For homogeneous reaction systems with inlet and outlet streams, this article proposes a linear transformation of the number of moles vector into three distinct parts, namely, the reaction variants, the inlet-flow variants, and the reaction and inlet-flow invariants. The transformed states can be interpreted physically as (i) the amount of material contributed by each reaction and still present in the reactor (extents of reaction), (ii) the amount of material contributed by each inlet stream and still present in the reactor (extents of inlet flow), and (iii) the fraction of the initial conditions that has left the reactor (extent of outlet flow). Furthermore, several implications of being able to compute the extents of reaction and inlet flow are discussed. The methodology is illustrated in simulation via the ethanolysis of phthalyl chloride. © 2010 American Institute of Chemical Engineers AIChE J, 2010
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