An explainable quantum neural network framework for reservoir permeability prediction from conventional well logs

Accurate prediction of reservoir permeability is essential for reservoir characterization, production forecasting, and hydrocarbon recovery optimization. Conventional empirical and machine learning approaches often struggle to capture the complex nonlinear relationships between petrophysical variables while providing limited model interpretability. This study presents an explainable permeability prediction framework based on a variational Quantum Neural Network (QNN) simulated on classical hardware using the PennyLane quantum machine learning platform. The proposed framework integrates Shapley Additive Explanations (SHAP) to improve model transparency and facilitate geological interpretation of the learned relationships. A total of 3213 depth-matched samples acquired from three wells in the Mpyo Field, Albertine Graben, Uganda, were used to develop and evaluate the model using five conventional well-log measurements: thermal neutron porosity (TNPH), effective porosity (PHIE), formation density (RHOZ), spectral gamma ray (SGR), and shale volume (VSH). Hyperparameters of the QNN were optimized through systematic grid search and compared with a classical Group Method of Data Handling (GMDH), Random Forest (RF) and Support Vector Regression (SVR) models under identical experimental conditions. The simulated QNN achieved superior predictive accuracy, yielding training RMSE and MAE values of 0.019 and 0.0105, respectively, while demonstrating improved generalization on a blind test well compared with the benchmark model. SHAP analysis identified effective porosity as the dominant predictor of permeability, followed by thermal neutron porosity and spectral gamma ray, with feature contributions remaining consistent with established petrophysical principles. Bootstrap-based uncertainty analysis further demonstrated reliable prediction intervals across different reservoir intervals. Although implemented on a classical simulator rather than physical quantum hardware, the proposed framework illustrates the potential of quantum-inspired learning architectures for nonlinear permeability prediction while maintaining model interpretability for practical reservoir characterization.