PRODUCT FORMATION
Product formation can be expressed as in Eq 10-22 if the product is very stable in culture broth.
Eq 10-22
However, for non-stable products such as proteinous substances that are degraded by proteinase in the culture or volatile compounds that evaporate as they are form, the rate of product accumulation in the culture broth can be expressed as in Eq 10-23
Eq 10-23
where Kd is the product decay constant, and P is the product concentration. It can also be calculated from the rate of substrate consumption as shown in Eq 10-24.
Eq 10-24
In some cases, products are formed both during cell growth and even when cell growth has seized. This is called partially growth associated product formation. In other words, growth and product formation are only partially linked. An example of such product is lactic acid production and it can be expressed asin Eq 10-25
Eq 10-25
are coefficients for growth-associated and non-growth associated product formation, respectively. This is shown in Figure 10-10。
Figure. Relationship between cell growth and partially growth associated product during cultivation of microorganisms.
In some other cases, products are formed only when the cells are growing. This is called growth-associated product formation. Such products are direct products of catabolic pathway or intermediate of the basic pathway. Examples include ethanol, single cell protein, and gluconic acid. This type of product formation can be expressed as in Eq 10-26
Eq 10-26
where YP/X is the amount of product formed per unit cell. This type of product formation is illustrated in Figure 10-11.
Figure. Relationship between cell growth and growth associated product during cultivation of microorganisms.
In other cases, products are formed only after cell growth has stopped. This is called non-growth associated product formation. The idiophase and trophophase are separated in time. Such products are secondary metabolites and are not necessary for cell growth. Examples include antibiotics and is illustrated in Figure 10-12.
Figure Relationship between cell growth and non-growth associated product during cultivation of microorganisms.
In such non-growth associated cultures, the product formation is not a function of the cell growth rate but a function of the cell concentration at the end of the trophophase. This is represented in Eq 10-27
Eq 10-27.
Section two: Repeated batch culture
Characteristics of repeated batch cultures
This is a process where by another batch culture is started at the end of each batch. This is the most frequently used process in industries. It is illustrated in Figure 10-13
Figure Schematic representation of a repeated batch culture.
Advantages of repeated batch cultures
- Time that is usually used to wash the bioreactor, and prepare another seed culture is saved, leading to higher productivity
- Since each batch is started with high concentration of cells from the previous batch, the time lag is minimized and the cell growth rate is higher, leading to higher productivity.
- The cost of washing the bioreactor and preparing fresh starter culture is saved.
- It is generally simpler than other culture methods.
Disadvantages of repeated batch cultures
- It is prone to contamination during the process of removing part of the culture broth and adding fresh medium.
- The cells may undergo mutation during long period of use
Kinetics of cell growth and product formation in repeated batch cultures
The total process time for a repeated batch culture can be represented by Eq 10-28
Eq 10-28
where tLis the lag time, tM is the time for active fermentation, tD is the decay time and tT is the turn around time (time used for empting and washing the bioreactor, preparing and sterilization of fresh medium etc).
Since
Eq 10-29
Thus, biomass productivity (PX) is expressed by Eq 10-30
Eq 10-30
Since ,
Eq 10-31
For n number of repeated batches, the biomass productivity can be calculated from Eq 10-32.
Eq 10-32
Product productivity in repeated batch cultures is represented by Eq 10-33
Eq 10-33
By definition,
thus
Eq 10-34
and
Eq 10-35
Section three: Fed-batch Cultures
Characteristics of fed-batch cultures
This is defined as a batch culture in which culture broth is not removed but substrate is fed to the bioreactor as shown in Figure 11-1.
Figure Schematic representation of a Fed-batch culture system.
