1Part IVBioreactor Engineering

2Chapter 10 Ideal BioreactorsThere are two kinds of ideal bioreactors. One is perfectly mixed bioreactor, including batch, fed-batch and continuous operated bioreactors; and the other plug flow bioreactor. By definition, there is no any gradient, including concentration, temperature, etc. existing within perfectly mixed bioreactor. Usually, small scale stirred vessels which are used for low viscosity cell culture or fermentation systems can be listed into this category. Conversely, the flow of biofluid through the plug flow bioreactor is completely orderly without any element of biofluid overtaking or mixing with any other element ahead or behind, the residence time for all material is the same. Usually, some tubular enzyme bioreactor when operated at relatively high flow rate can be listed into this category.

310.1 Batch Operation of Perfectly Mixed Bioreactors

10.1.1 Enzyme Reaction

V, S, P

Figure 10.1 Flowsheet fora batch bioreactor

4General Mass Balance:

Mass Balance for batch enzyme catalytic reaction

Usually, V is constant, so we have:

dtdM = iM

) oM) + RG RC

VSK

SdtVSd

m += max)(

SKS

dtdS

m += max

5Integrating:

For initial condition S = S0 at t = 0:

Enzymes are subject to deativation. Thus, the concentration of active enzyme in the reactor, and therefore the value of max, may change during reaction. When deactivation is significant, variation of max with time can be expressed by:

+= dSSSKdt mmax

max

00

maxln

+=f

f

mb

SSSSKt

6Therefore,

Separating variables gives:

with initial condition S = S0 at t = 0,

tk0

de= maxmax

SKSe

dtdS

m

tdk

+=

0max

+= dSSSKdte mtdk 0max

710.1.2 Cell CulturesSimilarly to the analysis for enzyme catalytic reaction, we have:

For V constant,

)]ln(1ln[1

0max

00

0max +=

f

f

md

db

SSSSKk

kt

xVkxVdtxVd

d=)(

xkdtdx

d )( =

8The initial condition x = x0 at t = 0, we have:

or

If the rate of cell death is negligible, we have:

tdkexx )max(0=

0maxln1

xx

kt f

db =

texx max0=

9and

Mass balance for limiting substrate:

If = max and V constant:

0maxln1

xx

t fb =

xVmYq

YdtSVd

SP

P

SX)()(

//++=

xmYq

YdtdS

SP

P

SX)(

//

max ++=

10

and

If no product is formed or if production is directly linked with energy metabolism, we have:

max0

//

max )( ++= exmYq

YdtdS

SP

P

SX

])1(

1ln[1

0max/max/

0

max xmY

qY

SSt

SP

P

SX

fb

+++=

])1(

1ln[1

0max/

0

max xmY

SSt

SX

fb

++=

11

If maintenance requirements can also be neglected:

Mass balance for product:

If cell death is negligible and V constant,

)](1ln[1 00

/

maxf

SXb SSx

Yt +=

xVdtPVd

P=)(

tP exdt

dP max0

=

12

If P is also constant, and with the initial condition P = P0 at t = 0

10.1.3 Total Time for Batch Culture CycleIn the above analysis, tb represents the time required for batch culture or enzyme conversion. In practice, batch operations involve very long unproductive periods. Following the fermentation or enzyme reactions, time thv is taken to harvest the contents inside the bioreactor and time tp is needed to clean, sterilize and otherwise prepare the bioreactor for the next operation. For cell culture, a lag time of duration t1 occurs after inoculation during which no growth or product formation occurs. These time periods are illustrated below for fermentation processes.

