Production-Profile Interpretation for Hydraulically Fractured Horizontal Gas Wells Using DTS Temperature Responses and Dual-Objective Inversion

Production-profile interpretation based on distributed temperature sensing (DTS) is an important method for the dynamic evaluation of hydraulically fractured horizontal gas wells. Because downhole temperature is jointly controlled by reservoir flow, variable-mass wellbore flow, and wellbore–formation heat transfer, the relationship between the temperature response and the production rate of an individual cluster is nonlinear, making inversion based solely on temperature fitting prone to non-uniqueness. In this study, a temperature forward model incorporating reservoir flow, wellbore flow, and heat-transfer processes was developed. Orthogonal experiments, sensitivity analysis, and error-surface analysis were combined to screen the key inversion parameters, and a dual-objective inversion function was constructed using the DTS temperature error and the relative total wellhead gas-production error. On this basis, the covariance matrix adaptation evolution strategy (CMA-ES) was used to jointly invert effective fracture half-lengths and the production profile. This framework uses the total wellhead gas production as an additional constraint during the search, allowing parameter combinations with similar temperature responses but different production responses to be distinguished. Controlled synthetic tests were further performed to assess inversion robustness under different initialization and model settings, followed by application to a field-case well. The analyses showed that the production constraint reduces the admissible low-error solution space but does not establish uniqueness. Results from the case well showed good agreement between the simulated temperature profile and the measured DTS profile, with temperature-drop errors of less than 0.05 °C near the potential producing clusters. The inverted total gas-production rate was 26,649.67 m3/d, with a relative error of 0.6492% compared with the measured wellhead value. These errors characterize the temperature fitting and whole-well production closure achieved for the present field case and are not used here as a quantitative measure of improvement over previous methods. The inversion results revealed a distinctly heterogeneous distribution of production contributions among the fracturing clusters. This method provides a model-constrained analytical approach for production-profile interpretation in hydraulically fractured horizontal gas wells without production logging tool (PLT) data. Without independent cluster-level flow measurements, the resulting production profile should be interpreted as a model-constrained estimate rather than a uniquely determined true profile.