Stochastic geomodelling and analysis of karst morphology
Keywords: Sustainability.
Energy Resources Engineering.

The growth of our global population and economy presents a challenge for mitigating climate change and creates an urgent demand for sustainable management of essential resources such as energy and water. Cave networks are excellent reservoirs of natural gas and ground water. They also offer enormous geologic storage capacity for carbon dioxide and green hydrogen. However, utilization of subsurface cave reservoirs has many challenges including drilling hazards, sustainable production, ground water contamination, and risks of leakage in the case of storage due to compromises in seal integrity. Decision making regarding these challenges involves a significant degree of uncertainty because the subsurface geology is largely unknown. One major source of uncertainty is the spatial distribution of cave systems. Quantifying the spatial uncertainty of caves in the subsurface requires computationally efficient algorithms that produce geologically realistic cave models. The main goal of this thesis is to develop efficient subsurface geologic modelling approaches for realistic cave network simulation to quantify their spatial uncertainty given observations such as well logs and geophysical data. There are two main types of caves: eogenetic and telogenetic caves. In this thesis, we develop stochastic methods for simulating both types of caves. First, we introduce Dynamic Graph Dissolution, a novel physics-based reduced order modelling approach for telogenetic caves using graphs. Dynamic Graph Dissolution simulates cave evolution through dissolution of fractures over geologic time based on evolving graph representations of discrete fracture networks. The model has the ability to incorporate geologic concepts and offers controls on recharge and sink configurations, dissolution rates, and initial fracture geometry and density. Realizations generated using the proposed algorithm are compared with real caves using graph topological metrics, such as central point dominance, connectivity degree, average degree, degree dispersion, and assortativity. The distributions of graph topological metrics of generated realizations overlap with the metrics of known caves suggesting that the graph structure of observed and simulated caves are at least globally similar. Unlike telogenetic caves, eogenetic caves are not very well understood and multiple competing hypotheses for their formation exist in literature, especially for banana holes; a particular type of eogenetic caves. Therefore, before developing a geomodelling approach for banana hole simulation, we first study their morphology using a Light Detection and Ranging survey on San Salvador Island, Bahamas. San Salvador Island has many collapsed banana holes in its surface topography and offers a tremendous opportunity for spatial analysis of these caves. To understand banana holes, we first employ graph theoretic and point pattern analyses to study their morphology and their relationship to nearby ridges. The study is also conducted to create an empirical reference of banana hole statistics in literature, which can be used to validate synthetic models of these caves. The relationship between banana holes and nearby ridges is quantitatively analyzed by assessing the spatial relationships between cave intensity and cave proximity to ridges, cave clustering and ridge elevation, and cave and ridge directions. Banana hole clustering, direction, and intensity are shown to be positively correlated to ridge elevation, direction, and proximity, respectively. Our findings using graph theoretic and point pattern analyses suggest that ridges play an important role in banana hole formation, which supports a particular model for banana hole origin, namely, the perched aquifer model. Finally, we explore deep generative models, specifically Generative Adversarial Networks and diffusion model, for banana hole simulation. Binary cave maps are extracted from the Light Detection and Ranging survey for training. The performance of the two models is evaluated by comparing their realizations to observed caves using point pattern and graph theoretic summary functions and statistics. The realizations of the deep generative models are shown to exhibit statistical similarity to the data. The two models are shown to be mostly comparable, with Generative Adversarial Networks slightly outperforming the diffusion model in equally reproducing the diversity of samples found in the data distribution. This dissertation introduces novel methods for analysis and geological modelling of cave networks that can be readily applied in decision making under uncertainty workflows in the hopes for a more sustainable management of subsurface resources or storage.