Prediction of Proppant Concentration Variations Between Different Perforation Clusters in a Hydraulically Fractured Stage

Hydraulic fracturing stimulation has unleashed the potential of unconventional reservoirs utilizing multistage and multi-cluster in the horizontal lateral of the wellbore. The treatment design plays a crucial role in placing the injected proppant from the surface to the induced fracture. This implies distributing the injected proppant concentration equally between different perforation clusters within the single stage. Data from several treatment designs conducted experimentally in the laboratory were utilized to determine the variations of the proppant concentrations between different perforation clusters. This work uses different ML techniques to predict the variations of proppant concentrations between different perforation clusters and optimize the completion parameters. Random forest (RF), gradient boosting regressor (GBR), and extra trees regressor (ETR) were employed to develop models predicting proppant concentrations and standard deviation (STD) values. The models were trained and evaluated using experimental data, and their performance was assessed based on R values and RMSE. Two scenarios were applied to predict the STD values. The first scenario is to predict the proppant concentration drained from each cluster and then the STD was calculated. The second scenario is to build ML models to predict the STD values based on the injection and the completion parameters directly. The ML models, particularly RF and ETR, demonstrated high accuracy in predicting proppant concentrations. They showed strong performance in both training and testing sets, indicating their ability to generalize well to unseen data with R values higher than 0.95 in the different cases. Estimation of STD using the first scenario showed slightly lower performance compared to the second scenario with an R value 0.98 in the first scenario compared to an R value of 0.94 in the second scenario. The models were then used to optimize completion parameters, such as injection rate, perforation design, proppant diameter, proppant density, and perforation angles, to minimize the STD of proppant drained from different clusters. The higher the injection rate and the number of perforations, the lower STD values were estimated. In addition, the model predicts that a proppant diameter of 0.0005 m with a proppant density less than 2100 kg/m3 with a phasing angle between 150 and 175° has the lowest relative standard deviation. The study concludes that ML models can effectively predict proppant concentrations and optimize completion parameters to improve proppant distribution in hydraulic fracturing stimulation. These models offer a novel approach to optimizing hydraulic fracturing treatments, leading to more efficient and effective reservoir stimulation processes.