A deep learning upscaling framework: Reactive transport and mineral precipitation in fracture-matrix systems

Pore -scale modeling has limited applicability at large scales due to its high computational cost. One common approach to upscale pore -scale models is the use of effective medium theories, which homogenize small-scale features in a porous structure and characterize the medium by macroscale properties (e.g., permeability) and equations (e.g., Darcy's law). However, there are classes of physical processes for which effective medium approximations may become inaccurate, e.g., mineral precipitation and clogging during reactive transport. We have developed a deep learning upscaling framework, in which pore -scale modeling is directly employed in macroscale systems, without relying on effective medium approximations. The upscaling framework is first developed for general multiscale systems and then applied to modeling reactive transport with mineral precipitation in the altered layer in fracture -matrix structures. Solute transport from the fractures to the matrix is modeled as a wall boundary condition for the fractures, which, in turn, is predicted by recurrent neural networks using the concentration histories at the fracture -matrix boundary. Specifically, we consider a meterscale fracture network embedded in sandstones, where the smallest feature is at the micron scale. The proposed framework allows us to span five orders of magnitude in length scales by capturing mineral precipitation in the altered layer of the rock matrix at the pore scale across the entire meter -scale fracture network.