Feeding can be done either continuously (Figure 11-2) or intermittently (Figure 11-3) using either concentrated medium or only the carbon source. Again a constant feed rate can be used or the feed rate can be made a function of the cell growth rate. Alternatively, the feed rate can be manually or automatically controlled in response to changes in the values of some indirect parameters which are co-related with the metabolism of the substrate. Such parameters include the pH of the broth, PO2-value, and Carbon dioxide content in the exhaust gas. A low concentration of the substrate is used to start the culture and the activity of the cell is controlled by adjusting the concentration of the growth-limiting substrate fed into the bioreactor. Since the volume of the culture broth increases with time (medium is fed into the bioreactor but nothing is removed), the cultivation is terminated when the volume of the culture broth increases to the maximum working volume of the reactor. The concentrations of both the cells and the product(s) increase with time, and the cultivation can be terminated when the product increases to an inhibitory concentration.
Figure Changes in substrate, cell and product concentrations in a Fed-batch culture with continuous feeding.
Figure Changes in substrate, cell and product concentrations in a Fed-batch culture with intermittent feeding. The arrows indicate when medium is fed into the bioreactor.
Conditions when fedbatch culture is used
1. When high concentration of substrate is inhibitory to cell growth
2. When the solubility of substrate is very low
3. When high concentration of the substrate produces very high viscous medium that affects mass transfer.
4. When the cell concentration is high and the oxygen demand is higher than the oxygen supply to the bioreactor. In this case, the substrate feed rate is controlled so that the oxygen demand is equal or less than the oxygen supply capacity of the reactor. In high density culture of E. coli, for example, under excess supply of substrate the oxygen demand becomes higher than the oxygen supply and the culture becomes anaerobic, leading to accumulation of organic acids with subsequent inhibition of cell growth. Also in baker’s yeast production, when the cell concentration increases under excess substrate supply, the oxygen demand becomes higher than oxygen supply, and consequently, the condition becomes anaerobic with consequent decrease in cell growth and increase in ethanol production. Under such conditions, Fed-batch culture is used so that only the amount of substrate that can be supported by available oxygen is fed to the bioreactor.
Advantages of Fedbach cultures
1. The activity of the cells can be controlled by adjusting the concentration of the growth-limiting substrate.
2. High substrate concentration can be achieved and this leads to decrease in the cost of downstream processing.
3. Substrate inhibition is avoided by controlling the substrate concentration below the inhibitory level. Thus even toxic substrates can be successfully used for cell cultivation.
4. The risk of contamination is relatively low because of the low substrate concentration, and high biomass and high product concentrations.
5. It can be used to attain zero-growth rate in a culture by limiting the substrate feed to the amount required for cell maintenance. This is very useful in physiological studies.
6. It is used to maintain aerobic condition in the culture regardless of the cell concentration. The substrate feed rate controlled in such a way that the oxygen demand is less than the oxygen supply to the culture.
7. It is simpler than the continuous culture
Mathematical modeling of Fedbatch cultures
11.3.1 Substrate consumption
Eq 11-1
where F=substrate feed rate (L/h), SR = substrate concentration in the feed reserviour (g/L), V=liquid volume in the bioreactor (L), S= substrate concentration inside the bioreactor.
If the increase in volume is negligibly small as can be observed when highly concentrated substrate is fed at low flow rate(remember that some part of the substrate is metabolized into gasses that escape the reactor, while the remaining is metabolized into cell biomass or products), then
, and
Thus
Eq 11-2
If highly diluted substrate is used (SR is low), the rate of increase in the broth volume is the same as the feed rate, thus
Eq 11-3
In most cases, however, the rate of increase in the volume is not equal but directly proportional to the feed rate.
where C is a proportionate constant. Thus
Eq 11-4
11.3.2 Cell growth
Eq 11-5
If (i.e. the increase in volume due medium addition is negligibly small)
Eq 11-6
Eq 11-6 implies that if there is no change in the volume of the culture broth, Fed-batch culture behaves like an ordinary batch culture in term of cell growth rate.
If (i.e. increase in volume is the same as the fed rate)
Eq 11-7
If (i.e. increase in volue is not equal to, but proportional to the feed rate)
Eq 11-8
Product formation
This can be growth associated in which case
Eq 11-9
For non growth-associated
Eq 11-10
For partially growth associated
Eq 11-11
Section four: Continuous cultures
Characteristics of continuous cultures
This is an open system where a nutrient solution is added to the bioreactor continuously and an equivalent amount of the culture broth is simultaneously taken out of the bioreactor. This can be schematically represented in Figure 12-1.
