Traditional fossil fuels like coal and oil have been major energy sources, but their emissions significantly contribute to climate change and environmental degradation. Natural gas has emerged as a cleaner alternative, yet ensuring its safe and efficient production remains challenging. Current methods for detecting anomalies in gas well operations rely heavily on manual real-time monitoring and empirical rules, which are labor-intensive, subjective, and prone to missed and false alarms. This paper presents a robust, unsupervised and adaptive framework that harnesses advanced machine learning techniques for automated real-time detection in natural gas wells. In addition, we modify a change-point detection algorithm as a group anomaly detection algorithm to detect group anomalies. We systematically evaluate the 21 state-of-the-art machine learning methods to detect such anomalous status on 6 real-world natural gas well datasets, the superiority of the proposed methods over other approaches is demonstrated, highlighting its potential to optimize natural gas production while upholding environmental sustainability commitments within the industry.