Development of a Hybrid Modelling Approach for Estimating Bottom Hole Pressure in Shale and Tight Sand Wells Using Smart Production Data and Machine Learning Techniques

Well flowing bottom hole pressure is an important input parameter for well and reservoir performance evaluation. However, there are limitations in accurate downhole measurements due to a faulty gauge and, sometimes, the inability to obtain complete well test data to implement theoretical models. The goal of this work is to create a hybrid modeling approach for estimating bottom hole pressure in tight sand and shale wells using smart production data, engineering features and machine learning (ML) techniques. The robust feature selection process integrated the critical attributes in the traditional PTA methods. Four out of eight adopted variables were split into training, cross validation and test sets in 60:20:20 proportion and preprocessed by z-score normalization scaling. For the first time, the combination of gradient descent optimization (GDO) algorithm and Cauchy cost function was used in the estimate of bottom hole pressure from production data in this study. A smart data approach for developing ML models was used in this study. Starting with 100 data points, the training and validation input size were incremented and subject to the learning process using both Cauchy and traditional MSE cost function-based GDO algorithm to determine the optimum batch size required to train the BHP model with lowest cost. The results showed that the Cauchy based GDO algorithm provides slightly better performance in training, cross validation and testing data with a global minimum error of 0.82%, 0.64% and 0.41% respectively compared to the traditional MSE-based GD that reaches a global minimum with higher cost. However, the improved metrics scores with Cauchy loss optimization required additional expense of one to ten seconds execution time. The Cauchy cost function presents an alternative technique to obtain better optimized prediction models from production data and can be utilized in sensitivity studies for reservoir characterization and asset management purposes.