Development of Machine Learning Based Propped Fracture Conductivity Correlations in Shale Formations

Propped hydraulic fracturing is a stimulation technique used in tight formations to create conductive fractures. To predict the fractured well productivity, the conductivity of those propped fractures should be estimated. It is common to measure the conductivity of propped fractures in the laboratory under controlled conditions. Nonetheless, it is costly and time-consuming which encouraged developing many empirical and analytical propped fracture conductivity models. Previous empirical models, however, were based on limited datasets producing questionable correlations. We propose herein new empirical models based on an extensive data set utilizing machine learning (ML) methods. In this study, an artificial neural network (ANN) was utilized. A dataset comprised of 351 data points of propped hydraulic fracture experiments on different shale types with different mineralogy under various confining stresses was collected and studied. Several statistical and data science approaches such as box and whisker plots, correlation crossplots, and Z-score techniques were used to remove the outliers and extreme data points. The performance of the developed model was evaluated using powerful metrics such as correlation coefficient and root mean squared error. After several executions and function evaluations, an ANN was found to be the best technique to predict propped fracture conductivity for different mineralogy. The proposed ANN models resulted in less than 7% error between actual and predicted values. In this study, in addition to the development of an optimized ANN model, explicit empirical correlations are also extracted from the weights and biases of the fine-tuned model. The proposed model of propped fracture conductivity was then compared with the commonly available correlations. The results revealed that the proposed mineralogy based propped fracture conductivity models made the predictions with a high correlation coefficient of 94%. This work clearly shows the potential of computer-based ML techniques in the determination of mineralogy based propped fracture conductivity. The proposed empirical correlation can be implemented without requiring any ML-based software.