Surrogate Modeling-Based Analysis of Concentration Decay in Diffusion-Reaction Mass Transfer Problems

Abstract

Diffusion-reaction phenomena occur commonly in heat and mass transfer problems. Determining the decay characteristics of such problems by solving the underlying energy/mass conservation equation is often mathematically cumbersome. In contrast, there is continued interest in simplified decay models that may offer reasonable accuracy at significantly reduced mathematical complexity. While simplified decay modeling has been presented before for pure diffusion problems, there remains a lack of similar work on diffusion-reaction problems. This work presents analysis of decay characteristics of diffusion-reaction problems using surrogate modeling, wherein the decay constant is determined using the moment matching method. Results are derived for homogeneous and two-layer Cartesian, cylindrical and spherical geometries. Under special conditions, results from this work are shown to correctly reduce to previously presented pure diffusion analysis. Good agreement with past work on a diffusion-reaction drug delivery problem is also demonstrated. Surrogate modeling using a single exponential function is shown to agree well with exact solutions. A two-term exponential model is also proposed to further reduce the error under certain conditions. This work extends surrogate decay modeling to the technologically important class of diffusion-reaction problems. Results presented here may help analyze and optimize several heat/mass transfer problems, such as drug delivery and reactor safety.