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Chapter V
Black box growth
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Growth without non-catabolic product
Single substrate limited growth
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Hyperbolic kinetic equation for specific
substrate uptake rate (qS)
-qS
0.5 qSmax
qSmax
0 KS CS
SS
S
SS CK
Cqq
max)(
KS: substrate affinity [kg substrate/m3]
qSmax: maximal uptake rate [kg S consumed/ kg X present-h]
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Substrate uptake for maintenance
Some part of substrate is used for producing energy needed for
cells maintenance. This part is catabolized with a rate mS.
Hence, mS= kg substrate catabolized for maintenance / kg
biomass presenthour.
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Herbert-Pirt relation for substrate
)(Y
)( maxSX
SS mq
It means the substrate taken into cells are used for growth and
maintenance only. Both mSand YSXmaxare model parameters.
-qS
0
(-mS)
max
1
SXY
Herbert-Pirt linear plot for
substrate, non-catabolic
product is absent
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Combination of the qSequation with Herbert-
Pirt relation
maxmaxSq-
SXSSS
S YmCK
C
CS= 0 , = mSYSXmax= -kd
CS>>>, = [-qSmax-(mS)]YSX
max= max
= 0, (-qS) = (-mS), which occurs at CS= CSmin.
The specific growth rate equation based on single substrate is
then:
SS
SS
CK
CC
minmax
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The plot of - CS
max
-kd CSmin
CS
For mS= 0, (Monod equation)SS
S
CK
C
max
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Using Herbert-Pirt relation to calculate other
rates
Example:
The case of aerobic growth on glucose, N-source is ammonia
SupposeqS= 0.3125 + 0.0015
Growth reaction:
-0.3125 C6H12O6+ aNH4++ bO2+ cH
++ dH2O +
C1H1.8O0.5N0.2+ eCO2
Use the yield and elemental balance to obtain a, b, c, d, e
The catabolic reaction is: -C6H12O6- 6O2+ 6CO2 + 6H2O
What are (-qNH4+), (-qO2), qCO2, qH+, qH2O?
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How to measure the kinetic parameters?
Obtaining
max
and YSXmax
.Using batch fermentation at constant volume where CS>>
Hence = max(constant, during the exponential phase)
qS= qSmax
(constant),YSX= YSX
max= (CX-CXo)/(CSo-CS)
Obtaining KSand mS.
Using chemostats, is the variable to get -qS. Apply Herbert-
Pirt relation and plotqSvs. to get YSXmaxand mS.
PlotqSvs. CSto obtain KSand qSmax.
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Further reading
The Herbert-Pirt relation including non catabolic productformation
Extended Herbert-Pirt relation
Different qP- functionEffect of temperature and pH.
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Chapter VI
Growth and product formation in
bioreactors
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Fermentation processes
substratefermenter
Downstream
processing
wastes
products
The upstream processing costs about 2050 %, whereas thedownstream processing costs about 50-80 %
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The type of reactors and processes
The reactors systems:
Aerated stirred tank reactor 0.11000 m3with cooling
equipment
Bubble column 0.110,000 m
3
with airlift and coolingequipment
Bioreactors for immobilized cells/biocatalysts (packed bed,
fluidized bed, trickle bed)
The types of processes used are batch, continuous, and fedbatch systems. Mostly, batch and fed batch reactors are used in
industry whereas continuous reactors (chemostats) are used in
laboratories.
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Fermenter utilities (contd)
Air filtration, using membrane / bed filter with dry air about 60
m3air/m3broth-h.
Compressor, 2 bar, 150oC.
Heat removal
Cooling jacket
Coil
With cool water temperature at 10oC and capacity is about
50,000 kJ/m3reactor-h.
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Packed bed fermenter
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What do we want?
High yield of biomass
High max
High temperature tolerant
Grow on low cost substrate
High qPat low
Extra cellular products
Low viscous biomass
Generally regarded as safe (GRAS)
Mineral medium
Thus, it is important to
analyze the kinetics of
growth and product
formation, designing the
optimal feed profile, role
of transport processes,
maybe use bigger
reactors.