Figure Schematic representation of a continuous culture system
It consists of a bioreactor with volume (V). It is mixed to maintain homogeneous condition inside the bioreactor. The growth-limiting substrate concentration (SR) is fed continuously at a flow rate (F). The feed rate must be constant in order to achieve a steady state. It is inoculated with cell biomass that grows to cell concentration (X). As a result of the cell growth, the concentration of the growth-limiting substrate inside the bioreactor is reduced to (S), and the product concentration increases to (P). The ratio of the feed rate (F) to the volume of the bioreactor (V) is called the dilution rate (D).
Eq 12-1.
The dilution rate means the number of volume changes achieved within a given period of time. In other words, a dilution rate of 1.0 h-1 means that in one hour, the amount of fresh medium that is fed to the bioreactor is equal to the volume of the bioreactor (an equivalent volume of the culture broth is pumped out of the bioreactor). The reciprocal of the dilution rate is called the mean residence time(). This means the average time a cell remains within the bioreactor before it is carried out with the effluent.
Eq 12-2
Continuous cultures can be classified as chemostat or turbidostat depending on the method used to control the cell growth rate. In chemostat cultures, the cell growth is controlled by adjusting the concentration of the growth-limiting substrate. The growth-limiting substrate can be the carbon source or the nitrogen source. In the case of turbidostat, the cell growth is controlled by using turbidity to monitor the biomass concentration. The rate of feed of nutrient solution is appropriately adjusted. Changes in growth-limiting substrate (S), biomass (X), and product (P) concentrations during continuous cultivation at a constant dilution rate is illustrated in figure 12-2.
Figure. An example of changes in growth-limiting substrate (S), biomass (X), and product (P) concentrations during continuous cultivation. Initially, it is operated as a batch culture and thus there were increases in both the biomass (X) and the product (P) concentrations. However, when the feeding starts, these parameter will initiall fluctuate depending on the flow rate and the growth rate and when the specific growth rate becomes equal to the dilution rate, a steady state is reached and S, X and P become constant.
Major characteristics of continuous culture systems
a) The concentrations of culture broth components are constant at steady state.
b) Steady state cannot be achieved at very high dilution rates. Near the maximum dilution rate, the system is very sensitive to external influences. High dilution rates means that the cells are maintained at specific growth rates very close to the and even slight change in the culture conditions (pH, temperature, oxygen supply etc) will drastically reduce the specific growth rate.
c) Monod equation is not applicable at very low or high dilution rates. At low dilution rates, greater proportion of the substrate is used for cell maintenance, and at high dilution rates, added substrate is not completely metabolized. Some fraction is washed out of the reactor without being metabolized.
Advantages and disadvantages of continuous cultures
Advantages
1. Continuous culture can be used to maintain the organisms in the exponential growth phase because both the products and substrates are maintained at desired levels. This is unlike batch cultures, where there is continuous decrease in substrate concentration and the period of exponential growth phase is usually very short.
2. Continuous culture saves labour because most of the processes such as feeding of the nutrient solution and removal of the culture broth are automated.
3. The time lag between one batch and another (usually in terms of cleaning the system, preparation of culture medium for the next batch, etc) is saved. This leads to increase in the productivity of the system.
4. A uniform process operation ensures consistent product quality over a long period of time. During the steady state, the concentrations of all the broth components are constant.
5. The formation of many secondary metabolites is subject to catabolic repression by high concentrations of glucose, other carbohydrates or nitrogenous compounds. This catabolic repression is very pronounced in batch cultures where all the media components are added at the same time. In continuous cultures, the critical elements of the nutrient solution are added in small concentrations continuously during the cultivation. In this way, none of the media components is in excess and thus the problem of fed back inhibition is minimized.