)](1ln[1 00

max

maxPP

xt f

Pb

+=

13

The total downtime tdn and operation time tT are:

hvpdn tttt ++= 1

dnbT ttt +=

C

e

l

l

c

o

n

c

e

n

t

r

a

t

i

o

n

tp t1 bt thv

0x

x f

tt 1p hvtt b

Figure 10.2 The entire time period needed for batch cell culture

14

10.2 Fed-Batch Operation of Well-mixed BioreactorsIn fed-batch operation, intermittent or continuous feeding of nutrients is used to supplement the bioreactor contents and provide control over the substrate concentration. By starting with relatively dilute solution of substrate and adding more nutrients as the bioreaction proceeds, high growth rates are avoided. This is important, for example, in cultures where the oxygen demand during fast growth is too high for the mass-transfer capabilities of the bioreactor. Alternatively, high substrate concentration may be

inhibitory or switch on undesirable metabolic pathways.

15

Fed-batch culture is used extensively in production of bakers yeast to overcome catabolic repression and control oxygen demand; it is also used routinely for penicillin production. Space must be allowed in fed-batch bioreactors for addition of fresh medium; in some cases a portion of the broth is removed before injection of additional material. The flow rate and timing of the feed are often determined by monitoring parameters such as dissolved-oxygen level or exhaust gas composition. As enzyme reactions are rarelycarried out as fed-batch operations, we will consider fed-batch bioreactors for cell cultures or fermentations only.

16

V, x, S, P

Figure 10.3 Flow-sheet for a batch bioreactor

Feed stream

FxSP

i

i

i

17

For fed-batch bioreactor, we have:

A mass balance for cells:

Expand the differential equation gives:

FdtdV =

xVkxVFxdtxVd

di +=)(

xVkFxdtdxV

dtdVx di )( +=+

18

Therefore,

Dividing by V gives:

and

xVkFxdtdxVxF di )( +=+

xVFkx

VF

dtdx

di )( +=

xDkDxdtdx

di )( +=

19

Usually, the bioreactor is operated first in batch until a little high cell density is achieved and the substrate virtually exhausted, then, fed-batch operation is started with medium flow rate F. As a result, cell concentration x is maintained relatively high and approximately constant so that dx/dt 0 and D, therefore, Monod expression for cell growth can be written as:

or

SKSD

S += max

DDKS S= max

20

If no product is produced, or the product formation is directly coupled with energy metabolism, we have:

At high cell density, virtually all substrate entering the vessel is consumed immediately; therefore, S

21

For product synthesis directly coupled with energy metabolism, at the same time assuming the feed does not contain product:

Even though cell concentration remains virtually unchanged with time dx/dt 0, because the broth volume increases with time during fed-batch culture, the total biomass within the bioreactor also increases. Consider the rate of increase of total biomass in thebioreactor dX/dt:

iSP SYP /

22

Integrated with initial condition X = X0 at the start of feeding to give:

This indicates that, if YX/S, Si and F constant, the total biomass in fed-batch culture increases as a linear function of time.

Under conditions of high biomass density and almost depletion ofsubstrate, a quasi-steady-state condition previals in fed-batch bioreactors in which dx/dt 0, dS/dt 0 and dP/dt 0, and x, S and P are almost constant, but , V, D and X are changing with time.

FSYdtdxV

dtdVx

dtxVd

dtdX

iSX /)( =+==

bfiSX tFSYXX )( /0 +=

23

10.3 Continuous Operation of Well-mixed BioreactorsFrom the view of engineering application, continuous operation of bioreactors shows great advantage over batch and fed-batch processes discussed above. Not only a long downtime required by batch and fed-batch bioreactors is saved, but a steady condition can also be realized easily within the bioreactors, enzyme or cells will be maintained under optimum environments, therefore, the productivity of aimed product or biomass can be improved obviously. One of the biggest disadvantages of a continuous stirred-tank reactor(CSTR) is the withdrawn of biocatalyst contained within the product stream when used for freely suspended cell culture and enzyme reaction systems. Only when the enzymes are inexpensive and can be added continuously to maintain the required concentration, can a CSTR be appl ied. On the other hand, the high r isk of

