During the operational process of natural gas gathering and transmission pipelines, the formation of hydrates is highly probable, leading to uncontrolled movement and aggregation of hydrates. The continuous migration and accumulation of hydrates further contribute to the obstruction of natural gas pipelines, resulting in production reduction, shutdowns, and pressure build-ups. Consequently, a cascade of risks is prone to occur. To address this issue, this study focuses on the operational process of natural gas gathering and transmission pipelines, where a comprehensive framework is established. This framework includes theoretical models for pipeline temperature distribution, pipeline pressure distribution, multiphase flow within the pipeline, hydrate blockage, and numerical solution methods. By analyzing the influence of inlet temperature, inlet pressure, and terminal pressure on hydrate formation within the pipeline, the sensitivity patterns of hydrate blockage risks are derived. The research indicates that reducing inlet pressure and terminal pressure could lead to a decreased maximum hydrate formation rate, potentially mitigating pipeline blockage during natural gas transportation. Furthermore, an increase in inlet temperature and terminal pressure, and a decrease in inlet pressure, results in a displacement of the most probable location for hydrate blockage towards the terminal station. However, it is crucial to note that operating under low-pressure conditions significantly elevates energy consumption within the gathering system, contradicting the operational goal of energy efficiency and reduction of energy consumption. Consequently, for high-pressure gathering pipelines, measures such as raising the inlet temperature or employing inhibitors, electrical heat tracing, and thermal insulation should be adopted to prevent hydrate formation during natural gas transportation. Moreover, considering abnormal conditions such as gas well production and pipeline network shutdowns, which could potentially trigger hydrate formation, the installation of methanol injection connectors remains necessary to ensure production safety.