Transfer Learning in Subsurface Flow Surrogate Model with Physics-Guided Neural Network

Abstract It is a great challenge for reservoir engineers to accurately and quickly model the subsurface flow surrogate for oil and gas reservoirs. The traditional numerical simulation methods are high computational complexity and time-consuming. The widely used pure data- driven flow surrogate methods require massive high-quality data due to lack of theoretical foundation. Therefore, it is necessary to develop transfer learning methods integrating prior knowledge with data-driven deep learning methods to solve complex seepage problems. To reduce data requirements and improving modeling efficiency, a theory-guided and data-driven transfer learning method is proposed to build the fast and accurate subsurface flow surrogate model. Specifically, a data-driven machine learning method is first proposed to simulate and predict the flow processes and build the primary surrogate model. In addition, physical mechanism and constraints are embedded into the data-driven model to make the prediction results satisfy the prior domain knowledge. The transfer learning method based on physics-guided neural network (TL-PG) integrates the seepage theory with sparse spatial data to improve the prediction accuracy of the surrogate model. The proposed TL-PG method is verified by a subsurface flow problem in heterogeneous reservoir models. First, we build a flow field to simulate 50 years of production history. A physics-guided neural network model is trained based on the samples from the first 30 years and tested based on the last 20 years of data. The relative L2 loss and the coefficient of determination R2 are used for comparison. Compared with the purely data-driven method, the relative L2 loss of physics-guided neural network is increased by 16%, and the mean coefficient of determination R2 is up to 0.8932, which means the embedded physical mechanism can greatly improve the performance of neural networks. Secondly, the physics-guided neural network is selected as the pre-training model. Then, the random points from the year 31 to 40 are used to fine-tune the model. Finally, the TL-PG surrogate model is validated by the last 10 years of data. The mean coefficient of determination R2 is up to 0.9522, which has improved by 25% compared to purely data-driven deep neural network (DNN) method, and only when the number of training data and epochs are increased several times, the performance can be comparable to the TL-PG method. However, the training time of DNN is more than 3 times that of the proposed method. The results show that the transfer learning surrogate model can effectively capture the feature of subsurface flow fields and greatly reduce the demand for data while significantly increasing computational speed.