24

contamination also hinders CSTRs application in animal and plant cell cultures and other fermentations, such as penicillin, in which much lower growth rate of cells and complete nutrients increase the opportunity for undesirable microorganisms to grow quickly within the system. Different steady-state operating strategies are available for a CSTR. In a chemostat, the liquid volume within the bioreactor is maintained constant by setting the inlet and outlet flow rates equal; the dilution rate is therefore constant and steady state is achieved in the chemostat by adjusting itself to the feed rate. In a turbidostat, the liquid volume is kept constant by setting the outlet flow rate equal to the inlet flow rate; however, the inlet flow rate is adjusted to keep the biomass concentration constant. Thus, in a turbidostat the dilution rate adjusts to its steady-state value corresponding to the set biomass concentration.

25

V, x, S, P

Figure 10.4 Flowsheet for a CSTR

Feed stream

FxSP

i

i

i

PSxF

Product stream

26

Characteristic operating parameters for CSTRs are the dilution rate D and the average residence time . The following relationship exists:

For a given throughput, the bioreactor size V and associated capital and operating costs are minimized when is made as small as possible. Continuous bioreactor theory allows us to determine relationships between or D and steady-state substrate, product and cell concentrations.

FV

D== 1

27

10.3.1 Enzyme Reaction

Mass balance gives:

Dividing by V and applying the definition of dilution rate gives:

0max =+ V

SKSFSFS

mi

SKSSSD

mi +

= max)(

28

If kinetic parameters including max and Km and substrate concentration contained within the feed can be used directly to calculate the dilution rate required to achieve a particular level of substrate conversion, then, the steady-state product concentration and productivity can be evaluated from stoichiometry.

For immobilized enzyme system, we have:

where T is the total effectiveness factor, S is the bulk substrate concentration, and max and Km are intrinsic kinetic parameters.

SKSSSD

mi +

= maxT)(

29

10.3.2 Cell CultureIf cell death is also negligible compared with cell growth, the mass balance of biomass gives D = .When cell growth kinetics can be described by Monod equation:

The mass balance of substrate gives:

DDKS S= max

mYY

DSSDx

SP

P

SX

i

++=

//

)(

30

If no product synthesis other than biomass:

If, further, maintenance effects can further be ignored:

Therefore,

mY

DSSDx

SX

i

+=

/

)(

)(/ SSYx iSX =

)(max

/ DDKSYx SiSX =

31

The dilution rate for the highest biomass productivity is given by:

Now we consider the CSTR in which immobilized cells are used as illustrated below.

)1(maxoptiS

S

SKKD +=

32

V, x , S, P

Figure 10.6 Flowsheet for a CSTR

Feed stream

FxSP

i

i

i

PSxF

Product stream

im

s

with immobilized cells

33

Mass balance for biomass:

F xs + xsV + TximV = 0 Rearrange:

or)( imT xxDx ss +=

)1(s

imT

xxD +=

34

Mass balance for substrate:

and

also

0)(/

im

/= V

YxV

YxSSF

SX

T

SX

si

)()(/

imTsSX

i xxYSSD +=

imTSXi

SXi

S xYSSYSSD

SKS

+=+

/

/max

)()(

35

40

60

0

20

0 0.1 0.2 0.3 0.4 0.5

80

100

Dilution rate, D h1

S

u

b

s

t

r

a

t

e

c

o

n

v

e

r

s

i

o

n

,

%

Figure 10.7 Steady-state substrate conversion as a functionof dilution rate with and without immobilized cells

(calculated with max = 0.1 h1, KS = 103 g l1, YX/S = 0.5 and Si = 8 103 g l1)

xim = 0.1 g l1, T = 1.0

xim = 0.1 g l1, T = 0.3

xim = 0

Dcri

36

We can find for any xim > 0, dilution rate D at steady state is greater than . Accordingly, dilution rate is no longer limited by the maximum specific growth rate max, as discussed before, that means immobilized cell bioreactor can be operated at Dconsiderably greater than Dcrit for free cells without washout happening. We also can find that, at a given dilution rate, presence of immobilized cells improves substrate conversion and reduces the amount of substrate lost in the product stream. However, bioreaction rates with immobilized cells can be significantly affected by the mass transfer in and around the particles.

