140904_aut_cg4017_part a
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CG4017
Bioprocess Engineering 2
Denise Croker, BM-028
Course Structure/Assessment
Course structure
Lectures/tutorials: 3 lectures/tutorials week
Labs: Lab schedule on CES server, Friday week 1.Labs are compulsory, no repeat facility available
Assessment
Final exam 70%
Labs 30%
Completion of both assessment components to a satisfactory standardis compulsory in order to pass the module overall.
Attendance will be monitored on a random basis.
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Lab Sessions 4 Experimental Labs
EXP A: Determination of KLa
EXP B: Operation of a Lyophiliser
EXP C: Operation of a Bioreactor
EXP D: TBC
3 Computational Labs
EXP E: Fermentation simulation-Superpro
EXP F: Fermentation simulation-Polymath
EXP G: Activated Sludge Process simulation-Polymath
EXP H: Diffusion in a microbial film simulation-Polymath
Interview B.Eng. Only
Assessment B.Eng.: 6% interview, 6 % per lab submission = Total 30%
B.Sc.: 7.5 % per lab submission = Total = 30%
3
]Complete 2,
Submit 2
]
Complete as many as you can
Submit 2 ( 1 of each)
Lab Safety
Lab Safety Guidelines available on the server.
Safety is the MOST IMPORTANT thing in the lab.
Print & Read the guidelines.
Keep a signed copy of the guidelines with you inthe lab.
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RevisitBioprocess Engineering 1 (CG4003)
Biochemical kinetics: review of basics. Some advanced topics.
Material balances revisited. Mass transfer effects: bulk and internal.
Energy balances revisited. Heat transfer & heat exchanger design for
biochemical processing.
Bioreactor design, sizing, scale-up, operation & control.
Bioreaction product separation & purification processes 2.
Modelling & simulation of bioreaction processes.
Newer applications of bioprocess engineering.
Regulatory & licensing systems.
Syllabus
On completing this module you should:
1. Possess a knowledge of methodologies for the measurement and control of
oxygen mass transfer in aerobic fermentations.
2. Understand and apply the principles of bioreactor scale-up.
3. Demonstrate advanced skills in the design, sizing, operation and optimisation of
bioreactor systems.
4. Demonstrate advanced skills in the selection, sizing and efficiency evaluation of
bioproduct separation and purification systems.
5. Possess a knowledge of the regulatory and licensing systems used in the
biochemical industries.
6. Be competent in the use of a computer package for the simulation of
bioprocessing systems.
7. Show competence in the practical operation of bioprocessing units.
Learning Outcomes
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Textbooks
CG4017 Outline course notes available from the CES server (DCroker) & SULIS
Recommended: P.M. Doran, 2012, Bioprocess Engineering Principles, Academic
Press, ISBN: 9780122208515. Available in print and electronic formats 65.
M. L. Shuler, and F. Kargi, 2001, Bioprocess Engineering: Basic Concepts, 2nded.,
Prentice Hall, ISBN: 0-13-081908-5. (ca. 97 hardback).
R. G. Harrison, P. W. Todd, S. R. Rudge, and D. P. Petrides, 2002, Bioseparations Science
and Engineering, Oxford University Press, ISBN: 978-0-19-512340-1.
G. Walsh, 2007, Pharmaceutical Biotechnology: Concepts and Applications, Wiley,
ISBN: 978-0-470-01245-1
1. REVIEW BIOPROCESS
ENGINEERING
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The application of process engineering principles to biochemical
systems on an industrial scale
An historical perspective
Bioprocess engineering essentially began with the requirement for industrial scale
production of antibiotics.
Penicillin discovered in 1928 by Alexander Fleming (UK). Discovery lay dormant for over
a decade.
Renewed interest during World War 2 to treat infection from battlefield wounds: clinical
trials very impressive.
Large scale production initially very difficult due to:
- low product concentration (only 0.001 g/dm3 !) in final fermentation broth
- requirement for large volumes of sterile air for the aerobic fermentation
- necessity for aseptic fermenter operation
- fragile nature of penicillin: recovery & purification challenges
Problems solved by US companies such as Merck, Pfizer, and Squibb: strain & fermenter
improvement gave over 50 g/dm3product conc. Fermenter volumes of 40,000 dm3
used to meet capacity for treatment of 100,000 per year by 1945.
What is Bioprocess Engineering?
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Local PerspectiveMSD Brinny
Co. Cork
Product - Interferon alpha, 2Beta
Process - Bacterial fermentation of a
strain of E. coli bearing a genetically
engineered plasmid containing an
interferon alfa- 2b gene from human
leukocytes
TreatmentHepatitis and
Rheumathoid Arthritis
Upstream Processing
Frozen Mother
Cell Strain
Shake Flask,
5 -6 hours
Seed Reactor
6-8 hours
Full Scale Bioreactor, 30,000L
< 25 Hours
Critical Process Parameters
- Oxygen Supply
- Medium quality
- Contamination
Process Checks
pH, dissolved Oxygen, temperature, agitation rat eautomatically
Cell densityOff line Testaseptic sampling loop required
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Downstream Processing
Precipitation & Centrifugation
Product = 5070 Kg of Sludge
All expressed proteins, cell debris
Cycles of Micro/Ultra Filtration &
Chromatography (15 process steps)
~ 15 L of liquid product solution,
11mg/ml interferon alpha 2 beta
Isolate product from the fermenter Separate the product form the sludge
& Purify
Traditional Chemical Processes Biochemical Processes
Non-biological reactant mixture, non sterile
facilities
More complex reactant mixturemicrobes etc,
sterile facilities
Reactant [] will decrease as the reaction
proceeds
Increase in reactant biomass concentration as
reaction progresses
Catalyst will be supplied if needed Ability of microorganisms to synthesise their
own reaction catalysts (enzymes)
Extreme reaction conditions often needed Mild conditions of temperature/pH
Typically organic solvents, or mixtures of same. Usually restricted to aqueous phase
Should be robust crystal products Mechanically fragile
Aiming for high [] of product in final reaction
mixture
Relatively low [] of product in reaction mixture
complex product solution
Comparing Chemical/Biochemical Processes
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Current status of biochemical engineering
This is a forefront area of modern technological activity, with many opportunities for
individuals who have competence in the field. It demands the following skills:
Numeracy
Understanding of biochemical systems
Knowledge and practice of process engineering
Conceptual/design/original thinking capabilities
Current status of this field can be classified by type of biochemical activity:
1.Microbial (fairly mature technology, with some new developments)
2.Animal cell culture (newer)
3.Plant cell culture (newer)
4.Genetically modified organisms (newer)
5.Medical applications: tissue engineering, gene therapy etc. (very new)
6.Mixed cultures: food products, waste treatment, etc. (old, but poorly understood,
yet important, technologies)
Single Use Technologies
Single use disposable technologies arebecoming popular in many process industriesincluding biochemicals.
Why? Greater flexibility
Faster time to market
Cleaning time is the single biggest contributor to turnaround
time in the process industry Fixed vessels represent large capital expense
Eliminates possibility of cross contamination
What does it look like?
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CSTR Type- Reaction in a Bag
Cell Culture ReactorWave Reactor
https://www.youtube.com/watch?v=LiYT5b3CsLk&index=4&list=PLUSfjij8XMn7mLVIGnBoaeUf1zMBrK9HW
https://www.youtube.com/watch?v=LiYT5b3CsLk&index=4&list=PLUSfjij8XMn7mLVIGnBoaeUf1zMBrK9HWhttps://www.youtube.com/watch?v=LiYT5b3CsLk&index=4&list=PLUSfjij8XMn7mLVIGnBoaeUf1zMBrK9HWhttps://www.youtube.com/watch?v=LiYT5b3CsLk&index=4&list=PLUSfjij8XMn7mLVIGnBoaeUf1zMBrK9HW -
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2. BIOCHEMICAL KINETICS
2. Biochemical Kinetics
A quantitative knowledge of biochemical kinetics is essential in order to design,
size, and predict the efficiency of bioreactors:
2.1 Quantifying biochemical kinetics
Biochemical systems are complex in two major respects:
1. Structuralcomplexity:
stepkineticslowestofSpeed
rateproductionDesiredsizeBioreactor
Some structural features
of a typical cell
http://teachernotes.paramus.k12.nj.us/nolan/cp%20bio.htm
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2. Segregationalcomplexity:
Segregational complexity can also be modelled in terms of other parameters
such as cell age.
