Physics-Informed Machine Learning for Hydraulic Fracturing—Part II: The Transfer Learning Experiment
Authors: Khan Abdul Muqtadir , Ugarte Esteban , BinZiad Abdullah , Alsubaii Abdullah 
Published: November 2024

Abstract
The growth of machine learning (ML) approaches has sparked innovations in many applications, including hydraulic fracturing design. The crucial drawback in these models is the subjectivity and expertise of the design engineers, which could risk underrealizing the true reservoir and production potential. In Part I, a physics-based dataset was constructed using the physics of fracturing design theory and transformed into an ML model. Recent experiments aimed at testing this dataset with a transfer learning approach to enhance predictive capabilities in a real field dataset.
The physics-based dataset is comprised of 62 parameters. During the application to the real dataset, it is crucial for the model to accurately predict and optimize the design using only a limited set of available parameters. The dataset was skimmed and tailored to the real data available, with domain expertise. Three training-testing dataset combinations were used for ML experiments: (a) synthetic-synthetic, (b) synthetic-real, and (c) real-real. The idea is to compare the three approaches to demonstrate the effectiveness and validity of transfer learning from a synthetic to a real dataset. Neural networks were utilized with multiple hyperparameter optimization routines. Additionally, a particle swarm optimization loop was integrated into the ML model to maximize production results.
The dataset was reduced from 62 to 40 parameters based on domain understanding to tailor it to the real field dataset. A feed-forward multilayer perceptron (MLP) neural network was used for the ML modeling. Root mean square error (RMSE) and mean absolute percentage error (MAPE) were the key evaluation metrics used. Out of the three ML experiments, the primary comparison was between the pure real data-trained approach and the transfer learning approach by adjusting the synthetically trained backbone with the real data. The five outputs were fluid efficiency, pad ratio, proppant mass, maximum proppant concentration, and dimensionless productivity index (JD). The transfer learning technique demonstrated enhanced performance across all five outputs, with an average RMSE improvement of 15.12% and an average MAPE improvement of 15.88% compared to the pure real data-trained approach.
In the metaheuristic particle swarm optimizer, the parameter space was searched to maximize production. Multiple combinations of fluid efficiency, pad ratio, proppant mass, and concentration were varied within 10% of the initial prediction to maximize the objective function of JD. The optimized values were 14.2% higher on average compared to the initial prediction. Compared to the actual values, optimized values were optimal in 88% of the instances. The enhancement was even higher for lower initial JD values, where results were optimal 96% on average across models.
Physics-based ML provides the advantage of intrinsic causality in the synthetic dataset. Transfer predictive learning opens an array of opportunities for small data utilization. The method bolsters full-scale deep-learning model creation in fracturing and in similar domains where limited records are available.