| Heat and mass balances describing transient behavior of a continuous flow stirred tank reactor are written in dimensionless form for both first order, irreversible reaction processes A (--->) B (--->) C and A (--->) C, B (--->) D. The method of singularity theory is applied to study the steady state multiplicity. It is shown that the maximum number of steady states for the reaction A (--->) B (--->) C is seven. Numerical calculations are performed to provide concrete examples of the various multiplicities that occur. The stability of the critical points (steady states) is also considered.It is found that all critical points lie on a single plane and a positively invariant trapping block exists. Furthermore, each problem admits regions of parameter space for which there exists a single two dimensionally unstable critical point. A circulating attractor with accompanying circulating orbits is shown to exist when the critical point is unique and unstable. A numerical examination reveals that complex periodic and chaotic behavior is possible in these cases. |
