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Drilling safety and efficiency is always a primary focus for petroleum companies. The main objective is to minimize non-productive time during drilling while eliminating hazards for personnel and well control events. One of the severe hazards during drilling is overpressure in rock formations. This overpressure is typically caused by the geological conditions of specific formations and can be managed by optimizing mud weight during drilling. We propose achieving this with foundational seismic machine learning models. We employ autoencoder and transformer architectures for fine-tuning foundational models, enabling accurate predictions of mud weight values either for a target formation in a specific well or for the full vertical mud weight profile. Different architectures are used depending on whether seismic traces are handled individually or collectively within a local radius. The results are validated by real-time drilling data.