Evaluation of hydraulic fracturing of horizontal wells in tight reservoirs based on the deep neural network with physical constraints

Accurate diagnosis of fracture geometry and conductivity is of great challenge due to the complex morphology of volumetric fracture network. In this study, a DNN (deep neural network) model was proposed to predict fracture parameters for the evaluation of the fracturing effects. Field experience and the law of fracture volume conservation were incorporated as physical constraints to improve the prediction accuracy due to small amount of data. A combined neural network was adopted to input both static geological and dynamic fracturing data. The structure of the DNN was optimized and the model was validated through k-fold cross-validation. Results indicate that this DNN model is capable of predicting the fracture parameters accurately with a low relative error of under 10% and good generalization ability. The adoptions of the combined neural network, physical constraints, and k-fold cross-validation improve the model performance. Specifically, the root-mean-square error (RMSE) of the model decreases by 71.9% and 56% respectively with the combined neural network as the input model and the consideration of physical constraints. The mean square error (MRE) of fracture parameters reduces by 75% because the k-fold cross-validation improves the rationality of data set dividing. The model based on the DNN with physical constraints proposed in this study provides foundations for the optimization of fracturing design and improves the efficiency of fracture diagnosis in tight oil and gas reservoirs.