valuable end-products such as
reusable water, nutrients and biosolids. Wastewater
treatment can be achieved by combining a variety of
physical (e.g. screening, settling, filtration), chemical
(e.g. coagulation, oxidation), thermal (e.g. drying,
incineration) and biological (e.g. by suspended or
attached biomass) processes.
Biological wastewater treatment is based on the
natural role of bacteria to close the elemental cycles
(e.g. C, N, P) on earth. In a wastewater treatment plant,
naturally occurring bacteria are used. By engineering
the system, natural limitations for bioconversion such as
limited aeration and limited amount of biomass can be
overcome. Furthermore, the design of biological
processes is based on the creation and exploitation of
ecological niches that select for microorganisms best
adapted to reproduce under such environmental
conditions. Selective pressure may arise from various
conditions of availability of electron donor (most often
organic matter), electron acceptor (such as oxygen or
nitrate), nutrients, pH, temperature, hydrodynamic
(washing out non-attached microorganisms) or other
conditions.
Biological wastewater treatment, the central focus of
this book, aims at degrading or adsorbing dissolved,
colloidal, particulate and settleable matter into
biological flocs or biofilms. Soluble compounds include
In this chapter, elements of microbiology are first
reviewed to better understand the needs and functions of
microorganisms, and then the stochiometry, energetics
and kinetics of microbial growth are presented.
© 2008 Yves Comeau. Biological Wastewater Treatment: Principles, Modelling and Design. Edited by M. Henze, M.C.M. van Loosdrecht,
G.A. Ekama and D. Brdjanovic. ISBN: 9781843391883. Published by IWA Publishing, London, UK.
10
2.2
Biological Wastewater Treatment: Principles, Modelling and Design
ELEMENTS OF MICROBIOLOGY
Considering the dominant role of bacteria in wastewater
treatment, their relationship to other living organisms is
first presented followed by their cell structure and
components, functions, nutritional requirements, carbon
and energy sources, and sensitivity to environmental
conditions.
2.2.1
noticeable portion of them, pathogenic to humans.
Wastewater pathogens are found among each class of
microorganisms from viruses (e.g. Hepatitis A virus
causing hepatitis), to bacteria (e.g. Vibrio cholerae
causing cholera), to protozoa (e.g. Giardia lamblia
causing giardiasis) and even to animals such as helminth
worms (e.g. Taenia saginata causing taeniasis). A
concise description of pathogenic microorganisms can
be found in Chapter 8.
Classification of microorganisms
There are two types of organisms, prokaryotes and
eukaryotes (Figure 2.1). Prokaryotes are mostly
unicellular organisms which include bacteria,
cyanobacteria (blue-green algae) and archaea (some
found in extreme environments) while eukaryotes
include unicellular organisms (protozoa, algae, fungi)
and multicellular ones (fungi, plants, animals). Recent
genetic information has allowed grouping of organisms
according to their common evolutionary origins.
Coccus
Organisms found in wastewater and wastewater
treatment plants include mainly microorganisms
(viruses, bacteria, protozoa) and some higher organisms
(algae, plants, animals). The morphology of various
groups of microorganisms which are found in
wastewaters and can be observed by microscopy is
shown in Figures 2.2 to 2.5.
Sarcina (packets of eight)
Streptococci
Staphylococci
Bacillus
Chains of bacilli
Spirillum
Microorganisms are the catalysts of biological
wastewater treatment and, for a very small but
te
Prokaryo
Figure 2.2 Morphology of bacteria (adapted from Rittmann and
McCarty, 2001)
s
Archaea
Methanogens
Extreme halophiles
Bacteria
Hyperthermophiles
Eukarya
Gram-positive
bacteria
Proteobacteria
Animals
Mitochondrion
Slime molds
Fungi
Plants
Cyanobacteria
Flagellates
Chloroplast
Giardia
Hyperthermophiles
Root of the tree
Figure 2.1 Phylogenetic tree of life (adapted from Madigan and Martinko, 2006)
Euka
ryote
s
Eukaryotic
‘Crown species’
11
Microbial Metabolism
Zooflagallate
Ameba
A
Paramecium
Ciliate
B
Vorticella
Figure 2.3 Morphology of protozoa (adapted from Rittmann
and McCarty, 2001)
Figure 2.5 Activated sludge floc with good settling properties
(A) and with excessive filamentous growth (B) (photos: D.
Brdjanovic; Eikelboom, 2000; respectively)
2.2.2
Nematode
Rotifers
Cell structure and components
The structure of prokaryotes and of eukaryotes is
presented in Figure 2.6.
A
Crustacea
B
Chromatin
Endoplasmic Nucleolus
reticulum
Nucleus
(surrounded by
nuclear membrane)
Nucleoid DNA
Cytoplasm includes:
RNA, volutin granules
Plasmid
(polyphosphates,
sulfur), storage
products
(glycogen, lipids)
Cell wall
and
membrame
Microtubules
Figure 2.4 Morphology of multicellular microorganisms
(adapted from Rittmann and McCarty,2001)
Flagellum
Smooth
endoplasmic
reticulum
Lysosome
Mitochondrion
Centrioles
Cilium
Figure 2.6 Structure of (A) prokaryotic (0.5 to 5 microns) and
(B) eukaryotic (5 to 100 microns) cells (adapted from Metcalf &
Eddy, 2003)
12
Biological Wastewater Treatment: Principles, Modelling and Design
One essential difference between these types of
organisms is that the genetic material (deoxyribonucleic
acid, DNA) is found as a nucleoid in prokaryotes but in
a true nucleus surrounded by a membrane in eukaryotes
(the greek word karyon means nucleus). Bacteria may
also contain extra DNA material as shorter chain
plasmids. Energy, in eukaryotes, is mainly generated in
mitochondrion. In prokaryotes, the cytoplamic
membrane surrounding the cell fluid (or cytoplasm)
creates a separation between the intracellular and the
extracellular environment which limits the passage of
dissolved components and allows the creation of both a
pH (more H+ outside) and a charge gradient (more
positive charges outside) which is used as a major
mechanism to generate energy and to transport
metabolites. Internally cells maintain a relatively
constant composition.
Bacterial polymer compounds of significance in
wastewater treatment include poly-β-hydroxyalkanoates
(PHAs), glycogen and polyphosphates (Figures 2.8 to
2.10). These compounds play a role as energy reserves
as well as organic carbon (PHA, glycogen) and
phosphorus (polyphosphates) reserves.
A
...
CH2
O
CH3
O
CH3
O
CH3
C
CH
C
CH
C
CH
O
CH2
O
CH2
O
CH2 ...
beta carbon
B
Bacterial macromolecules include proteins, nucleic
acids (DNA and RNA: ribonucleic acids),
polysaccharides and lipids. These compounds are found
in various locations in bacteria (Figure 2.7).
Flagellum
Cytoplasmic
membrame
Cell wall
Cytoplasm
A Proteins
Nucleoid
Ribosomes
Figure 2.8 (A) Structure of poly-β-hydroxybutyrate (PHB). In
poly-β-hydroxyvalerate (PHV), the -CH3 group is replaced by
-CH2CH3 group. PHB and PHV are the two most common poly-βhydroxyalcanoates (PHAs). (B) White granules of PHA stored
inside the cells (cell size approximately 1 μm) (photo: M.C.M.
van Loosdrecht)
B Nucleic Acids: DNA RNA
C Polysaccharides
Storage granules
D Lipids
Figure 2.7 Bacterial macromolecules and location in the cell. (A)
Proteins are found in the flagellum, the cytoplasmic membrane,
the cell wall and the cytoplasm; (B) nucleic acids (DNA and
RNA) are found in the nucleoid and ribosomes; (C)
polysaccharides are found in the cell wall and sometimes in
storage granules and (D) lipids are found in the cytoplasmic
membrane, the cell wall and in storage granules (adapted from
Madigan and Martinko, 2006)
Starch, glycogen and cellulose are all polymers of
glucose that differ in the type of glycosidic bond
between molecules (Figure 2.9). Changing the linkage
or geometry of this bond results in polymers that vastly
differ in their strength. Cellulose is the strongest
polymer and is used as a structural material in plants
and trees. It is also the most difficult of these polymers
to biodegrade.
Polyphosphates are linear chains of phosphates
whose negative charge is stabilised by cations. The
energy-rich phosphate-ester bond is the same as in the
universal energy carrier molecule inside the cell,
adenosine triphosphate (ATP) which contains a chain of
13
Microbial Metabolism
3 phosphates. In most bacteria polyphosphate is used as
a phosphate reserve and only a limited group of bacteria
use it as an energy storage compound.
A
6 CH2OH
H
5
H
4
OH
OH 3
H
CH2OH
O
O
H
H
2
H
1
H
H
OH
H
OH
O
OH
H
OH
α-1,4-Glycosidic bond
CH2
CH2OH
O
O
H
H
1
H
O
2
H
H
OH
H
2
OH
OH
1
O
For growth to take place, bacteria must be able to
replicate their genetic material and carry-out chemical
transformations which allow the synthesis of all the
constituents from various precursors and energy (Figure
2.11). Chemical transformations are catalyzed by
enzymes which are proteins. The synthesis of any
protein requires its genetic expression. The first step is
the transcription of DNA (a double strand of nucleic
acids) into RNA (a single strand of nucleic acids),
followed by its translation into a protein that is then
processed to render it functional. With its constituents
replicated, a bacterial cell can then divide into two
daughter cells.
