Lecture 1: Kinetics of Substrate Utilization and Product Formation

Dr. AKM Shafiqul Islam

10/03/08

• When a small quantity of living cell is added to a liquid solution of essential nutrients at a suitable temperature and pH, the cell will grow.

• Cell growth process got two manifestation– Increase in biomass are accompanied by

increases in the number of cells present.– Increase the growth of mold size

• Cell growth another processes involve– Uptake of some materials from the cell’s

environment and release of metabolic end product in the surroundings

Ideal Batch Reactor for Kinetics Measurements

• It is difficult to obtain useful kinetic information on microbial population from reactor with no uniform conditions.

• The desired reactors are– Well mixed batch reactor – Well mixed continuous flow reactors

The Ideal Batch Reactor

• Many biochemical processes involve batch growth of cell populations. After seeding a liquid medium with an inoculums of living cell, nothing is added to the culture or remove from it as growth proceeds.

• In such a reactor, concentrations of the nutrients, cells and products vary with time as the growth proceeds

• A material balance on moles of component i shows that the rate of accumulation of component i (given by the time derivative of total amount of concentration i in the reactor) must be equal to the net rate of formation of component i due to chemical reaction in the vessel.

Thus

unit time volumecultureunit

reactionby formed moles. volumeculture

component ofion concentratmolar volumeculture

i

idt

d

or,

where volumeculture RV

ifRiR rVcV

dt

d

volumecultureunit

moles

ici

unit time volumecultureunit

reactionby formed of moles

irif

• If no liquid is added or removed from the reactor and if gas stripping of culture liquid is negligible, then VR is constant. Thus we can write

A similar balance may be formed in terms of mass or number of density of a component.

if the component i is contain in a gas stream entering or leaving the reactor, the corresponding terms giving the net rate of component i addition to the reactor by gas flow must by added to the above material balances.

ifi rdt

dc

• The measurement of the time rate of change of component I concentration allows direct determination of the overall rate of I formation due to reactions which takes place in the batch reactor

• The rate of formation rfi depends upon the state of the population and all the parameters which influence the rates of reactions in the cells and in the medium

The Ideal Continuous-Flow Stirred-Tank Reactor (CSTR)

Continuous Culture

• Chemostat– Control flow rate and concentration of growth-

limiting nutrient of liquid medium entering and exiting a growth chamber (bioreactor)

– Control• pH• Temperature• Concentration of terminal electron acceptor• Concentration of toxic by-products of metabolism

A completely mixed continuous stirred-tank reactor for the cultivation of cells are called chemostats.

It has the following configurations• Mixing is supplied by means of an impeller,

rising gas bubbles or both• The mixing is so vigorous that each phase of the

vessel contents is uniform composition• The liquid effluent has the same composition as

the reactor contents

• Because of complete mixing, the dissolved-oxygen is the same throughout the bulk liquid phase. This is the crucial importance in considering aerated CSTRs

• The aeration system maintains dissolved oxygen in the CSTR above the limiting concentration

• As the vessel is well stirred, has adequate heat removal capacity, and is equipped with a satisfactory temperature controller, we can assume it a isothermal at the desired temperature and proceed with investigation of microbial reaction process

• In the steady state, where all the concentrations within the vessel are independent of time, we can write

0reactor within

formation of rate

reactor from

removal of rate

reactor to

addition of Rate

• Let VR donate the total volume of culture within the reactor, the steady-state CSTR material balance can be write

Where F= volumetric flow rate of feed and effluent liquid stream

cif = component i molar concentration in the feed stream

ci = component i concentration in the reaction mixture and in the effluent stream

0 fiRiif rVccF

• Rearranging the equation we can write

The parameter D is called dilution rate and defined as

The rate of formation could be easily evaluated based upon measurements of the (steady state) inlet and exit stream.

ifiifiR

fi ccDccV

Fr

RV

FD

• The dilution rate is equal to the number of tank liquid volumes which pass through the vessel per unit time.

• D is reciprocal of the mean holding time or mean residence time or space time