Physical-inforced artificial intelligent model for prediction of water-hammar velocity

Abstract

The water hammer wave diagnostic method is a new promising fracture diagnostic method that can determine the fracture location underground. The key to this technology is the accurate calculation of the water-hammer pressure wave velocity (WHPWV). However, it is difficult to measure the pump shut-in WHPWV at hydraulic fracturing field. Furthermore, The commonly used WHPWV analytical prediction models are not able to comprehensively consider relevant factors, resulting in low prediction accuracy in construction site. Fully connected neural network (FCNN) as one of the artificial neural network (ANN), can discover the complex function relationship between lots of factors while training data is sufficient. But there is few data related to water-hammer in field of reservoir stimulation, which significantly limits the performance of FCNN. The existing study pointed out the prior imformation is beneficial to improve performance of ANN. In this article, a physical-inforced neural network is built to predict the WHPWV, in which the analytical model is used as prior information to construct the hidden layer called substructure mimic layer and full-structure mimic layer. Comparing with traditional FCNN, neural network we built have lower data cost, more accurate prediction and more stable performance, because the possible data mapping relationships are considered in advance. Furthermore, the mapping relationships implied by the model structure can be adapted to the actual situation. Due to the limited field data, a theoretical dataset was constructed to validate the model performance under different training environment.