H
Coding
functions
β-1,4-Glycosidic bond
α-1,6-Glycosidic bond
Functions of bacteria
H
OH
H
H
OH
2.2.3
Machine
functions
DNA
1. Energy: ADP +Pi
B
Replecation
Starch
α-1,4 bonds
Gene expression
Transcription
ATP
2. Metabolism: generation
of precursors of macromolecules
(sugars, amino acids, fatty
acids, etc.)
3. Enzymes: metabolic catalysts
RNA
α-1,6 bonds
Translation
α-1,4 bonds
Glycogen
Protein
β -1,4 bonds
Cellulose
Figure 2.9 Structure of the polysaccharides. (A) Differences in
the glycosidic bonds in the position of linkage between glucose
molecules and in geometry (α and β). (B) Structure of starch,
glycogen (a bacterial storage polymer) and cellulose (adapted
from Madigan and Martinko, 2006)
O
...
O
P
O
O
O
P
O
O
O
P
O
...
O
Figure 2.10 Structure of polyphosphates. Polyphosphates are
polymers of phosphate molecules and are stabilised by cations
(e.g. Ca2+, Mg2+, K+) interacting with charged oxygen (-O-)
molecule
Reproduction (growth)
Figure 2.11 Functions of cells. Growth requires both coding and
machine functions to be operational. DNA serves for replication
and gene expression, first by transcription of DNA into RNA,
then translation of RNA into proteins. Note: DNA:
deoxyribonucleic acid; RNA: ribonucleic acid (adapted from
Madigan and Martinko, 2006)
2.2.4
Characterization of bacteria
Microorganisms can be characterized by first isolating
single strains from microbial communities with
successive dilutions and enrichment cultures and then
testing their response to various conditions. More
recently, molecular tools have been developed which
allow the study of microorganisms without having to
isolate and cultivate them.
14
Biological Wastewater Treatment: Principles, Modelling and Design
Unique abilities of bacteria to produce a given
protein, and store its genetic code, can be used to detect
their presence in biological samples. The potential for
the expression of a protein is thus given by confirming
the presence of the gene in the DNA, while its actual
expression would be given by confirming the presence
of the associated RNA in the biomass.
2.2.4.1
Fluorescent in situ hybridization (FISH)
Fluorescent in situ hybridization (FISH) consists of
chemically preparing a short strand of the specific
sequence of nucleic acids, an oligonucleotide, and
appending a coloured fluorescent marker at its end.
Cells are then made porous to the marked
oligonucleotide which binds to its complementary
strand of RNA. After removing the unbound markers,
bacteria containing the target genetic material emit light
which can be observed under a fluorescent microscope
(Figure 2.12)
confirm its presence. In the polymerase chain reaction,
three components are added: a high temperature
resistant
polymerase
enzyme,
"flanking"
oligonucleotides that delimit the extremities of the
target gene, and nucleic acids so that copies of the target
gene can be made. A temperature cycle is imposed
which results in the opening (denaturation) of the DNA
and annealing with the added oligonucleotides. The
polymerase enzyme then completes the replication of
the gene between the two flanking oligonucleotides. As
this cycle is repeated the number of copies of the target
gene increases exponentially, facilitating its detection.
Instead of aiming for only one DNA sequence, many
gene sequences can be amplified at once and the
fragments of the various amplified genes can be
detected by DGGE. In DGGE, an electric current is
applied to a gel containing an increasing concentration
(gradient) of denaturant. As the various PCR-amplified
DNA gene sequences migrate, they start opening, being
denatured, which slows down their migration in the gel
and yields various bands which are characteristic of the
target genes of specific microorganisms.
2.2.5
Bacterial bioenergetics
The energy needed for the metabolism of bacteria is
obtained from chemical oxidation reduction reactions.
Two main pathways of energy generation are the
glycolysis and the tricarboxylic acid cycle (TCA; or
citric acid cycle or Krebs cycle) in which glucose (a
sugar) is degraded into pyruvate and to acetylCoA
(AcCoA) which feeds into the TCA cycle (Figure 2.13).
Figure 2.12 FISH image of a nitrifying sludge granule.
Ammonium oxidising Beta proteobacteria (probe NSO 190):
green; Nitrospira-like organism (probe NTSPA 662): red;
Eubacteria (probe EUB 338): blue (Eubacteria). Bar indicates 20
μm. (photo: from Kampschreur, 2008)
2.2.4.2
Polymerase chain reaction (PCR) and
denaturing gradient gel electrophoresis
(DGGE)
PCR is used to amplify the number of a specific gene in
the DNA. The DNA first needs to be extracted from a
biological sample, amplified (multiplied) by a
polymerase chain reaction and then identified to
Chemical energy is transferred to the energy-rich
compound adenosine triphosphate (ATP) and electrons
are transferred to the oxidized form of the coenzyme
nicotinamide dinucleotide (NAD+) that becomes
reduced to NADH. In the presence of an electron
acceptor such as oxygen (O2) or oxidized nitrogen
(NOx: nitrate, NO3- or nitrite, NO2-), the NADH can
transfer electrons via the electron transport chain
(E.T.C.) to the electron acceptor. In this electron
transport process, protons are transported across the cell
membrane to the outside of the cell. The pH and charge
gradient thus create a proton motive force (p.m.f.)
which is used for the transport of various compounds
across the cell membrane and for ATP production by
the ATP-ase enzyme. During this transport and ATP
generation, protons are transported back to the cell
interior. Some toxic chemical compounds such as
dinitrophenol (DNP) can neutralize the proton gradient
15
Microbial Metabolism
across the membrane and are called uncouplers as they
"uncouple" organic carbon consumption and ATP
production. Thus, there are three key central metabolites
in bacterial bioenergetics, acetylCoA, ATP and NADH.
The intracellular level of these compounds acts as a
powerful regulator of the metabolism of bacteria. In the
absence of an external electron acceptor, the cell cannot
regenerate the NADH produced by glycolysis. Under
these conditions the TCA cycle will not function to
oxidise the substrate further than pyruvate and
acetylCoA. By conducting fermentation, however,
pyruvate can be reduced with the NADH generated in
the glycolysis into products such as acetate and
propionate.
Bacteria
sugar
acetate
ATP glycolysis
NADH
pyruvate
fermentation
AcCoA
TCA
cycle
H+
H+
DNP
NADH
E.T.C
H+
H+
NADH
H+
NADH
CO2
H+
(e.g.:N2) H2O
ATP
ADP + Pi
NADHtranshydrogenase
H+
ATP-ase
(reversible)
H+
(NOx) O2
–
–
+
+
–
- +
OH- OH
charge gradient
+
H
H+
pH gradient
pmf
Figure 2.13 Overview of bacterial bioenergetics (adapted from
Comeau et al., 1986)
2.2.6
Nutritional requirements for microbial
growth
In addition to energy, microorganisms require sources
of carbon and inorganic compounds to synthesize
cellular components. Bacteria found in wastewater
treatment plants are typically composed of 75-80%
water and thus, of 20-25% dry matter.
The dry matter content is determined from a liquid
sample of known volume by retaining biomass on a
glass fiber filter having a nominal pore sizes of about
1.2 micron and evaporating the water to dryness in an
oven heated at 105ºC. After cooling, the dried biomass
is weighed on an analytical balance and the results
expressed as total suspended solids (TSS) in g/m3
(mg/l). The dried glass fibre filter that retained the
biomass can then be combusted at 550ºC in a muffle
furnace to burn the organic matter (considered to be
composed of C, H, O and N). The ash remaining is
considered to represent the inorganic components and is
termed ash or fixed suspended solids (FSS). By
difference, the organic matter is calculated which is
termed volatile suspended solids (VSS).
The typical composition of the dry matter (TSS) of
bacteria is presented in Table 2.1.
Table 2.1 Typical composition of bacteria (adapted from Metcalf
& Eddy 2003)
Constituent or element
Major cellular constituents
Protein
Polysaccharides
Lipid
DNA
RNA
Other (sugars, amino
acids)
Inorganic ions
As cell elements
Organic (VSS)
Carbon
Oxygen
Nitrogen
Hydrogen
Inorganics (FSS)
Phosphorus
Sulfur
Potassium
Sodium
Calcium
Magnesium
Chlorine
Iron
Other trace elements
%TSS
Empirical formula
for cells C5H7O2N
55.0
5.0
9.1
3.1
20.5
6.3
1.0
%VSS
93.0
50.0
22.0
12.0
9.0
7.0
2.0
1.0
1.0
1.0
0.5
0.5
0.5
0.2
0.3
53.1
28.3
12.4
6.2
The organic (VSS) and inorganic content of bacteria
are thus about 93% and 7%, respectively. Not only
should macro nutrients such as nitrogen and phosphorus
need to be present for cell growth but other elements are
also essential. These compounds are rarely missing in
municipal effluents but may be lacking in some
industrial effluents such as from sugar or pulp and paper
industries.
Empirical formulae proposed for cells (active
biomass) found in wastewater treatment processes are
16
Biological Wastewater Treatment: Principles, Modelling and Design
C5H7O2N and C60H87O23N12P which can be
approximated to C5H7O2NP1/12. These formulae give dry
matter contents (%TSS) for C, H, O, N and P that are in
relatively close agreement with the values presented in
Table 2.1. Other trace elements required include Zn,
Mn, Mo, Se, Co, Cu and Ni.
