Physics-Informed Machine Learning for Hydraulic Fracturing—Part IV: Sustainable Fracturing with Carbon Score

Abstract Hydraulic fracturing design has traditionally focused on production optimization; however, increasing environmental, social, and governance (ESG) pressures demand sustainability-driven workflows. This study extends previous physics-informed machine learning (PIML) work by incorporating carbon emissions as a secondary objective in a multi-objective optimization (MOO) framework. A synthetic physics-informed dataset was expanded to include emissions-related parameters. Proppant, water, chemical, and equipment associated carbon emissions were calculated using databases from GREET, EPA, LCA studies and other renowned models, combined with in-house models trained on real-time equipment metering. Random forest and XGBoost regressors were used to build predictive models for dimensionless productivity index (JD) and total emissions (C) or dimensionless carbon score (Csd), achieving R² of 0.7 and 0.96, respectively. Two optimization approaches were evaluated: (1) a coupled loop optimizing JD and C simultaneously, and (2) a nested sequential optimization prioritizing production before emissions, where the prior was implemented due to its superiority. Pareto-front analysis showed the coupled approach captured superior trade-offs, enabling up to 15% emissions reduction with a minimal ~2% reduction in JD simultaneously. Among the tested metaheuristics, the speed-constrained multi-objective particle swarm optimizer (SMPSO) converged faster and maintained better diversity than NSGA-II. This work demonstrates a robust methodology to jointly optimize productivity, economics, and emissions intensity in fracturing operations, providing a pathway toward sustainable completions. The workflow is extensible to field-scale real-time applications and can be adapted for basin-specific constraints, supporting ESG-driven decision-making while maintaining operational feasibility.