Additional Properties of the AR

Chapter 3 outlined a number of fundamental properties of the AR, which are founded primarily on the principles of concentration and mixing. Now that a better understanding of reaction has been established, a number of additional AR properties can be described. 

Property 6 All rate vectors evaluated on the boundary of the AR must either point into the current candidate region, or be tangent to the boundary. 

Point 1 has a rate vector that points into the region. If a PFR trajectory were to be initiated from this point, the resulting solution trajectory would need to travel, at least initially, into the region. This point may or may not serve to extend the region further. Nothing further may be concluded. 

Similar to that of point 1, point 2 may also lie on a mixing line. If a PFR were to be initiated with a feed concentration from point 2, the resulting trajectory would travel, at least initially, out of the region. This trajectory would hence serve to further expand the set of achievable points. 

The rate vector associated with point 3 is exactly tangent to the boundary. Point 3 must therefore be a concentration belonging to a PFR trajectory. Portions of the resulting curve therefore either lie on the AR boundary, or inside the region. 

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Chapter 4 In this chapter, we discuss how reaction may also be viewed from a geometric perspective. We introduce the three fundamental reactor types used in AR theory, and we also discuss additional properties of the AR related to reaction. 

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