2.2.7
Carbon and energy sources and microbial
diversity
Metabolism is the sum of all chemical processes that
take place in living cells (Figure 2.14). It is divided into
two categories, catabolism and anabolism. Catabolic
reactions are the energy supply of the cell. The catabolic
reaction is a redox reaction where the transport of
electrons from electron donor to electron acceptor is
generating a proton motive force which delivers ATP.
Anabolic reactions use this energy for the synthesis of
cellular components from carbon sources and other
nutrients. If organic carbon compounds are the substrate
then they function as well in the catabolic as in the
anabolic reactions. The anabolic processes are more or
less the same in all bacteria, while the catabolic
processes can vary widely between different microbial
groups.
Energy production requires the presence of an
electron donor and an electron acceptor. A reduced
compound acts as the electron donor (e.g. organic
matter or ammonium) while an oxidized compound acts
as the electron acceptor (e.g. oxygen or nitrate). The
minimum and maximum oxidation states, with an
example of a corresponding molecule, are shown in
Table 2.2 for significant elements in microbiology.
Carbon sources for biosynthesis are only of two
types, organic or inorganic. The energy sources are of
three types, organic, inorganic and from light, but the
variety of combinations of electron donors and
acceptors results in a broad diversity of microorganisms
(Table 2.3).
The name of these groups come from Greek roots:
chemo: chemical; troph: nourishment; organo: organic;
litho: inorganic; photo: light; auto: self; hetero: other.
Chemotrophs obtain energy from the oxidation of
electron donating molecules from their environment.
These molecules can be organic (chemo-organotrophs
or
chemo-organoheterotrophs)
or
inorganic
(chemolithotrophs or chemolithoautotrophs). Chemoorganotrophs
are
normally
heterotrophs
and
chemolithotrophs are normally autotrophs with these
names being used interchangeably. Not every microbial
type is presented in this table. Other groups include
dehalorespirers which use some types of chlorinated
compounds as electron acceptors.
Examples of microbial growth reactions with their
principal function in wastewater treatment are given
below. Neutral molecules are used for reactions even if
other ionic species may be dominant. The Eq. 2.1 to 2.6
are given for illustration of metabolism only and are not
balanced:
•
Aerobic heterotrophs: organic matter oxidation
C6 H 12O6 + O2 + NH 3 + other nutrients →
C5 H7 O2 N + CO2 + H 2O
•
Denitrifiers: nitrate removal
C6 H 12O6 + O2 + HNO3 + NH 3 + other nutrients →
C5 H7 O2 N + CO2 + H 2O + N 2
•
(2.2)
Fermenting organisms: conversion of larger organic
compounds: glucose to acetic acid,
Anabolism
Catabolism
(2.1)
Energy-yielding metabolism
Biosynthetic metabolism
Energy sources
Biopolymers
ATP
Biosynthetic intermediates
Utilizable energy
Heat
ADP
Intracellular precursor pool
Metabolic products
External nutrients
Figure 2.14 Metabolism as the combination of catabolism and anabolism (adapted from Todar, 2007)
17
Microbial Metabolism
C6 H 12O6 + O2 + NH 3 + other nutrients →
(2.3)
C5 H7 O2 N + CH 3CO2 H + CO2
•
Aerobic autotrophic bacteria (ammonia oxidizers):
removal of ammonia
CO2 + NH 3 + O2 + other nutrients →
(2.4)
C5 H7 O2 N + HNO3 + H 2O
•
Hydrogenotrophic methanogens: biogas production
H 2 + CO2 + NH 3 + other nutrients →
C5 H7 O2 N + CH 4
•
(2.5)
Plants: O2 production and greenhouse gas reduction
CO2 + light + NH 3 + other nutrients →
C5 H7 O2 N + O2
(2.6)
Table 2.2 Significant elements in microbiology
Name and symbol
Oxygen
Nitrogen
Carbon
Sulfur
Hydrogen
Iron
Manganese
O
N
C
S
H
Fe
Mn
Reference oxidation
state (=0) and phase
O2 (g)
N2 (g)
C (s)
S (s)
H2 (g)
Fe (s)
Mn (s)
Electro-negativity
(x)
3.50
3.07
2.50
2.44
2.10
1.64
1.60
Oxidation state
and state of min x
-II
H2O
-III
NH4+
-IV
CH4
-II
HS0
H2
0
Fe
II
Mn2+
Oxidation state
and state of max x
0
O2
V
NO3IV
HCO3VI
SO42I
H+
III
Fe3+
IV
Mn4+
Oxidation states shown: reference, min, max; phases shown are gas (g) and solid (s); Electro-negativity refers to an atom’s tendency to attract
electrons (e-); at a high oxidation state, these elements (except H+) are potential electron acceptors for catabolic reactions (adapted from
Heijnen et al., in preparation)
Table 2.3 Trophic classification of microorganisms (adapted from Rittmann and McCarty, 2001; Metcalf & Eddy, 2003)
Carbon source1
Energy source
2
Electron acceptor Typical products
Electron donor
Trophic group Microbial group
Chemotroph
Organotroph Aerobic heterotrophs
Denitrifiers
Fermenting organisms
Iron reducers
Sulfate reducers
Methanogens (acetoclastic)
Lithotroph
Nitrifiers: AOB4
Nitrifiers: NOB5
Anammox6 bacteria
Denitrifiers
Denitrifiers
Iron oxidizers
Sulphate reducers
Sulphate oxidizers
Aerobic hydrogenotrophs
Methanogens
(hydrogenotrophic)
Phototroph
Algae, plants
Photosynthetic bacteria
1
-
Type of e donor
Organic
Organic
Organic
Organic
Acetate
Acetate
NH4+
NO2NH4+
H2
S
Fe (II)
H2
H2S, S0,S2O32H2
H2
O2
NO3-, NO2Organic
Fe (III)
SO42acetate
O2
O2
NO2NO3-, NO2NO3-, NO2O2
SO42O2
O2
CO2
CO2, H2O
N2, CO2, H2O
Organic:VFAs3
Fe (II)
H2S
CH4
NO2NO3N2
N2, H2O
N2, SO42- ,H2O
Fe (III)
H2S, H2O
SO42H2O
CH4
Organic
Organic
Organic
Organic
Acetate
Acetate
CO2
CO2
CO2
CO2
CO2
CO2
CO2
CO2
CO2
CO2
H2O
H2S
CO2
CO2
O2
S (0)
CO2
CO2
Carbon source: organic for heterotrophs and inorganic (CO2) for autotrophs; mixotrophs can use both. 2 Typical products: CO2 and H2O are
products of catalysis (energy generation) by many micro-organisms. 3 VFAs: volatile fatty acids (typically acetate, propionate, butyrate).
4
AOB: ammonia oxidizing bacteria. 5 NOB: nitrite oxidizing bacteria. 6 Anammox: anaerobic ammonia oxidizing bacteria.
18
Biological Wastewater Treatment: Principles, Modelling and Design
Table 2.4 Oxygen and microorganisms (adapted from Madigan and Martinko, 2006)
Group
Aerobes
Obligate
Facultative
Microaerophilic
Anaerobes
Aerotolerant
Obligate
Type of metabolism
Required (e.g. 20%)
Better if present, not essential
Requires low levels (e.g. 1%)
Aerobic respiration
Aerobic or nitrate respiration, fermentation
Aerobic respiration
Not required, not affected by its presence Fermentation or sulphate reduction
Fermentation of anaerobic fermentation
O2 harmful or lethal
Environmental conditions (oxygen,
temperature, toxicity)
Environmental conditions must be favourable for
microorganisms to grow. Major factors affecting growth
are oxygen and temperature but pH (typically 6 to 8)
and osmotic pressure (depends on the concentration of
salts) must also be appropriate.
2.2.8.1
Oxygen
The need, tolerance or sensitivity to molecular oxygen
(O2) varies widely among micro-organisms (Table 2.4).
Aerobes use oxygen and may need it (obligate),
function in its absence (facultative) or require it in low
levels (microaerophilic). Anaerobes do not use oxygen
but may tolerate it (aerotolerant) or not (obligate).
In aerobes, enzymes for oxygen reduction (to use O2
as an electron acceptor) are always induced. In contrast,
denitrifiers which are facultative aerobes, also have
constitutive enzymes for oxygen reduction but enzymes
for nitrate (or nitrite) reduction need to be induced, a
condition that requires the absence of oxygen. All
denitrifying bacteria can also use oxygen, their catabolic
processes being relatively similar. Sulphate reducers on
the contrary cannot use oxygen, their catabolic process
being very different from aerobic respiration.
Table 2.5 Engineering definition of some environmental
conditions
Condition
Electron acceptor
Present
Absent
Aerobic
OX
O2
Anoxic
AX
NOx
Anaerobic
AN
O2
O2 and NOx
-
-
NOx refers to nitrate (NO3 ) plus nitrite (NO2 )
While the absence of oxygen is referred to as anoxic
(without O2) or anaerobic (without air) by
microbiologists, engineers make a distinction between
these two conditions. Thus, in the absence of oxygen,
the presence or absence of oxidized nitrogen (nitrate or
nitrite) is referred to as anoxic and anaerobic conditions,
respectively (Table 2.5).
