An experimental study was performed with an aged Co/Pt/Al 2 O 3 catalyst in a laboratory slurry reactor to develop a macrokinetic expression for the Fischer-Tropsch (FT) synthesis. A semiempirical model was found to be the preferred two-parameter rate equation of the reaction. However, it was shown that this model is virtually indistinguishable from a mechanistically derived three-parameter rate model that assumes the following kinetically relevant steps in the cobalt-FT synthesis: CO dissociation occurs without hydrogen interaction and is not a rate-limiting step; the first hydrogen addition to surface carbon and the second hydrogen addition to surface oxygen are the rate-determining steps.

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Previously, the attainable region has been constructed for systems where the rate vector is uniquely defined. In this paper we extend the attainable region approach to situations where the rate vector depends on a control parameter, such as temperature. In these cases, the rate vector can take on a range of values, depending on the value of the control parameter. Arguments based on the geometry of the boundary of the attainable region are used to derive equations that describe the optimal control policies. These conditions are applied to various examples and both the optimal reactor structures as well as optimal operating and control policies are derived by looking at the structures that make up the boundary of the attainable region. In particular, an example is given where the optimal reactor structure has a reactor with simultaneous side stream addition and temperature control.

Attainable region analysis has been used to solve a large number of previously unsolved optimization problems. This paper examines its relationship to Pontryagin's maximum principle and highlights the similarities and differences between the methods. It is shown that not all problems that can be solved by attainable region analysis are readily formulated as maximum principle problems. The fundamental process of mixing seems to be the main reason for this difference and the consequences of this are highlighted. The class of problems that can be formulated as maximum principle problems are then examined and the relationship between the two methods highlighted. Here, the maximum principle gives rise to a set of results that are very useful for finding an attainable region. In fact, from these results and the experience gained by solving AR problems, postulates on the nature of the boundary of the attainable region are proposed. Previous to this work the construction of the attainable region required a trial and error approach and the region thus generated was tested using the necessary conditions. These postulates should allow a more constructive approach to finding the attainable region boundary.

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