AN INVESTIGATION OF STABILITY AND MULTIPLICITY OF STEADY STATES IN A LABORATORY BIOLOGICAL REACTOR

DAVID DIBIASIO, Purdue University

Abstract

Methanol utilizing organisms have long been considered as potential sources of single cell protein. Since the growth rate of these organisms is a nonmonotonic function of the growth limiting substrate, multiple steady states, of which one is unstable, may exist for pure culture in a continuous stirred tank reactor. The existence of multiplicities and instabilities cannot be ignored in understanding microbial growth, and coping with such situations in practical applications like SCP production. This type of behavior has not previously been investigated experimentally. Thus, a laboratory demonstration of the existence of unstable and multiple steady states would provide confirmation of theoretical predictions as well as important information relative to modelling, optimization, and control. Classical feedback control was used to demonstrate the existence of unstable and multiple steady states in an isothermal biological reactor for the first time. Unstable steady states were stabilized through use of a turbidostat. The natural instability of the steady state was demonstrated by removing the feedback control and leaving the feed rate constant at the steady state value. Subsequent reactor transients were always away from the steady state. Using the open-loop reactor to obtain stable steady states, and the closed-loop reactor to obtain unstable steady states, multiple steady states were also demonstrated. The data, taken over a wide range of methanol concentrations, were used to fit an empirical growth model that incorporated variable yield. Phase-plane analysis of this model showed that when proportional-integral control was used to stabilize an otherwise unstable steady state, and the manipulated variable was sufficiently constrained, five steady states were possible. Cascade control could be applied to this system to show the existence of the two new unstable steady states. The fate of the reactor in terms of the stable steady state at the constraints, was shown to be a function of initial conditions. With the exception of the stable steady state at the upper constraint, this behavior was demonstrated experimentally for the first time. Control at an unstable steady state was shown for a PI controller with constraints. Cascade control was used to operate the laboratory reactor at both the upper and lower constraints. Washout of the closed-loop system was also demonstrated. Failure to reach the stable steady state at the upper constraint was attributed to inadequacies inherent in the perturbation methods used. In general, steady state predictions of stabilization of unstable steady states with simple, constrained, or cascaded control were relatively good. The dynamic behavior was not well predicted in many cases, and indicated that the idealized model was inadequate for such predictions. This was due to its lack of specific biochemical structure. The methanol, formaldehyde, and yield data taken at stable and unstable steady states and which were not previously available, were interpreted via a conceptual model for methanol metabolism proposed by other workers. This supported the proposed important role of formaldehyde in the kinetics and energetics of growth, and thus the stability behavior. The results, which showed relatively high formaldehyde concentrations and drastic yield reductions at the unstable steady states were consistent with ideas set forth in the model. The need for quantitative consideration of formaldehyde, at the least, was indicated.

Degree

Ph.D.

Subject Area

Chemical engineering

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