2.2.8.2
Temperature
Temperature has a significant effect on the growth rate
of microorganisms (Figure 2.15).
Hyperthermophile
Thermophile
Growth rate
2.2.8
Relationship to O2
Mesophile
Psychrophile
0
20
40
60
80
100
120
Temperature (˚C)
Figure 2.15 Effect of temperature on microbial growth rate
(adapted from Rittmann and McCarty, 2001)
Those operating at a higher temperature range have a
higher maximum growth rate than those operating at a
lower range. The optimal range of temperature for each
group is relatively narrow. With an increasing
temperature, a gradual increase in growth rate is
observed until an abrupt drop is observed due to the
denaturation of proteins at a higher temperature. The
generally used terms to describe these microorganisms
are psychrophile below about 15ºC, mesophile for 1540ºC, thermophile at 40-70ºC and hyperthermophile
which are active above 70ºC up to around 110ºC.
19
Microbial Metabolism
2.3
STOICHIOMETRY AND ENERGETICS
2.3.1
Theoretical chemical oxygen demand
(thCOD) and electron equivalents
For example (Eq 2.10), the mineralisation of glucose
gives,
C6 H 12O6 + 6O2 → 6CO2 + 6 H 2O
The chemical oxygen demand (COD) determination is
commonly conducted in laboratories and involves the
oxidation of organic compounds in the presence of an
acidic dichromate solution heated at 150ºC for 2 hours.
The number of electrons donated by dichromate in the
test is expressed as oxygen equivalents in gO2/m3 (or
mgO2/l).
The electron equivalents of oxygen can be
determined by noting that 1 mole of O2 weighs 32 g and
contains 4 electron equivalents (2 O molecules • 2 e-/O
molecule).
Thus,
1 electron
equivalent
(eeq)
corresponds to 8 g of COD (Eq. 2.7)
1 eeq = 8 gCOD
(2.7)
180 g
192 g
(2.10)
Thus, 1 g glucose represents 1.067 g thCOD
(192/180).
Considering that 8 g of O2 corresponds to 1 eeq, 1
mol of glucose donates 24 eeq. Thus, removing O2 from
the above equation, adding 24 electrons as products of
the reaction, and as many protons (H+) for charge
balance, and water for H balance gives the following
half reaction equation (Eq. 2.11).
C6 H12O6 + 6 H 2O → 6CO2 + 24e− + 24H +
(2.11)
For 1 eeq, Eq. 2.11 becomes:
Considering that organic matter is an electron donor
while O2 is an electron acceptor, dissolved O2 is
considered to represent negative COD (Eq. 2.8).
1
1
1
C6 H 12O6 + H 2O → CO2 + e − + H +
24
4
4
1 gO2 = −1 gCOD
A similar approach can be used for electron
acceptors. For oxygen this gives:
(2.8)
0.25O2 + H + + e− → 0.5H 2O
(2.12)
The theoretical chemical oxygen demand (thCOD) of
a substrate can be determined by writing a balanced
equation in which O2 is added and the compound is
mineralised to end products with ammonia remaining in
its NH3 (III) oxidation state. The theoretical COD may
deviate from the measured COD when a compound is
not reacting in the COD test.
Summing the above two equations again gives the
full reaction equation for glucose.
Eq. 2.9 gives a generalised equation for this purpose.
The equation refers to the thCOD of a C, H, N, O
containing substrate (adapted from Rittmann and
McCarty 2001).
HNO3 + 5H + + 5e− → 0.5N 2 + 3H 2O
1
( 2n + 0.5a − 1.5c − b ) O2 →
2
a − 3c
nCO2 + cNH 3 +
H 2O
2
(2.9)
thCOD/weight
( 2n + 0.5a − 1.5c − b) 16
12n + a + 16b + 14c
Similarly for the transformation of nitrate to nitrogen
gas (denitrification), the oxidation state of nitrogen is
reduced from +V to 0.
(2.14)
The COD equivalent of this reaction is 5 eeq/mol x 8
gCOD/eeq = 40 gCOD/molHNO3 = 2.86 gCOD/gNO3N. As electrons are accepted and not donated, the COD
equivalent of 1 g of nitrate-nitrogen is thus minus 2.86
gCOD (-2.86 gCOD/gNO3-N) = 40/(14 g/mol).
Cn H aOb N c +
and
(2.13)
Writing equations with neutral or charged molecules
does not change the number of electron equivalents of a
reaction as the number of protons (H+) will be adjusted.
20
Biological Wastewater Treatment: Principles, Modelling and Design
Table 2.6 Theoretical COD of various compounds by weight
Compound
Chemical formula
Weight
(VSS)
CHON
(g/mol)
C/wt
(%)
N/wt
(%)
P/wt
(%)
113
113
1343
131
393
960
86
53
52
52
55
55
50
56
12
12
12
11
4
10
0
0
2.2
2.3
0
0
3.1
0
160
160
1960
193
560
1369
144
1.42
1.42
1.46
1.48
1.42
1.43
1.67
184
393
282
134
254
320
180
46
60
74
88
16
2
52
55
43
72
85
53
40
26
40
49
55
75
-
15
4
0
0
0
9
0
0
0
0
0
0
-
0
0
0
0
0
0
0
0
0
0
0
0
-
256
560
320
272
880
384
192
16
64
112
160
64
16
1.39
1.42
1.13
2.03
3.46
1.20
1.07
0.35
1.07
1.51
1.82
4.00
8.00
thCOD COD/VSS
(g/mol)
(g/g)
Biomass
C5H7O2N
C5H7O2NP1/12
C60H87O23N12P
C6H7.7O2.3N
C18H19O9N
C41.3H64.6O18.8N7.04
C4H6O2
Organic substances
Casein
Average organics
Carbohydrates
Fats, oils
Oils: oleic acid
Proteins
Glucose
Formate
Acetate
Propionate
Butyrate
Methane
Hydrogen
C8H12O3N2
C18H19O9N
C10H18O9
C8H6O2
C18H34O2
C14H12O7N2
C6H12O6
CH2O2
C2H4O2
C3H6O2
C4H8O2
CH4
H2
Lag Exponential Stationary
phase
growth
phase
phase
For substrates, however, the thCOD/VSS ratio varies
greatly according to the degree of reduction of the
substrate. Ratios range between 0.35 for formate, a
highly oxidized substrate, to 4.00 gram COD per gram
substrate for methane, and to 8 gram COD per gram for
hydrogen. An average municipal wastewater would
have a typical COD to volatile solids (filtered plus
particulate) of 1.2 gCOD/gVS.
2.3.2
Cell growth
Cell growth in a batch test is characterized by four
phases during which the substrate and biomass
concentration evolve (Figure 2.16).
Concentration
The theoretical COD of a number of compounds is
presented in Table 2.6. Various biomass equations give
thCOD to dry weight ratios varying between 1.37 and
1.48 gCOD/gVSS, with 1.42 being considered typical
for municipal biological wastewater treatment.
Decay
phase
Substrate
Biomass
Time
Figure 2.16 Biomass growth in batch mode (adapted from
Metcalf & Eddy, 2003)
The four phases are:
(1) The lag phase during which there is little biomass
increase and little substrate consumed as the cells
acclimate to the new situation.
21
Microbial Metabolism
(2) The exponential growth phase follows during which
the biomass grows at its maximum rate consuming
much of the substrate which is readily available.
(3) The stationary phase is next during which little
external substrate is available and the biomass
concentration remains relatively constant.
(4) Finally, the decay phase is associated with biomass
decay due to the consumption of the internal carbon
and energy reserves for its maintenance needs, and
due to predation and lysis.
These growth conditions may be found in wastewater
treatment plants at start-up (lag phase), in highly loaded
plants or the front part of plug flow process (exponential
growth phase), in the mid and end section of a plug flow
process (stationary phase) and in a facultative lagoon or
aerobic sludge digester (decay phase).
2.3.3
Yield and energy
2.3.3.1
Energy from catabolism
Microbial metabolism requires energy for cell synthesis.
Depending on the electron acceptor and donor couple
and the associated energy production, a varying
proportion of the electrons available from the electron
donor will be available for biomass synthesis. For
example, aerobic oxidation of glucose generates much
more energy than the transformation of glucose into
methane explaining why the cell yield of the first
reaction is greater than that of the second. Bioenergetics
provides a tool to quantify the amount of energy
available for various biological reactions which can then
be used to determine the biomass yield of a reaction.
Energy production by catabolism depends on the
oxidation and reduction of chemicals available to
microorganisms. In a given reaction, the electron donor
(ED) is oxidized while the electron acceptor (EA) is
reduced. The electron donor is considered to be the high
energy substrate or "food" of the reaction and a large
variety of compounds can play this role. The electron
acceptor, conversely, is an oxidized form and a more
limited number is available for biological systems
(mainly oxygen, nitrate, nitrite, iron (III), sulfate, carbon
dioxide).
The change in Gibbs energy (ΔG0) is a useful
thermodynamic property of a reaction which
characterizes the maximum amount of energy (work)
obtainable for a given reaction. The superscript
indicates that the compounds involved are at standard
conditions (1 mole, 1 atmosphere) and 25ºC. For
biological processes often the standard Gibbs energy is
given for pH 7, which is then denoted by adding a prime
(’) to the symbol for the Gibbs energy. Some half
reactions for biological systems and Gibbs energy
changes per electron equivalent (ΔG0 kJ/eeq) are listed
in Table 2.7.
