• Alkhayyali
• Cappaccli
• Clarkosn

Post-fracture pressure decay (PFPD) analysis is an inexpensive method for performing reservoir/hydraulic fracture characterization along the horizontal section of multi-fractured horizontal wells (MFHWs). The method involves analyzing pressure decay data, recorded after each stage of the hydraulic fracturing treatment, to evaluate hydraulic fracturing efficiency, as determined from the ratio of unpropped fracture surface area to total fracture surface area. To obtain reliable results, the shut-in period must be long enough to be able to identify the required flow regimes. In some cases, due to the completion program and operational conditions, shut-in data might not be available, or may not be of sufficient quality to perform an analysis using analytical or numerical methods; in such cases, other tools should be employed to evaluate the efficiency of the hydraulic fracturing treatment.
In this study, machine learning (ML) tools are employed to develop a relationship between routinely-gathered well stimulation treatment data and PFPD analysis results. For this purpose, an analytical (straight-line analysis) method is used to estimate fracture surface area ratios along a well, while a Feed-Forward Neural Network (FNN) is utilized as the ML approach to relate the routine stimulation treatment data to the results of the analytical method (surface area ratios). In order to train the neural network, the treatment data are divided into two training and testing sets. ML algorithms are utilized to predict the surface area ratio by substituting PFPD analysis results with treatment data from two wells.
One well is designated for ML training and testing, while another is employed to evaluate the final model's accuracy against analytical method results. To account for limited inputs and avoid overfitting, data augmentation techniques, specifically, data synthesizer, are used. One hundred thousand stages are generated; 72,000 are stages used for training, 18,000 stages for validation, 10,000 stages for testing, and 40 field stages are used for testing the model. The model with augmented data provided the most accurate results.
The ML modeling approach developed herein can provide an important supplement to analytical PFPD analysis methods, by allowing for predictions where data are missing (i.e., not collected) or where data are of insufficient quality to perform quantitative analysis using analytical methods.