Degree of both structural and segregational complexity may also change with
time and culture environmental conditions.
Quantitative biochemical kinetic models may be:
Non-structured and non-segregated
Non-structured and segregated
Structured and non-segregated
Structured and segregated
Segregation of a cell culture into different functional units
Least realistic, least computationally complex
Most realistic, most computationally complex
2.2 Review of basic biochemical kinetics
Non-structured and non-segregated models: balanced growth (fixed cell
composition) is assumed. This assumption is normally valid for exponential
growth phase and for steady-state (single stage) continuous culture.
These models normally fail during transient conditions. In some cases
pseudobalanced growth can be assumed if cell response is fast compared to
speed of the environmental changes and if the magnitude of these changes is
not too large (
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Microbial floc
Intercellular gel: zone B
Cells
Cell wall: zone C
Cell inner metabolicregion: zone D
Substrate solution: zone A
Substrate molecule
1
2
3
4
Step 1: Transport of substrate from bulk liquid to floc surface
Step 2: 'Solid' phase diffusion of substrate through intercellular gel (or immobilising medium)
Step 3: Transport of substrate through cell wall 'outer transport zone'
Step 4: Metabolic conversion of substrate to biochemical products and/or cell reproduction, by biochemical reaction
2.2.1 Generalised non-structured, non-segregated (balanced growth) model
Microbial floc
Intercellular gel: zone B
Cells
Cell wall: zone C
Cell inner metabolicregion: zone D
Substrate solution: zone A
Substrate molecule
1
2
3
4
Step 1: Transport of substrate from bulk liquid to floc surface
Step 2: 'Solid' phase diffusion of substrate through intercellular gel (or immobilising medium)
Step 3: Transport of substrate through cell wall 'outer transport zone'
Step 4: Metabolic conversion of substrate to biochemical products and/or cell reproduction, by biochemical reaction
2.2.1 Generalised non-structured, non-segregated (balanced growth) model
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Microbial floc
Intercellular gel: zone B
Cells
Cell wall: zone C
Cell inner metabolicregion: zone D
Substrate solution: zone A
Substrate molecule
1
2
3
4
Step 1: Transport of substrate from bulk liquid to floc surface
Step 2: 'Solid' phase diffusion of substrate through intercellular gel (or immobilising medium)
Step 3: Transport of substrate through cell wall 'outer transport zone'
Step 4: Metabolic conversion of substrate to biochemical products and/or cell reproduction, by biochemical reaction
2.2.1 Generalised non-structured, non-segregated (balanced growth) model
Microbial floc
Intercellular gel: zone B
Cells
Cell wall: zone C
Cell inner metabolicregion: zone D
Substrate solution: zone A
Substrate molecule
1
2
3
4
Step 1: Transport of substrate from bulk liquid to floc surface
Step 2: 'Solid' phase diffusion of substrate through intercellular gel (or immobilising medium)
Step 3: Transport of substrate through cell wall 'outer transport zone'
Step 4: Metabolic conversion of substrate to biochemical products and/or cell reproduction, by biochemical reaction
2.2.1 Generalised non-structured, non-segregated (balanced growth) model
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Microbial floc
Intercellular gel: zone B
Cells
Cell wall: zone C
Cell inner metabolicregion: zone D
Substrate solution: zone A
Substrate molecule
1
2
3
4
Step 1: Transport of substrate from bulk liquid to floc surface
Step 2: 'Solid' phase diffusion of substrate through intercellular gel (or immobilising medium)
Step 3: Transport of substrate through cell wall 'outer transport zone'
Step 4: Metabolic conversion of substrate to biochemical products and/or cell reproduction, by biochemical reaction
2.2.1 Generalised non-structured, non-segregated (balanced growth) model
Classification of biochemical reaction types for balanced growth kinetic models
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Reactiontype #
Zone(s) involved General biochemical reaction name
Classification of biochemical reaction types for balanced growth kinetic models
Reactiontype #
Zone(s) involved General biochemical reaction name
(1) DCell-free enzyme reactions in non-viscous substratemedia
Classification of biochemical reaction types for balanced growth kinetic models
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Reactiontype #
Zone(s) involved General biochemical reaction name
(1) DCell-free enzyme reactions in non-viscous substrate
media
(2) C + D Single cell reactions in non-viscous substrate media
Classification of biochemical reaction types for balanced growth kinetic models
Reactiontype #
Zone(s) involved General biochemical reaction name
(1) DCell-free enzyme reactions in non-viscous substratemedia
(2) C + D Single cell reactions in non-viscous substrate media
(3) B + C + DBiological floc/film reactions in non-viscous substratemedia
Classification of biochemical reaction types for balanced growth kinetic models
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Reactiontype #
Zone(s) involved General biochemical reaction name
(1) DCell-free enzyme reactions in non-viscous substrate
media
(2) C + D Single cell reactions in non-viscous substrate media
(3) B + C + DBiological floc/film reactions in non-viscous substratemedia
(4) B + DCell-free immobilised enzyme reactions in non-viscoussubstrate media
Classification of biochemical reaction types for balanced growth kinetic models
Reactiontype #
Zone(s) involved General biochemical reaction name
(1) DCell-free enzyme reactions in non-viscous substratemedia
(2) C + D Single cell reactions in non-viscous substrate media
(3) B + C + DBiological floc/film reactions in non-viscous substratemedia
(4) B + DCell-free immobilised enzyme reactions in non-viscoussubstrate media
(5)
A + D
A + C + D
A + B + C + D
A + B + D
Any of the above (1)-(4) in v iscous substrate media
Classification of biochemical reaction types for balanced growth kinetic models
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2.2.2 Non-structured, non-segregated (balanced growth) kinetic models
Reaction type #1 - Cell-free enzyme reactions in non-viscous media
Time dependence of substrate concentration:
(Michaelis-Menten Equation or variant) (1)
s = concentration of substrate = rate of substrate utilisation = -ds/dt
max= maximum rate at high s Km= Michaelis constant t = time
Reaction type #2 - Single cell reactions (exponential growth phase) in non-viscous
media
Time dependence of cell amount: (2)
x = cell concentration = specific growth rate of cells
Effect of substrate concentration on (3)
(Monod Equation or variant):
max= maximum specific growth rate Ks= substrate utilisation constant
sKs
dtds
m
max
xdt
dx
sK
s
s max
Time dependence of
substrate concentration: (4)
qp= specific rate of product formation Ys = yield coefficients
ms= cell maintenance coefficient xo= initial (inoculum) cell concentration
Time dependence of product concentration: (5)
p = metabolic product concentration
Time dependence of cell amount on
substrate concentration (Logistic Equation):
Equations (2) and (3) can be combined to
give
(6)
This can be then developed as follows,
to give a Logistic Equation that represents
the sigmoidal batch growth curve.
toS
PS
P
XS
exmYq
Ydtds maxmax
t
oP exq
dt
dpmax
Sigmoidal shape of batch
cell growth curve
xsK
s
dt
dx
s max
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The relationship between microbial growth yield and substrate consumption (yield
coefficient relationship) is:
(7)
Combining this with (6) to eliminate s gives:
(8)
Integration of (8) yields a sigmoidal cell growth equation, graphically depicted in the
previous slide. Practical use of an equation such as (8) requires a predetermined
knowledge of the maximum cell amount produced, xmax, in a given reaction
environment. xmaxis identical to the ecological concept of carrying capacity.
