Uncertainties of Monod kinetic parameters nonlinearly estimated from batch experiments

Monod kinetic parameters (Ks, micromax, and Y) that are estimated from batch experimental data can have large uncertainties due to linear correlations between them. The degree of correlation and the resulting uncertainties of the Monod parameters are functions of the initial experimental conditions, the values of the parameters, the type and magnitude of measurement errors, and the sampling number. Careful manipulation of experimental conditions can reduce the correlations between Monod parameters allowing for the estimation of Monod kinetic parameters with the lowest degree of uncertainty. By dimensionless analysis, the correlation and relative standard deviations of Monod parameters were found to be functions of a few dimensionless variables involving the initial substrate (S0) and cell (X0) concentrations. Quantitative relationships were analyzed between the dimensionless variables and the correlation and the uncertainties of the Monod parameters. This analysis allowed for identification of the optimal experimental conditions for estimating Monod parameters under both no growth and growth conditions coupled with two kinds of measurement errors: those with constant absolute standard deviation and those with constant relative standard deviation. Examples involving the microbial reduction of iron(III) as an electron acceptor are used to illustrate the application of the developed technique.