Kinetics and Energetics of Photosynthetic Micro-Organisms in Photobioreactors
161
energy transfer already described in dense media by radiative transfer equations.
This places conditions on how the kinetic laws are expressed. A second
constraint concerns the mass conservation laws. Generally speaking, it is
always possible to build as many kinetic relations as there are substrates and
products that are consumed or evolved. However, such modeling does not
ensure mass conservation balances, which are the basic tool of macroscopic
description; this includes the determination of mass conversion yields,
particularly the biomass/CO2 and 02/C02 production yields in the case of
photosynthetic growth. The representation of the physiological processes that is
to be adopted will therefore be translated from the classical approach used for
chemical reaction engineering. It separates the establishment of stoichiometric
equations (which satisfy per se elemental conservation balances) and the
determination of the kinetic laws related to each stoichiometric equation.
This approach has been more extensively used in the last decade for modeling
aerobic or anaerobic cultures [1]; it can be effectively applied to cultures
of photosynthetic micro-organisms such as Spirulina platensis without significant modifications, affording stoichiometric models for growth and product
formation.
2.1.1 Characterization of Growth by a Single Stoichiometric Equation
It should be emphasized that the metabolism of photosynthetic micro-organisms is too complex to be modeled in all its intricacies. A reduction in the
complexity is therefore necessary. At ground state, the growth model will
contain a single stoichiometric equation and a single kinetic law that includes
the physical limitation by light energy transfer inside the medium.
The first difficulty is the determination of the elemental composition of dry
cell material. This can be done in two ways: (i) experimental determination of the
global content of carbon, oxygen, hydrogen, nitrogen, phosphorus and sulphur
in the dry matter, or (ii) determination of the mass fractions of different classes of
macromolecules such as proteins, lipids, carbohydrates, nucleic acids. The
second difficulty is the calculation of the different stoichiometric coefficients. In
general, the number of stoichiometric coefficients to be calculated is equal to the
number N of components involved minus one. As there are as many conservation laws as elements, e.g. P elements, the number of independent experimental
yields that have to be used to obtain the stoichiometric equation is equal to
(N-P-l).
Consequently, a stoichiometric model will contain two types of coefficients
that have to be identified from experimental results:
-
the yields, in the knowledge that the determination of a conversion yield
will affect all other conversion yields via the stoichiometric relation;
- the kinetic coefficients, which again must be split into two groups, (i) those
related to enzyme kinetics and (ii) those specific to transport phenomena, which
are generally dependent on reactor design and operating conditions.
161
energy transfer already described in dense media by radiative transfer equations.
This places conditions on how the kinetic laws are expressed. A second
constraint concerns the mass conservation laws. Generally speaking, it is
always possible to build as many kinetic relations as there are substrates and
products that are consumed or evolved. However, such modeling does not
ensure mass conservation balances, which are the basic tool of macroscopic
description; this includes the determination of mass conversion yields,
particularly the biomass/CO2 and 02/C02 production yields in the case of
photosynthetic growth. The representation of the physiological processes that is
to be adopted will therefore be translated from the classical approach used for
chemical reaction engineering. It separates the establishment of stoichiometric
equations (which satisfy per se elemental conservation balances) and the
determination of the kinetic laws related to each stoichiometric equation.
This approach has been more extensively used in the last decade for modeling
aerobic or anaerobic cultures [1]; it can be effectively applied to cultures
of photosynthetic micro-organisms such as Spirulina platensis without significant modifications, affording stoichiometric models for growth and product
formation.
2.1.1 Characterization of Growth by a Single Stoichiometric Equation
It should be emphasized that the metabolism of photosynthetic micro-organisms is too complex to be modeled in all its intricacies. A reduction in the
complexity is therefore necessary. At ground state, the growth model will
contain a single stoichiometric equation and a single kinetic law that includes
the physical limitation by light energy transfer inside the medium.
The first difficulty is the determination of the elemental composition of dry
cell material. This can be done in two ways: (i) experimental determination of the
global content of carbon, oxygen, hydrogen, nitrogen, phosphorus and sulphur
in the dry matter, or (ii) determination of the mass fractions of different classes of
macromolecules such as proteins, lipids, carbohydrates, nucleic acids. The
second difficulty is the calculation of the different stoichiometric coefficients. In
general, the number of stoichiometric coefficients to be calculated is equal to the
number N of components involved minus one. As there are as many conservation laws as elements, e.g. P elements, the number of independent experimental
yields that have to be used to obtain the stoichiometric equation is equal to
(N-P-l).
Consequently, a stoichiometric model will contain two types of coefficients
that have to be identified from experimental results:
-
the yields, in the knowledge that the determination of a conversion yield
will affect all other conversion yields via the stoichiometric relation;
- the kinetic coefficients, which again must be split into two groups, (i) those
related to enzyme kinetics and (ii) those specific to transport phenomena, which
are generally dependent on reactor design and operating conditions.