Logistic equations quantify cell growth in terms of
carrying capacity, usually by relating to the (10)
amount of unused carrying capacity:
Thus from (2), we have a general form of the logistic equation:
(11) where k = carrying capacity coefficient
ss
xxY
o
oXS
x
xxsYYK
xxsY
dt
dx
ooXSXSs
ooXS
)(
max
max
1x
xk
max
1x
xxk
dt
dx
Growth models for filamentous organisms: Here the organisms grow as microbial
pellets in submerged media, or as mold colonies on moist substrate surfaces. Inthese cases the (normally linear) growth rate is expressed in terms of pellet or
colony, radius (R) or mass (M). Thus in the absence of mass transfer limitations:
(12)
kp= growth rate coefficient = pellet/colony density = kp(36)1/3
Reaction type #3 - Biological floc/film reactions in non-viscous media
Microbial film substrate utilisation flux, N: (13)
Microbial floc substrate utilisation rate, R: (14)
= effectiveness factor a = area of active microorganism/unit film or floc volume
L = film thickness = floc density
, = biological rate coefficients
32
24 MRk
dt
dMp
s
sN
s
saL
N
max
ssR
s
saR
max
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Reaction type #4Cell-free immobilised enzyme reactions in non-viscous media
Sheet substrate utilisation flux, N: (15)
Spherical particle substrate utilisation rate, R: (16)
= effectiveness factor L = sheet thickness = particle density
(See equation 1. Note: k2is part of .)
[e] = active enzyme concentration
][1
][][
3
1
Sk
SLekN
])[1(
][][
3
1
Sk
SekR
mK
kmax
1
5.0
max2
emDKk
mKk
13
Reaction types #5Biochemical reactions in viscous media
Liquid phase substrate external mass transfer limitation, substrate transfer flux, Ns:
(17)
ks= liquid phase substrate mass transfer coefficient
a = (external surface area : volume) ratio of biochemically active particle
Gas phase substrate (O2) external mass transfer limitation, O2transfer flux, NO2:
(18)
SurfaceliquidBulkss ssakdt
dsN
LSa tLLLO OOakdt
OdN ][][
][2
.
22
2
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2.3 Advanced topics in biochemical kinetics
Basic non-structured/non-segregated models normally fail during transient
conditions. To address this issue, various workers have proposed more
sophisticated kinetic models, usually at the cost of increased computationalcomplexity, and difficulties in the experimental verification of key parameters
involved in these more complex mechanistic models.
For these reasons, it should be noted that, although such models may be of
use in representing transient (e.g. batch) behaviour, they are seldom used in
the design and control of steady state bioreactors.
Some examples are considered in the following sub-sections.
Cell reproduction video
http://www.youtube.com/watch?feature=endscreen&v=ofxDIS7fbCE&NR=1http://www.youtube.com/watch?feature=endscreen&v=ofxDIS7fbCE&NR=1 -
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Cell metabolic reactions are specified as follows:
Solution of the following simultaneous differential equations for rates of
substrate consumption, and biomass and product formation, allows prediction
of the time-concentration profile of the batch fermentation:
Model prediction results (smooth curves) for product formation show good
agreement with experimentally determined data (points), but as expected, donot show such good agreement for biomass production (see run 3):
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2.3.2 Non-structured segregated kinetic models
Normally involve the use of population balance equations(PBEs) to quantify the
distribution of different biochemical functional units (e.g. single cells, flocs,
vegetative cells, spores, etc.) and/or cells of different ages. PBEs are usually
complex integro-differential and/or partial differential equations involving three or
more interdependent variables, one of which is time. General form of PBE for a
bioreactor:
Rate of change Cell Cell Cell Cell
of cell = inflow outflow + birth death (19)
concentration rate rate rate rate
Or, in quantitative terms:
(20)
where: C = cell concentration t = time
y = segregated function, e.g. cell age function, or distribution of different
cell functional units (spores, vegetative cells, etc.)
= reactor space time = reactor volume/inflow rate
),(),(),()(),(
tyDtyBtyCyC
dt
tydC in
An example of a non-structured, segregated kinetic model can be found in the
paper on age segregated modelling of continuous production of Saccharomyces
cerevisiae(yeast)under aerobic fermentation conditions:
Such bioreactors
often show
oscillatory
behaviour:
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PBE to quantify living cell variations:
(21)
= reactor cell removal factor = cycle length function
An example of a non-structured, segregated kinetic model can be found in the
paper on age segregated modelling of continuous production of Saccharomyces
cerevisiae(yeast)under aerobic fermentation conditions:
FSin(t)
xLin(y,t)
xDin(y,t)
Air
Vent
V
DO
FS(t)xL(y,t)
xD(y,t)
S
M.V.E. Duarte et al, Braz. J. Chem. Eng., vol.20, no.1, Jan./Mar. 2003.http://dx.doi.org/10.1590/S0104-66322003000100002
F = volumetric flow rateV = reaction mixture volume
S = substrate concentration
DO = dissolved oxygen concentration
xL = living cell concentration
xD = dead cell concentration
y = cell age function (0 = birth, 1 = 1streproduction)
t = time
)(
),(),(),,(),(),,(),(),(
),(
0 y
tyx
dy
dtyxDOSyDdytyxDOSyKtyxtyx
V
F
dt
tydx LLLL
in
LL
Rate of
change
of living cell
conc.
Living cell inflow
rate outflow rateCell birth rate Cell death rate
)(
),(),(),,(),(),,(),(),(
),(
0 y
tyx
dy
dtyxDOSyDdytyxDOSyKtyxtyxV
F
dt
tydxLLLL
in
LL
(21)
where K = cell division probability density function:
(22)
The fs in eq. 22 are sigmoidal functions, all other parameters are
constants/coefficients, e.g.
(23)
2
22
121 1exp11),,(P
yT
P
yPffffDOSyK
K
y
K
y
K
S
K
DO
K
DO
K
DO
K
DO
K
DOe
f1
1
K
DOf
DO
M.V.E. Duarte et al, Braz. J. Chem. Eng., vol.20, no.1, Jan./Mar. 2003.http://dx.doi.org/10.1590/S0104-66322003000100002
http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002 -
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M.V.E. Duarte et al, Braz. J. Chem. Eng., vol.20, no.1, Jan./Mar. 2003.http://dx.doi.org/10.1590/S0104-66322003000100002
Graphical representation of cell division probability density function, K.
),,( DOSyK
)(ppmDO
)(, cyclesonreproductiyAge
M.V.E. Duarte et al, Braz. J. Chem. Eng., vol.20, no.1, Jan./Mar. 2003.http://dx.doi.org/10.1590/S0104-66322003000100002
Graphical representation of cell death probability density function, D.
)(
),(),(),,(),(),,(),(),(
),(
0 y
tyx
dy
dtyxDOSyDdytyxDOSyKtyxtyxV
F
dt
tydxLLLL
in
LL
(21)
where D = cell death probability density function:
(24)
(Again the fs in eq. 24 are sigmoidal functions.)
DyDyDSDDODDODDODD ffffDOSyD 2121 1))1((1),,(
)(ppmDO)(, cyclesonreproductiyAge
),,( DOSyD
http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002 -
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M.V.E. Duarte et al, Braz. J. Chem. Eng., vol.20, no.1, Jan./Mar. 2003.http://dx.doi.org/10.1590/S0104-66322003000100002
Full set of PBEs for this system:
Living cells (eq. 21):
Dead cells:
(25)
Substrate:
(26)
where Mx= total living cell mass.
Partial differential equations such as eqs. 21, 25, and 26 may be solved by a number ofmethods such as:
Finite element/method of lines/Galerkin method
Method of characteristics
Finite difference method
)(
),(),(),,(),(),,(),(),(
),(
0
y
tyx
dy
dtyxDOSyDdytyxDOSyKtyxtyx
V
F
dt
tydx LLLL
in
LL
dytyxDOK
DO
SK
SMtStS
V
F
dt
tdSL
DO
DODO
S
Sx
in ),()()()(
0
),(),,(),(),(),( tyxDOSyDtyxtyxV
F
dt
tydxLD
in
DD
M.V.E. Duarte et al, Braz. J. Chem. Eng., vol.20, no.1, Jan./Mar. 2003.http://dx.doi.org/10.1590/S0104-66322003000100002
Results give a successful replication of the experimentally observed periodic
behaviour:
)(, cyclesonreproductiyAge
),( tyxL
)(hrTime
),( tyxD
)(, cyclesonreproductiyAge )(hrTime
Modelling results for time variation of live and dead cell concentrations
http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002 -
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)(hrTime
)(hrTime
)/( LgmassCell
)/(., LgSconcSubstrate
Modelling results for time variation of total cell and substrate concentrations
2.3.3 Structured segregated kinetic models
These comprise the most sophisticated representations of biochemical reactions,
involving both a structured model of the system biochemistry and a quantification
of the segregational nature of the biochemical functional units. Essentially they
involve a combination of the approaches used in sections 2.3.1 and 2.3.2.
