Lecture 15

Outline

Fed-batch operation• Models• Advantages• Disadvantages• Example: penicillin production

Perfusion culture• Advantages• Disadvantages

Fed-Batch Operation

In fed-batch culture, nutrients are continuously or semi-continuously added to a system, while effluent is removed discontinuously• Usually used to overcome substrate inhibition or

catabolite repression

Recall that in batch culture the concentration of biomass at a certain time is given by:

)( 0/0 SSYXX MSX −+= (9.27)

Schematic of a Fed-Batch Culture1)

3)

2)

Fed-Batch CultureWhen biomass concentration in a fed-batch reactor reaches its maximum (Xm), the substrate concentration is very low (S<<S0), and also X>>X0, therefore:

If, for a fed batch reactor containing some cells (inoculum), a nutrient feed is started at a flow rate of F, with a substrate concentration of S0, the total amount of biomass in the vessel is Xt=VX, where V is the culture volume at time t, and Xt is the biomass at time t

0SYX MSXm =

Fed-Batch CultureThe rate of increase of culture volume in a fed batch reactor is:

Integrating:

The biomass concentration in the vessel at any time is:

FdtdV

=

FtVV += 0

VXX t=

(9.28)

(9.29)

(9.30)

Fed-Batch Culture

The rate of change in biomass concentration is:

Since dXt/dt=µnetXt, dV/dt=F, and F/V=D, eq. 9.31 becomes:

( ) ( )2V

dtdVXdtdXVdtdX tt −

=

( )XDdtdX

net −= µ

(9.31)

(9.32)

Fed-Batch Culture

When the substrate is totally consumed, S≈0, and X=Xm• At this point, dX/dt=0, and the system is at quasi-steady

state (nutrient consumption rate is nearly equal to nutrient feed rate), therefore:

If maintenance energy can be neglected,

Dnet =µ

SKS

smnet +

= µµ

(9.33)

(9.34)DDKS

m

s

−≅µ

and

Fed-Batch CultureThe balance on the rate-limiting substrate without maintenance energy is:

• Where St is the total amount of the rate-limiting substrate in the culture, and S0 is the concentration of Sin the feedstream

• At quasi-steady state, Xt=VXm, and essentially all substrate is consumed, therefore:

MSX

tnet

t

YXFS

dtdS µ

−= 0

0SFYFXdtdVX

dtdX M

SXmm

t

==

=

(9.36)

(9.37)

Fed-Batch CultureIntegration of eq. 9.37 from t=0 to t, with the initial biomass concentration in the reactor being yields:

• That is, the total amount of cells in the culture increases linearly with time

• Dilution rate and µnet decrease with time• Since µnet=D at quasi-steady state, the growth rate

is controlled by the dilution factor

tSFYXX MSX

tt00 +=

tX 0(9.38)

Fed-Batch CultureFor product formation in a fed-batch reactor, at quasi-steady state (S<<S0):Or the potential product output is:

When the specific rate of product formation (qp) is constant:

• Where Pt is the total amount of product in culture

0SYP SP≅

FSYFP SP 0≈

tp

t

XqdtdP

= (9.42)

(9.41)

(9.43)

Fed-Batch Culture

Substituting Xt=(V0+Ft)Xm into eq. 9.41 yields:

Integration of eq. 9.42 yields:

Eq. 9.43 can be written in terms of product:

tDtVVXq

VVPP mp

++=

200

0

( )FtVXqdtdP

mp

t

+= 0

tFtVXqPP mptt

++=

200 (9.42)

(9.44)

(9.43)

Fed-Batch Culture at Quasi-Steady State

(a)

(a) Variation of culture volume, V, specific growth rate, µ, cell, X, and substrate, S, concentration with time at quasi-steady state

(b) Variation of product concentration, P, with time at quasi-steady state in a single cycle of a fed-batch culture

Example 9.3

Solution

Advantages of Fed-Batch CultureProduction of high cell densities due to extension of working time (particularly important in the production of growth-associated products) Controlled conditions for the provision of substrates during the fermentationControl over the production of by-products, or cataboliterepression effects, due to limited provision of only those substrates solely required for product formation Allows the replacement of water lost via evaporation Alternative mode of operation for fermentations involving bioremediation of toxic substrates (cells can only metabolize a certain quantity at a time), or low solubility compounds No additional special pieces of equipment are required to convert from batch to fed-batch operation

Disadvantages of Fed-Batch Culture

Requires previous analysis of the microorganism, its requirements, and an understanding of its physiology with respect to productivity Requires a substantial amount of operator skill for set-up, definition and development of the processIn a cyclic fed-batch culture, care must be taken in the design of the process to ensure that toxins do not accumulate to inhibitory levels, and that nutrients other than those incorporated into the feed medium do not become limiting• Also, if many cycles are run, the accumulation of non-

producing or low-producing mutants may result

Fed Batch Culture: Penicillin Production

Fermentation is divided in two phases - the rapid-growth phase during which the culture grows at the maximum specific growth rate, and the slow-growth phase in which penicillin is producedDuring the rapid-growth phase:• An excess of glucose causes an accumulation of acids, and a

biomass oxygen demand greater than the aeration capacity of the fermentor

• Glucose starvation may result in the organic nitrogen in the medium being used as a carbon source, resulting in a high pH and inadequate biomass formation

During the production (slow-growth) phase:• Feed rates should be designed to limit the growth rate and

oxygen consumption, such that a high rate of penicillin synthesis is achieved, and sufficient dissolved oxygen is available in the medium

Perfusion Culture

Perfusion systems are most often used for animal cell cultureThe basic characteristics are constant medium flow, cell retention, and, in some cases, selective removal of dead cellsCell retention is usually achieved by membranes or screens, or by a centrifuge capable of selective cell removal• When a membrane is used, the system has some

characteristics of an immobilized cell system

Schematic of a Perfusion System

Advantages of Perfusion CulturePotential removal of cellular debris and inhibitory by-productsRemoval of enzymes (e.g. proteases) released by dead cells that may destroy or damage productShorter exposure time of product to potentially harsh production conditions (e.g. high or low pH)High per-unit volumetric productivity due to high cell density and metabolismEssentially constant environment

Disadvantages of Perfusion Culture

A large amount of medium is typically used• This is expensive, due to the high costs of raw

materials for the medium, in addition to the costs of preparing and sterilizing the medium

Nutrients in the medium are less completely utilized than in batch or fed-batch systemsCosts for waste treatment increaseMust consider the trade-off of improved product quality and reactor productivity with the associated increased expense