Generalization of the Concept of Extents to Distributed Reaction Systems

In the chemical industry, a large class of processes involving reactions can be described by partial differential equations that depend on time and on one or more spatial coordinates. Examples of such distributed reaction systems are tubular reactors and reactive separation columns. As in lumped reaction systems, the interaction between the different dynamic effects (reactions, mass and heat transfers, and inlet and outlet flows) complicates the analysis and operation of distributed reaction systems. In this article, the concept of extents, which has been applied to decouple the effects of dynamic processes in lumped reaction systems with one or multiple phases, is generalized to distributed reaction systems. The concept of extents and a linear transformation to extents are detailed for various configurations of tubular reactors and reactive separation columns, as well as for a more generic framework that is independent of the configuration and operating conditions. The application of extents to distributed reaction systems is illustrated through several case studies that show how the effect of each dynamic process can be expressed in terms of a corresponding extent.