This thesis investigates two mathematical models of a continuously stirred bioreactor. The basic model is described by systems of two non-linear ordinary differential equations. The dimensional form is scaled and the concepts of positively invariant and exponentially attracting regions are explained. The steady-state solutions are found and their stability is determined. Liapunov and Dulac functions are found to investigate the global stability and the absence of periodic solution respectively. Steady state diagrams are plotted for physically meaningful solution and also for asymptotic solutions at large residence time.
The basic model is extended to include a non-competitive product inhibition term, giving a system of three non-linear ordinary differential equations. The dimensional form is scaled and the concepts of positively invariant and exponentially attracting regions are explained. The steady state solutions are found. Also, we examined the growth rate function. We found the maximum value and the values of the substrate concentration at which it is turned off and on.
Since this is a six credit point project, and time is limited, the model has not been fully investigated. Some avenues of research are left for future study.
Photograph by Asma O.M. Alharbi. |