Physics-Informed Machine Learning for Hydraulic Fracturing—Part III: The Transfer Learning Validation
Authors: Khan Abdul Muqtadir , Ugarte Esteban , Kurniadi Stevanus , Al Shueili Ahmed , Wang Wei Kan 
Published: February 2025

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 under-realizing the true reservoir and production potential. In Part I, a physics-based dataset was constructed with physics of fracturing design theory and transformed into an ML model. In Part II, a small experiment for transfer learning with a real-field dataset was constructed and, in this part, we intend to conduct a transfer learning validation with another robust real-field dataset.
In this study we focus on predicting the different fracture design parameters by investigating the advantages of transfer learning using a pretrained backbone with physics-based data and tailoring it toward the real-field data. The five fracture design parameters were fluid efficiency, pad ratio (tip screenout and safe modes) proppant mass, maximum proppant concentration, and dimensionless productivity index (JD). Various ML models were trained and evaluated using different metrics such as root mean square error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE) combine with cross-validation technique to assess the performance of the models. The physics-based dataset consists of 62 parameters where 43 were meant to be used to train the models. However, the real-field dataset only had 20 available features that were the inputs used. It is crucial for the model to accurately predict and optimize the design using only a limited set of available parameters. A key component of the study involved highlighting the importance of the missing variables though a comparison of the complete against the partial data to observe the predictive capabilities.
For the application to a real dataset, a transfer learning approach was implemented using the knowledge from a physics-based trained backbone and adjust it with the real-field data. Neural networks were used with multiple hyperparameter optimization routines. Two types of transfer learning that included feature transfer and fine tuning were used to compare against a benchmark that consisted of a base model trained only on real-field data. Results showed a reduction in error metrics that ranged from 3% to 16.5% RMSE and 3.1% to 22.4% MAPE compared to the base model for the different fracture design parameters and the productivity index.
Further, the study integrates a heuristic particle swarm optimizer to refine fracture design parameters for maximizing the JD value. A constrained search space is searched to maximize production using multiple combinations of fluid efficiency, pad ratio, proppant mass and concentration that varied within 10% of initial prediction as these are controllable features during design. An analysis of the error propagation was done comparing the actual, predicted and optimized values. The optimized values were up to 15.8% higher on average compared to the actual values.
Physics-based ML gives the advantage of intrinsic causality in the synthetic dataset, allowing to train robust models. Transfer predictive learning opens an array of opportunities for small data utilization by tailoring the model towards the new real-field data. Results from this study showed the advantages of using the transfer learning approach. In addition, the couple optimizer ensures the optimized variables would lead to an increased production.