6. The production and plant building costs are lower than those of batch cultures. Fewer and smaller volume reactors can be used to achieve very high productivity.
7. The specific growth rate can be controlled by adjusting the feed rate of the growth-limiting substrate. This makes this system very useful in physiological studies. For example, continuous culture systems are used for determination of various kinetic parameters such as Ks, , m, and various yield coefficients. Also production of many useful metabolites are affected by cell growth rate. Thus, by controlling the cell growth rate, production of such metabolites can be controlled.
Disadvantages
1. The microbial strain may undergo mutation during long period of culture.
2. It is difficult to maintain steady operations such as mixing and feeding of the substrate.
3. Maintaining pure cultures over a long period of time is difficult. Care must be taken during sterilization, inoculation, and sampling. In some cases, selective antibiotics are added to the medium.
4. When the idiophase (product formation phase) is separate from the trophophase (growth phase) continuous production using optimally mixed bioreactor is not possible. In such cases, cascade bioreactors (several bioreactors connected in series) or a tower bioreactor, divided into sections by sieve plates are used. For example, when bioreactors with different working volumes are connected in series, the same feed rate (F) can be used but the dilution rate (D) and thus the specific growth rate of microorganisms will be different for the different sizes of the bioreactor. This is illustrated in Figure 12-3. In such a system, the smaller bioreactor with high growth rate serves as the trophase and supplies active cells to the larger bioreactor. On the other hand, the very large bioreactor where there is little or no cell growth serves as the idiophase.
5. There is a need to keep the composition of feed substrate constant. At industrial level, impure carbon and nitrogen sources are used. The compositions of such substrates vary greatly and there is a need to optimize each time a new batch of substrate is to be used.
Figure A tank-in-series system for continuous production of non-growth associated product. The first two tanks are used to produce biomass (very low product because of high growth rate) but the last tank is used for product formation (very low growth rate and thus high product formation rate).
Kinetics of continuous culture systems
Substrate
Changes in the substrate concentration in a continuous culture can be expressed by Eq 12-3.
Eq 12-3
where
represents the overall change of the growth-limiting substrate concentration inside the bioreactor;
is the rate of supply of the growth-limiting substrate
is the rate of removal (through the effluent) of the growth-limiting substrate
is the rate of consumption of the growth-limiting substrate by the cells.
is the rate of utilization of the growth-limiting substrate for product formation
is the rate at which the substrate is used for cell maintenance.
If no products are formed and maintenance energy is negligibly small, Eq 12-3 is reduced to Eq 12-4.
Eq 12-4
where
Since ,
Eq 12-4 can be transformed into Eq 12-5
Eq 12-5
At the steady state, there is no change in substrate concentration
Thus from Eq 12-5
and substrate concentration during the steady state can be calculated from Eq 12-6.
Eq 12-6
Thus the concentration of the growth-limiting substrate can be calculated if the two basic parameters are known.
Cell concentration
Changes in biomass concentration in a continuous culture system can be expressed by Eq 12-7.
Eq 12-7
Since
Eq 12-8
From the above equation, if the specific growth rate () is higher than the dilution rate (D), the cell concentration increases but if
<D, the cell concentration decreases. However, when
=D, a steady state is established and there is no change in biomass concentration.
Also, since , changes in substrate concentration can be expressed in terms of the kinetic parameters as shown in Eq 12-9.
Eq 12-9
Steady state biomass concentration can be calculated from substrate mass balance. When no product is formed and maintenance energy is neglected, Eq 12-4 can be rearranged as
Eq 12-10
At steady state
and steady state biomass concentration can be calculated from Eq 12-11
Eq 12-11
The steady cell concentration can also be calculated from the kinetic parameters (KS, m, and YX/S) and operation parameters (SR and D) as shown in Eq. 12-12.
Eq 12-12
Product formation
Changes in product concentrations in a continuous culture system can be expressed in Eq 12-13.
Eq 12-13
where Kd is the product decay coefficient.
