Reactor

Biochemical EngineeringCEN 551

Instructor: Dr. Christine Kelly

Chapter 9

Bioreactors• What two type of bioreactors have

we discussed in this course?

• What are the characteristics of each type of reactor?

• Which type is more efficient?

• Which type is more common?

Reactor Types• Batch and Chemostat (CSTR).

• Batch: changing conditions - transient (S, X, growth rate), high initial substrate, different phases of growth.

• Chemostat: steady-state, constant low concentration of substrate, constant growth rate that can be set by setting the dilution rate (i.e. the feed flow rate) .

• Chemostat more efficient.

• Batch more common.

Choice of continuous vs. batch production

• Productivity• Flexibility• Control• Genetic stability• Operability• Economics• Regulatory

What do each of these factors mean?

Reactor Choices• Productivity: rate of product per time

per volume. Chemostat better for growth associated products. Wasted time in batch process.

• Flexibility: ability to make more than one product with the same reactor. Batch better.

• Control: maintaining the same conditions for all of the product produced. In theory, chemostat better, steady state. In reality????

• Genetic stability: maintaining the organism with the desired characteristics. Chemostat selects for fast growing mutants that may not have the desired characteristics.

• Operability: maintaining a sterile system. Batch better.

• Regulatory: validating the process. Initially, many process batch, too expensive to re validate after clinical trials.

Comparison of Productivity: Batch vs. Chemostat

Consider production of a growth associated product (like cell mass) in suspension culture

F S0 X0

F S0 X0

F S X

F S X

airair airair

??

Batch Reactortcycle tgrowth tlBatch cycle time is:Batch cycle time is:

where tgrowth is the time required for growth and tl is the lag time + preparation and harvest time.

where tgrowth is the time required for growth and tl is the lag time + preparation and harvest time.

tcycle 1

max

lnXmax

X0

tl

where X0 is the initial concentration and Xmax is the maximum concentration (carrying capacity).

where X0 is the initial concentration and Xmax is the maximum concentration (carrying capacity).

Batch Production RateSo net biomass production rate is:So net biomass production rate is:

PrX batch YX /S S0

1max

lnXmax

X0

t l

Recall the definition of biomass yield:Recall the definition of biomass yield:

YX /S XS

Xmax X0

S0 0Xmax X0

S0

PrX batch Xmax X0

tcycle

(1)(1)

ChemostatFor negligible kd, negligible extracellular product formation and steady state, Lec. Notes 16, Eq. (10) gave:

For negligible kd, negligible extracellular product formation and steady state, Lec. Notes 16, Eq. (10) gave:

X YX / S S0 KSD

max D

For optimum cell productivity (X•D), calculate d(X•D)/dt, set equal to zero, and solve for Dopt:For optimum cell productivity (X•D), calculate d(X•D)/dt, set equal to zero, and solve for Dopt:

Dopt max 1 KS

KS S0

(3)(3)

(2)(2)

ChemostatSubstituting Eq. (2) into Eq. (3) gives the value of X at the maximum production rate. :Substituting Eq. (2) into Eq. (3) gives the value of X at the maximum production rate. :

S0SS0X/Sopt KSKKSY)D(at X

Optimum productivity is D•X when D=Dopt and X= X (at Dopt):

Optimum productivity is D•X when D=Dopt and X= X (at Dopt):

S0SS00S

SmaxX/Schemoopt,X KSKKS

SK

K1μYPr

(4)(4)

(5)(5)

Chemostat Productivity RateNoting that S0 is usually much larger than KS, we have:

Noting that S0 is usually much larger than KS, we have:

PrX opt , chemo maxYX /SS0

Comparing the rates for batch production and production in a chemostat:Comparing the rates for batch production and production in a chemostat:

Prx opt , chemoPrx batch

lnXmax

X0

maxtl

(6)(6)

(7)(7)

ComparisonXmax is always larger than X0 and is typically 10-20 times larger, so the chemostat outperforms the batch reactor. For E. coli growing on glucose, µmax is around 1/hr. Using tlag=5 hr and Xmax/X0=20,

Xmax is always larger than X0 and is typically 10-20 times larger, so the chemostat outperforms the batch reactor. For E. coli growing on glucose, µmax is around 1/hr. Using tlag=5 hr and Xmax/X0=20,

Prx opt , chemoPrx batch

8

Even so, most industrial fermentation processes occur in a batch reactor. Why?Even so, most industrial fermentation processes occur in a batch reactor. Why?

Reasons for Batch Popularity

• Equations were for cell mass (or other growth-associated product). Many industrial applications are for non-growth associated products.

• Selective pressure of a chemostat is detrimental to engineered organisms

• Batch is more mechanically reliable

• Batch system is more more flexible

Specialized Reactors

• Chemostat with recycle

• Multistage chemostat

• Fed-batch

• Perfusion

Chemostat with RecycleCan we operate a chemostat with a dilution

rate greater than maximum growth rate?

