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

Abstract

Multiplicity of steady states was experimentally obser®ed, 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 e®entually returning to the normal steady state. A diagnostic nonlinear analysis showed a plausible interpretation of this nonlinear beha®ior under two settings: 1. assuming that the controlled system is stable and moti®ated by simplicity, as it ob®iates 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 ha®ing to increase the analysis ( ) le®el. The first approach showed that the Stanton number for heat transfer St and H ( ) the Damkohler number Da could be two key process parameters accounting for thë obser®ed multiplicity characteristics of FT synthesis. The decrease in St , attributable to H 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 e®entual reco®ery of the original steady state is, spurred by a decrease in Da, possibly attributable to catalyst deacti®ation.Depending on the initial conditions andror startup history from the initial to the target conditions, the multiplicity beha®iors of FT synthesis may or may not be obser®ed, which is why the obser®ation of multiplicity is sporadic. The second approach incorporating the cooler's energy balance increases the region of multiplicity o®er that with the first. Simple proportional control law is applied to the system to examine the effect of the control parameter settings on reactor beha®ior. Except for this feature, the findings from the two analysis modes are in harmony.temperature-control performance not only reduces the undesirable conversion to methane rather than to liquid hydrocarbon but also makes the progress of catalyst deactivation sluggish. The rational design and operation of bubble-column FT processes requires an accurate understanding of the essential feature of the process, which is, however, hindered by its Ž . complex hydrodynamic behaviors Maretto and Krishna, 1999 Ž . and strong nonlinear characteristics Song et al., 2003 . This may be one reason why stirred-tank reactors are often used for fundamental studies of bubble-phase FT processing by Ž several investigators for example, Satterfield and Huff, 1982; .

Modeling of Surface Structure of Supported Catalysts. Application to Deactivation of FT Reactors

“…Therefore, the wax phase is a multicomponent mixture consisting of CO, H 2 , water, and hydrocarbons with different carbon numbers. As have been done by many past researchers, ,− the ASF equation is used to describe the product distribution. In this research, the hydrocarbons with carbon number over 50 are lumped into one virtual component with an average carbon number determined by the chain growth probability α because the molar fraction becomes very small when the carbon number is over 50.…”

“…According to Stern, the stoichiometic numbers for hydrocarbon with carbon number n can be calculated by the ASF factor α T is temperature and D e, i and K e are effective diffusion coefficient of component i and thermal conductivity, respectively. The ASF factor is calculated using the model proposed by Song …”

“…The ASF factor is calculated using the model proposed by Song. 34 Equations 1-6 thus form a complete catalyst scale model. This model involves partial differential equations and integral equations and requires complicated numerical techniques.…”