Machine Learning-Based Propped Fracture Conductivity Correlations of Several Shale Formations

In hydraulic fracturing operations, small rounded particles called proppants are mixed and injected with fracture fluids into the targeted formation. The proppant particles hold the fracture open against formation closure stresses, providing a conduit for the reservoir fluid flow. The fracture's capacity to transport fluids is called fracture conductivity and is the product of proppant permeability and fracture width. Prediction of the propped fracture conductivity is essential for fracture design optimization. Several theoretical and few empirical models have been developed in the literature to estimate fracture conductivity, but these models either suffer from complexity, making them impractical, or accuracy due to data limitations. In this research, and for the first time, a machine learning approach was used to generate simple and accurate propped fracture conductivity correlations in unconventional gas shale formations. Around 350 consistent data points were collected from experiments on several important shale formations, namely, Marcellus, Barnett, Fayetteville, and Eagle Ford. Several machine learning models were utilized in this research, such as artificial neural network (ANN), fuzzy logic, and functional network. The ANN model provided the highest accuracy in fracture conductivity estimation with R-2 of 0.89 and 0.93 for training and testing data sets, respectively. We observed that a higher accuracy could be achieved by creating a correlation specific for each shale formation individually. Easily obtained input parameters were used to predict the fracture conductivity, namely, fracture orientation, closure stress, proppant mesh size, proppant load, static Young's modulus, static Poisson's ratio, and brittleness index. Exploratory data analysis showed that the features above are important where the closure stress is the most significant.