The paper by Henson et al,on modelling of continuous culture of Saccharomyces
cerevisiae(budding yeast)in a chemostat under aerobic fermentation conditions,
provides an example of this type of approach. In this case the segregational
aspectinvolves the use of a PBE for the budding yeast cell reproduction cycle:
(27)
W = cell mass distribution t = time S = intracellular substrate concentration
m = mass associated with mother cells
m = mass associated with daughter cells
p = newborn cell mass distribution function
= cell division intensity function
D = dilution rate (= volumetric flow rate/reaction mixture volume)
M. A. Henson et al , Biotechnol. Prog., vol. 18, 10101026, (2002).
),()(),'()','()',(2
),()(),( '
0
'
tmWmDdmtmWSmmmpdm
tmWSKd
dt
tmdW m
http://www.youtube.com/watch?v=FcV1ydls9hg
http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://www.youtube.com/watch?v=FcV1ydls9hghttp://www.youtube.com/watch?v=FcV1ydls9hghttp://www.youtube.com/watch?v=FcV1ydls9hghttp://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002http://dx.doi.org/10.1590/S0104-66322003000100002 -
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M. A. Henson et al , Biotechnol. Prog., vol. 18, 10101026, (2002).
Glucose oxidation rate:
(32)
O = dissolved oxygen concentration go= glucose maximum oxidation rate
Kgo= glucose substrate utilisation coefficient for glucose oxidation
Kgd= dissolved oxygen substrate utilisation coefficient for glucose oxidation
This structured segregated model, whilst complex to implement, was shown,
under certain conditions, to give a good quantitative representation of both
oscillatory and long term behaviour of the chemostat bioreactor.
OK
O
GK
GOGk
gdgo
go
go
.'
'),'(
M. A. Henson et al , Biotechnol. Prog., vol. 18, 10101026, (2002).
Modelling versus experimental results for chemostat yeast fermentation oscillatory behaviour
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M. A. Henson et al , Biotechnol. Prog., vol. 18, 10101026, (2002).
Comparison of structured segregated model versus actual plant data showing
effect of dilution rate ramp increase at t = 96hours
Dilution rate
increase here
2.3.4 Biochemical kinetic models: the future?
The availability of cheap computational power, coupled with the intensive efforts
currently underway to understand more and more detail about the operation of cell
biochemistry, is paving the way for complete quantitative models of individual
microorganism species.
Scientists at Stanford University announced in July 2012, the first complete
computer model of the bacterium mycoplasma genitalium:
http://www.kurzweilai.net/first-complete-computer-model-of-an-organism
Mycoplasma genitalium
http://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/images/Mycoplasma_genitalium.jpghttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organismhttp://www.kurzweilai.net/first-complete-computer-model-of-an-organism -
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3. BIOCHEMICAL MATERIAL
BALANCE
3. Biochemical Material Balances
Material balances: very important for quantifying and keeping track of the amounts of
reactants and products in a biochemical process. A fundamental tool of process
engineering.
3.1 Material balances revisited
From the law of conservation: for the quantity S in a system, where S = mass or
number of moles of a chemical or biochemical species:
Rate of accumulation = Rate of input - Rate of output Rate of formation (33)
or dissipation of S of S of S or consumption of S
The General Material Balance Equation
For systems at steady state (no accumulation/depletion) the total massbalance is:
Rate of input = Rate of output (34)
of mass of mass
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In the case of reactive speciesin a system at steady state, equation (33) can
also be simplified to:
0 = Rate of input - Rate of output Rate of formation
of S of S or consumption of S
or:
Rate of input + Rate of formation = Rate of output + Rate of consumption (35)
(where S = mass of, or number of moles of, a chemical or biochemical species)
Essential good practice for carrying out material balance calculations
Draw a process diagram showing clearly all relevant information: a simple box diagram
showing all flows entering and leaving the system, together with the corresponding
known quantitative information (flow rates etc.).
Choose a consistent set of units and state it clearly. Units must be given for all
variables shown in the diagram.
Select a basis for the calculation and state it clearly. It is helpful to focus on a specific
quantity of material entering or leaving the system (flow rate for continuous processes,
total amount for batch or semi-batch).
State all assumptions made in order to carry out the calculation. For example: system
does not leak or cells do not burst during filtration
Identify which components of the system, if any, are involved in the reaction . This
is necessary for correct formulation of the material balance equation.
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Procedure for performing material balance calculations
A. Assemble: (1) Draw the flowsheet, showing all pertinent data with units.
(2) Define the system boundary and draw it on the flowsheet.
(3) Write down the reaction stoichiometric equation (if any).
B. Analyse: (4) State any assumptions
(5) Collect and state any extra data needed (e.g. constants, etc.).
(6) Select and state a basis for the calculation.
(7) List the compounds, if any, that are involved in reaction.
(8) Write down the appropriate material balance equation.
C. Calculate: (9) Set up a calculation table showing all components of all streams
passing across system boundaries.
(10) Calculate any unknown quantities by applying the material
balance equation.
(11) Check that your results are reasonable and make sense.
D. Finalise: (12) Answer the specific questions asked in the problem.
(13) State the answers clearly, using appropriate significant figures.
Important!!
From Bioprocess Engineering Principles by Pauline M. Doran
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From Bioprocess Engineering Principles by Pauline M. Doran
From Bioprocess Engineering Principles by Pauline M. Doran
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From Bioprocess Engineering Principles by Pauline M. Doran
From Bioprocess Engineering Principles by Pauline M. Doran
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From Bioprocess Engineering Principles by Pauline M. Doran
From Bioprocess Engineering Principles by Pauline M. Doran
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From Bioprocess Engineering Principles by Pauline M. Doran
From Bioprocess Engineering Principles by Pauline M. Doran
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3.2 Metabolic stoichiometry for growth and product formation
Material balances require stoichiometric equations to quantify the changes involved in
reactions. Although these are more complex in the case of biochemical reactions,
nevertheless the law of conservation of matter is still obeyed, the advantage being thatthe detailed intricacies of cell internal biochemisty can be overlooked and a
macroscopic quantification of the overall reaction can be achieved.
3.2.1 Growth stoichiometry and elemental balances
Basic stoichiometry for cell growth and primary metabolite formation
Taking one mole of substrate as the basis, we can write this as a balanced equation:
CwHxOyNz+ aO2 + bHgOhNi cCHONd+ dCO2+ eH2O + fCjHkOlNm (36)
Substrate Nitrogen Biomass Primary
source metabolic
product
where a, b, c, d, e, and f are the stoichiometric coefficients.
In the chemical formula for substrate, e.g. for glucose: w=6, x=12, y=6, z=0
In the chemical formula for nitrogen source, e.g. for ammonia: g=3, h=0, i=1
The chemical formula for dry biomass is given as CHONd
Note: eq. 36 only applies to reactions involving growth and/or primary metabolic
product formation. Secondary metabolite formation requires separate stoichiometricequations for growth and product formation.
Growth factors such as vitamins and minerals, additionally taken up in small amounts
during metabolism, are generally neglected in terms of their contribution to the
stoichiometry and energetics of the overall reaction.
Other substrates and primary products can easily be added to eq. 36, if appropriate.
Balancing eq. 36 requires a formula for the biomass involved.
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From Bioprocess Engineering Principles by Pauline M. Doran
As can be seen from this table, over 90% of cell biomass can be accounted for by the
elements C, H, O and N, so cell biomass formulae are normally expressed in terms of
these elements only.
From Bioprocess Engineering Principles by Pauline M. Doran
CH1.8O0.5N0.2
Average biomass molecular weight = 24.6(+5-10% as residual ash/other elements)
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CwHxOyNz+ aO2 + bHgOhNi cCHONd+ dCO2+ eH2O + fCjHkOlNm (36)
In order to balance eq. 36 for a particular biochemical reaction, we must determine the
stoichiometric coefficients a-f. As in balancing chemical equations, elemental balances
can be done:
Carbon: w = c + d+ fj (37)
Hydrogen: x + bg = c+ 2e+ fk (38)
Oxygen: y + 2a+ bh = c+2d+ e+ fl (39)
Nitrogen: z + bi = cd+ fm (40)
However we have six unknowns (a-f) and only four simultaneous equations, so these
cannot be solved for a-f. In addition, the fact that water is usually present in great
excess in biochemical reactions, often leads to difficulties in experimentally quantifying
changes in water concentration. This in turn means that H and O balances can be
unreliable.
