Equivalent Rate Constant for Numerical Simulation of Linear Convection-Diffusion-Reaction

Abstract

Abstract The accurate numerical modelling of reactive flow is essential for the interpretation of experimental measurements and the design of field-scale processes. Sharp reaction fronts are difficult to capture using traditional numerical schemes, unless fine grid numerical simulations are used; however, fine grid simulations are computationally expensive. On the other hand, using coarse grid block simulations leads to excessive front dissipation and inaccurate results. In most practical cases, it is not feasible to choose small grid blocks; therefore, one needs to account for the small-scale gradients that cannot be captured by coarse grid blocks when using traditional methods. As a first step toward the development of upscaling techniques for reaction kinetics, an equivalent reaction constant for a simple steady-state convection-diffusion-reaction (CDR) was determined. This shows how an effective reaction constant can be obtained as a function of the Peclet number, Thiele modulus and size of the reaction zone, such that the coarse grid simulation agrees with the fine grid simulation.