Sustituting D for F/V, Eq 12-13 can be simplified into Eq 12-14
Eq 12-14.
At steady state,
Thus the product concentration at steady state can be calculated from Eq 12-15
Eq 12-15
When there is no product decay, and products are not removed with the effluent, then the product concentration inside the bioreactor can be expressed as
Eq 12-16.
where YP/X is the amount of product formed per unit amount of cell. It has the same kinetic meaning as qP in Eq 12-13. Combination of Eq 12-12 and Eq 12-16 yields Eq 12-17.
Eq 12-17.
Since YP/X . YX/S = YP/S,
Eq 12-18
In order to calculate the product concentration, the value of product yield coefficient is required. Recall that it is very easy to determine the value of this parameter (). For simplicity, it is often assumed that it is a constant. However, depending on the cell, substrate, and culture conditions, this parameter can vary significantly.
Section five: Dialysis, cell recycling and multistage continuous cultures
Introduction
Some major limitations with continuous culture systems include
- It is difficult to maintain a very high cell concentration since the cells are constantly washed out with the effluent.
- It cannot be operated at dilution rates higher than the specific growth rate of the cell.
- It is not suitable for non-growth associated products – those products which are formed only when the cells have stopped growing.
Thus, some culture systems have been developed to overcome these problems. Some of such systems are discussed in this chapter.
Dialysis (membrane) bioreactor.
High cell density in the bioreactor is necessary to increase the productivity the concentration of product in the effluent. This in turn will reduce the cost of downstream processing. Dialysis bioreactors are used to achieve high biomass concentration while avoiding substrate and product/by-product inhibition. A simple dialysis bioreactor is schematically represented in figure 13-1.
Figure A schematic diagram of a simple dialysis bioreactor system
The bioreactor is divided into dialysis chamber and cell cultivation (growth) chamber by a permeable dialysis membrane. It is a type of continuous process whereby the nutrients are fed into the cell growth chamber through a memberane while the products, free from cell biomass, are removed from the dialysis chamber. Dialysis is achieved by continuously pumping in and removing dialyzing fluid from the dialysis chamber. The dialyzing fluid contains the growth-limiting substrate so that the substrate is supplied to the culture chamber through the membrane. The cells grow in the culture chamber and the products/by-products diffuse into the dialysis chamber through the membrane from where they are removed with the dialyzate. The feeding and dialysis strategies depend on the purpose of the culture. In some systems, an additional nutrient supply is done directly into the cell growth chamber.
Kinetics of cell growth, and substrate utilization in batch dialysis reactor
Cell growth
Since cell biomass is not removed with the effluent, cell mass balance in the cell growth chamber is similar to that of a simple batch culture (Eq 13-1).
Eq 13-1
Substrate mass balance
The rate of substrate diffusion from the dialysis chamber to the culture chamber is represented by Eq 13-2.
Eq 13-2
where =substrate transport across the membrane(g/h), S1 = substrate concentration in dialysis chamber, S2 = cell concentration in the cell growth chamber, P = permeability coefficient for the substrate (cm/h), and A=effective surface area of the membrane (cm2)
Changes in substrate concentrations in the dialysis and culture chambers can be expressed by Eqs 13-2 and 13-4, respectively.
Eq 13-3
Eq 13-4
Advantages and disadvantages of dialysis bioreactors
Advantages
1. Substrate inhibition is avoided because the rate of substrate supply to the culture chamber is regulated by the permeability of the membrane, the effective surface area of the membrane, and the concentration difference between the dialysis chamber and the culture chamber.
2. Product/by-product inhibition is avoided since they are removed from the culture chamber through dialysis.
3. The cost of downstream processing is reduced because very high cell concentration is achieved in the culture chamber. Furthermore, the effluent (product) does not contain cell biomass so there is no need for cell separation step in the downstream processing.
4. Very high productivity can be achieved because of the high cell concentration and the absence of substrate and product inhibition.
