In many engineering and industrial applications, such as oil and bitumen recovery, in situ upgrading, coal gasification, soil remediation and many others, chemical reactions take place in porous media. However, numerical simulation of reactive flow to predict the behavior of such systems under various conditions is a challenging task.
One of these challenges arises from the multiscale nature of reactive and associated diffusive processes. The chemical reactions are responsible for the generation of sharp temperature and concentration fronts in the media. The common numerical schemes have difficulty in capturing these steep fronts, unless very fine grid numerical schemes are utilized, which increases the computational expenses considerably and is not achievable in many practical cases, such as oil and gas reservoir simulations. One of the remedies for this problem is the development of upscaling methods to account for small-scale processes and capture their effects in coarse grid simulation schemes, thereby increasing computational speed. These methods should not compromise accuracy, maintain the realistic nature of the numerical model at an acceptable level and account for the important effects of the reactions.
In this research, our main objective was the development of equivalent reaction constants to capture small-scale phenomena and modify them so that they can be implemented into coarse-scale numerical simulations. Several different reactive systems were studied including solid-solid and gas-solid reactions. The effects of a correction parameter for coarse grid simulation of these systems were investigated, and it was concluded that this factor was only applicable for a constant front pattern of solid-solid systems and it did not improve the coarse grid simulation of strongly convective-dominant reactive systems, such as gas-solid ones.
Furthermore, in this study, an equivalent reaction kinetics constant for a system consisting of diffusion and convection with power law kinetics under isothermal and steady-state conditions was developed. Based on this research, type curves were developed for obtaining the equivalent reaction parameter for coarse grid simulation. In addition, approximate analytical solutions and subsequently analytical expressions were developed for obtaining the equivalent reaction constants in non-isothermal conditions. These solutions were developed for various conditions.