A Physically Constrained Dynamically Corrected Archie Saturation Model Based on Pore Size Distribution and Its Application to Tight Sandstone Reservoir Evaluation

Tight sandstone reservoirs are generally characterized by low porosity and permeability, complex pore structures, and ambiguous electrical responses, which significantly limit the applicability of conventional water saturation evaluation models. To address these challenges, this study proposes a physically constrained reinforcement learning–based symbolic regression framework that integrates nuclear magnetic resonance (NMR)–derived pore size distribution information to automatically derive a dynamic Archie water saturation model with explicit physical interpretability.In the proposed approach, pore size distribution features are embedded into the formation factor formulation, enabling a dynamic correction of the classical Archie equation. A policy neural network combined with reinforcement learning is employed to jointly optimize the model structure and parameters, while explicitly enforcing physical constraints such as monotonicity and nonlinear electrical response behavior.Experimental results demonstrate that, compared with the conventional Archie model, the proposed dynamic model achieves a significant improvement in water saturation prediction accuracy for tight sandstone reservoirs, reducing the mean absolute error by approximately 11%. Moreover, the model more effectively captures the influence of pore structure heterogeneity on the relationship between electrical resistivity and water saturation.This study provides a novel water saturation evaluation methodology that combines physical interpretability with data-driven adaptability for tight sandstone reservoirs and offers valuable insights into the intelligent construction of logging interpretation models for complex reservoirs.