Process models play an important role in the bioreactor design, optimisation and control. In previous work, the bioreactor models have mainly been developed by considering the microbial kinetics and the reactor environmental conditions with the assumption that the ideal mixing occurs inside the reactor. This assumption is relatively difficult to meet in the practical applications. In this paper, we propose a new approach to the bioreactor modelling by expanding the so-called Herbert's microbial kinetics (HMK) model so that the developed models are able to incorporate the mixing effects via the inclusion of the aeration rate and stirrer speed into the microbial kinetics. The expanded models of Herbert's microbial kinetics allow us to optimize the bioreactor's performances with respects to the aeration rate and stirrer speed as the decision variables, where this optimisation is not possible using the original HMK model of microbial kinetics. Simulation and experimental studies on a batch ethanolic fermentation demonstrates the use of the expanded HMK models for the optimisation of bioreactor's performances. It is shown that the integration of the expanded HMK model with the computational fluid dynamics (CFD) model of mixing, which we call it as a kinetics multi-scale (KMS) model, is able to predict the experimental values of yield and productivity of the batch fermentation process accurately (with less than 5% errors). (c) 2013 Elsevier Ltd. All rights reserved.