Equation-free high-fidelity algorithms for multiscale reactive systems
Keywords: Energy Resources Engineering.

High-fidelity models, such as molecular dynamics, mesoscopic simulations, and pore-scale modeling, have limited applicability to scale due to their high computational costs. One common approach to rigorously transfer information from high-fidelity models to large-scale problems is through mathematical upscaling strategies to derive coarse-grained models. For fluid flow and reactive transport in porous and fractured media, effective medium theory allows one to homogenize small-scale features and to characterize the medium by macroscale properties (e.g., permeability) and equations (e.g., Darcy's law). Although this conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately upscaled by effective medium approximations, e.g., mineral precipitation and clogging during reactive transport. In this dissertation, we upscale high-fidelity pore-scale models to large-scale systems using different strategies and without relying on effective medium formulations. We first propose a patch-based algorithm, which constructs the macroscale solution based on pore-scale modeling in small sampling regions (i.e., patches), while ensuring bottom-up top-down coupling across scales. To further improve the modeling efficiency and capability, we employ deep learning in upscaling. Pore-scale simulations are still performed in small sampling regions, and neural networks are trained on the pore-scale response to describe the behaviors of small-scale features. Specifically, we consider fluid flow, reactive transport and mineral precipitation in a multiscale fracture network composed of main fractures and microcracks. A recurrent neural network is constructed to predict the feedbacks of microcracks based on the inputs from the main fractures. The deep learning model is first employed in specific benchmark scenarios; then, a general model is trained which can work under various dynamic conditions. To accurately capture mineral precipitation and clogging in more complex structures, we develop a pore-scale model for mineral precipitation coupled with fluid flow and reactive transport. The fluid-solid interface is modeled as a smooth transitional region that provides the same drag force and precipitation rate as a sharp interface. A rigorous effective viscosity model is derived to immobilize the flow and the surface reaction is modeled equivalently by a volumetric reaction, without introducing any additional parameters. Finally, we consider the altered layer formed by mineral reactions in fracture-matrix systems, which does not lend itself to effective medium representations because remarkable property variations exist in a thin rock layer. This challenge is solved by employing pore-scale modeling in the altered layer and upscaling the modeling results by deep learning. We also propose a general upscaling framework with deep learning, for any systems that have multiscale features. The framework does not rely on macroscale equations, providing a reliable and efficient solution for problems that cannot be upscaled by effective medium approximations