The Bakken unconventional resource in Williston Basin is becoming an important component of hydrocarbon sources in North America. Although advanced horizontal drilling and multi-stage stimulation techniques being successful to exploit Bakken formations, appropriate completion and stimulation designs are crucial to maximize the well productivity and oil recovery of the shale or tight reservoirs. Data-driven approaches, such as deep neural network modeling and global sensitivity analysis, are promising methods to evaluate hidden correlations between multi-stage hydraulic fracturing strategies and well productions.

In this study, a total of 2919 wells including 2780 multi-stage hydraulically fractured horizontal wells and 139 vertical wells in the Bakken formation were collected and analyzed using a deep learning method and Sobol's sensitivity analysis. 18 features of a single horizontal well were extracted from the raw data resources. These features contain five aspects: well location and geometry, Bakken formation thickness, hydraulic fracture characterization, fracturing fluid, and proppant. 6 months' and 18 months' cumulative production were utilized to characterize the after-stimulation performance of horizontal wells. In the deep learning model, one-hot encoding method was used to deal with the categorical data. Xavier initialization, dropout technique, Batch Normalization, Adadelta optimizer were applied to develop the reliable deep neural network. Moreover, k-fold cross validation approach was used to evaluate the prediction ability and robustness of the models. Finally, the importance of each parameter was studied using the Sobol's sensitivity analysis.

Deep learning neural networks were firstly and successfully developed to predict the oil production of hydraulically fractured horizontal wells. The overall performance of deep network models is acceptable with a low mean squared error between estimated and measured oil production. The configuration type of networks has little effect on the performance of deep network models. While the number of layers and neurons in each layer have a significant effect on the performance of models. The best number of layers ranges from 4 to 7, and best number of neurons in each layer is between 100 and 200. Sobol's sensitivity analysis indicates that the average proppant placed per stage is the most important parameter contributing to ~ 35% of both the 6 months' and 18 months' cumulative oil production variability. Moreover, the interaction effects among parameters should be considered during the hydraulic fracturing design.

Results from this work can be used to optimize multi-stage hydraulic fracturing design for new Bakken wells. The proposed deep learning method and sensitivity analysis provide a potential workflow to evaluate well after-stimulation performance for multi-stage fractured horizontal wells and can be integrated into reservoir decision-making routines.

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