A Physics-Constrained Time-Spectrum Processing Framework for Pulsed Neutron Lifetime Logging Based on Borehole–Formation Separation and Bidirectional Constraints

Pulsed neutron lifetime logging (PNL) estimates the formation macroscopic neutron capture cross section, formation sigma (Σ), from the temporal decay of capture-gamma or thermal-neutron signals. However, practical time spectra contain overlapping borehole and formation responses, while late-time low counts introduce substantial counting-statistical fluctuations, limiting the accuracy and stability of conventional fitting methods. This study proposes a physics-constrained time-spectrum processing framework based on borehole–formation separation and bidirectional constraints. Instead of simultaneously fitting two exponential components to the mixed spectrum, the borehole and formation components are alternately reconstructed using single-exponential decay models over their respective characteristic intervals. The reconstructed borehole component is used to update the formation component, and the updated formation component subsequently constrains the borehole estimate. Signal superposition and component non-negativity are imposed as physical constraints, while formation-sigma convergence is used as the termination criterion. Monte Carlo simulations with region-selective gamma-ray production were used to obtain independent borehole- and formation-region reference spectra and to evaluate the method under diverse borehole and formation conditions. Across five validation models, the proposed method limited the relative error of apparent-sigma estimation to below 0.034% for the near detector and 0.026% for the far detector, compared with 1.25–8.20% and 0.32–11.67%, respectively, for double-exponential fitting. After applying the same multi-detector correction procedure, the mean relative error of formation-sigma estimation was reduced from 5.19% for double-exponential fitting to 0.78% for the proposed method. Field application in a mature producing well showed that the water-saturation interpretation obtained using the proposed method was more consistent with available production information in key intervals. Following additional perforation guided by the interpretation, the produced-fluid water cut decreased to 76%, and daily wellhead oil production increased by 109 m3/d. The results demonstrate the potential of the proposed framework to improve PNL time-spectrum interpretation under complex borehole and formation conditions.