37

10.4 Plug-Flow Bioreactor

No mixing occurs in an ideal plug-flow bioreactor (PFR); material entering the bioreactor passes through and does not interact with neighboring fluid elements. This is achieved at high flow rates which minimize backmixing and variation in fluid velocity. Plug flow is most readily achieved in column or tubular bioreactors which can be operated in upflow or downflow mode or, in some cases, horizontally.

PFR is mainly used for some enzyme catalytic reactions and medium sterilization during which contaminant microorganisms arekilled by heating.

38

Figure 10.8 Flowsheet for a PFRFeed stream F S i

F S

Product stream F S f

zLz

39

Mass balance for substrate:

Rearrange:

and

0max =+ + zA

SKSFSFS

mzzZ

SKS

zASSF

m

zzz

+=

+ max)(

SKS

zSSu

m

zzz

+=

+ max)(

40

That is:

Integrating with boundary condition S = Si at z = 0 gives:

SKS

zSS

um

zzz

z +=

+

max

0)lim(

SKS

dzdSu

m += max

)ln(maxmax +=

fi

f

im SSSSKuL

41

For

we have:

uL

AFAV

FV ===

maxmaxln

+=fi

f

im SSSSK

42

Only a few enzyme reactions, for example, liquification of starch slurry using -amylase before being saccharified to fermented sugar, are applying this operation mode. If enzyme is immobilized, mass-transfer effects should be considered, therefore:

Generally, PFR operation is not suitable for cell culture unless the biomass is recycled or there is a continuous inoculation operation. However, for sterilization of medium, PFR is widely used and will be discussed later. If cells are immobilized and packed within the column, PFR modified properly can be applied.

SKS

dzdSu

mT += max

43

10.5 Sterilization of Medium

10.5.1 Batch Heat Sterilization of MediumMedium can be sterilized in batch in the vessel where it will beused. The medium is heated to sterilization temperature by introducing steam into the coils or jacket of the vessel; alternatively, steam is bubbled directly into the medium. If direct steam injection is used, allowance must be made for dilution of the medium by condense which typically adds 10 ~ 20% water to the medium; quality of the steam must also be sufficiently high to avoid contamination of the medium by metal ions.

44

140120

80100

20 0

40 60

0 1 3 2

t hd

HeatingHolding

Cooling

Time (h)

T

e

m

p

e

r

a

t

u

r

e

C

Figure 10.9 Variation of temperature withtime for batch sterilization of medium

45

For operation of batch sterilization systems, we must be able toestimate the holding time required to achieve the desired level of cell destruction. As well as destroying contaminant organisms, heat sterilization also destroys nutrients in the medium. To minimize this loss, holding times at high sterilization temperature should be kept as short as possible. Cell death occurs at all times during batch sterilization, including the heating-up and cooling-down periods. The holding time thd can be minimized by taking into account cell destruction during these periods.

46

0 1 3 2

t hd

Heating

Holding

Cooling

Time (h)

N

u

m

b

e

r

o

f

v

i

a

b

l

e

c

e

l

l

s

Figure 10.10 Reductioin in number ofviable cells during batch sterilization

N0N1

N2Nf

47

In a batch vessel where cell death is the only process affecting the number of viable cells, we have:

