Multiscale Modeling of Reactive Systems through Symbolic Computing and Demonstration in Planar Fractures

Reactive transport involving a number of species often occurs in fractured rocks during subsurface engineering applications, including CO$_2$ sequestration, contaminant transport prediction, and resource extraction. To describe the behavior in these systems at the Darcy scale, multiscale and rigorously upscaled models are developed from pore-scale equations using mathematical upscaling strategies. However, due to the complex reactions that occur, such techniques become time-consuming, prone to error, and quickly intractable. In this presentation, we discuss the technical features and capabilities of Symbolica, a software for automating upscaling procedures through symbolic computation. Specifically, we demonstrate Symbolicas capabilities by modeling reactive transport in planar fractures considering large numbers of species. We also discuss features that allow for (i) the development of higher order upscaled models and (ii) the modeling of transport in multi-domain systems. These features may be applicable to upscaling multiphase flow, as well as transport in macroscopically heterogeneous domains.