Diagnostic nonlinear analysis of Fischer-Tropsch synthesis in stirred-tank slurry reactors



Multiplicity of steady states was experimentally observed, somewhat sporadically, for Fischer–Tropsch (FT) synthesis in stirred tank slurry reactors in the reactor originally at the wax-producing (normal) steady state suddenly jumping to a high-temperature (methane-producing) steady state for some time and eventually returning to the normal steady state. A diagnostic nonlinear analysis showed a plausible interpretation of this nonlinear behavior under two settings: 1. assuming that the controlled system is stable and motivated by simplicity, as it obviates the inclusion of an energy balance for the cooler, thus reducing the dimension of the problem; 2. examining the more realistic problem by discarding the foregoing assumption, thus having to increase the analysis level. The first approach showed that the Stanton number for heat transfer (StH) and the Damköhler number (Da) could be two key process parameters accounting for the observed multiplicity characteristics of FT synthesis. The decrease in StH, attributable to deteriorating performance of the cooler, is the likely cause for the sudden jump of the reactor from the normal to high-temperature steady state. The eventual recovery of the original steady state is, spurred by a decrease in Da, possibly attributable to catalyst deactivation. Depending on the initial conditions and/or startup history from the initial to the target conditions, the multiplicity behaviors of FT synthesis may or may not be observed, which is why the observation of multiplicity is sporadic. The second approach incorporating the cooler's energy balance increases the region of multiplicity over that with the first. Simple proportional control law is applied to the system to examine the effect of the control parameter settings on reactor behavior. Except for this feature, the findings from the two analysis modes are in harmony.