A new natural fracture width prediction method based on fluid dynamics constrained neural network

The width of natural fractures is an important parameter in the leak prevention and plugging operations for oil and gas drilling. To accurately predict the fracture width of the leaking formation when well leakage occurs during oilfield drilling, based on the mud logging data of adjacent oil wells during the loss process, the Spearman correlation analysis and data normalization methods were used to preprocess the data. A new method was then established to predict the natural fracture width based on FDCNN (Fluid Dynamics Constrained Neural Network), which is a neural network algorithm constrained by the prior knowledge of fluid dynamics. In this method, first, based on the fluid dynamics prior knowledge that there is a strict positive partial derivative relationship between the natural fracture width and the leakage volume and pressure difference in the fluid dynamics model, the constraint conditions of the neural network were optimized. Second, the augmented Lagrange multiplier method was used to establish the performance index of the neural network through a multiplier and a penalty factor. Finally, the model was trained using the backpropagation learning rule and gradient descent training methods. The results indicate that this method, utilizing FDCNN, can train the model with a small sample training set, demonstrating superior generalization ability and prediction accuracy compared to traditional fluid dynamics models and Data-Driven Neural Network (which refers to an algorithm training a neural network solely on data samples without using fluid dynamics prior knowledge). This approach can effectively reduce the prediction error of fracture width, providing valuable reference for the development of field plugging programs.