During the holding period:

or

NkdtdN

d=

hdd tkNN =

2

1ln

dhd k

NN

t 21ln

=

48

where

therefore

for heating

when heat transfer from isothermal steam

RTdE

d Aek=

NAedtdN RT

dE=

dtAeNN t RT

Ed = 101

0ln

)1( 0 pmCMUAt

s

ss eT

TTTT+=

49

when heating directly by sparging with stream

electrical heating

for cooling

)1(0

0 TCMQtTT

pm+=

dtAeNN t

tRTE

f

d = f2

2ln

)1

1( 00

tMM

TCMhtM

TT

m

s

pm

s

++=

50

where

+=

)]1)([(01

pwCwMUA

pm

pww eCM

tCM

ci

cici eT

TTTT

51

Heating Holding Cooling

Time

T

e

m

p

e

r

a

t

u

r

e

Figure 10.11 Generalized temperature-time profiles for the batch sterilization

Raw medium temperature

Fermentationtemperature

HyberbolicLinearExponential

ExponentialLinear

52

Normally, cell death below 100 C is minimal; however, when heating and cooling are relatively slow, temperatures remain close to the maximum for considerable periods of time, cell numbers can be reduced significantly outside the holding period. Usually, holding time is of the order of minutes whereas heating and cooling of large medium volumes take hours.

The design procedures outlined in this section apply to batch sterilization of medium when the temperature is uniform throughout the vessel. However, if the medium contains contaminant particles in the form of flocs or pellets, temperature gradient within the

53

particles may develop and the temperature at the center of the particles will lower than that in the bulk medium. As a result, cell death inside the particles is not as effective as in the bulk medium. Longer holding time is required to treat solid-phase substrates and media containing particles.

When batch sterilization is scaled up to larger volumes, much longer times are needed to achieve the same sterilization results as that of small-scale tanks, the destroy of nutrients is exacerbated extremely. Therefore, continuous sterilization process is developed for large-scale use.

54

10.5.2 Continuous Heat Sterilization of Medium

Fermenter

Heatexchanger

Raw medium

Steam

Jet

Holding sectioncooler

Vapor

Flash(a)

55

Fermenter

(b)

Steam

Raw medium

Holding sectionexchangerHeat

exchangerHeat

Figure 10.12 Continuous sterilization processes

Condensed water

56

Continuous sterilization, particularly a high-temperature, short-exposure-time process, can significantly reduce damage to medium nutrients while achieving high levels of cell destruction. Otheradvantages include improved steam economy and more liable scale-up. The amount of steam needed for continuous sterilization is only 20 ~ 25% that used in batch processes; the time required is also obviously reduced because heating and cooling are virtuallyinstantaneous.

57

Steam

Holding

cooling

Time

T

e

m

p

e

r

a

t

u

r

e

Figure 10.13 Variation of temperature with time in the continuous sterilisers of Figure 11.12

2 - 3 min

Heatexchange

injection

Flash

exchange

T

e

m

p

e

r

a

t

u

r

e

Time

Heat

2 - 3 minHolding

(a) (b)

58

An important variable affecting performance of continuous sterilisers is the characteristics of medium flow in the system. Ideally, all medium entering the system at a particular instant should spend the same time in the steriliser and exit the system at the same time also, that is plug-flow. Otherwise, if mixing occurs within the holding pipe, a risk of contamination will be transferred to the outlet of the sterilized medium from the inlet of raw material. Deviation from plug-flow behavior is characterized by the degree of axial dispersion along the pipe which will be further discussed later.

59

10.6 Comparison between Modes of Bioreactor Operation

Figure 10.14 Substrate concentration changes in PFR, batch, CSTR and CSTRs in cascade

S

S

i

f

Large number of CSTRs

Four CSTRs of equal size

PFR or batch

Single CSTR

60

SummaryAfter studying this chapter, you should: understand the concept of well-mixed flow and plug-flow modes,

two extremely flowing conditions; be able to predict batch bioreaction time required to achieve

designed substrate conversion for enzyme reaction and cell culture;

be able to predict the performance of fed-batch bioreactors operated at quasi-steady-state conditions;

for CSTR, know how to control its operation in order to avoid washout of cells and to obtain the optimum cell productivity; and finally

be able to compare the performance of batch, CSTR and PFR and select proper operation method for a designed bioprocess.