Knowing that accurate yet time-efficient multihpysical reservoir simulation is a major challenge, we have developed a deep neural network (DNN) based multiphysical simulator to acceletate the geomechanical calculation. We first generated 20,000 pressure -stress pairs by conducting regious multiphysical simulation with various mechanical properties using a full physics reservoir simulator. All data pairs are simulated by 128 *128 grid blocks.
We then developed a U-Net network, a proven structure in image segmentation based on convolutional neural network (CNN), and trained the network with the generated data using Tensorflow. The U-Net network takes the pressure field as the input and regresses the stress field in a pixel-to-pixel manner. The model is trained with 100 epochs using Adam optimizer with a learning rate of 0.001 on GPU. The trained network is thereafter deployed in the reservoir simulator to predict the stress field from numerically solved pressure field at time step level. Hence the geomechanical simulation is replaced by the DNN proxy.
Our results show that the accuracy of the U-Net network is above 97%, in the metric of mean square error. Moreover, the U-Net network possesses excellent capability for dimension generalization. With the implementation of the proxy DNN simulator, the simulation time spent in the geomechanical module has been reduced by more than 95% on a 256*256 case study.
The novelty of our work lies in the pioneering application of DNN method to train and predict the time-dependent stress field, avoiding the curse of dimensionality. Our trained model can be conveniently connected with an existing reservoir simulator, which greatly saves the efforts of code development.