Periodic Optimization of Continuous Microbial Growth Processes: Higher-order corrections to the Pi criterion
Systematic methods and tools for managing the complexity
Process Simulation & Optimization - II (T4-9b)
Keywords: optimization, periodic operation, Pi criterion, continuous operation, bioreactors
Continuous bioreactors have been traditionally operated around a set point. However steady state operation is not necessarily the optimum type of operation. Periodic variation of a selected input around a steady state has been shown to result in substantial yield improvement in certain cases.
The frequency-dependent Pi criterion of Bittanti et al. (1973) has been used extensively in applications to predict potential performance improvement under periodic forcing in a nonlinear system. This criterion states a sufficient condition for improvement of the performance of a dynamic system via cycling as well as an estimate of the optimum cycling frequencies.
The criterion, however, is local in nature and is limited to periodic forcing functions of small magnitude. Recently Kravaris et al (2002) have developed a method to determine higher-order corrections to the Pi criterion, derived from basic results of center manifold theory. This method, besides allowing for greater accuracy under a wider range of forcing amplitudes, also provides a natural framework to analyze the effect various complex periodic inputs can have on the long-term response of the dynamic system.
Selecting a dynamic model that takes into account the desired mode of operation can be critical for accurate predictions. Common unstructured models for microbial growth in a continuous chemostat culture do not account for the dynamics of the biomass adjustment to changing substrate levels, thus predicting a steeper response than experimentally observed. If this time lag is accounted for in the dynamic model, then improvement under periodic operation can be predicted.
To this end, we utilize a first-order delay model for biomass production proposed by Abulesz & Lyberatos (1987) and study the effect the increasing forcing amplitude of the sinusoidal input has on the optimal frequencies. Furthermore, we expand the range of studied inputs by testing several other periodic functions.
Presented Tuesday 18, 09:05 to 09:25, in session Process Simulation & Optimization - II (T4-9b).
