Multiple steady states, dynamics and optimal control of a biological reactor

An engineering model was proposed to describe the dynamic behavior of Methylomonas L3 in batch, fed-batch cultures and near steady states after methanol perturbations in continuous cultures as well as steady state behaviors in continuous cultures with methanol as sole substrate. The model contains three mass balance equations with respect to methanol, formaldehyde and cell concentrations in the culture and thirteen parameters. The values of these parameters were estimated by a nonlinear regression method and two sets of batch data.;The steady state behavior of M. L3 in continuous cultures was obtained from simulation of the model developed in this work and these behaviors were confirmed by experiments. The unusual steady state behaviors observed were believed to be related to the extracellular and intracellular formaldehyde concentrations and can change patterns depending on the feed methanol concentration. At low feed methanol concentrations, three steady states are possible, while at high feed methanol concentrations, five steady states are possible. An explanation was proposed for this behavior, which suggests that formaldehyde may be used intracellularly to obtain optimal growth conditions. The dynamics at different operating modes were also obtained and compared with the simulation results from the present model.;The model developed in this work was used to maximize the cell production in a fed-batch fermentor with the help of the variational method and an embedding technique. The theoretically optimal feed policies obtained by solving the model at different feed methanol concentrations were used to run the fermentor to obtain the experimental responses. The final amount of cells in the fermentor operated by the optimal feed rate from the present model was compared with that in the same fermentor operated by constant feed rate. It was found that the experimental responses agreed well with the simulation results from the present model. The final amount of cells in the fermentor operated by the optimal feed rate from the present model was 150% more than that in the same fermentor operated by constant feed rate when feed methanol concentration was 32 g/l.