Natural Fracture Density Prediction in Tight Sandstone Oil Reservoirs Using Multiscale Residual Fractal Responses and Heterogeneous Ensemble Learning

Continuous fracture-density prediction in tight sandstone reservoirs remains challenging because image-log data are limited, conventional-log fracture responses are non-unique, and discrete fracture events are scale-mismatched with continuous well-log sequences. Taking the Chang 81 tight sandstone oil reservoir in the southwestern Ordos Basin as a case study, this study proposes a multiscale residual fractal-response constrained framework for predicting natural fracture density from conventional logs. Image-log-interpreted fracture events were converted into a P101.0m fracture-density target. Five fractal-related indicators, including the Higuchi fractal dimension, DFA/Hurst exponent, structure-function exponent, Haar local abruptness energy, and roughness index, were extracted within 2, 4, 8, and 16 m windows, residualized against ordinary statistical backgrounds, and integrated into curve-scale residual FRI, physical-group FRI, and full MA-MFRS to characterize multiscale residual fractal responses beyond conventional amplitude statistics. High-P10 intervals show curve- and scale-selective fractal responses, with CNL at 4 m and CLL8 at 2 m being the most stable positive-response combinations. Full MA-MFRS enriches high-P10 intervals mainly in the high-score tail, indicating its suitability as a fractal-response constraint rather than a standalone fracture discriminator. Based on this constraint, an MFRS-LFI Net was developed for log-response encoding, fractal-response gating, latent fracture-intensity reconstruction, and scale aggregation, and a gated heterogeneous ensemble was used to fuse multiple base learners. The final ensemble achieved R2 = 0.8929 and RMSE = 0.1435 on the two held-out test wells, G13 and Y15, whereas removing MA-MFRS reduced performance to R2 = 0.8474 and RMSE = 0.1678. Core and image-log evidence, together with 3D modeling and water-injection response comparisons, provide additional geological and dynamic consistency checks.