Desenvolvimento e Análise da solução analítica de um problema convectivo dominante com reação química

Abstract

Modeling and simulation is a tool used in industrial to assess the behavior of a process under different operating conditions. In the literature, there are many researches related to mathematical modeling and simulation of reactors. However, there is a numerical difficulty in problems with dominant convective term. Thus, the present work develops the analytical solution from a partial differential equation for the problem of a transient reactor, considering diffusion and dominant convection. This analytical solution depends on the dimensionless Peclet’s number mass and Thiele's modulus. As the Peclet’s number provides a ratio between convective and diffusive flows, the analytical solution was used to simulate a process using high Peclet values to simulate flow conditions with a more significant convective effect than the diffusive one, and consequently, high values for the Thiele modulus were also used. Profiles with the number of Peclet varying from 2 to 50 are simulated, with the highest value evidencing the dominance of convection by the practically linear profile of reagent concentration along the reactor in steady state. The results obtained are physically consistent and the analytical solution can be used in the analysis of convergence and stability of numerical solutions.