Effect of Maximum Courant Number on Carbonate Acidizing 3D Simulations

The representation of physical phenomena in numerical simulations generally requires the discretization of the space and time domains, that is, dividing them into finite quantities. As the size of the spatial or temporal discretization approaches zero, the simulation more accurately represents the real phenomenon. It is observed that the discretizations of the space and time domains are intrinsically linked; there is a constraint on how much the spatial mesh can be refined without an accompanying change in time step size, known as the CFL condition, represented by the Courant number. This condition serves as a metric for assessing the stability and accuracy of numerical schemes. Instabilities are particularly observed when the Courant number exceeds critical thresholds. In this work, the 3D problem of reactive flow through porous media during carbonate acidizing was analyzed at different values of the maximum Courant number for varying mesh refinements and injection velocities, with the time step adjusting accordingly. We also investigated an alternative approach by performing a set of simulations where the maximum time step size was constrained based on an estimation of the flux residence time within each cell, allowing for a relaxation of the Courant number limit. The results showed a progressive loss of numerical stability and accuracy as the maximum Courant number increased, particularly with the more refined meshes and lower velocities. Moreover, the decrease in the Courant limit is accompanied by an increase in simulation time, as the time step gets smaller. When limited by the time step size instead, the results showed good agreement with the lowest Courant limits imposed, while the simulation time was reduced in comparison. This demonstrates the possibility of improving computational time in carbonate acidizing 3D simulations by estimating a maximum time step size without greatly limiting the Courant number, while still maintaining good stability and accuracy.