Alternative stoichiometric information can be obtained by using an experimentally
determined respiratory quotient (RQ)for the reaction of interest:
or aRQ = d (41)a
d
consumedOmoles
producedCOmolesRQ
2
2
3.2.2 Electron balances and yield coefficients
Additional information for balancing stoichiometric equations can be obtained using
electron balances and yield coefficients. In the former, the principle of conservation of
reducing power or available electrons, is applied to obtain quantitative relationships
between substrates and products. An electron balance shows how the available
substrate electrons are distributed in the reaction.
Available electrons, = number of electrons available for transfer to oxygen on
combustion of a substance to CO2, H2O and N-containing
compounds.
Calculated from elemental valences: C=4, H=1, O=-2, P=5, S=6. For N, the number of
available electrons depends on the reference state: -3 if NH3, 0 if N
2, 5 if NO
3
-.
Reference state for cell growth is normally that of the reaction N source. (Here well
take it as NH3).
Degree of reduction, = number of equivalents of available electrons in the amount of
material containing 1g atom of carbon
Thus for substrate CwHxOyNz: s= 4w + x2y3z, and s= s/w (or s= w s)
Note: degree of reduction relative to CO2, H2O, and NH3is zero.
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Applying this idea (i.e. LHS = RHS) to eq. (36), for the case where there is no
product formation (cell growth only):
(36a)
gives: wS4a= cB (42)
where S and B refer to substrate and biomass respectively.
Experimentally determined yield coefficients (Y) provide another source of quantitative
information to allow balancing of stoichiometic equations for biochemical reactions.
For biomass from substrate: (43)
Many factors can affect the value of a yield coefficient including nature of C and N
sources, pH, temperature, and in aerobic cultures nature of the oxidising agent.
However, when the yield coefficient is constant, its experimentally measured value can
be used to determine cin equations (36) or (36a), since eq. (43) can be written in
stoichiometric terms (assuming 1 mole substrate as the basis) as:
(44)
where MW = molecular weight of substrate or biomass
CwHxOyNz+ aO2 + bHgOhNi cCHONd+ dCO2+ eH2O
consumedsubstratemass
producedcellsmassYXS
)(
)(
substrateMW
biomassMWcYXS
Care must be exercised when using eq. (44), since it does not apply if a significant
amount of substrate is used for maintenance activities instead of growth. In such casesthe experimentally measured values of YXSmust be adjusted to account for this.
We can also have a yield coefficient for primary metabolic product from substrate
(45)
Again we must remember that eq. (45) only applies for primary metabolic product.
3.2.3 Metabolic stoichiometric calculations: summary
From our considerations in the previous two sections, we can see that it is now
possible to balance our stoichiometric metabolism equation (36) for all 6 unknowns:
Carbon balance: w = c + d+ fj (37)
Nitrogen balance: z + bi = cd+ fm (40)
Respiratory quotient: aRQ = d (41)
Electron balance: wS4a= cB (42)
Yield coefficient biomass: c= YXS(MW substrate)/(MW biomass) (44)
Yield coefficient product: f= YXP(MW substrate)/(MW product) (45)
substrateMW
productMWf
consumedsubstratemass
producedproductmassYPS
)(
CwHxOyNz+ aO2 + bHgOhNi cCHONd+ dCO2+ eH2O + fCjHkOlNm (36)
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3.3 Material balances for processes with recycle streams
In microbial reactions, bioreactor productivity can be significantly improved by retaining
the active biomass within the reaction system. One way to do this is to separate out the
cellular material from the reactor effluent stream and recycle it to the reactor.
Chemostat bioreactor with recycle of biomass
In performing material balances on such a system, we need to be aware that various
system boundaries may be chosen (e.g. around the entire system, around the reactor
only, or around the separator only).
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Assumptions: reaction occurs only in the chemostat; separation occurs only in separator; no
biomass in the feed or product streams (only in the cell waste stream). Let rX= biomass growth
rate and rS= substrate consumption rate.
Biomassbalance around the entire system:
Accumulation/depletion = Input Output Reaction
At steady state:
0 = 0 - FWXR + rXVR
Thus wastage rate of biomass must equal growth rate of biomass to maintain s.s.
RXRWRSR VrXFdt
dXVdt
dXV 0
1
Assumptions: reaction occurs only in the chemostat; separation occurs only in separator; no
biomass in the feed or product streams (only in the cell waste stream). Let rX= biomass growth
rate and rS= substrate consumption rate.
Substratebalance around the entire system:
Accumulation/depletion = Input Output Reaction
At steady state:
0 = FS0 - F1SP- FWSR + rSVR
Here the consumption rate of S equals the difference between the inlet and outlet mass
flow rates of S.
RsRWPR
SR VrSFSFSFdt
dSV
dt
dSV 10
1
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Material balances around individual units are often more useful for quantifying dynamic
(non-steady state) behaviour.
Biomass balance around the chemostat:
Substrate balance around the chemostat:
RsRRRR VrSFFSFSFdt
dSV 10
1 )(
RXRRRR VrXFFXFdt
dXV 1
1 )(
Biomass balance around the separator:
Substrate balance around the separator:
0)()( 11 PRRWRS
S SFSFFSFFdt
dSV
0)()( 1 RRWR
R
S XFFXFFdt
dX
V
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Other important flow rate equations necessary to solve material balances with recycle:
Recycle flow rate: FR = R . F where R = recycle ratio
Cell concentrate flow: FW+FR = (F+FR)/C where C = settler concentration factor
Values of R and C must be chosen so that the cell waste flow rate (FW) is positive.
