Pulse-response analysis of a simple reaction-advection-diffusion equation

TL;DR

This paper analyzes a reaction-advection-diffusion equation using pulse-response methods, focusing on how advection velocity influences system behavior, and provides analytical expressions for flow properties related to chemical reactions in a reactor tube.

Contribution

It offers a novel analytical approach to characterize chemical activity in a reaction-advection-diffusion system using pulse-response analysis and flow curve ratios.

Findings

Exit flow properties depend on Péclet number

Chemical activity can be inferred from flow curve ratios

Analytical expressions for moments and peak characteristics

Abstract

We undertake a detailed analysis of a reaction-advection-diffusion (RAD) equation from the viewpoint of pulse-response studies, with particular attention to effects due to the advection velocity. Our boundary-value problem is a mathematical model for a system consisting of a narrow reactor tube into which a short pulse of reactant gas is injected at one end and a mixture of reaction product and unreacted gas flows out at the opposite end. Exit flow properties such as moments and peak characteristics are obtained analytically as functions of the P\'eclet number. The description of a standard transport curve\ -- -including diffusion and advection but no reaction\ -- -can serve as the baseline for further characterization of chemical activity. This characterization is done here for a first order irreversible reaction. Among our main observations is that chemical activity is easily obtained from the ratio of the exit flow curve in the presence of reaction over the standard transport curve.