Upscaling Reactive Transport in Fractured Shales by Deep Learning

Abstract:

Fracture networks in shales exhibit multiscale features. A rock system may contain a few main fractures and thousands of micro fractures, whose length and aperture are orders of magnitude smaller than the former. It is computationally prohibitive to resolve all the fractures explicitly for such multiscale fracture networks. One traditional approach is to model the small-scale features (e.g. the micro fractures) as an effective medium. Although this fracture-matrix conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately described with effective medium approximations, e.g. when the micro fractures are clogged during mineral reactions. In this work, we employ deep learning in place of effective medium theory to model small-scale features. Specifically, we consider reactive transport in a multiscale fracture network where micro fractures can be clogged due to precipitation. A multiscale algorithm is developed, in which the main fractures are explicitly resolved while the impact of the micro fractures is incorporated as a wall boundary condition of the main fractures. The wall boundary condition is constructed by recurrent neural networks, which take the concentration history as input and predict the diffusive mass flux at the walls, i.e. the transport from the main fractures to the micro fractures. The neural network is firstly trained for a specific scenario, then a more general neural network is trained over a range of Peclet number. The new approach is validated against fully resolved simulations with a speed-up factor from ten to fifty, which can be improved further if the system contains more micro fractures.