Data-driven model for hydraulic fracturing design optimization. Part II: Inverse problem

We describe a stacked model for predicting the cumulative fluid production for an oil well with a multistage-fracture completion based on a combination of Ridge Regression and CatBoost algorithms. The model is developed based on an extended digital field data base of reservoir, well and fracturing design parameters. The database now includes more than 5000 wells from 23 oilfields of Western Siberia (Russia), with 6687 fracturing operations in total. Starting with 387 parameters characterizing each well, including construction, reservoir properties, fracturing design features and production, we end up with 38 key parameters used as input features for each well in the model training process. The model demonstrates physically explainable dependencies plots of the target on the design parameters (number of stages, proppant mass, average and final proppant concentrations and fluid rate). We developed a set of methods including those based on the use of Euclidean distance and clustering techniques to perform similar (offset) wells search, which is useful for a field engineer to analyze earlier fracturing treatments on similar wells. These approaches are also adapted for obtaining the optimization parameters boundaries for the particular pilot well, as part of the field testing campaign of the methodology. An inverse problem (selecting an optimum set of fracturing design parameters to maximize production) is formulated as optimizing a high dimensional black box approximation function constrained by boundaries and solved with four different optimization methods: surrogate-based optimization, sequential least squares programming, particle swarm optimization and differential evolution. A recommendation system containing all the above methods is designed to advise a production stimulation engineer on an optimized fracturing design.