Anomalies in oil-producing wells can have detrimental financial implications, leading to production disruptions and increased maintenance costs. Machine learning techniques offer a promising solution for detecting and preventing such anomalies, minimizing these disruptions and expenses. In this study, we focused on detecting faults in naturally flowing offshore oil and subsea gas-producing wells, utilizing the publicly available 3W dataset comprising multivariate time series data. We conducted a comparison of different anomaly detection methods, specifically one-class classifiers, including Isolation Forest, One-class Support Vector Machine (OCSVM), Local Outlier Factor (LOF), Elliptical Envelope, and Autoencoder with feedforward and LSTM architectures. Our evaluation encompassed two variations: one with feature extraction and the other without, each assessed in both simulated and real data scenarios. Across all scenarios, the LOF classifier consistently outperformed its counterparts. In real instances, the LOF classifier achieved an F1-measure of 87.0% with feature extraction and 85.9% without. In simulated instances, the LOF classifier demonstrated superior performance, attaining F1 measures of 91.5% with feature extraction and 92.0% without. These results show an improvement over the benchmark established by the 3W dataset. Considering the more challenging nature of real data, the inclusion of feature extraction is recommended to improve the effectiveness of anomaly detection in offshore wells. The superior performance of the LOF classifier suggests that the boundaries of normal cases as a single class may be ill-defined, with normal cases better represented by multiple clusters. The statistical analysis conducted further reinforces the reliability and robustness of these findings, instilling confidence in their generalizability to a larger population. The utilization of individual classifiers per instance allows for tailored hyperparameter configurations, accommodating the specific characteristics of each offshore well.