Generalization of the concept of extents to distributed reaction systems

- The concept of extents is generalized to distributed reaction systems.
- Each extent describes a rate effect subject to advection and outlets.
- Extents are defined for various tubular reactors and reactive separation columns.
- Concentrations and extents are expressed as linear transformations of each other.
- The transformations use stoichiometry and knowledge of transferring/diffusing species.

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 rate processes (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 rate processes in lumped reaction systems with one or multiple phases, is generalized to distributed reaction systems. Both 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 rate process can be expressed in terms of a corresponding extent.