Entropy-Weighted TOPSIS and Grey Relational Analysis Method for Optimizing Lost Circulation Formulations in Stress-Sensitive Fractured Formations

During drilling in stress-sensitive fractured formations, fracture aperture dynamically evolves with wellbore pressure fluctuations. The sealing layer often undergoes repeated cycles of sealing, destabilization, and re-sealing. Formulation selection based on a single metric or empirical selection cannot simultaneously satisfy multiple objectives, including pressure-bearing capacity, loss control, and dynamic adaptability. This study proposes an entropy-weighted TOPSIS and grey relational analysis method to optimize lost circulation formulations for stress-sensitive fractured formations. A hierarchical evaluation system is established with four criteria layers and eight indicator metrics. A baseline formulation framework is determined through static fracture sealing tests. Experimental data for different elastic-material systems are obtained using a self-developed DTDL dynamic fracture plugging apparatus. Indicator weights are objectively determined using the entropy weight method. A Grey–TOPSIS model is applied to compute grey relational closeness to the positive and negative ideal solutions, enabling formulation ranking and optimal scheme identification. A case study shows that the ternary elastic formulation with Rubber:Graphite:Net = 3:2:1 achieves the highest grey relational closeness and delivers the best overall sealing performance. The ranking remains unchanged when the distinguishing coefficient ρ varies from 0.1 to 0.9, confirming the robustness and feasibility of the proposed method. Compared with entropy-weighted TOPSIS and classical TOPSIS, the proposed method provides a more integrated treatment of the multi-metric data and better aligns the evaluation with the underlying sealing behavior in stress-sensitive fractures. Therefore, it leads to more reliable and comprehensive evaluation results for formulation selection. The results demonstrate that the proposed model provides reliable support and a methodological basis for formulation optimization in dynamic fracture loss control.