Disadvantages
1. Substrate and product diffusion can be rate-limiting processes.
2. Membrane plugging (membrane fouling) can become major problems.
3. It is relatively complex to construct and operate.
4. The operational stability is low, because the process is stoped once the membrane is damaged or plugged.
5. Substrate is lost with the dialyzate. As a solution to this, very cheap media components can be used for dialysis while expensive components are fed directly to the culture chamber.
Continuous culture system with cell recycling
. In normal continuous culture systems, the dilution rate cannot be increased above the specific growth rate of the cells. As discussed in Chapter 12, when the dilution rate is higher than the specific growth rate of the cells, there will be continuous decrease in cell concentration until all the cells are washed out of the bioreactor. This is greatly limits productivity in continous cultures. Cell recycling makes it possible to operate a continuous cell culture at high steady state cell concentration, and at dilution rates higher than the specific growth rate of the cells. This is because a part of the cell in the effluent is recycled back to make up for the defference betaeen the specific growth rate and the dilution rate. A schematic diagram of continuous cell culture with cell recycling is shown in Figure 13-2.
Figure Continuous cell culture with cell recycling.
F= substrate flow rate, SR = feed substrate concentration, α=recycling ratio, C=concentration factor, X1=cell concentration inside the bioreactor, X2= cell concentration leaving the separator, S = substrate concentration inside the bioreactor, P = product concentration.
It consists of a continuously stirred bioreactor. The bioreactor is fed with a growth-limiting substrate at a concentration of SR and flow rate of F. The effluent is pumped out from the bioreactor at a flow rate equal to the sum of the flow rate into the bioreactor and the fraction of the effluent that is recycled back to the bioreactor. This is necessary to keep the volume constant. The effluent is passed into a cell separator, which can be a simple cell sedimentation column. From the separator, the desired amount of cell is separated and recycled back to the bioreactor while the product (P) and excess cell (X2) are taken out of the system at a flow rate (F).
Kinetics of cell growth and substrate utilization
Chamges in cell concentration inside the bioreactor can be expressed as
Eq 13-5.
Here,
is the rate of cell growth inside the bioreactor,
is the rate at which cells are recycled back to the bioreactor
is the rate at which the cells are removed from the system.
By definition, D=F/V, and at steady state,
Thus,
Eq 13-6
From Eq 13-2, it is clear that if the biomass is concentrated twice (C = 2) and half of it is recycled back into the system (α=0.5), then at steady state the system is operating at a dilution rate two times higher than the specific growth rate. Changes in the growth limiting substrate (S) concentration can be represented by Eq 13-7.
Eq 13-7
Here
is the rate of substrate supply from the reservior
is the rate at which substrate is recycled back with the cells
is the rate at which substrate is taken out of the system
is the rate at which substrate is taken up by the cells
At steady state, ,
Thus
Eq 13-8
Substituting the value of (Eq 13-6)
Eq 13-9
Since is always less than 1.0, the steady state cell concentration in systems with cell recycling will always be higher than the cell concentration obtained in normal continuous process without cell recycling under the same experimental conditions.
In terms of Monod equation
Thus
Eq 13-10
Eq 13-10 is very useful in the sense that the biomass concentration inside the bioreactor can be predicted without measurement. In other words, all the components of the equation are kinetic and operational parameters which are fixed before an experiment.
Limitations of cell recycling process
1. The risk of contamination in the cell separator is high. Thus, industrial applications is very few, except in waste water treatment industries where it is extensively used in activated sludge processes.
2. Efficient cell separators such as centrifuge are very expensive to install and operate. However, ordinary cell sedimentation systems can be employed if the cells form floccs or have good sedimentation properties.
Multistage Continuous Culture Systems
When the trophophase is clearly separated from the idiophase, products are not formed in continuous cultures since the cells are continuously growing (the system is always in trophophase). In such cases, multistage continuous culture systems are used to spatially separate the trophophase from the idiophase. The system consists of two or more bioreactors connected in series. The volumes of the bioreactors are varied (the smaller reactors are used for trophophase while the large bioreacrtors are used for idiophase. However, multistage systems can also be used for production of growth associated products where growth phase and product formation phase require different culture conditions or even different strains of microorganisms. In such case, the working volumes of the bioreactors can be the same or different, depending on the relative growth rates or precursor production rates. A mustistage system with three unequal volume bioreactors has already been explained in Chapter 12 (Figure 12-3). A schematic representation of a two stage system is shown in Figure 13-3.