Simulating Chemostat Operation with Polymath
RRXRRR
RXRRRR
VVrXFFXFdt
dX
VrXFFXFdt
dXV
/])([
)(
11
11
RRsRRR
RsRRRR
VVrSFFSFSFdt
dS
VrSFFSFSFdt
dSV
/])([
)(
101
101
Biomass balance around Chemostat
Substrate balance around Chemostat
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#Chemostat with separation and biomass recycle Chemostat with recycle.pol
d(x1) / d(t) = (fr*xr-(f+fr)*x1+rx*V)/Vr # Reactor biomass balance
x1(0) = 2
d(s1) / d(t) = (f*so+fr*sr-(f+fr)*s1+rs*Vr)/Vr # Reactor substrate balance
s1(0) = 10d(xr) / d(t) = ((f+fr)*x1-(fw+fr)*xr)/Vs # Separator biomass balance
xr(0) = 10
d(ss) / d(t) = ((f+fr)*s1-(fw+fr)*sr-f1*sp)/Vs # Separator substrate balance
ss(0) = 5
fr=r*f # Recycle flow equation
fw=((f+fr)/c)-fr # Separator biomass concentrator efficiency
f1=f-fw # Separator total mass balance
rs=-rx/Yxs # Yield coefficient substrate to biomass
rx=mumax*x1*s1/(Ks+s1) # Biochemical kinetics
Vr=1000 # Operating parameters & constants
Vs=100
so=10
sp=ss
sr=ss
Yxs=0.6mumax=0.5
Ks=0.5
c= 3 # Settler concentration factor
r=0.2 # Recycle ratio value
f=10 # Inlet feed flow rate
t(0) = 0 # Start time
t(f) = 100 # End time
POLYMATH model for chemostat with biomass recycle
#Chemostat with separation and biomass recycle Chemostat with recycle.pol
d(x1) / d(t) = (fr*xr-(f+fr)*x1+rx*V)/Vr # Biomass in Reactor
x1(0) = 2
d(s1) / d(t) = (f*so+fr*sr-(f+fr)*s1+rs*Vr)/Vr # Substrate in Reactor
s1(0) = 10
d(xr) / d(t) = ((f+fr)*x1-(fw+fr)*xr)/Vs # Biomass in Separator
xr(0) = 10
d(ss) / d(t) = ((f+fr)*s1-(fw+fr)*sr-f1*sp)/Vs # Substrate in Separator
ss(0) = 5
fr=r*f # Recycle flow equation
fw=((f+fr)/c)-fr # Separator biomass concentrator efficiency
f1=f-fw # Separator total mass balance
rs=-rx/Yxs # Yield coefficient substrate to biomass
rx=mumax*x1*s1/(Ks+s1) # Biochemical kinetics
Vr=1000 # Operating parameters & constants
Vs=100
so=10
sp=ss
sr=ss
Yxs=0.6
mumax=0.5
Ks=0.5
c= 3 # Settler concentration factor
r=0.2 # Recycle ratio value
f=10 # Inlet feed flow rate
t(0) = 0 # Start time
t(f) = 100 # End time
POLYMATH model for chemostat with biomass recycle
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Chemostat with Biomass Recycle; Standard Operating Conditions, F = 10, R = 0.2, C = 3
At t = 60 min
X1 (biomass in Reactor) = ~8
S1 (Substrate in the Reactor = 0
XR (Biomass in Recycle Line) = ~25
SS (Substrate in Settler = 0
All substrate removed at ~ t = 20- mins
At t = 60 min
X1 (biomass in Reactor) = ~8
S1 (Substrate in the Reactor = 0
XR (Biomass in Recycle Line) = ~30
SS (Substrate in Settler = 0
All substrate removed at ~ t = 5 mins
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At t = 60 min
X1 (biomass in Reactor) = 0
S1 (Substrate in the Reactor = 0
XR (Biomass in Recycle Line) = 0
SS (Substrate in Settler = 10
At t = 60 min
X1 (biomass in Reactor) = ~8
S1 (Substrate in the Reactor = 0
XR (Biomass in Recycle Line) = ~30
SS (Substrate in Settler = 0
All substrate removed at ~ t = 18 mins
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At t = 60 min
X1 (biomass in Reactor) = ~8
S1 (Substrate in the Reactor = 0
XR (Biomass in Recycle Line) = ~38
SS (Substrate in Settler = 0
All substrate removed at ~ t = 22 mins
At t = 60 min
X1 (biomass in Reactor) = ~8
S1 (Substrate in the Reactor = 0
XR (Biomass in Recycle Line) = ~12
SS (Substrate in Settler) = 0
All substrate removed at ~ t = 25 mins
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4. MASS TRANSFER
Doran (2ndEdition), Chapter 13.
4. Mass Transfer
Due to the complex nature and rheological behaviour of many biochemical systems, a
detailed understanding of mass transfer is often important in order to be able to quantify
biochemical processing operations.
There are two major aspects to mass transfer in biochemical processes: internal and
external.
Internal mass transfer is concerned with the movement of substrates and products
within cellular agglomerates or immobilised enzyme systems, and is of major
importance in quantifying reaction rates.
External mass transfer deals with the transport of materials in the fluid phase(s)
surrounding the biochemically reactive entity, and features prominently in both
reactions (particularly in aerobic and/or highly viscous reaction media), and in
separation processes.
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Immobilised biocatalysts:
(a) cells; (b) enzymes
Substrate concentration profile for
a spherical biocatalyst particle
From Bioprocess Engineering Principles by Pauline M. Doran
Ext. m.t.
Int. m.t.
4.1 Review of mass transfer concepts previously encountered
4.1.1 Internal m.t.: the effectiveness factor,
Recall eq. 14 for the substrate utilisation rate, R, in a microbial floc :
(14)
a = area of active microorganism/unit floc volume
= floc density , = biological rate coefficients
is a complex function of many of the chemical and physical properties of the reaction
system, including: Substrate concentration Diffusion coefficient(s) for transport through the intercellular gel/immobilising
medium
Physical structure of the intercellular gel/immobilising medium Floc/film size/thickness Microorganism effective surface area Reaction rate coefficients
ssR
s
saR
max
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The effectiveness factor can be defined in practical terms:
(46)
is related to the tortuosity factor (Thiele modulus), , of the gel/medium, for example
for 1storder reaction kinetics in a flat plate:
mediumgsinimmobilielgofabsenceinnutilisatiosubstrateofrate
nutilisatiosubstrateofrateactual
/
tanh
4.1.2 External mass transfer
The two major situations in biochemical processing where external mass transfer is of
importance are with viscous substrate media (liquid-solid m.t.) and in aerobic
fermentations (gas-liquid m.t.).
Liquid-solid mass transfer in viscous substrate media
Poorly mixed and/or high viscosity substrate soln: CAsCab : (17)
NA= rate of substrate mass transfer ks= liquid phase substrate mass transfer coefficient
a = (external surface area:volume) ratio of biochemically active particle
Floc,
film,
or particle
Bulk substrate (A) solution
Concentration of A in bulk = CAb
Liquid boundary layer atparticle surface
CAs
Concentration of A atparticle surface = CAs
AsAbsAA CCakdt
dCN
Substrate concentrations near
biochemical solid surfaces
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Gas-liquid mass transfer of oxygen in aerobic fermentations
(18)
NO2= oxygen transfer rate kL= oxygen mass transfer coefficient
a = gas bubble/liquid interfacial area per unit liquid volume
[O2]Lsat= dissolved oxygen concentration when liquid is saturated with oxygen
Major factor affecting NO2: agitation efficiency in the aerated medium
Bulk liquid(substratesolution)
Liquidfilm
Gasfilm
Bulk gas(bubble)
Gas-liquidinterface
[O2]
[O2]L
[O2]L(i)
[O2]G(i)
[O2]G
Oxygen concentrations at
the gas-liquid interface
LSa tLLLO OOakdt
OdN ][][
][2
.
22
2
4.2 Internal m.t. concepts as applied to heterogeneous reactions
4.2.1 Fickslaw of diffusion
Consider a binary mixture of molecular component A and B. In the case where
concentration of A is non-uniform, and where there is no large-scale fluid motion e.g.
due to stirring, then mixing occurs by random molecular motion.
Fickslaw of diffusion states that mass
flux is proportional to the concentration
gradient:
(47)
JA= mass flux of A
NA= rate of mass transfer of A
a = mass transfer area
DAB= diffusivity of A in a mixture of A and B
Concentration gradient of component A
inducing mass transfer across area a
dy
dCD
a
NJ A
AB
A
A
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4.2.2 Steady-state shell mass balance on a biocatalyst particle
The exact equations describing internal mass transfer
depend on the particle geometry and the reaction
kinetics. Consider first a spherical particle.
A mass balance may be performed by considering
the processes of mass transfer and reaction occurring
in the shell of radius r.
Recall the general material balance equation:
Rate of accumulation = Rate of input - Rate of output Rate of formation (33)
or dissipation of A of A of A or consumption of A
We can apply this with the following assumptions:
(i) The particle is isothermal (vi) The particle is homogeneous
(ii) Mass transfer occurs only by diffusion (v) The partition coefficient for A is unity
(iii) Ficks law applies with constant DAe (vii) The system is at steady state
(iv) [A] varies with a single spatial variable
Shell mass balance on
a spherical particle
From Bioprocess Engineering Principles by Pauline M. Doran
Accum. = Input - Output Formation/ (33)
/dissip. of A of A consumption
of A of A
0 = - -
(CA= concn.of A)
Dividing by 4r gives:
or
where the numerator term refers to the difference in the two numerator terms from
the previous equation.
rr
AAe r
dr
dCD
24r
AAe r
dr
dCD 24 rrrA
24
02
22
rr
r
rdr
dCDr
dr
dCD
A
r
AAe
rr
AAe
02
2
rrr
rdr
dCD
A
AAe
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As r tends towards 0, we can write:
Since DAe
is independent of r, it can be moved outside the differential:
The bracketed term is the derivative of a product, d(u.v)/dx, where u = dCA/dr and
v = r2. Thus we can expand this derivative to give:
(48)
Integration of this 2ndorder differential equation yields an expression for how CAvarieswith distance (r) inside the particle. This must be done on a case-by-case basis
according to the reaction kinetics however, since rAis a function of CAin most cases.
