Bioprocess and Biosystems Engineering

, Volume 31, Issue 2, pp 145–152 | Cite as

Software sensors for fermentation processes

Original Paper


Four software sensors based on standard on-line data from fermentation processes and simple mathematical models were used to monitor a number of state variables in Escherichia coli fed-batch processes: the biomass concentration, the specific growth rate, the oxygen transfer capacity of the bioreactor, and the new RO/S sensor which is the ratio between oxygen and energy substrate consumption. The RO/S variable grows continuously in a fed-batch culture with constant glucose feed, which reflects the increasing maintenance demand at declining specific growth rate. The RO/S sensor also responded to rapid pH shift-downs reflecting the increasing demand for maintenance energy. It is suggested that this sensor may be used to monitor the extent of physiological stress that demands energy for survival.


Software sensor Oxygen transfer Biomass Growth rate Stress Process analytical technology (PAT) 

List of symbols


specific growth rate (h−1)


specific area of air bubbles (m−1)


O2 conc. in bulk liquid (mol m−3)


O2 conc. at gas/liquid interface (mol m−3)

\( C_{{{\text{CO}}_{{\text{2}}} }} \)

carbon dioxide concentration in gas phase % (v/v)

\( C_{{{\text{NH}}_{{\text{4}}} {\text{OH}}}} \)

concentration of ammonia feed % (w/w)

\( C_{{{\text{O}}_{{\text{2}}} }} \)

oxygen concentration in gas phase % (v/v)


concentration of substrate (glucose) in feed (g kg−1)


water vapour concentration in gas phase % (v/v)


dissolved oxygen tension %


DOT in equilibrium with the air bubbles in the medium %

\( F_{{{\text{NH}}_{{\text{4}}} {\text{OH}}}} \)

feed rate of ammonia solution (g h−1)


feed rate of substrate solution (kg h−1)


substrate (glucose) consumption rate (mol h−1)


initial value


initial biomass in NH4OH units (Eq. 9) (g)


oxygen transfer coefficient (m h−1)


volumetric oxygen transfer coefficient (h−1)


molecular weight of substrate (g mol−1)


oxygen consumption rate (mol h−1)


air-flow rate (L min−1)


maintenance coefficient (g g−1 h−1)


specific substrate consumption rate (g g−1 h−1)


part of qS used for anabolism (g g−1 h−1)


part of qS used for energy metabolism (g g−1 h−1)


part of qSen used for biomass synthesis (g g−1 h−1)


the ratio of oxygen consumed per C/energy-substrate (mol mol−1)


medium volume (L)

\( V_{{{\text{O}}_{{\text{2}}} {\text{,m}}}} \)

molar volume of oxygen (L mol−1)

\( W_{{{\text{NH}}_{{\text{4}}} {\text{OH}}}} \)

weight of ammonia solution reservoir (g)


biomass concentration (g L−1)


yield of biomass per consumed NH4OH (g g−1)


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of BiotechnologyRoyal Institute of TechnologyStockholmSweden

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