Physics-Informed Machine Learning for Hydraulic Fracturing—Part I: The Backbone Model
Authors: Khan Abdul Muqtadir , Luo Yin , Ugarte Esteban , Bannikov Denis 
Published: April 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 under-realizing the true reservoir and production potential. To overcome this, we incorporate the physics of fracturing design theory into ML models through a hybridized approach.
A method consolidating complete physics that integrated reservoir characteristics, fracturing diagnostics, and production performance was applied to 71 parameters of which 22 were generated randomly with practical minimum-maximum ranges and 49 were generated using empirical and analytical correlations. The inputs included reservoir rock and fluid properties, fracturing fluid, proppant and treatment parameters, and fracture conductivity results. The dataset was built so that only two outputs from the analysis of a small injection/falloff test were required: transmissibility from the after-closure analysis and the net pressure. The final model outputs included crosslinked fluid efficiency, pad percent for safe mode and tip screenout mode, proppant mass, maximum allowable proppant concentration, and dimensionless productivity index. The ML model also has a genetic algorithm optimizer loop downstream to optimize the fracturing treatment design to maximize the production.
The approach yielded a broad range of output values, and 10,000 rows of the dataset were finalized. The dataset is also appended with the optimized dimensionless fracture conductivity and dimensionless productivity index calculated with the classical boundary element routine. This synthetically constructed dataset was then subjected to a feed-forward neural network to generate data-based models after tuning the hyperparameters. The multilayer perceptron model was used here and all variables provided coupled performance metric. Root mean square error, mean absolute percentage error, and coefficient of determination were used as performance metrics and showed the model significance with values of 0.16, 0.77, and 0.96, respectively. The trained model is a backbone to be used to solve with iterative updates of a small real-field dataset. The cost functions of predictors can be optimized by tuning the hyperparameters, which are generated with the governing equations for fluid flow through porous media, fluid leakoff, and fracturing theory presented in the literature guided by specific field data. A comparison is also performed using the same performance metrics on a small real-field dataset using a purely data-driven (classification) ML approach versus this hybrid ML approach, where the latter shows significant improvement in predictions.
Physics-based ML gives 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.