Dimensional analysis for establishing the testing criteria of kinetic study with respirometry

The kinetic study of a microbial system requires the determination of kinetic parameters under a set of operating variables. Previous researchers indicated that initial conditions, such as S0/X0 and S0/KS may influence the reliability of the parameter estimation. However, little study has been done to identify the sensitivity of system variables to the parameter estimation. This study proposes a novel dimensional analysis and identifies six dimensionless groups: mu(m)/fw, kd/fw, Yg, S0/KS, KS/S0, and 1/(fw theta(c) - 1). By incorporating the SP-moving algorithm proposed by Wu and coworkers in 2001, an algorithm was proposed in this study to perform a sensitivity analysis on the six dimensionless groups. Results of this analysis reveal that S0/X0 is more sensitive than S0/KS, as also evidenced by the fact that gross growth yield (Yg) is sensitive and affecting S0/X0. The analysis also suggests that the theta(c)-based wasting frequency (fw theta(c)) is more sensitive than the daily wasting frequency (fw). A critical minimum value of 1.3 for S0/X0 and a maximum value of 0.1 for S0/KS were suggested to establish the testing criteria for the kinetic study under the respirometric conditions.