Scalable Simulation Models for Fractured Porous Media with Complex Geometries

Abstract

In various geo-engineering fields, accurate and scalable modeling of fluid and heat transport in the subsurface fractured porous media is important in order to fulfill scientific, economical and societal expectations on successful field development plans. Such models and the predictions they provide, contribute to efficient and safe operations on the production or storage facilities. However, while attempting to provide accurate results, a number of key challenges exist. Over the past decades, the scientific community have been developing various advanced numerical techniques to address these challenges. In this work, a number of scientific contributions have been made to help address specific challenges, by developing scalable numerical methods for fractured porous media, some with complex geometries. The primary aim of these methods is to provide computational efficiency while delivering accurate results on a desired level. Chapter 1 starts with background information on why these computer models are needed and the key challenges that exist along the way. Moreover, the contribution of the scientific community in various aspects are highlighted. In addition, the numerical methods developed in this work are briefly pointed out in this chapter. Chapter 2 covers the governing equations as well as the mathematical and physical relations for various flow models in great detail. These equations include capturing the effect of fractures and faults in the subsurface flowaswell. Chapter 3 attempts to provide detailed explanation of the discretized equations. The fine-scale simulation approaches as well as the coupling strategies for the governing equations are described. Moreover, the linearization of the non-linear equations is covered as well. Afterwards, the embedded discrete fracture models are thoroughly explained, where the effect of fractures on the patterns of flow are explicitly captured. In chapter 4, the mentioned fracture models are extended and applied to geologically relevant field-scale models. This is an important part of this work as the real field-scale geological formations cannot be represented by the Cartesian grid geometry (orthogonal box-shaped grids), but they are better represented by unstructured grids (such as corner-point grids). Using a number of numerical results, the capabilities of the developed model are showcased. It is also discussed how this model can offer great flexibility in the gridding strategies for field-scale models. In the above-mentioned chapters, the focus is on the fine-scale approaches in the numerical simulations. However, despite the technological advancements in computer hardware and high performance computation, the large size of the real field-scale domains, makes it impractical for the current computers to provide simulation results using fine-scale numerical methods. From this point onward, the focus shifts towards the multilevel multiscale methods. Chapter 5 covers the static multilevel multiscale methods for simulation of fluid flow in fractured domains, where the domain is subdivided in coarser grids across multiple levels of coarsening. With the help of the locally computed functions (also known as the basis functions), an approximated solution is obtained for the entire domain, reducing the size of the linear system of equations and providing computational efficiency. In chapter 6 and 7, the dynamic multilevel method is described in which different parts of the domain are treated and processed at different resolutions and coarsening levels. Due to different physical processes at various scales in the domain, while some parts of the domain can be treated on a lower resolution, certain regions need a higher resolution to capture the physics accurately, which can dynamically change across simulation time. The dynamic multilevel method uses fine-scale high resolution grids only when and where needed, providing a robust and efficient performance while keeping the accuracy at a desired level. Various numerical tests compare the results of the dynamic multilevel method against those of the fine-scale approach. It is shown that accurate results can be obtained while using only a fraction of the high resolution grids. For large-scale domains, such model can offer a significant reduction in the size of the linear systems, providing an optimal scalability. This dissertation is concluded in chapter 8 and references used in this work are followed afterwards.