A novel domain adaptation method with physical constraints for shale gas production forecasting

Effective forecasting of shale gas production is essential for optimizing exploration strategies and guiding subsequent fracturing. However, in the new development of shale gas blocks, two main challenges are encountered: (1) data is insufficient, and (2) the dynamic production characteristics of shale gas wells, influenced by factors such as reservoirs and engineering, exhibit complex non-linear and non-stationary features. The inherent black-box nature of deep learning models raises concerns among decision-makers about the reliability of results. The current artificial intelligence model overlooks these factors, resulting in limitations in the accuracy and interpretability of the model. To address these problems, a novel domain adaptation methodology is proposed using physical constraints. First, production data from the source domain is segmented into multiple subdomains to enhance sample diversity. Subsequently, the positive transfer learning subdomains are identified by comparing maximum mean discrepancy (MMD) and global average distance metrics. Then, we integrate all transferable knowledge to create a more comprehensive target model. Finally, by incorporating drilling, completion, and geological data as physical constraints, we develop a hybrid model consisting of a multi-layer perceptron (MLP) and a Transformer, aiming to maximize interpretability, which is proved through comparison of symbolic transfer entropy (STE). The performance of the proposed method is experimentally validated on shale gas production data from two blocks in China. The average RMSE, MAE, and R2 on the target domain are 0.2454 (104 m3/d), 0.1552 (104 m3/d), and 0.88, respectively. These values are significantly superior to the traditional methods. Additionally, we demonstrate the superiority of our method in terms of causality through a comparison with Granger causality. The interpretability of static and dynamic data in the prediction process was studied using zero-value masking and attention mechanisms, respectively. Experimental results demonstrate the effectiveness and superiority of the proposed method for forecasting shale gas production under data insufficiency.