Why or why not?

What conditions would we want to operate a chemostat with a dilution rate higher than the maximum growth rate?

High dilution rate

• No

• Because the cell growth cannot keep up with how fast the cells are removed from the reactor, and after some time the cells would washout of the reactor.

• We want a high dilution rate when we have a high volume of feed with a low concentration of substrate. Waste water treatment has these characteristics.

Operation of Chemostats at High Dilution Rates

Chemostats cannot be operated if µmax<D. Higher dilution rates can be achieved with recycle.

F S0 X0

F S0 X0

(1+)F S,X

(1+)F S,X

F S,XF

S,X

F X’F X’

Chemostat with RecycleBiomass balance on the chemostat:

μVXFXα1αFβXFXdt

dXV 0

where =volumetric recycle ratio and =the concentration factor of the separator. At steady state and with X0=0:

where =volumetric recycle ratio and =the concentration factor of the separator. At steady state and with X0=0:

0μXXV

Fα1βX

V

Fα

Dβ1α1μ

Note that for >1, µ<D.Note that for >1, µ<D.

(8)(8)

(9)(9)

(10)(10)

Substrate Mass Balance

VdSdt

FS0 FS VXYX /S

1 FS

FVS0 F

VS

XYX /S

1 FVS0

X DYX /S S0 S

At steady state:At steady state:

(11)(11)

(12)(12)

(13)(13)

Steady-state ValuesSubstituting µ given by Eq. (10) into Eq. (13):Substituting µ given by Eq. (10) into Eq. (13):

X YX /SS0 S

1 1 (14)(14)

We can get the expression for the substrate concentration by equating the expression for µ from Monod kinetics to Eq. (10):

We can get the expression for the substrate concentration by equating the expression for µ from Monod kinetics to Eq. (10):

Steady-state Values

maxSKS S

1 1 D

or:or:S

KSD 1 1 max D 1 1 (16)(16)

(15)(15)

So now we can get X entirely as a function of D:So now we can get X entirely as a function of D:

X YX /S

1 1 S0

KSD 1 1 max D 1 1

(17)(17)

Special Cases - Chemostat• Recombinant product under the control of

an inducible promoter.

• Recombinant strain and wild type grow at the same rate if the recombinant product is not expressed.

• If the recombinant product is expressed, the recombinant strain grows much slower.

• Design a continuous reactor system to produce this product efficiently.

Mulistage chemostat• First chemostat is fed with a non-inducing

growth substrate, allowing the recombinant strain to be produced.

• The effluent from the first chemostat feeds a second chemostat that is fed inducer, and the product is produced.

• Note: new recombinant cells are continually added to the second chemostat not allowing take-over by a fast growing mutant.

Fed-batch Operation• Fed-batch reactors gain some advantages

of a CSTR, retain some disadvantages of batch.– Reduces substrate inhibition or

catabolic repression, allows for high conversion, and the extension of stationary phase.

– Semi-batch nature usually leads to higher operations cost and batch variability.

Fed-batch OperationF, S0F, S0

V0, X, S, PV0, X, S, P

Start fed-batchStart fed-batch Fed batch fillFed batch fill HarvestHarvest

Vw, X, S, PVw, X, S, PV, X, S, PV, X, S, P

F, S0F, S0

Fed-batch Operation• Fed-batch cultures are started as batch

cultures and grown to an initial cell concentration X, after which fed-batch operation begins.

• Notation:

S0= initial substrate concentration of batch

V0= initial volume of batch

F= constant flow rate of addition stream during fed-batch

X0= initial concentration of batch

S0= initial substrate concentration of batch

V0= initial volume of batch

F= constant flow rate of addition stream during fed-batch

X0= initial concentration of batch

Since liquid is being added, the volume is changing:Since liquid is being added, the volume is changing:

dVdt

F V V0 Ft

X X0 YX / S S0 S For a batch culture:For a batch culture:

or:or:

If the total amount of biomass (grams) in the reactor is Xt then the concentration X is:

If the total amount of biomass (grams) in the reactor is Xt then the concentration X is:

X X t /V

(1)(1)

(2)(2)

(3)(3)

So the change in the biomass concentration with time is:So the change in the biomass concentration with time is:

dXdt

VdX t

dt

X t

dVdt

V2

Using the definition of the growth rate:Using the definition of the growth rate:

...the dilution rate:...the dilution rate:

...and the expression for dV/dt:...and the expression for dV/dt:

1X tdX t

dt

DFV

dVdt

F

we have:we have: dXdt

D X

(4)(4)

(5)(5)

Now, consider the case when the fed-batch is started from a culture in the initial substrate concentration was S0 and nutrient feed is begun at flow rate F and concentration S0. Just as nutrient feed begins:

Now, consider the case when the fed-batch is started from a culture in the initial substrate concentration was S0 and nutrient feed is begun at flow rate F and concentration S0. Just as nutrient feed begins:

Quasi-steady State• Substrate is consumed at the same rate it is

added.