In combining electron donor and electron acceptor
reactions it should be noted that all reactions in Table
2.7 are presented as electron acceptors with the electron
on the left hand side. Thus, for an electron donor
reaction, the reagents and products of the reaction
should be exchanged and the sign of the Gibbs energy
change should be changed.
If the net reaction results in a negative ΔGo’, this
means that energy can be released and the reaction can
occur spontaneously, an exergonic reaction. Conversely,
if the net reaction results in a positive ΔGo’, energy
input would be needed for the reaction to take place and
it will not occur spontaneously, an endergonic reaction.
The energy available from the transformation of
glucose (electron donor) by aerobic oxidation (with O2
as electron acceptor) and by methanogenesis (with
carbon dioxide as electron acceptor) is illustrated in
Table 2.8.
These two oxidation reactions of glucose illustrate
that aerobic metabolism provides nearly 7 times more
energy than anaerobic methanogenesis. Consequently,
the cell yield would be expected to be much higher with
oxygen than with carbon dioxide as electron acceptors.
Other biological reactions are illustrated on Figure 2.17.
2.3.3.2
Synthesis fraction and biomass yield
A portion of the electron-donor substrate is used for cell
synthesis (fs0: true synthesis fraction) and the rest for
energy production (fe0: true energy fraction) (Figure
2.18). On an electron equivalent (eeq) basis, the sum of
fs0 plus fe0 equals 1. The electron balance, and thus the
COD balance, is maintained.
f s 0 + f e0 = 1
(2.44)
22
Biological Wastewater Treatment: Principles, Modelling and Design
Table 2.7 Half reactions for biological systems (Metcalf & Eddy, 2003 a), (unit for ΔG0’ is kJ per electron equivalent b)
Parameter
Half reaction
Reactions for bacterial cell synthesis (Rcs)
1 CO + 1 HCO + 1 NH + + H − + e − = 1 C H O N + 9 H O
Ammonia as nitrogen
2 20
3 20
4
5
20 5 7 2
20 2
source
5 CO + 1 NO − + 29 H + + e −
Nitrate as nitrogen
= 1 C5 H7 O2 N + 11 H 2O
2 28
3 28
28
28
28
source
ΔG0’
Nitrite
-93.23
(2.17)
-78.14
(2.18)
-71.67
(2.19)
= 1 H 2 S + 1 HS - + 1 H 2O
12
12
2
13.60
(2.20)
= 1 H 2 S + 1 HS - + 1 H 2O
21.27
(2.21)
24.11
(2.22)
Organic donors (heterotrophic reactions)
9 CO + 1 NH + +
Domestic wastewater
31.80
(2.23)
Proteins
+
−
9
1
1
2 50
4 50 HCO3 + H + e = 50 C10 H 19 O3 N + 25 H 2O
50
8 CO + 2 NH + + 31 H + + e −
= 1 C16 H 24 O5 N 4 + 27 H 2O
2 33
4 33
33
66
66
1 HCO - + H + + e −
1 HCOO - + 1 H O
=
3
2
2
2 2
1 CO + H + + e −
1
= C6 H 12O6 + 1 H 2O
2
4
24
4
1 CO + H + + e −
= 1 CH 2O + 1 H 2O
2
4
4
4
32.22
(2.24)
48.07
(2.25)
41.96
(2.26)
41.84
(2.27)
1 CO + H + + e−
2
6
1 CO + 1 HCO - + H + + e −
2 10
3
5
1 CO + H + + e−
2
6
= 1 CH 3OH + 1 H 2O
37.51
(2.28)
35.78
(2.29)
31.79
(2.30)
1 CO + 1 HCO - + H + + e −
2 14
3
7
1 CO + 1 HCO - + H + + e −
2 8
3
8
= 1 CH 3CH 2COO - + 5 H 2O
27.91
(2.31)
27.68
(2.32)
27.61
(2.33)
Eq.
(2.15)
(2.16)
Reactions for electron acceptors (Ra)
Oxygen
Nitrate
Sulfite
Sulfate
Carbon dioxide (methane
fermentation)
1 NO 2 − + 4 H + + e −
2
3
3
1 O + H + + e−
2
4
1 NO − + 6 H + + e−
3 5
5
1 SO 2 − + 5 H + + e −
3
6
4
:
1 SO 2 − + 19 H + + e −
4
8
16
1 CO + H + + e −
2
8
= 1 N 2 + 2 H 2O
6
3
= 1 H 2O
2
= 1 N 2 + 3 H 2O
10
5
16
16
= 1 CH 4 + 1 H 2O
8
4
2
Reactions for electron donors (Rd)
Formate
Glucose
Carbohydrates
Methanol
Pyruvate
Ethanol
Propionate
Acetate:
Grease (fats and oils)
4 CO + H + + e −
2
23
6
6
= 1 CH 3COCOO - + 2 H 2O
10
5
= 1 CH 3CH 2OH + 1 H 2O
12
4
14
14
= 1 CH 3COO - + 3 H 2O
8
8
= 1 C8 H 16 O + 15 H 2O
46
46
Inorganic donors (autotrophic reactions)
Fe3 + + e −
= Fe 2 +
-74.40
(2.34)
1 NO − + H + + e −
3
2
1 NO − + 5 H + + e −
3 4
8
1 NO - + 4 H + + e −
2 3
6
1 SO 2- + 4 H + + e −
4
6
3
1 SO 2- + 19 H + + e −
4
8
16
1 SO 2- + 5 H + + e −
4
4
4
= 1 NO2- + 1 H 2O
-40.15
(2.35)
=
-34.50
(2.36)
-32.62
(2.37)
19.48
(2.38)
21.28
(2.39)
21.30
(2.40)
27.47
(2.41)
40.46
(2.42)
44.33
(2.43)
1 N + 4 H + + e−
6 2 3
H + + e−
1 SO 2- + H + + e −
4
2
a
=
=
=
=
2
2
1 NH + + 3 H O
4 8 2
8
1 NH + + 1 H O
4 3 2
6
1S+2H O
6
3 2
1 H S + 1 HS - + 1 H O
16 2
16
2 2
1 S O2− + 5 H O
8 2 3
8 2
= 1 NH 4+
3
= 1 H2
2
= SO32 − + H 2O
Adapted from McCarty (1975) and Sawyer et al. (1994). b Reactants and products at unit activity except [H+] = 10-7 M
23
Microbial Metabolism
Table 2.8 Energy available from the transformation of glucose
Aerobic oxidation of glucose
Anaerobic oxidation of glucose (methanogenesis)
ΔG0’
ED: glucose to CO2; EA: CO2 to CH4
(kJ/eeq)
1
1
1
C6 H 12O6 + H 2O → CO2 + H + + e −
-41.96 Donor:
24
4
4
ED: glucose to CO2; EA: O2 to H2O
Donor:
1
1
1
C6 H 12O6 + H 2O → CO2 + H + + e −
24
4
4
1
1
O2 + H + + e − → H 2O
4
2
Acceptor:
-78.14
1
1
1
1
C6 H 12O6 + O2 → CO2 + H 2O
24
4
4
4
On a 1 mole basis for glucose, the net equation
would become (• 24):
C6 H 12O6 + 6O2 = 6CO2 + 6 H 2O
Net:
60
58
Acceptor:
1
1
1
CO2 + H + + e − → CH 4 + H 2O
8
8
4
1
1
1
C6 H 12O6 = CH 4 + CO2
24
8
8
On a 1 mole basis for glucose, the net equation
becomes (• 24):
C6 H 12O6 = 3CH 4 + 3CO2
-120.10 Net:
-2882
ΔG0’
(kJ/eeq)
-41.96
24.11
-17.85
-428
-0.6
50
-0.5
30
-0.3
20
-0.2
+
CO2 + 101 HCO3 + H + e =
1
10
CH3COCOO +
Glucose/CO2
+
Hydrogen/H
2
5
H2O
+
1
6
1
8
CO2 + H +e = 121 CH3CH2OH + 41 H2O
+
CO2 + 81 HCO3 + H + e = 81 CH3COO + 83 H2O
1
8
CO2 + H + e =
1
8
SO4 + 1619 H + e = 161 H2S + 161 HS + 21 H2O
+
1
8
CH4 + 41 H2O
+
2
Pyruvate/CO2
Ethanol/CO2
Acetate/CO2
Denitrification
1
5
C6H12O6 + 14 H2O
Methanogenesis
-0.4
1
24
Fermentation
40
CO2 + H + e =
+
H + e = 12 H2
Methane/CO2
Sulfide/Sulfate
2+
3+
10
-0.1
0
0.0
CH4 + CO2
CO2 + H2O + N2
CO2 + H2O
Denitrification:
Aerobic oxidation:
0.4
0.5
0.6
-60
0.7
-70
-77
Acetate
-50
0.3
Methanogenesis:
-40
0.2
Product:
-30
0.1
Fermentation:
-20
NO3 + H + e = N2 + H2O
Fe + e = Fe
O2 + H + e = H2O
Reaction:
-10
E0’(volts)
ΔG0’ (kJ/eeq)
+
+
1
1
CO2 + H + +e = C
6H12O6 +
H
2O
24
4
H ++e = H21 2
+
1
2
1
1
CO
2 + HCO
3 + H + e =
CH
3
COCOO + H
2O
10
5
10
5
+
1
1
CO
2 + H +e =
CH
3CH2OH +
H41 2O
6
12
+
1
1
3
1
CO
2+
HCO
3 + H + e =
CH
3COO +
H8 2O
8
8
8
+
1
1
2+ H + e =
CH
4 +
H41 2O
CO
8
8
2
1
19 +
1
1
1
SO
4+
H
+
e
=
H
2S +
HS
+
H
2O
8
16
2
16
16
+
1
6
3
1
5 NO3 + 5 H + e = 10 N2 + 5 H2O
3+
Fe + e = Fe2+
0.8
1
4
+
1
2
O2 + H + e = H2O
N2/Nitrate
Fe(II)/Fe(III)
H2O/O2
-80
Figure 2.17 Energy scale for redox couples with glucose as electron donor (adapted from Rittmann and McCarty, 2001)
Aerobic oxidation
Substrate: Glucose
+
1
4
24
Biological Wastewater Treatment: Principles, Modelling and Design
The active bacterial cells generated by growth using
the initial electron donor then undergo decay due to
maintenance, predation and cell lysis. During decay, a
portion of the active bacterial cells become the electron
donor to generate more energy and more reaction end
products. The global split of electron equivalents
between active residual cells (fs: observed synthesis
fraction) and reaction end products (fe: observed energy
fraction) remains equal to 1.
