Quantifying Uncertainty in Permeability Estimation Using Deep Learning and Generative Models

Uncertainty quantification of well-log interpretation is essential to derisking subsurface exploration and development decision-making by providing possible scenarios for reservoir property distribution, fluid flow behaviors, and hydrocarbon potential. Well-log interpretation offers crucial insights into permeability variations, reservoir compartmentalization, mineral composition, and fluid mobility. Inherent uncertainties, such as those arising from geological heterogeneity, limited sampling, and non-uniform distribution of rock properties, can lead to inaccuracies that compromise petrophysical interpretation and formation evaluation. However, traditional data-driven well-log interpretation methods, which map well logs to formation properties based on core measurements, are primarily deterministic and fail to quantify uncertainty accurately. By leveraging deep learning and generative models, we introduce a probabilistic approach that significantly improves permeability estimation and uncertainty quantification. Our methodology integrates co-kriging techniques with Conditional Generative Adversarial Networks (cGANs) and Conditional Variational Autoencoders (cVAEs), establishing a quantitative relationship between kriged core, well-log data and permeability. Our approach enhances petrophysical property uncertainty estimations based on geostatistics by establishing a quantitative relationship between kriged estimates and flow-related properties. Training features are constructed using collocated co-kriging, capturing the cross-correlation between well logs (input features) and core data (output formation properties). Core bulk density, calculated from grain density, is kriged to well-log resolution to enable porosity estimation, while permeability is similarly kriged. A low-pass filter is then applied to smooth the kriged core bulk density, permeability, and estimated porosity, ensuring more accurate interpretations. The results reveal that cGANs and cVAEs consistently produce lower uncertainty estimates compared to traditional machine learning models. High-permeability zones exhibit lower uncertainty (approximately 3–5%), while low-permeability zones show higher uncertainty (10–15%). Traditional deep learning models tend to overestimate uncertainty, whereas generative models provide more reliable estimates. Additionally, applying kriged permeability data improves uncertainty estimations, further reducing uncertainty to 3% in high-permeability zones and 10% in low-permeability zones. To ensure broad applicability, the methods were tested on datasets from both carbonate and clastic reservoirs. In carbonate formations, prior classification steps are necessary to achieve accurate permeability predictions. The interpretation workflow improves permeability estimation accuracy and enhances uncertainty quantification across conventional and unconventional reservoirs. Additionally, this method is adaptable for CO₂ injection and H₂ storage wells, demonstrating versatility across various reservoir types.