Chap 7 Microbial Process Kinetics

Chap 7 Microbial Process Kinetics

I.Introduction

Design of fermentation processes requires quantitative description of cellular processes.

Two important parameters:

Yield:specifies the amount of product obtained from the substrate, important when the raw material costs make up a large portion of the total cost.

Productivity:specifies the rate of product formation (g/l/h), important when time is an important issue.

To understand how the parameters (e.g. cell concentration) would change in response to other conditions or parameters (nutrient concentration), a mathematical model is required.

Procedures for modeling:

1. Specify model complexity: define the number of reactions to be considered, and the stoichiometry for these reactions.
2. Set up kinetics: describe the rates of cellular reactions with mathematical expressions (expressed as functions of variables). The values of parameters can be obtained from literature or from experiments.
3. Set up mass balances: combine the kinetics with a model for the reactor. Such a model specifies how the concentration of substrates, biomass, and metabolic products change with time and what flows in and out of the bioreactor. These models are normally represented in terms of mass balances over the whole reactor.
4. Simulate fermentation processes (i.e. solve the equations): if simulation does not fit well with the experimental dataredefine model complexity.

II.Kinetic modeling of cell growth

Rates and yield coefficients:

Substrate uptake rate:the inflow rate of a substrate into the total pool of cells,can be measured by the concentration change of these substrates in the medium.

Product formation rate: outflow rate of a metabolic product, can be determined by measuring corresponding concentrations.

Specific rate ri: normalized rate with respect to the amount of biomass present

Specific growth rate  (1/h): ()

(x: cell concentration, g/l or cells/ml)

Doubling time td:the time required for the biomass to double

yield coefficient:

yield of biomass on a substrate: (rs: specific substrate uptake rate)

yield of a metabolic product on a substrate: (rp: specific product formation rate)

It is important to optimize the yield of product on the substrate so as to minimize the carbon flow to by-products and maximize as much as carbon to the product.

Black box model

All cellular reactions are lumped into a single overall reaction, this implies that Yxs is constant  (s can be any substrate including O2)

Specific growth rate is described as a function of other variables (Table 6.2)

Monod model:

where max=maximum specific growth rate

Ks= saturation constant (the Cs at which the specific growth rate=0.5 max), common values are listed in Table 6.1

If growth is inhibited by high Cs, Monod model can be modified as

where Ki is aconstant

If growth is inhibited by the presence of the product, Monod model can be modified as

(Cp: product concentration)


Other models:

Note:

1. In Contois model, the influence of biomass is included, i.e. high biomass (cell concentration) inhibits the cell growth (could be due to side effects such as formation of inhibitory compound, viscous medium that hinders the mass transfer, etc.).
2. These models are all empirical expressions, it is futile to debate which one is the best.Simply choose the one that best fits the microorganism growth.

Effect of endogenous metabolism

The black box model is based on the assumption that the distribution of fluxes is constant through all different cellular pathways under different growth conditions it is false in realty=>may need to consider endogenous metabolism.

(linear rate equation,true for many microbial species)

where the first terms is the substrate consumption dedicated to cell growth, the secodn term (ms, the maintenance coefficient) is the substrate consumption dedicated to maintaining cell functions. msis normally given as a constant (see Table 6.3 for values of ms and Yxs)

With the linear correlations, the yield coefficient is not a constant

For large  (when cells are actively growing in the exponential phase and the substrate used for the maintenance is negligible),

But Ysx decreases at low specific growth rates (an increasing fraction of the substrate is used for maintenance).

III.Mass balances for ideal bioreactors

Three modes of operations:

General mass balance (MB) equations

General MB equations:

Rate of Accumulation= Rate In –Rate out-Rate of disappearance due to consumption (mol/h)

Or Rate of Accumulation= Rate In – Rate out + Rate of increase due to production

Mass balances for the ith substrate(consumed in the culture):

(= )

Rearrange, divide both sides by V

(1)

For fed-batch reactor:

and Fout=0

the term within the parentheses becomes

Define the dilution rate D (1/h),

Then for fed-batch reactor

For both continuous and batch reactors, the volume is constant (dV/dt=0) and F=Fout, so

(2)

The above equation is a general representation for these three operational modes. The first term on the r.h.s. accounts for the substrate consumption by the cells, the second term accounts for the addition and removal of substrate from the bioreactor.

MB for the metabolic products

(3)

usually is zero (rpalso has different forms, e.g. where  and  are constants)

MB for the total biomass, assuming sterile feed

Similarly rearrange (for continuous reactor)

(4)

IV.Simulation of the Process

The batch reactor (consider only cell concentration x and 1 substrate)

Classical operation of the bioreactor, still used extensively

D=0, therefore

with I.C. x=x0 at t=0 (5)

Cs=Cs,0 at t=0 (6)

Assume Monod kinetics () and , substitute and rs into Eq. 5 and 6. Solve the coupled ordinary differential equations (ODEs) simultaneously with ODE solvers (using numerical methods).

The chemostat

Continuous bioreactor in which the medium is added so that there is a single limiting substrate.

The productivity is high but the product concentration is often lower than what can be obtained in the fed-batch culture.

Relatively rarely used in industry because it is prone to contamination.

At steady state, the MB (eq. 4) becomes

=D

Thus, by varying the dilution rate (or the feed flow rate), the growth rate can be controlled, this allows detailed physiological studies of the cells when they are grown at a specified specific growth rate.

At S.S., the MB for substrate becomes

combining =D and gives

Thus the yield coefficient can be determined by the measurement of the biomass and the substrate concentrations in the bioreactor.

If Monod model applies,

rearrange

(so Cs increases with increasing D), and

The maximum substrate concentration is its concentration in the feed, and the corresponding dilution rate is critical dilution rate. At this rate, washout occurs.

(and x=0)

Chemostat can also be used to :

Study the influence of the substrate on the cellular function, e.g. product formation, since by changing the dilution rate it is possible to change the substrate concentration as the only variable.

Study the influence of different limiting substrates on the cellular physiology, e.g. glucose and ammonia.

For production of biomass (e.g. baker’s yeast or single cell protein),the productivity of biomass (g/l/h) is:

To find the optimal dilution rate for the maximal productivity, set d(Dx)/dD=0

for Monod kinetics with negligible maintenance

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