Multi-timescale modeling framework for natural gas desulfurization process: Integrating time-lagged causal relationships with machine learning

• A novel temporal causality-driven modeling framework was developed for the natural gas desulfurization process. • Integrated time constant-based temporal hierarchy with time-lagged causality to capture lag effects. • TE-based analysis outperformed other methods in revealing time-lagged causal structures and reducing redundancy. • Causality-informed Random Forest models achieved R ² > 0.8, RMSE < 0.5 mg/m³ within a 100-minute prediction horizon. • Model interpretation provided theoretical insights by mapping feature importance to process knowledge. Traditional modeling techniques for industrial processes, such as natural gas desulfurization, often struggle to capture high dimensionality, strong nonlinearity, and time-varying behavior arising from coupled heat and mass transfer under dynamic operating conditions. A multi-timescale causal modeling framework was developed by integrating time-lagged causality detection with machine learning. The temporal hierarchy of process variables was first quantified using the symmetric uncertainty coefficient. Transfer entropy (TE) was then applied to identify variable-specific time-lagged causality between operational parameters and desulfurization performance, while redundant causal relationships were eliminated. Machine learning models were constructed based on the determined causal structure for multi-step forecasts ranging from minutes to hours. An industrial case study demonstrates that TE-based analysis outperforms traditional methods in identifying process-driving factors, revealing time-lagged causal structures, and removing irrelevant variables. Causality-informed Random Forest models achieve strong predictive performance ( R 2 > 0.80, RMSE < 0.5 mg/m 3 for a 100-min horizon), and improve medium- to long-term accuracy by over 15% compared to other machine learning models. Model interpretation reveals time-dependent influence patterns of key parameters, offering physically consistent insights. The proposed framework provides a practical causality-driven approach for modeling complex industrial processes by bridging physical insights with data-driven predictive power.