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Mass and energy balances for microbial growth kinetics

  • S. Nagai
Conference paper
Part of the Advances in Biochemical Engineering book series (ABE, volume 11)

Abstract

First, quantitative aspects on the problems of any sort of microbial growth are depicted starting from the most general term of growth yield, YX/S, followed by more meaningful parameters, i.e., growth yields based on total energy available in the medium, Ykcal and based on catabolic activity, Y X/C involved physicochemical features, and in addition growth yield based on ATP generation, YATP being connected with physiological features. Second, quantitative relationships with respect to stoichiometry, and mass and energy balances in the growth reactions are discussed to establish kinetic equations, including growth, substrate consumption, respiration, heat evolution and noncellular product formation applicable to process control in microbial cultivations.

Keywords

Minimal Medium Complex Medium Growth Yield Heat Evolution Oxygen Balance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

amount of oxygen required for the combustion of substrate, mole · mole −1

B

amount of oxygen required for the combustion of dry cell, mole · g− 1

C

amount of oxygen required for the combustion of noncellular product, mole · mole−1

Cp

concentration of noncellular product in culture medium, mole · 1 −1

D

dilution rate, h−1

DO

dissolved oxygen concentration in culture medium, mole · l−1

DO*

saturation concentration of DO, mole · l−1

ΔHa

heat of combustion of dry cells, kcal · g−1

ΔhC

heat generation by catabolism, kcal · l−1

ΔHO

heat generation based on oxygen consumed, kcal · mole− 1

ΔHP

heat of combustion of noncellular product, kcal · mole−1

ΔHS

heat of combustion of substrate, kcal · mole−1

\(I_{CO_2 }\)

rate of carbon dioxide evolution, mole · 1−1 · h−1

\(I_{O_2 }\)

rate of oxygen consumption, mole · l−1 · h−1

\(k_{L^a }\)

volumetric oxygen-transfer coefficient, h−1

m

maintenance coefficient for substrate, mole · g−1 · h−1

m′

maintenance coefficient based on heat generation, kcal · g−1 · h−1

mA

maintenance coefficient for ATP generation, mole · g−1 · h −1

mO

maintenance coefficient for oxygen, mole · g−1 · h−1

P

total pressure in gas phase, atm

Pc

partial pressure of carbon dioxide in gas phase, atm

PO

partial pressure of oxygen in gas phase, atm

PW

partial pressure of water in gas phase, atm

QATP

specific rate of ATP generation, mole · g−1 · h−1

\(Q_{CO_2 }\)

specific rate of carbon dioxide evolution, mole · g−1 · h −1

\(Q_{O_2 }\)

specific rate of oxygen uptake, mole · g−1 · h−1

Qp

specific rate of noncellular product formation, mole · g−1 · h−1

RQ

respiratory quotient = \({{I_{CO_2 } } \mathord{\left/{\vphantom {{I_{CO_2 } } {I_{O_2 } }}} \right.\kern-\nulldelimiterspace} {I_{O_2 } }}\), mole · mole−1

S

substrate concentration in culture medium, mole · l−1

So

substrate concentration in fresh medium, mole · l−1

t

culture time, h

V

culture volume, 1

X

biomass concentration in culture medium, g · l−1

Yav e/S

total electron available from substrate, av e · mole−1

Yav e

growth yield based on electron available, g · av e−1

YATP

growth yield based on ATP generation, g · mole−1

YATPMAX

maximum growth yield based on ATP generation, g · mole−1

YA/S

ATP yield from substrate catabolized, mole · mole−1

YG

true growth yield from substrate, g · mole−1

YGO

true growth yield based on oxygen consumed, g · mole−1

Ykcal

growth yield based on total energy available, g · kcal−1

YP/S

noncellular-product yield from substrate, mole · mole−1

YX/C

growth yield based on catabolic activity, g · kcal−1

YX/O

growth yield based on oxygen consumed, g · mole−1

YX/S

growth yield from substrate, g · mole−1

YW

substrate catabolized for true biosynthesis, mole · g−1

α1

carbon content of substrate, g · mole−1

α2

carbon content of cells, g · g−1

α3

carbon content of carbon dioxide, g · mole−1

α4

carbon content of noncellular product, g · mole−1

μ

specific growth rate, h−1

ν

specific rate of substrate consumption, mole · g−1 · h− 1

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • S. Nagai
    • 1
  1. 1.Department of Fermentation Technology, Faculty of EngineeringHiroshima UniversityHiroshimaJapan

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