Remember!
qS or completelydetermines the microbial
behavior. It must be
controlled at an optimal
value
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Batch, continuous, and fed batch processes
In batch reactor: and qSare at the maximum value and notcontrolled.
In chemostat: is controlled at optimum
In fed batch reactor: qSis controlled.
batch fed
batchchemostat
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Constant volume batch reactor
The steps:1. Add sterile growth medium solution (substrate consist of
C, N, P source, K+, Mg+, salts, vitamin, trace elements)
and choose the right T and pH.
2. Add electron acceptors (O2, NO3-, etc)
3. Inoculate microorganism at initial time with concentration
CXo.
4. Run the fermentation and harvest the broth, proceed to thedownstream processing.
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Constant volume batch reactor
What is the plot CSand CXwith time?
Derive from the mass balance, one can obtain that the growth
is exponential, the slope of the curve CXvs. time is rX.
Parameters State
variables
reactor operator micro
organism
V CS0
CX0
qSmax
maxYSX
max
mS
KS
CS
CX
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Substrate concentration profile
At constant volume:
For batch reactor:
t = 0, CS= Cso ;
Hence, by putting CS= 0, t end of batch is obtained
The slope in CSvs. t plot is rS.
XSSS Cqr
dt
dC
t
XoSXS
S eCqCqdt
dC maxmaxmax
1)exp(
max
max
max
tCq
CC XoS
SSo
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Conclusion for the batch reactor
, YSX, and qSare constant at the maximum values
Microbial model parameters are determined by combining the
exponential equation with CSand CXdata versus time.
, the most important rate, can not be controlled
Try to sketch the curve CS, CX, , -qS, YSX, rX, -rSversus
time for batch reactor!
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Chemostat
Parameters State
variables
reactor operator micro
organism
V
L,out
CS,in
L,in
qSmax
YSXmaxmS
KS
CS
CX
Steady state: constant volume, constant in and out flow rates.Constant CSand CX.
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Steps in operating continuous culture Sterilized reactor is filled with sterile growth medium
solution containing substrate at CS,in
Air sparging starts to provide electron acceptor
Add a small amount of microorganism (inoculum)
Start the medium in flow (often L,inand L,outare nearly
equal, not always)
Wait until steady state is achieved
The main property of chemostat:
1. CSand CXare independently manipulated by the user bymanipulating transport (to and from the reactor) of substrate
and biomass.
2. Excellent experimental tool to study microbial kinetics,
stoichiometry, under controlled conditions.
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Biomass mass balance in chemostat
Inout + gen = acc
The is chosen by manipulating exit flow rate
Hence, all other qi-values are set (stoichiometric coupling)
Does CSdepend on CS,in? Use (CS) to prove it.
DV
VCC
VrC
outL
XoutLX
XoutLX
,
,
,
00
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Critical dilution rate
The maximal value for D (=) attainable in the chemostat, is
achieved when the maximal CSin achieved. At critical dilution
rate, CSCS,in.
Note: CS,innormally in order 10000 mg/l, CS,minorder 1 mg/l, KS
order 10 mg/l.
Wash out
If D > Dcrit, the cell will be washed out
Then, sketch the graph CSvs. D.
max
,
min,,max
inSS
SinS
crit CK
CCD
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Substrate mass balance
outL
inL
SS,inS
SoutSoutLinSinL
DCCr
VrCC
,
,
,,,,
0
This equation together with Herbert-Pirt relation provide rSand
(-qS) from measured concentration, flows, and volume.
What about CX?
SinSSXS
SX
SinS
S
SX CCY
mY
D
CCD
q
rC
,
max
,
)(
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The application of chemostat
1. Kinetic studies, at different = D one can varies qS, CStoobtain YSX
max, mS, qSmax, KS.
2. Physiological and genomic micro array study studies of
microorganisms under defined steady state, I.e. substrate,
electron acceptor, N-source, type of limitation for growth.
