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CG4017

Bioprocess Engineering 2

Denise Croker, BM-028

[email protected]

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.

2
mailto:[email protected]:[email protected]

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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.

4

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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?

9

10

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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


Cells

Cell wall: zone C



Substrate molecule

1

2

3

4






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Microbial floc


Cells

Cell wall: zone C



Substrate molecule

1

2

3

4






Microbial floc


Cells

Cell wall: zone C



Substrate molecule

1

2

3

4






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Microbial floc


Cells

Cell wall: zone C



Substrate molecule

1

2

3

4






Classification of biochemical reaction types for balanced growth kinetic models

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Reactiontype #

Zone(s) involved General biochemical reaction name


Reactiontype #


(1) DCell-free enzyme reactions in non-viscous substratemedia


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Reactiontype #


(1) DCell-free enzyme reactions in non-viscous substrate

media

(2) C + D Single cell reactions in non-viscous substrate media


Reactiontype #




(3) B + C + DBiological floc/film reactions in non-viscous substratemedia


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Reactiontype #


(1) DCell-free enzyme reactions in non-viscous substrate

media



(4) B + DCell-free immobilised enzyme reactions in non-viscoussubstrate media


Reactiontype #





(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


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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

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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Graphical representation of cell division probability density function, K.

),,( DOSyK

)(ppmDO

)(, cyclesonreproductiyAge


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

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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


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

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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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3


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

.'

'),'(


Modelling versus experimental results for chemostat yeast fermentation oscillatory behaviour

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3


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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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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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.


CH1.8O0.5N0.2

Average biomass molecular weight = 24.6(+5-10% as residual ash/other elements)

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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

)(


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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





All substrate removed at ~ t = 5 mins

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At t = 60 min

X1 (biomass in Reactor) = 0


XR (Biomass in Recycle Line) = 0


At t = 60 min






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At t = 60 min






At t = 60 min




SS (Substrate in Settler) = 0


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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


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


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: )


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Generalised Thiele moduli for various

kinetics and particle geometries.


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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