Permeability prediction in carbonate reservoirs: A systematic comparison of empirical, statistical, and machine learning approaches

Permeability prediction is central to petrophysical evaluation, governing fluid flow, reservoir quality, and dynamic model reliability. In carbonate reservoirs, this challenge is amplified by complex dual- or triple-porosity systems—matrix, vuggy, and fracture porosity—further complicated by diagenetic overprinting and strong spatial variability. These factors render permeability highly nonlinear, heterogeneous, and difficult to predict continuously from well logs, particularly where core coverage is sparse.

This study presents a controlled, multi-method comparison of permeability prediction workflows using core-calibrated data from four wells in a carbonate reservoir, aiming to identify the most reliable approach for generating continuous permeability curves from available subsurface data.

Two phases were evaluated. Phase I applied three classical empirical correlations— Wyllie C Rose, Timur, and Morris C Biggs—as standalone formulations. Phase II examined three data-driven models—Multiple Linear Regression (MLR), K-Mod (KMOD), and Self- Organizing Maps (SOM)—trained using a consistent set of well-log-derived predictors: Total Porosity (PHIT), Volume of Shale (Vsh), and Gamma Ray (GR). All outputs were benchmarked against measured core permeability to evaluate agreement, deviation, and well-to-well consistency.

Among empirical correlations, Morris C Biggs produced the closest match to core permeability. The data-driven methods showed progressive improvement over the empirical baseline: MLR achieved moderate predictive agreement, KMOD demonstrated good agreement, and SOM reached the strongest statistical fit with the lowest dispersion and most stable behaviour across all four wells. When validated models were applied to 100 uncored wells, MLR showed the highest prediction consistency (87%), followed by SOM (81%) and KMOD (78%). This divergence highlights a key distinction: MLR offers superior statistical consistency at field scale, while SOM delivers more geologically reliable estimates with stronger alignment to measured core trends. KMOD provides an intermediate balance between stability and geological representation.

The results reveal a performance hierarchy that depends on application context. Although MLR showed the highest prediction consistency across 100 wells (87%), its weaker agreement with core data limits its ability to capture nonlinear reservoir behaviour. SOM consistently provided the best match to core measurements, confirming its robustness in representing complex petrophysical-permeability relationships. KMOD exhibited intermediate performance without surpassing SOM in accuracy or MLR in consistency. Because the primary objective was to populate permeability in a 3D static reservoir model, SOM-derived permeability was selected as the most reliable input based on superior geological realism and core consistency, while MLR served as a supplementary validation tool for large-scale stability. Overall, the findings underscore the need to balance statistical consistency with geological accuracy in reservoir characterization workflows.

Keywords: Permeability Prediction, Core Calibration, Empirical Correlations, Multiple Linear Regression, K-Mod · Self-Organizing Maps, Petrophysical Modeling, Reservoir Characterization, Machine Learning, Carbonate Reservoir