Currently, methane emissions account for approximately 25% of human-induced global warming, with the oil and gas sector ranking among the leading contributors. Early detection of methane leaks in pipelines significantly reduces the greenhouse gases emissions, aiding in the mitigation of adverse economic and environmental consequences associated with climate change. Computational Pipeline Monitoring (CPM) systems, tailored for leak detection, provide continuous pipeline monitoring and offer early identification of leaks while minimizing false alarms. This study harnesses advancements in tracking and estimation methodologies and integrates them with physics-based models to address the intricacies of modeling gas pipelines and introduces a real-time transient model (RTTM) used for leak detection of natural gas pipelines.