f s + fe = 1
The fraction fs and fs can be expressed in mass units,
rather than on an eeq basis, and are then called true
yield (or maximum theoretical yield; Y) and observed
yield (Yobs), respectively.
The fraction fs0 can be used to estimate the true yield
Y:
f s0 M c
8ne
where:
Mc
8
(2.46)
gram cells per empirical mol of cells
number of gram thCOD per eeq (see half
reaction Eq.2.18 in Table 2.7)
number of eeq per empirical mol of cells
ne
With C5H7O2N as the empirical formula for cells, the
molecular weight is 113 g/mol. With ammonia as the
nitrogen source for its synthesis, there are 20 eeq per
empirical mole of cells (Table 2.7, reaction Eq. 2.15)
and the above equation can be simplified to:
f s0
Y = f s 0.706 =
1.42 gCOD/gCells
0
fe0
1
(2.47)
fs0
fs
Growth
Yobs =
fsM c
8ne
(2.48)
Active
residual
cells
Decay
Figure 2.18 Use of electron donor for energy production and
cell synthesis. Note: f: fraction of electrons donated; e: energy;
s: synthesis (adapted from Rittmann and McCarty, 2001).
2.3.3.3
Observed yield from stoichiometry
If an empirically balanced stoichiometric equation can
be obtained for biomass synthesis from a given
wastewater, the biomass observed yield can be
calculated. Using the protein casein to represent
wastewater in laboratory experimentation with activated
sludge, Porges et al. (1956) proposed the following
equation:
C8 H 12O3 N 2 + 3O2 →
casein
C5 H7 O2 N + NH 3 + 3CO2 + H 2O
(2.49)
bacterial cells
g weight
C8H12O3N2
3O2
184
96
Sum
C5H7O2N NH3 3CO2 H2O
113
280
g /gCasein
1.00
gCOD/mol
1.42
g COD
256
g COD/gCOD
Similarly, fs can be used to estimate the observed
yield Yobs,
Active
bacterial
cells
Cell
synthesis
Sum
where the ratio of 1.42 gram COD per gram cells
was also calculated in Table 2.6.
Reaction
end
products
fe
Electron
donor
(2.45)
0
Y=
Energy production
18
0.61 (Yobs)
-1.00
1.39
-96
160
160
1.00
17 132
280
-0.38 (-fe)
0
0
0
0
0
0
160
0.62 (fs)
Thus, consuming 184 g of casein requires 96 g of
oxygen and produces 113 g bacterial cells and other
reaction end products. Similar proportions would be
expected for a full-scale wastewater treatment plant
treating this compound (which is of comparable
composition to typical domestic wastewater). The
biomass true yield (Y) is thus, 0.61 g biomass per g
substrate consumed (= 113/184). Note that the mass of
products equals that of reactants (280 g/mol of casein
consumed).
25
Microbial Metabolism
On a COD basis, the thCOD of casein being 1.39
gCOD/gCasein (Table 2.5) gives 256 gCOD/molCasein,
and the thCOD of bacterial cells of composition
C5H7NO2 being 1.42 gCOD/gVSS, gives 160
gCOD/molCells. The observed synthesis fraction (fs) is
thus 0.62 gCOD/gCOD (0.61x1.42/1.39).
The oxygen requirement is 96 g O2 per mole of
casein consumed, corresponding to 0.52 gO2/gCasein
(96/184). Thus, the energy production fraction (fe) is
0.38 g COD of O2 per g COD of casein (0.52/1.39).
Note that oxygen has a negative COD (-1.0 gCOD/gO2)
and the COD balance is maintained.
f s + fe = 0.62 + 0.38 = 1.00
(2.50)
The experimentally reported observed (and not
“true”) synthesis fraction (fs) of 0.62 is quite high in
comparison to other values published in the literature
for wastewater treatment. Thus, the true synthesis
fraction (fs0) should only be a little higher and the cells
were probably close to their exponential growth phase, a
condition in which the fraction of energy obtained from
endogenous decay is minimal. Indeed, using the
methodology presented in the next section, and the half
reaction and free energy change value presented in
Table 2.7 for protein, which has a very similar chemical
structure to that of casein, a true synthesis fraction (fs0)
of 0.64 can be calculated.
The nitrogen and phosphorus requirements for cell
growth can be evaluated by considering that they
constitute 12.0 and 2.0%, respectively, of the volatile
fraction of the biomass produced (the CHON fraction)
as can be estimated in the empirical equation
C5H7NO2P1/12 (Table 2.5). In the above example, for 113
g of biomass produced (corresponding to 184 g of
casein degraded), 13.4 g of nitrogen would need to be
added either from organic (e.g. casein) or inorganic
sources (e.g. ammonia). Similarly, 2.26 g of phosphorus
would need to be added per 113 g of biomass produced.
2.3.3.4
True yield estimation from bioenergetics
Bioenergetics can be used as an alternative to
conducting careful laboratory scale experimentation to
determine the true (or maximum) yield of a reaction.
The approach presented below is adapted from that of
Metcalf & Eddy (2003) which is a simplification of that
of Rittmann and McCarty (2001) which was recently
updated by McCarty (2007). An alternative approach
has been developed by Heijnen et al. (in preparation)
which mainly differs from the above ones in its
estimation of anabolic energy need by an energy
dissipation function instead of an efficiency factor.
These references provide additional details to those
presented below for the development of other half
reactions and their free energy changes, complex
fermentation reactions, autotrophic reactions and non
standard conditions.
The simplified procedure presented below is divided
into 4 steps which consist in determining, (i) the energy
provided from catabolism knowing the electron donor,
the electron acceptor and the source of nitrogen for
growth, (ii) the energy needed for cell synthesis
(anabolism), (iii) the energy needed for the overall
growth reaction (metabolism) and (iv) the true yield (Y)
coefficient.
A. Energy providing reaction (catabolism)
The methodology to develop the reaction and associated
Gibbs energy production for the catabolic reaction of
the electron donor (ED) and electron acceptor (EA) was
presented in section 2.3.3.1. The method of Rittman &
McCarty (2001) assumes that only a fraction (40 to
80%, typically 60%) of the energy available from an
oxidation-reduction reaction is used in the anabolism
while the rest is lost as heat.
ΔGcata = K ΔGR
where:
ΔGcata
K
ΔGR
(2.51)
Gibbs energy available for catabolism from 1
eeq of ED (kJ/eeq)
fraction of energy transfer captured (typically
0.60)
Gibbs energy released from 1 eeq of ED
(kJ/eeq)
B. Energy needed for cell synthesis (anabolism)
The energy needed to synthesise heterotrophic biomass
from an electron donor is estimated by considering
pyruvate as a central metabolic intermediate and a
source of nitrogen for biomass synthesis.
ΔGana =
where:
ΔGana
ΔGp
ΔGP
Km
+ ΔGc +
ΔGN
K
(2.52)
Gibbs energy required for anabolism from 1
eeq of ED (kJ/eeqED)
Gibbs energy required to convert 1 eeq of ED
to pyruvate (kJ/eeqED)
26
Biological Wastewater Treatment: Principles, Modelling and Design
m
ΔGc
ΔGN
constant: +1 if ΔGp is positive (endergonic)
and -1 if ΔGp is negative (exergonic)
Gibbs energy required to convert 1 eeq of
pyruvate to cells = 31.41 kJ/eeqCells
free energy required per eeq of cells to reduce
nitrogen to ammonia (kJ/eeqCells) = 17.46,
13.61, 15.85, 0.00 for NO3-, NO2-, N2 and
NH4+, respectively.
The first term of the equation describing the
conversion of the electron donor to pyruvate has an
exponent m on the efficiency fraction K. Should ΔGp be
positive, as would be the case for acetate being
transformed to pyruvate, this reaction would require
energy (endergonic) and the positive value to m results
in a greater value (more energy needed) for this first
term. Should ΔGp be negative, as would be the case for
glucose being transformed to pyruvate, this reaction
would release energy (exergonic) and the negative value
to m would result in a lower value (less energy needed)
for this first term.
