Sizing of reactors by charts of Damköhler's number for solutions of dimensionless design equations

Abstract

The reaction kinetic rate and mass transport play an important role in the sizing and scale-up of reactors. The Damköhler's dimensionless number ( $Da$ ) is the quotient of these effects. A new interpretation of $Da$ as a local property is introduced $Da(\text{x},\text{y},\text{z},\text{t})$ . A new graphical methodology is proposed for the sizing and scale-up of unidirectional flow reactors and CSTRs. The partial differential equation (PDE) and algebraic that describe the continuity within these reactors transform into dimensionless variables, and the conversion at the output is expressed as a function of the conditions at the input $D{a}_0$ . The operating conditions as volumetric flow, residence time; design variables as reactor volume; and intrinsic reaction rate are involved in $D{a}_0$ . The equations are solved numerically to develop the design charts $D{a}_0$ vs X. The design volume is linear with $D{a}_0$ , and the conversion is obtained from the charts ( $D{a}_0$ vs X) or vice versa. Using these charts avoids the analytical or numerical solution of the PDE that governs the unidirectional flow reactors becoming an easy tool for scale-up. The article portrays how to use these diagrams. Reactors with $D{a}_0$ < 0.1 have a low conversion per pass, the charts also allow estimating the number of recirculations required as a function of the overall conversion. Reactors with the same conversion have the same $D{a}_0$ , both laboratory and industrial scale. Then, the $Da$ number is presented as a fundamental parameter for design and scaling-up these reactors.

Keywords: Catalyst; Chemical engineering; Chemical reaction engineering; Computer-aided engineering; Environmental chemical engineering; Kinetic rate; Modeling; Reaction engineering; Reactor design; Scale-up.