New approach for the dimensionless analysis of a unidirectional flow solar reactor based on Damköhler's number profiles.

A methodology for the analysis of the behavior of complex reactors based on the construction of profiles of a dimensionless number (Damköhler) for each main chemical species ( D a i ) was proposed. A 4-chlorophenol mineralization reaction in a heterogeneous solar reactor with suspended TiO2 and addition of H2O2 with tubular geometry and radiation collectors, fluid flow and a recirculation system was selected as a complex model system in order to validate the approach. The dynamic behavior of the reactor in dimensionless variables was modeled as a function of D a i . Where D a i ( z , t ) is a local property and grouped the optical and surface's properties of the catalyst, catalyst load, radiation intensity, the photon absorption rate, rate of non-photochemical reactions, the H2O2 effect, the reaction rate of different stages like adsorption, attack of radicals, surface reactions, plus design and operation variables like reactor volume and volumetric flow. A coupling of orthogonal collocation and Runge-Kutta methods were used to solve the PDEs and carry out the simulations to the different experimental conditions, resulting in profiles of D a i , C i , and conversion in function of time and space. The D a i profiles proposed in the new methodology are capable of describing the disturbances in solar reactors, to indicate consumption and generation rates, instantaneous changes of reaction rate, to describe competitive reactions and quenching effects and to determine equilibrium concentrations, all of the above at each time and space. Therefore, this approach is a analysis tool of reactors which complements the concentration profile. This methodology can be extended to other reactive systems, adapting the intrinsic reaction rates.

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

The reaction kinetic rate and mass transport play an important role in the sizing and scale-up of reactors. The Damköhler's dimensionless number ( D a ) is the quotient of these effects. A new interpretation of D a as a local property is introduced D a ( x , y , z , 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 D a number is presented as a fundamental parameter for design and scaling-up these reactors.