02
2
rrdr
rdr
dCDd
A
AAe
02
2
rrdr
rdr
dCd
D A
A
Ae
02 222
2
rr
dr
dCrr
dr
CdD A
AAAe
4.2.3 Substrate concentration profile: 1storder kinetics & spherical geometry
With 1storder kinetics, eq. (48) becomes: (49)(k1= 1
storder rate constant)
According to assumptions (i), (iii) and (vi) above, k1and DAecan be considered
constant. Since this is a 2ndorder differential equation, two boundary conditions are
required:
CA= CAs at r = R, and at r = 0
where CAsis substrate concentration at the particle surface. The latter boundary
condition is called the symmetry condition: the substrate concentration profile is
symmetrical at the centre of the particle, thus the slope (dCA/dr) is zero at r=0.
02 212
2
2
rCk
dr
dCrr
dr
CdD A
AAAe
0dr
dCA
From Bioprocess Engineering Principles
by Pauline M. Doran
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Integration of (49) with these boundary conditions yields:
(50) , where
Eq. (50) can be used to calculate the particle substrate concentration profile.
4.2.4 Substrate concentration profile: zero order kinetics & spherical geometry
In this case eq. (48) becomes: (51)(k0= zero order rate constant)
Assuming that CAcan be zero only at r = 0 (centre of the sphere), integration of eq. (51)
with the same boundary conditions as before, gives:
(52)
It is important, from a practical perspective, that the particle core does not become
starved of substrate. This is more likely with larger particles. Here we can calculate
the maximum particle size, Rmaxwhere CA> 0 (depletion only occurs at r = 0) from
eq. (51), since then CA= r = 0, and:
(53)
Ae
Ae
AsADkR
Dkr
r
RCC
/sinh
/sinh
1
1 2)sinh(
xx eex
02 202
2
2
rk
dr
dCrr
dr
CdD AAAe
2206
RrD
kCC
Ae
AsA
0
max
6
k
CDR AsAe
4.2.5 Substrate concentration profile: Michaelis-Menten kinetics & spherical
geometry
In this case eq. (48) becomes: (54)
Analytical integration of eq. (54) is difficult,
so it is usually resolved using numerical
computational means. Remembering that the
limiting cases of the M-M equation are zero
and 1storder kinetics, we can expect that the
solutions found in the previous two sections
can be used to determine the extremities of
the M-M solution.
Experimental verification of these types of
calculated concentration profiles has been
done in a number of studies, using micro-
analytical techniques (e.g. opposite).
02 2max22
2
r
CK
C
dr
dCrr
dr
CdD
Am
AAAAe
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4.2.8 Prediction of observed reaction rate
Equations such as (50), (52), (55) and (56) allow prediction of the overall reaction
rates, rA,obs, over the entire particle. Consider the case of spherical particles.
1storder reaction: (57)
Substituting eq. (50) for CAin (57), and integrating gives:
(58) , where:
Zero order reaction:Assuming CA> 0 everywhere in the particle, then the rate will be
constant and independent of CA. Thus the overall rate is simply the rate constant
multiplied by the particle volume:
(59)
Michaelis-Menten kinetics: Since CAcannot be expressed explicitly as a function of r,
then numerical methods must again be used.
Rr
r pAObsA dVCkr
0 1,
1/coth/4 11, AeAeAsAeObsA DkRDkRCDRr xxxx
ee
eex
coth
0
3
, 3
4kRr
ObsA
4.2.9 Thiele modulus () and effectiveness factor ()
Recall eq. (46):
which in our present considerations can be written as: (60)
At this stage it is useful to distinguish between
internaleffectiveness factor, i, and external
effectiveness factor, e, to be used in later considerations of external mass transfer.
From section 4.2.8, for a given kinetics and particle geometry, we have an expression
for rA,Obs, so combining this with a term for rAsallows the formulation of an expression
for the effectiveness factor from eq.(60). In the case of 1 storder kinetics and spherical
geometry:
(61), since the rate is k1CAsmultiplied by the particle volume.
Thus, substituting (58) and (61) into (60) gives:
(62)
mediumgsinimmobilielgofabsenceinnutilisatiosubstrateofrate
nutilisatiosubstrateofrateactual
/
As
ObsA
ir
r ,
AsAs CkRr 13
3
4
1/coth/3 111
21, AeAe
Aei DkRDkR
kR
D
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In general terms, i, depends only on four types of parameter:
(i) reaction kinetic constants/coefficients
(ii) surface concentration of substrate
(iii) effective diffusivity
(iv) particle size
The Thiele modulus or tortuosity factor, , for a given kinetics and particle geometry, is
a dimensionless combination of the important parameters that quantify mass transfer
and reaction in a heterogeneous catalyst system. The generalised Thiele modulus is
given as:
(63)
where: Vp= particle volume, Sx= external surface area, CA,eq= equilibrium [A] (=0 for
most biochemical reactions), and rA= reaction rate. From geometry, Vp/Sx= R/3 for
spheres, and = b for flat plates.
For 1storder kinetics with spherical geometry, we have: (64)
and:
(65)
and ifor other kinetics and geometries can be quantified by similar equations or
numerical methods.
21
,2
As
eqA
C
C AAAe
As
x
pdCrD
r
S
V
AeDkR 1
13
13coth33
1112
1
1,
i
Effectiveness factor versus generalised
Thiele modulus for 1storder kinetics,
e.g. from eq. (65). (Note: )
From Bioprocess Engineering Principles by Pauline M. Doran
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Generalised Thiele moduli for various
kinetics and particle geometries.
From Bioprocess Engineering Principles by Pauline M. Doran
Internal effectiveness factor versus generalised Thiele modulus for
Michaelis-Menten kinetics, obtained by numerical methods
(Note: and =Km/CAs)
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4.3 External m.t. concepts as applied to heterogeneous reactions
4.3.1 Liquid-solid mass transfer correlations
L-S mass transfer equation: (17)
Since ksdepends on reactor hydrodynamics and liquid properties, it is often difficult to
measure accurately, especially for neutrally buoyant entities such as microbial flocs.
Values of ks, accurate to within 10-20%, can however be estimated using various
correlations available in the literature. These correlations are expressed in terms of
dimensionless groups or numbers.
Sherwood number: (67)
Schmidt number: (68)
Particle Reynolds no: (69)
Grashof number: (70)
Dp= particle diameter, DAL= diffusivity of component A in the liquid,
upL= particle linear velocity relative to the liquid (slip velocity), L= liquid density,
L= liquid viscosity, p= particle density, g = gravitational acceleration.
AsAbsA
A CCak
dt
dCN
AL
ps
D
DkSh
L
LpLp
p
uD
Re
ALL
L
DSc
2
3 )(
L
LpLpgDGr
AL
ps
DDkSh
L
LpLpp uD
Re
ALL
L
DSc
2
3
)(L
LpLpgDGr
Sh: ratio of overall to diffusive mass transfer across the boundary layer
Sc: ratio of momentum (viscous) diffusivity to mass diffusivity
ReP: ratio of inertial to viscous forces acting on the particle
Gr: ratio of gravitational to viscous forces acting on the particle (important with
neutrally buoyant particles)
The form of the correlation(s) used to estimate ksdepends on the configuration of themass transfer system, the flow conditions and other factors. In all cases, ultimately the
Sherwood number, Sh, must be evaluated.
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AL
ps
D
DkSh
L
LpLp
p
uD
Re
ALL
L
DSc
2
3 )(
L
LpLpgDGr
Free-moving spherical particles.For this situation, the rate of mass transfer depends
on the slip velocity, upL, which is difficult to measure and must be estimated before
calculating ksfrom Sh.
1. Calculate Gr: For Gr
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4.3.2 Observable external mass transfer modulus
From eq. (17), if external mass transfer is rate limiting then rA,obs= NA, and:
, or (77)
Define as , the observable external mass transfer modulus:
(78)
All of the rhs terms are usually measurable. To assess whether or not external diffusion
is important in determining the overall rate determining step, apply the following criteria:
If
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5. BIOCHEMICAL ENERGY
BALANCES
Chapter 5 + Chapter 6, Bioprocess Engineering Principles, 2ndEd., P.M. Doran.
