| dc.description.abstract | Numerical simulation of problems involving media with multiple spatial scales has important applications in many engineering and scientific areas, including material science, chemistry and unconventional reservoir simulation. While performing high-fidelity simulations is a primitive method in obtaining accurate approximation results, explicitness for complex models naturally gives rise to the need of large system of equations, due to the multiple scales and high contrast properties intrinsic to the reservoir. This will result in large degrees of freedom and will require enormous computational costs.
From the perspective of simulation, performing optimal reservoir management has always been challenging and extensive research efforts have been devoted to developing numerical methods with both accuracy and efficiency. One category of typical approaches include Heterogeneous Multiscale Methods, Variational Multiscale Methods and Multiscale Finite Element Methods. In such methods, effective properties are computed on a coarse-grid scale, which is much coarser than the fine-grid scale while multiscale basis functions are constructed to capture local oscillatory effects and to recover fine-scale information as needed. However, with more complex high-contrast heterogeneous media, such methods are insufficient in representing medium properties. In this dissertation, we discuss and analyze a novel multiscale model reduction approach for dual-continuum model, which serves as a powerful tool in subsurface formation applications from reservoir simulation.
Another category of approaches over the decades falls into surrogate modeling and physics-based model reductions to mitigate the difficulties induced by discretization of the nonlinear partial differential equations. Such techniques, such as POD-based methods, have been applied successfully in multi-phase flow problems and can efficiently maintain accuracy while establishing models with reduced complexity. However, such methods has no guarantee on solution stability and may lead to unphysical solutions, especially in the case of multi-phase flow simulation. Consequently, many ad-hoc remedies have been implemented in recent years, including techniques based on deep learning, which has been proved with capability in approximating a wide variety of functions. In this dissertation, we also investigate methodologies of performing numerical simulations in combination with deep learning approaches for predicting nonlinear multi-phase dynamics in reservoir simulation. | |