C. Energy for the overall growth reaction (metabolism)
Two mass balance equations can be written, one that
was already presented for the electron donor for which
its electrons are used for energy and synthesis
fe0 + fs0 = 1
From the ED mass balance, fs0 and fe0 can be found
f s0 =
1
⎛ f0⎞
1 + ⎜ e0 ⎟
⎝ fs ⎠
(2.57)
and
f e0 = 1 − f s 0
(2.58)
D. True yield (Y)
The true yield, Y, can then be expressed in mass
fraction once fs0 has been determined by using Eq. 2.47
presented earlier for an empirical biomass equation of
C5H7O2N produced with ammonia as the nitrogen
source.
Y = f s 0 0.706 =
f s0
1.42 gCOD/gCells
(2.59)
An example is presented below for estimating the
true yield from bioenergetics.
2.3.3.5
Example: Estimating true yield from
bioenergetics for the aerobic oxidation of
glucose with ammonia as nitrogen source
(2.53)
A. Energy providing reaction (catabolism)
and one for energy where as much energy is
consumed for anabolism as provided by catabolism. The
negative sign accounts for the fact that anabolism
consumes rather than produces energy:
-fs0 ΔGana = fe0 ΔGcata
(2.54)
This equation can be rewritten to visualise that the
energy required for cell growth (anabolism) is provided
by the energy released from catabolism times the ratio
of ED oxidised to ED used for cell synthesis.
− ΔGana =
The reaction and energy available from the aerobic
oxidation of glucose were developed above from half
reactions
1
1
1
1
C6 H 12O6 + O2 = CO2 + H 2O
24
4
4
4
-120.10 kJ/eeq
and
ΔGcata = K ΔGR = 0.6 × ( −120.10) = −72.06 kJ/eeq
0
fe
ΔGcata
f s0
(2.55)
It can also be rewritten to isolate the unknowns
(fe0/fs0).
fe
ΔGana
=−
ΔGcata
f s0
0
(2.56)
1
1
1
C6 H 12O6 + H 2O = CO2 + H + + e −
24
4
4
B. Energy needed for cell synthesis (anabolism)
The reaction and Gibbs energy required to convert 1 eeq
of glucose to pyruvate is:
27
Microbial Metabolism
ED:
1
1
1
C6 H 12O6 + H 2O = CO2 + H + + e −
24
4
4
(ΔG0’ = -41.96 kJ/eeq)
EA:
1
1
CO2 +
HCO3 + H + + e− =
5
10
1
2
CH 3COCOO − + H 2O
10
5
(ΔG0’ = +35.78 kJ/eeq)
Net:
1
1
1
1
C6 H 12O6 +
H 2O + CO2 +
HCO3 − =
24
20
5
10
1
1
CH 3COCOO − + H 2O
10
4
(ΔG0’ = -6.18 kJ/eeq)
and:
ED:
EA:
ΔGp
M
also:
K
ΔGc
ΔGN
thus:
ΔGana
glucose to CO2; (ΔG0’, kJ/eeq)
CO2 to pyruvate, (ΔG0’, kJ/eeq)
-6.18 kJ/eeq
-1 (since ΔGp is negative)
0.6
31.41 kJ/eeqCells
0.00 kJ/eeqCells with NH4+ as the nitrogen
source
= (ΔGp / Km ) + ΔGc + (ΔGN/K)
= (-6.18 / 0.6-1) + 31.41 + 0
= +27.70 kJ/eeq
C. Overall reaction for growth (metabolism)
The ratio of the fractions fe0 / fs0 can now be calculated.
⎛ ΔGana
f e0 / f s 0 = − ⎜
⎝ ΔGcata
⎞
⎛ 27.70 ⎞
⎟ = −⎜
⎟ = 0.38
⎝ −72.06 ⎠
⎠
and
fs0 = 1 / (1 + (fe0 / fs0)) = 1 / (1 + 0.38)
= 0.72 gCellCOD/gCOD consumed
fe0 = 1 - fs0 = 0.28 gCOD/gCOD consumed
D. True yield in mass units.
The true yield in mass units, considering an empirical
biomass equation of C5H7O2N is:
Y=
f s0
=0.51 gVSS/gCOD consumed
1.42
2.4
KINETICS
2.4.1
Substrate utilisation rate
The rate of substrate utilisation by bacteria depends on a
number of factors that are characteristic of a given
microbial group. The most important parameters are the
maximum substrate utilisation rate and half saturation
and inhibition constants.
2.4.1.1
Saturation function
The microbial substrate utilisation rate mainly depends
on its maximum substrate utilisation rate, the amount of
biomass present and the concentration of substrate used
for growth.
rs = k M s X
(2.60)
where:
substrate utilisation rate (g COD/m3.h)
maximum specific substrate utilisation rate
(g COD/gVSS.h)
saturation function for soluble substrate SS
(gCOD/gCOD)
biomass concentration (gVSS/m3)
rs
k
MS
X
The effect of substrate concentration on the rate of
reaction is considered by the saturation function.
MS =
SS
( K S + SS )
where:
SS
KS
(2.61)
substrate concentration (gCOD/m3)
substrate half saturation constant (gCOD/m3)
The saturation function (MS) varies from 0 to 1 as a
function of the concentration of substrate available in
solution near the biomass (Figure 2.19).
The substrate utilisation rate is null in the absence of
substrate. At the half saturation constant concentration,
the saturation function value is 0.5 and the substrate
utilisation rate is half of the maximum value. At nine
times the half saturation value, the substrate utilisation
rate is 90% of its maximum and at an infinitely high
concentration, the saturation function reaches a value of
1.0 and the substrate utilisation rate is at its maximum
value.
28
One form of inhibition function that is commonly
used is the following.
Figure 2.19 Effect of substrate concentration on the saturation
function and kinetic of substrate utilisation. Constants used
were: KS = 5 gCOD/m3, k = 4 gCOD /gVSS.d, X = 250 gVSS/m3
The effect of varying the inhibitory concentration
from 0 to 10 times its half saturation value is illustrated
in Figure 2.20.
1.0
1000
0.8
800
0.6
600
0.4
400
0.2
200
KS
0
0
0
10
20
30
40
50
II =
KI
( K I + SI )
where:
KI
half saturation constant of the inhibitory
compound (g/m3)
concentration of the inhibitory compound
(g/m3)
SI
rS = k M S M SO2 M SNH 3 M SPO4 X
(2.62)
where MSO2, MSNH3 and MSPO4 represent the
saturation functions for oxygen, ammonia and
phosphate, respectively.
Inhibition function , II
Substrate concentration, SS (gCOD/m3)
The effect of other limiting nutrients (e.g. oxygen,
ammonia, phosphate) could also be considered in this
substrate utilisation rate formulation by multiplying
with the various saturation functions (also called
switching functions).
(2.65)
1.0
1000
0.8
800
0.6
600
0.4
400
0.2
200
KI
0
0
100
200
300
400
0
500
Substrate utilisation rate, rS (gVSS/m3.d)
Saturation function (MS)
Substrate utilisation rate, rS (gVSS/m3.d)
Biological Wastewater Treatment: Principles, Modelling and Design
Inhibiter concentration, SI (g/m3)
According to Liebig's law of minimum, however,
growth is considered to be limited by only one nutrient.
Thus, a more appropriate formulation would be to
consider only the minimum of the various saturation
functions in the above equation.
Eq. 2.62 needs adjustment with the MIN operator
which applies to the functions between parentheses and
not k:
rs = k ⋅MIN ( M S M SO2 M SNH3 M SPO4 ) ⋅ X
2.4.1.2
(2.63)
Inhibition function
In the presence of an inhibitory compound, a saturation
function can be used to slow down the substrate
utilisation rate.
rS = k I I X
where:
II
(2.64)
Figure 2.20 Inhibition kinetics. Constants used were: KI = 50
g/m3, k = 4 gCOD/gVSS.d, X = 250 gVSS/m3
The inhibition function considered here has a mirror
effect to that of the saturation function. No effect on the
substrate utilisation rate is seen at a null value of
inhibitor concentration. At the half saturation constant
concentration, the inhibition function value is 0.5 and
the substrate utilisation rate is half of the maximum
value. At nine times the half saturation value, the
substrate utilisation rate is only 10% of its maximum
and at an infinitely high inhibitor concentration, the
substrate utilisation rate is completely inhibited. More
details on inhibition are provided in Chapter 10.
2.4.2
Growth rate
When the rate of substrate utilisation is at its maximum,
the growth rate is also at its maximum and their ratio is,
theoretically, that of the true yield.
