<p> A novel mathematical model has been developed for biofilms and bioflocs. The model is based on the use of the effectiveness factor and the effect of cell density is included. The key assumption in the model is that cell density decreases in proportion to the substrate concentration within the biofilm or biofloc, reflecting lower rates of cellular metabolism. The equations given by the model were solved numerically for three types of reaction kinetics: Monod, Andrews (substrate inhibition), and multiple-Monod (twolimiting substrates), as well as for two geometries: a slab, as a representation of a biofilm and a sphere, as a representation of a biofloc. The simulations indicate that a decrease of the cell density in the biofilm and biofloc results in a decline of the effectiveness factor. Furthermore, the analytical solutions and approximate analytical versions of the effectiveness factor for the biofilm in two cell growth models: Monod and Andrews, have been derived. The effectiveness factors derived analytically are in agreement with those calculated numerically, and the approximate analytical versions are valid for the Thiele modulus greater than five. This new model was tested using operational data available in the literature, by including the effectiveness factor as a part of the design equations for an upflow anaerobic sludge blanket (UASB) reactor. </p> <p> For any biologically mediated transformation, it is critical to uniquely identify the parameters associated with microbial growth models. In this study, it is proved that the parameters of the integrated Andrews model are identifiable if the experimental data does not contain any random noise based on a criterion proposed by Beck and Arnold [1977]. When noise is present, the parameters may or may not be identifiable, depending on noise levels. A new approach has been developed based on the calculation of dimensionless sensitivity coefficients. Plotting these coefficients provides straightforward visualization of parameter identification. This method was used for quantitative evaluation of the noise level that can be associated with measurements, while still allowing parameter identification. It was demonstrated that an indirect cause of the parameter nonidentification of the integrated Andrews model is the linearization of the Andrews model at a low or high substrate concentration. Robinson [1985] obtained a similar result with the Monod model. </p> / Thesis / Master of Science (MSc)