Figure Schematic diagram of a two stage continuous culture system.
The growth-limiting substrate at a concentration of (SR) is fed into the first bioreactor with a volume (V1) at a feed rate of (F). The cells grow inside the reactor (X1), reduces substrate concentration to S1 and produces products (P1). The effluent from the first bioreactor is pumped into the second bioreactor with volume (V2) at the same flow rate (F). The cell, substrate and product concentrations in the second bioreactors are X2, S2 and P2, respectively. The effluent from the second bioreactor is then pumped out at a flow rate (F) from where the cells and/or the products are harvested and purified.
Kinetics of cell growth and substrate utilization
The material balances in the first bioreactor are the same as those of single-stage continuous culture systems (See Chapter 12). At steady state, , and assuming that product formation and maintenance energy are neglected
For the second bioreactor, cell growth rate can be expressed as shown in Eq 13-11
Eq 13-11
Here
is the cell growth rate in the second bioreactor.
is the rate of cell addition from first bioreactor.
is the rate of cell removal with the effluent.
At steady state,
Eq 13-12
For substrate mass balance in the second bioreactor
Eq 13-13
is the rate of substrate influent from the first bioreactor
is the rate of decrease in substrate concentration due to effluent
is the rate of decrease in substrate concentration due to uptake by the cells.
From Eq 13-13, it is obvious that the substrate concentration in the first bioreactor (S1) must be high enough to ensure that substrate is not limiting in the second bioreactor. This is achieved by either operating at a very high dilution rate or increasing the feed substrate concentration (SR). In other words, even if the reactor volume are the same (V1 = V2), the second bioreactor can be maintained at zero growth rate (for production of non-growth associated products) by maintaining very low S1 (just enough for cell maintenance).
At steady state, , and F/V = D. Thus
Eq 13-14
A modification of the operation of two stage continuous culture system is where aside from the influent from the first bioreactor, the second bioreactor is additionally fed with a substrate at a concentration and a feed rate
. This is schematically represented in Figure 13-4.
Figure A two stage continuous culture system where aside from the influent from the first bioreactor, the second bioreactor is additionally fed with a substrate at a concentration and a feed rate
.
The mass balance in the first bioreactor is the same as described for the single-state continuous process. However, in the second bioreactor,
Eq 13-15
Here, in order to maintain constant volume in the second bioreactor.
is the rate of decrease in cell concentration due to removal of effluent from the second bioreactor.
At steady state,
Eq 13-16
The substrate mass balance is expressed as
Eq 13-17
At steady state,
Eq 13-18
Characteristics of multistage continuous culture systems
The specific growth rate in the two bioreactors can be controlled independent of each other by
a) Varying the working volumes of the bioreactor so that. Thus, even if all the effluent from the first bioreactor is passed to the second bioreactor (F1=F2), and there there is no additional feeding stream to the second bioreactor, D1 will not be equal to D2, and at steady state,
b) By keeping the substrate concentration in the first bioreactor low (low SR, and or low F1), the growth in the second bioreactor will be limited by very low substrate concentration. In fact, if very S1 is very low and no additional substrate is supplied to the first bioreactor, all the supplied substrate will be used for cell maintenance and no cell growth will be observed.
c) By having additional feed stream to the second bioreactor. Growth inhibitors or inducers can be added to the second bioreactor. In this way, there is constant supply of fresh cells from the first bioreactor while the second bioreactor is used for product formation.
d) By having additional feed stream, the second bioreactor can be operated at dilution rates higher than the maximum specific growth rate without cell wash out since the first bioreactor constantly supplies cells to the second bioreactor.