Biochemical Engineering CEN 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.
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Instructor: Dr. Christine Kelly
What do each of these factors mean?
Consider production of a growth associated product (like cell mass) in suspension culture
F S0 X0
F S X
Batch cycle time is:
where tgrowth is the time required for growth and tl is the lag time + preparation and harvest time.
where X0 is the initial concentration and Xmax is the maximum concentration (carrying capacity).
So net biomass production rate is:
Recall the definition of biomass yield:
For negligible kd, negligible extracellular product formation and steady state, Lec. Notes 16, Eq. (10) gave:
For optimum cell productivity (X•D), calculate d(X•D)/dt, set equal to zero, and solve for Dopt:
Substituting Eq. (2) into Eq. (3) gives the value of X at the maximum production rate. :
Optimum productivity is D•X when D=Dopt and X= X (at Dopt):
Noting that S0 is usually much larger than KS, we have:
Comparing the rates for batch production and production in a chemostat:
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,
Even so, most industrial fermentation processes occur in a batch reactor. Why?
Can 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?
Chemostats cannot be operated if µmax<D. Higher dilution rates can be achieved with recycle.
F S0 X0
Biomass balance on the chemostat:
where a=volumetric recycle ratio and b=the concentration factor of the separator. At steady state and with X0=0:
Note that for b>1, µ<D.
At steady state:
Substituting µ given by Eq. (10) into Eq. (13):
We can get the expression for the substrate concentration by equating the expression for µ from Monod kinetics to Eq. (10):
So now we can get X entirely as a function of D:
V0, X, S, P
V, X, S, P
Vw, X, S, P
Fed batch fill
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:
If the total amount of biomass (grams) in the reactor is Xt then the concentration X is:
Using the definition of the growth rate:
...the dilution rate:
...and the expression for dV/dt:
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:
So X is constant (but not Xt). Now we have:
Assuming Monod growth kinetics, this gives (just as in the case of a chemostat):
If the total amount of substrate in the reactor is St, then a substrate mass balance gives:
which, for quasi-steady state gives:
Returning to Equation (4), we have, at quasi-steady state:
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:
Often, S<<S0 and X0<<YX/SS0 and so:
If the specific productivity (g product/g cells/ hr) is constant:
where Pt is the total product concentration in the reactor:
Integrating this expression, we have:
or in terms of concentration:
Usually, 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.
Where Vw is the volume just before harvesting, V0 is the volume after harvesting, Dw=F/Vw and:
tw is the cycle time and is given by:
Mass transfer (diffusional) resistances
Whole cells provide cofactors, reducing power, energy that many enzymatic reactions require.
Advantage over immobilized enzymes