Nonlinear Parameter Estimation in Microbiological Degradation Systems and Statistic Test for Common Estimation

Three identical microbiological experiments were carried out and analysed in order to examine the variability of the parameter estimates. The microbiological system consisted of a substrate (toluene) and a biomass (pure culture) mixed together in an aquifer medium. The degradation of the substrate and the growth of the biomass are described by the Monod model consisting of two nonlinear coupled first-order differential equations. The objective of this study was to estimate the kinetic parameters in the Monod model and to test whether the parameters from the three identical experiments have the same values. Estimation of the parameters was obtained using an iterative maximum likelihood method and the test used was an approximative likelihood ratio test. The test showed that the three sets of parameters were identical only on a 4% α level.