3. Waste water treatment
4. Industrial fermentation, which is not widely applied
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Chemostat optimization
Normally, the maximal rX
andrS
are needed as the economic
parameter
Try to find the optimum D where drS/dD and drX/dD = 0.
Note that rShas a maximum at higher D.
Chemostat wash out dynamic
What happen when D is close to Dcrit?
What happen to CXwhen D = D>Dcrit?
tDCC
CDCdt
dC
ssXX
XXX
'exp
'
max,
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Pro and cons of chemostat
(+)
Excellent experimental tool because is defined
(-)
Low biomass and product concentration
Loss of biomass in outflow
Relatively prone to be contaminated compare to batch or fed
batch reactors
Microbial selection for non-producing mutants
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Fed batch fermentation
In batch reactor, CS
and CX
are high. No transport of S or X and
no control on .
In chemostat, CSand CXare low. Transport of S or X and
control on .
In fed batch reactor. Substrate transport in, not out. No biomasstransport.
Why fed batch?
1. Low CS
no toxicity / osmotic problem2. High CXhigh CPeasier downstream processing
3. Control of ?
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Fed batch fermentation
Batch phase
time
CSO
CS
Start feeding
Feeding phase under substrate
limited conditions
CS= 150 mg/l.
CSO5000
20000 mg/l
In substrate limited feeding phase, CS is very low. Thus, one
can use the pseudo steady state condition for substrate mass
balance
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Substrate mass balance in fed batch reactor
V
Cr
VrCdt
VCd
inSinSS
SinSinS
S
,,
,, 00
Hence, in a fed batch reactor the substrate conversion (-rS
) is
controlled by the operator.
Through controlled rS, is controlled.
It is obvious that the reactor volume changes with time.
However, since the change is very small, for simplicity we canassume constant volume, constant density.
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Rates in fed batch reactor
We start with an assumption that volume is a variable
Biomass mass balance
Pseudo steady state substrate mass balance
Product mass balance
X
X
XXX
VCdt
VCd
VCVrdt
VCd
1
X
insins
X
SS
VC
C
C
rq
,,
X
PP
XPP
VCdt
VCdq
VCqdt
VCd
1
P ibl b f di i i f d
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Possible substrate feeding strategies in a fed
batch fermentation
1. Substrate input (S,inCS,in) is constant
2. is maintained at optimum that gives maximal qPor
maximal YSP.
3. Substrate input is determined by other known reactorlimitations (oxygen, heat, etc)
Apply Herbert-Pirt equation and biomass mass balance to
calculate rXand CX.
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Biomass mass balance in fed batch reactor
Assume constant volume (DV
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Biomass mass balance in fed batch reactor
XSSXinSinS
SXX CmY
V
CY
dt
dC
max,,max
The first explains growth, the later is about maintenance.
InitiallyCXis low in a fed batch reactor. By neglecting
maintenance:
CXincreases linearly with time
Later, CX increases, more and more substrate needed for
maintenance
dCX/dt decreases.End, all substrate needed for maintenance, dCX/dt = 0
constant
,,max
V
C
Ydt
dC inSinS
SX
X
SinSinS
Xm
VCC
/,,max
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Fed batch reactor with constant feeding rate
The analytical solution for CX(t) in feeding phase.
t = time after start feeding
CXf= biomass concentration at start feeding
Note:
For t >>> 0,For t
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Fed batch reactor with constant feeding rate
rXdecreases
sharply decreases
qSdecreasesCSdecreases slowly
)(max,,max tCmYVCY
dtdC
XSSXinSinS
SXX
tC
trt
X
X
tC
rtq
X
SS-
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Fed batch reactor with constant optimum
= opt
= constant qi, Yijare all constant.
qSconstant at qSoptCSconstant.
Biomass concentration increases exponentially
All rates increases exponentially
Substrate feeding rate increases exponentially
tf= time when feeding starts
XoptXX Crdt
dC
tCqtr Xoptii
ttCVrtC optfinSinSSinSinS exp,,,,