X X0 YX / S S0 S (6)(6)

At quasi-steady state, for this case we will have:At quasi-steady state, for this case we will have: dX

dt0

So X is constant (but not Xt). Now we have:So X is constant (but not Xt). Now we have: D

Assuming Monod growth kinetics, this gives (just as in the case of a chemostat):

Assuming Monod growth kinetics, this gives (just as in the case of a chemostat): S

KsDmax D

(7)(7)

(8)(8)

(9)(9)

If the total amount of substrate in the reactor is St, then a substrate mass balance gives:If the total amount of substrate in the reactor is St, then a substrate mass balance gives:

dS t

dtFS0

X t

YX /S

which, for quasi-steady state gives:which, for quasi-steady state gives:

FS0 X t

YX /S

Returning to Equation (4), we have, at quasi-steady state:Returning to Equation (4), we have, at quasi-steady state:

dX t

dtX t

VdVdt

XF

(10)(10)

(11)(11)

(12)(12)

Integrating, we have:Integrating, we have:

X t X0t FXt

since X is constant (dX/dt=0). Therefore, the total biomass in a fed-batch reactor operated as assumed here increases linearly with time. Substituting the appropriate expression for X:

since X is constant (dX/dt=0). Therefore, the total biomass in a fed-batch reactor operated as assumed here increases linearly with time. Substituting the appropriate expression for X:

tSSYXFXX 0X/S0t0

t

Often, S<<S0 and X0<<YX/SS0 and so:Often, S<<S0 and X0<<YX/SS0 and so:

X t X0t FYX / SSo t

(13)(13)

(14)(14)

(15)(15)

If the specific productivity (g product/g cells/ hr) is constant:If the specific productivity (g product/g cells/ hr) is constant:

Product Output

1X tdP t

dtqp

dP t

dtqpX

t

where Pt is the total product concentration in the reactor:where Pt is the total product concentration in the reactor:

or:or:

Substituting:Substituting:X t VX V0 Ft X

(16)(16)

we have:we have: dP t

dtqpX V0 Ft

Integrating this expression, we have:Integrating this expression, we have:

P t P0t qpX V0

Ft2

t

or in terms of concentration:or in terms of concentration:

P P0

V0

V qpX

V0

VDt2

t

(17)(17)

(18)(18)

(19)(19)

Repeated Fed-batchUsually, fed-batch cultures are taken

through many feeding cycles, with each feeding cycle followed by a harvest cycle during which the volume is drawn back down to V0 and the cycle begun again.

For the case of repeated fed-batch cultures:For the case of repeated fed-batch cultures:

Pw P0 qpX Dwtw

2

tw

Where Vw is the volume just before harvesting, V0 is the volume after harvesting, Dw=F/Vw and:

Where Vw is the volume just before harvesting, V0 is the volume after harvesting, Dw=F/Vw and:

V0

Vwtw is the cycle time and is given by:tw is the cycle time and is given by:

tw Vw V0

FVw VwF

1 Dw

(20)(20)

(21)(21)

(22)(22)

With this definition, we now have:With this definition, we now have:

2

w

p0w γ1

2D

XqγPP (23)(23)

Perfusion Culture• Animal Cell Culture

• Constant medium flow

• Cell retention

• Selective removal of dead cells

• Removal of cell debris, inhibitory by products

• High medium use, costs raw materials and sterilization

Immobilized Cell Systems• High cell concentrations• Cell reuse• Eliminates cell washout at high

dilution rates• High volumetric productivities• May provide favorable

microenvironment• Genetic stability• Protection from shear damage

Major Limitation

Mass transfer (diffusional) resistances

Whole cells provide cofactors, reducing power, energy that many enzymatic reactions require.

Advantage over immobilized enzymes

Types of Immobilization

• Active Immobilization: similar to enzyme immobilization. Entrapment and binding.

• Passive Immobilization: Biofilm – multilayer growth on solid surfaces.

Diffusional Limitations

• Analysis similar to immobilized enzymes

• Damkohler number

• Effectiveness factor

• Thiele modulus

Immobilized Bioreactors• Packed-column: feed flows through a

column packed with immobilized cells. Similar to a plug flow reactor. Can be recycle chamber.

• Fluidized-bed: feed flows up through a bed of immobilized cells, fluidizing the immobilized cell particles.

• Airlift: air bubbles suspend the immobilized cell particles in a reactor.

Solid-state Fermentations

• Fermentations of solid materials

• Low moisture levels

• Agricultural products or foods

• Smaller reactor volume

• Low contamination due to low moisture

• Easy product separation

• Energy efficiency

• Differentiated microbiological structures