5. Biochemical Energy Balances
Although bioprocesses in general are not as energy intensive as chemical processes,
energy effects are nevertheless important since biologically active species are very
sensitive to heat. Heat released during reaction or generated during separation
operations, can cause cell death and denaturation of enzymes, if it is not quickly
removed. For good design of heat exchange equipment, energy flows in the system
must be evaluated using energy balances.
Energy ofin-flowing
materials
The bioprocessing
system
Energy ofout-flowing
materials
Energy in/out by
shaft work, Ws
Energy in/out by
heat transfer, Q
Energy changes in a bioprocessing system
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5.1 Law of conservation of energy
In the case of reaction systems, we are usually interested only in the total energy of
the system, rather than the energy of individual biochemical species, so a situation
analogous to that for total mass applies:
Energy accumulated or = Energy in through - Energy out through (79)
depleted within system system boundaries system boundaries
Referring to the various energy transfer modes possible, we can quantify eq. (79) to
obtain a series of general energy balance equations:
E = Mi(Ek+ Ep+ U + pV)i - Mo(Ek+ Ep+ U + pV)o - Q + Ws (80)
where E = energy accumulated/depleted, M = mass, Ek= kinetic, Ep= potential, and
U = internal energies, pV = flow work, Q = heat exchanged, Ws= shaft work, and
subscripts i and o refer to the inlet and outlet streams.
Enthalpy, h, can be defined as: h = U +pV (81)
so we have for equation (80):
E = Mi(Ek+ Ep+ h)i - Mo(Ek+ Ep+ h)o - Q + Ws (82)
In the case (true for many biochemical reaction systems) where there is little change in
kinetic or potential energy, and where the system is operating at steady state (noenergy accumulation/depletion), we can further simplify (82) to give:
Mi hi - Mo ho- Q + Ws = 0 ,
or, in cases where there may be more than one input and one output streams:
(M h)inlet streams - (M h)outlet streams - Q + Ws = 0 (83)
Steady-state Energy Balance Equation
Another case can be considered when no heat is transferredinto or out of the system
(i.e. Q=0):
(M h)inlet streams - (M h)outlet streams + Ws = E (84)
Adiabatic Energy Balance Equation
These equations or variations of them can be used in performing energy balance
calculations for chemical and biochemical systems.
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5.2 Calculation of enthalpy changes
Equation (81) showed that enthalpy is comprised of both the internal energy (U) of a
substance and the flow work term (pV). It is not possible to have an absolute measure
of U, therefore it is also not possible to know absolute enthalpy values. In energy
balance calculations, what is more important is to determine enthalpy changesas thesubstance is processed in a given plant unit. This can be done if the calculations are
performed with respect to a chosen reference state, at which the enthalpy is assigned
a value of 0.
Enthalpy changes can occur as a result of:
i. Temperature changes
ii. Change of phase e.g. liquid to gas
iii. Mixing or dissolution
iv. Reaction
5.2.1 Change in temperature
Sensible heat: this is the term given to heat exchanges to raise or lower the
temperature of a substance. The corresponding change in enthalpy of a system
due to temperature change is called sensible heat change.
Changes in enthalpy, H, due to temperature change, T, are given by:
H = M.Cp.T , (85)
where: M = mass
Cp= heat capacity at constant pressure.
The heat capacity value for a given substance can vary with temperature. These are
often given in the literature as a polynomial function of temperature, such as :
, (86)
where the coefficients , and are tabulated for difference substances.
In other cases, mean heat capacity values ,Cpm, are quoted as a function of
temperature relative to a reference temperature (usually 0oC) in the literature. To
calculate H for a temperature change from T1to T2, the corresponding values are
inserted into:
H = M[(Cpm)T2(T2- Tref) - [(Cpm)T1(T1- Tref)] (87)
Since large temperature changes do not often occur in bioprocessing, in many cases
Cps are assumed constant.
Cp,i i i i2 T T
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5.2.2 Phase changes
Relatively large changes in internal energy and enthalpy occur as intermolecular
bonds are broken during phase changes such as evaporation or melting. Latent heat
is the term given to the heat exchange that occur during phase changes at constant
temperature and pressure.
Enthalpy changes that result from phase changes can be calculated directly from the
corresponding latent heat literature values for that substance. For example, for
evaporation of a mass of liquid, M:
H = M. hv , (88)
where hv is the latent heat of vaporisation.
Literature values of latent heats are usually given for substances at their normal
boiling, melting or sublimation points at 1 atm. pressure. Latent heat, like heat capacity
can also be temperature dependent, so when phase change occurs at some non-
standard temperature, e.g. evaporation of water at 70oC, the corresponding enthalpy
change must be calculated by including the relevant sensible heat changes into an
appropriate energy cycle.
5.2.3 Mixing and dissolution
In a similar vein to phase change, enthalpy changes can also occur on mixing of two
liquid components or on dissolution of substances in a solvent. Thus for example
dissolution of sodium hydroxide pellets in water can release enough heat to boil the
water in some cases.
Heat of mixing is property of the mixture components, their concentrations and the
temperature, and can be quantified from integral heats of mixing data, available in
the literature. Since most biochemical processes operate with dilute aqueous mixtures,
enthalpy of mixing effects can often be assumed to be minimal in energy balance
calculations.
5.2.4 Reaction enthalpy changes
For chemical reactions, Hesss Law allows us to calculate reaction enthalpy change,
Hr:
(89)
where: Ni= number of moles of component i involved in the reaction
H0f,i= standard enthalpy of formation of component i.
Whereas H0f,ivalues are often available for chemical components, this is often not
the case for biochemicals.
tsreacifiprod uctsifir HNHNH tan0,0,0 )()(
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Instead heats of combustion, h0c,i are used. These are relatively easily measured
since all biochemical materials are combustible, giving simple gases such as CO2, H2O
vapour and N2. Thus:
(90)
Equation (90) allows calculation of the standardenthalpy of reaction (i.e. normally at
25oC). For reactions carried out at other temperatures, then sensible heat changes
have also to be taken into account, as outlined in section 5.2.1. For most biochemical
reactions, this is not an issue. However one major exception is in the case of single
enzyme conversion reactions. These have very small reaction enthalpy changes, and
hence any additional sensible heat effects can be quite significant in determining the
overall enthalpy change.
The enthalpy of reaction at non-standard conditions can be quantified by considering
the hypothetical path that involves the same initial and final states of the reaction
mixture, but takes place via the standard reaction conditions.
productsicitstanreacicir hNhNH )()( 0,0,0
Actual path
Hypothetical path for calculating Hrxn
at non-standard conditions
3
0
1)( HHHTatH rxnrxn
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In aerobic fermentations, where oxygen is the main oxidising agent in cell
metabolism, it is possible to calculate the enthalpy of reaction, based on the amount of
oxygen consumed:
(91)
Thus either equation (91) (for aerobic fermentations) or equation (90) (for all
fermentation types) can be used to calculate Hrif either the fermentation oxygen
consumption or the reaction component heats of combustion are known.
Heat of combustion of biomasshave been found experimentally to fall into two
broad groups:
Bacteria h0c 23.2 kJ.g-1
Yeasts h0c 21.2 kJ.g-1
consumedOmoleperkJH Aerob icr 2, 460
5.2.5 Energy balance equation for cell bioreactors
In fermentation reactors, reaction enthalpy changes usually dominate the energy
balance, compared to the small enthalpy contributions due to sensible heat and heat of
mixing changes, so that the latter terms can often be ignored. (Note: this only applies
to cell bioreactors, not to other process units such as heat exchangers, etc.).
Thus the only significant factors to be accounted for in the energy balance for such
reactor units are:
reaction enthalpy changes, Hr
latent heat enthalpy changes (usually due to evaporation), Hv(=Mv.hv, eq.88) shaft work, Ws(usually due to stirring/agitation)
Recalling the steady state energy balance equation:
(M h)inlet streams - (M h)outlet streams - Q + Ws = 0 , (83)
it is possible to formulate a useful version for this particular case (cell bioreactors):
-Hr - Mv.hv - Q + Ws = 0 (92)
since reaction and latent heat are the only significant contributors to enthalpy change
between the inlet steams and the outlet streams.
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5.2.6 Essential good practice and procedure for performing energy balance
calculations
These are essentially the same as for material balances (section 3.1).
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