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 S_o/X_o and S_o/K_s, 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: μ_m/f_w, k_d/f_w, Y_g, S_o/K_s, K_s/S_o, and 1/(f_wθ_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 S_o/X_o is more sensitive than S_o/K_s, as also evidenced by the fact that gross growth yield (Y_g) is sensitive and affecting S_o/X_o. The analysis also suggests that the θc-based wasting frequency (f_wθ_c) is more sensitive than the daily wasting frequency (f_w). A critical minimum value of 1.3 for S_o/X_o and a maximum value of 0.1 for S_o/K_s were suggested to establish the testing criteria for the kinetic study under the respirometric conditions.