μmax = Y k
inhibition function
compound (g/g)
for
the
inhibitory
where:
(2.66)
29
Microbial Metabolism
μmax
maximum growth
(gVSS/gVSS.d)
rate
of
biomass
The growth rate of a biomass depends on its rate of
substrate utilisation for cell synthesis and on its decay
rate which is proportional to the concentration of
biomass present.
rg = Y rs − b X
where:
rg
b
(2.67)
biomass growth rate (gVSS/m3.d)
specific biomass decay rate (gVSS/gVSS.d)
Substituting in equations presented earlier gives:
rg = Y k M S X − b X
(2.68)
rg = μmax M S X − b X
(2.69)
⎛ SS ⎞
rg = μ max ⎜
⎟X −b X
⎝ K S + SS ⎠
(2.70)
The specific growth rate is obtained by dividing the
growth rate by the biomass concentration.
rg
where:
μ
specific biomass growth rate (gVSS/gVSS.d)
or
⎛
SS
K
⎝ S + SS
μ = μ max ⎜
⎞
⎟−b
⎠
(2.72)
(2.74)
μmax = Y k − b
(2.75)
(ii) The minimum substrate concentration required at
which the rate of cell synthesis just equals its rate of
decay is when the specific growth rate (μ) is zero
which gives:
S S min =
b KS
Y k −b
where:
SSmin
(2.76)
minimum concentration required to achieve a
null growth rate (gCOD/m3)
(iii) At a null substrate concentration (SS = 0 gCOD/m3),
the specific growth rate becomes negative and is equal
to the rate of decay.
μ = −b
(2.71)
X
Ss
=1
( K S + SS )
and
(2.77)
2.5
Specific growth rate, μ
(gVSS/gVSS.d)
μ=
MS =
2.0
μmax = 2.3 gVSS/gVSS.d
1.5
SSmin = 0.22 gCOD/m3
1.0
0.5
-b = -0.1 gVSS/gVSS.d
0
0
or
1
2
3
4
5
Substrate concentration, SS (gCOD/m3)
⎛
SS
K
⎝ S + SS
μ =Y k⎜
⎞
⎟−b
⎠
(2.73)
The effect of substrate concentration on the specific
growth rate, as calculated from the above equation, is
illustrated in Figure 2.21.
The following aspects are apparent from this graph:
(i) The maximum specific growth rate is obtained at a
high (infinite) substrate concentration at which
point:
Figure 2.21 Effect of substrate concentration on biomass
growth rate. Constants used were b = 0.1 gVSS/gVSS.d, k = 4
gVSS/gVSS.d, KS = 5 gCOD/m3, Y = 0.6 gVSS/gCOD
2.4.3
Stoichiometric and kinetic parameter
values
Typical values of stoichiometric and kinetic parameters
for various bacterial groups are presented in Table 2.9.
In general, a higher fS0 (or true yield, Y) results in a
higher maximum specific growth rate (μmax) which
results in higher specific removal rates (k = μmax / Y).
30
Biological Wastewater Treatment: Principles, Modelling and Design
Table 2.9 Typical values of stoichiometric (fS0, Y) and kinetic (qmax, μmax ) parameters for various bacterial groups, (adapted from
Rittmann and McCarty 2001)
Electron
acceptor
Electron donor
fS 0
Y
µmax
K
-
Microbial group
e donor
Chemotrophic organotrophs
Aerobic heterotrophs
Sugar
No sugar
Aerobic heterotrophs
Denitrifiers
Organic
Fermenting organisms
Sugar
Sulphate reducers
Acetate
Methanogens
Acetate
(acetoclastic)
Chemotrophic lithotrophs
Nitrifiers :AOB
NH4Nitrifiers :NOB
NO2Methanogens
H2
(hydrogenotrophic)
O2
O2
NO3-, NO2Organic
SO42Acetate
0.70
0.60
0.50
0.18
0.08
0.05
0.49 gVSS/gbCOD
0.42 gVSS/gbCOD
0.25 gVSS/gbCOD
0.18 gVSS/gbCOD
0.057 gVSS/gbCOD
0.035 gVSS/gbCOD
13.2
8.4
4.0
1.2
0.5
0.3
27.0 g bCOD/gVSS.d
17.0 g bCOD/gVSS.d
16.0 g bCOD/gVSS.d
10.0 g bCOD/gVSS.d
8.7 g bCOD/gVSS.d
8.4 g bCOD/gVSS.d
O2
O2
CO2
0.14
0.10
0.08
0.34 gVSS/gNH4-N
0.08 gVSS/gNO2-N
0.45 gVSS/gH2
0.9
0.5
0.3
2.7 g NH4-N /gVSS.d
1.1 g NO2-N/gVSS.d
1.1 g H2/gVSS.d
bCOD: biodegradable COD
µmax in gVSS /gVSS d
k = µmax /Y= specific rmax (per unit biomass)
REFERENCES
Comeau Y., Hall K.J., Hancock R.E.W. and Oldham W. K.
(1986) Biochemical model for biological enhanced
phosphorus removal. Wat. Res. 20, 1511-1521.
Eikelboom D.H. (2000) Process Control of Activated
Sludge Plants by Microscopic Investigation
ISBN: 9781900222297, pg.156
Heijnen J.J., Kleerebezem R. and van Loosdrecht M.C.M.
(in preparation) A generalized method for
thermodynamic state analysis of environmental
systems.
Kampschreur M.J. Tan N.C.G., Kleerebezem R.,
Picioreanu C., Jetten M.S.M., van Loosdrecht M.C.M.
(2008) Effect of dynamic process conditions on
nitrogen oxides emission from a nitrifying culture.
Environ. Sci. Techn., 42(2), 429-435.
McCarty P.L. (2007) Thermodynamic electron equivalents
model for bacterial yield prediction: Modifications and
comparative evaluations. Biotech. Bioeng. 97(2), 377388.
Metcalf & Eddy Inc. (2003) Wastewater Engineering Treatment and Reuse, 4th ed., McGraw-Hill, New York.
Madigan M.T. and Martinko J.M. (2006) Brock Biology of
Microorganisms (11th ed.). San Francisco, CA,Pearson
Education, Inc.
Rittmann B.E. and McCarty P.L. (2001) Environmental
Biotechnology - Principles and Applications. New
York, McGraw-Hill.
Todar K. (2007) Microbial metabolism (Electronic
version). Retrieved September 17, 2007 from
http://www.bact.wisc.edu/themicrobialworld/metabolis
m.html
NOMENCLATURE
Symbol
Description
Unit
b
Specific biomass decay rate
gVSS/VSS.d
fe
Observed energy fraction of COD used
gCOD/gCOD
fe0
True energy fraction of COD used
gCOD/gCOD
fs
Observed synthesis fraction of COD used
gCOD/gCOD
fs0
True synthesis fraction of COD used
gCOD/gCOD
II
Inhibition function for the inhibitory compound
g/g
31
Microbial Metabolism
k
Maximum specific substrate utilization rate
gCOD/gVSS.h
K
Fraction of energy transfer captured
kJ/kJ
KI
Half saturation constant of the inhibitory compound
g/m3
KS
Substrate half saturation constant
gCOD/m3
m
Constant: +1 if ΔGp is positive and -1 if ΔGp is negative
Mc
Weight of cells per empirical mole of cells
g/mol
MS
Saturation function for soluble substrate SS
gCOD/gCOD
ne
Number of electron equivalents per empirical mol of cells
eeq/mol
rg
Biomass growth rate
gVSS/m3.d
rS
Substrate utilisation rate
g COD/m3.h
SI
Concentration of the inhibitory compound
g/m3
SS
Substrate concentration
gCOD/m3
SSmin
Minimum concentration required to achieve a null growth rate
gCOD/m3
X
Biomass concentration
gVSS/m3
Y
True yield
gVSS/gCOD
Yobs
Observed yield
gVSS/gCOD
ΔGana
Gibbs energy required for anabolism from 1 eeq of electron donor (ED)
kJ/eeqED
ΔGc
Gibbs energy required to convert 1 eeq of pyruvate to cells
kJ/eeqED
ΔGcata
Gibbs energy available for catabolism from 1 eeq of ED
kJ/eeq
ΔGN
Free energy required per eeq of cells to reduce nitrogen to ammonia
kJ/eeqED
o’
o
ΔG
Change in Gibbs free energy at standard conditions (25 C, 1 M, 1 atm) but pH 7 kJ/mol
ΔGp
Gibbs energy required to convert 1 eeq of electron donor (ED)to pyruvate
kJ/eeqED
ΔGR
Gibbs energy released from 1 eeq of ED
kJ/eeq
Abbreviation
Description
ADP
Adenosine diphosphate
AMP
Adenosine monophosphate
AN
Anaerobic
AOB
Ammonia oxidizing bacteria
ATP
Adenosine triphosphate
AX
Anoxic
bCOD
Biodegradable COD
COD
Chemical oxygen demand
DGGE
Denaturing gradient gel electrophoresis
DNA
Deoxyribonucleic acid
ETC
Electron transport chain
FISH
Fluorescent in situ hybridization
FSS
Fixed (inorganic) suspended solids
GAO
Glycogen accumulating organisms
NOB
Nitrite oxidizing bacteria
OX
Aerobic
PAO
Phosphorus accumulating organism
PCR
Polymerase chain reaction
PHA
Polyhydroxyalcanoates
32
Biological Wastewater Treatment: Principles, Modelling and Design
Pi
Inorganic phosphate
pmf
Proton motive force
RNA
Ribonucleic acid
thCOD
Theoretical chemical oxygen demand
TSS
Total suspended solids
VSS
Volatile suspended solids
Greek symbols
Explanation
Unit
μ
Specific growth rate of biomass
gVSS/gVSS.d
μmax
Maximum specific growth rate of biomass
gVSS/gVSS.d
Colony of protozoa in an activated sludge ecosystem: (photo: D. Brdjanovic)