Optimized Transformer and GRU Models for Forecasting Lost Circulation Volume in Drilling Operations

Lost circulation remains a persistent challenge in drilling operations, often resulting in increased non-productive time (NPT), elevated operational costs, and heightened well control risks. While prior research has primarily focused on the detection or classification of mud losses, this study addresses the short-term forecasting of the lost circulation volume (LCV) using advanced deep learning techniques. We investigated two modeling approaches. First, a series of deep recurrent neural network (RNN) models based on Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and hybrid configurations were developed to predict the LCV (in barrels) for the next short time interval. Second, a Transformer-based approach was introduced, with nine models exploring various architectural configurations. In total, twenty-two models were developed, including thirteen RNN-based models and 9 Transformer-based models. The dataset was divided into training, testing, and validation sets. A final validation set was held out from the initial split to simulate unseen conditions. The models were evaluated using standard regression metrics, with a particular focus on the coefficient of determination (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) and the Mean Absolute Error (MAE). Our Transformer-based model outperforms traditional ML benchmarks, achieving up to 3.21% higher <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and reducing MAE by approximately 36.3%. Specifically, for the 15-minute aggregated testing data, our model achieves a 2.69% improvement in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and a 33.5% reduction in MAE compared to the Random Forest model. For the 30-minute aggregated testing data, our model achieves a 2.99% improvement in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and a 35.1% reduction in MAE compared to the Gradient Boosting model. For the 60-minute aggregated testing data, our model achieves a 3.21% improvement in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and a 36.3% reduction in MAE compared to the MLP model. The best-performing model achieved <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> scores of 0.9882, 0.9910, and 0.9932 on the 15-minute, 30-minute, and 60-minute aggregated testing data, respectively. Corresponding MAE scores were 0.0243, 0.0459, and 0.0837 barrels. These findings highlight the effectiveness of deep learning, especially Transformer architectures, for accurate and timely forecasting of LCV. This provides a practical tool for early loss detection, proactive fluid management, and improved operational efficiency in drilling workflows.